%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG254^1 : TPTP v9.3.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 Sep 30 07:45:13 AM UTC 2026
% Result : Theorem 0.68s 0.38s
% Output : Refutation 0.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 17
% Syntax : Number of formulae : 104 ( 24 unt; 0 typ; 11 def)
% Number of atoms : 986 ( 333 equ; 0 cnn)
% Maximal formula atoms : 56 ( 9 avg)
% Number of connectives : 886 ( 196 ~; 197 |; 81 &; 316 @)
% ( 18 <=>; 78 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 159 ( 156 usr; 138 con; 0-4 aty)
% Number of variables : 103 ( 0 sgn 78 !; 25 ?; 103 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
term: $tType ).
thf(type_def_6,type,
subst: $tType ).
thf(type_def_7,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
one: term ).
thf(func_def_1,type,
ap: term > term > term ).
thf(func_def_2,type,
lam: term > term ).
thf(func_def_3,type,
sub: term > subst > term ).
thf(func_def_4,type,
id: subst ).
thf(func_def_5,type,
sh: subst ).
thf(func_def_6,type,
push: term > subst > subst ).
thf(func_def_7,type,
comp: subst > subst > subst ).
thf(func_def_8,type,
var: term > $o ).
thf(func_def_9,type,
pushprop_lem1v2: $o ).
thf(func_def_10,type,
pushprop_lem1_gthm: $o ).
thf(func_def_11,type,
axmap: $o ).
thf(func_def_12,type,
pushprop_lem0_gthm: $o ).
thf(func_def_13,type,
shinj: $o ).
thf(func_def_14,type,
hoasinduction_lem1v2: $o ).
thf(func_def_15,type,
hoasinduction_lem1v2_gthm: $o ).
thf(func_def_16,type,
hoasap: subst > term > subst > term > term ).
thf(func_def_17,type,
induction2lem: $o ).
thf(func_def_18,type,
hoasinduction_lem3v2_f: $o ).
thf(func_def_19,type,
axvarshift: $o ).
thf(func_def_20,type,
hoasapinj2: $o ).
thf(func_def_21,type,
hoasapnotvar_gthm: $o ).
thf(func_def_22,type,
hoasapinj1: $o ).
thf(func_def_23,type,
ulamvar1: $o ).
thf(func_def_24,type,
induction2lem_lthm: $o ).
thf(func_def_25,type,
hoasinduction_lem3v2_gthm: $o ).
thf(func_def_26,type,
apnotvar: $o ).
thf(func_def_27,type,
pushprop_lthm_orig: $o ).
thf(func_def_28,type,
hoasinduction_lem3v2_f_lthm: $o ).
thf(func_def_29,type,
hoasinduction_lthm: $o ).
thf(func_def_30,type,
hoasinduction_no_psi_cond_lthm: $o ).
thf(func_def_31,type,
hoaslaminj: $o ).
thf(func_def_32,type,
hoasinduction_lem3aaa: $o ).
thf(func_def_33,type,
induction2lem_gthm: $o ).
thf(func_def_34,type,
hoasinduction_lem3aa_lthm: $o ).
thf(func_def_35,type,
hoasinduction_lem3: $o ).
thf(func_def_36,type,
hoasinduction_lem2: $o ).
thf(func_def_37,type,
termmset_lthm: $o ).
thf(func_def_38,type,
hoasinduction_lem1: $o ).
thf(func_def_39,type,
hoaslamnotap_lthm: $o ).
thf(func_def_40,type,
pushprop_lem1v2_lthm: $o ).
thf(func_def_41,type,
hoasapnotvar: $o ).
thf(func_def_42,type,
hoasinduction_lem0: $o ).
thf(func_def_43,type,
hoasinduction: $o ).
thf(func_def_44,type,
hoasinduction_gthm: $o ).
thf(func_def_45,type,
axapp: $o ).
thf(func_def_46,type,
hoaslamnotvar_lthm: $o ).
thf(func_def_47,type,
pushprop_lem3v2_lthm: $o ).
thf(func_def_48,type,
hoasinduction_lem3b_lthm: $o ).
thf(func_def_49,type,
ulamvarind: $o ).
thf(func_def_50,type,
induction: $o ).
thf(func_def_51,type,
hoasinduction_lem3a_lthm: $o ).
thf(func_def_52,type,
termmset_gthm: $o ).
thf(func_def_53,type,
hoasinduction_lem3aa: $o ).
thf(func_def_54,type,
pushprop_lem1v2_gthm: $o ).
thf(func_def_55,type,
hoaslamnotap_gthm: $o ).
thf(func_def_56,type,
hoaslamnotvar_gthm: $o ).
thf(func_def_57,type,
hoasinduction_lem3b_gthm: $o ).
thf(func_def_58,type,
pushprop_lem2v2: $o ).
thf(func_def_59,type,
hoasinduction_lem3a_gthm: $o ).
thf(func_def_60,type,
axclos: $o ).
thf(func_def_61,type,
axassoc: $o ).
thf(func_def_62,type,
hoasinduction_lem2v2: $o ).
thf(func_def_63,type,
pushprop_lthm: $o ).
thf(func_def_64,type,
apinj2: $o ).
thf(func_def_65,type,
apinj1: $o ).
thf(func_def_66,type,
hoasapinj2_lthm: $o ).
thf(func_def_67,type,
hoasinduction_lem3v2a: $o ).
thf(func_def_68,type,
hoasapinj1_lthm: $o ).
thf(func_def_69,type,
hoaslaminj_lthm: $o ).
thf(func_def_70,type,
axvarcons: $o ).
thf(func_def_71,type,
hoaslam: subst > ( subst > term > term ) > term ).
thf(func_def_72,type,
axscons: $o ).
thf(func_def_73,type,
hoasinduction_lem2v2_gthm: $o ).
thf(func_def_74,type,
axidr: $o ).
thf(func_def_75,type,
pushprop_lem1: $o ).
thf(func_def_76,type,
laminj: $o ).
thf(func_def_77,type,
hoasinduction_lem3_lthm: $o ).
