%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU557^2 : TPTP v9.3.1. Bugfixed v5.2.0.
% 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 : 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 10:45:04 AM UTC 2026
% Result : Theorem 60.18s 15.25s
% Output : CNFRefutation 60.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 4
% Syntax : Number of formulae : 130 ( 62 unt; 0 typ; 3 def)
% Number of atoms : 872 ( 428 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 1375 ( 456 ~; 340 |; 9 &; 541 @)
% ( 4 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 62 ( 62 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 414 ( 86 ^; 327 !; 1 ?; 414 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_descr,type,
descr: ( $i > $o ) > $i ).
thf(tp_descrp,type,
descrp: $o ).
thf(tp_exu,type,
exu: ( $i > $o ) > $o ).
thf(tp_exuEu,type,
exuEu: $o ).
thf(tp_sK1_Xphi,type,
sK1_Xphi: $i > $o ).
thf(tp_sK2_SY0,type,
sK2_SY0: $i > $o ).
thf(tp_sK3_SX0,type,
sK3_SX0: $i ).
thf(tp_sK4_SY24,type,
sK4_SY24: $i > ( $i > $o ) > $i ).
thf(tp_sK5_SY25,type,
sK5_SY25: $i > ( $i > $o ) > $i ).
thf(tp_sK6_SX0,type,
sK6_SX0: $i ).
thf(tp_sK7_E,type,
sK7_E: $i ).
thf(descrp,definition,
( descrp
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ( Xphi
@ ( descr
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',descrp_def) ).
thf(exu,definition,
( exu
= ( ^ [Xphi: $i > $o] :
? [Xx: $i] :
( ( Xphi @ Xx )
& ! [Xy: $i] :
( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exu_def) ).
thf(exuEu,definition,
( exuEu
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ! [Xx: $i,Xy: $i] :
( ( Xphi @ Xx )
=> ( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuEu_def) ).
thf(1,conjecture,
( descrp
=> ( exuEu
=> ! [Xphi: $i > $o,Xpsi: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( Xphi @ Xx )
<=> ( Xpsi @ Xy ) ) )
=> ( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ( ( exu
@ ^ [Xx: $i] : ( Xpsi @ Xx ) )
=> ( ( descr
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
= ( descr
@ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',descr__Cong) ).
thf(2,negated_conjecture,
( ( descrp
=> ( exuEu
=> ! [Xphi: $i > $o,Xpsi: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( Xphi @ Xx )
<=> ( Xpsi @ Xy ) ) )
=> ( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ( ( exu
@ ^ [Xx: $i] : ( Xpsi @ Xx ) )
=> ( ( descr
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
= ( descr
@ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
descrp = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(4,plain,
exuEu = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(5,plain,
( ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( Xphi @ Xx )
<=> ( Xpsi @ Xy ) ) )
=> ( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ( ( exu
@ ^ [Xx: $i] : ( Xpsi @ Xx ) )
=> ( ( descr
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
= ( descr
@ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[2]) ).
thf(6,plain,
( ( ~ ! [Xphi: $i > $o,Xpsi: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( Xphi @ Xx )
<=> ( Xpsi @ Xy ) ) )
=> ( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ( ( exu
@ ^ [Xx: $i] : ( Xpsi @ Xx ) )
=> ( ( descr
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
= ( descr
@ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(7,plain,
( ( ! [SY9: $i,SY10: $i] :
( ( SY9 != SY10 )
| ~ ( sK1_Xphi @ SY9 )
| ( sK2_SY0 @ SY10 ) )
& ! [SY11: $i,SY12: $i] :
( ( SY11 != SY12 )
| ~ ( sK2_SY0 @ SY12 )
| ( sK1_Xphi @ SY11 ) )
& ( exu
@ ^ [SY5: $i] : ( sK1_Xphi @ SY5 ) )
& ( exu
@ ^ [SY14: $i] : ( sK2_SY0 @ SY14 ) )
& ( ( descr
@ ^ [SY7: $i] : ( sK1_Xphi @ SY7 ) )
!= ( descr
@ ^ [SY16: $i] : ( sK2_SY0 @ SY16 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(8,plain,
exuEu = $true,
inference(copy,[status(thm)],[4]) ).
thf(9,plain,
descrp = $true,
inference(copy,[status(thm)],[3]) ).
thf(10,plain,
( ( ! [SY9: $i,SY10: $i] :
( ( SY9 != SY10 )
| ~ ( sK1_Xphi @ SY9 )
| ( sK2_SY0 @ SY10 ) )
& ! [SY11: $i,SY12: $i] :
( ( SY11 != SY12 )
| ~ ( sK2_SY0 @ SY12 )
| ( sK1_Xphi @ SY11 ) )
& ( exu
@ ^ [SY5: $i] : ( sK1_Xphi @ SY5 ) )
& ( exu
@ ^ [SY14: $i] : ( sK2_SY0 @ SY14 ) )
& ( ( descr
@ ^ [SY7: $i] : ( sK1_Xphi @ SY7 ) )
!= ( descr
@ ^ [SY16: $i] : ( sK2_SY0 @ SY16 ) ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(11,plain,
( ( ! [SX0: $i > $o] :
( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) )
| ! [SX1: $i,SX2: $i] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8,descrp,exu,exuEu]) ).
thf(12,plain,
( ( ! [SX0: $i > $o] :
( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) )
| ( SX0
@ ( descr
@ ^ [SX1: $i] : ( SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9,descrp,exu,exuEu]) ).
