%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU800^2 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 1.11s 0.41s
% Output : CNFRefutation 1.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 3
% Syntax : Number of formulae : 89 ( 30 unt; 0 typ; 2 def)
% Number of atoms : 748 ( 227 equ; 0 cnn)
% Maximal formula atoms : 5 ( 8 avg)
% Number of connectives : 2303 ( 57 ~; 115 |; 0 &;2118 @)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 113 ( 113 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 7 con; 0-3 aty)
% Number of variables : 492 ( 287 ^; 205 !; 0 ?; 492 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_dsetconstr,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(tp_dsetconstrER,type,
dsetconstrER: $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(tp_sK9_E,type,
sK9_E: $i ).
thf(dsetconstrER,definition,
( dsetconstrER
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( Xphi @ Xx ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrER) ).
thf(injFuncSet,definition,
( injFuncSet
= ( ^ [A: $i,B: $i] :
( dsetconstr @ ( funcSet @ A @ B )
@ ^ [Xf: $i] : ( injective @ A @ B @ Xf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',injFuncSet) ).
thf(1,conjecture,
( dsetconstrER
=> ! [Xx: $i,Xy: $i,Xf: $i] :
( ( in @ Xf @ ( injFuncSet @ Xx @ Xy ) )
=> ( injective @ Xx @ Xy @ Xf ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',injFuncSetFuncInj) ).
thf(2,negated_conjecture,
( ( dsetconstrER
=> ! [Xx: $i,Xy: $i,Xf: $i] :
( ( in @ Xf @ ( injFuncSet @ Xx @ Xy ) )
=> ( injective @ Xx @ Xy @ Xf ) ) )
= $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 ) ) )
=> ( Xphi @ Xx ) )
=> ! [SY0: $i,SY1: $i,SY2: $i] :
( ( in @ SY2
@ ( dsetconstr @ ( funcSet @ SY0 @ SY1 )
@ ^ [SY5: $i] : ( injective @ SY0 @ SY1 @ SY5 ) ) )
=> ( injective @ SY0 @ SY1 @ SY2 ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,dsetconstrER,injFuncSet]) ).
thf(4,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( Xphi @ Xx ) ) )
= $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 ) ) )
=> ( injective @ SY0 @ SY1 @ SY2 ) ) )
= $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 ) ) )
=> ( injective @ SY0 @ SY1 @ SY2 ) ) )
= $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 ) ) )
=> ( Xphi @ Xx ) ) )
= $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 ) ) )
=> ( injective @ SY0 @ SY1 @ SY2 ) ) )
= $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 ) ) )
| ( injective @ SX0 @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8,dsetconstrER,injFuncSet]) ).
thf(10,plain,
( ( ! [SX0: $i,SX1: $i > $o,SX2: $i] :
( ~ ( in @ SX2
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) )
| ( SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7,dsetconstrER,injFuncSet]) ).
thf(11,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2
@ ( dsetconstr @ ( funcSet @ SX0 @ SX1 )
@ ^ [SX3: $i] : ( injective @ SX0 @ SX1 @ SX3 ) ) )
| ( injective @ SX0 @ SX1 @ SX2 ) ) )
= $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 ) ) )
| ( SY14 @ SY15 ) ) )
= $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 ) ) )
| ( injective @ sK1_SX0 @ SY17 @ SY18 ) ) )
= $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 ) ) )
| ( SV2 @ SY20 ) ) )
= $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 ) ) )
| ( injective @ sK1_SX0 @ sK2_SY17 @ SY22 ) ) )
= $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 ) ) )
| ( SV2 @ SV3 ) )
= $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 ) ) )
| ( injective @ sK1_SX0 @ sK2_SY17 @ sK3_SY22 ) )
= $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 )
| ( ( SV2 @ SV3 )
= $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,
( ( injective @ sK1_SX0 @ sK2_SY17 @ sK3_SY22 )
= $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 )
| ( ( SV2 @ SV3 )
= $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,
! [SV2: $i > $o,SV1: $i,SV3: $i] :
( ( ( SV2 @ SV3 )
= $true )
| ( ( ( SV2 @ SV3 )
= ( ~ ( in @ SV3
@ ( dsetconstr @ SV1
@ ^ [SY21: $i] : ( SV2 @ SY21 ) ) ) ) )
= $false ) ),
inference(fac_restr,[status(thm)],[21]) ).
thf(24,plain,
! [SV1: $i,SV3: $i,SV2: $i > $o] :
( ( ( ~ ( ( SV2 @ SV3 )
| ~ ( in @ SV3
@ ( dsetconstr @ SV1
@ ^ [SY21: $i] : ( SV2 @ SY21 ) ) ) )
| ~ ( ~ ( SV2 @ SV3 )
| ~ ~ ( in @ SV3
@ ( dsetconstr @ SV1
@ ^ [SY21: $i] : ( SV2 @ SY21 ) ) ) ) )
= $false )
| ( ( SV2 @ SV3 )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[23]) ).
thf(25,plain,
! [SV1: $i,SV3: $i,SV2: $i > $o] :
( ( ( ( SV2 @ SV3 )
= ( ~ ( in @ SV3
@ ( dsetconstr @ SV1
@ ^ [SY21: $i] : ( SV2 @ SY21 ) ) ) ) )
= $false )
| ( ( SV2 @ SV3 )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[23]) ).
thf(26,plain,
! [SV1: $i,SV3: $i,SV2: $i > $o] :
( ( ( ~ ( ( SV2 @ SV3 )
| ~ ( in @ SV3
@ ( dsetconstr @ SV1
@ ^ [SY21: $i] : ( SV2 @ SY21 ) ) ) ) )
= $false )
| ( ( SV2 @ SV3 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[24]) ).
thf(28,plain,
! [SV1: $i,SV3: $i,SV2: $i > $o] :
( ( ( ( SV2 @ SV3 )
| ~ ( in @ SV3
@ ( dsetconstr @ SV1
@ ^ [SY21: $i] : ( SV2 @ SY21 ) ) ) )
= $true )
| ( ( SV2 @ SV3 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[26]) ).
thf(30,plain,
! [SV1: $i,SV3: $i,SV2: $i > $o] :
( ( ( SV2 @ SV3 )
= $true )
| ( ( ~ ( in @ SV3
@ ( dsetconstr @ SV1
@ ^ [SY21: $i] : ( SV2 @ SY21 ) ) ) )
= $true )
| ( ( SV2 @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[28]) ).
thf(32,plain,
! [SV2: $i > $o,SV1: $i,SV3: $i] :
( ( ( in @ SV3
@ ( dsetconstr @ SV1
@ ^ [SY21: $i] : ( SV2 @ SY21 ) ) )
= $false )
| ( ( SV2 @ SV3 )
= $true )
| ( ( SV2 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(37,plain,
! [SV1: $i,SV10: $i > $i,SV3: $i,SV9: $i > $i] :
( ( ( ~ ( in @ ( SV9 @ SV3 ) @ ( SV10 @ SV3 ) ) )
= $true )
| ( ( in @ ( SV9 @ SV3 ) @ ( SV10 @ SV3 ) )
= $false )
| ( ( in @ SV3
@ ( dsetconstr @ SV1
@ ^ [SX0: $i] :
~ ( in @ ( SV9 @ SX0 ) @ ( SV10 @ SX0 ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[25:[bind(SV2,$thf( ^ [SX0: $i] : ~ ( in @ ( SV9 @ SX0 ) @ ( SV10 @ SX0 ) ) ))]]) ).
thf(38,plain,
! [SV1: $i,SV3: $i,SV6: $i > $o] :
( ( ( ~ ( SV6 @ SV3 ) )
= $true )
| ( ( ~ ( SV6 @ SV3 ) )
= $true )
| ( ( ~ ( in @ SV3
@ ( dsetconstr @ SV1
@ ^ [SX0: $i] :
~ ( SV6 @ SX0 ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[25:[bind(SV2,$thf( ^ [SX0: $i] : ~ ( SV6 @ SX0 ) ))]]) ).
thf(41,plain,
! [SV1: $i,SV3: $i,SV6: $i > $o] :
( ( ( SV6 @ SV3 )
= $false )
| ( ( ~ ( SV6 @ SV3 ) )
= $true )
| ( ( ~ ( in @ SV3
@ ( dsetconstr @ SV1
@ ^ [SX0: $i] :
~ ( SV6 @ SX0 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(42,plain,
! [SV1: $i,SV10: $i > $i,SV3: $i,SV9: $i > $i] :
( ( ( in @ ( SV9 @ SV3 ) @ ( SV10 @ SV3 ) )
= $false )
| ( ( in @ ( SV9 @ SV3 ) @ ( SV10 @ SV3 ) )
= $false )
| ( ( in @ SV3
@ ( dsetconstr @ SV1
@ ^ [SX0: $i] :
~ ( in @ ( SV9 @ SX0 ) @ ( SV10 @ SX0 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(45,plain,
! [SV1: $i,SV3: $i,SV6: $i > $o] :
( ( ( SV6 @ SV3 )
= $false )
| ( ( SV6 @ SV3 )
= $false )
| ( ( ~ ( in @ SV3
@ ( dsetconstr @ SV1
@ ^ [SX0: $i] :
~ ( SV6 @ SX0 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[41]) ).