thf(func_def_78,type,
pushprop_lem0: $o ).
thf(func_def_79,type,
pushprop_gthm: $o ).
thf(func_def_80,type,
axabs: $o ).
thf(func_def_81,type,
hoasinduction_lem3v2a_lthm: $o ).
thf(func_def_82,type,
hoasinduction_lem2_lthm: $o ).
thf(func_def_83,type,
hoasapinj2_gthm: $o ).
thf(func_def_84,type,
hoasinduction_p_and_p_prime: ( subst > term > subst > $o ) > ( term > $o ) > $o ).
thf(func_def_85,type,
hoasinduction_lem1_lthm: $o ).
thf(func_def_86,type,
lamnotap: $o ).
thf(func_def_87,type,
hoasapinj1_gthm: $o ).
thf(func_def_88,type,
hoaslamnotvar: $o ).
thf(func_def_89,type,
axidl: $o ).
thf(func_def_90,type,
hoaslaminj_gthm: $o ).
thf(func_def_91,type,
induction2_lthm: $o ).
thf(func_def_92,type,
hoasinduction_lem0_lthm: $o ).
thf(func_def_93,type,
substmonoid_lthm: $o ).
thf(func_def_94,type,
pushprop: $o ).
thf(func_def_95,type,
hoasinduction_lem3_gthm: $o ).
thf(func_def_96,type,
hoasinduction_lem2_gthm: $o ).
thf(func_def_97,type,
hoasinduction_lem3b: $o ).
thf(func_def_98,type,
substmonoid: $o ).
thf(func_def_99,type,
lamnotvar: $o ).
thf(func_def_100,type,
hoasinduction_lem3a: $o ).
thf(func_def_101,type,
hoasinduction_lem1_gthm: $o ).
thf(func_def_102,type,
hoasinduction_no_psi_cond: $o ).
thf(func_def_103,type,
induction2_gthm: $o ).
thf(func_def_104,type,
pushprop_lem2v2_lthm: $o ).
thf(func_def_105,type,
hoasvar: subst > term > subst > $o ).
thf(func_def_106,type,
hoaslamnotap: $o ).
thf(func_def_107,type,
substmonoid_gthm: $o ).
thf(func_def_108,type,
ulamvarsh: $o ).
thf(func_def_109,type,
induction2: $o ).
thf(func_def_110,type,
pushprop_lem3v2: $o ).
thf(func_def_111,type,
pushprop_lem2v2_gthm: $o ).
thf(func_def_112,type,
pushprop_lem1_lthm: $o ).
thf(func_def_113,type,
hoasinduction_lem3v2: $o ).
thf(func_def_114,type,
axshiftcons: $o ).
thf(func_def_115,type,
termmset: $o ).
thf(func_def_116,type,
pushprop_lem0_lthm: $o ).
thf(func_def_117,type,
hoasapnotvar_lthm: $o ).
thf(func_def_118,type,
hoasinduction_lem3v2_lthm: $o ).
thf(func_def_119,type,
pushprop_p_and_p_prime: term > subst > ( term > $o ) > ( term > $o ) > $o ).
thf(func_def_120,type,
axvarid: $o ).
thf(func_def_121,type,
hoasinduction_lthm_3: $o ).
thf(func_def_125,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_126,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_127,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_128,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_129,type,
vIFF: $o > $o > $o ).
thf(func_def_130,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_131,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_132,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_133,type,
sK0: subst ).
thf(func_def_134,type,
sK1: subst ).
thf(func_def_135,type,
sK2: subst ).
thf(func_def_136,type,
sK3: subst ).
thf(func_def_137,type,
sK4: subst ).
thf(func_def_138,type,
sK5: subst ).
thf(func_def_139,type,
sK6: subst ).
thf(func_def_140,type,
sK7: subst ).
thf(func_def_141,type,
sK8: subst ).
thf(func_def_142,type,
sK9: subst ).
thf(func_def_143,type,
sK10: subst ).
thf(func_def_144,type,
sK11: subst ).
thf(func_def_145,type,
sK12: term ).
thf(func_def_146,type,
sK13: term ).
thf(f6,axiom,
( axidl
= ( ! [X0: subst] :
( ( comp @ id @ X0 )
= X0 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',axidl) ).
thf(f8,axiom,
( axassoc
= ( ! [X2: subst,X0: subst,X1: subst] :
( ( comp @ ( comp @ X0 @ X1 ) @ X2 )
= ( comp @ X0 @ ( comp @ X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',axassoc) ).
thf(f10,axiom,
( axidr
= ( ! [X0: subst] :
( ( comp @ X0 @ id )
= X0 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',axidr) ).
thf(f49,axiom,
( ! [X1: subst,X2: subst,X0: subst] :
( ( comp @ ( comp @ X0 @ X1 ) @ X2 )
= ( comp @ X0 @ ( comp @ X1 @ X2 ) ) )
& ! [X0: subst] :
( ( comp @ X0 @ id )
= X0 )
& ! [X0: subst] :
( ( ( comp @ id @ X0 )
= X0 )
= substmonoid ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',substmonoid) ).
thf(f50,axiom,
( ( substmonoid_gthm = axapp )
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> substmonoid ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',substmonoid_gthm) ).
thf(f114,conjecture,
substmonoid_gthm,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(f115,negated_conjecture,
~ substmonoid_gthm,
inference(negated_conjecture,[status(cth)],[f114]) ).
thf(f194,plain,
~ substmonoid_gthm,
inference(rectify,[],[f115]) ).
thf(f195,plain,
substmonoid_gthm != $true,
inference(fool_elimination,[],[f194]) ).
thf(f208,plain,
( axassoc
= ( ! [X0: subst,X1: subst,X2: subst] :
( ( comp @ ( comp @ X1 @ X2 ) @ X0 )
= ( comp @ X1 @ ( comp @ X2 @ X0 ) ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f209,plain,
( ( axassoc = $true )
<=> ! [X2: subst,X0: subst,X1: subst] :
( ( comp @ ( comp @ X1 @ X2 ) @ X0 )
= ( comp @ X1 @ ( comp @ X2 @ X0 ) ) ) ),
inference(fool_elimination,[],[f208]) ).