thf(13,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ( sK1_Xphi @ SX0 )
| ( sK2_SY0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ( sK2_SY0 @ SX1 )
| ( sK1_Xphi @ SX0 ) ) )
| ~ ~ ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( sK1_Xphi @ SX0 )
| ~ ! [SX1: $i] :
( ~ ( sK1_Xphi @ SX1 )
| ( SX0 = SX1 ) ) )
| ~ ~ ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( sK2_SY0 @ SX0 )
| ~ ! [SX1: $i] :
( ~ ( sK2_SY0 @ SX1 )
| ( SX0 = SX1 ) ) )
| ~ ( ( ( descr
@ ^ [SX0: $i] : ( sK1_Xphi @ SX0 ) )
!= ( descr
@ ^ [SX0: $i] : ( sK2_SY0 @ SX0 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10,descrp,exu,exuEu]) ).
thf(14,plain,
! [SV1: $i > $o] :
( ( ~ ~ ! [SY17: $i] :
~ ~ ( ~ ( SV1 @ SY17 )
| ~ ! [SY18: $i] :
( ~ ( SV1 @ SY18 )
| ( SY17 = SY18 ) ) )
| ! [SY19: $i,SY20: $i] :
( ~ ( SV1 @ SY19 )
| ~ ( SV1 @ SY20 )
| ( SY19 = SY20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(15,plain,
! [SV2: $i > $o] :
( ( ~ ~ ! [SY21: $i] :
~ ~ ( ~ ( SV2 @ SY21 )
| ~ ! [SY22: $i] :
( ~ ( SV2 @ SY22 )
| ( SY21 = SY22 ) ) )
| ( SV2
@ ( descr
@ ^ [SY23: $i] : ( SV2 @ SY23 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(16,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ( sK1_Xphi @ SX0 )
| ( sK2_SY0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ( sK2_SY0 @ SX1 )
| ( sK1_Xphi @ SX0 ) ) )
| ~ ~ ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( sK1_Xphi @ SX0 )
| ~ ! [SX1: $i] :
( ~ ( sK1_Xphi @ SX1 )
| ( SX0 = SX1 ) ) )
| ~ ~ ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( sK2_SY0 @ SX0 )
| ~ ! [SX1: $i] :
( ~ ( sK2_SY0 @ SX1 )
| ( SX0 = SX1 ) ) )
| ~ ( ( ( descr
@ ^ [SX0: $i] : ( sK1_Xphi @ SX0 ) )
!= ( descr
@ ^ [SX0: $i] : ( sK2_SY0 @ SX0 ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[13]) ).
thf(17,plain,
! [SV1: $i > $o] :
( ( ( ~ ~ ! [SY17: $i] :
~ ~ ( ~ ( SV1 @ SY17 )
| ~ ! [SY18: $i] :
( ~ ( SV1 @ SY18 )
| ( SY17 = SY18 ) ) ) )
= $true )
| ( ( ! [SY19: $i,SY20: $i] :
( ~ ( SV1 @ SY19 )
| ~ ( SV1 @ SY20 )
| ( SY19 = SY20 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[14]) ).
thf(18,plain,
! [SV2: $i > $o] :
( ( ( ~ ~ ! [SY21: $i] :
~ ~ ( ~ ( SV2 @ SY21 )
| ~ ! [SY22: $i] :
( ~ ( SV2 @ SY22 )
| ( SY21 = SY22 ) ) ) )
= $true )
| ( ( SV2
@ ( descr
@ ^ [SY23: $i] : ( SV2 @ SY23 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[15]) ).
thf(19,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ( sK1_Xphi @ SX0 )
| ( sK2_SY0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ( sK2_SY0 @ SX1 )
| ( sK1_Xphi @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[16]) ).
thf(20,plain,
( ( ~ ~ ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( sK1_Xphi @ SX0 )
| ~ ! [SX1: $i] :
( ~ ( sK1_Xphi @ SX1 )
| ( SX0 = SX1 ) ) )
| ~ ~ ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( sK2_SY0 @ SX0 )
| ~ ! [SX1: $i] :
( ~ ( sK2_SY0 @ SX1 )
| ( SX0 = SX1 ) ) )
| ~ ( ( ( descr
@ ^ [SX0: $i] : ( sK1_Xphi @ SX0 ) )
!= ( descr
@ ^ [SX0: $i] : ( sK2_SY0 @ SX0 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[16]) ).
thf(21,plain,
! [SV1: $i > $o] :
( ( ( ~ ! [SY17: $i] :
~ ~ ( ~ ( SV1 @ SY17 )
| ~ ! [SY18: $i] :
( ~ ( SV1 @ SY18 )
| ( SY17 = SY18 ) ) ) )
= $false )
| ( ( ! [SY19: $i,SY20: $i] :
( ~ ( SV1 @ SY19 )
| ~ ( SV1 @ SY20 )
| ( SY19 = SY20 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[17]) ).
thf(22,plain,
! [SV2: $i > $o] :
( ( ( ~ ! [SY21: $i] :
~ ~ ( ~ ( SV2 @ SY21 )
| ~ ! [SY22: $i] :
( ~ ( SV2 @ SY22 )
| ( SY21 = SY22 ) ) ) )
= $false )
| ( ( SV2
@ ( descr
@ ^ [SY23: $i] : ( SV2 @ SY23 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(23,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ( sK1_Xphi @ SX0 )
| ( sK2_SY0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ( sK2_SY0 @ SX1 )
| ( sK1_Xphi @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[19]) ).
thf(24,plain,
( ( ~ ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( sK1_Xphi @ SX0 )
| ~ ! [SX1: $i] :
( ~ ( sK1_Xphi @ SX1 )
| ( SX0 = SX1 ) ) )
| ~ ~ ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( sK2_SY0 @ SX0 )
| ~ ! [SX1: $i] :
( ~ ( sK2_SY0 @ SX1 )
| ( SX0 = SX1 ) ) )
| ~ ( ( ( descr
@ ^ [SX0: $i] : ( sK1_Xphi @ SX0 ) )
!= ( descr
@ ^ [SX0: $i] : ( sK2_SY0 @ SX0 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[20]) ).
