%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG251^3 : 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 : n012.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 07:45:12 AM UTC 2026
% Result : Theorem 0.48s 0.33s
% Output : Refutation 0.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 9
% Syntax : Number of formulae : 126 ( 84 unt; 0 typ; 2 def)
% Number of atoms : 598 ( 193 equ; 0 cnn)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 1063 ( 34 ~; 62 |; 0 &; 739 @)
% ( 2 <=>; 141 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 41 ( 41 >; 0 *; 0 +; 0 <<)
% Number of symbols : 148 ( 144 usr; 119 con; 0-4 aty)
% ( 85 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 205 ( 0 sgn 93 !; 0 ?; 205 :)
% 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,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_124,type,
vIMP: $o > $o > $o ).
thf(func_def_125,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_126,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_127,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_128,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_129,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_130,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_131,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_132,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_133,type,
vNOT: $o > $o ).
thf(func_def_134,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_135,type,
vAND: $o > $o > $o ).
thf(func_def_136,type,
vIFF: $o > $o > $o ).
thf(func_def_139,type,
sK0: term ).
thf(func_def_140,type,
sK1: subst ).
thf(func_def_141,type,
sK2: term > $o ).
thf(func_def_142,type,
sK3: term ).
thf(func_def_143,type,
sK4: ( term > $o ) > term ).
thf(f2,axiom,
! [X0: term,X1: subst] :
( ( ( sub @ one @ ( push @ X0 @ X1 ) )
= X0 )
= axvarcons ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',axvarcons) ).
thf(f5,axiom,
( axclos
= ( ! [X0: term,X2: subst,X1: subst] :
( ( sub @ ( sub @ X0 @ X1 ) @ X2 )
= ( sub @ X0 @ ( comp @ X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',axclos) ).
thf(f7,axiom,
! [X1: subst,X0: term] :
( ( ( comp @ sh @ ( push @ X0 @ X1 ) )
= X1 )
= axshiftcons ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',axshiftcons) ).
thf(f15,axiom,
! [X0: term > $o] :
( ( ( X0 @ one )
=> ( ! [X1: term] :
( ( var @ X1 )
=> ( ( X0 @ X1 )
=> ( X0 @ ( sub @ X1 @ sh ) ) ) )
=> ! [X1: term] :
( ( var @ X1 )
=> ( X0 @ X1 ) ) ) )
= ulamvarind ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',ulamvarind) ).
thf(f39,axiom,
! [X0: term > $o,X2: subst,X1: term] :
( ( ! [X3: term] :
( ( var @ X3 )
=> ( X0 @ ( sub @ X3 @ X2 ) ) )
=> ( ( X0 @ X1 )
=> ! [X3: term] :
( ( var @ X3 )
=> ( X0 @ ( sub @ X3 @ ( push @ X1 @ X2 ) ) ) ) ) )
= pushprop ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',pushprop) ).
thf(f41,axiom,
( ( pushprop_lthm_orig = ulamvar1 )
=> ( axvarcons
=> ( axclos
=> ( axshiftcons
=> ( ulamvarind
=> pushprop ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',pushprop_lthm_orig) ).
thf(f114,conjecture,
pushprop_lthm_orig,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(f115,negated_conjecture,
~ pushprop_lthm_orig,
inference(negated_conjecture,[status(cth)],[f114]) ).
thf(f124,plain,
( axvarcons
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sub @ one @ ( push @ Y1 @ Y0 ) )
= Y1 ) ) ) ),
inference(fool_elimination,[],[f2]) ).
thf(f145,plain,
! [X0: subst,X1: term] :
( ( ( comp @ sh @ ( push @ X1 @ X0 ) )
= X0 )
= axshiftcons ),
inference(rectify,[],[f7]) ).
thf(f146,plain,
( axshiftcons
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( comp @ sh @ ( push @ Y0 @ Y1 ) )
= Y1 ) ) ) ),
inference(fool_elimination,[],[f145]) ).
thf(f172,plain,
! [X0: term > $o] :
( ( ( X0 @ one )
=> ( ! [X1: term] :
( ( var @ X1 )
=> ( ( X0 @ X1 )
=> ( X0 @ ( sub @ X1 @ sh ) ) ) )
=> ! [X2: term] :
( ( var @ X2 )
=> ( X0 @ X2 ) ) ) )
= ulamvarind ),
inference(rectify,[],[f15]) ).
thf(f173,plain,
( ulamvarind
= ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f172]) ).
thf(f189,plain,
( ( pushprop_lthm_orig = ulamvar1 )
=> ( axvarcons
=> ( axclos
=> ( axshiftcons
=> ( ulamvarind
=> pushprop ) ) ) ) ),
inference(rectify,[],[f41]) ).
thf(f190,plain,
( pushprop_lthm_orig
= ( ulamvar1
=> ( axvarcons
=> ( axclos
=> ( axshiftcons
=> ( ulamvarind
=> pushprop ) ) ) ) ) ),
inference(fool_elimination,[],[f189]) ).
thf(f211,plain,
! [X0: term > $o,X1: subst,X2: term] :
( ( ! [X3: term] :
( ( var @ X3 )
=> ( X0 @ ( sub @ X3 @ X1 ) ) )
=> ( ( X0 @ X2 )
=> ! [X4: term] :
( ( var @ X4 )
=> ( X0 @ ( sub @ X4 @ ( push @ X2 @ X1 ) ) ) ) ) )
= pushprop ),
inference(rectify,[],[f39]) ).
thf(f212,plain,
( pushprop
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ ( term > $o )
@ ^ [Y2: term > $o] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y2 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y2 @ Y0 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y2 @ ( sub @ Y3 @ ( push @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f211]) ).
thf(f262,plain,
~ pushprop_lthm_orig,
inference(rectify,[],[f115]) ).
thf(f263,plain,
pushprop_lthm_orig != $true,
inference(fool_elimination,[],[f262]) ).
thf(f289,plain,
( axclos
= ( ! [X0: term,X1: subst,X2: subst] :
( ( sub @ X0 @ ( comp @ X2 @ X1 ) )
= ( sub @ ( sub @ X0 @ X2 ) @ X1 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f290,plain,
( axclos
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y0 @ Y1 ) )
= ( sub @ ( sub @ Y2 @ Y0 ) @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f289]) ).
thf(f321,plain,
pushprop_lthm_orig != $true,
inference(flattening,[],[f263]) ).
thf(f322,plain,
pushprop_lthm_orig != $true,
inference(cnf_transformation,[],[f321]) ).
thf(f323,plain,
( ulamvarind
= ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f173]) ).
thf(f324,plain,
( axshiftcons
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( comp @ sh @ ( push @ Y0 @ Y1 ) )
= Y1 ) ) ) ),
inference(cnf_transformation,[],[f146]) ).
thf(f325,plain,
( axclos
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y0 @ Y1 ) )
= ( sub @ ( sub @ Y2 @ Y0 ) @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f290]) ).
thf(f327,plain,
( pushprop_lthm_orig
= ( ulamvar1
=> ( axvarcons
=> ( axclos
=> ( axshiftcons
=> ( ulamvarind
=> pushprop ) ) ) ) ) ),
inference(cnf_transformation,[],[f190]) ).