thf(f214,plain,
( ( axidr = $true )
<=> ! [X0: subst] :
( ( comp @ X0 @ id )
= X0 ) ),
inference(fool_elimination,[],[f10]) ).
thf(f222,plain,
( ! [X0: subst,X1: subst,X2: subst] :
( ( comp @ X2 @ ( comp @ X0 @ X1 ) )
= ( comp @ ( comp @ X2 @ X0 ) @ X1 ) )
& ! [X3: subst] :
( ( comp @ X3 @ id )
= X3 )
& ! [X4: subst] :
( ( ( comp @ id @ X4 )
= X4 )
= substmonoid ) ),
inference(rectify,[],[f49]) ).
thf(f223,plain,
( ( ! [X4: subst] :
( ( comp @ id @ X4 )
= X4 )
& ! [X3: subst] :
( ( comp @ X3 @ id )
= X3 )
& ! [X1: subst,X2: subst,X0: subst] :
( ( comp @ X2 @ ( comp @ X0 @ X1 ) )
= ( comp @ ( comp @ X2 @ X0 ) @ X1 ) ) )
<=> ( substmonoid = $true ) ),
inference(fool_elimination,[],[f222]) ).
thf(f295,plain,
( ( substmonoid_gthm = axapp )
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> substmonoid ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f50]) ).
thf(f296,plain,
( ( ( axapp = $true )
=> ( ( axvarcons = $true )
=> ( ( axvarid = $true )
=> ( ( axabs = $true )
=> ( ( axclos = $true )
=> ( ( axidl = $true )
=> ( ( axshiftcons = $true )
=> ( ( axassoc = $true )
=> ( ( axmap = $true )
=> ( ( axidr = $true )
=> ( ( axvarshift = $true )
=> ( ( axscons = $true )
=> ( ( ulamvar1 = $true )
=> ( ( ulamvarsh = $true )
=> ( ( ulamvarind = $true )
=> ( ( apinj1 = $true )
=> ( ( apinj2 = $true )
=> ( ( laminj = $true )
=> ( ( shinj = $true )
=> ( ( lamnotap = $true )
=> ( ( apnotvar = $true )
=> ( ( lamnotvar = $true )
=> ( ( induction = $true )
=> ( ( pushprop = $true )
=> ( ( induction2lem = $true )
=> ( ( induction2 = $true )
=> ( substmonoid = $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
<=> ( substmonoid_gthm = $true ) ),
inference(fool_elimination,[],[f295]) ).
thf(f300,plain,
( ( axidl = $true )
<=> ! [X0: subst] :
( ( comp @ id @ X0 )
= X0 ) ),
inference(fool_elimination,[],[f6]) ).
thf(f318,plain,
substmonoid_gthm != $true,
inference(flattening,[],[f195]) ).
thf(f319,plain,
( ( ( substmonoid = $true )
| ( induction2 != $true )
| ( induction2lem != $true )
| ( pushprop != $true )
| ( induction != $true )
| ( lamnotvar != $true )
| ( apnotvar != $true )
| ( lamnotap != $true )
| ( shinj != $true )
| ( laminj != $true )
| ( apinj2 != $true )
| ( apinj1 != $true )
| ( ulamvarind != $true )
| ( ulamvarsh != $true )
| ( ulamvar1 != $true )
| ( axscons != $true )
| ( axvarshift != $true )
| ( axidr != $true )
| ( axmap != $true )
| ( axassoc != $true )
| ( axshiftcons != $true )
| ( axidl != $true )
| ( axclos != $true )
| ( axabs != $true )
| ( axvarid != $true )
| ( axvarcons != $true )
| ( axapp != $true ) )
<=> ( substmonoid_gthm = $true ) ),
inference(ennf_transformation,[],[f296]) ).
thf(f320,plain,
( ( ( axabs != $true )
| ( lamnotap != $true )
| ( induction != $true )
| ( shinj != $true )
| ( lamnotvar != $true )
| ( apinj1 != $true )
| ( ulamvarind != $true )
| ( ulamvarsh != $true )
| ( axvarid != $true )
| ( induction2 != $true )
| ( axscons != $true )
| ( pushprop != $true )
| ( axclos != $true )
| ( axapp != $true )
| ( substmonoid = $true )
| ( axshiftcons != $true )
| ( axidl != $true )
| ( ulamvar1 != $true )
| ( apinj2 != $true )
| ( apnotvar != $true )
| ( axmap != $true )
| ( axvarcons != $true )
| ( induction2lem != $true )
| ( axassoc != $true )
| ( laminj != $true )
| ( axvarshift != $true )
| ( axidr != $true ) )
<=> ( substmonoid_gthm = $true ) ),
inference(flattening,[],[f319]) ).
thf(f321,plain,
( ( ( axidl = $true )
| ? [X0: subst] :
( ( comp @ id @ X0 )
!= X0 ) )
& ( ! [X0: subst] :
( ( comp @ id @ X0 )
= X0 )
| ( axidl != $true ) ) ),
inference(nnf_transformation,[],[f300]) ).
thf(f322,plain,
( ( ( axidl = $true )
| ? [X0: subst] :
( ( comp @ id @ X0 )
!= X0 ) )
& ( ! [X1: subst] :
( ( comp @ id @ X1 )
= X1 )
| ( axidl != $true ) ) ),
inference(rectify,[],[f321]) ).
thf(f323,plain,
( ( ( axidl = $true )
| ( ( comp @ id @ sK0 )
!= sK0 ) )
& ( ! [X1: subst] :
( ( comp @ id @ X1 )
= X1 )
| ( axidl != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f322]) ).