thf(25,plain,
! [SV1: $i > $o] :
( ( ( ! [SY17: $i] :
~ ~ ( ~ ( SV1 @ SY17 )
| ~ ! [SY18: $i] :
( ~ ( SV1 @ SY18 )
| ( SY17 = SY18 ) ) ) )
= $true )
| ( ( ! [SY19: $i,SY20: $i] :
( ~ ( SV1 @ SY19 )
| ~ ( SV1 @ SY20 )
| ( SY19 = SY20 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[21]) ).
thf(26,plain,
! [SV2: $i > $o] :
( ( ( ! [SY21: $i] :
~ ~ ( ~ ( SV2 @ SY21 )
| ~ ! [SY22: $i] :
( ~ ( SV2 @ SY22 )
| ( SY21 = SY22 ) ) ) )
= $true )
| ( ( SV2
@ ( descr
@ ^ [SY23: $i] : ( SV2 @ SY23 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[22]) ).
thf(27,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ( sK1_Xphi @ SX0 )
| ( sK2_SY0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ( sK2_SY0 @ SX1 )
| ( sK1_Xphi @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(28,plain,
( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( sK1_Xphi @ SX0 )
| ~ ! [SX1: $i] :
( ~ ( sK1_Xphi @ SX1 )
| ( SX0 = SX1 ) ) )
| ~ ~ ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( sK2_SY0 @ SX0 )
| ~ ! [SX1: $i] :
( ~ ( sK2_SY0 @ SX1 )
| ( SX0 = SX1 ) ) )
| ~ ( ( ( descr
@ ^ [SX0: $i] : ( sK1_Xphi @ SX0 ) )
!= ( descr
@ ^ [SX0: $i] : ( sK2_SY0 @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(29,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( ~ ~ ( ~ ( SV1 @ SV3 )
| ~ ! [SY24: $i] :
( ~ ( SV1 @ SY24 )
| ( SV3 = SY24 ) ) ) )
= $true )
| ( ( ! [SY19: $i,SY20: $i] :
( ~ ( SV1 @ SY19 )
| ~ ( SV1 @ SY20 )
| ( SY19 = SY20 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(30,plain,
! [SV4: $i,SV2: $i > $o] :
( ( ( ~ ~ ( ~ ( SV2 @ SV4 )
| ~ ! [SY25: $i] :
( ~ ( SV2 @ SY25 )
| ( SV4 = SY25 ) ) ) )
= $true )
| ( ( SV2
@ ( descr
@ ^ [SY23: $i] : ( SV2 @ SY23 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(31,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ( sK1_Xphi @ SX0 )
| ( sK2_SY0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[27]) ).
thf(32,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ( sK2_SY0 @ SX1 )
| ( sK1_Xphi @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[27]) ).
thf(33,plain,
( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( sK1_Xphi @ SX0 )
| ~ ! [SX1: $i] :
( ~ ( sK1_Xphi @ SX1 )
| ( SX0 = SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[28]) ).
thf(34,plain,
( ( ~ ~ ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( sK2_SY0 @ SX0 )
| ~ ! [SX1: $i] :
( ~ ( sK2_SY0 @ SX1 )
| ( SX0 = SX1 ) ) )
| ~ ( ( ( descr
@ ^ [SX0: $i] : ( sK1_Xphi @ SX0 ) )
!= ( descr
@ ^ [SX0: $i] : ( sK2_SY0 @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[28]) ).
thf(35,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( ~ ( ~ ( SV1 @ SV3 )
| ~ ! [SY24: $i] :
( ~ ( SV1 @ SY24 )
| ( SV3 = SY24 ) ) ) )
= $false )
| ( ( ! [SY19: $i,SY20: $i] :
( ~ ( SV1 @ SY19 )
| ~ ( SV1 @ SY20 )
| ( SY19 = SY20 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[29]) ).
thf(36,plain,
! [SV4: $i,SV2: $i > $o] :
( ( ( ~ ( ~ ( SV2 @ SV4 )
| ~ ! [SY25: $i] :
( ~ ( SV2 @ SY25 )
| ( SV4 = SY25 ) ) ) )
= $false )
| ( ( SV2
@ ( descr
@ ^ [SY23: $i] : ( SV2 @ SY23 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(37,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ( sK1_Xphi @ SX0 )
| ( sK2_SY0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[31]) ).
thf(38,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ( sK2_SY0 @ SX1 )
| ( sK1_Xphi @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[32]) ).
thf(39,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( sK1_Xphi @ SX0 )
| ~ ! [SX1: $i] :
( ~ ( sK1_Xphi @ SX1 )
| ( SX0 = SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[33]) ).
thf(40,plain,
( ( ~ ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( sK2_SY0 @ SX0 )
| ~ ! [SX1: $i] :
( ~ ( sK2_SY0 @ SX1 )
| ( SX0 = SX1 ) ) )
| ~ ( ( ( descr
@ ^ [SX0: $i] : ( sK1_Xphi @ SX0 ) )
!= ( descr
@ ^ [SX0: $i] : ( sK2_SY0 @ SX0 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[34]) ).
thf(41,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( ~ ( SV1 @ SV3 )
| ~ ! [SY24: $i] :
( ~ ( SV1 @ SY24 )
| ( SV3 = SY24 ) ) )
= $true )
| ( ( ! [SY19: $i,SY20: $i] :
( ~ ( SV1 @ SY19 )
| ~ ( SV1 @ SY20 )
| ( SY19 = SY20 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[35]) ).
