%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG266^2 : 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 : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 07:45:16 AM UTC 2026
% Result : Theorem 2.02s 0.58s
% Output : Refutation 2.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 12
% Syntax : Number of formulae : 191 ( 49 unt; 0 typ; 6 def)
% Number of atoms : 1417 ( 407 equ; 0 cnn)
% Maximal formula atoms : 7 ( 7 avg)
% Number of connectives : 4317 ( 189 ~; 364 |; 0 &;3392 @)
% ( 6 <=>; 181 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 314 ( 314 >; 0 *; 0 +; 0 <<)
% Number of symbols : 157 ( 153 usr; 121 con; 0-4 aty)
% ( 185 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 468 ( 0 sgn 238 !; 0 ?; 468 :)
% 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,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_125,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_126,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_127,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_128,type,
vIMP: $o > $o > $o ).
thf(func_def_129,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_130,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_131,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_132,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_133,type,
vAND: $o > $o > $o ).
thf(func_def_134,type,
vNOT: $o > $o ).
thf(func_def_135,type,
vIFF: $o > $o > $o ).
thf(func_def_138,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_140,type,
sK1: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_141,type,
sK2: ( subst > term > subst > $o ) > term > term ).
thf(func_def_142,type,
sK3: subst > term > subst > $o ).
thf(func_def_143,type,
sK4: ( subst > term > term ) > term ).
thf(func_def_144,type,
sK5: ( subst > term > term ) > term ).
thf(func_def_145,type,
sK6: ( subst > term > term ) > subst ).
thf(func_def_146,type,
sK7: ( subst > term > term ) > subst ).
thf(func_def_147,type,
sK8: ( subst > term > term ) > subst ).
thf(func_def_148,type,
sK9: ( subst > term > term ) > subst ).
thf(func_def_149,type,
sK10: term ).
thf(f3,axiom,
( axvarid
= ( ! [X0: term] :
( ( sub @ X0 @ id )
= X0 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',axvarid) ).
thf(f11,axiom,
( axvarshift
= ( ( push @ one @ sh )
= id ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',axvarshift) ).
thf(f96,axiom,
( hoasinduction_lem3aa
= ( ! [X0: subst > term > subst > $o] :
( ! [X1: subst > term > term] :
( ! [X3: term,X2: subst,X4: subst] :
( ( sub @ ( X1 @ X2 @ X3 ) @ X4 )
= ( X1 @ ( comp @ X2 @ X4 ) @ ( sub @ X3 @ X4 ) ) )
=> ( ! [X3: term] :
( ( X0 @ id @ X3 @ id )
=> ( X0 @ id @ ( X1 @ id @ X3 ) @ id ) )
=> ( X0 @ id
@ ( hoaslam @ id
@ ^ [X2: subst,X3: term] : ( X1 @ X2 @ X3 ) )
@ id ) ) )
=> ! [X3: term] :
( ! [X5: term] :
( ( X0 @ id @ X5 @ id )
=> ( X0 @ id @ ( sub @ X3 @ ( push @ X5 @ id ) ) @ id ) )
=> ( X0 @ id @ ( lam @ ( sub @ X3 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',hoasinduction_lem3aa) ).
thf(f102,axiom,
! [X0: subst > term > subst > $o] :
( ( ! [X1: subst > term > term] :
( ! [X2: subst,X4: subst,X3: term] :
( ( sub @ ( X1 @ X2 @ X3 ) @ X4 )
= ( X1 @ ( comp @ X2 @ X4 ) @ ( sub @ X3 @ X4 ) ) )
=> ( ! [X3: term] :
( ( X0 @ id @ X3 @ id )
=> ( X0 @ id @ ( X1 @ id @ X3 ) @ id ) )
=> ( X0 @ id
@ ( hoaslam @ id
@ ^ [X2: subst,X3: term] : ( X1 @ X2 @ X3 ) )
@ id ) ) )
=> ! [X3: term] :
( ! [X5: term] :
( ( X0 @ id @ X5 @ id )
=> ( X0 @ id @ ( sub @ X3 @ ( push @ X5 @ id ) ) @ id ) )
=> ( X0 @ id @ ( lam @ X3 ) @ id ) ) )
= hoasinduction_lem3a ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',hoasinduction_lem3a) ).
thf(f104,axiom,
( ( hoasinduction_lem3a_lthm = axvarid )
=> ( axvarshift
=> ( hoasinduction_lem3aa
=> hoasinduction_lem3a ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',hoasinduction_lem3a_lthm) ).
thf(f114,conjecture,
hoasinduction_lem3a_lthm,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(f115,negated_conjecture,
~ hoasinduction_lem3a_lthm,
inference(negated_conjecture,[status(cth)],[f114]) ).
thf(f119,plain,
! [X0: subst > term > subst > $o] :
( ( ! [X1: subst > term > term] :
( ! [X2: subst,X3: subst,X4: term] :
( ( X1 @ ( comp @ X2 @ X3 ) @ ( sub @ X4 @ X3 ) )
= ( sub @ ( X1 @ X2 @ X4 ) @ X3 ) )
=> ( ! [X5: term] :
( ( X0 @ id @ X5 @ id )
=> ( X0 @ id @ ( X1 @ id @ X5 ) @ id ) )
=> ( X0 @ id
@ ( hoaslam @ id
@ ^ [X6: subst,X7: term] : ( X1 @ X6 @ X7 ) )
@ id ) ) )
=> ! [X8: term] :
( ! [X9: term] :
( ( X0 @ id @ X9 @ id )
=> ( X0 @ id @ ( sub @ X8 @ ( push @ X9 @ id ) ) @ id ) )
=> ( X0 @ id @ ( lam @ X8 ) @ id ) ) )
= hoasinduction_lem3a ),
inference(rectify,[],[f102]) ).
thf(f120,plain,
( hoasinduction_lem3a
= ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) )
= ( sub @ ( Y1 @ Y4 @ Y2 ) @ Y3 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( Y1 @ id @ Y2 ) @ id ) ) )
=> ( Y0 @ id
@ ( hoaslam @ id
@ ^ [Y2: subst,Y3: term] : ( Y1 @ Y2 @ Y3 ) )
@ id ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ Y1 ) @ id ) ) ) ) ) ),
inference(fool_elimination,[],[f119]) ).
thf(f178,plain,
( axvarshift
= ( id
= ( push @ one @ sh ) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f241,plain,
~ hoasinduction_lem3a_lthm,
inference(rectify,[],[f115]) ).
thf(f242,plain,
hoasinduction_lem3a_lthm != $true,
inference(fool_elimination,[],[f241]) ).
thf(f273,plain,
( ( hoasinduction_lem3a_lthm = axvarid )
=> ( axvarshift
=> ( hoasinduction_lem3aa
=> hoasinduction_lem3a ) ) ),
inference(rectify,[],[f104]) ).
thf(f274,plain,
( hoasinduction_lem3a_lthm
= ( axvarid
=> ( axvarshift
=> ( hoasinduction_lem3aa
=> hoasinduction_lem3a ) ) ) ),
inference(fool_elimination,[],[f273]) ).
thf(f289,plain,
( hoasinduction_lem3aa
= ( ! [X0: subst > term > subst > $o] :
( ! [X1: subst > term > term] :
( ! [X2: term,X3: subst,X4: subst] :
( ( X1 @ ( comp @ X3 @ X4 ) @ ( sub @ X2 @ X4 ) )
= ( sub @ ( X1 @ X3 @ X2 ) @ X4 ) )
=> ( ! [X5: term] :
( ( X0 @ id @ X5 @ id )
=> ( X0 @ id @ ( X1 @ id @ X5 ) @ id ) )
=> ( X0 @ id
@ ( hoaslam @ id
@ ^ [X6: subst,X7: term] : ( X1 @ X6 @ X7 ) )
@ id ) ) )
=> ! [X8: term] :
( ! [X9: term] :
( ( X0 @ id @ X9 @ id )
=> ( X0 @ id @ ( sub @ X8 @ ( push @ X9 @ id ) ) @ id ) )
=> ( X0 @ id @ ( lam @ ( sub @ X8 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) ),
inference(rectify,[],[f96]) ).