thf(47,plain,
! [SV6: $i > $o,SV1: $i,SV3: $i] :
( ( ( in @ SV3
@ ( dsetconstr @ SV1
@ ^ [SX0: $i] :
~ ( SV6 @ SX0 ) ) )
= $false )
| ( ( SV6 @ SV3 )
= $false )
| ( ( SV6 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(48,plain,
! [SV2: $i > $o,SV1: $i,SV3: $i] :
( ( ( in @ SV3
@ ( dsetconstr @ SV1
@ ^ [SY21: $i] : ( SV2 @ SY21 ) ) )
= $false )
| ( ( SV2 @ SV3 )
= $true ) ),
inference(sim,[status(thm)],[32]) ).
thf(49,plain,
! [SV6: $i > $o,SV1: $i,SV3: $i] :
( ( ( in @ SV3
@ ( dsetconstr @ SV1
@ ^ [SX0: $i] :
~ ( SV6 @ SX0 ) ) )
= $false )
| ( ( SV6 @ SV3 )
= $false ) ),
inference(sim,[status(thm)],[47]) ).
thf(50,plain,
! [SV1: $i,SV10: $i > $i,SV3: $i,SV9: $i > $i] :
( ( ( in @ ( SV9 @ SV3 ) @ ( SV10 @ SV3 ) )
= $false )
| ( ( in @ SV3
@ ( dsetconstr @ SV1
@ ^ [SX0: $i] :
~ ( in @ ( SV9 @ SX0 ) @ ( SV10 @ SX0 ) ) ) )
= $false ) ),
inference(sim,[status(thm)],[42]) ).
thf(52,plain,
! [SV11: $i > $o,SV12: $i,SV13: $i] :
( ( ( in @ SV13
@ ( dsetconstr @ SV12
@ ^ [SX0: $i] : ( SV11 @ SX0 ) ) )
= $false )
| ( ( SV11 @ SV13 )
= $true ) ),
inference(rename,[status(thm)],[21]) ).
thf(55,plain,
! [SV11: $i > $o,SV12: $i,SV13: $i] :
( ( ( ( in @ SV13
@ ( dsetconstr @ SV12
@ ^ [SX0: $i] : ( SV11 @ SX0 ) ) )
= ( in @ sK3_SY22
@ ( dsetconstr @ ( funcSet @ sK1_SX0 @ sK2_SY17 )
@ ^ [SY23: $i] : ( injective @ sK1_SX0 @ sK2_SY17 @ SY23 ) ) ) )
= $false )
| ( ( SV11 @ SV13 )
= $true ) ),
inference(res,[status(thm)],[52,22]) ).
thf(56,plain,
! [SV11: $i > $o,SV12: $i,SV13: $i] :
( ( ( ( SV11 @ SV13 )
= ( injective @ sK1_SX0 @ sK2_SY17 @ sK3_SY22 ) )
= $false )
| ( ( in @ SV13
@ ( dsetconstr @ SV12
@ ^ [SX0: $i] : ( SV11 @ SX0 ) ) )
= $false ) ),
inference(res,[status(thm)],[52,20]) ).
thf(57,plain,
! [SV11: $i > $o,SV12: $i,SV13: $i] :
( ( ( SV11 @ SV13 )
= $true )
| ( ( ( SV11 @ SV13 )
= ( ~ ( in @ SV13
@ ( dsetconstr @ SV12
@ ^ [SX0: $i] : ( SV11 @ SX0 ) ) ) ) )
= $false ) ),
inference(fac_restr,[status(thm)],[52]) ).
thf(58,plain,
! [SV12: $i] :
( ( ( in @ sK1_SX0
@ ( dsetconstr @ SV12
@ ^ [SX0: $i] : ( injective @ SX0 @ SX0 @ SX0 ) ) )
= $false )
| ( ( sK1_SX0 = sK3_SY22 )
= $false )
| ( ( sK1_SX0 = sK2_SY17 )
= $false ) ),
inference(extuni,[status(esa)],[56:[bind(SV13,$thf( sK1_SX0 )),bind(SV11,$thf( ^ [SX0: $i] : ( injective @ SX0 @ SX0 @ SX0 ) ))]]) ).
thf(59,plain,
! [SV12: $i] :
( ( ( in @ sK1_SX0
@ ( dsetconstr @ SV12
@ ^ [SX0: $i] : ( injective @ SX0 @ SX0 @ sK3_SY22 ) ) )
= $false )
| ( ( sK1_SX0 = sK2_SY17 )
= $false ) ),
inference(extuni,[status(esa)],[56:[bind(SV13,$thf( sK1_SX0 )),bind(SV11,$thf( ^ [SX0: $i] : ( injective @ SX0 @ SX0 @ sK3_SY22 ) ))]]) ).
thf(60,plain,
! [SV12: $i] :
( ( ( in @ sK1_SX0
@ ( dsetconstr @ SV12
@ ^ [SX0: $i] : ( injective @ SX0 @ sK2_SY17 @ SX0 ) ) )
= $false )
| ( ( sK1_SX0 = sK3_SY22 )
= $false ) ),
inference(extuni,[status(esa)],[56:[bind(SV13,$thf( sK1_SX0 )),bind(SV11,$thf( ^ [SX0: $i] : ( injective @ SX0 @ sK2_SY17 @ SX0 ) ))]]) ).
thf(61,plain,
! [SV12: $i] :
( ( in @ sK1_SX0
@ ( dsetconstr @ SV12
@ ^ [SX0: $i] : ( injective @ SX0 @ sK2_SY17 @ sK3_SY22 ) ) )
= $false ),
inference(extuni,[status(esa)],[56:[bind(SV13,$thf( sK1_SX0 )),bind(SV11,$thf( ^ [SX0: $i] : ( injective @ SX0 @ sK2_SY17 @ sK3_SY22 ) ))]]) ).
thf(62,plain,
! [SV12: $i] :
( ( ( in @ sK2_SY17
@ ( dsetconstr @ SV12
@ ^ [SX0: $i] : ( injective @ sK1_SX0 @ SX0 @ SX0 ) ) )
= $false )
| ( ( sK2_SY17 = sK3_SY22 )
= $false ) ),
inference(extuni,[status(esa)],[56:[bind(SV13,$thf( sK2_SY17 )),bind(SV11,$thf( ^ [SX0: $i] : ( injective @ sK1_SX0 @ SX0 @ SX0 ) ))]]) ).
thf(63,plain,
! [SV12: $i] :
( ( in @ sK2_SY17
@ ( dsetconstr @ SV12
@ ^ [SX0: $i] : ( injective @ sK1_SX0 @ SX0 @ sK3_SY22 ) ) )
= $false ),
inference(extuni,[status(esa)],[56:[bind(SV13,$thf( sK2_SY17 )),bind(SV11,$thf( ^ [SX0: $i] : ( injective @ sK1_SX0 @ SX0 @ sK3_SY22 ) ))]]) ).
thf(64,plain,
! [SV12: $i] :
( ( in @ sK3_SY22
@ ( dsetconstr @ SV12
@ ^ [SX0: $i] : ( injective @ sK1_SX0 @ sK2_SY17 @ SX0 ) ) )
= $false ),
inference(extuni,[status(esa)],[56:[bind(SV13,$thf( sK3_SY22 )),bind(SV11,$thf( ^ [SX0: $i] : ( injective @ sK1_SX0 @ sK2_SY17 @ SX0 ) ))]]) ).
thf(65,plain,
! [SV12: $i,SV13: $i] :
( ( in @ SV13
@ ( dsetconstr @ SV12
@ ^ [SX0: $i] : ( injective @ sK1_SX0 @ sK2_SY17 @ sK3_SY22 ) ) )
= $false ),
inference(extuni,[status(esa)],[56:[bind(SV11,$thf( ^ [SX0: $i] : ( injective @ sK1_SX0 @ sK2_SY17 @ sK3_SY22 ) ))]]) ).
thf(66,plain,
! [SV18: $i > $i,SV17: $i > $i,SV16: $i > $i,SV12: $i,SV13: $i] :
( ( ( in @ SV13
@ ( dsetconstr @ SV12
@ ^ [SX0: $i] : ( injective @ ( SV16 @ SX0 ) @ ( SV17 @ SX0 ) @ ( SV18 @ SX0 ) ) ) )
= $false )
| ( ( injective @ ( SV16 @ SV13 ) @ ( SV17 @ SV13 ) @ ( SV18 @ SV13 ) )
= $true )
| ( ( injective @ sK1_SX0 @ sK2_SY17 @ sK3_SY22 )
= $true ) ),
inference(extuni,[status(esa)],[56:[bind(SV11,$thf( ^ [SX0: $i] : ( injective @ ( SV16 @ SX0 ) @ ( SV17 @ SX0 ) @ ( SV18 @ SX0 ) ) ))]]) ).
thf(67,plain,
! [SV18: $i > $i,SV17: $i > $i,SV16: $i > $i,SV12: $i,SV13: $i] :
( ( ( in @ SV13
@ ( dsetconstr @ SV12
@ ^ [SX0: $i] : ( injective @ ( SV16 @ SX0 ) @ ( SV17 @ SX0 ) @ ( SV18 @ SX0 ) ) ) )
= $false )
| ( ( injective @ ( SV16 @ SV13 ) @ ( SV17 @ SV13 ) @ ( SV18 @ SV13 ) )
= $false )
| ( ( injective @ sK1_SX0 @ sK2_SY17 @ sK3_SY22 )
= $false ) ),
inference(extuni,[status(esa)],[56:[bind(SV11,$thf( ^ [SX0: $i] : ( injective @ ( SV16 @ SX0 ) @ ( SV17 @ SX0 ) @ ( SV18 @ SX0 ) ) ))]]) ).