thf(f324,plain,
( ( ( axassoc = $true )
| ? [X2: subst,X0: subst,X1: subst] :
( ( comp @ ( comp @ X1 @ X2 ) @ X0 )
!= ( comp @ X1 @ ( comp @ X2 @ X0 ) ) ) )
& ( ! [X2: subst,X0: subst,X1: subst] :
( ( comp @ ( comp @ X1 @ X2 ) @ X0 )
= ( comp @ X1 @ ( comp @ X2 @ X0 ) ) )
| ( axassoc != $true ) ) ),
inference(nnf_transformation,[],[f209]) ).
thf(f325,plain,
( ( ( axassoc = $true )
| ? [X0: subst,X1: subst,X2: subst] :
( ( comp @ X2 @ ( comp @ X0 @ X1 ) )
!= ( comp @ ( comp @ X2 @ X0 ) @ X1 ) ) )
& ( ! [X3: subst,X4: subst,X5: subst] :
( ( comp @ X5 @ ( comp @ X3 @ X4 ) )
= ( comp @ ( comp @ X5 @ X3 ) @ X4 ) )
| ( axassoc != $true ) ) ),
inference(rectify,[],[f324]) ).
thf(f326,plain,
( ( ( axassoc = $true )
| ( ( comp @ sK3 @ ( comp @ sK1 @ sK2 ) )
!= ( comp @ ( comp @ sK3 @ sK1 ) @ sK2 ) ) )
& ( ! [X3: subst,X4: subst,X5: subst] :
( ( comp @ X5 @ ( comp @ X3 @ X4 ) )
= ( comp @ ( comp @ X5 @ X3 ) @ X4 ) )
| ( axassoc != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3)],[f325]) ).
thf(f327,plain,
( ( ( ! [X4: subst] :
( ( comp @ id @ X4 )
= X4 )
& ! [X3: subst] :
( ( comp @ X3 @ id )
= X3 )
& ! [X1: subst,X2: subst,X0: subst] :
( ( comp @ X2 @ ( comp @ X0 @ X1 ) )
= ( comp @ ( comp @ X2 @ X0 ) @ X1 ) ) )
| ( substmonoid != $true ) )
& ( ( substmonoid = $true )
| ? [X4: subst] :
( ( comp @ id @ X4 )
!= X4 )
| ? [X3: subst] :
( ( comp @ X3 @ id )
!= X3 )
| ? [X1: subst,X2: subst,X0: subst] :
( ( comp @ X2 @ ( comp @ X0 @ X1 ) )
!= ( comp @ ( comp @ X2 @ X0 ) @ X1 ) ) ) ),
inference(nnf_transformation,[],[f223]) ).
thf(f328,plain,
( ( ( ! [X4: subst] :
( ( comp @ id @ X4 )
= X4 )
& ! [X3: subst] :
( ( comp @ X3 @ id )
= X3 )
& ! [X1: subst,X2: subst,X0: subst] :
( ( comp @ X2 @ ( comp @ X0 @ X1 ) )
= ( comp @ ( comp @ X2 @ X0 ) @ X1 ) ) )
| ( substmonoid != $true ) )
& ( ( substmonoid = $true )
| ? [X4: subst] :
( ( comp @ id @ X4 )
!= X4 )
| ? [X3: subst] :
( ( comp @ X3 @ id )
!= X3 )
| ? [X1: subst,X2: subst,X0: subst] :
( ( comp @ X2 @ ( comp @ X0 @ X1 ) )
!= ( comp @ ( comp @ X2 @ X0 ) @ X1 ) ) ) ),
inference(flattening,[],[f327]) ).
thf(f329,plain,
( ( ( ! [X0: subst] :
( ( comp @ id @ X0 )
= X0 )
& ! [X1: subst] :
( ( comp @ X1 @ id )
= X1 )
& ! [X2: subst,X3: subst,X4: subst] :
( ( comp @ ( comp @ X3 @ X4 ) @ X2 )
= ( comp @ X3 @ ( comp @ X4 @ X2 ) ) ) )
| ( substmonoid != $true ) )
& ( ( substmonoid = $true )
| ? [X5: subst] :
( ( comp @ id @ X5 )
!= X5 )
| ? [X6: subst] :
( ( comp @ X6 @ id )
!= X6 )
| ? [X7: subst,X8: subst,X9: subst] :
( ( comp @ X8 @ ( comp @ X9 @ X7 ) )
!= ( comp @ ( comp @ X8 @ X9 ) @ X7 ) ) ) ),
inference(rectify,[],[f328]) ).
thf(f330,plain,
( ( ( ! [X0: subst] :
( ( comp @ id @ X0 )
= X0 )
& ! [X1: subst] :
( ( comp @ X1 @ id )
= X1 )
& ! [X2: subst,X3: subst,X4: subst] :
( ( comp @ ( comp @ X3 @ X4 ) @ X2 )
= ( comp @ X3 @ ( comp @ X4 @ X2 ) ) ) )
| ( substmonoid != $true ) )
& ( ( substmonoid = $true )
| ( sK4
!= ( comp @ id @ sK4 ) )
| ( sK5
!= ( comp @ sK5 @ id ) )
| ( ( comp @ sK7 @ ( comp @ sK8 @ sK6 ) )
!= ( comp @ ( comp @ sK7 @ sK8 ) @ sK6 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7,sK8]),skolemize(X5,sK4),skolemize(X6,sK5),skolemize(X7,sK6),skolemize(X8,sK7),skolemize(X9,sK8)],[f329]) ).
thf(f331,plain,
( ( ( axidr = $true )
| ? [X0: subst] :
( ( comp @ X0 @ id )
!= X0 ) )
& ( ! [X0: subst] :
( ( comp @ X0 @ id )
= X0 )
| ( axidr != $true ) ) ),
inference(nnf_transformation,[],[f214]) ).
thf(f332,plain,
( ( ( axidr = $true )
| ? [X0: subst] :
( ( comp @ X0 @ id )
!= X0 ) )
& ( ! [X1: subst] :
( ( comp @ X1 @ id )
= X1 )
| ( axidr != $true ) ) ),
inference(rectify,[],[f331]) ).
thf(f333,plain,
( ( ( axidr = $true )
| ( sK9
!= ( comp @ sK9 @ id ) ) )
& ( ! [X1: subst] :
( ( comp @ X1 @ id )
= X1 )
| ( axidr != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X0,sK9)],[f332]) ).
