%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG254^2 : 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 : n011.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 0.61s 0.39s
% Output : Refutation 0.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 17
% Syntax : Number of formulae : 103 ( 24 unt; 0 typ; 11 def)
% Number of atoms : 455 ( 172 equ; 0 cnn)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 582 ( 100 ~; 104 |; 35 &; 316 @)
% ( 18 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 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_123,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_124,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_125,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_128,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_129,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_130,type,
vIFF: $o > $o > $o ).
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: term ).
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: term ).
thf(func_def_144,type,
sK11: subst ).
thf(func_def_145,type,
sK12: subst ).
thf(func_def_146,type,
sK13: subst ).
thf(f6,axiom,
( axidl
= ( ! [X0: subst] :
( ( comp @ id @ X0 )
= X0 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',axidl) ).
thf(f8,axiom,
( axassoc
= ( ! [X0: subst,X2: 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,
! [X0: subst] :
( ( ( comp @ X0 @ id )
= X0 )
= axidr ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',axidr) ).
thf(f49,axiom,
( ! [X2: subst,X1: 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(f51,axiom,
( axidl
=> ( ( axassoc
=> ( axidr
=> substmonoid ) )
= substmonoid_lthm ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',substmonoid_lthm) ).
thf(f114,conjecture,
substmonoid_lthm,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(f115,negated_conjecture,
~ substmonoid_lthm,
inference(negated_conjecture,[status(cth)],[f114]) ).
thf(f141,plain,
( ! [X0: subst] :
( ( comp @ X0 @ id )
= X0 )
<=> ( axidr = $true ) ),
inference(fool_elimination,[],[f10]) ).
thf(f146,plain,
( axassoc
= ( ! [X0: subst,X1: subst,X2: subst] :
( ( comp @ ( comp @ X0 @ X2 ) @ X1 )
= ( comp @ X0 @ ( comp @ X2 @ X1 ) ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f147,plain,
( ( axassoc = $true )
<=> ! [X2: subst,X0: subst,X1: subst] :
( ( comp @ ( comp @ X0 @ X2 ) @ X1 )
= ( comp @ X0 @ ( comp @ X2 @ X1 ) ) ) ),
inference(fool_elimination,[],[f146]) ).
thf(f151,plain,
~ substmonoid_lthm,
inference(rectify,[],[f115]) ).
thf(f152,plain,
substmonoid_lthm != $true,
inference(fool_elimination,[],[f151]) ).
thf(f167,plain,
( axidl
=> ( ( axassoc
=> ( axidr
=> substmonoid ) )
= substmonoid_lthm ) ),
inference(rectify,[],[f51]) ).
thf(f168,plain,
( ( substmonoid_lthm = $true )
<=> ( ( axidl = $true )
=> ( ( axassoc = $true )
=> ( ( axidr = $true )
=> ( substmonoid = $true ) ) ) ) ),
inference(fool_elimination,[],[f167]) ).
thf(f265,plain,
( ( axidl = $true )
<=> ! [X0: subst] :
( ( comp @ id @ X0 )
= X0 ) ),
inference(fool_elimination,[],[f6]) ).
thf(f305,plain,
( ! [X0: subst,X1: subst,X2: subst] :
( ( comp @ ( comp @ X2 @ X1 ) @ X0 )
= ( comp @ X2 @ ( comp @ X1 @ X0 ) ) )
& ! [X3: subst] :
( ( comp @ X3 @ id )
= X3 )
& ! [X4: subst] :
( ( ( comp @ id @ X4 )
= X4 )
= substmonoid ) ),
inference(rectify,[],[f49]) ).
thf(f306,plain,
( ( substmonoid = $true )
<=> ( ! [X0: subst,X1: subst,X2: subst] :
( ( comp @ ( comp @ X2 @ X1 ) @ X0 )
= ( comp @ X2 @ ( comp @ X1 @ X0 ) ) )
& ! [X4: subst] :
( ( comp @ id @ X4 )
= X4 )
& ! [X3: subst] :
( ( comp @ X3 @ id )
= X3 ) ) ),
inference(fool_elimination,[],[f305]) ).
thf(f317,plain,
substmonoid_lthm != $true,
inference(flattening,[],[f152]) ).
thf(f318,plain,
( ( substmonoid_lthm = $true )
<=> ( ( substmonoid = $true )
| ( axidr != $true )
| ( axassoc != $true )
| ( axidl != $true ) ) ),
inference(ennf_transformation,[],[f168]) ).