thf(42,plain,
! [SV4: $i,SV2: $i > $o] :
( ( ( ~ ( SV2 @ SV4 )
| ~ ! [SY25: $i] :
( ~ ( SV2 @ SY25 )
| ( SV4 = SY25 ) ) )
= $true )
| ( ( SV2
@ ( descr
@ ^ [SY23: $i] : ( SV2 @ SY23 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[36]) ).
thf(43,plain,
! [SV5: $i] :
( ( ! [SY26: $i] :
( ( SV5 != SY26 )
| ~ ( sK1_Xphi @ SV5 )
| ( sK2_SY0 @ SY26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(44,plain,
! [SV6: $i] :
( ( ! [SY27: $i] :
( ( SV6 != SY27 )
| ~ ( sK2_SY0 @ SY27 )
| ( sK1_Xphi @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(45,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( sK1_Xphi @ SX0 )
| ~ ! [SX1: $i] :
( ~ ( sK1_Xphi @ SX1 )
| ( SX0 = SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(46,plain,
( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( sK2_SY0 @ SX0 )
| ~ ! [SX1: $i] :
( ~ ( sK2_SY0 @ SX1 )
| ( SX0 = SX1 ) ) )
| ~ ( ( ( descr
@ ^ [SX0: $i] : ( sK1_Xphi @ SX0 ) )
!= ( descr
@ ^ [SX0: $i] : ( sK2_SY0 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(47,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( ~ ( SV1 @ SV3 ) )
= $true )
| ( ( ~ ! [SY24: $i] :
( ~ ( SV1 @ SY24 )
| ( SV3 = SY24 ) ) )
= $true )
| ( ( ! [SY19: $i,SY20: $i] :
( ~ ( SV1 @ SY19 )
| ~ ( SV1 @ SY20 )
| ( SY19 = SY20 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[41]) ).
thf(48,plain,
! [SV4: $i,SV2: $i > $o] :
( ( ( ~ ( SV2 @ SV4 ) )
= $true )
| ( ( ~ ! [SY25: $i] :
( ~ ( SV2 @ SY25 )
| ( SV4 = SY25 ) ) )
= $true )
| ( ( SV2
@ ( descr
@ ^ [SY23: $i] : ( SV2 @ SY23 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[42]) ).
thf(49,plain,
! [SV7: $i,SV5: $i] :
( ( ( SV5 != SV7 )
| ~ ( sK1_Xphi @ SV5 )
| ( sK2_SY0 @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(50,plain,
! [SV8: $i,SV6: $i] :
( ( ( SV6 != SV8 )
| ~ ( sK2_SY0 @ SV8 )
| ( sK1_Xphi @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(51,plain,
( ( ~ ~ ( ~ ( sK1_Xphi @ sK3_SX0 )
| ~ ! [SY28: $i] :
( ~ ( sK1_Xphi @ SY28 )
| ( sK3_SX0 = SY28 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[45]) ).
thf(52,plain,
( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( sK2_SY0 @ SX0 )
| ~ ! [SX1: $i] :
( ~ ( sK2_SY0 @ SX1 )
| ( SX0 = SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[46]) ).
thf(53,plain,
( ( ~ ( ( ( descr
@ ^ [SX0: $i] : ( sK1_Xphi @ SX0 ) )
!= ( descr
@ ^ [SX0: $i] : ( sK2_SY0 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[46]) ).
thf(54,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( SV1 @ SV3 )
= $false )
| ( ( ~ ! [SY24: $i] :
( ~ ( SV1 @ SY24 )
| ( SV3 = SY24 ) ) )
= $true )
| ( ( ! [SY19: $i,SY20: $i] :
( ~ ( SV1 @ SY19 )
| ~ ( SV1 @ SY20 )
| ( SY19 = SY20 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(55,plain,
! [SV4: $i,SV2: $i > $o] :
( ( ( SV2 @ SV4 )
= $false )
| ( ( ~ ! [SY25: $i] :
( ~ ( SV2 @ SY25 )
| ( SV4 = SY25 ) ) )
= $true )
| ( ( SV2
@ ( descr
@ ^ [SY23: $i] : ( SV2 @ SY23 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(56,plain,
! [SV7: $i,SV5: $i] :
( ( ( SV5 != SV7 )
= $true )
| ( ( ~ ( sK1_Xphi @ SV5 )
| ( sK2_SY0 @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[49]) ).
thf(57,plain,
! [SV8: $i,SV6: $i] :
( ( ( SV6 != SV8 )
= $true )
| ( ( ~ ( sK2_SY0 @ SV8 )
| ( sK1_Xphi @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[50]) ).
thf(58,plain,
( ( ~ ( ~ ( sK1_Xphi @ sK3_SX0 )
| ~ ! [SY28: $i] :
( ~ ( sK1_Xphi @ SY28 )
| ( sK3_SX0 = SY28 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[51]) ).
thf(59,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( sK2_SY0 @ SX0 )
| ~ ! [SX1: $i] :
( ~ ( sK2_SY0 @ SX1 )
| ( SX0 = SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[52]) ).
thf(60,plain,
( ( ( descr
@ ^ [SX0: $i] : ( sK1_Xphi @ SX0 ) )
!= ( descr
@ ^ [SX0: $i] : ( sK2_SY0 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[53]) ).
thf(61,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( ! [SY24: $i] :
( ~ ( SV1 @ SY24 )
| ( SV3 = SY24 ) ) )
= $false )
| ( ( SV1 @ SV3 )
= $false )
| ( ( ! [SY19: $i,SY20: $i] :
( ~ ( SV1 @ SY19 )
| ~ ( SV1 @ SY20 )
| ( SY19 = SY20 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(62,plain,
! [SV4: $i,SV2: $i > $o] :
( ( ( ! [SY25: $i] :
( ~ ( SV2 @ SY25 )
| ( SV4 = SY25 ) ) )
= $false )
| ( ( SV2 @ SV4 )
= $false )
| ( ( SV2
@ ( descr
@ ^ [SY23: $i] : ( SV2 @ SY23 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(63,plain,
! [SV7: $i,SV5: $i] :
( ( ( SV5 = SV7 )
= $false )
| ( ( ~ ( sK1_Xphi @ SV5 )
| ( sK2_SY0 @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[56]) ).