thf(f337,plain,
( ( ( axabs != $true )
| ( lamnotap != $true )
| ( induction != $true )
| ( shinj != $true )
| ( lamnotvar != $true )
| ( apinj1 != $true )
| ( ulamvarind != $true )
| ( ulamvarsh != $true )
| ( axvarid != $true )
| ( induction2 != $true )
| ( axscons != $true )
| ( pushprop != $true )
| ( axclos != $true )
| ( axapp != $true )
| ( substmonoid = $true )
| ( axshiftcons != $true )
| ( axidl != $true )
| ( ulamvar1 != $true )
| ( apinj2 != $true )
| ( apnotvar != $true )
| ( axmap != $true )
| ( axvarcons != $true )
| ( induction2lem != $true )
| ( axassoc != $true )
| ( laminj != $true )
| ( axvarshift != $true )
| ( axidr != $true )
| ( substmonoid_gthm != $true ) )
& ( ( substmonoid_gthm = $true )
| ( ( axabs = $true )
& ( lamnotap = $true )
& ( induction = $true )
& ( shinj = $true )
& ( lamnotvar = $true )
& ( apinj1 = $true )
& ( ulamvarind = $true )
& ( ulamvarsh = $true )
& ( axvarid = $true )
& ( induction2 = $true )
& ( axscons = $true )
& ( pushprop = $true )
& ( axclos = $true )
& ( axapp = $true )
& ( substmonoid != $true )
& ( axshiftcons = $true )
& ( axidl = $true )
& ( ulamvar1 = $true )
& ( apinj2 = $true )
& ( apnotvar = $true )
& ( axmap = $true )
& ( axvarcons = $true )
& ( induction2lem = $true )
& ( axassoc = $true )
& ( laminj = $true )
& ( axvarshift = $true )
& ( axidr = $true ) ) ) ),
inference(nnf_transformation,[],[f320]) ).
thf(f338,plain,
( ( ( axabs != $true )
| ( lamnotap != $true )
| ( induction != $true )
| ( shinj != $true )
| ( lamnotvar != $true )
| ( apinj1 != $true )
| ( ulamvarind != $true )
| ( ulamvarsh != $true )
| ( axvarid != $true )
| ( induction2 != $true )
| ( axscons != $true )
| ( pushprop != $true )
| ( axclos != $true )
| ( axapp != $true )
| ( substmonoid = $true )
| ( axshiftcons != $true )
| ( axidl != $true )
| ( ulamvar1 != $true )
| ( apinj2 != $true )
| ( apnotvar != $true )
| ( axmap != $true )
| ( axvarcons != $true )
| ( induction2lem != $true )
| ( axassoc != $true )
| ( laminj != $true )
| ( axvarshift != $true )
| ( axidr != $true )
| ( substmonoid_gthm != $true ) )
& ( ( substmonoid_gthm = $true )
| ( ( axabs = $true )
& ( lamnotap = $true )
& ( induction = $true )
& ( shinj = $true )
& ( lamnotvar = $true )
& ( apinj1 = $true )
& ( ulamvarind = $true )
& ( ulamvarsh = $true )
& ( axvarid = $true )
& ( induction2 = $true )
& ( axscons = $true )
& ( pushprop = $true )
& ( axclos = $true )
& ( axapp = $true )
& ( substmonoid != $true )
& ( axshiftcons = $true )
& ( axidl = $true )
& ( ulamvar1 = $true )
& ( apinj2 = $true )
& ( apnotvar = $true )
& ( axmap = $true )
& ( axvarcons = $true )
& ( induction2lem = $true )
& ( axassoc = $true )
& ( laminj = $true )
& ( axvarshift = $true )
& ( axidr = $true ) ) ) ),
inference(flattening,[],[f337]) ).
thf(f342,plain,
! [X1: subst] :
( ( ( comp @ id @ X1 )
= X1 )
| ( axidl != $true ) ),
inference(cnf_transformation,[],[f323]) ).
thf(f344,plain,
! [X3: subst,X4: subst,X5: subst] :
( ( ( comp @ X5 @ ( comp @ X3 @ X4 ) )
= ( comp @ ( comp @ X5 @ X3 ) @ X4 ) )
| ( axassoc != $true ) ),
inference(cnf_transformation,[],[f326]) ).
thf(f346,plain,
( ( sK5
!= ( comp @ sK5 @ id ) )
| ( substmonoid = $true )
| ( ( comp @ sK7 @ ( comp @ sK8 @ sK6 ) )
!= ( comp @ ( comp @ sK7 @ sK8 ) @ sK6 ) )
| ( sK4
!= ( comp @ id @ sK4 ) ) ),
inference(cnf_transformation,[],[f330]) ).
thf(f350,plain,
! [X1: subst] :
( ( ( comp @ X1 @ id )
= X1 )
| ( axidr != $true ) ),
inference(cnf_transformation,[],[f333]) ).
thf(f352,plain,
substmonoid_gthm != $true,
inference(cnf_transformation,[],[f318]) ).
thf(f355,plain,
( ( axidr = $true )
| ( substmonoid_gthm = $true ) ),
inference(cnf_transformation,[],[f338]) ).
thf(f358,plain,
( ( axassoc = $true )
| ( substmonoid_gthm = $true ) ),
inference(cnf_transformation,[],[f338]) ).
thf(f365,plain,
( ( axidl = $true )
| ( substmonoid_gthm = $true ) ),
inference(cnf_transformation,[],[f338]) ).
thf(f367,plain,
( ( substmonoid_gthm = $true )
| ( substmonoid != $true ) ),
inference(cnf_transformation,[],[f338]) ).
thf(f388,definition,
( spl14_1
<=> ( axassoc = $true ) ),
introduced(definition,[new_symbols(definition,[spl14_1])],[avatar_definition]) ).