thf(f319,plain,
( ( ( axidr != $true )
| ( substmonoid = $true )
| ( axidl != $true )
| ( axassoc != $true ) )
<=> ( substmonoid_lthm = $true ) ),
inference(flattening,[],[f318]) ).
thf(f320,plain,
( ( ! [X0: subst] :
( ( comp @ X0 @ id )
= X0 )
| ( axidr != $true ) )
& ( ( axidr = $true )
| ? [X0: subst] :
( ( comp @ X0 @ id )
!= X0 ) ) ),
inference(nnf_transformation,[],[f141]) ).
thf(f321,plain,
( ( ! [X0: subst] :
( ( comp @ X0 @ id )
= X0 )
| ( axidr != $true ) )
& ( ( axidr = $true )
| ? [X1: subst] :
( ( comp @ X1 @ id )
!= X1 ) ) ),
inference(rectify,[],[f320]) ).
thf(f322,plain,
( ( ! [X0: subst] :
( ( comp @ X0 @ id )
= X0 )
| ( axidr != $true ) )
& ( ( axidr = $true )
| ( sK0
!= ( comp @ sK0 @ id ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0)],[f321]) ).
thf(f323,plain,
( ( ( axidr != $true )
| ( substmonoid = $true )
| ( axidl != $true )
| ( axassoc != $true )
| ( substmonoid_lthm != $true ) )
& ( ( substmonoid_lthm = $true )
| ( ( axidr = $true )
& ( substmonoid != $true )
& ( axidl = $true )
& ( axassoc = $true ) ) ) ),
inference(nnf_transformation,[],[f319]) ).
thf(f324,plain,
( ( ( axidr != $true )
| ( substmonoid = $true )
| ( axidl != $true )
| ( axassoc != $true )
| ( substmonoid_lthm != $true ) )
& ( ( substmonoid_lthm = $true )
| ( ( axidr = $true )
& ( substmonoid != $true )
& ( axidl = $true )
& ( axassoc = $true ) ) ) ),
inference(flattening,[],[f323]) ).
thf(f328,plain,
( ( ( substmonoid = $true )
| ? [X0: subst,X1: subst,X2: subst] :
( ( comp @ ( comp @ X2 @ X1 ) @ X0 )
!= ( comp @ X2 @ ( comp @ X1 @ X0 ) ) )
| ? [X4: subst] :
( ( comp @ id @ X4 )
!= X4 )
| ? [X3: subst] :
( ( comp @ X3 @ id )
!= X3 ) )
& ( ( ! [X0: subst,X1: subst,X2: subst] :
( ( comp @ ( comp @ X2 @ X1 ) @ X0 )
= ( comp @ X2 @ ( comp @ X1 @ X0 ) ) )
& ! [X4: subst] :
( ( comp @ id @ X4 )
= X4 )
& ! [X3: subst] :
( ( comp @ X3 @ id )
= X3 ) )
| ( substmonoid != $true ) ) ),
inference(nnf_transformation,[],[f306]) ).
thf(f329,plain,
( ( ( substmonoid = $true )
| ? [X0: subst,X1: subst,X2: subst] :
( ( comp @ ( comp @ X2 @ X1 ) @ X0 )
!= ( comp @ X2 @ ( comp @ X1 @ X0 ) ) )
| ? [X4: subst] :
( ( comp @ id @ X4 )
!= X4 )
| ? [X3: subst] :
( ( comp @ X3 @ id )
!= X3 ) )
& ( ( ! [X0: subst,X1: subst,X2: subst] :
( ( comp @ ( comp @ X2 @ X1 ) @ X0 )
= ( comp @ X2 @ ( comp @ X1 @ X0 ) ) )
& ! [X4: subst] :
( ( comp @ id @ X4 )
= X4 )
& ! [X3: subst] :
( ( comp @ X3 @ id )
= X3 ) )
| ( substmonoid != $true ) ) ),
inference(flattening,[],[f328]) ).
