%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU799^2 : 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 : n005.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 10:48:26 AM UTC 2026
% Result : Theorem 0.43s 0.40s
% Output : CNFRefutation 0.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 3
% Syntax : Number of formulae : 51 ( 27 unt; 0 typ; 2 def)
% Number of atoms : 481 ( 120 equ; 0 cnn)
% Maximal formula atoms : 5 ( 9 avg)
% Number of connectives : 1815 ( 14 ~; 55 |; 0 &;1733 @)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 77 ( 77 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 6 con; 0-3 aty)
% Number of variables : 344 ( 241 ^; 103 !; 0 ?; 344 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_dsetconstr,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(tp_dsetconstrEL,type,
dsetconstrEL: $o ).
thf(tp_funcSet,type,
funcSet: $i > $i > $i ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_injFuncSet,type,
injFuncSet: $i > $i > $i ).
thf(tp_injective,type,
injective: $i > $i > $i > $o ).
thf(tp_sK1_SX0,type,
sK1_SX0: $i ).
thf(tp_sK2_SY17,type,
sK2_SY17: $i ).
thf(tp_sK3_SY22,type,
sK3_SY22: $i ).
thf(tp_sK4_E,type,
sK4_E: ( $i > $o ) > $i ).
thf(tp_sK5_E,type,
sK5_E: ( $i > $i > $o ) > $i ).
thf(tp_sK6_E,type,
sK6_E: ( $i > $i > $o ) > $i ).
thf(tp_sK7_E,type,
sK7_E: ( $i > $i > $o ) > $i ).
thf(tp_sK8_E,type,
sK8_E: ( $i > $i > $o ) > $i ).
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(injFuncSet,definition,
( injFuncSet
= ( ^ [A: $i,B: $i] :
( dsetconstr @ ( funcSet @ A @ B )
@ ^ [Xf: $i] : ( injective @ A @ B @ Xf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',injFuncSet) ).
thf(1,conjecture,
( dsetconstrEL
=> ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( injFuncSet @ A @ B ) )
=> ( in @ Xf @ ( funcSet @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',injFuncSetFuncIn) ).
thf(2,negated_conjecture,
( ( dsetconstrEL
=> ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( injFuncSet @ A @ B ) )
=> ( in @ Xf @ ( funcSet @ A @ B ) ) ) )
= $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 @ ( funcSet @ SY0 @ SY1 )
@ ^ [SY5: $i] : ( injective @ SY0 @ SY1 @ SY5 ) ) )
=> ( in @ SY2 @ ( funcSet @ SY0 @ SY1 ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,dsetconstrEL,injFuncSet]) ).
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 @ ( funcSet @ SY0 @ SY1 )
@ ^ [SY5: $i] : ( injective @ SY0 @ SY1 @ SY5 ) ) )
=> ( in @ SY2 @ ( funcSet @ SY0 @ SY1 ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ~ ! [SY0: $i,SY1: $i,SY2: $i] :
( ( in @ SY2
@ ( dsetconstr @ ( funcSet @ SY0 @ SY1 )
@ ^ [SY5: $i] : ( injective @ SY0 @ SY1 @ SY5 ) ) )
=> ( in @ SY2 @ ( funcSet @ SY0 @ SY1 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(7,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( in @ Xx @ A ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(8,plain,
( ( ~ ! [SY0: $i,SY1: $i,SY2: $i] :
( ( in @ SY2
@ ( dsetconstr @ ( funcSet @ SY0 @ SY1 )
@ ^ [SY5: $i] : ( injective @ SY0 @ SY1 @ SY5 ) ) )
=> ( in @ SY2 @ ( funcSet @ SY0 @ SY1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(9,plain,
( ( ~ ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2
@ ( dsetconstr @ ( funcSet @ SX0 @ SX1 )
@ ^ [SX3: $i] : ( injective @ SX0 @ SX1 @ SX3 ) ) )
| ( in @ SX2 @ ( funcSet @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8,dsetconstrEL,injFuncSet]) ).
thf(10,plain,
( ( ! [SX0: $i,SX1: $i > $o,SX2: $i] :
( ~ ( in @ SX2
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) )
| ( in @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7,dsetconstrEL,injFuncSet]) ).
thf(11,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2
@ ( dsetconstr @ ( funcSet @ SX0 @ SX1 )
@ ^ [SX3: $i] : ( injective @ SX0 @ SX1 @ SX3 ) ) )
| ( in @ SX2 @ ( funcSet @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[9]) ).
thf(12,plain,
! [SV1: $i] :
( ( ! [SY14: $i > $o,SY15: $i] :
( ~ ( in @ SY15
@ ( dsetconstr @ SV1
@ ^ [SX3: $i] : ( SY14 @ SX3 ) ) )
| ( in @ SY15 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[10]) ).
thf(13,plain,
( ( ! [SY17: $i,SY18: $i] :
( ~ ( in @ SY18
@ ( dsetconstr @ ( funcSet @ sK1_SX0 @ SY17 )
@ ^ [SY19: $i] : ( injective @ sK1_SX0 @ SY17 @ SY19 ) ) )
| ( in @ SY18 @ ( funcSet @ sK1_SX0 @ SY17 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[11]) ).
thf(14,plain,
! [SV2: $i > $o,SV1: $i] :
( ( ! [SY20: $i] :
( ~ ( in @ SY20
@ ( dsetconstr @ SV1
@ ^ [SY21: $i] : ( SV2 @ SY21 ) ) )
| ( in @ SY20 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(15,plain,
( ( ! [SY22: $i] :
( ~ ( in @ SY22
@ ( dsetconstr @ ( funcSet @ sK1_SX0 @ sK2_SY17 )
@ ^ [SY23: $i] : ( injective @ sK1_SX0 @ sK2_SY17 @ SY23 ) ) )
| ( in @ SY22 @ ( funcSet @ sK1_SX0 @ sK2_SY17 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[13]) ).
thf(16,plain,
! [SV2: $i > $o,SV1: $i,SV3: $i] :
( ( ~ ( in @ SV3
@ ( dsetconstr @ SV1
@ ^ [SY21: $i] : ( SV2 @ SY21 ) ) )
| ( in @ SV3 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(17,plain,
( ( ~ ( in @ sK3_SY22
@ ( dsetconstr @ ( funcSet @ sK1_SX0 @ sK2_SY17 )
@ ^ [SY23: $i] : ( injective @ sK1_SX0 @ sK2_SY17 @ SY23 ) ) )
| ( in @ sK3_SY22 @ ( funcSet @ sK1_SX0 @ sK2_SY17 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[15]) ).
thf(18,plain,
! [SV2: $i > $o,SV1: $i,SV3: $i] :
( ( ( ~ ( in @ SV3
@ ( dsetconstr @ SV1
@ ^ [SY21: $i] : ( SV2 @ SY21 ) ) ) )
= $true )
| ( ( in @ SV3 @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[16]) ).
thf(19,plain,
( ( ~ ( in @ sK3_SY22
@ ( dsetconstr @ ( funcSet @ sK1_SX0 @ sK2_SY17 )
@ ^ [SY23: $i] : ( injective @ sK1_SX0 @ sK2_SY17 @ SY23 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(20,plain,
( ( in @ sK3_SY22 @ ( funcSet @ sK1_SX0 @ sK2_SY17 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(21,plain,
! [SV2: $i > $o,SV1: $i,SV3: $i] :
( ( ( in @ SV3
@ ( dsetconstr @ SV1
@ ^ [SY21: $i] : ( SV2 @ SY21 ) ) )
= $false )
| ( ( in @ SV3 @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(22,plain,
( ( in @ sK3_SY22
@ ( dsetconstr @ ( funcSet @ sK1_SX0 @ sK2_SY17 )
@ ^ [SY23: $i] : ( injective @ sK1_SX0 @ sK2_SY17 @ SY23 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[19]) ).