thf(f290,plain,
( hoasinduction_lem3aa
= ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y1 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y4 @ Y2 ) )
= ( sub @ ( Y1 @ Y3 @ Y4 ) @ Y2 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( Y1 @ id @ Y2 ) @ id ) ) )
=> ( Y0 @ id
@ ( hoaslam @ id
@ ^ [Y2: subst,Y3: term] : ( Y1 @ Y2 @ Y3 ) )
@ id ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ ( sub @ Y1 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) ) ),
inference(fool_elimination,[],[f289]) ).
thf(f314,plain,
( axvarid
= ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f319,plain,
hoasinduction_lem3a_lthm != $true,
inference(flattening,[],[f242]) ).
thf(f320,plain,
( hoasinduction_lem3a_lthm
= ( axvarid
=> ( axvarshift
=> ( hoasinduction_lem3aa
=> hoasinduction_lem3a ) ) ) ),
inference(cnf_transformation,[],[f274]) ).
thf(f321,plain,
( axvarid
= ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) ),
inference(cnf_transformation,[],[f314]) ).
thf(f322,plain,
( axvarshift
= ( id
= ( push @ one @ sh ) ) ),
inference(cnf_transformation,[],[f178]) ).
thf(f324,plain,
hoasinduction_lem3a_lthm != $true,
inference(cnf_transformation,[],[f319]) ).
thf(f325,plain,
( hoasinduction_lem3a
= ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) )
= ( sub @ ( Y1 @ Y4 @ Y2 ) @ Y3 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( Y1 @ id @ Y2 ) @ id ) ) )
=> ( Y0 @ id
@ ( hoaslam @ id
@ ^ [Y2: subst,Y3: term] : ( Y1 @ Y2 @ Y3 ) )
@ id ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ Y1 ) @ id ) ) ) ) ) ),
inference(cnf_transformation,[],[f120]) ).
thf(f326,plain,
( hoasinduction_lem3aa
= ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y1 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y4 @ Y2 ) )
= ( sub @ ( Y1 @ Y3 @ Y4 ) @ Y2 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( Y1 @ id @ Y2 ) @ id ) ) )
=> ( Y0 @ id
@ ( hoaslam @ id
@ ^ [Y2: subst,Y3: term] : ( Y1 @ Y2 @ Y3 ) )
@ id ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ ( sub @ Y1 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) ) ),
inference(cnf_transformation,[],[f290]) ).
thf(f328,plain,
( hoasinduction_lem3a
= ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) )
= ( sub @ ( Y1 @ Y4 @ Y2 ) @ Y3 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( Y1 @ id @ Y2 ) @ id ) ) )
=> ( Y0 @ id @ ( hoaslam @ id @ Y1 ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ Y1 ) @ id ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f325]) ).
thf(f329,plain,
( hoasinduction_lem3aa
= ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y1 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y4 @ Y2 ) )
= ( sub @ ( Y1 @ Y3 @ Y4 ) @ Y2 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( Y1 @ id @ Y2 ) @ id ) ) )
=> ( Y0 @ id @ ( hoaslam @ id @ Y1 ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ ( sub @ Y1 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f326]) ).
thf(f330,plain,
( ( hoasinduction_lem3a_lthm = $false )
| ( $true != $true ) ),
inference(fool_paramodulation,[],[f324]) ).
thf(f331,plain,
hoasinduction_lem3a_lthm = $false,
inference(trivial_inequality_removal,[],[f330]) ).
thf(f333,plain,
( ( axvarid
=> ( axvarshift
=> ( hoasinduction_lem3aa
=> hoasinduction_lem3a ) ) )
= $false ),
inference(backward_demodulation,[],[f320,f331]) ).
thf(f334,plain,
( ( axvarshift
=> ( hoasinduction_lem3aa
=> hoasinduction_lem3a ) )
= $false ),
inference(imp_proxy_clausification,[],[f333]) ).
thf(f335,plain,
axvarid = $true,
inference(imp_proxy_clausification,[],[f333]) ).
thf(f336,plain,
( ( hoasinduction_lem3aa
=> hoasinduction_lem3a )
= $false ),
inference(imp_proxy_clausification,[],[f334]) ).
thf(f337,plain,
axvarshift = $true,
inference(imp_proxy_clausification,[],[f334]) ).
thf(f338,plain,
hoasinduction_lem3a = $false,
inference(imp_proxy_clausification,[],[f336]) ).
thf(f339,plain,
hoasinduction_lem3aa = $true,
inference(imp_proxy_clausification,[],[f336]) ).
thf(f341,plain,
( $true
= ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) ),
inference(backward_demodulation,[],[f321,f335]) ).
thf(f454,plain,
! [X1: term] :
( $true
= ( ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f341]) ).
thf(f455,plain,
! [X1: term] :
( $true
= ( ( sub @ X1 @ id )
= X1 ) ),
inference(beta-eta_normalization,[],[f454]) ).
thf(f456,plain,
! [X1: term] :
( ( sub @ X1 @ id )
= X1 ),
inference(equality_proxy_clausification,[],[f455]) ).
thf(f656,definition,
( spl0_48
<=> ( axvarshift = $true ) ),
introduced(definition,[new_symbols(definition,[spl0_48])],[avatar_definition]) ).
thf(f658,plain,
( ( axvarshift = $true )
| ~ spl0_48 ),
inference(avatar_component_clause,[],[f656]) ).
thf(f786,definition,
( spl0_74
<=> ( hoasinduction_lem3a = $false ) ),
introduced(definition,[new_symbols(definition,[spl0_74])],[avatar_definition]) ).
thf(f788,plain,
( ( hoasinduction_lem3a = $false )
| ~ spl0_74 ),
inference(avatar_component_clause,[],[f786]) ).
thf(f790,plain,
spl0_48,
inference(avatar_split_clause,[],[f337,f656]) ).
thf(f791,plain,
spl0_74,
inference(avatar_split_clause,[],[f338,f786]) ).
thf(f792,plain,
( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y1 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y4 @ Y2 ) )
= ( sub @ ( Y1 @ Y3 @ Y4 ) @ Y2 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( Y1 @ id @ Y2 ) @ id ) ) )
=> ( Y0 @ id @ ( hoaslam @ id @ Y1 ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ ( sub @ Y1 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
= $true ),
inference(backward_demodulation,[],[f329,f339]) ).
thf(f794,plain,
! [X1: subst > term > subst > $o] :
( $true
= ( ^ [Y0: subst > term > subst > $o] :
( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y1 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y4 @ Y2 ) )
= ( sub @ ( Y1 @ Y3 @ Y4 ) @ Y2 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( Y1 @ id @ Y2 ) @ id ) ) )
=> ( Y0 @ id @ ( hoaslam @ id @ Y1 ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ ( sub @ Y1 @ ( push @ one @ sh ) ) ) @ id ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f792]) ).
thf(f795,plain,
! [X1: subst > term > subst > $o] :
( ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( X1 @ id @ Y1 @ id )
=> ( X1 @ id @ ( Y0 @ id @ Y1 ) @ id ) ) )
=> ( X1 @ id @ ( hoaslam @ id @ Y0 ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( X1 @ id @ Y1 @ id )
=> ( X1 @ id @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ Y0 @ ( push @ one @ sh ) ) ) @ id ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f794]) ).