thf(f328,plain,
( axvarcons
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sub @ one @ ( push @ Y1 @ Y0 ) )
= Y1 ) ) ) ),
inference(cnf_transformation,[],[f124]) ).
thf(f329,plain,
( pushprop
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ ( term > $o )
@ ^ [Y2: term > $o] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y2 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y2 @ Y0 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y2 @ ( sub @ Y3 @ ( push @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f212]) ).
thf(f331,plain,
( ( pushprop_lthm_orig = $false )
| ( $true != $true ) ),
inference(fool_paramodulation,[],[f322]) ).
thf(f332,plain,
pushprop_lthm_orig = $false,
inference(trivial_inequality_removal,[],[f331]) ).
thf(f334,plain,
( $false
= ( ulamvar1
=> ( axvarcons
=> ( axclos
=> ( axshiftcons
=> ( ulamvarind
=> pushprop ) ) ) ) ) ),
inference(backward_demodulation,[],[f327,f332]) ).
thf(f335,plain,
( $false
= ( axvarcons
=> ( axclos
=> ( axshiftcons
=> ( ulamvarind
=> pushprop ) ) ) ) ),
inference(imp_proxy_clausification,[],[f334]) ).
thf(f337,plain,
( $false
= ( axclos
=> ( axshiftcons
=> ( ulamvarind
=> pushprop ) ) ) ),
inference(imp_proxy_clausification,[],[f335]) ).
thf(f338,plain,
axvarcons = $true,
inference(imp_proxy_clausification,[],[f335]) ).
thf(f339,plain,
( $false
= ( axshiftcons
=> ( ulamvarind
=> pushprop ) ) ),
inference(imp_proxy_clausification,[],[f337]) ).
thf(f340,plain,
axclos = $true,
inference(imp_proxy_clausification,[],[f337]) ).
thf(f341,plain,
( $false
= ( ulamvarind
=> pushprop ) ),
inference(imp_proxy_clausification,[],[f339]) ).
thf(f342,plain,
axshiftcons = $true,
inference(imp_proxy_clausification,[],[f339]) ).
thf(f343,plain,
pushprop = $false,
inference(imp_proxy_clausification,[],[f341]) ).
thf(f344,plain,
ulamvarind = $true,
inference(imp_proxy_clausification,[],[f341]) ).
thf(f347,plain,
( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sub @ one @ ( push @ Y1 @ Y0 ) )
= Y1 ) ) )
= $true ),
inference(backward_demodulation,[],[f328,f338]) ).
thf(f349,plain,
! [X1: subst] :
( ( ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sub @ one @ ( push @ Y1 @ Y0 ) )
= Y1 ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f347]) ).
thf(f350,plain,
! [X1: subst] :
( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ one @ ( push @ Y0 @ X1 ) )
= Y0 ) )
= $true ),
inference(beta-eta_normalization,[],[f349]) ).
thf(f351,plain,
! [X2: term,X1: subst] :
( $true
= ( ^ [Y0: term] :
( ( sub @ one @ ( push @ Y0 @ X1 ) )
= Y0 )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f350]) ).
thf(f352,plain,
! [X2: term,X1: subst] :
( ( ( sub @ one @ ( push @ X2 @ X1 ) )
= X2 )
= $true ),
inference(beta-eta_normalization,[],[f351]) ).
thf(f353,plain,
! [X2: term,X1: subst] :
( ( sub @ one @ ( push @ X2 @ X1 ) )
= X2 ),
inference(equality_proxy_clausification,[],[f352]) ).
thf(f354,plain,
( $true
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y0 @ Y1 ) )
= ( sub @ ( sub @ Y2 @ Y0 ) @ Y1 ) ) ) ) ) ),
inference(backward_demodulation,[],[f325,f340]) ).
thf(f356,plain,
! [X1: subst] :
( ( ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y0 @ Y1 ) )
= ( sub @ ( sub @ Y2 @ Y0 ) @ Y1 ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f354]) ).
thf(f357,plain,
! [X1: subst] :
( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sub @ Y1 @ ( comp @ X1 @ Y0 ) )
= ( sub @ ( sub @ Y1 @ X1 ) @ Y0 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f356]) ).
thf(f358,plain,
! [X2: subst,X1: subst] :
( ( ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sub @ Y1 @ ( comp @ X1 @ Y0 ) )
= ( sub @ ( sub @ Y1 @ X1 ) @ Y0 ) ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f357]) ).
thf(f359,plain,
! [X2: subst,X1: subst] :
( $true
= ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ ( comp @ X1 @ X2 ) )
= ( sub @ ( sub @ Y0 @ X1 ) @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f358]) ).
thf(f360,plain,
! [X2: subst,X3: term,X1: subst] :
( ( ^ [Y0: term] :
( ( sub @ Y0 @ ( comp @ X1 @ X2 ) )
= ( sub @ ( sub @ Y0 @ X1 ) @ X2 ) )
@ X3 )
= $true ),
inference(pi_proxy_clausification,[],[f359]) ).
thf(f361,plain,
! [X2: subst,X3: term,X1: subst] :
( ( ( sub @ X3 @ ( comp @ X1 @ X2 ) )
= ( sub @ ( sub @ X3 @ X1 ) @ X2 ) )
= $true ),
inference(beta-eta_normalization,[],[f360]) ).
thf(f362,plain,
! [X2: subst,X3: term,X1: subst] :
( ( sub @ ( sub @ X3 @ X1 ) @ X2 )
= ( sub @ X3 @ ( comp @ X1 @ X2 ) ) ),
inference(equality_proxy_clausification,[],[f361]) ).
thf(f363,plain,
( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( comp @ sh @ ( push @ Y0 @ Y1 ) )
= Y1 ) ) )
= $true ),
inference(backward_demodulation,[],[f324,f342]) ).
thf(f365,plain,
! [X1: term] :
( ( ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( comp @ sh @ ( push @ Y0 @ Y1 ) )
= Y1 ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f363]) ).
thf(f366,plain,
! [X1: term] :
( $true
= ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ sh @ ( push @ X1 @ Y0 ) )
= Y0 ) ) ),
inference(beta-eta_normalization,[],[f365]) ).
thf(f367,plain,
! [X2: subst,X1: term] :
( ( ^ [Y0: subst] :
( ( comp @ sh @ ( push @ X1 @ Y0 ) )
= Y0 )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f366]) ).
thf(f368,plain,
! [X2: subst,X1: term] :
( $true
= ( ( comp @ sh @ ( push @ X1 @ X2 ) )
= X2 ) ),
inference(beta-eta_normalization,[],[f367]) ).
thf(f369,plain,
! [X2: subst,X1: term] :
( ( comp @ sh @ ( push @ X1 @ X2 ) )
= X2 ),
inference(equality_proxy_clausification,[],[f368]) ).
thf(f370,plain,
( $false
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ ( term > $o )
@ ^ [Y2: term > $o] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y2 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y2 @ Y0 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y2 @ ( sub @ Y3 @ ( push @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) ) ),
inference(backward_demodulation,[],[f329,f343]) ).
thf(f371,plain,
( $false
= ( ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ ( term > $o )
@ ^ [Y2: term > $o] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y2 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y2 @ Y0 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y2 @ ( sub @ Y3 @ ( push @ Y0 @ Y1 ) ) ) ) ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f370]) ).