thf(64,plain,
! [SV8: $i,SV6: $i] :
( ( ( SV6 = SV8 )
= $false )
| ( ( ~ ( sK2_SY0 @ SV8 )
| ( sK1_Xphi @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(65,plain,
( ( ~ ( sK1_Xphi @ sK3_SX0 )
| ~ ! [SY28: $i] :
( ~ ( sK1_Xphi @ SY28 )
| ( sK3_SX0 = SY28 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(66,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( sK2_SY0 @ SX0 )
| ~ ! [SX1: $i] :
( ~ ( sK2_SY0 @ SX1 )
| ( SX0 = SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(67,plain,
( ( ( descr
@ ^ [SX0: $i] : ( sK1_Xphi @ SX0 ) )
= ( descr
@ ^ [SX0: $i] : ( sK2_SY0 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(68,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( ~ ( SV1 @ ( sK4_SY24 @ SV3 @ SV1 ) )
| ( SV3
= ( sK4_SY24 @ SV3 @ SV1 ) ) )
= $false )
| ( ( SV1 @ SV3 )
= $false )
| ( ( ! [SY19: $i,SY20: $i] :
( ~ ( SV1 @ SY19 )
| ~ ( SV1 @ SY20 )
| ( SY19 = SY20 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[61]) ).
thf(69,plain,
! [SV4: $i,SV2: $i > $o] :
( ( ( ~ ( SV2 @ ( sK5_SY25 @ SV4 @ SV2 ) )
| ( SV4
= ( sK5_SY25 @ SV4 @ SV2 ) ) )
= $false )
| ( ( SV2 @ SV4 )
= $false )
| ( ( SV2
@ ( descr
@ ^ [SY23: $i] : ( SV2 @ SY23 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[62]) ).
thf(70,plain,
! [SV7: $i,SV5: $i] :
( ( ( ~ ( sK1_Xphi @ SV5 ) )
= $true )
| ( ( sK2_SY0 @ SV7 )
= $true )
| ( ( SV5 = SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[63]) ).
thf(71,plain,
! [SV6: $i,SV8: $i] :
( ( ( ~ ( sK2_SY0 @ SV8 ) )
= $true )
| ( ( sK1_Xphi @ SV6 )
= $true )
| ( ( SV6 = SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[64]) ).
thf(72,plain,
( ( ~ ( sK1_Xphi @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[65]) ).
thf(73,plain,
( ( ~ ! [SY28: $i] :
( ~ ( sK1_Xphi @ SY28 )
| ( sK3_SX0 = SY28 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[65]) ).
thf(74,plain,
( ( ~ ~ ( ~ ( sK2_SY0 @ sK6_SX0 )
| ~ ! [SY29: $i] :
( ~ ( sK2_SY0 @ SY29 )
| ( sK6_SX0 = SY29 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[66]) ).
thf(75,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( ~ ( SV1 @ ( sK4_SY24 @ SV3 @ SV1 ) ) )
= $false )
| ( ( SV1 @ SV3 )
= $false )
| ( ( ! [SY19: $i,SY20: $i] :
( ~ ( SV1 @ SY19 )
| ~ ( SV1 @ SY20 )
| ( SY19 = SY20 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[68]) ).
thf(76,plain,
! [SV1: $i > $o,SV3: $i] :
( ( ( SV3
= ( sK4_SY24 @ SV3 @ SV1 ) )
= $false )
| ( ( SV1 @ SV3 )
= $false )
| ( ( ! [SY19: $i,SY20: $i] :
( ~ ( SV1 @ SY19 )
| ~ ( SV1 @ SY20 )
| ( SY19 = SY20 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[68]) ).
thf(77,plain,
! [SV4: $i,SV2: $i > $o] :
( ( ( ~ ( SV2 @ ( sK5_SY25 @ SV4 @ SV2 ) ) )
= $false )
| ( ( SV2 @ SV4 )
= $false )
| ( ( SV2
@ ( descr
@ ^ [SY23: $i] : ( SV2 @ SY23 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[69]) ).
thf(78,plain,
! [SV2: $i > $o,SV4: $i] :
( ( ( SV4
= ( sK5_SY25 @ SV4 @ SV2 ) )
= $false )
| ( ( SV2 @ SV4 )
= $false )
| ( ( SV2
@ ( descr
@ ^ [SY23: $i] : ( SV2 @ SY23 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[69]) ).
thf(79,plain,
! [SV7: $i,SV5: $i] :
( ( ( sK1_Xphi @ SV5 )
= $false )
| ( ( sK2_SY0 @ SV7 )
= $true )
| ( ( SV5 = SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(80,plain,
! [SV6: $i,SV8: $i] :
( ( ( sK2_SY0 @ SV8 )
= $false )
| ( ( sK1_Xphi @ SV6 )
= $true )
| ( ( SV6 = SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(81,plain,
( ( sK1_Xphi @ sK3_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[72]) ).
thf(82,plain,
( ( ! [SY28: $i] :
( ~ ( sK1_Xphi @ SY28 )
| ( sK3_SX0 = SY28 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[73]) ).
thf(83,plain,
( ( ~ ( ~ ( sK2_SY0 @ sK6_SX0 )
| ~ ! [SY29: $i] :
( ~ ( sK2_SY0 @ SY29 )
| ( sK6_SX0 = SY29 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[74]) ).