thf(68,plain,
! [SV96: $i > $i > $i,SV95: $i > $i > $i,SV94: $i > $i > $i] :
( ( ( injective @ sK3_SY22 @ sK3_SY22
@ ( sK4_E
@ ^ [SX0: $i] : ( injective @ ( SV94 @ sK3_SY22 @ SX0 ) @ ( SV95 @ sK3_SY22 @ SX0 ) @ ( SV96 @ sK3_SY22 @ SX0 ) ) ) )
= $true )
| ( ( injective
@ ( SV94
@ ( sK4_E
@ ^ [SX0: $i] :
( injective @ SX0 @ SX0
@ ( sK4_E
@ ^ [SX1: $i] : ( injective @ ( SV94 @ SX0 @ SX1 ) @ ( SV95 @ SX0 @ SX1 ) @ ( SV96 @ SX0 @ SX1 ) ) ) ) )
@ ( sK8_E
@ ^ [SX0: $i,SX1: $i] : ( injective @ ( SV94 @ SX0 @ SX1 ) @ ( SV95 @ SX0 @ SX1 ) @ ( SV96 @ SX0 @ SX1 ) ) ) )
@ ( SV95
@ ( sK4_E
@ ^ [SX0: $i] :
( injective @ SX0 @ SX0
@ ( sK4_E
@ ^ [SX1: $i] : ( injective @ ( SV94 @ SX0 @ SX1 ) @ ( SV95 @ SX0 @ SX1 ) @ ( SV96 @ SX0 @ SX1 ) ) ) ) )
@ ( sK8_E
@ ^ [SX0: $i,SX1: $i] : ( injective @ ( SV94 @ SX0 @ SX1 ) @ ( SV95 @ SX0 @ SX1 ) @ ( SV96 @ SX0 @ SX1 ) ) ) )
@ ( SV96
@ ( sK4_E
@ ^ [SX0: $i] :
( injective @ SX0 @ SX0
@ ( sK4_E
@ ^ [SX1: $i] : ( injective @ ( SV94 @ SX0 @ SX1 ) @ ( SV95 @ SX0 @ SX1 ) @ ( SV96 @ SX0 @ SX1 ) ) ) ) )
@ ( sK8_E
@ ^ [SX0: $i,SX1: $i] : ( injective @ ( SV94 @ SX0 @ SX1 ) @ ( SV95 @ SX0 @ SX1 ) @ ( SV96 @ SX0 @ SX1 ) ) ) ) )
= $true )
| ( ( injective
@ ( sK8_E
@ ^ [SX0: $i,SX1: $i] : ( injective @ ( SV94 @ SX0 @ SX1 ) @ ( SV95 @ SX0 @ SX1 ) @ ( SV96 @ SX0 @ SX1 ) ) )
@ ( sK8_E
@ ^ [SX0: $i,SX1: $i] : ( injective @ ( SV94 @ SX0 @ SX1 ) @ ( SV95 @ SX0 @ SX1 ) @ ( SV96 @ SX0 @ SX1 ) ) )
@ ( sK4_E
@ ^ [SX0: $i] :
( injective
@ ( SV94
@ ( sK8_E
@ ^ [SX1: $i,SX2: $i] : ( injective @ ( SV94 @ SX1 @ SX2 ) @ ( SV95 @ SX1 @ SX2 ) @ ( SV96 @ SX1 @ SX2 ) ) )
@ SX0 )
@ ( SV95
@ ( sK8_E
@ ^ [SX1: $i,SX2: $i] : ( injective @ ( SV94 @ SX1 @ SX2 ) @ ( SV95 @ SX1 @ SX2 ) @ ( SV96 @ SX1 @ SX2 ) ) )
@ SX0 )
@ ( SV96
@ ( sK8_E
@ ^ [SX1: $i,SX2: $i] : ( injective @ ( SV94 @ SX1 @ SX2 ) @ ( SV95 @ SX1 @ SX2 ) @ ( SV96 @ SX1 @ SX2 ) ) )
@ SX0 ) ) ) )
= $true )
| ( ( ( sK4_E
@ ^ [SX0: $i] :
( injective @ SX0 @ SX0
@ ( sK4_E
@ ^ [SX1: $i] : ( injective @ ( SV94 @ SX0 @ SX1 ) @ ( SV95 @ SX0 @ SX1 ) @ ( SV96 @ SX0 @ SX1 ) ) ) ) )
= sK2_SY17 )
= $false )
| ( ( ( sK4_E
@ ^ [SX0: $i] :
( injective @ SX0 @ SX0
@ ( sK4_E
@ ^ [SX1: $i] : ( injective @ ( SV94 @ SX0 @ SX1 ) @ ( SV95 @ SX0 @ SX1 ) @ ( SV96 @ SX0 @ SX1 ) ) ) ) )
= sK1_SX0 )
= $false ) ),
inference(extuni,[status(esa)],[55:[bind(SV11,$thf( ^ [SX0: $i] : ( injective @ SX0 @ SX0 @ ( sK4_E @ ^ [SX1: $i] : ( injective @ ( SV94 @ SX0 @ SX1 ) @ ( SV95 @ SX0 @ SX1 ) @ ( SV96 @ SX0 @ SX1 ) ) ) ) )),bind(SV12,$thf( funcSet @ sK1_SX0 @ sK2_SY17 )),bind(SV13,$thf( sK3_SY22 ))]]) ).
thf(69,plain,
! [SV96: $i > $i > $i,SV95: $i > $i > $i,SV94: $i > $i > $i] :
( ( ( injective @ sK3_SY22 @ sK3_SY22
@ ( sK4_E
@ ^ [SX0: $i] : ( injective @ ( SV94 @ sK3_SY22 @ SX0 ) @ ( SV95 @ sK3_SY22 @ SX0 ) @ ( SV96 @ sK3_SY22 @ SX0 ) ) ) )
= $true )
| ( ( injective
@ ( SV94
@ ( sK4_E
@ ^ [SX0: $i] :
( injective @ SX0 @ SX0
@ ( sK4_E
@ ^ [SX1: $i] : ( injective @ ( SV94 @ SX0 @ SX1 ) @ ( SV95 @ SX0 @ SX1 ) @ ( SV96 @ SX0 @ SX1 ) ) ) ) )
@ ( sK8_E
@ ^ [SX0: $i,SX1: $i] : ( injective @ ( SV94 @ SX0 @ SX1 ) @ ( SV95 @ SX0 @ SX1 ) @ ( SV96 @ SX0 @ SX1 ) ) ) )
@ ( SV95
@ ( sK4_E
@ ^ [SX0: $i] :
( injective @ SX0 @ SX0
@ ( sK4_E
@ ^ [SX1: $i] : ( injective @ ( SV94 @ SX0 @ SX1 ) @ ( SV95 @ SX0 @ SX1 ) @ ( SV96 @ SX0 @ SX1 ) ) ) ) )
@ ( sK8_E
@ ^ [SX0: $i,SX1: $i] : ( injective @ ( SV94 @ SX0 @ SX1 ) @ ( SV95 @ SX0 @ SX1 ) @ ( SV96 @ SX0 @ SX1 ) ) ) )
@ ( SV96
@ ( sK4_E
@ ^ [SX0: $i] :
( injective @ SX0 @ SX0
@ ( sK4_E
@ ^ [SX1: $i] : ( injective @ ( SV94 @ SX0 @ SX1 ) @ ( SV95 @ SX0 @ SX1 ) @ ( SV96 @ SX0 @ SX1 ) ) ) ) )
@ ( sK8_E
@ ^ [SX0: $i,SX1: $i] : ( injective @ ( SV94 @ SX0 @ SX1 ) @ ( SV95 @ SX0 @ SX1 ) @ ( SV96 @ SX0 @ SX1 ) ) ) ) )
= $false )
| ( ( injective
@ ( sK8_E
@ ^ [SX0: $i,SX1: $i] : ( injective @ ( SV94 @ SX0 @ SX1 ) @ ( SV95 @ SX0 @ SX1 ) @ ( SV96 @ SX0 @ SX1 ) ) )
@ ( sK8_E
@ ^ [SX0: $i,SX1: $i] : ( injective @ ( SV94 @ SX0 @ SX1 ) @ ( SV95 @ SX0 @ SX1 ) @ ( SV96 @ SX0 @ SX1 ) ) )
@ ( sK4_E
@ ^ [SX0: $i] :
( injective
@ ( SV94
@ ( sK8_E
@ ^ [SX1: $i,SX2: $i] : ( injective @ ( SV94 @ SX1 @ SX2 ) @ ( SV95 @ SX1 @ SX2 ) @ ( SV96 @ SX1 @ SX2 ) ) )
@ SX0 )
@ ( SV95
@ ( sK8_E
@ ^ [SX1: $i,SX2: $i] : ( injective @ ( SV94 @ SX1 @ SX2 ) @ ( SV95 @ SX1 @ SX2 ) @ ( SV96 @ SX1 @ SX2 ) ) )
@ SX0 )
@ ( SV96
@ ( sK8_E
@ ^ [SX1: $i,SX2: $i] : ( injective @ ( SV94 @ SX1 @ SX2 ) @ ( SV95 @ SX1 @ SX2 ) @ ( SV96 @ SX1 @ SX2 ) ) )
@ SX0 ) ) ) )
= $false )
| ( ( ( sK4_E
@ ^ [SX0: $i] :
( injective @ SX0 @ SX0
@ ( sK4_E
@ ^ [SX1: $i] : ( injective @ ( SV94 @ SX0 @ SX1 ) @ ( SV95 @ SX0 @ SX1 ) @ ( SV96 @ SX0 @ SX1 ) ) ) ) )
= sK2_SY17 )
= $false )
| ( ( ( sK4_E
@ ^ [SX0: $i] :
( injective @ SX0 @ SX0
@ ( sK4_E
@ ^ [SX1: $i] : ( injective @ ( SV94 @ SX0 @ SX1 ) @ ( SV95 @ SX0 @ SX1 ) @ ( SV96 @ SX0 @ SX1 ) ) ) ) )
= sK1_SX0 )
= $false ) ),
inference(extuni,[status(esa)],[55:[bind(SV11,$thf( ^ [SX0: $i] : ( injective @ SX0 @ SX0 @ ( sK4_E @ ^ [SX1: $i] : ( injective @ ( SV94 @ SX0 @ SX1 ) @ ( SV95 @ SX0 @ SX1 ) @ ( SV96 @ SX0 @ SX1 ) ) ) ) )),bind(SV12,$thf( funcSet @ sK1_SX0 @ sK2_SY17 )),bind(SV13,$thf( sK3_SY22 ))]]) ).