thf(23,plain,
( ( ( in @ sK3_SY22
@ ( dsetconstr @ ( funcSet @ sK1_SX0 @ sK2_SY17 )
@ ^ [SY23: $i] : ( injective @ sK1_SX0 @ sK2_SY17 @ SY23 ) ) )
= ( in @ sK3_SY22 @ ( funcSet @ sK1_SX0 @ sK2_SY17 ) ) )
= $false ),
inference(res,[status(thm)],[22,20]) ).
thf(24,plain,
( ( ( dsetconstr @ ( funcSet @ sK1_SX0 @ sK2_SY17 )
@ ^ [SY23: $i] : ( injective @ sK1_SX0 @ sK2_SY17 @ SY23 ) )
= ( funcSet @ sK1_SX0 @ sK2_SY17 ) )
= $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)],[21]) ).
thf(30,plain,
! [SV4: $i > $o,SV5: $i,SV6: $i] :
( ( ( ( in @ SV6
@ ( dsetconstr @ SV5
@ ^ [SX0: $i] : ( SV4 @ SX0 ) ) )
= ( in @ sK3_SY22
@ ( dsetconstr @ ( funcSet @ sK1_SX0 @ sK2_SY17 )
@ ^ [SY23: $i] : ( injective @ sK1_SX0 @ sK2_SY17 @ SY23 ) ) ) )
= $false )
| ( ( in @ SV6 @ SV5 )
= $true ) ),
inference(res,[status(thm)],[26,22]) ).
thf(31,plain,
! [SV4: $i > $o,SV5: $i,SV6: $i] :
( ( ( ( in @ SV6 @ SV5 )
= ( in @ sK3_SY22 @ ( funcSet @ sK1_SX0 @ sK2_SY17 ) ) )
= $false )
| ( ( in @ SV6
@ ( dsetconstr @ SV5
@ ^ [SX0: $i] : ( SV4 @ SX0 ) ) )
= $false ) ),
inference(res,[status(thm)],[26,20]) ).
thf(32,plain,
! [SV4: $i > $o] :
( ( in @ sK3_SY22
@ ( dsetconstr @ ( funcSet @ sK1_SX0 @ sK2_SY17 )
@ ^ [SX0: $i] : ( SV4 @ SX0 ) ) )
= $false ),
inference(extuni,[status(esa)],[31:[bind(SV5,$thf( funcSet @ sK1_SX0 @ sK2_SY17 )),bind(SV6,$thf( sK3_SY22 ))]]) ).
thf(33,plain,
! [SV70: $i > $i > $i,SV69: $i > $i > $i,SV68: $i > $i > $i] :
( ( ( in @ sK3_SY22 @ ( funcSet @ sK1_SX0 @ sK2_SY17 ) )
= $true )
| ( ( injective
@ ( SV68
@ ( sK4_E
@ ^ [SX0: $i] :
( injective @ SX0 @ SX0
@ ( sK4_E
@ ^ [SX1: $i] : ( injective @ ( SV68 @ SX0 @ SX1 ) @ ( SV69 @ SX0 @ SX1 ) @ ( SV70 @ SX0 @ SX1 ) ) ) ) )
@ ( sK8_E
@ ^ [SX0: $i,SX1: $i] : ( injective @ ( SV68 @ SX0 @ SX1 ) @ ( SV69 @ SX0 @ SX1 ) @ ( SV70 @ SX0 @ SX1 ) ) ) )
@ ( SV69
@ ( sK4_E
@ ^ [SX0: $i] :
( injective @ SX0 @ SX0
@ ( sK4_E
@ ^ [SX1: $i] : ( injective @ ( SV68 @ SX0 @ SX1 ) @ ( SV69 @ SX0 @ SX1 ) @ ( SV70 @ SX0 @ SX1 ) ) ) ) )
@ ( sK8_E
@ ^ [SX0: $i,SX1: $i] : ( injective @ ( SV68 @ SX0 @ SX1 ) @ ( SV69 @ SX0 @ SX1 ) @ ( SV70 @ SX0 @ SX1 ) ) ) )
@ ( SV70
@ ( sK4_E
@ ^ [SX0: $i] :
( injective @ SX0 @ SX0
@ ( sK4_E
@ ^ [SX1: $i] : ( injective @ ( SV68 @ SX0 @ SX1 ) @ ( SV69 @ SX0 @ SX1 ) @ ( SV70 @ SX0 @ SX1 ) ) ) ) )
@ ( sK8_E
@ ^ [SX0: $i,SX1: $i] : ( injective @ ( SV68 @ SX0 @ SX1 ) @ ( SV69 @ SX0 @ SX1 ) @ ( SV70 @ SX0 @ SX1 ) ) ) ) )
= $true )
| ( ( injective
@ ( sK8_E
@ ^ [SX0: $i,SX1: $i] : ( injective @ ( SV68 @ SX0 @ SX1 ) @ ( SV69 @ SX0 @ SX1 ) @ ( SV70 @ SX0 @ SX1 ) ) )
@ ( sK8_E
@ ^ [SX0: $i,SX1: $i] : ( injective @ ( SV68 @ SX0 @ SX1 ) @ ( SV69 @ SX0 @ SX1 ) @ ( SV70 @ SX0 @ SX1 ) ) )
@ ( sK4_E
@ ^ [SX0: $i] :
( injective
@ ( SV68
@ ( sK8_E
@ ^ [SX1: $i,SX2: $i] : ( injective @ ( SV68 @ SX1 @ SX2 ) @ ( SV69 @ SX1 @ SX2 ) @ ( SV70 @ SX1 @ SX2 ) ) )
@ SX0 )
@ ( SV69
@ ( sK8_E
@ ^ [SX1: $i,SX2: $i] : ( injective @ ( SV68 @ SX1 @ SX2 ) @ ( SV69 @ SX1 @ SX2 ) @ ( SV70 @ SX1 @ SX2 ) ) )
@ SX0 )
@ ( SV70
@ ( sK8_E
@ ^ [SX1: $i,SX2: $i] : ( injective @ ( SV68 @ SX1 @ SX2 ) @ ( SV69 @ SX1 @ SX2 ) @ ( SV70 @ SX1 @ SX2 ) ) )
@ SX0 ) ) ) )
= $true )
| ( ( ( sK4_E
@ ^ [SX0: $i] :
( injective @ SX0 @ SX0
@ ( sK4_E
@ ^ [SX1: $i] : ( injective @ ( SV68 @ SX0 @ SX1 ) @ ( SV69 @ SX0 @ SX1 ) @ ( SV70 @ SX0 @ SX1 ) ) ) ) )
= sK2_SY17 )
= $false )
| ( ( ( sK4_E
@ ^ [SX0: $i] :
( injective @ SX0 @ SX0
@ ( sK4_E
@ ^ [SX1: $i] : ( injective @ ( SV68 @ SX0 @ SX1 ) @ ( SV69 @ SX0 @ SX1 ) @ ( SV70 @ SX0 @ SX1 ) ) ) ) )
= sK1_SX0 )
= $false ) ),
inference(extuni,[status(esa)],[30:[bind(SV4,$thf( ^ [SX0: $i] : ( injective @ SX0 @ SX0 @ ( sK4_E @ ^ [SX1: $i] : ( injective @ ( SV68 @ SX0 @ SX1 ) @ ( SV69 @ SX0 @ SX1 ) @ ( SV70 @ SX0 @ SX1 ) ) ) ) )),bind(SV5,$thf( funcSet @ sK1_SX0 @ sK2_SY17 )),bind(SV6,$thf( sK3_SY22 ))]]) ).