thf(f372,plain,
( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( ( !! @ term
@ ^ [Y2: term] :
( ( var @ Y2 )
=> ( Y1 @ ( sub @ Y2 @ Y0 ) ) ) )
=> ( ( Y1 @ sK0 )
=> ( !! @ term
@ ^ [Y2: term] :
( ( var @ Y2 )
=> ( Y1 @ ( sub @ Y2 @ ( push @ sK0 @ Y0 ) ) ) ) ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f371]) ).
thf(f373,plain,
( $false
= ( ^ [Y0: subst] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( ( !! @ term
@ ^ [Y2: term] :
( ( var @ Y2 )
=> ( Y1 @ ( sub @ Y2 @ Y0 ) ) ) )
=> ( ( Y1 @ sK0 )
=> ( !! @ term
@ ^ [Y2: term] :
( ( var @ Y2 )
=> ( Y1 @ ( sub @ Y2 @ ( push @ sK0 @ Y0 ) ) ) ) ) ) ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f372]) ).
thf(f374,plain,
( $false
= ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sK1 ) ) ) )
=> ( ( Y0 @ sK0 )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ sK0 @ sK1 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f373]) ).
thf(f375,plain,
( $false
= ( ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sK1 ) ) ) )
=> ( ( Y0 @ sK0 )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ sK0 @ sK1 ) ) ) ) ) ) )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f374]) ).
thf(f376,plain,
( $false
= ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( sK2 @ ( sub @ Y0 @ sK1 ) ) ) )
=> ( ( sK2 @ sK0 )
=> ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( sK2 @ ( sub @ Y0 @ ( push @ sK0 @ sK1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f375]) ).
thf(f377,plain,
( $false
= ( ( sK2 @ sK0 )
=> ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( sK2 @ ( sub @ Y0 @ ( push @ sK0 @ sK1 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f376]) ).
thf(f378,plain,
( $true
= ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( sK2 @ ( sub @ Y0 @ sK1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f376]) ).
thf(f379,plain,
! [X1: term] :
( ( ^ [Y0: term] :
( ( var @ Y0 )
=> ( sK2 @ ( sub @ Y0 @ sK1 ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f378]) ).
thf(f380,plain,
! [X1: term] :
( $true
= ( ( var @ X1 )
=> ( sK2 @ ( sub @ X1 @ sK1 ) ) ) ),
inference(beta-eta_normalization,[],[f379]) ).
thf(f381,plain,
! [X1: term] :
( ( ( sK2 @ ( sub @ X1 @ sK1 ) )
= $true )
| ( ( var @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f380]) ).
thf(f382,plain,
( $false
= ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( sK2 @ ( sub @ Y0 @ ( push @ sK0 @ sK1 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f377]) ).
thf(f383,plain,
( $true
= ( sK2 @ sK0 ) ),
inference(imp_proxy_clausification,[],[f377]) ).
thf(f384,plain,
( $false
= ( ^ [Y0: term] :
( ( var @ Y0 )
=> ( sK2 @ ( sub @ Y0 @ ( push @ sK0 @ sK1 ) ) ) )
@ sK3 ) ),
inference(sigma_proxy_clausification,[],[f382]) ).
thf(f385,plain,
( $false
= ( ( var @ sK3 )
=> ( sK2 @ ( sub @ sK3 @ ( push @ sK0 @ sK1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f384]) ).
thf(f386,plain,
( $false
= ( sK2 @ ( sub @ sK3 @ ( push @ sK0 @ sK1 ) ) ) ),
inference(imp_proxy_clausification,[],[f385]) ).
thf(f387,plain,
( ( var @ sK3 )
= $true ),
inference(imp_proxy_clausification,[],[f385]) ).
thf(f388,plain,
( $true
= ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) ) ),
inference(backward_demodulation,[],[f323,f344]) ).
thf(f390,plain,
! [X1: term > $o] :
( ( ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f388]) ).
thf(f391,plain,
! [X1: term > $o] :
( ( ( X1 @ one )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( ( X1 @ Y0 )
=> ( X1 @ ( sub @ Y0 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( X1 @ Y0 ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f390]) ).
thf(f392,plain,
! [X1: term > $o] :
( ( ( X1 @ one )
= $false )
| ( $true
= ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( ( X1 @ Y0 )
=> ( X1 @ ( sub @ Y0 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( X1 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f391]) ).
thf(f393,plain,
! [X1: term > $o] :
( ( ( X1 @ one )
= $false )
| ( $false
= ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( ( X1 @ Y0 )
=> ( X1 @ ( sub @ Y0 @ sh ) ) ) ) ) )
| ( $true
= ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( X1 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f392]) ).
thf(f394,plain,
! [X1: term > $o] :
( ( ( X1 @ one )
= $false )
| ( $false
= ( ^ [Y0: term] :
( ( var @ Y0 )
=> ( ( X1 @ Y0 )
=> ( X1 @ ( sub @ Y0 @ sh ) ) ) )
@ ( sK4 @ X1 ) ) )
| ( $true
= ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( X1 @ Y0 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f393]) ).
thf(f395,plain,
! [X2: term,X1: term > $o] :
( ( ( ^ [Y0: term] :
( ( var @ Y0 )
=> ( X1 @ Y0 ) )
@ X2 )
= $true )
| ( ( X1 @ one )
= $false )
| ( $false
= ( ^ [Y0: term] :
( ( var @ Y0 )
=> ( ( X1 @ Y0 )
=> ( X1 @ ( sub @ Y0 @ sh ) ) ) )
@ ( sK4 @ X1 ) ) ) ),
inference(pi_proxy_clausification,[],[f394]) ).
thf(f396,plain,
! [X2: term,X1: term > $o] :
( ( $true
= ( ( var @ X2 )
=> ( X1 @ X2 ) ) )
| ( ( X1 @ one )
= $false )
| ( $false
= ( ( var @ ( sK4 @ X1 ) )
=> ( ( X1 @ ( sK4 @ X1 ) )
=> ( X1 @ ( sub @ ( sK4 @ X1 ) @ sh ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f395]) ).
thf(f397,plain,
! [X2: term,X1: term > $o] :
( ( $false
= ( ( var @ ( sK4 @ X1 ) )
=> ( ( X1 @ ( sK4 @ X1 ) )
=> ( X1 @ ( sub @ ( sK4 @ X1 ) @ sh ) ) ) ) )
| ( ( var @ X2 )
= $false )
| ( ( X1 @ one )
= $false )
| ( ( X1 @ X2 )
= $true ) ),
inference(imp_proxy_clausification,[],[f396]) ).
thf(f398,plain,
! [X2: term,X1: term > $o] :
( ( ( var @ X2 )
= $false )
| ( ( X1 @ X2 )
= $true )
| ( $false
= ( ( X1 @ ( sK4 @ X1 ) )
=> ( X1 @ ( sub @ ( sK4 @ X1 ) @ sh ) ) ) )
| ( ( X1 @ one )
= $false ) ),
inference(imp_proxy_clausification,[],[f397]) ).
thf(f399,plain,
! [X2: term,X1: term > $o] :
( ( ( var @ ( sK4 @ X1 ) )
= $true )
| ( ( var @ X2 )
= $false )
| ( ( X1 @ X2 )
= $true )
| ( ( X1 @ one )
= $false ) ),
inference(imp_proxy_clausification,[],[f397]) ).