thf(70,plain,
! [SV89: $i > $i > $o] :
( ( ( injective @ sK3_SY22 @ sK3_SY22 @ ( sK4_E @ ( SV89 @ sK3_SY22 ) ) )
= $true )
| ( ( ( sK4_E
@ ( SV89
@ ( sK4_E
@ ^ [SX0: $i] : ( injective @ SX0 @ SX0 @ ( sK4_E @ ( SV89 @ SX0 ) ) ) ) ) )
= ( sK4_E
@ ^ [SX0: $i] : ( injective @ SX0 @ SX0 @ ( sK4_E @ ( SV89 @ SX0 ) ) ) ) )
= $false )
| ( ( ( sK4_E
@ ^ [SX0: $i] : ( injective @ SX0 @ SX0 @ ( sK4_E @ ( SV89 @ SX0 ) ) ) )
= sK2_SY17 )
= $false )
| ( ( ( sK4_E
@ ^ [SX0: $i] : ( injective @ SX0 @ SX0 @ ( sK4_E @ ( SV89 @ SX0 ) ) ) )
= sK1_SX0 )
= $false ) ),
inference(extuni,[status(esa)],[55:[bind(SV11,$thf( ^ [SX0: $i] : ( injective @ SX0 @ SX0 @ ( sK4_E @ ( SV89 @ SX0 ) ) ) )),bind(SV12,$thf( funcSet @ sK1_SX0 @ sK2_SY17 )),bind(SV13,$thf( sK3_SY22 ))]]) ).
thf(71,plain,
( ( ( injective @ sK3_SY22 @ sK3_SY22 @ sK3_SY22 )
= $true )
| ( ( ( sK4_E
@ ^ [SX0: $i] : ( injective @ SX0 @ SX0 @ SX0 ) )
= sK2_SY17 )
= $false )
| ( ( ( sK4_E
@ ^ [SX0: $i] : ( injective @ SX0 @ SX0 @ SX0 ) )
= sK1_SX0 )
= $false ) ),
inference(extuni,[status(esa)],[55:[bind(SV11,$thf( ^ [SX0: $i] : ( injective @ SX0 @ SX0 @ SX0 ) )),bind(SV12,$thf( funcSet @ sK1_SX0 @ sK2_SY17 )),bind(SV13,$thf( sK3_SY22 ))]]) ).
thf(72,plain,
! [SV81: $i > $i > $i,SV80: $i > $i > $i,SV79: $i > $i > $i] :
( ( ( injective @ sK3_SY22 @ sK2_SY17
@ ( sK4_E
@ ^ [SX0: $i] : ( injective @ ( SV79 @ sK3_SY22 @ SX0 ) @ ( SV80 @ sK3_SY22 @ SX0 ) @ ( SV81 @ sK3_SY22 @ SX0 ) ) ) )
= $true )
| ( ( injective
@ ( SV79
@ ( sK4_E
@ ^ [SX0: $i] :
( injective @ SX0 @ sK2_SY17
@ ( sK4_E
@ ^ [SX1: $i] : ( injective @ ( SV79 @ SX0 @ SX1 ) @ ( SV80 @ SX0 @ SX1 ) @ ( SV81 @ SX0 @ SX1 ) ) ) ) )
@ ( sK7_E
@ ^ [SX0: $i,SX1: $i] : ( injective @ ( SV79 @ SX0 @ SX1 ) @ ( SV80 @ SX0 @ SX1 ) @ ( SV81 @ SX0 @ SX1 ) ) ) )
@ ( SV80
@ ( sK4_E
@ ^ [SX0: $i] :
( injective @ SX0 @ sK2_SY17
@ ( sK4_E
@ ^ [SX1: $i] : ( injective @ ( SV79 @ SX0 @ SX1 ) @ ( SV80 @ SX0 @ SX1 ) @ ( SV81 @ SX0 @ SX1 ) ) ) ) )
@ ( sK7_E
@ ^ [SX0: $i,SX1: $i] : ( injective @ ( SV79 @ SX0 @ SX1 ) @ ( SV80 @ SX0 @ SX1 ) @ ( SV81 @ SX0 @ SX1 ) ) ) )
@ ( SV81
@ ( sK4_E
@ ^ [SX0: $i] :
( injective @ SX0 @ sK2_SY17
@ ( sK4_E
@ ^ [SX1: $i] : ( injective @ ( SV79 @ SX0 @ SX1 ) @ ( SV80 @ SX0 @ SX1 ) @ ( SV81 @ SX0 @ SX1 ) ) ) ) )
@ ( sK7_E
@ ^ [SX0: $i,SX1: $i] : ( injective @ ( SV79 @ SX0 @ SX1 ) @ ( SV80 @ SX0 @ SX1 ) @ ( SV81 @ SX0 @ SX1 ) ) ) ) )
= $true )
| ( ( injective
@ ( sK7_E
@ ^ [SX0: $i,SX1: $i] : ( injective @ ( SV79 @ SX0 @ SX1 ) @ ( SV80 @ SX0 @ SX1 ) @ ( SV81 @ SX0 @ SX1 ) ) )
@ sK2_SY17
@ ( sK4_E
@ ^ [SX0: $i] :
( injective
@ ( SV79
@ ( sK7_E
@ ^ [SX1: $i,SX2: $i] : ( injective @ ( SV79 @ SX1 @ SX2 ) @ ( SV80 @ SX1 @ SX2 ) @ ( SV81 @ SX1 @ SX2 ) ) )
@ SX0 )
@ ( SV80
@ ( sK7_E
@ ^ [SX1: $i,SX2: $i] : ( injective @ ( SV79 @ SX1 @ SX2 ) @ ( SV80 @ SX1 @ SX2 ) @ ( SV81 @ SX1 @ SX2 ) ) )
@ SX0 )
@ ( SV81
@ ( sK7_E
@ ^ [SX1: $i,SX2: $i] : ( injective @ ( SV79 @ SX1 @ SX2 ) @ ( SV80 @ SX1 @ SX2 ) @ ( SV81 @ SX1 @ SX2 ) ) )
@ SX0 ) ) ) )
= $true )
| ( ( ( sK4_E
@ ^ [SX0: $i] :
( injective @ SX0 @ sK2_SY17
@ ( sK4_E
@ ^ [SX1: $i] : ( injective @ ( SV79 @ SX0 @ SX1 ) @ ( SV80 @ SX0 @ SX1 ) @ ( SV81 @ SX0 @ SX1 ) ) ) ) )
= sK1_SX0 )
= $false ) ),
inference(extuni,[status(esa)],[55:[bind(SV11,$thf( ^ [SX0: $i] : ( injective @ SX0 @ sK2_SY17 @ ( sK4_E @ ^ [SX1: $i] : ( injective @ ( SV79 @ SX0 @ SX1 ) @ ( SV80 @ SX0 @ SX1 ) @ ( SV81 @ SX0 @ SX1 ) ) ) ) )),bind(SV12,$thf( funcSet @ sK1_SX0 @ sK2_SY17 )),bind(SV13,$thf( sK3_SY22 ))]]) ).