thf(f330,plain,
( ( ( substmonoid = $true )
| ? [X0: subst,X1: subst,X2: subst] :
( ( comp @ ( comp @ X2 @ X1 ) @ X0 )
!= ( comp @ X2 @ ( comp @ X1 @ X0 ) ) )
| ? [X3: subst] :
( ( comp @ id @ X3 )
!= X3 )
| ? [X4: subst] :
( ( comp @ X4 @ id )
!= X4 ) )
& ( ( ! [X5: subst,X6: subst,X7: subst] :
( ( comp @ X7 @ ( comp @ X6 @ X5 ) )
= ( comp @ ( comp @ X7 @ X6 ) @ X5 ) )
& ! [X8: subst] :
( ( comp @ id @ X8 )
= X8 )
& ! [X9: subst] :
( ( comp @ X9 @ id )
= X9 ) )
| ( substmonoid != $true ) ) ),
inference(rectify,[],[f329]) ).
thf(f331,plain,
( ( ( substmonoid = $true )
| ( ( comp @ ( comp @ sK6 @ sK5 ) @ sK4 )
!= ( comp @ sK6 @ ( comp @ sK5 @ sK4 ) ) )
| ( sK7
!= ( comp @ id @ sK7 ) )
| ( ( comp @ sK8 @ id )
!= sK8 ) )
& ( ( ! [X5: subst,X6: subst,X7: subst] :
( ( comp @ X7 @ ( comp @ X6 @ X5 ) )
= ( comp @ ( comp @ X7 @ X6 ) @ X5 ) )
& ! [X8: subst] :
( ( comp @ id @ X8 )
= X8 )
& ! [X9: subst] :
( ( comp @ X9 @ id )
= X9 ) )
| ( substmonoid != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7,sK8]),skolemize(X0,sK4),skolemize(X1,sK5),skolemize(X2,sK6),skolemize(X3,sK7),skolemize(X4,sK8)],[f330]) ).
thf(f332,plain,
( ( ( axidl = $true )
| ? [X0: subst] :
( ( comp @ id @ X0 )
!= X0 ) )
& ( ! [X0: subst] :
( ( comp @ id @ X0 )
= X0 )
| ( axidl != $true ) ) ),
inference(nnf_transformation,[],[f265]) ).
thf(f333,plain,
( ( ( axidl = $true )
| ? [X0: subst] :
( ( comp @ id @ X0 )
!= X0 ) )
& ( ! [X1: subst] :
( ( comp @ id @ X1 )
= X1 )
| ( axidl != $true ) ) ),
inference(rectify,[],[f332]) ).
thf(f334,plain,
( ( ( axidl = $true )
| ( ( comp @ id @ sK9 )
!= sK9 ) )
& ( ! [X1: subst] :
( ( comp @ id @ X1 )
= X1 )
| ( axidl != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X0,sK9)],[f333]) ).
thf(f338,plain,
( ( ( axassoc = $true )
| ? [X2: subst,X0: subst,X1: subst] :
( ( comp @ ( comp @ X0 @ X2 ) @ X1 )
!= ( comp @ X0 @ ( comp @ X2 @ X1 ) ) ) )
& ( ! [X2: subst,X0: subst,X1: subst] :
( ( comp @ ( comp @ X0 @ X2 ) @ X1 )
= ( comp @ X0 @ ( comp @ X2 @ X1 ) ) )
| ( axassoc != $true ) ) ),
inference(nnf_transformation,[],[f147]) ).
thf(f339,plain,
( ( ( axassoc = $true )
| ? [X0: subst,X1: subst,X2: subst] :
( ( comp @ X1 @ ( comp @ X0 @ X2 ) )
!= ( comp @ ( comp @ X1 @ X0 ) @ X2 ) ) )
& ( ! [X3: subst,X4: subst,X5: subst] :
( ( comp @ ( comp @ X4 @ X3 ) @ X5 )
= ( comp @ X4 @ ( comp @ X3 @ X5 ) ) )
| ( axassoc != $true ) ) ),
inference(rectify,[],[f338]) ).
thf(f340,plain,
( ( ( axassoc = $true )
| ( ( comp @ sK12 @ ( comp @ sK11 @ sK13 ) )
!= ( comp @ ( comp @ sK12 @ sK11 ) @ sK13 ) ) )
& ( ! [X3: subst,X4: subst,X5: subst] :
( ( comp @ ( comp @ X4 @ X3 ) @ X5 )
= ( comp @ X4 @ ( comp @ X3 @ X5 ) ) )
| ( axassoc != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12,sK13]),skolemize(X0,sK11),skolemize(X1,sK12),skolemize(X2,sK13)],[f339]) ).