thf(f400,plain,
! [X2: term,X1: term > $o] :
( ( $false
= ( X1 @ ( sub @ ( sK4 @ X1 ) @ sh ) ) )
| ( ( var @ X2 )
= $false )
| ( ( X1 @ X2 )
= $true )
| ( ( X1 @ one )
= $false ) ),
inference(imp_proxy_clausification,[],[f398]) ).
thf(f402,plain,
! [X2: term,X0: subst,X1: term] :
( ( sub @ X1 @ X0 )
= ( sub @ ( sub @ X1 @ sh ) @ ( push @ X2 @ X0 ) ) ),
inference(constrained_superposition,[],[f362,f369]) ).
thf(f411,plain,
! [X0: term > $o] :
( ( $false = $true )
| ( ( X0 @ one )
= $false )
| ( $true
= ( X0 @ sK3 ) )
| ( ( var @ ( sK4 @ X0 ) )
= $true ) ),
inference(constrained_superposition,[],[f399,f387]) ).
thf(f425,plain,
! [X0: term > $o] :
( ( ( var @ ( sK4 @ X0 ) )
= $true )
| ( $true
= ( X0 @ sK3 ) )
| ( ( X0 @ one )
= $false ) ),
inference(trivial_inequality_removal,[],[f411]) ).
thf(f464,plain,
( ( one = sK3 )
| ( $true
= ( var
@ ( sK4
@ ^ [Y0: term] : ( Y0 != sK3 ) ) ) ) ),
inference(leibniz_equality_elimination,[],[f425]) ).
thf(f470,definition,
( spl5_6
<=> ( one = sK3 ) ),
introduced(definition,[new_symbols(definition,[spl5_6])],[avatar_definition]) ).
thf(f471,plain,
( ( one != sK3 )
| spl5_6 ),
inference(avatar_component_clause,[],[f470]) ).
thf(f472,plain,
( ( one = sK3 )
| ~ spl5_6 ),
inference(avatar_component_clause,[],[f470]) ).
thf(f475,definition,
( spl5_7
<=> ( $true
= ( var
@ ( sK4
@ ^ [Y0: term] : ( Y0 != sK3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl5_7])],[avatar_definition]) ).
thf(f477,plain,
( ( $true
= ( var
@ ( sK4
@ ^ [Y0: term] : ( Y0 != sK3 ) ) ) )
| ~ spl5_7 ),
inference(avatar_component_clause,[],[f475]) ).
thf(f478,plain,
( spl5_6
| spl5_7 ),
inference(avatar_split_clause,[],[f464,f475,f470]) ).
thf(f481,plain,
( ! [X2: term,X1: subst] :
( ( sub @ sK3 @ ( push @ X2 @ X1 ) )
= X2 )
| ~ spl5_6 ),
inference(backward_demodulation,[],[f353,f472]) ).
thf(f483,plain,
( ( $false
= ( sK2 @ sK0 ) )
| ~ spl5_6 ),
inference(backward_demodulation,[],[f386,f481]) ).
thf(f484,plain,
( ( $false = $true )
| ~ spl5_6 ),
inference(backward_demodulation,[],[f383,f483]) ).
thf(f485,plain,
( $false
| ~ spl5_6 ),
inference(trivial_inequality_removal,[],[f484]) ).
thf(f486,plain,
~ spl5_6,
inference(avatar_contradiction_clause,[],[f485]) ).
thf(f894,plain,
! [X0: term > $o] :
( ( $true
= ( X0 @ sK3 ) )
| ( $false = $true )
| ( $false
= ( X0 @ ( sub @ ( sK4 @ X0 ) @ sh ) ) )
| ( ( X0 @ one )
= $false ) ),
inference(constrained_superposition,[],[f387,f400]) ).
thf(f926,plain,
! [X0: term > $o] :
( ( $false
= ( X0 @ ( sub @ ( sK4 @ X0 ) @ sh ) ) )
| ( $true
= ( X0 @ sK3 ) )
| ( ( X0 @ one )
= $false ) ),
inference(trivial_inequality_removal,[],[f894]) ).
thf(f981,plain,
( ( $false
= ( ^ [Y0: term] : ( Y0 != sK3 )
@ one ) )
| ( sK3
= ( sub
@ ( sK4
@ ^ [Y0: term] : ( Y0 != sK3 ) )
@ sh ) ) ),
inference(leibniz_equality_elimination,[],[f926]) ).
thf(f1011,plain,
( ( $false
= ( one != sK3 ) )
| ( sK3
= ( sub
@ ( sK4
@ ^ [Y0: term] : ( Y0 != sK3 ) )
@ sh ) ) ),
inference(beta-eta_normalization,[],[f981]) ).
thf(f1012,plain,
( ( sK3
= ( sub
@ ( sK4
@ ^ [Y0: term] : ( Y0 != sK3 ) )
@ sh ) )
| ( ( one = sK3 )
= $true ) ),
inference(not_proxy_clausification,[],[f1011]) ).
thf(f1013,plain,
( ( one = sK3 )
| ( sK3
= ( sub
@ ( sK4
@ ^ [Y0: term] : ( Y0 != sK3 ) )
@ sh ) ) ),
inference(equality_proxy_clausification,[],[f1012]) ).
thf(f1022,plain,
( ( sK3
= ( sub
@ ( sK4
@ ^ [Y0: term] : ( Y0 != sK3 ) )
@ sh ) )
| spl5_6 ),
inference(forward_subsumption_resolution,[],[f1013,f471]) ).
thf(f1025,plain,
( ! [X0: subst,X1: term] :
( ( sub
@ ( sK4
@ ^ [Y0: term] : ( Y0 != sK3 ) )
@ X0 )
= ( sub @ sK3 @ ( push @ X1 @ X0 ) ) )
| spl5_6 ),
inference(constrained_superposition,[],[f402,f1022]) ).
thf(f1041,plain,
( ! [X0: term] :
( ( ( sK2 @ ( sub @ sK3 @ ( push @ X0 @ sK1 ) ) )
= $true )
| ( $false
= ( var
@ ( sK4
@ ^ [Y0: term] : ( Y0 != sK3 ) ) ) ) )
| spl5_6 ),
inference(constrained_superposition,[],[f381,f1025]) ).
thf(f1059,plain,
( ! [X0: term] :
( ( $false = $true )
| ( ( sK2 @ ( sub @ sK3 @ ( push @ X0 @ sK1 ) ) )
= $true ) )
| spl5_6
| ~ spl5_7 ),
inference(forward_demodulation,[],[f1041,f477]) ).
thf(f1060,plain,
( ! [X0: term] :
( ( sK2 @ ( sub @ sK3 @ ( push @ X0 @ sK1 ) ) )
= $true )
| spl5_6
| ~ spl5_7 ),
inference(trivial_inequality_removal,[],[f1059]) ).
thf(f1071,plain,
( ( $false = $true )
| spl5_6
| ~ spl5_7 ),
inference(backward_demodulation,[],[f386,f1060]) ).
thf(f1073,plain,
( $false
| spl5_6
| ~ spl5_7 ),
inference(trivial_inequality_removal,[],[f1071]) ).