thf(f796,plain,
! [X1: subst > term > subst > $o] :
( ( $true
= ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( X1 @ id @ Y1 @ id )
=> ( X1 @ id @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ Y0 @ ( push @ one @ sh ) ) ) @ id ) ) ) )
| ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( X1 @ id @ Y1 @ id )
=> ( X1 @ id @ ( Y0 @ id @ Y1 ) @ id ) ) )
=> ( X1 @ id @ ( hoaslam @ id @ Y0 ) @ id ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f795]) ).
thf(f797,plain,
! [X2: term,X1: subst > term > subst > $o] :
( ( $true
= ( ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( X1 @ id @ Y1 @ id )
=> ( X1 @ id @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ Y0 @ ( push @ one @ sh ) ) ) @ id ) )
@ X2 ) )
| ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( X1 @ id @ Y1 @ id )
=> ( X1 @ id @ ( Y0 @ id @ Y1 ) @ id ) ) )
=> ( X1 @ id @ ( hoaslam @ id @ Y0 ) @ id ) ) ) )
= $false ) ),
inference(pi_proxy_clausification,[],[f796]) ).
thf(f798,plain,
! [X2: term,X1: subst > term > subst > $o] :
( ( $true
= ( ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( X1 @ id @ Y1 @ id )
=> ( X1 @ id @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ Y0 @ ( push @ one @ sh ) ) ) @ id ) )
@ X2 ) )
| ( ( ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( X1 @ id @ Y1 @ id )
=> ( X1 @ id @ ( Y0 @ id @ Y1 ) @ id ) ) )
=> ( X1 @ id @ ( hoaslam @ id @ Y0 ) @ id ) ) )
@ ( sK1 @ X1 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f797]) ).
thf(f799,plain,
! [X2: term,X1: subst > term > subst > $o] :
( ( ( ( !! @ term
@ ^ [Y0: term] :
( ( X1 @ id @ Y0 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ Y0 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) )
= $true )
| ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sK1 @ X1 @ ( comp @ Y1 @ Y0 ) @ ( sub @ Y2 @ Y0 ) )
= ( sub @ ( sK1 @ X1 @ Y1 @ Y2 ) @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( X1 @ id @ Y0 @ id )
=> ( X1 @ id @ ( sK1 @ X1 @ id @ Y0 ) @ id ) ) )
=> ( X1 @ id @ ( hoaslam @ id @ ( sK1 @ X1 ) ) @ id ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f798]) ).
thf(f800,plain,
! [X2: term,X1: subst > term > subst > $o] :
( ( ( !! @ term
@ ^ [Y0: term] :
( ( X1 @ id @ Y0 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ Y0 @ id ) ) @ id ) ) )
= $false )
| ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sK1 @ X1 @ ( comp @ Y1 @ Y0 ) @ ( sub @ Y2 @ Y0 ) )
= ( sub @ ( sK1 @ X1 @ Y1 @ Y2 ) @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( X1 @ id @ Y0 @ id )
=> ( X1 @ id @ ( sK1 @ X1 @ id @ Y0 ) @ id ) ) )
=> ( X1 @ id @ ( hoaslam @ id @ ( sK1 @ X1 ) ) @ id ) ) )
= $false )
| ( $true
= ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ),
inference(imp_proxy_clausification,[],[f799]) ).
thf(f801,plain,
! [X2: term,X1: subst > term > subst > $o] :
( ( $true
= ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) )
| ( $false
= ( ^ [Y0: term] :
( ( X1 @ id @ Y0 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ Y0 @ id ) ) @ id ) )
@ ( sK2 @ X1 @ X2 ) ) )
| ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sK1 @ X1 @ ( comp @ Y1 @ Y0 ) @ ( sub @ Y2 @ Y0 ) )
= ( sub @ ( sK1 @ X1 @ Y1 @ Y2 ) @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( X1 @ id @ Y0 @ id )
=> ( X1 @ id @ ( sK1 @ X1 @ id @ Y0 ) @ id ) ) )
=> ( X1 @ id @ ( hoaslam @ id @ ( sK1 @ X1 ) ) @ id ) ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f800]) ).
thf(f802,plain,
! [X2: term,X1: subst > term > subst > $o] :
( ( $true
= ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) )
| ( $false
= ( ^ [Y0: term] :
( ( X1 @ id @ Y0 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ Y0 @ id ) ) @ id ) )
@ ( sK2 @ X1 @ X2 ) ) )
| ( ( ( !! @ term
@ ^ [Y0: term] :
( ( X1 @ id @ Y0 @ id )
=> ( X1 @ id @ ( sK1 @ X1 @ id @ Y0 ) @ id ) ) )
=> ( X1 @ id @ ( hoaslam @ id @ ( sK1 @ X1 ) ) @ id ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f801]) ).
thf(f803,plain,
! [X2: term,X1: subst > term > subst > $o] :
( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sK1 @ X1 @ ( comp @ Y1 @ Y0 ) @ ( sub @ Y2 @ Y0 ) )
= ( sub @ ( sK1 @ X1 @ Y1 @ Y2 ) @ Y0 ) ) ) ) )
= $true )
| ( $false
= ( ^ [Y0: term] :
( ( X1 @ id @ Y0 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ Y0 @ id ) ) @ id ) )
@ ( sK2 @ X1 @ X2 ) ) )
| ( $true
= ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ),
inference(imp_proxy_clausification,[],[f801]) ).
thf(f804,plain,
! [X2: term,X3: subst,X1: subst > term > subst > $o] :
( ( ( ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sK1 @ X1 @ ( comp @ Y1 @ Y0 ) @ ( sub @ Y2 @ Y0 ) )
= ( sub @ ( sK1 @ X1 @ Y1 @ Y2 ) @ Y0 ) ) ) )
@ X3 )
= $true )
| ( $true
= ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) )
| ( $false
= ( ^ [Y0: term] :
( ( X1 @ id @ Y0 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ Y0 @ id ) ) @ id ) )
@ ( sK2 @ X1 @ X2 ) ) ) ),
inference(pi_proxy_clausification,[],[f803]) ).
thf(f805,plain,
! [X2: term,X3: subst,X1: subst > term > subst > $o] :
( ( $true
= ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) )
| ( ( ( X1 @ id @ ( sK2 @ X1 @ X2 ) @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ ( sK2 @ X1 @ X2 ) @ id ) ) @ id ) )
= $false )
| ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sK1 @ X1 @ ( comp @ Y0 @ X3 ) @ ( sub @ Y1 @ X3 ) )
= ( sub @ ( sK1 @ X1 @ Y0 @ Y1 ) @ X3 ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f804]) ).
thf(f806,plain,
! [X2: term,X3: subst,X1: subst > term > subst > $o] :
( ( $true
= ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) )
| ( ( X1 @ id @ ( sub @ X2 @ ( push @ ( sK2 @ X1 @ X2 ) @ id ) ) @ id )
= $false )
| ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sK1 @ X1 @ ( comp @ Y0 @ X3 ) @ ( sub @ Y1 @ X3 ) )
= ( sub @ ( sK1 @ X1 @ Y0 @ Y1 ) @ X3 ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f805]) ).
thf(f807,plain,
! [X2: term,X3: subst,X1: subst > term > subst > $o] :
( ( $true
= ( X1 @ id @ ( sK2 @ X1 @ X2 ) @ id ) )
| ( $true
= ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) )
| ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sK1 @ X1 @ ( comp @ Y0 @ X3 ) @ ( sub @ Y1 @ X3 ) )
= ( sub @ ( sK1 @ X1 @ Y0 @ Y1 ) @ X3 ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f805]) ).
thf(f808,plain,
! [X2: term,X3: subst,X1: subst > term > subst > $o,X4: subst] :
( ( ( ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sK1 @ X1 @ ( comp @ Y0 @ X3 ) @ ( sub @ Y1 @ X3 ) )
= ( sub @ ( sK1 @ X1 @ Y0 @ Y1 ) @ X3 ) ) )
@ X4 )
= $true )
| ( $true
= ( X1 @ id @ ( sK2 @ X1 @ X2 ) @ id ) )
| ( $true
= ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ),
inference(pi_proxy_clausification,[],[f807]) ).