thf(73,plain,
! [SV81: $i > $i > $i,SV80: $i > $i > $i,SV79: $i > $i > $i] :
( ( ( injective @ sK3_SY22 @ sK2_SY17
@ ( sK4_E
@ ^ [SX0: $i] : ( injective @ ( SV79 @ sK3_SY22 @ SX0 ) @ ( SV80 @ sK3_SY22 @ SX0 ) @ ( SV81 @ sK3_SY22 @ SX0 ) ) ) )
= $true )
| ( ( injective
@ ( SV79
@ ( sK4_E
@ ^ [SX0: $i] :
( injective @ SX0 @ sK2_SY17
@ ( sK4_E
@ ^ [SX1: $i] : ( injective @ ( SV79 @ SX0 @ SX1 ) @ ( SV80 @ SX0 @ SX1 ) @ ( SV81 @ SX0 @ SX1 ) ) ) ) )
@ ( sK7_E
@ ^ [SX0: $i,SX1: $i] : ( injective @ ( SV79 @ SX0 @ SX1 ) @ ( SV80 @ SX0 @ SX1 ) @ ( SV81 @ SX0 @ SX1 ) ) ) )
@ ( SV80
@ ( sK4_E
@ ^ [SX0: $i] :
( injective @ SX0 @ sK2_SY17
@ ( sK4_E
@ ^ [SX1: $i] : ( injective @ ( SV79 @ SX0 @ SX1 ) @ ( SV80 @ SX0 @ SX1 ) @ ( SV81 @ SX0 @ SX1 ) ) ) ) )
@ ( sK7_E
@ ^ [SX0: $i,SX1: $i] : ( injective @ ( SV79 @ SX0 @ SX1 ) @ ( SV80 @ SX0 @ SX1 ) @ ( SV81 @ SX0 @ SX1 ) ) ) )
@ ( SV81
@ ( sK4_E
@ ^ [SX0: $i] :
( injective @ SX0 @ sK2_SY17
@ ( sK4_E
@ ^ [SX1: $i] : ( injective @ ( SV79 @ SX0 @ SX1 ) @ ( SV80 @ SX0 @ SX1 ) @ ( SV81 @ SX0 @ SX1 ) ) ) ) )
@ ( sK7_E
@ ^ [SX0: $i,SX1: $i] : ( injective @ ( SV79 @ SX0 @ SX1 ) @ ( SV80 @ SX0 @ SX1 ) @ ( SV81 @ SX0 @ SX1 ) ) ) ) )
= $false )
| ( ( injective
@ ( sK7_E
@ ^ [SX0: $i,SX1: $i] : ( injective @ ( SV79 @ SX0 @ SX1 ) @ ( SV80 @ SX0 @ SX1 ) @ ( SV81 @ SX0 @ SX1 ) ) )
@ sK2_SY17
@ ( sK4_E
@ ^ [SX0: $i] :
( injective
@ ( SV79
@ ( sK7_E
@ ^ [SX1: $i,SX2: $i] : ( injective @ ( SV79 @ SX1 @ SX2 ) @ ( SV80 @ SX1 @ SX2 ) @ ( SV81 @ SX1 @ SX2 ) ) )
@ SX0 )
@ ( SV80
@ ( sK7_E
@ ^ [SX1: $i,SX2: $i] : ( injective @ ( SV79 @ SX1 @ SX2 ) @ ( SV80 @ SX1 @ SX2 ) @ ( SV81 @ SX1 @ SX2 ) ) )
@ SX0 )
@ ( SV81
@ ( sK7_E
@ ^ [SX1: $i,SX2: $i] : ( injective @ ( SV79 @ SX1 @ SX2 ) @ ( SV80 @ SX1 @ SX2 ) @ ( SV81 @ SX1 @ SX2 ) ) )
@ SX0 ) ) ) )
= $false )
| ( ( ( sK4_E
@ ^ [SX0: $i] :
( injective @ SX0 @ sK2_SY17
@ ( sK4_E
@ ^ [SX1: $i] : ( injective @ ( SV79 @ SX0 @ SX1 ) @ ( SV80 @ SX0 @ SX1 ) @ ( SV81 @ SX0 @ SX1 ) ) ) ) )
= sK1_SX0 )
= $false ) ),
inference(extuni,[status(esa)],[55:[bind(SV11,$thf( ^ [SX0: $i] : ( injective @ SX0 @ sK2_SY17 @ ( sK4_E @ ^ [SX1: $i] : ( injective @ ( SV79 @ SX0 @ SX1 ) @ ( SV80 @ SX0 @ SX1 ) @ ( SV81 @ SX0 @ SX1 ) ) ) ) )),bind(SV12,$thf( funcSet @ sK1_SX0 @ sK2_SY17 )),bind(SV13,$thf( sK3_SY22 ))]]) ).
thf(74,plain,
! [SV74: $i > $i > $o] :
( ( ( injective @ sK3_SY22 @ sK2_SY17 @ ( sK4_E @ ( SV74 @ sK3_SY22 ) ) )
= $true )
| ( ( ( sK4_E
@ ( SV74
@ ( sK4_E
@ ^ [SX0: $i] : ( injective @ SX0 @ sK2_SY17 @ ( sK4_E @ ( SV74 @ SX0 ) ) ) ) ) )
= ( sK4_E
@ ^ [SX0: $i] : ( injective @ SX0 @ sK2_SY17 @ ( sK4_E @ ( SV74 @ SX0 ) ) ) ) )
= $false )
| ( ( ( sK4_E
@ ^ [SX0: $i] : ( injective @ SX0 @ sK2_SY17 @ ( sK4_E @ ( SV74 @ SX0 ) ) ) )
= sK1_SX0 )
= $false ) ),
inference(extuni,[status(esa)],[55:[bind(SV11,$thf( ^ [SX0: $i] : ( injective @ SX0 @ sK2_SY17 @ ( sK4_E @ ( SV74 @ SX0 ) ) ) )),bind(SV12,$thf( funcSet @ sK1_SX0 @ sK2_SY17 )),bind(SV13,$thf( sK3_SY22 ))]]) ).
thf(75,plain,
( ( ( injective @ sK3_SY22 @ sK2_SY17 @ sK3_SY22 )
= $true )
| ( ( ( sK4_E
@ ^ [SX0: $i] : ( injective @ SX0 @ sK2_SY17 @ SX0 ) )
= sK1_SX0 )
= $false ) ),
inference(extuni,[status(esa)],[55:[bind(SV11,$thf( ^ [SX0: $i] : ( injective @ SX0 @ sK2_SY17 @ SX0 ) )),bind(SV12,$thf( funcSet @ sK1_SX0 @ sK2_SY17 )),bind(SV13,$thf( sK3_SY22 ))]]) ).
thf(76,plain,
! [SV65: $i > $i > $i,SV64: $i > $i > $i,SV63: $i > $i > $i] :
( ( ( injective @ sK1_SX0 @ sK3_SY22
@ ( sK4_E
@ ^ [SX0: $i] : ( injective @ ( SV63 @ sK3_SY22 @ SX0 ) @ ( SV64 @ sK3_SY22 @ SX0 ) @ ( SV65 @ sK3_SY22 @ SX0 ) ) ) )
= $true )
| ( ( injective
@ ( SV63
@ ( sK4_E
@ ^ [SX0: $i] :
( injective @ sK1_SX0 @ SX0
@ ( sK4_E
@ ^ [SX1: $i] : ( injective @ ( SV63 @ SX0 @ SX1 ) @ ( SV64 @ SX0 @ SX1 ) @ ( SV65 @ SX0 @ SX1 ) ) ) ) )
@ ( sK6_E
@ ^ [SX0: $i,SX1: $i] : ( injective @ ( SV63 @ SX0 @ SX1 ) @ ( SV64 @ SX0 @ SX1 ) @ ( SV65 @ SX0 @ SX1 ) ) ) )
@ ( SV64
@ ( sK4_E
@ ^ [SX0: $i] :
( injective @ sK1_SX0 @ SX0
@ ( sK4_E
@ ^ [SX1: $i] : ( injective @ ( SV63 @ SX0 @ SX1 ) @ ( SV64 @ SX0 @ SX1 ) @ ( SV65 @ SX0 @ SX1 ) ) ) ) )
@ ( sK6_E
@ ^ [SX0: $i,SX1: $i] : ( injective @ ( SV63 @ SX0 @ SX1 ) @ ( SV64 @ SX0 @ SX1 ) @ ( SV65 @ SX0 @ SX1 ) ) ) )
@ ( SV65
@ ( sK4_E
@ ^ [SX0: $i] :
( injective @ sK1_SX0 @ SX0
@ ( sK4_E
@ ^ [SX1: $i] : ( injective @ ( SV63 @ SX0 @ SX1 ) @ ( SV64 @ SX0 @ SX1 ) @ ( SV65 @ SX0 @ SX1 ) ) ) ) )
@ ( sK6_E
@ ^ [SX0: $i,SX1: $i] : ( injective @ ( SV63 @ SX0 @ SX1 ) @ ( SV64 @ SX0 @ SX1 ) @ ( SV65 @ SX0 @ SX1 ) ) ) ) )
= $true )
| ( ( injective @ sK1_SX0
@ ( sK6_E
@ ^ [SX0: $i,SX1: $i] : ( injective @ ( SV63 @ SX0 @ SX1 ) @ ( SV64 @ SX0 @ SX1 ) @ ( SV65 @ SX0 @ SX1 ) ) )
@ ( sK4_E
@ ^ [SX0: $i] :
( injective
@ ( SV63
@ ( sK6_E
@ ^ [SX1: $i,SX2: $i] : ( injective @ ( SV63 @ SX1 @ SX2 ) @ ( SV64 @ SX1 @ SX2 ) @ ( SV65 @ SX1 @ SX2 ) ) )
@ SX0 )
@ ( SV64
@ ( sK6_E
@ ^ [SX1: $i,SX2: $i] : ( injective @ ( SV63 @ SX1 @ SX2 ) @ ( SV64 @ SX1 @ SX2 ) @ ( SV65 @ SX1 @ SX2 ) ) )
@ SX0 )
@ ( SV65
@ ( sK6_E
@ ^ [SX1: $i,SX2: $i] : ( injective @ ( SV63 @ SX1 @ SX2 ) @ ( SV64 @ SX1 @ SX2 ) @ ( SV65 @ SX1 @ SX2 ) ) )
@ SX0 ) ) ) )
= $true )
| ( ( ( sK4_E
@ ^ [SX0: $i] :
( injective @ sK1_SX0 @ SX0
@ ( sK4_E
@ ^ [SX1: $i] : ( injective @ ( SV63 @ SX0 @ SX1 ) @ ( SV64 @ SX0 @ SX1 ) @ ( SV65 @ SX0 @ SX1 ) ) ) ) )
= sK2_SY17 )
= $false ) ),
inference(extuni,[status(esa)],[55:[bind(SV11,$thf( ^ [SX0: $i] : ( injective @ sK1_SX0 @ SX0 @ ( sK4_E @ ^ [SX1: $i] : ( injective @ ( SV63 @ SX0 @ SX1 ) @ ( SV64 @ SX0 @ SX1 ) @ ( SV65 @ SX0 @ SX1 ) ) ) ) )),bind(SV12,$thf( funcSet @ sK1_SX0 @ sK2_SY17 )),bind(SV13,$thf( sK3_SY22 ))]]) ).