thf(f1074,plain,
( spl5_6
| ~ spl5_7 ),
inference(avatar_contradiction_clause,[],[f1073]) ).
cnf(s5,plain,
( spl5_6
| spl5_7 ),
inference(sat_conversion,[],[f478]) ).
cnf(s6,plain,
~ spl5_6,
inference(sat_conversion,[],[f486]) ).
cnf(s21,plain,
( spl5_6
| ~ spl5_7 ),
inference(sat_conversion,[],[f1074]) ).
cnf(s22,plain,
~ spl5_7,
inference(rat,[],[s21,s6]) ).
cnf(s27,plain,
$false,
inference(rat,[],[s5,s22,s6]) ).
thf(f1075,plain,
$false,
inference(avatar_sat_refutation,[],[s27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : ALG251^3 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.00/0.11 % Computer : n012.cluster.edu
% 0.00/0.11 % Model : x86_64 x86_64
% 0.00/0.11 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.11 % Memory : 8046.5625MB
% 0.00/0.11 % OS : Linux 6.8.0-71-generic
% 0.00/0.11 % CPULimit : 300
% 0.00/0.11 % WCLimit : 300
% 0.00/0.11 % DateTime : Tue Sep 29 17:32:04 UTC 2026
% 0.07/0.11 % CPUTime :
% 0.07/0.11 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.13 Running higher-order theorem proving
% 0.07/0.15 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
% 0.07/0.23 % (428108)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.07/0.23 % (428119)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.07/0.23 % (428119)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
% 0.07/0.23 % (428119)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=1463325474:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.07/0.23 % (428115)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1883485936:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.07/0.23 % (428113)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=46245145:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.07/0.23 % (428114)lrs+10_16_si=on:nwc=1.5:random_seed=4239907177:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.07/0.23 % (428117)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2127306839:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.07/0.23 % (428116)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=484452776: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)
% 0.07/0.23 % (428118)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1966737599:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.07/0.23 % (428115)Instruction limit reached!
% 0.07/0.23 % (428115)------------------------------
% 0.07/0.23 % (428115)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.23 % (428115)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.23 % (428115)CaDiCaL version: 2.1.3
% 0.07/0.23 % (428115)Termination reason: Instruction limit
% 0.07/0.23 % (428115)Termination phase: shuffling
% 0.07/0.23 % (428115)Time elapsed: 0.001 s
% 0.07/0.23 % (428115)Peak memory usage: 10 MB
% 0.07/0.23 % (428115)Instructions burned: 3 (million)
% 0.07/0.23 % (428114)Instruction limit reached!
% 0.07/0.23 % (428114)------------------------------
% 0.07/0.23 % (428114)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.23 % (428114)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.23 % (428114)CaDiCaL version: 2.1.3
% 0.07/0.23 % (428114)Termination reason: Instruction limit
% 0.07/0.23 % (428114)Termination phase: Property scanning
% 0.07/0.23 % (428114)Time elapsed: 0.005 s
% 0.07/0.23 % (428114)Peak memory usage: 10 MB
% 0.07/0.23 % (428114)Instructions burned: 21 (million)
% 0.07/0.23 % (428117)Instruction limit reached!
% 0.07/0.23 % (428117)------------------------------
% 0.07/0.23 % (428117)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.23 % (428117)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.23 % (428117)CaDiCaL version: 2.1.3
% 0.07/0.23 % (428117)Termination reason: Instruction limit
% 0.07/0.23 % (428117)Termination phase: Naming
% 0.07/0.23 % (428117)Time elapsed: 0.006 s
% 0.07/0.23 % (428117)Peak memory usage: 11 MB
% 0.07/0.23 % (428117)Instructions burned: 25 (million)
% 0.07/0.23 % (428127)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3997248722:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.07/0.23 % (428127)Instruction limit reached!
% 0.07/0.23 % (428127)------------------------------
% 0.07/0.23 % (428127)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.23 % (428127)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.23 % (428127)CaDiCaL version: 2.1.3
% 0.07/0.23 % (428127)Termination reason: Instruction limit
% 0.07/0.23 % (428127)Termination phase: shuffling
% 0.07/0.23 % (428127)Time elapsed: 0.001 s
% 0.07/0.23 % (428127)Peak memory usage: 10 MB
% 0.07/0.23 % (428127)Instructions burned: 3 (million)
% 0.07/0.23 % (428129)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.07/0.23 % (428128)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3654563951:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.48/0.25 % (428129)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=357544243:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.48/0.25 % (428128)Instruction limit reached!
% 0.48/0.25 % (428128)------------------------------
% 0.48/0.25 % (428128)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.25 % (428128)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.25 % (428128)CaDiCaL version: 2.1.3
% 0.48/0.25 % (428128)Termination reason: Instruction limit
% 0.48/0.25 % (428128)Termination phase: shuffling
% 0.48/0.25 % (428128)Time elapsed: 0.002 s
% 0.48/0.25 % (428128)Peak memory usage: 10 MB
% 0.48/0.25 % (428128)Instructions burned: 8 (million)
% 0.48/0.25 % (428118)Instruction limit reached!
% 0.48/0.25 % (428118)------------------------------
% 0.48/0.25 % (428118)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.25 % (428118)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.25 % (428118)CaDiCaL version: 2.1.3
% 0.48/0.25 % (428118)Termination reason: Instruction limit
% 0.48/0.25 % (428118)Termination phase: Property scanning
% 0.48/0.25 % (428118)Time elapsed: 0.019 s
% 0.48/0.25 % (428118)Peak memory usage: 12 MB
% 0.48/0.25 % (428118)Instructions burned: 78 (million)
% 0.48/0.25 % (428129)Instruction limit reached!
% 0.48/0.25 % (428129)------------------------------
% 0.48/0.25 % (428129)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.25 % (428129)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.25 % (428129)CaDiCaL version: 2.1.3
% 0.48/0.25 % (428129)Termination reason: Instruction limit
% 0.48/0.25 % (428129)Termination phase: shuffling
% 0.48/0.25 % (428129)Time elapsed: 0.002 s
% 0.48/0.25 % (428129)Peak memory usage: 10 MB
% 0.48/0.25 % (428129)Instructions burned: 8 (million)
% 0.48/0.25 % (428113)Instruction limit reached!
% 0.48/0.25 % (428113)------------------------------
% 0.48/0.25 % (428113)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.25 % (428113)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.25 % (428113)CaDiCaL version: 2.1.3
% 0.48/0.25 % (428113)Termination reason: Instruction limit
% 0.48/0.25 % (428113)Termination phase: Function definition elimination
% 0.48/0.25 % (428113)Time elapsed: 0.021 s
% 0.48/0.25 % (428113)Peak memory usage: 12 MB
% 0.48/0.25 % (428113)Instructions burned: 89 (million)
% 0.48/0.25 % (428131)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=3930474259:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.48/0.25 % (428134)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
% 0.48/0.25 % (428134)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.48/0.25 % (428131)Instruction limit reached!