thf(34,plain,
! [SV70: $i > $i > $i,SV69: $i > $i > $i,SV68: $i > $i > $i] :
( ( ( in @ sK3_SY22 @ ( funcSet @ sK1_SX0 @ sK2_SY17 ) )
= $true )
| ( ( injective
@ ( SV68
@ ( sK4_E
@ ^ [SX0: $i] :
( injective @ SX0 @ SX0
@ ( sK4_E
@ ^ [SX1: $i] : ( injective @ ( SV68 @ SX0 @ SX1 ) @ ( SV69 @ SX0 @ SX1 ) @ ( SV70 @ SX0 @ SX1 ) ) ) ) )
@ ( sK8_E
@ ^ [SX0: $i,SX1: $i] : ( injective @ ( SV68 @ SX0 @ SX1 ) @ ( SV69 @ SX0 @ SX1 ) @ ( SV70 @ SX0 @ SX1 ) ) ) )
@ ( SV69
@ ( sK4_E
@ ^ [SX0: $i] :
( injective @ SX0 @ SX0
@ ( sK4_E
@ ^ [SX1: $i] : ( injective @ ( SV68 @ SX0 @ SX1 ) @ ( SV69 @ SX0 @ SX1 ) @ ( SV70 @ SX0 @ SX1 ) ) ) ) )
@ ( sK8_E
@ ^ [SX0: $i,SX1: $i] : ( injective @ ( SV68 @ SX0 @ SX1 ) @ ( SV69 @ SX0 @ SX1 ) @ ( SV70 @ SX0 @ SX1 ) ) ) )
@ ( SV70
@ ( sK4_E
@ ^ [SX0: $i] :
( injective @ SX0 @ SX0
@ ( sK4_E
@ ^ [SX1: $i] : ( injective @ ( SV68 @ SX0 @ SX1 ) @ ( SV69 @ SX0 @ SX1 ) @ ( SV70 @ SX0 @ SX1 ) ) ) ) )
@ ( sK8_E
@ ^ [SX0: $i,SX1: $i] : ( injective @ ( SV68 @ SX0 @ SX1 ) @ ( SV69 @ SX0 @ SX1 ) @ ( SV70 @ SX0 @ SX1 ) ) ) ) )
= $false )
| ( ( injective
@ ( sK8_E
@ ^ [SX0: $i,SX1: $i] : ( injective @ ( SV68 @ SX0 @ SX1 ) @ ( SV69 @ SX0 @ SX1 ) @ ( SV70 @ SX0 @ SX1 ) ) )
@ ( sK8_E
@ ^ [SX0: $i,SX1: $i] : ( injective @ ( SV68 @ SX0 @ SX1 ) @ ( SV69 @ SX0 @ SX1 ) @ ( SV70 @ SX0 @ SX1 ) ) )
@ ( sK4_E
@ ^ [SX0: $i] :
( injective
@ ( SV68
@ ( sK8_E
@ ^ [SX1: $i,SX2: $i] : ( injective @ ( SV68 @ SX1 @ SX2 ) @ ( SV69 @ SX1 @ SX2 ) @ ( SV70 @ SX1 @ SX2 ) ) )
@ SX0 )
@ ( SV69
@ ( sK8_E
@ ^ [SX1: $i,SX2: $i] : ( injective @ ( SV68 @ SX1 @ SX2 ) @ ( SV69 @ SX1 @ SX2 ) @ ( SV70 @ SX1 @ SX2 ) ) )
@ SX0 )
@ ( SV70
@ ( sK8_E
@ ^ [SX1: $i,SX2: $i] : ( injective @ ( SV68 @ SX1 @ SX2 ) @ ( SV69 @ SX1 @ SX2 ) @ ( SV70 @ SX1 @ SX2 ) ) )
@ SX0 ) ) ) )
= $false )
| ( ( ( sK4_E
@ ^ [SX0: $i] :
( injective @ SX0 @ SX0
@ ( sK4_E
@ ^ [SX1: $i] : ( injective @ ( SV68 @ SX0 @ SX1 ) @ ( SV69 @ SX0 @ SX1 ) @ ( SV70 @ SX0 @ SX1 ) ) ) ) )
= sK2_SY17 )
= $false )
| ( ( ( sK4_E
@ ^ [SX0: $i] :
( injective @ SX0 @ SX0
@ ( sK4_E
@ ^ [SX1: $i] : ( injective @ ( SV68 @ SX0 @ SX1 ) @ ( SV69 @ SX0 @ SX1 ) @ ( SV70 @ SX0 @ SX1 ) ) ) ) )
= sK1_SX0 )
= $false ) ),
inference(extuni,[status(esa)],[30:[bind(SV4,$thf( ^ [SX0: $i] : ( injective @ SX0 @ SX0 @ ( sK4_E @ ^ [SX1: $i] : ( injective @ ( SV68 @ SX0 @ SX1 ) @ ( SV69 @ SX0 @ SX1 ) @ ( SV70 @ SX0 @ SX1 ) ) ) ) )),bind(SV5,$thf( funcSet @ sK1_SX0 @ sK2_SY17 )),bind(SV6,$thf( sK3_SY22 ))]]) ).
thf(35,plain,
! [SV63: $i > $i > $o] :
( ( ( in @ sK3_SY22 @ ( funcSet @ sK1_SX0 @ sK2_SY17 ) )
= $true )
| ( ( ( sK4_E
@ ( SV63
@ ( sK4_E
@ ^ [SX0: $i] : ( injective @ SX0 @ SX0 @ ( sK4_E @ ( SV63 @ SX0 ) ) ) ) ) )
= ( sK4_E
@ ^ [SX0: $i] : ( injective @ SX0 @ SX0 @ ( sK4_E @ ( SV63 @ SX0 ) ) ) ) )
= $false )
| ( ( ( sK4_E
@ ^ [SX0: $i] : ( injective @ SX0 @ SX0 @ ( sK4_E @ ( SV63 @ SX0 ) ) ) )
= sK2_SY17 )
= $false )
| ( ( ( sK4_E
@ ^ [SX0: $i] : ( injective @ SX0 @ SX0 @ ( sK4_E @ ( SV63 @ SX0 ) ) ) )
= sK1_SX0 )
= $false ) ),
inference(extuni,[status(esa)],[30:[bind(SV4,$thf( ^ [SX0: $i] : ( injective @ SX0 @ SX0 @ ( sK4_E @ ( SV63 @ SX0 ) ) ) )),bind(SV5,$thf( funcSet @ sK1_SX0 @ sK2_SY17 )),bind(SV6,$thf( sK3_SY22 ))]]) ).