thf(f342,plain,
! [X0: subst] :
( ( ( comp @ X0 @ id )
= X0 )
| ( axidr != $true ) ),
inference(cnf_transformation,[],[f322]) ).
thf(f343,plain,
( ( substmonoid_lthm = $true )
| ( axassoc = $true ) ),
inference(cnf_transformation,[],[f324]) ).
thf(f344,plain,
( ( axidl = $true )
| ( substmonoid_lthm = $true ) ),
inference(cnf_transformation,[],[f324]) ).
thf(f345,plain,
( ( substmonoid_lthm = $true )
| ( substmonoid != $true ) ),
inference(cnf_transformation,[],[f324]) ).
thf(f346,plain,
( ( substmonoid_lthm = $true )
| ( axidr = $true ) ),
inference(cnf_transformation,[],[f324]) ).
thf(f353,plain,
( ( ( comp @ sK8 @ id )
!= sK8 )
| ( ( comp @ ( comp @ sK6 @ sK5 ) @ sK4 )
!= ( comp @ sK6 @ ( comp @ sK5 @ sK4 ) ) )
| ( substmonoid = $true )
| ( sK7
!= ( comp @ id @ sK7 ) ) ),
inference(cnf_transformation,[],[f331]) ).
thf(f354,plain,
! [X1: subst] :
( ( axidl != $true )
| ( ( comp @ id @ X1 )
= X1 ) ),
inference(cnf_transformation,[],[f334]) ).
thf(f358,plain,
substmonoid_lthm != $true,
inference(cnf_transformation,[],[f317]) ).
thf(f359,plain,
! [X3: subst,X4: subst,X5: subst] :
( ( ( comp @ ( comp @ X4 @ X3 ) @ X5 )
= ( comp @ X4 @ ( comp @ X3 @ X5 ) ) )
| ( axassoc != $true ) ),
inference(cnf_transformation,[],[f340]) ).
thf(f364,definition,
( spl14_1
<=> ( sK7
= ( comp @ id @ sK7 ) ) ),
introduced(definition,[new_symbols(definition,[spl14_1])],[avatar_definition]) ).
thf(f366,plain,
( ( sK7
!= ( comp @ id @ sK7 ) )
| spl14_1 ),
inference(avatar_component_clause,[],[f364]) ).
thf(f368,definition,
( spl14_2
<=> ( ( comp @ ( comp @ sK6 @ sK5 ) @ sK4 )
= ( comp @ sK6 @ ( comp @ sK5 @ sK4 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl14_2])],[avatar_definition]) ).
thf(f370,plain,
( ( ( comp @ ( comp @ sK6 @ sK5 ) @ sK4 )
!= ( comp @ sK6 @ ( comp @ sK5 @ sK4 ) ) )
| spl14_2 ),
inference(avatar_component_clause,[],[f368]) ).
thf(f372,definition,
( spl14_3
<=> ( substmonoid = $true ) ),
introduced(definition,[new_symbols(definition,[spl14_3])],[avatar_definition]) ).
thf(f376,definition,
( spl14_4
<=> ( ( comp @ sK8 @ id )
= sK8 ) ),
introduced(definition,[new_symbols(definition,[spl14_4])],[avatar_definition]) ).
thf(f378,plain,
( ( ( comp @ sK8 @ id )
!= sK8 )
| spl14_4 ),
inference(avatar_component_clause,[],[f376]) ).
thf(f379,plain,
( ~ spl14_1
| ~ spl14_2
| spl14_3
| ~ spl14_4 ),
inference(avatar_split_clause,[],[f353,f376,f372,f368,f364]) ).
thf(f381,definition,
( spl14_5
<=> ! [X4: subst,X5: subst,X3: subst] :
( ( comp @ ( comp @ X4 @ X3 ) @ X5 )
= ( comp @ X4 @ ( comp @ X3 @ X5 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl14_5])],[avatar_definition]) ).
thf(f382,plain,
( ! [X3: subst,X4: subst,X5: subst] :
( ( comp @ ( comp @ X4 @ X3 ) @ X5 )
= ( comp @ X4 @ ( comp @ X3 @ X5 ) ) )
| ~ spl14_5 ),
inference(avatar_component_clause,[],[f381]) ).
thf(f384,definition,
( spl14_6
<=> ( axassoc = $true ) ),
introduced(definition,[new_symbols(definition,[spl14_6])],[avatar_definition]) ).