% 0.48/0.25 % (428131)------------------------------
% 0.48/0.25 % (428131)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.25 % (428131)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.25 % (428131)CaDiCaL version: 2.1.3
% 0.48/0.25 % (428131)Termination reason: Instruction limit
% 0.48/0.25 % (428131)Termination phase: shuffling
% 0.48/0.25 % (428131)Time elapsed: 0.003 s
% 0.48/0.25 % (428131)Peak memory usage: 10 MB
% 0.48/0.25 % (428131)Instructions burned: 12 (million)
% 0.48/0.25 % (428134)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3029687154:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.48/0.25 % (428135)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=3110573565:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.48/0.25 % (428137)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.48/0.25 % (428136)lrs+10_1_si=on:cs=on:random_seed=526520350:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.48/0.26 % (428137)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=1741221233:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.48/0.26 % (428136)Instruction limit reached!
% 0.48/0.26 % (428136)------------------------------
% 0.48/0.26 % (428136)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.26 % (428136)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.26 % (428136)CaDiCaL version: 2.1.3
% 0.48/0.26 % (428136)Termination reason: Instruction limit
% 0.48/0.26 % (428136)Termination phase: shuffling
% 0.48/0.26 % (428136)Time elapsed: 0.002 s
% 0.48/0.26 % (428136)Peak memory usage: 10 MB
% 0.48/0.26 % (428136)Instructions burned: 8 (million)
% 0.48/0.26 % (428137)Instruction limit reached!
% 0.48/0.26 % (428137)------------------------------
% 0.48/0.26 % (428137)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.26 % (428137)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.26 % (428137)CaDiCaL version: 2.1.3
% 0.48/0.26 % (428137)Termination reason: Instruction limit
% 0.48/0.26 % (428137)Termination phase: shuffling
% 0.48/0.26 % (428137)Time elapsed: 0.001 s
% 0.48/0.26 % (428137)Peak memory usage: 10 MB
% 0.48/0.26 % (428137)Instructions burned: 3 (million)
% 0.48/0.26 % (428134)Instruction limit reached!
% 0.48/0.26 % (428134)------------------------------
% 0.48/0.26 % (428134)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.26 % (428134)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.26 % (428134)CaDiCaL version: 2.1.3
% 0.48/0.26 % (428134)Termination reason: Instruction limit
% 0.48/0.26 % (428134)Termination phase: Property scanning
% 0.48/0.26 % (428134)Time elapsed: 0.007 s
% 0.48/0.26 % (428134)Peak memory usage: 10 MB
% 0.48/0.26 % (428134)Instructions burned: 32 (million)
% 0.48/0.26 % (428119)Instruction limit reached!
% 0.48/0.26 % (428119)------------------------------
% 0.48/0.26 % (428119)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.26 % (428119)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.26 % (428119)CaDiCaL version: 2.1.3
% 0.48/0.26 % (428119)Termination reason: Instruction limit
% 0.48/0.26 % (428119)Termination phase: Saturation
% 0.48/0.26 % (428119)Time elapsed: 0.036 s
% 0.48/0.26 % (428119)Peak memory usage: 13 MB
% 0.48/0.26 % (428119)Instructions burned: 160 (million)
% 0.48/0.26 % (428139)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=2325777166:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.48/0.26 % (428144)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=1519486282:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.48/0.26 % (428145)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=4273574459:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/25Mi)
% 0.48/0.26 % (428139)Refutation not found, incomplete strategy
% 0.48/0.26 % (428139)------------------------------
% 0.48/0.26 % (428139)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.26 % (428139)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.26 % (428139)CaDiCaL version: 2.1.3
% 0.48/0.26 % (428139)Termination reason: Refutation not found, incomplete strategy
% 0.48/0.26 % (428139)Time elapsed: 0.007 s
% 0.48/0.26 % (428139)Peak memory usage: 12 MB
% 0.48/0.26 % (428139)Instructions burned: 25 (million)
% 0.48/0.26 % (428139)------------------------------
% 0.48/0.26 % (428139)------------------------------
% 0.48/0.26 % (428146)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=2369516140:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2999 on theBenchmark for (2999ds/14Mi)
% 0.48/0.26 % (428147)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=3716863227:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/327Mi)
% 0.48/0.26 % (428135)Instruction limit reached!
% 0.48/0.26 % (428135)------------------------------
% 0.48/0.26 % (428135)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.26 % (428135)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.26 % (428135)CaDiCaL version: 2.1.3
% 0.48/0.26 % (428135)Termination reason: Instruction limit
% 0.48/0.30 % (428135)Termination phase: Saturation
% 0.48/0.30 % (428135)Time elapsed: 0.019 s
% 0.48/0.30 % (428135)Peak memory usage: 12 MB
% 0.48/0.30 % (428135)Instructions burned: 88 (million)
% 0.48/0.30 % (428146)Instruction limit reached!
% 0.48/0.30 % (428146)------------------------------
% 0.48/0.30 % (428146)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.30 % (428146)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.30 % (428146)CaDiCaL version: 2.1.3
% 0.48/0.30 % (428146)Termination reason: Instruction limit
% 0.48/0.30 % (428146)Termination phase: shuffling
% 0.48/0.30 % (428146)Time elapsed: 0.003 s
% 0.48/0.30 % (428146)Peak memory usage: 10 MB
% 0.48/0.30 % (428146)Instructions burned: 14 (million)
% 0.48/0.30 % (428145)Instruction limit reached!
% 0.48/0.30 % (428145)------------------------------
% 0.48/0.30 % (428145)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.30 % (428145)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.30 % (428145)CaDiCaL version: 2.1.3
% 0.48/0.30 % (428145)Termination reason: Instruction limit
% 0.48/0.30 % (428145)Termination phase: Preprocessing 3
% 0.48/0.30 % (428145)Time elapsed: 0.007 s
% 0.48/0.30 % (428145)Peak memory usage: 11 MB
% 0.48/0.30 % (428145)Instructions burned: 28 (million)
% 0.48/0.30 % (428144)Refutation not found, incomplete strategy
% 0.48/0.30 % (428144)------------------------------
% 0.48/0.30 % (428144)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.30 % (428144)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.30 % (428144)CaDiCaL version: 2.1.3
% 0.48/0.30 % (428144)Termination reason: Refutation not found, incomplete strategy
% 0.48/0.30 % (428144)Time elapsed: 0.011 s
% 0.48/0.30 % (428144)Peak memory usage: 12 MB
% 0.48/0.30 % (428144)Instructions burned: 50 (million)
% 0.48/0.30 % (428144)------------------------------
% 0.48/0.30 % (428144)------------------------------
% 0.48/0.30 % (428151)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=1701418572:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/14Mi)
% 0.48/0.30 % (428154)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=447370795:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.48/0.30 % (428151)Instruction limit reached!
% 0.48/0.30 % (428151)------------------------------
% 0.48/0.30 % (428151)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.30 % (428151)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.30 % (428151)CaDiCaL version: 2.1.3
% 0.48/0.30 % (428151)Termination reason: Instruction limit
% 0.48/0.30 % (428151)Termination phase: shuffling
% 0.48/0.30 % (428151)Time elapsed: 0.004 s
% 0.48/0.30 % (428151)Peak memory usage: 10 MB
% 0.48/0.30 % (428151)Instructions burned: 16 (million)
% 0.48/0.30 % (428155)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=3942633523:i=26:ep=R:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/26Mi)
% 0.48/0.30 % (428154)Instruction limit reached!