thf(84,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( SV1 @ ( sK4_SY24 @ SV3 @ SV1 ) )
= $true )
| ( ( SV1 @ SV3 )
= $false )
| ( ( ! [SY19: $i,SY20: $i] :
( ~ ( SV1 @ SY19 )
| ~ ( SV1 @ SY20 )
| ( SY19 = SY20 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[75]) ).
thf(85,plain,
! [SV3: $i,SV9: $i,SV1: $i > $o] :
( ( ( ! [SY30: $i] :
( ~ ( SV1 @ SV9 )
| ~ ( SV1 @ SY30 )
| ( SV9 = SY30 ) ) )
= $true )
| ( ( SV1 @ SV3 )
= $false )
| ( ( SV3
= ( sK4_SY24 @ SV3 @ SV1 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(86,plain,
! [SV4: $i,SV2: $i > $o] :
( ( ( SV2 @ ( sK5_SY25 @ SV4 @ SV2 ) )
= $true )
| ( ( SV2 @ SV4 )
= $false )
| ( ( SV2
@ ( descr
@ ^ [SY23: $i] : ( SV2 @ SY23 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[77]) ).
thf(87,plain,
! [SV10: $i] :
( ( ~ ( sK1_Xphi @ SV10 )
| ( sK3_SX0 = SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(88,plain,
( ( ~ ( sK2_SY0 @ sK6_SX0 )
| ~ ! [SY29: $i] :
( ~ ( sK2_SY0 @ SY29 )
| ( sK6_SX0 = SY29 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[83]) ).
thf(89,plain,
! [SV3: $i,SV11: $i,SV1: $i > $o] :
( ( ( ! [SY31: $i] :
( ~ ( SV1 @ SV11 )
| ~ ( SV1 @ SY31 )
| ( SV11 = SY31 ) ) )
= $true )
| ( ( SV1 @ SV3 )
= $false )
| ( ( SV1 @ ( sK4_SY24 @ SV3 @ SV1 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(90,plain,
! [SV3: $i,SV12: $i,SV9: $i,SV1: $i > $o] :
( ( ( ~ ( SV1 @ SV9 )
| ~ ( SV1 @ SV12 )
| ( SV9 = SV12 ) )
= $true )
| ( ( SV1 @ SV3 )
= $false )
| ( ( SV3
= ( sK4_SY24 @ SV3 @ SV1 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(91,plain,
! [SV10: $i] :
( ( ( ~ ( sK1_Xphi @ SV10 ) )
= $true )
| ( ( sK3_SX0 = SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[87]) ).
thf(92,plain,
( ( ~ ( sK2_SY0 @ sK6_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[88]) ).
thf(93,plain,
( ( ~ ! [SY29: $i] :
( ~ ( sK2_SY0 @ SY29 )
| ( sK6_SX0 = SY29 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[88]) ).
thf(94,plain,
! [SV3: $i,SV13: $i,SV11: $i,SV1: $i > $o] :
( ( ( ~ ( SV1 @ SV11 )
| ~ ( SV1 @ SV13 )
| ( SV11 = SV13 ) )
= $true )
| ( ( SV1 @ SV3 )
= $false )
| ( ( SV1 @ ( sK4_SY24 @ SV3 @ SV1 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(95,plain,
! [SV3: $i,SV12: $i,SV9: $i,SV1: $i > $o] :
( ( ( ~ ( SV1 @ SV9 ) )
= $true )
| ( ( ~ ( SV1 @ SV12 )
| ( SV9 = SV12 ) )
= $true )
| ( ( SV1 @ SV3 )
= $false )
| ( ( SV3
= ( sK4_SY24 @ SV3 @ SV1 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[90]) ).
thf(96,plain,
! [SV10: $i] :
( ( ( sK1_Xphi @ SV10 )
= $false )
| ( ( sK3_SX0 = SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(97,plain,
( ( sK2_SY0 @ sK6_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[92]) ).
thf(98,plain,
( ( ! [SY29: $i] :
( ~ ( sK2_SY0 @ SY29 )
| ( sK6_SX0 = SY29 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[93]) ).
thf(99,plain,
! [SV3: $i,SV13: $i,SV11: $i,SV1: $i > $o] :
( ( ( ~ ( SV1 @ SV11 ) )
= $true )
| ( ( ~ ( SV1 @ SV13 )
| ( SV11 = SV13 ) )
= $true )
| ( ( SV1 @ SV3 )
= $false )
| ( ( SV1 @ ( sK4_SY24 @ SV3 @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(100,plain,
! [SV3: $i,SV12: $i,SV9: $i,SV1: $i > $o] :
( ( ( SV1 @ SV9 )
= $false )
| ( ( ~ ( SV1 @ SV12 )
| ( SV9 = SV12 ) )
= $true )
| ( ( SV1 @ SV3 )
= $false )
| ( ( SV3
= ( sK4_SY24 @ SV3 @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(101,plain,
! [SV14: $i] :
( ( ~ ( sK2_SY0 @ SV14 )
| ( sK6_SX0 = SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(102,plain,
! [SV3: $i,SV13: $i,SV11: $i,SV1: $i > $o] :
( ( ( SV1 @ SV11 )
= $false )
| ( ( ~ ( SV1 @ SV13 )
| ( SV11 = SV13 ) )
= $true )
| ( ( SV1 @ SV3 )
= $false )
| ( ( SV1 @ ( sK4_SY24 @ SV3 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(103,plain,
! [SV3: $i,SV9: $i,SV12: $i,SV1: $i > $o] :
( ( ( ~ ( SV1 @ SV12 ) )
= $true )
| ( ( SV9 = SV12 )
= $true )
| ( ( SV1 @ SV9 )
= $false )
| ( ( SV1 @ SV3 )
= $false )
| ( ( SV3
= ( sK4_SY24 @ SV3 @ SV1 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[100]) ).