thf(f387,plain,
( spl14_5
| ~ spl14_6 ),
inference(avatar_split_clause,[],[f359,f384,f381]) ).
thf(f390,definition,
( spl14_7
<=> ( substmonoid_lthm = $true ) ),
introduced(definition,[new_symbols(definition,[spl14_7])],[avatar_definition]) ).
thf(f393,plain,
( spl14_6
| spl14_7 ),
inference(avatar_split_clause,[],[f343,f390,f384]) ).
thf(f421,definition,
( spl14_14
<=> ( axidr = $true ) ),
introduced(definition,[new_symbols(definition,[spl14_14])],[avatar_definition]) ).
thf(f424,plain,
( spl14_7
| spl14_14 ),
inference(avatar_split_clause,[],[f346,f421,f390]) ).
thf(f426,definition,
( spl14_15
<=> ( axidl = $true ) ),
introduced(definition,[new_symbols(definition,[spl14_15])],[avatar_definition]) ).
thf(f430,plain,
( spl14_15
| spl14_7 ),
inference(avatar_split_clause,[],[f344,f390,f426]) ).
thf(f431,plain,
~ spl14_7,
inference(avatar_split_clause,[],[f358,f390]) ).
thf(f433,definition,
( spl14_16
<=> ! [X0: subst] :
( ( comp @ X0 @ id )
= X0 ) ),
introduced(definition,[new_symbols(definition,[spl14_16])],[avatar_definition]) ).
thf(f434,plain,
( ! [X0: subst] :
( ( comp @ X0 @ id )
= X0 )
| ~ spl14_16 ),
inference(avatar_component_clause,[],[f433]) ).
thf(f435,plain,
( ~ spl14_14
| spl14_16 ),
inference(avatar_split_clause,[],[f342,f433,f421]) ).
thf(f442,definition,
( spl14_18
<=> ! [X8: subst] :
( ( comp @ id @ X8 )
= X8 ) ),
introduced(definition,[new_symbols(definition,[spl14_18])],[avatar_definition]) ).
thf(f443,plain,
( ! [X8: subst] :
( ( comp @ id @ X8 )
= X8 )
| ~ spl14_18 ),
inference(avatar_component_clause,[],[f442]) ).
thf(f445,plain,
( ~ spl14_15
| spl14_18 ),
inference(avatar_split_clause,[],[f354,f442,f426]) ).
thf(f452,plain,
( ~ spl14_3
| spl14_7 ),
inference(avatar_split_clause,[],[f345,f390,f372]) ).
thf(f459,plain,
( ( sK8 != sK8 )
| spl14_4
| ~ spl14_16 ),
inference(backward_demodulation,[],[f378,f434]) ).
thf(f460,plain,
( $false
| spl14_4
| ~ spl14_16 ),
inference(trivial_inequality_removal,[],[f459]) ).
thf(f461,plain,
( spl14_4
| ~ spl14_16 ),
inference(avatar_contradiction_clause,[],[f460]) ).
thf(f464,plain,
( ( sK7 != sK7 )
| spl14_1
| ~ spl14_18 ),
inference(backward_demodulation,[],[f366,f443]) ).
thf(f465,plain,
( $false
| spl14_1
| ~ spl14_18 ),
inference(trivial_inequality_removal,[],[f464]) ).
thf(f466,plain,
( spl14_1
| ~ spl14_18 ),
inference(avatar_contradiction_clause,[],[f465]) ).
thf(f467,plain,
( ( ( comp @ sK6 @ ( comp @ sK5 @ sK4 ) )
!= ( comp @ sK6 @ ( comp @ sK5 @ sK4 ) ) )
| spl14_2
| ~ spl14_5 ),
inference(backward_demodulation,[],[f370,f382]) ).
thf(f468,plain,
( $false
| spl14_2
| ~ spl14_5 ),
inference(trivial_inequality_removal,[],[f467]) ).
thf(f469,plain,
( spl14_2
| ~ spl14_5 ),
inference(avatar_contradiction_clause,[],[f468]) ).
cnf(s1,plain,
( ~ spl14_1
| ~ spl14_2
| spl14_3
| ~ spl14_4 ),
inference(sat_conversion,[],[f379]) ).
cnf(s2,plain,
( spl14_5
| ~ spl14_6 ),
inference(sat_conversion,[],[f387]) ).