thf(f809,plain,
! [X2: term,X3: subst,X1: subst > term > subst > $o,X4: subst] :
( ( $true
= ( X1 @ id @ ( sK2 @ X1 @ X2 ) @ id ) )
| ( $true
= ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) )
| ( $true
= ( !! @ term
@ ^ [Y0: term] :
( ( sK1 @ X1 @ ( comp @ X4 @ X3 ) @ ( sub @ Y0 @ X3 ) )
= ( sub @ ( sK1 @ X1 @ X4 @ Y0 ) @ X3 ) ) ) ) ),
inference(beta-eta_normalization,[],[f808]) ).
thf(f810,plain,
! [X2: term,X3: subst,X1: subst > term > subst > $o,X4: subst,X5: term] :
( ( $true
= ( X1 @ id @ ( sK2 @ X1 @ X2 ) @ id ) )
| ( $true
= ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) )
| ( $true
= ( ^ [Y0: term] :
( ( sK1 @ X1 @ ( comp @ X4 @ X3 ) @ ( sub @ Y0 @ X3 ) )
= ( sub @ ( sK1 @ X1 @ X4 @ Y0 ) @ X3 ) )
@ X5 ) ) ),
inference(pi_proxy_clausification,[],[f809]) ).
thf(f811,plain,
! [X2: term,X3: subst,X1: subst > term > subst > $o,X4: subst,X5: term] :
( ( ( ( sK1 @ X1 @ ( comp @ X4 @ X3 ) @ ( sub @ X5 @ X3 ) )
= ( sub @ ( sK1 @ X1 @ X4 @ X5 ) @ X3 ) )
= $true )
| ( $true
= ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) )
| ( $true
= ( X1 @ id @ ( sK2 @ X1 @ X2 ) @ id ) ) ),
inference(beta-eta_normalization,[],[f810]) ).
thf(f812,plain,
! [X2: term,X3: subst,X1: subst > term > subst > $o,X4: subst,X5: term] :
( ( $true
= ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) )
| ( $true
= ( X1 @ id @ ( sK2 @ X1 @ X2 ) @ id ) )
| ( ( sub @ ( sK1 @ X1 @ X4 @ X5 ) @ X3 )
= ( sK1 @ X1 @ ( comp @ X4 @ X3 ) @ ( sub @ X5 @ X3 ) ) ) ),
inference(equality_proxy_clausification,[],[f811]) ).
thf(f813,plain,
! [X2: term,X3: subst,X1: subst > term > subst > $o,X4: subst] :
( ( ( ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sK1 @ X1 @ ( comp @ Y0 @ X3 ) @ ( sub @ Y1 @ X3 ) )
= ( sub @ ( sK1 @ X1 @ Y0 @ Y1 ) @ X3 ) ) )
@ X4 )
= $true )
| ( $true
= ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) )
| ( ( X1 @ id @ ( sub @ X2 @ ( push @ ( sK2 @ X1 @ X2 ) @ id ) ) @ id )
= $false ) ),
inference(pi_proxy_clausification,[],[f806]) ).
thf(f814,plain,
! [X2: term,X3: subst,X1: subst > term > subst > $o,X4: subst] :
( ( $true
= ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) )
| ( $true
= ( !! @ term
@ ^ [Y0: term] :
( ( sK1 @ X1 @ ( comp @ X4 @ X3 ) @ ( sub @ Y0 @ X3 ) )
= ( sub @ ( sK1 @ X1 @ X4 @ Y0 ) @ X3 ) ) ) )
| ( ( X1 @ id @ ( sub @ X2 @ ( push @ ( sK2 @ X1 @ X2 ) @ id ) ) @ id )
= $false ) ),
inference(beta-eta_normalization,[],[f813]) ).
thf(f815,plain,
! [X2: term,X3: subst,X1: subst > term > subst > $o,X4: subst,X5: term] :
( ( ( X1 @ id @ ( sub @ X2 @ ( push @ ( sK2 @ X1 @ X2 ) @ id ) ) @ id )
= $false )
| ( $true
= ( ^ [Y0: term] :
( ( sK1 @ X1 @ ( comp @ X4 @ X3 ) @ ( sub @ Y0 @ X3 ) )
= ( sub @ ( sK1 @ X1 @ X4 @ Y0 ) @ X3 ) )
@ X5 ) )
| ( $true
= ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ),
inference(pi_proxy_clausification,[],[f814]) ).
thf(f816,plain,
! [X2: term,X3: subst,X1: subst > term > subst > $o,X4: subst,X5: term] :
( ( $true
= ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) )
| ( ( X1 @ id @ ( sub @ X2 @ ( push @ ( sK2 @ X1 @ X2 ) @ id ) ) @ id )
= $false )
| ( ( ( sK1 @ X1 @ ( comp @ X4 @ X3 ) @ ( sub @ X5 @ X3 ) )
= ( sub @ ( sK1 @ X1 @ X4 @ X5 ) @ X3 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f815]) ).
thf(f817,plain,
! [X2: term,X3: subst,X1: subst > term > subst > $o,X4: subst,X5: term] :
( ( ( sub @ ( sK1 @ X1 @ X4 @ X5 ) @ X3 )
= ( sK1 @ X1 @ ( comp @ X4 @ X3 ) @ ( sub @ X5 @ X3 ) ) )
| ( ( X1 @ id @ ( sub @ X2 @ ( push @ ( sK2 @ X1 @ X2 ) @ id ) ) @ id )
= $false )
| ( $true
= ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ),
inference(equality_proxy_clausification,[],[f816]) ).
thf(f818,plain,
! [X2: term,X1: subst > term > subst > $o] :
( ( $false
= ( ^ [Y0: term] :
( ( X1 @ id @ Y0 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ Y0 @ id ) ) @ id ) )
@ ( sK2 @ X1 @ X2 ) ) )
| ( $true
= ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) )
| ( ( X1 @ id @ ( hoaslam @ id @ ( sK1 @ X1 ) ) @ id )
= $false ) ),
inference(imp_proxy_clausification,[],[f802]) ).
thf(f819,plain,
! [X2: term,X1: subst > term > subst > $o] :
( ( $true
= ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) )
| ( ( !! @ term
@ ^ [Y0: term] :
( ( X1 @ id @ Y0 @ id )
=> ( X1 @ id @ ( sK1 @ X1 @ id @ Y0 ) @ id ) ) )
= $true )
| ( $false
= ( ^ [Y0: term] :
( ( X1 @ id @ Y0 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ Y0 @ id ) ) @ id ) )
@ ( sK2 @ X1 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f802]) ).
thf(f820,plain,
! [X2: term,X3: term,X1: subst > term > subst > $o] :
( ( ( ^ [Y0: term] :
( ( X1 @ id @ Y0 @ id )
=> ( X1 @ id @ ( sK1 @ X1 @ id @ Y0 ) @ id ) )
@ X3 )
= $true )
| ( $false
= ( ^ [Y0: term] :
( ( X1 @ id @ Y0 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ Y0 @ id ) ) @ id ) )
@ ( sK2 @ X1 @ X2 ) ) )
| ( $true
= ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ),
inference(pi_proxy_clausification,[],[f819]) ).
thf(f821,plain,
! [X2: term,X3: term,X1: subst > term > subst > $o] :
( ( $true
= ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) )
| ( ( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sK1 @ X1 @ id @ X3 ) @ id ) )
= $true )
| ( ( ( X1 @ id @ ( sK2 @ X1 @ X2 ) @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ ( sK2 @ X1 @ X2 ) @ id ) ) @ id ) )
= $false ) ),
inference(beta-eta_normalization,[],[f820]) ).