thf(77,plain,
! [SV65: $i > $i > $i,SV64: $i > $i > $i,SV63: $i > $i > $i] :
( ( ( injective @ sK1_SX0 @ sK3_SY22
@ ( sK4_E
@ ^ [SX0: $i] : ( injective @ ( SV63 @ sK3_SY22 @ SX0 ) @ ( SV64 @ sK3_SY22 @ SX0 ) @ ( SV65 @ sK3_SY22 @ SX0 ) ) ) )
= $true )
| ( ( injective
@ ( SV63
@ ( sK4_E
@ ^ [SX0: $i] :
( injective @ sK1_SX0 @ SX0
@ ( sK4_E
@ ^ [SX1: $i] : ( injective @ ( SV63 @ SX0 @ SX1 ) @ ( SV64 @ SX0 @ SX1 ) @ ( SV65 @ SX0 @ SX1 ) ) ) ) )
@ ( sK6_E
@ ^ [SX0: $i,SX1: $i] : ( injective @ ( SV63 @ SX0 @ SX1 ) @ ( SV64 @ SX0 @ SX1 ) @ ( SV65 @ SX0 @ SX1 ) ) ) )
@ ( SV64
@ ( sK4_E
@ ^ [SX0: $i] :
( injective @ sK1_SX0 @ SX0
@ ( sK4_E
@ ^ [SX1: $i] : ( injective @ ( SV63 @ SX0 @ SX1 ) @ ( SV64 @ SX0 @ SX1 ) @ ( SV65 @ SX0 @ SX1 ) ) ) ) )
@ ( sK6_E
@ ^ [SX0: $i,SX1: $i] : ( injective @ ( SV63 @ SX0 @ SX1 ) @ ( SV64 @ SX0 @ SX1 ) @ ( SV65 @ SX0 @ SX1 ) ) ) )
@ ( SV65
@ ( sK4_E
@ ^ [SX0: $i] :
( injective @ sK1_SX0 @ SX0
@ ( sK4_E
@ ^ [SX1: $i] : ( injective @ ( SV63 @ SX0 @ SX1 ) @ ( SV64 @ SX0 @ SX1 ) @ ( SV65 @ SX0 @ SX1 ) ) ) ) )
@ ( sK6_E
@ ^ [SX0: $i,SX1: $i] : ( injective @ ( SV63 @ SX0 @ SX1 ) @ ( SV64 @ SX0 @ SX1 ) @ ( SV65 @ SX0 @ SX1 ) ) ) ) )
= $false )
| ( ( injective @ sK1_SX0
@ ( sK6_E
@ ^ [SX0: $i,SX1: $i] : ( injective @ ( SV63 @ SX0 @ SX1 ) @ ( SV64 @ SX0 @ SX1 ) @ ( SV65 @ SX0 @ SX1 ) ) )
@ ( sK4_E
@ ^ [SX0: $i] :
( injective
@ ( SV63
@ ( sK6_E
@ ^ [SX1: $i,SX2: $i] : ( injective @ ( SV63 @ SX1 @ SX2 ) @ ( SV64 @ SX1 @ SX2 ) @ ( SV65 @ SX1 @ SX2 ) ) )
@ SX0 )
@ ( SV64
@ ( sK6_E
@ ^ [SX1: $i,SX2: $i] : ( injective @ ( SV63 @ SX1 @ SX2 ) @ ( SV64 @ SX1 @ SX2 ) @ ( SV65 @ SX1 @ SX2 ) ) )
@ SX0 )
@ ( SV65
@ ( sK6_E
@ ^ [SX1: $i,SX2: $i] : ( injective @ ( SV63 @ SX1 @ SX2 ) @ ( SV64 @ SX1 @ SX2 ) @ ( SV65 @ SX1 @ SX2 ) ) )
@ SX0 ) ) ) )
= $false )
| ( ( ( sK4_E
@ ^ [SX0: $i] :
( injective @ sK1_SX0 @ SX0
@ ( sK4_E
@ ^ [SX1: $i] : ( injective @ ( SV63 @ SX0 @ SX1 ) @ ( SV64 @ SX0 @ SX1 ) @ ( SV65 @ SX0 @ SX1 ) ) ) ) )
= sK2_SY17 )
= $false ) ),
inference(extuni,[status(esa)],[55:[bind(SV11,$thf( ^ [SX0: $i] : ( injective @ sK1_SX0 @ SX0 @ ( sK4_E @ ^ [SX1: $i] : ( injective @ ( SV63 @ SX0 @ SX1 ) @ ( SV64 @ SX0 @ SX1 ) @ ( SV65 @ SX0 @ SX1 ) ) ) ) )),bind(SV12,$thf( funcSet @ sK1_SX0 @ sK2_SY17 )),bind(SV13,$thf( sK3_SY22 ))]]) ).
thf(78,plain,
! [SV58: $i > $i > $o] :
( ( ( injective @ sK1_SX0 @ sK3_SY22 @ ( sK4_E @ ( SV58 @ sK3_SY22 ) ) )
= $true )
| ( ( ( sK4_E
@ ( SV58
@ ( sK4_E
@ ^ [SX0: $i] : ( injective @ sK1_SX0 @ SX0 @ ( sK4_E @ ( SV58 @ SX0 ) ) ) ) ) )
= ( sK4_E
@ ^ [SX0: $i] : ( injective @ sK1_SX0 @ SX0 @ ( sK4_E @ ( SV58 @ SX0 ) ) ) ) )
= $false )
| ( ( ( sK4_E
@ ^ [SX0: $i] : ( injective @ sK1_SX0 @ SX0 @ ( sK4_E @ ( SV58 @ SX0 ) ) ) )
= sK2_SY17 )
= $false ) ),
inference(extuni,[status(esa)],[55:[bind(SV11,$thf( ^ [SX0: $i] : ( injective @ sK1_SX0 @ SX0 @ ( sK4_E @ ( SV58 @ SX0 ) ) ) )),bind(SV12,$thf( funcSet @ sK1_SX0 @ sK2_SY17 )),bind(SV13,$thf( sK3_SY22 ))]]) ).
thf(79,plain,
( ( ( injective @ sK1_SX0 @ sK3_SY22 @ sK3_SY22 )
= $true )
| ( ( ( sK4_E
@ ^ [SX0: $i] : ( injective @ sK1_SX0 @ SX0 @ SX0 ) )
= sK2_SY17 )
= $false ) ),
inference(extuni,[status(esa)],[55:[bind(SV11,$thf( ^ [SX0: $i] : ( injective @ sK1_SX0 @ SX0 @ SX0 ) )),bind(SV12,$thf( funcSet @ sK1_SX0 @ sK2_SY17 )),bind(SV13,$thf( sK3_SY22 ))]]) ).
thf(80,plain,
! [SV51: $i > $i > $i,SV50: $i > $i > $i,SV49: $i > $i > $i] :
( ( ( injective @ sK1_SX0 @ sK2_SY17
@ ( sK4_E
@ ^ [SX0: $i] : ( injective @ ( SV49 @ sK3_SY22 @ SX0 ) @ ( SV50 @ sK3_SY22 @ SX0 ) @ ( SV51 @ sK3_SY22 @ SX0 ) ) ) )
= $true )
| ( ( injective
@ ( SV49
@ ( sK4_E
@ ^ [SX0: $i] :
( injective @ sK1_SX0 @ sK2_SY17
@ ( sK4_E
@ ^ [SX1: $i] : ( injective @ ( SV49 @ SX0 @ SX1 ) @ ( SV50 @ SX0 @ SX1 ) @ ( SV51 @ SX0 @ SX1 ) ) ) ) )
@ ( sK5_E
@ ^ [SX0: $i,SX1: $i] : ( injective @ ( SV49 @ SX0 @ SX1 ) @ ( SV50 @ SX0 @ SX1 ) @ ( SV51 @ SX0 @ SX1 ) ) ) )
@ ( SV50
@ ( sK4_E
@ ^ [SX0: $i] :
( injective @ sK1_SX0 @ sK2_SY17
@ ( sK4_E
@ ^ [SX1: $i] : ( injective @ ( SV49 @ SX0 @ SX1 ) @ ( SV50 @ SX0 @ SX1 ) @ ( SV51 @ SX0 @ SX1 ) ) ) ) )
@ ( sK5_E
@ ^ [SX0: $i,SX1: $i] : ( injective @ ( SV49 @ SX0 @ SX1 ) @ ( SV50 @ SX0 @ SX1 ) @ ( SV51 @ SX0 @ SX1 ) ) ) )
@ ( SV51
@ ( sK4_E
@ ^ [SX0: $i] :
( injective @ sK1_SX0 @ sK2_SY17
@ ( sK4_E
@ ^ [SX1: $i] : ( injective @ ( SV49 @ SX0 @ SX1 ) @ ( SV50 @ SX0 @ SX1 ) @ ( SV51 @ SX0 @ SX1 ) ) ) ) )
@ ( sK5_E
@ ^ [SX0: $i,SX1: $i] : ( injective @ ( SV49 @ SX0 @ SX1 ) @ ( SV50 @ SX0 @ SX1 ) @ ( SV51 @ SX0 @ SX1 ) ) ) ) )
= $true )
| ( ( injective @ sK1_SX0 @ sK2_SY17
@ ( sK4_E
@ ^ [SX0: $i] :
( injective
@ ( SV49
@ ( sK5_E
@ ^ [SX1: $i,SX2: $i] : ( injective @ ( SV49 @ SX1 @ SX2 ) @ ( SV50 @ SX1 @ SX2 ) @ ( SV51 @ SX1 @ SX2 ) ) )
@ SX0 )
@ ( SV50
@ ( sK5_E
@ ^ [SX1: $i,SX2: $i] : ( injective @ ( SV49 @ SX1 @ SX2 ) @ ( SV50 @ SX1 @ SX2 ) @ ( SV51 @ SX1 @ SX2 ) ) )
@ SX0 )
@ ( SV51
@ ( sK5_E
@ ^ [SX1: $i,SX2: $i] : ( injective @ ( SV49 @ SX1 @ SX2 ) @ ( SV50 @ SX1 @ SX2 ) @ ( SV51 @ SX1 @ SX2 ) ) )
@ SX0 ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[55:[bind(SV11,$thf( ^ [SX0: $i] : ( injective @ sK1_SX0 @ sK2_SY17 @ ( sK4_E @ ^ [SX1: $i] : ( injective @ ( SV49 @ SX0 @ SX1 ) @ ( SV50 @ SX0 @ SX1 ) @ ( SV51 @ SX0 @ SX1 ) ) ) ) )),bind(SV12,$thf( funcSet @ sK1_SX0 @ sK2_SY17 )),bind(SV13,$thf( sK3_SY22 ))]]) ).