thf(104,plain,
! [SV14: $i] :
( ( ( ~ ( sK2_SY0 @ SV14 ) )
= $true )
| ( ( sK6_SX0 = SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[101]) ).
thf(105,plain,
! [SV3: $i,SV11: $i,SV13: $i,SV1: $i > $o] :
( ( ( ~ ( SV1 @ SV13 ) )
= $true )
| ( ( SV11 = SV13 )
= $true )
| ( ( SV1 @ SV11 )
= $false )
| ( ( SV1 @ SV3 )
= $false )
| ( ( SV1 @ ( sK4_SY24 @ SV3 @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[102]) ).
thf(106,plain,
! [SV3: $i,SV9: $i,SV12: $i,SV1: $i > $o] :
( ( ( SV1 @ SV12 )
= $false )
| ( ( SV9 = SV12 )
= $true )
| ( ( SV1 @ SV9 )
= $false )
| ( ( SV1 @ SV3 )
= $false )
| ( ( SV3
= ( sK4_SY24 @ SV3 @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(107,plain,
! [SV14: $i] :
( ( ( sK2_SY0 @ SV14 )
= $false )
| ( ( sK6_SX0 = SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[104]) ).
thf(108,plain,
! [SV3: $i,SV11: $i,SV13: $i,SV1: $i > $o] :
( ( ( SV1 @ SV13 )
= $false )
| ( ( SV11 = SV13 )
= $true )
| ( ( SV1 @ SV11 )
= $false )
| ( ( SV1 @ SV3 )
= $false )
| ( ( SV1 @ ( sK4_SY24 @ SV3 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(116,plain,
! [SV4: $i,SV24: $i > $o] :
( ( ( ~ ( SV24
@ ( sK5_SY25 @ SV4
@ ^ [SX0: $i] :
~ ( SV24 @ SX0 ) ) ) )
= $true )
| ( ( ~ ( SV24 @ SV4 ) )
= $false )
| ( ( ~ ( SV24
@ ( descr
@ ^ [SX0: $i] :
~ ( SV24 @ SX0 ) ) ) )
= $true ) ),
inference(prim_subst,[status(thm)],[86:[bind(SV2,$thf( ^ [SV23: $i] : ~ ( SV24 @ SV23 ) ))]]) ).
thf(117,plain,
! [SV4: $i] :
( ( ( ( sK5_SY25 @ SV4
@ ^ [SX0: $i] : ( SX0 = sK6_SX0 ) )
= sK6_SX0 )
= $true )
| ( ( SV4 = sK6_SX0 )
= $false )
| ( ( ( descr
@ ^ [SX0: $i] : ( SX0 = sK6_SX0 ) )
= sK6_SX0 )
= $true ) ),
inference(prim_subst,[status(thm)],[86:[bind(SV2,$thf( ^ [SV21: $i] : ( SV21 = sK6_SX0 ) ))]]) ).
thf(118,plain,
! [SV4: $i] :
( ( ( ( sK5_SY25 @ SV4
@ ^ [SX0: $i] : ( SX0 = sK3_SX0 ) )
= sK3_SX0 )
= $true )
| ( ( SV4 = sK3_SX0 )
= $false )
| ( ( ( descr
@ ^ [SX0: $i] : ( SX0 = sK3_SX0 ) )
= sK3_SX0 )
= $true ) ),
inference(prim_subst,[status(thm)],[86:[bind(SV2,$thf( ^ [SV22: $i] : ( SV22 = sK3_SX0 ) ))]]) ).
thf(126,plain,
! [SV3: $i,SV11: $i,SV13: $i,SV18: $i > $o] :
( ( ( ~ ( SV18 @ SV13 ) )
= $false )
| ( ( SV11 = SV13 )
= $true )
| ( ( ~ ( SV18 @ SV11 ) )
= $false )
| ( ( ~ ( SV18 @ SV3 ) )
= $false )
| ( ( ~ ( SV18
@ ( sK4_SY24 @ SV3
@ ^ [SX0: $i] :
~ ( SV18 @ SX0 ) ) ) )
= $true ) ),
inference(prim_subst,[status(thm)],[108:[bind(SV1,$thf( ^ [SV17: $i] : ~ ( SV18 @ SV17 ) ))]]) ).
thf(129,plain,
( ( ( sK1_Xphi @ sK7_E )
= $true )
| ( ( sK2_SY0 @ sK7_E )
= $true ) ),
inference(extuni,[status(esa)],[67]) ).
thf(130,plain,
( ( ( sK1_Xphi @ sK7_E )
= $false )
| ( ( sK2_SY0 @ sK7_E )
= $false ) ),
inference(extuni,[status(esa)],[67]) ).
thf(131,plain,
! [SV7: $i] :
( ( ( sK2_SY0 @ SV7 )
= $true )
| ( ( sK1_Xphi @ SV7 )
= $false ) ),
inference(extuni,[status(esa)],[79:[bind(SV5,$thf( SV7 ))]]) ).
thf(132,plain,
! [SV8: $i] :
( ( ( sK1_Xphi @ SV8 )
= $true )
| ( ( sK2_SY0 @ SV8 )
= $false ) ),
inference(extuni,[status(esa)],[80:[bind(SV6,$thf( SV8 ))]]) ).