thf(f822,plain,
! [X2: term,X3: term,X1: subst > term > subst > $o] :
( ( ( ( X1 @ id @ ( sK2 @ X1 @ X2 ) @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ ( sK2 @ X1 @ X2 ) @ id ) ) @ id ) )
= $false )
| ( $true
= ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) )
| ( ( X1 @ id @ X3 @ id )
= $false )
| ( ( X1 @ id @ ( sK1 @ X1 @ id @ X3 ) @ id )
= $true ) ),
inference(imp_proxy_clausification,[],[f821]) ).
thf(f823,plain,
! [X2: term,X3: term,X1: subst > term > subst > $o] :
( ( ( X1 @ id @ ( sK1 @ X1 @ id @ X3 ) @ id )
= $true )
| ( ( X1 @ id @ X3 @ id )
= $false )
| ( ( X1 @ id @ ( sub @ X2 @ ( push @ ( sK2 @ X1 @ X2 ) @ id ) ) @ id )
= $false )
| ( $true
= ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ),
inference(imp_proxy_clausification,[],[f822]) ).
thf(f824,plain,
! [X2: term,X3: term,X1: subst > term > subst > $o] :
( ( $true
= ( X1 @ id @ ( sK2 @ X1 @ X2 ) @ id ) )
| ( ( X1 @ id @ X3 @ id )
= $false )
| ( $true
= ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) )
| ( ( X1 @ id @ ( sK1 @ X1 @ id @ X3 ) @ id )
= $true ) ),
inference(imp_proxy_clausification,[],[f822]) ).
thf(f825,plain,
! [X2: term,X1: subst > term > subst > $o] :
( ( ( X1 @ id @ ( hoaslam @ id @ ( sK1 @ X1 ) ) @ id )
= $false )
| ( $true
= ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) )
| ( ( ( X1 @ id @ ( sK2 @ X1 @ X2 ) @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ ( sK2 @ X1 @ X2 ) @ id ) ) @ id ) )
= $false ) ),
inference(beta-eta_normalization,[],[f818]) ).
thf(f826,plain,
! [X2: term,X1: subst > term > subst > $o] :
( ( $true
= ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) )
| ( ( X1 @ id @ ( sub @ X2 @ ( push @ ( sK2 @ X1 @ X2 ) @ id ) ) @ id )
= $false )
| ( ( X1 @ id @ ( hoaslam @ id @ ( sK1 @ X1 ) ) @ id )
= $false ) ),
inference(imp_proxy_clausification,[],[f825]) ).
thf(f827,plain,
! [X2: term,X1: subst > term > subst > $o] :
( ( $true
= ( X1 @ id @ ( sK2 @ X1 @ X2 ) @ id ) )
| ( $true
= ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) )
| ( ( X1 @ id @ ( hoaslam @ id @ ( sK1 @ X1 ) ) @ id )
= $false ) ),
inference(imp_proxy_clausification,[],[f825]) ).
thf(f829,plain,
( ( ( id
= ( push @ one @ sh ) )
= $true )
| ~ spl0_48 ),
inference(backward_demodulation,[],[f322,f658]) ).
thf(f831,plain,
( ( id
= ( push @ one @ sh ) )
| ~ spl0_48 ),
inference(equality_proxy_clausification,[],[f829]) ).
thf(f832,plain,
( ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) )
= ( sub @ ( Y1 @ Y4 @ Y2 ) @ Y3 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( Y1 @ id @ Y2 ) @ id ) ) )
=> ( Y0 @ id @ ( hoaslam @ id @ Y1 ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ Y1 ) @ id ) ) ) ) )
= $false )
| ~ spl0_74 ),
inference(backward_demodulation,[],[f328,f788]) ).
thf(f833,plain,
( ( ( ^ [Y0: subst > term > subst > $o] :
( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) )
= ( sub @ ( Y1 @ Y4 @ Y2 ) @ Y3 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( Y1 @ id @ Y2 ) @ id ) ) )
=> ( Y0 @ id @ ( hoaslam @ id @ Y1 ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ Y1 ) @ id ) ) ) )
@ sK3 )
= $false )
| ~ spl0_74 ),
inference(sigma_proxy_clausification,[],[f832]) ).
thf(f834,plain,
( ( ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( sK3 @ id @ Y1 @ id )
=> ( sK3 @ id @ ( Y0 @ id @ Y1 ) @ id ) ) )
=> ( sK3 @ id @ ( hoaslam @ id @ Y0 ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( sK3 @ id @ Y1 @ id )
=> ( sK3 @ id @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) @ id ) ) )
=> ( sK3 @ id @ ( lam @ Y0 ) @ id ) ) ) )
= $false )
| ~ spl0_74 ),
inference(beta-eta_normalization,[],[f833]) ).
thf(f835,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( sK3 @ id @ Y1 @ id )
=> ( sK3 @ id @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) @ id ) ) )
=> ( sK3 @ id @ ( lam @ Y0 ) @ id ) ) )
= $false )
| ~ spl0_74 ),
inference(imp_proxy_clausification,[],[f834]) ).
thf(f836,plain,
( ( $true
= ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( sK3 @ id @ Y1 @ id )
=> ( sK3 @ id @ ( Y0 @ id @ Y1 ) @ id ) ) )
=> ( sK3 @ id @ ( hoaslam @ id @ Y0 ) @ id ) ) ) ) )
| ~ spl0_74 ),
inference(imp_proxy_clausification,[],[f834]) ).
thf(f837,plain,
( ! [X1: subst > term > term] :
( $true
= ( ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( sK3 @ id @ Y1 @ id )
=> ( sK3 @ id @ ( Y0 @ id @ Y1 ) @ id ) ) )
=> ( sK3 @ id @ ( hoaslam @ id @ Y0 ) @ id ) ) )
@ X1 ) )
| ~ spl0_74 ),
inference(pi_proxy_clausification,[],[f836]) ).
thf(f838,plain,
( ! [X1: subst > term > term] :
( $true
= ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( X1 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y0 @ Y1 ) )
= ( sub @ ( X1 @ Y2 @ Y0 ) @ Y1 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( sK3 @ id @ Y0 @ id )
=> ( sK3 @ id @ ( X1 @ id @ Y0 ) @ id ) ) )
=> ( sK3 @ id @ ( hoaslam @ id @ X1 ) @ id ) ) ) )
| ~ spl0_74 ),
inference(beta-eta_normalization,[],[f837]) ).
thf(f839,plain,
( ! [X1: subst > term > term] :
( ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sK3 @ id @ Y0 @ id )
=> ( sK3 @ id @ ( X1 @ id @ Y0 ) @ id ) ) )
=> ( sK3 @ id @ ( hoaslam @ id @ X1 ) @ id ) )
= $true )
| ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( X1 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y0 @ Y1 ) )
= ( sub @ ( X1 @ Y2 @ Y0 ) @ Y1 ) ) ) ) )
= $false ) )
| ~ spl0_74 ),
inference(imp_proxy_clausification,[],[f838]) ).
thf(f840,plain,
( ! [X1: subst > term > term] :
( ( $true
= ( sK3 @ id @ ( hoaslam @ id @ X1 ) @ id ) )
| ( ( !! @ term
@ ^ [Y0: term] :
( ( sK3 @ id @ Y0 @ id )
=> ( sK3 @ id @ ( X1 @ id @ Y0 ) @ id ) ) )
= $false )
| ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( X1 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y0 @ Y1 ) )
= ( sub @ ( X1 @ Y2 @ Y0 ) @ Y1 ) ) ) ) )
= $false ) )
| ~ spl0_74 ),
inference(imp_proxy_clausification,[],[f839]) ).
thf(f841,plain,
( ! [X1: subst > term > term] :
( ( $true
= ( sK3 @ id @ ( hoaslam @ id @ X1 ) @ id ) )
| ( ( ^ [Y0: term] :
( ( sK3 @ id @ Y0 @ id )
=> ( sK3 @ id @ ( X1 @ id @ Y0 ) @ id ) )
@ ( sK4 @ X1 ) )
= $false )
| ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( X1 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y0 @ Y1 ) )
= ( sub @ ( X1 @ Y2 @ Y0 ) @ Y1 ) ) ) ) )
= $false ) )
| ~ spl0_74 ),
inference(sigma_proxy_clausification,[],[f840]) ).