% 0.48/0.30 % (428154)------------------------------
% 0.48/0.30 % (428154)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.30 % (428154)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.30 % (428154)CaDiCaL version: 2.1.3
% 0.48/0.30 % (428154)Termination reason: Instruction limit
% 0.48/0.30 % (428154)Termination phase: shuffling
% 0.48/0.30 % (428154)Time elapsed: 0.001 s
% 0.48/0.30 % (428154)Peak memory usage: 10 MB
% 0.48/0.30 % (428154)Instructions burned: 3 (million)
% 0.48/0.30 % (428156)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=3439495225:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/23Mi)
% 0.48/0.30 % (428158)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=3652230047:cond=on:i=60:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/60Mi)
% 0.48/0.30 % (428155)Instruction limit reached!
% 0.48/0.30 % (428155)------------------------------
% 0.48/0.30 % (428155)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.30 % (428155)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.30 % (428155)CaDiCaL version: 2.1.3
% 0.48/0.30 % (428155)Termination reason: Instruction limit
% 0.48/0.30 % (428155)Termination phase: Property scanning
% 0.48/0.33 % (428155)Time elapsed: 0.006 s
% 0.48/0.33 % (428155)Peak memory usage: 10 MB
% 0.48/0.33 % (428155)Instructions burned: 27 (million)
% 0.48/0.33 % (428156)Instruction limit reached!
% 0.48/0.33 % (428156)------------------------------
% 0.48/0.33 % (428156)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.33 % (428156)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.33 % (428156)CaDiCaL version: 2.1.3
% 0.48/0.33 % (428156)Termination reason: Instruction limit
% 0.48/0.33 % (428156)Termination phase: Property scanning
% 0.48/0.33 % (428156)Time elapsed: 0.006 s
% 0.48/0.33 % (428156)Peak memory usage: 10 MB
% 0.48/0.33 % (428156)Instructions burned: 26 (million)
% 0.48/0.33 % (428161)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) 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
% 0.48/0.33 % (428161)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 0.48/0.33 % (428162)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 0.48/0.33 % (428161)ott+21_1_to=kbo:sil=128000:cnfonf=lazy_gen:bsd=on:si=on:sp=const_frequency:lma=off:uwa=off:foolp=on:s2agt=10:lwlo=on:random_seed=281807440:i=14:add=off:nm=40:rtra=on:rawr=on_2999 on theBenchmark for (2999ds/14Mi)
% 0.48/0.33 % (428162)lrs+1010_4:1_slsqr=8,1:to=kbo:cha=on:drc=off:si=on:sp=arity:lcm=predicate:uwa=off:fd=preordered:gs=on:nwc=5:s2agt=32:slsqc=1:kmz=on:updr=off:chr=on:pe=on:slsq=on:random_seed=2072763630:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.48/0.33 % (428162)Instruction limit reached!
% 0.48/0.33 % (428162)------------------------------
% 0.48/0.33 % (428162)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.33 % (428162)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.33 % (428162)CaDiCaL version: 2.1.3
% 0.48/0.33 % (428162)Termination reason: Instruction limit
% 0.48/0.33 % (428162)Termination phase: shuffling
% 0.48/0.33 % (428162)Time elapsed: 0.002 s
% 0.48/0.33 % (428162)Peak memory usage: 10 MB
% 0.48/0.33 % (428162)Instructions burned: 8 (million)
% 0.48/0.33 % (428161)Instruction limit reached!
% 0.48/0.33 % (428161)------------------------------
% 0.48/0.33 % (428161)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.33 % (428161)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.33 % (428161)CaDiCaL version: 2.1.3
% 0.48/0.33 % (428161)Termination reason: Instruction limit
% 0.48/0.33 % (428161)Termination phase: shuffling
% 0.48/0.33 % (428161)Time elapsed: 0.004 s
% 0.48/0.33 % (428161)Peak memory usage: 10 MB
% 0.48/0.33 % (428161)Instructions burned: 17 (million)
% 0.48/0.33 % (428165)dis+1004_50_to=lpo:drc=off:fde=unused:cnfonf=lazy_not_gen_be_off:si=on:sp=reverse_arity:spb=units:cbe=off:foolp=on:random_seed=3429829133:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2999 on theBenchmark for (2999ds/31Mi)
% 0.48/0.33 % (428166)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=2606668856:i=7:hud=5:bd=preordered:rtra=on:bet=on_2999 on theBenchmark for (2999ds/7Mi)
% 0.48/0.33 % (428166)Instruction limit reached!
% 0.48/0.33 % (428166)------------------------------
% 0.48/0.33 % (428166)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.33 % (428166)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.33 % (428166)CaDiCaL version: 2.1.3
% 0.48/0.33 % (428166)Termination reason: Instruction limit
% 0.48/0.33 % (428166)Termination phase: shuffling
% 0.48/0.33 % (428166)Time elapsed: 0.002 s
% 0.48/0.33 % (428166)Peak memory usage: 10 MB
% 0.48/0.33 % (428166)Instructions burned: 8 (million)
% 0.48/0.33 % (428158)Instruction limit reached!
% 0.48/0.33 % (428158)------------------------------
% 0.48/0.33 % (428158)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.33 % (428158)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.33 % (428158)CaDiCaL version: 2.1.3
% 0.48/0.33 % (428158)Termination reason: Instruction limit
% 0.48/0.33 % (428158)Termination phase: Property scanning
% 0.48/0.33 % (428158)Time elapsed: 0.016 s
% 0.48/0.33 % (428158)Peak memory usage: 12 MB
% 0.48/0.33 % (428158)Instructions burned: 64 (million)
% 0.48/0.33 % (428169)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=670782026:i=23:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/23Mi)
% 0.48/0.33 % (428165)Instruction limit reached!
% 0.48/0.33 % (428165)------------------------------
% 0.48/0.33 % (428165)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.33 % (428165)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.33 % (428165)CaDiCaL version: 2.1.3
% 0.48/0.33 % (428165)Termination reason: Instruction limit
% 0.48/0.33 % (428165)Termination phase: Property scanning
% 0.48/0.33 % (428165)Time elapsed: 0.007 s
% 0.48/0.33 % (428165)Peak memory usage: 10 MB
% 0.48/0.33 % (428165)Instructions burned: 32 (million)
% 0.48/0.33 % (428170)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=1174882221:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/20Mi)
% 0.48/0.33 % (428169)Instruction limit reached!
% 0.48/0.33 % (428169)------------------------------
% 0.48/0.33 % (428169)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.33 % (428169)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.33 % (428169)CaDiCaL version: 2.1.3
% 0.48/0.33 % (428169)Termination reason: Instruction limit
% 0.48/0.33 % (428169)Termination phase: Property scanning
% 0.48/0.33 % (428169)Time elapsed: 0.006 s
% 0.48/0.33 % (428169)Peak memory usage: 10 MB
% 0.48/0.33 % (428169)Instructions burned: 27 (million)
% 0.48/0.33 % (428173)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=2642554606:i=1240:rtra=on:ixr=off_2998 on theBenchmark for (2998ds/1240Mi)
% 0.48/0.33 % (428170)Instruction limit reached!