thf(36,plain,
( ( ( in @ sK3_SY22 @ ( funcSet @ sK1_SX0 @ sK2_SY17 ) )
= $true )
| ( ( ( sK4_E
@ ^ [SX0: $i] : ( injective @ SX0 @ SX0 @ SX0 ) )
= sK2_SY17 )
= $false )
| ( ( ( sK4_E
@ ^ [SX0: $i] : ( injective @ SX0 @ SX0 @ SX0 ) )
= sK1_SX0 )
= $false ) ),
inference(extuni,[status(esa)],[30:[bind(SV4,$thf( ^ [SX0: $i] : ( injective @ SX0 @ SX0 @ SX0 ) )),bind(SV5,$thf( funcSet @ sK1_SX0 @ sK2_SY17 )),bind(SV6,$thf( sK3_SY22 ))]]) ).
thf(37,plain,
! [SV55: $i > $i > $i,SV54: $i > $i > $i,SV53: $i > $i > $i] :
( ( ( in @ sK3_SY22 @ ( funcSet @ sK1_SX0 @ sK2_SY17 ) )
= $true )
| ( ( injective
@ ( SV53
@ ( sK4_E
@ ^ [SX0: $i] :
( injective @ SX0 @ sK2_SY17
@ ( sK4_E
@ ^ [SX1: $i] : ( injective @ ( SV53 @ SX0 @ SX1 ) @ ( SV54 @ SX0 @ SX1 ) @ ( SV55 @ SX0 @ SX1 ) ) ) ) )
@ ( sK7_E
@ ^ [SX0: $i,SX1: $i] : ( injective @ ( SV53 @ SX0 @ SX1 ) @ ( SV54 @ SX0 @ SX1 ) @ ( SV55 @ SX0 @ SX1 ) ) ) )
@ ( SV54
@ ( sK4_E
@ ^ [SX0: $i] :
( injective @ SX0 @ sK2_SY17
@ ( sK4_E
@ ^ [SX1: $i] : ( injective @ ( SV53 @ SX0 @ SX1 ) @ ( SV54 @ SX0 @ SX1 ) @ ( SV55 @ SX0 @ SX1 ) ) ) ) )
@ ( sK7_E
@ ^ [SX0: $i,SX1: $i] : ( injective @ ( SV53 @ SX0 @ SX1 ) @ ( SV54 @ SX0 @ SX1 ) @ ( SV55 @ SX0 @ SX1 ) ) ) )
@ ( SV55
@ ( sK4_E
@ ^ [SX0: $i] :
( injective @ SX0 @ sK2_SY17
@ ( sK4_E
@ ^ [SX1: $i] : ( injective @ ( SV53 @ SX0 @ SX1 ) @ ( SV54 @ SX0 @ SX1 ) @ ( SV55 @ SX0 @ SX1 ) ) ) ) )
@ ( sK7_E
@ ^ [SX0: $i,SX1: $i] : ( injective @ ( SV53 @ SX0 @ SX1 ) @ ( SV54 @ SX0 @ SX1 ) @ ( SV55 @ SX0 @ SX1 ) ) ) ) )
= $true )
| ( ( injective
@ ( sK7_E
@ ^ [SX0: $i,SX1: $i] : ( injective @ ( SV53 @ SX0 @ SX1 ) @ ( SV54 @ SX0 @ SX1 ) @ ( SV55 @ SX0 @ SX1 ) ) )
@ sK2_SY17
@ ( sK4_E
@ ^ [SX0: $i] :
( injective
@ ( SV53
@ ( sK7_E
@ ^ [SX1: $i,SX2: $i] : ( injective @ ( SV53 @ SX1 @ SX2 ) @ ( SV54 @ SX1 @ SX2 ) @ ( SV55 @ SX1 @ SX2 ) ) )
@ SX0 )
@ ( SV54
@ ( sK7_E
@ ^ [SX1: $i,SX2: $i] : ( injective @ ( SV53 @ SX1 @ SX2 ) @ ( SV54 @ SX1 @ SX2 ) @ ( SV55 @ SX1 @ SX2 ) ) )
@ SX0 )
@ ( SV55
@ ( sK7_E
@ ^ [SX1: $i,SX2: $i] : ( injective @ ( SV53 @ SX1 @ SX2 ) @ ( SV54 @ SX1 @ SX2 ) @ ( SV55 @ SX1 @ SX2 ) ) )
@ SX0 ) ) ) )
= $true )
| ( ( ( sK4_E
@ ^ [SX0: $i] :
( injective @ SX0 @ sK2_SY17
@ ( sK4_E
@ ^ [SX1: $i] : ( injective @ ( SV53 @ SX0 @ SX1 ) @ ( SV54 @ SX0 @ SX1 ) @ ( SV55 @ SX0 @ SX1 ) ) ) ) )
= sK1_SX0 )
= $false ) ),
inference(extuni,[status(esa)],[30:[bind(SV4,$thf( ^ [SX0: $i] : ( injective @ SX0 @ sK2_SY17 @ ( sK4_E @ ^ [SX1: $i] : ( injective @ ( SV53 @ SX0 @ SX1 ) @ ( SV54 @ SX0 @ SX1 ) @ ( SV55 @ SX0 @ SX1 ) ) ) ) )),bind(SV5,$thf( funcSet @ sK1_SX0 @ sK2_SY17 )),bind(SV6,$thf( sK3_SY22 ))]]) ).
thf(38,plain,
! [SV55: $i > $i > $i,SV54: $i > $i > $i,SV53: $i > $i > $i] :
( ( ( in @ sK3_SY22 @ ( funcSet @ sK1_SX0 @ sK2_SY17 ) )
= $true )
| ( ( injective
@ ( SV53
@ ( sK4_E
@ ^ [SX0: $i] :
( injective @ SX0 @ sK2_SY17
@ ( sK4_E
@ ^ [SX1: $i] : ( injective @ ( SV53 @ SX0 @ SX1 ) @ ( SV54 @ SX0 @ SX1 ) @ ( SV55 @ SX0 @ SX1 ) ) ) ) )
@ ( sK7_E
@ ^ [SX0: $i,SX1: $i] : ( injective @ ( SV53 @ SX0 @ SX1 ) @ ( SV54 @ SX0 @ SX1 ) @ ( SV55 @ SX0 @ SX1 ) ) ) )
@ ( SV54
@ ( sK4_E
@ ^ [SX0: $i] :
( injective @ SX0 @ sK2_SY17
@ ( sK4_E
@ ^ [SX1: $i] : ( injective @ ( SV53 @ SX0 @ SX1 ) @ ( SV54 @ SX0 @ SX1 ) @ ( SV55 @ SX0 @ SX1 ) ) ) ) )
@ ( sK7_E
@ ^ [SX0: $i,SX1: $i] : ( injective @ ( SV53 @ SX0 @ SX1 ) @ ( SV54 @ SX0 @ SX1 ) @ ( SV55 @ SX0 @ SX1 ) ) ) )
@ ( SV55
@ ( sK4_E
@ ^ [SX0: $i] :
( injective @ SX0 @ sK2_SY17
@ ( sK4_E
@ ^ [SX1: $i] : ( injective @ ( SV53 @ SX0 @ SX1 ) @ ( SV54 @ SX0 @ SX1 ) @ ( SV55 @ SX0 @ SX1 ) ) ) ) )
@ ( sK7_E
@ ^ [SX0: $i,SX1: $i] : ( injective @ ( SV53 @ SX0 @ SX1 ) @ ( SV54 @ SX0 @ SX1 ) @ ( SV55 @ SX0 @ SX1 ) ) ) ) )
= $false )
| ( ( injective
@ ( sK7_E
@ ^ [SX0: $i,SX1: $i] : ( injective @ ( SV53 @ SX0 @ SX1 ) @ ( SV54 @ SX0 @ SX1 ) @ ( SV55 @ SX0 @ SX1 ) ) )
@ sK2_SY17
@ ( sK4_E
@ ^ [SX0: $i] :
( injective
@ ( SV53
@ ( sK7_E
@ ^ [SX1: $i,SX2: $i] : ( injective @ ( SV53 @ SX1 @ SX2 ) @ ( SV54 @ SX1 @ SX2 ) @ ( SV55 @ SX1 @ SX2 ) ) )
@ SX0 )
@ ( SV54
@ ( sK7_E
@ ^ [SX1: $i,SX2: $i] : ( injective @ ( SV53 @ SX1 @ SX2 ) @ ( SV54 @ SX1 @ SX2 ) @ ( SV55 @ SX1 @ SX2 ) ) )
@ SX0 )
@ ( SV55
@ ( sK7_E
@ ^ [SX1: $i,SX2: $i] : ( injective @ ( SV53 @ SX1 @ SX2 ) @ ( SV54 @ SX1 @ SX2 ) @ ( SV55 @ SX1 @ SX2 ) ) )
@ SX0 ) ) ) )
= $false )
| ( ( ( sK4_E
@ ^ [SX0: $i] :
( injective @ SX0 @ sK2_SY17
@ ( sK4_E
@ ^ [SX1: $i] : ( injective @ ( SV53 @ SX0 @ SX1 ) @ ( SV54 @ SX0 @ SX1 ) @ ( SV55 @ SX0 @ SX1 ) ) ) ) )
= sK1_SX0 )
= $false ) ),
inference(extuni,[status(esa)],[30:[bind(SV4,$thf( ^ [SX0: $i] : ( injective @ SX0 @ sK2_SY17 @ ( sK4_E @ ^ [SX1: $i] : ( injective @ ( SV53 @ SX0 @ SX1 ) @ ( SV54 @ SX0 @ SX1 ) @ ( SV55 @ SX0 @ SX1 ) ) ) ) )),bind(SV5,$thf( funcSet @ sK1_SX0 @ sK2_SY17 )),bind(SV6,$thf( sK3_SY22 ))]]) ).