cnf(s4,plain,
( spl14_6
| spl14_7 ),
inference(sat_conversion,[],[f393]) ).
cnf(s9,plain,
( spl14_7
| spl14_14 ),
inference(sat_conversion,[],[f424]) ).
cnf(s11,plain,
( spl14_7
| spl14_15 ),
inference(sat_conversion,[],[f430]) ).
cnf(s12,plain,
~ spl14_7,
inference(sat_conversion,[],[f431]) ).
cnf(s13,plain,
( ~ spl14_14
| spl14_16 ),
inference(sat_conversion,[],[f435]) ).
cnf(s16,plain,
( ~ spl14_15
| spl14_18 ),
inference(sat_conversion,[],[f445]) ).
cnf(s19,plain,
( ~ spl14_3
| spl14_7 ),
inference(sat_conversion,[],[f452]) ).
cnf(s21,plain,
( spl14_4
| ~ spl14_16 ),
inference(sat_conversion,[],[f461]) ).
cnf(s23,plain,
( spl14_1
| ~ spl14_18 ),
inference(sat_conversion,[],[f466]) ).
cnf(s24,plain,
( spl14_2
| ~ spl14_5 ),
inference(sat_conversion,[],[f469]) ).
cnf(s27,plain,
~ spl14_3,
inference(rat,[],[s19,s12]) ).
cnf(s28,plain,
spl14_15,
inference(rat,[],[s11,s12]) ).
cnf(s29,plain,
spl14_18,
inference(rat,[],[s16,s28]) ).
cnf(s31,plain,
spl14_1,
inference(rat,[],[s23,s29]) ).
cnf(s32,plain,
spl14_14,
inference(rat,[],[s9,s12]) ).
cnf(s33,plain,
spl14_16,
inference(rat,[],[s13,s32]) ).
cnf(s35,plain,
spl14_4,
inference(rat,[],[s21,s33]) ).
cnf(s36,plain,
spl14_6,
inference(rat,[],[s4,s12]) ).
cnf(s37,plain,
spl14_5,
inference(rat,[],[s2,s36]) ).
cnf(s39,plain,
spl14_2,
inference(rat,[],[s24,s37]) ).
cnf(s40,plain,
$false,
inference(rat,[],[s1,s35,s27,s39,s31]) ).
thf(f474,plain,
$false,
inference(avatar_sat_refutation,[],[s40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG254^2 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n011.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 17:34:01 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.26 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
% 0.61/0.39 % (408092)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.61/0.39 % (408103)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.61/0.39 % (408103)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
% 0.61/0.39 % (408103)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=2086832597:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.61/0.39 % (408097)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3021802084:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.61/0.39 % (408098)lrs+10_16_si=on:nwc=1.5:random_seed=2662642731:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.61/0.39 % (408099)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=4277923913:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.61/0.39 % (408101)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3701905093:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.61/0.39 % (408100)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=2367879762: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)
% 0.61/0.39 % (408102)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3222619125:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.61/0.39 % (408099)Instruction limit reached!
% 0.61/0.39 % (408099)------------------------------
% 0.61/0.39 % (408099)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.39 % (408099)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.39 % (408099)CaDiCaL version: 2.1.3
% 0.61/0.39 % (408099)Termination reason: Instruction limit
% 0.61/0.39 % (408099)Termination phase: shuffling
% 0.61/0.39 % (408099)Time elapsed: 0.002 s
% 0.61/0.39 % (408099)Peak memory usage: 10 MB
% 0.61/0.39 % (408099)Instructions burned: 3 (million)
% 0.61/0.39 % (408098)Instruction limit reached!
% 0.61/0.39 % (408098)------------------------------
% 0.61/0.39 % (408098)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.39 % (408098)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.39 % (408098)CaDiCaL version: 2.1.3
% 0.61/0.39 % (408098)Termination reason: Instruction limit
% 0.61/0.39 % (408098)Termination phase: shuffling
% 0.61/0.39 % (408098)Time elapsed: 0.008 s
% 0.61/0.39 % (408098)Peak memory usage: 10 MB
% 0.61/0.39 % (408098)Instructions burned: 19 (million)
% 0.61/0.39 % (408101)Instruction limit reached!