thf(f392,definition,
( spl14_2
<=> ! [X4: subst,X5: subst,X3: subst] :
( ( comp @ X5 @ ( comp @ X3 @ X4 ) )
= ( comp @ ( comp @ X5 @ X3 ) @ X4 ) ) ),
introduced(definition,[new_symbols(definition,[spl14_2])],[avatar_definition]) ).
thf(f393,plain,
( ! [X3: subst,X4: subst,X5: subst] :
( ( comp @ X5 @ ( comp @ X3 @ X4 ) )
= ( comp @ ( comp @ X5 @ X3 ) @ X4 ) )
| ~ spl14_2 ),
inference(avatar_component_clause,[],[f392]) ).
thf(f394,plain,
( ~ spl14_1
| spl14_2 ),
inference(avatar_split_clause,[],[f344,f392,f388]) ).
thf(f409,definition,
( spl14_6
<=> ( substmonoid_gthm = $true ) ),
introduced(definition,[new_symbols(definition,[spl14_6])],[avatar_definition]) ).
thf(f439,definition,
( spl14_12
<=> ! [X1: subst] :
( ( comp @ X1 @ id )
= X1 ) ),
introduced(definition,[new_symbols(definition,[spl14_12])],[avatar_definition]) ).
thf(f440,plain,
( ! [X1: subst] :
( ( comp @ X1 @ id )
= X1 )
| ~ spl14_12 ),
inference(avatar_component_clause,[],[f439]) ).
thf(f442,definition,
( spl14_13
<=> ( substmonoid = $true ) ),
introduced(definition,[new_symbols(definition,[spl14_13])],[avatar_definition]) ).
thf(f451,definition,
( spl14_15
<=> ( axidl = $true ) ),
introduced(definition,[new_symbols(definition,[spl14_15])],[avatar_definition]) ).
thf(f456,definition,
( spl14_16
<=> ( axidr = $true ) ),
introduced(definition,[new_symbols(definition,[spl14_16])],[avatar_definition]) ).
thf(f459,plain,
( spl14_12
| ~ spl14_16 ),
inference(avatar_split_clause,[],[f350,f456,f439]) ).
thf(f468,plain,
( spl14_6
| spl14_16 ),
inference(avatar_split_clause,[],[f355,f456,f409]) ).
thf(f470,definition,
( spl14_19
<=> ( sK4
= ( comp @ id @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl14_19])],[avatar_definition]) ).
thf(f472,plain,
( ( sK4
!= ( comp @ id @ sK4 ) )
| spl14_19 ),
inference(avatar_component_clause,[],[f470]) ).
thf(f474,definition,
( spl14_20
<=> ( ( comp @ sK7 @ ( comp @ sK8 @ sK6 ) )
= ( comp @ ( comp @ sK7 @ sK8 ) @ sK6 ) ) ),
introduced(definition,[new_symbols(definition,[spl14_20])],[avatar_definition]) ).
thf(f476,plain,
( ( ( comp @ sK7 @ ( comp @ sK8 @ sK6 ) )
!= ( comp @ ( comp @ sK7 @ sK8 ) @ sK6 ) )
| spl14_20 ),
inference(avatar_component_clause,[],[f474]) ).
thf(f478,definition,
( spl14_21
<=> ( sK5
= ( comp @ sK5 @ id ) ) ),
introduced(definition,[new_symbols(definition,[spl14_21])],[avatar_definition]) ).
thf(f480,plain,
( ( sK5
!= ( comp @ sK5 @ id ) )
| spl14_21 ),
inference(avatar_component_clause,[],[f478]) ).
thf(f481,plain,
( spl14_13
| ~ spl14_19
| ~ spl14_20
| ~ spl14_21 ),
inference(avatar_split_clause,[],[f346,f478,f474,f470,f442]) ).
thf(f508,plain,
( spl14_15
| spl14_6 ),
inference(avatar_split_clause,[],[f365,f409,f451]) ).
thf(f509,plain,
~ spl14_6,
inference(avatar_split_clause,[],[f352,f409]) ).
thf(f510,plain,
( spl14_1
| spl14_6 ),
inference(avatar_split_clause,[],[f358,f409,f388]) ).
thf(f522,definition,
( spl14_29
<=> ! [X1: subst] :
( ( comp @ id @ X1 )
= X1 ) ),
introduced(definition,[new_symbols(definition,[spl14_29])],[avatar_definition]) ).
thf(f523,plain,
( ! [X1: subst] :
( ( comp @ id @ X1 )
= X1 )
| ~ spl14_29 ),
inference(avatar_component_clause,[],[f522]) ).
thf(f524,plain,
( spl14_29
| ~ spl14_15 ),
inference(avatar_split_clause,[],[f342,f451,f522]) ).
thf(f556,plain,
( ~ spl14_13
| spl14_6 ),
inference(avatar_split_clause,[],[f367,f409,f442]) ).
thf(f589,plain,
( ( ( comp @ sK7 @ ( comp @ sK8 @ sK6 ) )
!= ( comp @ sK7 @ ( comp @ sK8 @ sK6 ) ) )
| ~ spl14_2
| spl14_20 ),
inference(backward_demodulation,[],[f476,f393]) ).
thf(f590,plain,
( $false
| ~ spl14_2
| spl14_20 ),
inference(trivial_inequality_removal,[],[f589]) ).
thf(f591,plain,
( ~ spl14_2
| spl14_20 ),
inference(avatar_contradiction_clause,[],[f590]) ).
thf(f599,plain,
( ( sK4 != sK4 )
| spl14_19
| ~ spl14_29 ),
inference(backward_demodulation,[],[f472,f523]) ).
thf(f602,plain,
( $false
| spl14_19
| ~ spl14_29 ),
inference(trivial_inequality_removal,[],[f599]) ).
thf(f603,plain,
( spl14_19
| ~ spl14_29 ),
inference(avatar_contradiction_clause,[],[f602]) ).
thf(f604,plain,
( ( sK5 != sK5 )
| ~ spl14_12
| spl14_21 ),
inference(backward_demodulation,[],[f480,f440]) ).
thf(f606,plain,
( $false
| ~ spl14_12
| spl14_21 ),
inference(trivial_inequality_removal,[],[f604]) ).