thf(81,plain,
! [SV51: $i > $i > $i,SV50: $i > $i > $i,SV49: $i > $i > $i] :
( ( ( injective @ sK1_SX0 @ sK2_SY17
@ ( sK4_E
@ ^ [SX0: $i] : ( injective @ ( SV49 @ sK3_SY22 @ SX0 ) @ ( SV50 @ sK3_SY22 @ SX0 ) @ ( SV51 @ sK3_SY22 @ SX0 ) ) ) )
= $true )
| ( ( injective
@ ( SV49
@ ( sK4_E
@ ^ [SX0: $i] :
( injective @ sK1_SX0 @ sK2_SY17
@ ( sK4_E
@ ^ [SX1: $i] : ( injective @ ( SV49 @ SX0 @ SX1 ) @ ( SV50 @ SX0 @ SX1 ) @ ( SV51 @ SX0 @ SX1 ) ) ) ) )
@ ( sK5_E
@ ^ [SX0: $i,SX1: $i] : ( injective @ ( SV49 @ SX0 @ SX1 ) @ ( SV50 @ SX0 @ SX1 ) @ ( SV51 @ SX0 @ SX1 ) ) ) )
@ ( SV50
@ ( sK4_E
@ ^ [SX0: $i] :
( injective @ sK1_SX0 @ sK2_SY17
@ ( sK4_E
@ ^ [SX1: $i] : ( injective @ ( SV49 @ SX0 @ SX1 ) @ ( SV50 @ SX0 @ SX1 ) @ ( SV51 @ SX0 @ SX1 ) ) ) ) )
@ ( sK5_E
@ ^ [SX0: $i,SX1: $i] : ( injective @ ( SV49 @ SX0 @ SX1 ) @ ( SV50 @ SX0 @ SX1 ) @ ( SV51 @ SX0 @ SX1 ) ) ) )
@ ( SV51
@ ( sK4_E
@ ^ [SX0: $i] :
( injective @ sK1_SX0 @ sK2_SY17
@ ( sK4_E
@ ^ [SX1: $i] : ( injective @ ( SV49 @ SX0 @ SX1 ) @ ( SV50 @ SX0 @ SX1 ) @ ( SV51 @ SX0 @ SX1 ) ) ) ) )
@ ( sK5_E
@ ^ [SX0: $i,SX1: $i] : ( injective @ ( SV49 @ SX0 @ SX1 ) @ ( SV50 @ SX0 @ SX1 ) @ ( SV51 @ SX0 @ SX1 ) ) ) ) )
= $false )
| ( ( injective @ sK1_SX0 @ sK2_SY17
@ ( sK4_E
@ ^ [SX0: $i] :
( injective
@ ( SV49
@ ( sK5_E
@ ^ [SX1: $i,SX2: $i] : ( injective @ ( SV49 @ SX1 @ SX2 ) @ ( SV50 @ SX1 @ SX2 ) @ ( SV51 @ SX1 @ SX2 ) ) )
@ SX0 )
@ ( SV50
@ ( sK5_E
@ ^ [SX1: $i,SX2: $i] : ( injective @ ( SV49 @ SX1 @ SX2 ) @ ( SV50 @ SX1 @ SX2 ) @ ( SV51 @ SX1 @ SX2 ) ) )
@ SX0 )
@ ( SV51
@ ( sK5_E
@ ^ [SX1: $i,SX2: $i] : ( injective @ ( SV49 @ SX1 @ SX2 ) @ ( SV50 @ SX1 @ SX2 ) @ ( SV51 @ SX1 @ SX2 ) ) )
@ SX0 ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[55:[bind(SV11,$thf( ^ [SX0: $i] : ( injective @ sK1_SX0 @ sK2_SY17 @ ( sK4_E @ ^ [SX1: $i] : ( injective @ ( SV49 @ SX0 @ SX1 ) @ ( SV50 @ SX0 @ SX1 ) @ ( SV51 @ SX0 @ SX1 ) ) ) ) )),bind(SV12,$thf( funcSet @ sK1_SX0 @ sK2_SY17 )),bind(SV13,$thf( sK3_SY22 ))]]) ).
thf(82,plain,
! [SV44: $i > $i > $o] :
( ( ( injective @ sK1_SX0 @ sK2_SY17 @ ( sK4_E @ ( SV44 @ sK3_SY22 ) ) )
= $true )
| ( ( ( sK4_E
@ ( SV44
@ ( sK4_E
@ ^ [SX0: $i] : ( injective @ sK1_SX0 @ sK2_SY17 @ ( sK4_E @ ( SV44 @ SX0 ) ) ) ) ) )
= ( sK4_E
@ ^ [SX0: $i] : ( injective @ sK1_SX0 @ sK2_SY17 @ ( sK4_E @ ( SV44 @ SX0 ) ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[55:[bind(SV11,$thf( ^ [SX0: $i] : ( injective @ sK1_SX0 @ sK2_SY17 @ ( sK4_E @ ( SV44 @ SX0 ) ) ) )),bind(SV12,$thf( funcSet @ sK1_SX0 @ sK2_SY17 )),bind(SV13,$thf( sK3_SY22 ))]]) ).
thf(83,plain,
( ( injective @ sK1_SX0 @ sK2_SY17 @ sK3_SY22 )
= $true ),
inference(extuni,[status(esa)],[55:[bind(SV11,$thf( ^ [SX0: $i] : ( injective @ sK1_SX0 @ sK2_SY17 @ SX0 ) )),bind(SV12,$thf( funcSet @ sK1_SX0 @ sK2_SY17 )),bind(SV13,$thf( sK3_SY22 ))]]) ).
thf(84,plain,
! [SV37: $i > $i,SV36: $i > $i,SV35: $i > $i] :
( ( ( injective @ ( SV35 @ sK3_SY22 ) @ ( SV36 @ sK3_SY22 ) @ ( SV37 @ sK3_SY22 ) )
= $true )
| ( ( injective
@ ( SV35
@ ( sK4_E
@ ^ [SX0: $i] : ( injective @ ( SV35 @ SX0 ) @ ( SV36 @ SX0 ) @ ( SV37 @ SX0 ) ) ) )
@ ( SV36
@ ( sK4_E
@ ^ [SX0: $i] : ( injective @ ( SV35 @ SX0 ) @ ( SV36 @ SX0 ) @ ( SV37 @ SX0 ) ) ) )
@ ( SV37
@ ( sK4_E
@ ^ [SX0: $i] : ( injective @ ( SV35 @ SX0 ) @ ( SV36 @ SX0 ) @ ( SV37 @ SX0 ) ) ) ) )
= $true )
| ( ( injective @ sK1_SX0 @ sK2_SY17
@ ( sK4_E
@ ^ [SX0: $i] : ( injective @ ( SV35 @ SX0 ) @ ( SV36 @ SX0 ) @ ( SV37 @ SX0 ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[55:[bind(SV11,$thf( ^ [SX0: $i] : ( injective @ ( SV35 @ SX0 ) @ ( SV36 @ SX0 ) @ ( SV37 @ SX0 ) ) )),bind(SV12,$thf( funcSet @ sK1_SX0 @ sK2_SY17 )),bind(SV13,$thf( sK3_SY22 ))]]) ).