thf(39,plain,
! [SV48: $i > $i > $o] :
( ( ( in @ sK3_SY22 @ ( funcSet @ sK1_SX0 @ sK2_SY17 ) )
= $true )
| ( ( ( sK4_E
@ ( SV48
@ ( sK4_E
@ ^ [SX0: $i] : ( injective @ SX0 @ sK2_SY17 @ ( sK4_E @ ( SV48 @ SX0 ) ) ) ) ) )
= ( sK4_E
@ ^ [SX0: $i] : ( injective @ SX0 @ sK2_SY17 @ ( sK4_E @ ( SV48 @ SX0 ) ) ) ) )
= $false )
| ( ( ( sK4_E
@ ^ [SX0: $i] : ( injective @ SX0 @ sK2_SY17 @ ( sK4_E @ ( SV48 @ SX0 ) ) ) )
= sK1_SX0 )
= $false ) ),
inference(extuni,[status(esa)],[30:[bind(SV4,$thf( ^ [SX0: $i] : ( injective @ SX0 @ sK2_SY17 @ ( sK4_E @ ( SV48 @ SX0 ) ) ) )),bind(SV5,$thf( funcSet @ sK1_SX0 @ sK2_SY17 )),bind(SV6,$thf( sK3_SY22 ))]]) ).
thf(40,plain,
( ( ( in @ sK3_SY22 @ ( funcSet @ sK1_SX0 @ sK2_SY17 ) )
= $true )
| ( ( ( sK4_E
@ ^ [SX0: $i] : ( injective @ SX0 @ sK2_SY17 @ SX0 ) )
= sK1_SX0 )
= $false ) ),
inference(extuni,[status(esa)],[30:[bind(SV4,$thf( ^ [SX0: $i] : ( injective @ SX0 @ sK2_SY17 @ SX0 ) )),bind(SV5,$thf( funcSet @ sK1_SX0 @ sK2_SY17 )),bind(SV6,$thf( sK3_SY22 ))]]) ).
thf(41,plain,
! [SV39: $i > $i > $i,SV38: $i > $i > $i,SV37: $i > $i > $i] :
( ( ( in @ sK3_SY22 @ ( funcSet @ sK1_SX0 @ sK2_SY17 ) )
= $true )
| ( ( injective
@ ( SV37
@ ( sK4_E
@ ^ [SX0: $i] :
( injective @ sK1_SX0 @ SX0
@ ( sK4_E
@ ^ [SX1: $i] : ( injective @ ( SV37 @ SX0 @ SX1 ) @ ( SV38 @ SX0 @ SX1 ) @ ( SV39 @ SX0 @ SX1 ) ) ) ) )
@ ( sK6_E
@ ^ [SX0: $i,SX1: $i] : ( injective @ ( SV37 @ SX0 @ SX1 ) @ ( SV38 @ SX0 @ SX1 ) @ ( SV39 @ SX0 @ SX1 ) ) ) )
@ ( SV38
@ ( sK4_E
@ ^ [SX0: $i] :
( injective @ sK1_SX0 @ SX0
@ ( sK4_E
@ ^ [SX1: $i] : ( injective @ ( SV37 @ SX0 @ SX1 ) @ ( SV38 @ SX0 @ SX1 ) @ ( SV39 @ SX0 @ SX1 ) ) ) ) )
@ ( sK6_E
@ ^ [SX0: $i,SX1: $i] : ( injective @ ( SV37 @ SX0 @ SX1 ) @ ( SV38 @ SX0 @ SX1 ) @ ( SV39 @ SX0 @ SX1 ) ) ) )
@ ( SV39
@ ( sK4_E
@ ^ [SX0: $i] :
( injective @ sK1_SX0 @ SX0
@ ( sK4_E
@ ^ [SX1: $i] : ( injective @ ( SV37 @ SX0 @ SX1 ) @ ( SV38 @ SX0 @ SX1 ) @ ( SV39 @ SX0 @ SX1 ) ) ) ) )
@ ( sK6_E
@ ^ [SX0: $i,SX1: $i] : ( injective @ ( SV37 @ SX0 @ SX1 ) @ ( SV38 @ SX0 @ SX1 ) @ ( SV39 @ SX0 @ SX1 ) ) ) ) )
= $true )
| ( ( injective @ sK1_SX0
@ ( sK6_E
@ ^ [SX0: $i,SX1: $i] : ( injective @ ( SV37 @ SX0 @ SX1 ) @ ( SV38 @ SX0 @ SX1 ) @ ( SV39 @ SX0 @ SX1 ) ) )
@ ( sK4_E
@ ^ [SX0: $i] :
( injective
@ ( SV37
@ ( sK6_E
@ ^ [SX1: $i,SX2: $i] : ( injective @ ( SV37 @ SX1 @ SX2 ) @ ( SV38 @ SX1 @ SX2 ) @ ( SV39 @ SX1 @ SX2 ) ) )
@ SX0 )
@ ( SV38
@ ( sK6_E
@ ^ [SX1: $i,SX2: $i] : ( injective @ ( SV37 @ SX1 @ SX2 ) @ ( SV38 @ SX1 @ SX2 ) @ ( SV39 @ SX1 @ SX2 ) ) )
@ SX0 )
@ ( SV39
@ ( sK6_E
@ ^ [SX1: $i,SX2: $i] : ( injective @ ( SV37 @ SX1 @ SX2 ) @ ( SV38 @ SX1 @ SX2 ) @ ( SV39 @ SX1 @ SX2 ) ) )
@ SX0 ) ) ) )
= $true )
| ( ( ( sK4_E
@ ^ [SX0: $i] :
( injective @ sK1_SX0 @ SX0
@ ( sK4_E
@ ^ [SX1: $i] : ( injective @ ( SV37 @ SX0 @ SX1 ) @ ( SV38 @ SX0 @ SX1 ) @ ( SV39 @ SX0 @ SX1 ) ) ) ) )
= sK2_SY17 )
= $false ) ),
inference(extuni,[status(esa)],[30:[bind(SV4,$thf( ^ [SX0: $i] : ( injective @ sK1_SX0 @ SX0 @ ( sK4_E @ ^ [SX1: $i] : ( injective @ ( SV37 @ SX0 @ SX1 ) @ ( SV38 @ SX0 @ SX1 ) @ ( SV39 @ SX0 @ SX1 ) ) ) ) )),bind(SV5,$thf( funcSet @ sK1_SX0 @ sK2_SY17 )),bind(SV6,$thf( sK3_SY22 ))]]) ).