thf(f842,plain,
( ! [X1: subst > term > term] :
( ( ( ^ [Y0: term] :
( ( sK3 @ id @ Y0 @ id )
=> ( sK3 @ id @ ( X1 @ id @ Y0 ) @ id ) )
@ ( sK4 @ X1 ) )
= $false )
| ( ( ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( X1 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y0 @ Y1 ) )
= ( sub @ ( X1 @ Y2 @ Y0 ) @ Y1 ) ) ) )
@ ( sK5 @ X1 ) )
= $false )
| ( $true
= ( sK3 @ id @ ( hoaslam @ id @ X1 ) @ id ) ) )
| ~ spl0_74 ),
inference(sigma_proxy_clausification,[],[f841]) ).
thf(f843,plain,
( ! [X1: subst > term > term] :
( ( $true
= ( sK3 @ id @ ( hoaslam @ id @ X1 ) @ id ) )
| ( ( ( sK3 @ id @ ( sK4 @ X1 ) @ id )
=> ( sK3 @ id @ ( X1 @ id @ ( sK4 @ X1 ) ) @ id ) )
= $false )
| ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( ( X1 @ ( comp @ Y1 @ Y0 ) @ ( sub @ ( sK5 @ X1 ) @ Y0 ) )
= ( sub @ ( X1 @ Y1 @ ( sK5 @ X1 ) ) @ Y0 ) ) ) )
= $false ) )
| ~ spl0_74 ),
inference(beta-eta_normalization,[],[f842]) ).
thf(f844,plain,
( ! [X1: subst > term > term] :
( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( ( X1 @ ( comp @ Y1 @ Y0 ) @ ( sub @ ( sK5 @ X1 ) @ Y0 ) )
= ( sub @ ( X1 @ Y1 @ ( sK5 @ X1 ) ) @ Y0 ) ) ) )
= $false )
| ( $true
= ( sK3 @ id @ ( hoaslam @ id @ X1 ) @ id ) )
| ( ( sK3 @ id @ ( X1 @ id @ ( sK4 @ X1 ) ) @ id )
= $false ) )
| ~ spl0_74 ),
inference(imp_proxy_clausification,[],[f843]) ).
thf(f845,plain,
( ! [X1: subst > term > term] :
( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( ( X1 @ ( comp @ Y1 @ Y0 ) @ ( sub @ ( sK5 @ X1 ) @ Y0 ) )
= ( sub @ ( X1 @ Y1 @ ( sK5 @ X1 ) ) @ Y0 ) ) ) )
= $false )
| ( $true
= ( sK3 @ id @ ( hoaslam @ id @ X1 ) @ id ) )
| ( ( sK3 @ id @ ( sK4 @ X1 ) @ id )
= $true ) )
| ~ spl0_74 ),
inference(imp_proxy_clausification,[],[f843]) ).
thf(f846,plain,
( ! [X1: subst > term > term] :
( ( ( ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( ( X1 @ ( comp @ Y1 @ Y0 ) @ ( sub @ ( sK5 @ X1 ) @ Y0 ) )
= ( sub @ ( X1 @ Y1 @ ( sK5 @ X1 ) ) @ Y0 ) ) )
@ ( sK6 @ X1 ) )
= $false )
| ( $true
= ( sK3 @ id @ ( hoaslam @ id @ X1 ) @ id ) )
| ( ( sK3 @ id @ ( sK4 @ X1 ) @ id )
= $true ) )
| ~ spl0_74 ),
inference(sigma_proxy_clausification,[],[f845]) ).
thf(f847,plain,
( ! [X1: subst > term > term] :
( ( ( sK3 @ id @ ( sK4 @ X1 ) @ id )
= $true )
| ( $true
= ( sK3 @ id @ ( hoaslam @ id @ X1 ) @ id ) )
| ( $false
= ( !! @ subst
@ ^ [Y0: subst] :
( ( X1 @ ( comp @ Y0 @ ( sK6 @ X1 ) ) @ ( sub @ ( sK5 @ X1 ) @ ( sK6 @ X1 ) ) )
= ( sub @ ( X1 @ Y0 @ ( sK5 @ X1 ) ) @ ( sK6 @ X1 ) ) ) ) ) )
| ~ spl0_74 ),
inference(beta-eta_normalization,[],[f846]) ).
thf(f848,plain,
( ! [X1: subst > term > term] :
( ( ( sK3 @ id @ ( sK4 @ X1 ) @ id )
= $true )
| ( ( ^ [Y0: subst] :
( ( X1 @ ( comp @ Y0 @ ( sK6 @ X1 ) ) @ ( sub @ ( sK5 @ X1 ) @ ( sK6 @ X1 ) ) )
= ( sub @ ( X1 @ Y0 @ ( sK5 @ X1 ) ) @ ( sK6 @ X1 ) ) )
@ ( sK7 @ X1 ) )
= $false )
| ( $true
= ( sK3 @ id @ ( hoaslam @ id @ X1 ) @ id ) ) )
| ~ spl0_74 ),
inference(sigma_proxy_clausification,[],[f847]) ).
thf(f849,plain,
( ! [X1: subst > term > term] :
( ( $true
= ( sK3 @ id @ ( hoaslam @ id @ X1 ) @ id ) )
| ( ( sK3 @ id @ ( sK4 @ X1 ) @ id )
= $true )
| ( $false
= ( ( X1 @ ( comp @ ( sK7 @ X1 ) @ ( sK6 @ X1 ) ) @ ( sub @ ( sK5 @ X1 ) @ ( sK6 @ X1 ) ) )
= ( sub @ ( X1 @ ( sK7 @ X1 ) @ ( sK5 @ X1 ) ) @ ( sK6 @ X1 ) ) ) ) )
| ~ spl0_74 ),
inference(beta-eta_normalization,[],[f848]) ).
thf(f850,plain,
( ! [X1: subst > term > term] :
( ( ( X1 @ ( comp @ ( sK7 @ X1 ) @ ( sK6 @ X1 ) ) @ ( sub @ ( sK5 @ X1 ) @ ( sK6 @ X1 ) ) )
!= ( sub @ ( X1 @ ( sK7 @ X1 ) @ ( sK5 @ X1 ) ) @ ( sK6 @ X1 ) ) )
| ( ( sK3 @ id @ ( sK4 @ X1 ) @ id )
= $true )
| ( $true
= ( sK3 @ id @ ( hoaslam @ id @ X1 ) @ id ) ) )
| ~ spl0_74 ),
inference(equality_proxy_clausification,[],[f849]) ).
thf(f851,plain,
( ! [X1: subst > term > term] :
( ( ( sK3 @ id @ ( X1 @ id @ ( sK4 @ X1 ) ) @ id )
= $false )
| ( ( ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( ( X1 @ ( comp @ Y1 @ Y0 ) @ ( sub @ ( sK5 @ X1 ) @ Y0 ) )
= ( sub @ ( X1 @ Y1 @ ( sK5 @ X1 ) ) @ Y0 ) ) )
@ ( sK8 @ X1 ) )
= $false )
| ( $true
= ( sK3 @ id @ ( hoaslam @ id @ X1 ) @ id ) ) )
| ~ spl0_74 ),
inference(sigma_proxy_clausification,[],[f844]) ).