thf(85,plain,
! [SV37: $i > $i,SV36: $i > $i,SV35: $i > $i] :
( ( ( injective @ ( SV35 @ sK3_SY22 ) @ ( SV36 @ sK3_SY22 ) @ ( SV37 @ sK3_SY22 ) )
= $true )
| ( ( injective
@ ( SV35
@ ( sK4_E
@ ^ [SX0: $i] : ( injective @ ( SV35 @ SX0 ) @ ( SV36 @ SX0 ) @ ( SV37 @ SX0 ) ) ) )
@ ( SV36
@ ( sK4_E
@ ^ [SX0: $i] : ( injective @ ( SV35 @ SX0 ) @ ( SV36 @ SX0 ) @ ( SV37 @ SX0 ) ) ) )
@ ( SV37
@ ( sK4_E
@ ^ [SX0: $i] : ( injective @ ( SV35 @ SX0 ) @ ( SV36 @ SX0 ) @ ( SV37 @ SX0 ) ) ) ) )
= $false )
| ( ( injective @ sK1_SX0 @ sK2_SY17
@ ( sK4_E
@ ^ [SX0: $i] : ( injective @ ( SV35 @ SX0 ) @ ( SV36 @ SX0 ) @ ( SV37 @ SX0 ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[55:[bind(SV11,$thf( ^ [SX0: $i] : ( injective @ ( SV35 @ SX0 ) @ ( SV36 @ SX0 ) @ ( SV37 @ SX0 ) ) )),bind(SV12,$thf( funcSet @ sK1_SX0 @ sK2_SY17 )),bind(SV13,$thf( sK3_SY22 ))]]) ).
thf(86,plain,
! [SV12: $i,SV11: $i > $o] :
( ( ( SV11 @ sK3_SY22 )
= $true )
| ( ( ( dsetconstr @ SV12
@ ^ [SX0: $i] : ( SV11 @ SX0 ) )
= ( dsetconstr @ ( funcSet @ sK1_SX0 @ sK2_SY17 )
@ ^ [SX0: $i] : ( injective @ sK1_SX0 @ sK2_SY17 @ SX0 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[55:[bind(SV13,$thf( sK3_SY22 ))]]) ).
thf(90,plain,
! [SV12: $i,SV112: $i > $i,SV13: $i,SV111: $i > $i] :
( ( ( in @ ( SV111 @ SV13 ) @ ( SV112 @ SV13 ) )
= $false )
| ( ( in @ SV13
@ ( dsetconstr @ SV12
@ ^ [SX0: $i] :
~ ( in @ ( SV111 @ SX0 ) @ ( SV112 @ SX0 ) ) ) )
= $false )
| ( ( ~ ( in @ ( SV111 @ SV13 ) @ ( SV112 @ SV13 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[57:[bind(SV11,$thf( ^ [SX0: $i] : ~ ( in @ ( SV111 @ SX0 ) @ ( SV112 @ SX0 ) ) ))]]) ).
thf(91,plain,
! [SV12: $i,SV13: $i,SV108: $i > $o] :
( ( ( ~ ( SV108 @ SV13 ) )
= $true )
| ( ( ~ ( in @ SV13
@ ( dsetconstr @ SV12
@ ^ [SX0: $i] :
~ ( SV108 @ SX0 ) ) ) )
= $true )
| ( ( ~ ( SV108 @ SV13 ) )
= $true ) ),
inference(extuni,[status(esa)],[57:[bind(SV11,$thf( ^ [SX0: $i] : ~ ( SV108 @ SX0 ) ))]]) ).
thf(94,plain,
! [SV12: $i,SV13: $i,SV108: $i > $o] :
( ( ( SV108 @ SV13 )
= $false )
| ( ( ~ ( in @ SV13
@ ( dsetconstr @ SV12
@ ^ [SX0: $i] :
~ ( SV108 @ SX0 ) ) ) )
= $true )
| ( ( ~ ( SV108 @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(95,plain,
! [SV12: $i,SV112: $i > $i,SV13: $i,SV111: $i > $i] :
( ( ( in @ ( SV111 @ SV13 ) @ ( SV112 @ SV13 ) )
= $false )
| ( ( in @ SV13
@ ( dsetconstr @ SV12
@ ^ [SX0: $i] :
~ ( in @ ( SV111 @ SX0 ) @ ( SV112 @ SX0 ) ) ) )
= $false )
| ( ( in @ ( SV111 @ SV13 ) @ ( SV112 @ SV13 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(98,plain,
! [SV108: $i > $o,SV12: $i,SV13: $i] :
( ( ( in @ SV13
@ ( dsetconstr @ SV12
@ ^ [SX0: $i] :
~ ( SV108 @ SX0 ) ) )
= $false )
| ( ( SV108 @ SV13 )
= $false )
| ( ( ~ ( SV108 @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(100,plain,
! [SV12: $i,SV13: $i,SV108: $i > $o] :
( ( ( SV108 @ SV13 )
= $false )
| ( ( SV108 @ SV13 )
= $false )
| ( ( in @ SV13
@ ( dsetconstr @ SV12
@ ^ [SX0: $i] :
~ ( SV108 @ SX0 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(101,plain,
! [SV12: $i,SV13: $i,SV108: $i > $o] :
( ( ( SV108 @ SV13 )
= $false )
| ( ( in @ SV13
@ ( dsetconstr @ SV12
@ ^ [SX0: $i] :
~ ( SV108 @ SX0 ) ) )
= $false ) ),
inference(sim,[status(thm)],[100]) ).
thf(102,plain,
! [SV12: $i,SV112: $i > $i,SV13: $i,SV111: $i > $i] :
( ( ( in @ ( SV111 @ SV13 ) @ ( SV112 @ SV13 ) )
= $false )
| ( ( in @ SV13
@ ( dsetconstr @ SV12
@ ^ [SX0: $i] :
~ ( in @ ( SV111 @ SX0 ) @ ( SV112 @ SX0 ) ) ) )
= $false ) ),
inference(sim,[status(thm)],[95]) ).
thf(103,plain,
! [SV113: $i] :
( ( in @ sK1_SX0
@ ( dsetconstr @ SV113
@ ^ [SX0: $i] : ( injective @ SX0 @ sK2_SY17 @ sK3_SY22 ) ) )
= $false ),
inference(rename,[status(thm)],[61]) ).
thf(105,plain,
! [SV113: $i] :
( ( ( in @ sK1_SX0
@ ( dsetconstr @ SV113
@ ^ [SX0: $i] : ( injective @ SX0 @ sK2_SY17 @ sK3_SY22 ) ) )
= ( in @ sK3_SY22
@ ( dsetconstr @ ( funcSet @ sK1_SX0 @ sK2_SY17 )
@ ^ [SY23: $i] : ( injective @ sK1_SX0 @ sK2_SY17 @ SY23 ) ) ) )
= $false ),
inference(res,[status(thm)],[103,22]) ).
thf(106,plain,
( ( ( sK3_SY22 = sK9_E )
= $false )
| ( ( sK9_E = sK1_SX0 )
= $false )
| ( ( sK1_SX0 = sK3_SY22 )
= $false ) ),
inference(extuni,[status(esa)],[105:[bind(SV113,$thf( funcSet @ sK1_SX0 @ sK2_SY17 ))]]) ).
thf(107,plain,
( ( ( injective @ sK9_E @ sK2_SY17 @ sK3_SY22 )
= $true )
| ( ( injective @ sK1_SX0 @ sK2_SY17 @ sK9_E )
= $true )
| ( ( sK1_SX0 = sK3_SY22 )
= $false ) ),
inference(extuni,[status(esa)],[105:[bind(SV113,$thf( funcSet @ sK1_SX0 @ sK2_SY17 ))]]) ).
thf(108,plain,
( ( ( injective @ sK9_E @ sK2_SY17 @ sK3_SY22 )
= $false )
| ( ( injective @ sK1_SX0 @ sK2_SY17 @ sK9_E )
= $false )
| ( ( sK1_SX0 = sK3_SY22 )
= $false ) ),
inference(extuni,[status(esa)],[105:[bind(SV113,$thf( funcSet @ sK1_SX0 @ sK2_SY17 ))]]) ).
thf(109,plain,
! [SV113: $i] :
( ( ( ( dsetconstr @ SV113
@ ^ [SX0: $i] : ( injective @ SX0 @ sK2_SY17 @ sK3_SY22 ) )
= ( dsetconstr @ ( funcSet @ sK1_SX0 @ sK2_SY17 )
@ ^ [SY23: $i] : ( injective @ sK1_SX0 @ sK2_SY17 @ SY23 ) ) )
= $false )
| ( ( sK1_SX0 = sK3_SY22 )
= $false ) ),
inference(extuni,[status(esa)],[105]) ).
thf(110,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[20,109,108,107,106,103,102,101,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,60,59,58,52,50,49,48,22]) ).
thf(111,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[110]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU800^2 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.18 % Computer : n018.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 15:37:37 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.11/0.41
% 1.11/0.41 No.of.Axioms: 0
% 1.11/0.41
% 1.11/0.41 Length.of.Defs: 410
% 1.11/0.41
% 1.11/0.41 Contains.Choice.Funs: false
% 1.11/0.41 ..
% 1.11/0.41
% 1.11/0.41 ********************************
% 1.11/0.41 * All subproblems solved! *
% 1.11/0.41 ********************************
% 1.11/0.41 % SZS status Theorem for /export/starexec/sandbox2/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:110,loop_count:5,foatp_calls:3,translation:fof_full)
% 1.11/0.41
% 1.11/0.41 %**** Beginning of derivation protocol ****
% 1.11/0.41 % SZS output start CNFRefutation
% See solution above
% 1.11/0.41
% 1.11/0.41 %**** End of derivation protocol ****
% 1.11/0.41 %**** no. of clauses in derivation: 87 ****
% 1.11/0.41 %**** clause counter: 110 ****
% 1.11/0.41
% 1.11/0.41 % SZS status Theorem for /export/starexec/sandbox2/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:110,loop_count:5,foatp_calls:3,translation:fof_full)
%------------------------------------------------------------------------------