% 0.48/0.33 % (428170)------------------------------
% 0.48/0.33 % (428170)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.33 % (428170)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.33 % (428170)CaDiCaL version: 2.1.3
% 0.48/0.33 % (428170)Termination reason: Instruction limit
% 0.48/0.33 % (428170)Termination phase: Property scanning
% 0.48/0.33 % (428170)Time elapsed: 0.005 s
% 0.48/0.33 % (428170)Peak memory usage: 10 MB
% 0.48/0.33 % (428170)Instructions burned: 22 (million)
% 0.48/0.33 % (428174)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=25689638:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/143Mi)
% 0.48/0.33 % (428176)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=4222692425:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/193Mi)
% 0.48/0.33 % (428180)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.48/0.33 % (428179)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=980230389:i=42:hud=10:rtra=on_2998 on theBenchmark for (2998ds/42Mi)
% 0.48/0.33 % (428180)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3203277336:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2998 on theBenchmark for (2998ds/7Mi)
% 0.48/0.33 % (428180)Instruction limit reached!
% 0.48/0.33 % (428180)------------------------------
% 0.48/0.33 % (428180)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.33 % (428180)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.33 % (428180)CaDiCaL version: 2.1.3
% 0.48/0.33 % (428180)Termination reason: Instruction limit
% 0.48/0.33 % (428180)Termination phase: shuffling
% 0.48/0.33 % (428180)Time elapsed: 0.002 s
% 0.48/0.33 % (428180)Peak memory usage: 10 MB
% 0.48/0.33 % (428180)Instructions burned: 8 (million)
% 0.48/0.33 % (428179)Instruction limit reached!
% 0.48/0.33 % (428179)------------------------------
% 0.48/0.33 % (428179)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.33 % (428179)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.33 % (428179)CaDiCaL version: 2.1.3
% 0.48/0.33 % (428179)Termination reason: Instruction limit
% 0.48/0.33 % (428179)Termination phase: Property scanning
% 0.48/0.33 % (428179)Time elapsed: 0.009 s
% 0.48/0.33 % (428179)Peak memory usage: 10 MB
% 0.48/0.33 % (428179)Instructions burned: 43 (million)
% 0.48/0.33 % (428185)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=2239816060:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/181Mi)
% 0.48/0.33 % (428186)dis+10_8_sil=128000:plsq=on:plsqc=1:si=on:sp=unary_first:sos=on:lma=off:plsqr=64,1:uwa=interpreted_only:foolp=on:random_seed=2528140183:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/169Mi)
% 0.48/0.33 % (428185)Refutation not found, incomplete strategy
% 0.48/0.33 % (428185)------------------------------
% 0.48/0.33 % (428185)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.33 % (428185)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.33 % (428185)CaDiCaL version: 2.1.3
% 0.48/0.33 % (428185)Termination reason: Refutation not found, incomplete strategy
% 0.48/0.33 % (428185)Time elapsed: 0.011 s
% 0.48/0.33 % (428185)Peak memory usage: 13 MB
% 0.48/0.33 % (428185)Instructions burned: 49 (million)
% 0.48/0.33 % (428174)Instruction limit reached!
% 0.48/0.33 % (428174)------------------------------
% 0.48/0.33 % (428174)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.33 % (428174)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.33 % (428174)CaDiCaL version: 2.1.3
% 0.48/0.33 % (428174)Termination reason: Instruction limit
% 0.48/0.33 % (428174)Termination phase: Saturation
% 0.48/0.33 % (428174)Time elapsed: 0.033 s
% 0.48/0.33 % (428174)Peak memory usage: 13 MB
% 0.48/0.33 % (428174)Instructions burned: 146 (million)
% 0.48/0.33 % (428185)------------------------------
% 0.48/0.33 % (428185)------------------------------
% 0.48/0.33 % (428189)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 0.48/0.33 % (428189)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=4069208766:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2998 on theBenchmark for (2998ds/6Mi)
% 0.48/0.33 % (428190)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=2740492659:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2998 on theBenchmark for (2998ds/22Mi)
% 0.48/0.33 % (428147)Instruction limit reached!
% 0.48/0.33 % (428147)------------------------------
% 0.48/0.33 % (428147)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.33 % (428147)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.33 % (428147)CaDiCaL version: 2.1.3
% 0.48/0.33 % (428147)Termination reason: Instruction limit
% 0.48/0.33 % (428147)Termination phase: Saturation
% 0.48/0.33 % (428147)Time elapsed: 0.091 s
% 0.48/0.33 % (428147)Peak memory usage: 15 MB
% 0.48/0.33 % (428147)Instructions burned: 328 (million)
% 0.48/0.33 % (428189)Instruction limit reached!
% 0.48/0.33 % (428189)------------------------------
% 0.48/0.33 % (428189)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.33 % (428189)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.33 % (428189)CaDiCaL version: 2.1.3
% 0.48/0.33 % (428189)Termination reason: Instruction limit
% 0.48/0.33 % (428189)Termination phase: shuffling
% 0.48/0.33 % (428189)Time elapsed: 0.002 s
% 0.48/0.33 % (428189)Peak memory usage: 10 MB
% 0.48/0.33 % (428189)Instructions burned: 9 (million)
% 0.48/0.33 % (428176)Instruction limit reached!
% 0.48/0.33 % (428176)------------------------------
% 0.48/0.33 % (428176)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.33 % (428176)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.33 % (428176)CaDiCaL version: 2.1.3
% 0.48/0.33 % (428176)Termination reason: Instruction limit
% 0.48/0.33 % (428176)Termination phase: Saturation
% 0.48/0.33 % (428176)Time elapsed: 0.045 s
% 0.48/0.33 % (428176)Peak memory usage: 13 MB
% 0.48/0.33 % (428176)Instructions burned: 198 (million)
% 0.48/0.33 % (428190)Instruction limit reached!
% 0.48/0.33 % (428190)------------------------------
% 0.48/0.33 % (428190)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.33 % (428190)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.33 % (428190)CaDiCaL version: 2.1.3
% 0.48/0.33 % (428190)Termination reason: Instruction limit
% 0.48/0.33 % (428190)Termination phase: Property scanning
% 0.48/0.33 % (428190)Time elapsed: 0.007 s
% 0.48/0.33 % (428190)Peak memory usage: 10 MB
% 0.48/0.33 % (428190)Instructions burned: 32 (million)
% 0.48/0.33 % (428186) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-428108-428186"...
% 0.48/0.33 % (428186)...printing done.
% 0.48/0.33 % (428186)Refutation found. Thanks to Tanya!
% 0.48/0.33 % SZS status Theorem for theBenchmark
% 0.48/0.33 % SZS output start Proof for theBenchmark
% See solution above
% 0.48/0.33 % (428186)------------------------------
% 0.48/0.33 % (428186)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.33 % (428186)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.33 % (428186)CaDiCaL version: 2.1.3
% 0.48/0.33 % (428186)Termination reason: Refutation
% 0.48/0.33 % (428186)Time elapsed: 0.026 s
% 0.48/0.33 % (428186)Peak memory usage: 14 MB
% 0.48/0.33 % (428186)Instructions burned: 98 (million)
% 0.48/0.33 % (428108)Success in time 0.175 s
% 0.48/0.33 % Vampire exiting
%------------------------------------------------------------------------------