thf(f852,plain,
( ! [X1: subst > term > term] :
( ( $true
= ( sK3 @ id @ ( hoaslam @ id @ X1 ) @ id ) )
| ( ( sK3 @ id @ ( X1 @ id @ ( sK4 @ X1 ) ) @ id )
= $false )
| ( ( !! @ subst
@ ^ [Y0: subst] :
( ( X1 @ ( comp @ Y0 @ ( sK8 @ X1 ) ) @ ( sub @ ( sK5 @ X1 ) @ ( sK8 @ X1 ) ) )
= ( sub @ ( X1 @ Y0 @ ( sK5 @ X1 ) ) @ ( sK8 @ X1 ) ) ) )
= $false ) )
| ~ spl0_74 ),
inference(beta-eta_normalization,[],[f851]) ).
thf(f853,plain,
( ! [X1: subst > term > term] :
( ( $false
= ( ^ [Y0: subst] :
( ( X1 @ ( comp @ Y0 @ ( sK8 @ X1 ) ) @ ( sub @ ( sK5 @ X1 ) @ ( sK8 @ X1 ) ) )
= ( sub @ ( X1 @ Y0 @ ( sK5 @ X1 ) ) @ ( sK8 @ X1 ) ) )
@ ( sK9 @ X1 ) ) )
| ( ( sK3 @ id @ ( X1 @ id @ ( sK4 @ X1 ) ) @ id )
= $false )
| ( $true
= ( sK3 @ id @ ( hoaslam @ id @ X1 ) @ id ) ) )
| ~ spl0_74 ),
inference(sigma_proxy_clausification,[],[f852]) ).
thf(f854,plain,
( ! [X1: subst > term > term] :
( ( ( sK3 @ id @ ( X1 @ id @ ( sK4 @ X1 ) ) @ id )
= $false )
| ( ( ( X1 @ ( comp @ ( sK9 @ X1 ) @ ( sK8 @ X1 ) ) @ ( sub @ ( sK5 @ X1 ) @ ( sK8 @ X1 ) ) )
= ( sub @ ( X1 @ ( sK9 @ X1 ) @ ( sK5 @ X1 ) ) @ ( sK8 @ X1 ) ) )
= $false )
| ( $true
= ( sK3 @ id @ ( hoaslam @ id @ X1 ) @ id ) ) )
| ~ spl0_74 ),
inference(beta-eta_normalization,[],[f853]) ).
thf(f855,plain,
( ! [X1: subst > term > term] :
( ( ( X1 @ ( comp @ ( sK9 @ X1 ) @ ( sK8 @ X1 ) ) @ ( sub @ ( sK5 @ X1 ) @ ( sK8 @ X1 ) ) )
!= ( sub @ ( X1 @ ( sK9 @ X1 ) @ ( sK5 @ X1 ) ) @ ( sK8 @ X1 ) ) )
| ( $true
= ( sK3 @ id @ ( hoaslam @ id @ X1 ) @ id ) )
| ( ( sK3 @ id @ ( X1 @ id @ ( sK4 @ X1 ) ) @ id )
= $false ) )
| ~ spl0_74 ),
inference(equality_proxy_clausification,[],[f854]) ).
thf(f856,plain,
( ( $false
= ( ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( sK3 @ id @ Y1 @ id )
=> ( sK3 @ id @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) @ id ) ) )
=> ( sK3 @ id @ ( lam @ Y0 ) @ id ) )
@ sK10 ) )
| ~ spl0_74 ),
inference(sigma_proxy_clausification,[],[f835]) ).
thf(f857,plain,
( ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sK3 @ id @ Y0 @ id )
=> ( sK3 @ id @ ( sub @ sK10 @ ( push @ Y0 @ id ) ) @ id ) ) )
=> ( sK3 @ id @ ( lam @ sK10 ) @ id ) )
= $false )
| ~ spl0_74 ),
inference(beta-eta_normalization,[],[f856]) ).
thf(f858,plain,
( ( ( sK3 @ id @ ( lam @ sK10 ) @ id )
= $false )
| ~ spl0_74 ),
inference(imp_proxy_clausification,[],[f857]) ).
thf(f859,plain,
( ( $true
= ( !! @ term
@ ^ [Y0: term] :
( ( sK3 @ id @ Y0 @ id )
=> ( sK3 @ id @ ( sub @ sK10 @ ( push @ Y0 @ id ) ) @ id ) ) ) )
| ~ spl0_74 ),
inference(imp_proxy_clausification,[],[f857]) ).
thf(f860,plain,
( ! [X1: term] :
( ( ^ [Y0: term] :
( ( sK3 @ id @ Y0 @ id )
=> ( sK3 @ id @ ( sub @ sK10 @ ( push @ Y0 @ id ) ) @ id ) )
@ X1 )
= $true )
| ~ spl0_74 ),
inference(pi_proxy_clausification,[],[f859]) ).
thf(f861,plain,
( ! [X1: term] :
( ( ( sK3 @ id @ X1 @ id )
=> ( sK3 @ id @ ( sub @ sK10 @ ( push @ X1 @ id ) ) @ id ) )
= $true )
| ~ spl0_74 ),
inference(beta-eta_normalization,[],[f860]) ).
thf(f862,plain,
( ! [X1: term] :
( ( ( sK3 @ id @ ( sub @ sK10 @ ( push @ X1 @ id ) ) @ id )
= $true )
| ( ( sK3 @ id @ X1 @ id )
= $false ) )
| ~ spl0_74 ),
inference(imp_proxy_clausification,[],[f861]) ).
thf(f863,plain,
( ! [X2: term,X1: subst > term > subst > $o] :
( ( ( X1 @ id @ ( hoaslam @ id @ ( sK1 @ X1 ) ) @ id )
= $false )
| ( ( X1 @ id @ ( lam @ ( sub @ X2 @ id ) ) @ id )
= $true )
| ( $true
= ( X1 @ id @ ( sK2 @ X1 @ X2 ) @ id ) ) )
| ~ spl0_48 ),
inference(forward_demodulation,[],[f827,f831]) ).
thf(f864,plain,
( ! [X2: term,X1: subst > term > subst > $o] :
( ( ( X1 @ id @ ( hoaslam @ id @ ( sK1 @ X1 ) ) @ id )
= $false )
| ( $true
= ( X1 @ id @ ( sK2 @ X1 @ X2 ) @ id ) )
| ( $true
= ( X1 @ id @ ( lam @ X2 ) @ id ) ) )
| ~ spl0_48 ),
inference(forward_demodulation,[],[f863,f456]) ).
thf(f865,plain,
( ! [X2: term,X3: subst,X1: subst > term > subst > $o,X4: subst,X5: term] :
( ( ( X1 @ id @ ( lam @ ( sub @ X2 @ id ) ) @ id )
= $true )
| ( $true
= ( X1 @ id @ ( sK2 @ X1 @ X2 ) @ id ) )
| ( ( sub @ ( sK1 @ X1 @ X4 @ X5 ) @ X3 )
= ( sK1 @ X1 @ ( comp @ X4 @ X3 ) @ ( sub @ X5 @ X3 ) ) ) )
| ~ spl0_48 ),
inference(forward_demodulation,[],[f812,f831]) ).
thf(f866,plain,
( ! [X2: term,X3: subst,X1: subst > term > subst > $o,X4: subst,X5: term] :
( ( ( sub @ ( sK1 @ X1 @ X4 @ X5 ) @ X3 )
= ( sK1 @ X1 @ ( comp @ X4 @ X3 ) @ ( sub @ X5 @ X3 ) ) )
| ( $true
= ( X1 @ id @ ( sK2 @ X1 @ X2 ) @ id ) )
| ( $true
= ( X1 @ id @ ( lam @ X2 ) @ id ) ) )
| ~ spl0_48 ),
inference(forward_demodulation,[],[f865,f456]) ).