thf(134,plain,
! [SV4: $i,SV24: $i > $o] :
( ( ( SV24
@ ( sK5_SY25 @ SV4
@ ^ [SX0: $i] :
~ ( SV24 @ SX0 ) ) )
= $false )
| ( ( ~ ( SV24 @ SV4 ) )
= $false )
| ( ( ~ ( SV24
@ ( descr
@ ^ [SX0: $i] :
~ ( SV24 @ SX0 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(136,plain,
! [SV3: $i,SV11: $i,SV13: $i,SV18: $i > $o] :
( ( ( SV18 @ SV13 )
= $true )
| ( ( SV11 = SV13 )
= $true )
| ( ( ~ ( SV18 @ SV11 ) )
= $false )
| ( ( ~ ( SV18 @ SV3 ) )
= $false )
| ( ( ~ ( SV18
@ ( sK4_SY24 @ SV3
@ ^ [SX0: $i] :
~ ( SV18 @ SX0 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[126]) ).
thf(138,plain,
! [SV4: $i,SV24: $i > $o] :
( ( ( SV24 @ SV4 )
= $true )
| ( ( SV24
@ ( sK5_SY25 @ SV4
@ ^ [SX0: $i] :
~ ( SV24 @ SX0 ) ) )
= $false )
| ( ( ~ ( SV24
@ ( descr
@ ^ [SX0: $i] :
~ ( SV24 @ SX0 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[134]) ).
thf(140,plain,
! [SV3: $i,SV13: $i,SV11: $i,SV18: $i > $o] :
( ( ( SV18 @ SV11 )
= $true )
| ( ( SV11 = SV13 )
= $true )
| ( ( SV18 @ SV13 )
= $true )
| ( ( ~ ( SV18 @ SV3 ) )
= $false )
| ( ( ~ ( SV18
@ ( sK4_SY24 @ SV3
@ ^ [SX0: $i] :
~ ( SV18 @ SX0 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[136]) ).
thf(141,plain,
! [SV4: $i,SV24: $i > $o] :
( ( ( SV24
@ ( descr
@ ^ [SX0: $i] :
~ ( SV24 @ SX0 ) ) )
= $false )
| ( ( SV24
@ ( sK5_SY25 @ SV4
@ ^ [SX0: $i] :
~ ( SV24 @ SX0 ) ) )
= $false )
| ( ( SV24 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(143,plain,
! [SV11: $i,SV13: $i,SV3: $i,SV18: $i > $o] :
( ( ( SV18 @ SV3 )
= $true )
| ( ( SV18 @ SV13 )
= $true )
| ( ( SV11 = SV13 )
= $true )
| ( ( SV18 @ SV11 )
= $true )
| ( ( ~ ( SV18
@ ( sK4_SY24 @ SV3
@ ^ [SX0: $i] :
~ ( SV18 @ SX0 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[140]) ).
thf(144,plain,
! [SV13: $i,SV11: $i,SV3: $i,SV18: $i > $o] :
( ( ( SV18
@ ( sK4_SY24 @ SV3
@ ^ [SX0: $i] :
~ ( SV18 @ SX0 ) ) )
= $false )
| ( ( SV18 @ SV11 )
= $true )
| ( ( SV11 = SV13 )
= $true )
| ( ( SV18 @ SV13 )
= $true )
| ( ( SV18 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[143]) ).
thf(145,plain,
( ( ( ( descr
@ ^ [SX0: $i] : ( SX0 = sK6_SX0 ) )
= sK6_SX0 )
= $true )
| ( ( ( sK5_SY25 @ sK6_SX0
@ ^ [SX0: $i] : ( SX0 = sK6_SX0 ) )
= sK6_SX0 )
= $true ) ),
inference(extuni,[status(esa)],[117:[bind(SV4,$thf( sK6_SX0 ))]]) ).
thf(146,plain,
( ( ( ( descr
@ ^ [SX0: $i] : ( SX0 = sK3_SX0 ) )
= sK3_SX0 )
= $true )
| ( ( ( sK5_SY25 @ sK3_SX0
@ ^ [SX0: $i] : ( SX0 = sK3_SX0 ) )
= sK3_SX0 )
= $true ) ),
inference(extuni,[status(esa)],[118:[bind(SV4,$thf( sK3_SX0 ))]]) ).
thf(151,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[67,146,145,144,141,132,131,130,129,108,107,106,97,96,86,81,80,79,78]) ).
thf(152,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[151]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU557^2 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.03 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.16 % Computer : n020.cluster.edu
% 0.11/0.16 % Model : x86_64 x86_64
% 0.11/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.16 % Memory : 8046.5625MB
% 0.11/0.16 % OS : Linux 6.8.0-71-generic
% 0.11/0.16 % CPULimit : 300
% 0.11/0.16 % WCLimit : 300
% 0.11/0.16 % DateTime : Tue Oct 6 15:28:51 UTC 2026
% 0.11/0.16 % CPUTime :
% 0.11/0.16 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 60.18/15.25
% 60.18/15.25 No.of.Axioms: 0
% 60.18/15.25
% 60.18/15.25 Length.of.Defs: 587
% 60.18/15.25
% 60.18/15.25 Contains.Choice.Funs: true
% 60.18/15.25 ...eprover: CPU time limit exceeded, terminating
% 60.18/15.25 .
% 60.18/15.25
% 60.18/15.25 ********************************
% 60.18/15.25 * All subproblems solved! *
% 60.18/15.25 ********************************
% 60.18/15.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:2,ps:3,u:1,ude:false,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:151,loop_count:0,foatp_calls:2,translation:fof_full)
% 60.18/15.25
% 60.18/15.25 %**** Beginning of derivation protocol ****
% 60.18/15.25 % SZS output start CNFRefutation
% See solution above
% 60.18/15.26
% 60.18/15.26 %**** End of derivation protocol ****
% 60.18/15.26 %**** no. of clauses in derivation: 127 ****
% 60.18/15.26 %**** clause counter: 151 ****
% 60.18/15.26
% 60.18/15.26 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:2,ps:3,u:1,ude:false,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:151,loop_count:0,foatp_calls:2,translation:fof_full)
%------------------------------------------------------------------------------