% 0.61/0.39 % (408101)------------------------------
% 0.61/0.39 % (408101)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.39 % (408101)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.39 % (408101)CaDiCaL version: 2.1.3
% 0.61/0.39 % (408101)Termination reason: Instruction limit
% 0.61/0.39 % (408101)Termination phase: Naming
% 0.61/0.39 % (408101)Time elapsed: 0.012 s
% 0.61/0.39 % (408101)Peak memory usage: 11 MB
% 0.61/0.39 % (408101)Instructions burned: 24 (million)
% 0.61/0.39 % (408111)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=389855479:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.61/0.39 % (408111)Instruction limit reached!
% 0.61/0.39 % (408111)------------------------------
% 0.61/0.39 % (408111)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.39 % (408111)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.39 % (408111)CaDiCaL version: 2.1.3
% 0.61/0.39 % (408111)Termination reason: Instruction limit
% 0.61/0.39 % (408111)Termination phase: shuffling
% 0.61/0.39 % (408111)Time elapsed: 0.002 s
% 0.61/0.39 % (408111)Peak memory usage: 10 MB
% 0.61/0.39 % (408111)Instructions burned: 3 (million)
% 0.61/0.39 % (408113)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.61/0.39 % (408112)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3975215253:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.61/0.39 % (408103)Instruction limit reached!
% 0.61/0.39 % (408103)------------------------------
% 0.61/0.39 % (408103)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.39 % (408103)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.39 % (408103)CaDiCaL version: 2.1.3
% 0.61/0.39 % (408103)Termination reason: Instruction limit
% 0.61/0.39 % (408103)Termination phase: Saturation
% 0.61/0.39 % (408103)Time elapsed: 0.037 s
% 0.61/0.39 % (408103)Peak memory usage: 13 MB
% 0.61/0.39 % (408103)Instructions burned: 160 (million)
% 0.61/0.39 % (408113)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=928656128:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.61/0.39 % (408112)Instruction limit reached!
% 0.61/0.39 % (408112)------------------------------
% 0.61/0.39 % (408112)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.39 % (408112)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.39 % (408112)CaDiCaL version: 2.1.3
% 0.61/0.39 % (408112)Termination reason: Instruction limit
% 0.61/0.39 % (408112)Termination phase: shuffling
% 0.61/0.39 % (408112)Time elapsed: 0.003 s
% 0.61/0.39 % (408112)Peak memory usage: 10 MB
% 0.61/0.39 % (408112)Instructions burned: 5 (million)
% 0.61/0.39 % (408102)Instruction limit reached!
% 0.61/0.39 % (408102)------------------------------
% 0.61/0.39 % (408102)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.39 % (408102)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.39 % (408102)CaDiCaL version: 2.1.3
% 0.61/0.39 % (408102)Termination reason: Instruction limit
% 0.61/0.39 % (408102)Termination phase: Property scanning
% 0.61/0.39 % (408102)Time elapsed: 0.035 s
% 0.61/0.39 % (408102)Peak memory usage: 12 MB
% 0.61/0.39 % (408102)Instructions burned: 77 (million)
% 0.61/0.39 % (408113)Instruction limit reached!
% 0.61/0.39 % (408113)------------------------------
% 0.61/0.39 % (408113)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.39 % (408113)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.39 % (408113)CaDiCaL version: 2.1.3
% 0.61/0.39 % (408113)Termination reason: Instruction limit
% 0.61/0.39 % (408113)Termination phase: shuffling
% 0.61/0.39 % (408113)Time elapsed: 0.005 s
% 0.61/0.39 % (408113)Peak memory usage: 10 MB
% 0.61/0.39 % (408113)Instructions burned: 10 (million)
% 0.61/0.39 % (408097)Instruction limit reached!
% 0.61/0.39 % (408097)------------------------------
% 0.61/0.39 % (408097)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.39 % (408097)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.39 % (408097)CaDiCaL version: 2.1.3
% 0.61/0.39 % (408097)Termination reason: Instruction limit
% 0.61/0.39 % (408097)Termination phase: Function definition elimination
% 0.61/0.39 % (408097)Time elapsed: 0.041 s
% 0.61/0.39 % (408097)Peak memory usage: 12 MB
% 0.61/0.39 % (408097)Instructions burned: 91 (million)
% 0.61/0.39 % (408118)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
% 0.61/0.39 % (408118)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.61/0.39 % (408115)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1161932327:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.61/0.39 % (408118)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2886078144:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.61/0.39 % (408115)Instruction limit reached!