thf(f607,plain,
( ~ spl14_12
| spl14_21 ),
inference(avatar_contradiction_clause,[],[f606]) ).
cnf(s1,plain,
( ~ spl14_1
| spl14_2 ),
inference(sat_conversion,[],[f394]) ).
cnf(s11,plain,
( spl14_12
| ~ spl14_16 ),
inference(sat_conversion,[],[f459]) ).
cnf(s13,plain,
( spl14_6
| spl14_16 ),
inference(sat_conversion,[],[f468]) ).
cnf(s14,plain,
( spl14_13
| ~ spl14_19
| ~ spl14_20
| ~ spl14_21 ),
inference(sat_conversion,[],[f481]) ).
cnf(s21,plain,
( spl14_6
| spl14_15 ),
inference(sat_conversion,[],[f508]) ).
cnf(s22,plain,
~ spl14_6,
inference(sat_conversion,[],[f509]) ).
cnf(s23,plain,
( spl14_1
| spl14_6 ),
inference(sat_conversion,[],[f510]) ).
cnf(s26,plain,
( ~ spl14_15
| spl14_29 ),
inference(sat_conversion,[],[f524]) ).
cnf(s34,plain,
( spl14_6
| ~ spl14_13 ),
inference(sat_conversion,[],[f556]) ).
cnf(s44,plain,
( ~ spl14_2
| spl14_20 ),
inference(sat_conversion,[],[f591]) ).
cnf(s48,plain,
( spl14_19
| ~ spl14_29 ),
inference(sat_conversion,[],[f603]) ).
cnf(s49,plain,
( ~ spl14_12
| spl14_21 ),
inference(sat_conversion,[],[f607]) ).
cnf(s57,plain,
~ spl14_13,
inference(rat,[],[s34,s22]) ).
cnf(s64,plain,
spl14_1,
inference(rat,[],[s23,s22]) ).
cnf(s65,plain,
spl14_15,
inference(rat,[],[s21,s22]) ).
cnf(s66,plain,
spl14_29,
inference(rat,[],[s26,s65]) ).
cnf(s67,plain,
spl14_19,
inference(rat,[],[s48,s66]) ).
cnf(s77,plain,
( ~ spl14_20
| ~ spl14_21 ),
inference(rat,[],[s14,s67,s57]) ).
cnf(s78,plain,
spl14_16,
inference(rat,[],[s13,s22]) ).
cnf(s81,plain,
spl14_12,
inference(rat,[],[s11,s78]) ).
cnf(s83,plain,
spl14_21,
inference(rat,[],[s49,s81]) ).
cnf(s84,plain,
~ spl14_20,
inference(rat,[],[s77,s83]) ).
cnf(s85,plain,
~ spl14_2,
inference(rat,[],[s44,s84]) ).
cnf(s92,plain,
$false,
inference(rat,[],[s1,s85,s64]) ).
thf(f612,plain,
$false,
inference(avatar_sat_refutation,[],[s92]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG254^1 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n013.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 17:32:06 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 Running higher-order theorem proving
% 0.09/0.24 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.68/0.38 % (2415659)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.68/0.38 % (2415666)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3464890814:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.68/0.38 % (2415666)Instruction limit reached!
% 0.68/0.38 % (2415666)------------------------------
% 0.68/0.38 % (2415666)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.38 % (2415666)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.38 % (2415666)CaDiCaL version: 2.1.3
% 0.68/0.38 % (2415666)Termination reason: Instruction limit
% 0.68/0.38 % (2415666)Termination phase: shuffling
% 0.68/0.38 % (2415666)Time elapsed: 0.001 s
% 0.68/0.38 % (2415666)Peak memory usage: 10 MB
% 0.68/0.38 % (2415666)Instructions burned: 4 (million)
% 0.68/0.38 % (2415665)lrs+10_16_si=on:nwc=1.5:random_seed=447252586:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.68/0.38 % (2415664)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3453717259:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.68/0.38 % (2415667)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=1743187734:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.68/0.38 % (2415672)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1024061766:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.68/0.38 % (2415672)Instruction limit reached!
% 0.68/0.38 % (2415672)------------------------------
% 0.68/0.38 % (2415672)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.38 % (2415672)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.38 % (2415672)CaDiCaL version: 2.1.3
% 0.68/0.38 % (2415672)Termination reason: Instruction limit
% 0.68/0.38 % (2415672)Termination phase: shuffling
% 0.68/0.38 % (2415672)Time elapsed: 0.001 s
% 0.68/0.38 % (2415672)Peak memory usage: 10 MB
% 0.68/0.38 % (2415672)Instructions burned: 3 (million)
% 0.68/0.38 % (2415670)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.68/0.38 % (2415670)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.68/0.38 % (2415665)Instruction limit reached!
% 0.68/0.38 % (2415665)------------------------------
% 0.68/0.38 % (2415665)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.38 % (2415665)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.38 % (2415665)CaDiCaL version: 2.1.3
% 0.68/0.38 % (2415665)Termination reason: Instruction limit
% 0.68/0.38 % (2415665)Termination phase: shuffling
% 0.68/0.38 % (2415665)Time elapsed: 0.009 s
% 0.68/0.38 % (2415665)Peak memory usage: 10 MB
% 0.68/0.38 % (2415665)Instructions burned: 20 (million)
% 0.68/0.38 % (2415669)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2471678821:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.68/0.38 % (2415670)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=291861861:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.68/0.38 % (2415677)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2698044159:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.68/0.38 % (2415668)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=4067476161:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.68/0.38 % (2415677)Instruction limit reached!
% 0.68/0.38 % (2415677)------------------------------
% 0.68/0.38 % (2415677)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.38 % (2415677)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.38 % (2415677)CaDiCaL version: 2.1.3
% 0.68/0.38 % (2415677)Termination reason: Instruction limit
% 0.68/0.38 % (2415677)Termination phase: shuffling
% 0.68/0.38 % (2415677)Time elapsed: 0.001 s
% 0.68/0.38 % (2415677)Peak memory usage: 10 MB
% 0.68/0.38 % (2415677)Instructions burned: 6 (million)
% 0.68/0.38 % (2415678)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.68/0.38 % (2415678)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1352717505:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.68/0.38 % (2415682)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=3358531927:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.68/0.38 % (2415678)Instruction limit reached!