thf(42,plain,
! [SV39: $i > $i > $i,SV38: $i > $i > $i,SV37: $i > $i > $i] :
( ( ( in @ sK3_SY22 @ ( funcSet @ sK1_SX0 @ sK2_SY17 ) )
= $true )
| ( ( injective
@ ( SV37
@ ( sK4_E
@ ^ [SX0: $i] :
( injective @ sK1_SX0 @ SX0
@ ( sK4_E
@ ^ [SX1: $i] : ( injective @ ( SV37 @ SX0 @ SX1 ) @ ( SV38 @ SX0 @ SX1 ) @ ( SV39 @ SX0 @ SX1 ) ) ) ) )
@ ( sK6_E
@ ^ [SX0: $i,SX1: $i] : ( injective @ ( SV37 @ SX0 @ SX1 ) @ ( SV38 @ SX0 @ SX1 ) @ ( SV39 @ SX0 @ SX1 ) ) ) )
@ ( SV38
@ ( sK4_E
@ ^ [SX0: $i] :
( injective @ sK1_SX0 @ SX0
@ ( sK4_E
@ ^ [SX1: $i] : ( injective @ ( SV37 @ SX0 @ SX1 ) @ ( SV38 @ SX0 @ SX1 ) @ ( SV39 @ SX0 @ SX1 ) ) ) ) )
@ ( sK6_E
@ ^ [SX0: $i,SX1: $i] : ( injective @ ( SV37 @ SX0 @ SX1 ) @ ( SV38 @ SX0 @ SX1 ) @ ( SV39 @ SX0 @ SX1 ) ) ) )
@ ( SV39
@ ( sK4_E
@ ^ [SX0: $i] :
( injective @ sK1_SX0 @ SX0
@ ( sK4_E
@ ^ [SX1: $i] : ( injective @ ( SV37 @ SX0 @ SX1 ) @ ( SV38 @ SX0 @ SX1 ) @ ( SV39 @ SX0 @ SX1 ) ) ) ) )
@ ( sK6_E
@ ^ [SX0: $i,SX1: $i] : ( injective @ ( SV37 @ SX0 @ SX1 ) @ ( SV38 @ SX0 @ SX1 ) @ ( SV39 @ SX0 @ SX1 ) ) ) ) )
= $false )
| ( ( injective @ sK1_SX0
@ ( sK6_E
@ ^ [SX0: $i,SX1: $i] : ( injective @ ( SV37 @ SX0 @ SX1 ) @ ( SV38 @ SX0 @ SX1 ) @ ( SV39 @ SX0 @ SX1 ) ) )
@ ( sK4_E
@ ^ [SX0: $i] :
( injective
@ ( SV37
@ ( sK6_E
@ ^ [SX1: $i,SX2: $i] : ( injective @ ( SV37 @ SX1 @ SX2 ) @ ( SV38 @ SX1 @ SX2 ) @ ( SV39 @ SX1 @ SX2 ) ) )
@ SX0 )
@ ( SV38
@ ( sK6_E
@ ^ [SX1: $i,SX2: $i] : ( injective @ ( SV37 @ SX1 @ SX2 ) @ ( SV38 @ SX1 @ SX2 ) @ ( SV39 @ SX1 @ SX2 ) ) )
@ SX0 )
@ ( SV39
@ ( sK6_E
@ ^ [SX1: $i,SX2: $i] : ( injective @ ( SV37 @ SX1 @ SX2 ) @ ( SV38 @ SX1 @ SX2 ) @ ( SV39 @ SX1 @ SX2 ) ) )
@ SX0 ) ) ) )
= $false )
| ( ( ( sK4_E
@ ^ [SX0: $i] :
( injective @ sK1_SX0 @ SX0
@ ( sK4_E
@ ^ [SX1: $i] : ( injective @ ( SV37 @ SX0 @ SX1 ) @ ( SV38 @ SX0 @ SX1 ) @ ( SV39 @ SX0 @ SX1 ) ) ) ) )
= sK2_SY17 )
= $false ) ),
inference(extuni,[status(esa)],[30:[bind(SV4,$thf( ^ [SX0: $i] : ( injective @ sK1_SX0 @ SX0 @ ( sK4_E @ ^ [SX1: $i] : ( injective @ ( SV37 @ SX0 @ SX1 ) @ ( SV38 @ SX0 @ SX1 ) @ ( SV39 @ SX0 @ SX1 ) ) ) ) )),bind(SV5,$thf( funcSet @ sK1_SX0 @ sK2_SY17 )),bind(SV6,$thf( sK3_SY22 ))]]) ).
thf(43,plain,
! [SV32: $i > $i > $o] :
( ( ( in @ sK3_SY22 @ ( funcSet @ sK1_SX0 @ sK2_SY17 ) )
= $true )
| ( ( ( sK4_E
@ ( SV32
@ ( sK4_E
@ ^ [SX0: $i] : ( injective @ sK1_SX0 @ SX0 @ ( sK4_E @ ( SV32 @ SX0 ) ) ) ) ) )
= ( sK4_E
@ ^ [SX0: $i] : ( injective @ sK1_SX0 @ SX0 @ ( sK4_E @ ( SV32 @ SX0 ) ) ) ) )
= $false )
| ( ( ( sK4_E
@ ^ [SX0: $i] : ( injective @ sK1_SX0 @ SX0 @ ( sK4_E @ ( SV32 @ SX0 ) ) ) )
= sK2_SY17 )
= $false ) ),
inference(extuni,[status(esa)],[30:[bind(SV4,$thf( ^ [SX0: $i] : ( injective @ sK1_SX0 @ SX0 @ ( sK4_E @ ( SV32 @ SX0 ) ) ) )),bind(SV5,$thf( funcSet @ sK1_SX0 @ sK2_SY17 )),bind(SV6,$thf( sK3_SY22 ))]]) ).
thf(44,plain,
( ( ( in @ sK3_SY22 @ ( funcSet @ sK1_SX0 @ sK2_SY17 ) )
= $true )
| ( ( ( sK4_E
@ ^ [SX0: $i] : ( injective @ sK1_SX0 @ SX0 @ SX0 ) )
= sK2_SY17 )
= $false ) ),
inference(extuni,[status(esa)],[30:[bind(SV4,$thf( ^ [SX0: $i] : ( injective @ sK1_SX0 @ SX0 @ SX0 ) )),bind(SV5,$thf( funcSet @ sK1_SX0 @ sK2_SY17 )),bind(SV6,$thf( sK3_SY22 ))]]) ).