% 0.61/0.39 % (408115)------------------------------
% 0.61/0.39 % (408115)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.39 % (408115)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.39 % (408115)CaDiCaL version: 2.1.3
% 0.61/0.39 % (408115)Termination reason: Instruction limit
% 0.61/0.39 % (408115)Termination phase: shuffling
% 0.61/0.39 % (408115)Time elapsed: 0.006 s
% 0.61/0.39 % (408115)Peak memory usage: 10 MB
% 0.61/0.39 % (408115)Instructions burned: 12 (million)
% 0.61/0.39 % (408118)Instruction limit reached!
% 0.61/0.39 % (408118)------------------------------
% 0.61/0.39 % (408118)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.39 % (408118)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.39 % (408118)CaDiCaL version: 2.1.3
% 0.61/0.39 % (408118)Termination reason: Instruction limit
% 0.61/0.39 % (408118)Termination phase: Property scanning
% 0.61/0.39 % (408118)Time elapsed: 0.006 s
% 0.61/0.39 % (408118)Peak memory usage: 10 MB
% 0.61/0.39 % (408118)Instructions burned: 28 (million)
% 0.61/0.39 % (408121)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.61/0.39 % (408119)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=4054544167:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.61/0.39 % (408120)lrs+10_1_si=on:cs=on:random_seed=2956492766:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.61/0.39 % (408121)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=3077949971:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.61/0.39 % (408121)Instruction limit reached!
% 0.61/0.39 % (408121)------------------------------
% 0.61/0.39 % (408121)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.39 % (408121)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.39 % (408121)CaDiCaL version: 2.1.3
% 0.61/0.39 % (408121)Termination reason: Instruction limit
% 0.61/0.39 % (408121)Termination phase: shuffling
% 0.61/0.39 % (408121)Time elapsed: 0.002 s
% 0.61/0.39 % (408121)Peak memory usage: 10 MB
% 0.61/0.39 % (408121)Instructions burned: 4 (million)
% 0.61/0.39 % (408120)Instruction limit reached!
% 0.61/0.39 % (408120)------------------------------
% 0.61/0.39 % (408120)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.39 % (408120)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.39 % (408120)CaDiCaL version: 2.1.3
% 0.61/0.39 % (408120)Termination reason: Instruction limit
% 0.61/0.39 % (408120)Termination phase: shuffling
% 0.61/0.39 % (408120)Time elapsed: 0.004 s
% 0.61/0.39 % (408120)Peak memory usage: 10 MB
% 0.61/0.39 % (408120)Instructions burned: 9 (million)
% 0.61/0.39 % (408122)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=593830058:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.61/0.39 % (408126)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=1373584555:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/25Mi)
% 0.61/0.39 % (408126)Instruction limit reached!
% 0.61/0.39 % (408126)------------------------------
% 0.61/0.39 % (408126)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.39 % (408126)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.39 % (408126)CaDiCaL version: 2.1.3
% 0.61/0.39 % (408126)Termination reason: Instruction limit
% 0.61/0.39 % (408126)Termination phase: Preprocessing 1
% 0.61/0.39 % (408126)Time elapsed: 0.006 s
% 0.61/0.39 % (408126)Peak memory usage: 10 MB
% 0.61/0.39 % (408126)Instructions burned: 25 (million)
% 0.61/0.39 % (408125)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=129824920:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.61/0.39 % (408122) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-408092-408122"...
% 0.61/0.39 % (408130)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=495279008:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.61/0.39 % (408122)...printing done.
% 0.61/0.39 % (408135)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=3888190771:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 0.61/0.39 % (408132)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=1659505869:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.61/0.39 % (408122)Refutation found. Thanks to Tanya!
% 0.61/0.39 % SZS status Theorem for theBenchmark
% 0.61/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.61/0.39 % (408122)------------------------------
% 0.61/0.39 % (408122)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.39 % (408122)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.39 % (408122)CaDiCaL version: 2.1.3
% 0.61/0.39 % (408122)Termination reason: Refutation
% 0.61/0.39 % (408122)Time elapsed: 0.016 s
% 0.61/0.39 % (408122)Peak memory usage: 13 MB
% 0.61/0.39 % (408122)Instructions burned: 31 (million)
% 0.61/0.39 % (408092)Success in time 0.124 s
% 0.61/0.39 % Vampire exiting
%------------------------------------------------------------------------------