% 0.68/0.38 % (2415678)------------------------------
% 0.68/0.38 % (2415678)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.38 % (2415678)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.38 % (2415678)CaDiCaL version: 2.1.3
% 0.68/0.38 % (2415678)Termination reason: Instruction limit
% 0.68/0.38 % (2415678)Termination phase: shuffling
% 0.68/0.38 % (2415678)Time elapsed: 0.003 s
% 0.68/0.38 % (2415678)Peak memory usage: 10 MB
% 0.68/0.38 % (2415678)Instructions burned: 7 (million)
% 0.68/0.38 % (2415682)Instruction limit reached!
% 0.68/0.38 % (2415682)------------------------------
% 0.68/0.38 % (2415682)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.38 % (2415682)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.38 % (2415682)CaDiCaL version: 2.1.3
% 0.68/0.38 % (2415682)Termination reason: Instruction limit
% 0.68/0.38 % (2415682)Termination phase: shuffling
% 0.68/0.38 % (2415682)Time elapsed: 0.003 s
% 0.68/0.38 % (2415682)Peak memory usage: 10 MB
% 0.68/0.38 % (2415682)Instructions burned: 13 (million)
% 0.68/0.38 % (2415664)Instruction limit reached!
% 0.68/0.38 % (2415664)------------------------------
% 0.68/0.38 % (2415664)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.38 % (2415664)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.38 % (2415664)CaDiCaL version: 2.1.3
% 0.68/0.38 % (2415664)Termination reason: Instruction limit
% 0.68/0.38 % (2415664)Termination phase: Function definition elimination
% 0.68/0.38 % (2415664)Time elapsed: 0.039 s
% 0.68/0.38 % (2415664)Peak memory usage: 12 MB
% 0.68/0.38 % (2415664)Instructions burned: 87 (million)
% 0.68/0.38 % (2415668)Instruction limit reached!
% 0.68/0.38 % (2415668)------------------------------
% 0.68/0.38 % (2415668)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.38 % (2415668)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.38 % (2415668)CaDiCaL version: 2.1.3
% 0.68/0.38 % (2415668)Termination reason: Instruction limit
% 0.68/0.38 % (2415668)Termination phase: Naming
% 0.68/0.38 % (2415668)Time elapsed: 0.024 s
% 0.68/0.38 % (2415668)Peak memory usage: 11 MB
% 0.68/0.38 % (2415668)Instructions burned: 25 (million)
% 0.68/0.38 % (2415687)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=4272185061:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.68/0.38 % (2415686)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.68/0.38 % (2415686)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.68/0.38 % (2415687)Instruction limit reached!
% 0.68/0.38 % (2415687)------------------------------
% 0.68/0.38 % (2415687)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.38 % (2415687)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.38 % (2415687)CaDiCaL version: 2.1.3
% 0.68/0.38 % (2415687)Termination reason: Instruction limit
% 0.68/0.38 % (2415687)Termination phase: Saturation
% 0.68/0.38 % (2415687)Time elapsed: 0.019 s
% 0.68/0.38 % (2415687)Peak memory usage: 12 MB
% 0.68/0.38 % (2415687)Instructions burned: 90 (million)
% 0.68/0.38 % (2415686)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3947352279:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.68/0.38 % (2415691)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=2452737674:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 0.68/0.38 % (2415690)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.68/0.38 % (2415688)lrs+10_1_si=on:cs=on:random_seed=1095097952:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.68/0.38 % (2415669)Instruction limit reached!
% 0.68/0.38 % (2415669)------------------------------
% 0.68/0.38 % (2415669)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.38 % (2415669)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.38 % (2415669)CaDiCaL version: 2.1.3
% 0.68/0.38 % (2415669)Termination reason: Instruction limit
% 0.68/0.38 % (2415669)Termination phase: Property scanning
% 0.68/0.38 % (2415669)Time elapsed: 0.064 s
% 0.68/0.38 % (2415669)Peak memory usage: 12 MB
% 0.68/0.38 % (2415669)Instructions burned: 76 (million)
% 0.68/0.38 % (2415690)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=1085701174:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.68/0.38 % (2415690)Instruction limit reached!
% 0.68/0.38 % (2415690)------------------------------
% 0.68/0.38 % (2415690)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.38 % (2415690)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.38 % (2415690)CaDiCaL version: 2.1.3
% 0.68/0.38 % (2415690)Termination reason: Instruction limit
% 0.68/0.38 % (2415690)Termination phase: shuffling
% 0.68/0.38 % (2415690)Time elapsed: 0.001 s
% 0.68/0.38 % (2415690)Peak memory usage: 10 MB
% 0.68/0.38 % (2415690)Instructions burned: 2 (million)
% 0.68/0.38 % (2415691) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2415659-2415691"...
% 0.68/0.38 % (2415691)...printing done.
% 0.68/0.38 % (2415688)Instruction limit reached!
% 0.68/0.38 % (2415688)------------------------------
% 0.68/0.38 % (2415688)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.38 % (2415691)Refutation found. Thanks to Tanya!
% 0.68/0.38 % SZS status Theorem for theBenchmark
% 0.68/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.68/0.38 % (2415691)------------------------------
% 0.68/0.38 % (2415691)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.38 % (2415691)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.38 % (2415691)CaDiCaL version: 2.1.3
% 0.68/0.38 % (2415691)Termination reason: Refutation
% 0.68/0.38 % (2415691)Time elapsed: 0.009 s
% 0.68/0.38 % (2415691)Peak memory usage: 13 MB
% 0.68/0.38 % (2415691)Instructions burned: 34 (million)
% 0.68/0.38 % (2415659)Success in time 0.127 s
% 0.68/0.38 % Vampire exiting
%------------------------------------------------------------------------------