thf(45,plain,
! [SV25: $i > $i > $i,SV24: $i > $i > $i,SV23: $i > $i > $i] :
( ( ( in @ sK3_SY22 @ ( funcSet @ sK1_SX0 @ sK2_SY17 ) )
= $true )
| ( ( injective
@ ( SV23
@ ( sK4_E
@ ^ [SX0: $i] :
( injective @ sK1_SX0 @ sK2_SY17
@ ( sK4_E
@ ^ [SX1: $i] : ( injective @ ( SV23 @ SX0 @ SX1 ) @ ( SV24 @ SX0 @ SX1 ) @ ( SV25 @ SX0 @ SX1 ) ) ) ) )
@ ( sK5_E
@ ^ [SX0: $i,SX1: $i] : ( injective @ ( SV23 @ SX0 @ SX1 ) @ ( SV24 @ SX0 @ SX1 ) @ ( SV25 @ SX0 @ SX1 ) ) ) )
@ ( SV24
@ ( sK4_E
@ ^ [SX0: $i] :
( injective @ sK1_SX0 @ sK2_SY17
@ ( sK4_E
@ ^ [SX1: $i] : ( injective @ ( SV23 @ SX0 @ SX1 ) @ ( SV24 @ SX0 @ SX1 ) @ ( SV25 @ SX0 @ SX1 ) ) ) ) )
@ ( sK5_E
@ ^ [SX0: $i,SX1: $i] : ( injective @ ( SV23 @ SX0 @ SX1 ) @ ( SV24 @ SX0 @ SX1 ) @ ( SV25 @ SX0 @ SX1 ) ) ) )
@ ( SV25
@ ( sK4_E
@ ^ [SX0: $i] :
( injective @ sK1_SX0 @ sK2_SY17
@ ( sK4_E
@ ^ [SX1: $i] : ( injective @ ( SV23 @ SX0 @ SX1 ) @ ( SV24 @ SX0 @ SX1 ) @ ( SV25 @ SX0 @ SX1 ) ) ) ) )
@ ( sK5_E
@ ^ [SX0: $i,SX1: $i] : ( injective @ ( SV23 @ SX0 @ SX1 ) @ ( SV24 @ SX0 @ SX1 ) @ ( SV25 @ SX0 @ SX1 ) ) ) ) )
= $true )
| ( ( injective @ sK1_SX0 @ sK2_SY17
@ ( sK4_E
@ ^ [SX0: $i] :
( injective
@ ( SV23
@ ( sK5_E
@ ^ [SX1: $i,SX2: $i] : ( injective @ ( SV23 @ SX1 @ SX2 ) @ ( SV24 @ SX1 @ SX2 ) @ ( SV25 @ SX1 @ SX2 ) ) )
@ SX0 )
@ ( SV24
@ ( sK5_E
@ ^ [SX1: $i,SX2: $i] : ( injective @ ( SV23 @ SX1 @ SX2 ) @ ( SV24 @ SX1 @ SX2 ) @ ( SV25 @ SX1 @ SX2 ) ) )
@ SX0 )
@ ( SV25
@ ( sK5_E
@ ^ [SX1: $i,SX2: $i] : ( injective @ ( SV23 @ SX1 @ SX2 ) @ ( SV24 @ SX1 @ SX2 ) @ ( SV25 @ SX1 @ SX2 ) ) )
@ SX0 ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[30:[bind(SV4,$thf( ^ [SX0: $i] : ( injective @ sK1_SX0 @ sK2_SY17 @ ( sK4_E @ ^ [SX1: $i] : ( injective @ ( SV23 @ SX0 @ SX1 ) @ ( SV24 @ SX0 @ SX1 ) @ ( SV25 @ SX0 @ SX1 ) ) ) ) )),bind(SV5,$thf( funcSet @ sK1_SX0 @ sK2_SY17 )),bind(SV6,$thf( sK3_SY22 ))]]) ).
thf(46,plain,
! [SV25: $i > $i > $i,SV24: $i > $i > $i,SV23: $i > $i > $i] :
( ( ( in @ sK3_SY22 @ ( funcSet @ sK1_SX0 @ sK2_SY17 ) )
= $true )
| ( ( injective
@ ( SV23
@ ( sK4_E
@ ^ [SX0: $i] :
( injective @ sK1_SX0 @ sK2_SY17
@ ( sK4_E
@ ^ [SX1: $i] : ( injective @ ( SV23 @ SX0 @ SX1 ) @ ( SV24 @ SX0 @ SX1 ) @ ( SV25 @ SX0 @ SX1 ) ) ) ) )
@ ( sK5_E
@ ^ [SX0: $i,SX1: $i] : ( injective @ ( SV23 @ SX0 @ SX1 ) @ ( SV24 @ SX0 @ SX1 ) @ ( SV25 @ SX0 @ SX1 ) ) ) )
@ ( SV24
@ ( sK4_E
@ ^ [SX0: $i] :
( injective @ sK1_SX0 @ sK2_SY17
@ ( sK4_E
@ ^ [SX1: $i] : ( injective @ ( SV23 @ SX0 @ SX1 ) @ ( SV24 @ SX0 @ SX1 ) @ ( SV25 @ SX0 @ SX1 ) ) ) ) )
@ ( sK5_E
@ ^ [SX0: $i,SX1: $i] : ( injective @ ( SV23 @ SX0 @ SX1 ) @ ( SV24 @ SX0 @ SX1 ) @ ( SV25 @ SX0 @ SX1 ) ) ) )
@ ( SV25
@ ( sK4_E
@ ^ [SX0: $i] :
( injective @ sK1_SX0 @ sK2_SY17
@ ( sK4_E
@ ^ [SX1: $i] : ( injective @ ( SV23 @ SX0 @ SX1 ) @ ( SV24 @ SX0 @ SX1 ) @ ( SV25 @ SX0 @ SX1 ) ) ) ) )
@ ( sK5_E
@ ^ [SX0: $i,SX1: $i] : ( injective @ ( SV23 @ SX0 @ SX1 ) @ ( SV24 @ SX0 @ SX1 ) @ ( SV25 @ SX0 @ SX1 ) ) ) ) )
= $false )
| ( ( injective @ sK1_SX0 @ sK2_SY17
@ ( sK4_E
@ ^ [SX0: $i] :
( injective
@ ( SV23
@ ( sK5_E
@ ^ [SX1: $i,SX2: $i] : ( injective @ ( SV23 @ SX1 @ SX2 ) @ ( SV24 @ SX1 @ SX2 ) @ ( SV25 @ SX1 @ SX2 ) ) )
@ SX0 )
@ ( SV24
@ ( sK5_E
@ ^ [SX1: $i,SX2: $i] : ( injective @ ( SV23 @ SX1 @ SX2 ) @ ( SV24 @ SX1 @ SX2 ) @ ( SV25 @ SX1 @ SX2 ) ) )
@ SX0 )
@ ( SV25
@ ( sK5_E
@ ^ [SX1: $i,SX2: $i] : ( injective @ ( SV23 @ SX1 @ SX2 ) @ ( SV24 @ SX1 @ SX2 ) @ ( SV25 @ SX1 @ SX2 ) ) )
@ SX0 ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[30:[bind(SV4,$thf( ^ [SX0: $i] : ( injective @ sK1_SX0 @ sK2_SY17 @ ( sK4_E @ ^ [SX1: $i] : ( injective @ ( SV23 @ SX0 @ SX1 ) @ ( SV24 @ SX0 @ SX1 ) @ ( SV25 @ SX0 @ SX1 ) ) ) ) )),bind(SV5,$thf( funcSet @ sK1_SX0 @ sK2_SY17 )),bind(SV6,$thf( sK3_SY22 ))]]) ).
thf(47,plain,
! [SV18: $i > $i > $o] :
( ( ( in @ sK3_SY22 @ ( funcSet @ sK1_SX0 @ sK2_SY17 ) )
= $true )
| ( ( ( sK4_E
@ ( SV18
@ ( sK4_E
@ ^ [SX0: $i] : ( injective @ sK1_SX0 @ sK2_SY17 @ ( sK4_E @ ( SV18 @ SX0 ) ) ) ) ) )
= ( sK4_E
@ ^ [SX0: $i] : ( injective @ sK1_SX0 @ sK2_SY17 @ ( sK4_E @ ( SV18 @ SX0 ) ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[30:[bind(SV4,$thf( ^ [SX0: $i] : ( injective @ sK1_SX0 @ sK2_SY17 @ ( sK4_E @ ( SV18 @ SX0 ) ) ) )),bind(SV5,$thf( funcSet @ sK1_SX0 @ sK2_SY17 )),bind(SV6,$thf( sK3_SY22 ))]]) ).
thf(48,plain,
( ( in @ sK3_SY22 @ ( funcSet @ sK1_SX0 @ sK2_SY17 ) )
= $true ),
inference(extuni,[status(esa)],[30:[bind(SV4,$thf( ^ [SX0: $i] : ( injective @ sK1_SX0 @ sK2_SY17 @ SX0 ) )),bind(SV5,$thf( funcSet @ sK1_SX0 @ sK2_SY17 )),bind(SV6,$thf( sK3_SY22 ))]]) ).
thf(49,plain,
! [SV11: $i > $i,SV10: $i > $i,SV9: $i > $i] :
( ( ( in @ sK3_SY22 @ ( funcSet @ sK1_SX0 @ sK2_SY17 ) )
= $true )
| ( ( injective
@ ( SV9
@ ( sK4_E
@ ^ [SX0: $i] : ( injective @ ( SV9 @ SX0 ) @ ( SV10 @ SX0 ) @ ( SV11 @ SX0 ) ) ) )
@ ( SV10
@ ( sK4_E
@ ^ [SX0: $i] : ( injective @ ( SV9 @ SX0 ) @ ( SV10 @ SX0 ) @ ( SV11 @ SX0 ) ) ) )
@ ( SV11
@ ( sK4_E
@ ^ [SX0: $i] : ( injective @ ( SV9 @ SX0 ) @ ( SV10 @ SX0 ) @ ( SV11 @ SX0 ) ) ) ) )
= $true )
| ( ( injective @ sK1_SX0 @ sK2_SY17
@ ( sK4_E
@ ^ [SX0: $i] : ( injective @ ( SV9 @ SX0 ) @ ( SV10 @ SX0 ) @ ( SV11 @ SX0 ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[30:[bind(SV4,$thf( ^ [SX0: $i] : ( injective @ ( SV9 @ SX0 ) @ ( SV10 @ SX0 ) @ ( SV11 @ SX0 ) ) )),bind(SV5,$thf( funcSet @ sK1_SX0 @ sK2_SY17 )),bind(SV6,$thf( sK3_SY22 ))]]) ).
thf(50,plain,
! [SV11: $i > $i,SV10: $i > $i,SV9: $i > $i] :
( ( ( in @ sK3_SY22 @ ( funcSet @ sK1_SX0 @ sK2_SY17 ) )
= $true )
| ( ( injective
@ ( SV9
@ ( sK4_E
@ ^ [SX0: $i] : ( injective @ ( SV9 @ SX0 ) @ ( SV10 @ SX0 ) @ ( SV11 @ SX0 ) ) ) )
@ ( SV10
@ ( sK4_E
@ ^ [SX0: $i] : ( injective @ ( SV9 @ SX0 ) @ ( SV10 @ SX0 ) @ ( SV11 @ SX0 ) ) ) )
@ ( SV11
@ ( sK4_E
@ ^ [SX0: $i] : ( injective @ ( SV9 @ SX0 ) @ ( SV10 @ SX0 ) @ ( SV11 @ SX0 ) ) ) ) )
= $false )
| ( ( injective @ sK1_SX0 @ sK2_SY17
@ ( sK4_E
@ ^ [SX0: $i] : ( injective @ ( SV9 @ SX0 ) @ ( SV10 @ SX0 ) @ ( SV11 @ SX0 ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[30:[bind(SV4,$thf( ^ [SX0: $i] : ( injective @ ( SV9 @ SX0 ) @ ( SV10 @ SX0 ) @ ( SV11 @ SX0 ) ) )),bind(SV5,$thf( funcSet @ sK1_SX0 @ sK2_SY17 )),bind(SV6,$thf( sK3_SY22 ))]]) ).
thf(51,plain,
! [SV4: $i > $o,SV5: $i] :
( ( ( in @ sK3_SY22 @ SV5 )
= $true )
| ( ( ( dsetconstr @ SV5
@ ^ [SX0: $i] : ( SV4 @ SX0 ) )
= ( dsetconstr @ ( funcSet @ sK1_SX0 @ sK2_SY17 )
@ ^ [SX0: $i] : ( injective @ sK1_SX0 @ sK2_SY17 @ SX0 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[30:[bind(SV6,$thf( sK3_SY22 ))]]) ).
thf(52,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[20,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,26,24,22]) ).
thf(53,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU799^2 : 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
% 0.12/0.19 % Computer : n005.cluster.edu
% 0.12/0.19 % Model : x86_64 x86_64
% 0.12/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.19 % Memory : 8046.5625MB
% 0.12/0.19 % OS : Linux 6.8.0-71-generic
% 0.12/0.19 % CPULimit : 300
% 0.12/0.19 % WCLimit : 300
% 0.12/0.19 % DateTime : Tue Oct 6 15:34:59 UTC 2026
% 0.12/0.19 % CPUTime :
% 0.12/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.43/0.40
% 0.43/0.40 No.of.Axioms: 0
% 0.43/0.40
% 0.43/0.40 Length.of.Defs: 410
% 0.43/0.40
% 0.43/0.40 Contains.Choice.Funs: false
% 0.43/0.40 .
% 0.43/0.40
% 0.43/0.40 ********************************
% 0.43/0.40 * All subproblems solved! *
% 0.43/0.40 ********************************
% 0.43/0.40 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:1,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:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:52,loop_count:5,foatp_calls:2,translation:fof_full)
% 0.43/0.40
% 0.43/0.40 %**** Beginning of derivation protocol ****
% 0.43/0.40 % SZS output start CNFRefutation
% See solution above
% 0.43/0.40
% 0.43/0.40 %**** End of derivation protocol ****
% 0.43/0.40 %**** no. of clauses in derivation: 49 ****
% 0.43/0.40 %**** clause counter: 52 ****
% 0.43/0.40
% 0.43/0.40 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:1,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:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:52,loop_count:5,foatp_calls:2,translation:fof_full)
%------------------------------------------------------------------------------