thf(f867,plain,
( ! [X2: term,X3: term,X1: subst > term > subst > $o] :
( ( ( X1 @ id @ X3 @ id )
= $false )
| ( ( X1 @ id @ ( lam @ ( sub @ X2 @ id ) ) @ id )
= $true )
| ( ( X1 @ id @ ( sK1 @ X1 @ id @ X3 ) @ id )
= $true )
| ( $true
= ( X1 @ id @ ( sK2 @ X1 @ X2 ) @ id ) ) )
| ~ spl0_48 ),
inference(forward_demodulation,[],[f824,f831]) ).
thf(f868,plain,
( ! [X2: term,X3: term,X1: subst > term > subst > $o] :
( ( ( X1 @ id @ ( sK1 @ X1 @ id @ X3 ) @ id )
= $true )
| ( $true
= ( X1 @ id @ ( sK2 @ X1 @ X2 ) @ id ) )
| ( $true
= ( X1 @ id @ ( lam @ X2 ) @ id ) )
| ( ( X1 @ id @ X3 @ id )
= $false ) )
| ~ spl0_48 ),
inference(forward_demodulation,[],[f867,f456]) ).
thf(f869,plain,
( ! [X2: term,X1: subst > term > subst > $o] :
( ( ( X1 @ id @ ( sub @ X2 @ ( push @ ( sK2 @ X1 @ X2 ) @ id ) ) @ id )
= $false )
| ( ( X1 @ id @ ( hoaslam @ id @ ( sK1 @ X1 ) ) @ id )
= $false )
| ( ( X1 @ id @ ( lam @ ( sub @ X2 @ id ) ) @ id )
= $true ) )
| ~ spl0_48 ),
inference(forward_demodulation,[],[f826,f831]) ).
thf(f870,plain,
( ! [X2: term,X1: subst > term > subst > $o] :
( ( ( X1 @ id @ ( sub @ X2 @ ( push @ ( sK2 @ X1 @ X2 ) @ id ) ) @ id )
= $false )
| ( ( X1 @ id @ ( hoaslam @ id @ ( sK1 @ X1 ) ) @ id )
= $false )
| ( $true
= ( X1 @ id @ ( lam @ X2 ) @ id ) ) )
| ~ spl0_48 ),
inference(forward_demodulation,[],[f869,f456]) ).
thf(f871,plain,
( ! [X2: term,X3: term,X1: subst > term > subst > $o] :
( ( ( X1 @ id @ ( lam @ ( sub @ X2 @ id ) ) @ id )
= $true )
| ( ( X1 @ id @ ( sK1 @ X1 @ id @ X3 ) @ id )
= $true )
| ( ( X1 @ id @ ( sub @ X2 @ ( push @ ( sK2 @ X1 @ X2 ) @ id ) ) @ id )
= $false )
| ( ( X1 @ id @ X3 @ id )
= $false ) )
| ~ spl0_48 ),
inference(forward_demodulation,[],[f823,f831]) ).
thf(f872,plain,
( ! [X2: term,X3: term,X1: subst > term > subst > $o] :
( ( ( X1 @ id @ ( sub @ X2 @ ( push @ ( sK2 @ X1 @ X2 ) @ id ) ) @ id )
= $false )
| ( ( X1 @ id @ ( sK1 @ X1 @ id @ X3 ) @ id )
= $true )
| ( $true
= ( X1 @ id @ ( lam @ X2 ) @ id ) )
| ( ( X1 @ id @ X3 @ id )
= $false ) )
| ~ spl0_48 ),
inference(forward_demodulation,[],[f871,f456]) ).
thf(f873,plain,
( ! [X2: term,X3: subst,X1: subst > term > subst > $o,X4: subst,X5: term] :
( ( ( sub @ ( sK1 @ X1 @ X4 @ X5 ) @ X3 )
= ( sK1 @ X1 @ ( comp @ X4 @ X3 ) @ ( sub @ X5 @ X3 ) ) )
| ( ( X1 @ id @ ( lam @ ( sub @ X2 @ id ) ) @ id )
= $true )
| ( ( X1 @ id @ ( sub @ X2 @ ( push @ ( sK2 @ X1 @ X2 ) @ id ) ) @ id )
= $false ) )
| ~ spl0_48 ),
inference(forward_demodulation,[],[f817,f831]) ).
thf(f874,plain,
( ! [X2: term,X3: subst,X1: subst > term > subst > $o,X4: subst,X5: term] :
( ( ( sub @ ( sK1 @ X1 @ X4 @ X5 ) @ X3 )
= ( sK1 @ X1 @ ( comp @ X4 @ X3 ) @ ( sub @ X5 @ X3 ) ) )
| ( ( X1 @ id @ ( sub @ X2 @ ( push @ ( sK2 @ X1 @ X2 ) @ id ) ) @ id )
= $false )
| ( $true
= ( X1 @ id @ ( lam @ X2 ) @ id ) ) )
| ~ spl0_48 ),
inference(forward_demodulation,[],[f873,f456]) ).
thf(f1079,plain,
( ( ( sK3 @ id @ ( sK2 @ sK3 @ sK10 ) @ id )
= $false )
| ( ( sK3 @ id @ ( lam @ sK10 ) @ id )
= $true )
| ( ( sK3 @ id @ ( hoaslam @ id @ ( sK1 @ sK3 ) ) @ id )
= $false )
| ( $true = $false )
| ~ spl0_48
| ~ spl0_74 ),
inference(constrained_superposition,[],[f870,f862]) ).
thf(f1100,plain,
( ( ( sK3 @ id @ ( lam @ sK10 ) @ id )
= $true )
| ( ( sK3 @ id @ ( hoaslam @ id @ ( sK1 @ sK3 ) ) @ id )
= $false )
| ( ( sK3 @ id @ ( sK2 @ sK3 @ sK10 ) @ id )
= $false )
| ~ spl0_48
| ~ spl0_74 ),
inference(trivial_inequality_removal,[],[f1079]) ).
thf(f1103,plain,
( ( ( sK3 @ id @ ( hoaslam @ id @ ( sK1 @ sK3 ) ) @ id )
= $false )
| ( ( sK3 @ id @ ( sK2 @ sK3 @ sK10 ) @ id )
= $false )
| ( $true = $false )
| ~ spl0_48
| ~ spl0_74 ),
inference(forward_demodulation,[],[f1100,f858]) ).
thf(f1104,plain,
( ( ( sK3 @ id @ ( hoaslam @ id @ ( sK1 @ sK3 ) ) @ id )
= $false )
| ( ( sK3 @ id @ ( sK2 @ sK3 @ sK10 ) @ id )
= $false )
| ~ spl0_48
| ~ spl0_74 ),
inference(trivial_inequality_removal,[],[f1103]) ).
thf(f1106,definition,
( spl0_75
<=> ( ( sK3 @ id @ ( sK2 @ sK3 @ sK10 ) @ id )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl0_75])],[avatar_definition]) ).
thf(f1108,plain,
( ( ( sK3 @ id @ ( sK2 @ sK3 @ sK10 ) @ id )
= $false )
| ~ spl0_75 ),
inference(avatar_component_clause,[],[f1106]) ).
thf(f1110,definition,
( spl0_76
<=> ( ( sK3 @ id @ ( hoaslam @ id @ ( sK1 @ sK3 ) ) @ id )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl0_76])],[avatar_definition]) ).
thf(f1112,plain,
( ( ( sK3 @ id @ ( hoaslam @ id @ ( sK1 @ sK3 ) ) @ id )
= $false )
| ~ spl0_76 ),
inference(avatar_component_clause,[],[f1110]) ).
thf(f1114,plain,
( spl0_75
| spl0_76
| ~ spl0_48
| ~ spl0_74 ),
inference(avatar_split_clause,[],[f1104,f786,f656,f1110,f1106]) ).
thf(f1121,plain,
( ( $true = $false )
| ( ( sK3 @ id @ ( lam @ sK10 ) @ id )
= $true )
| ( ( sK3 @ id @ ( hoaslam @ id @ ( sK1 @ sK3 ) ) @ id )
= $false )
| ~ spl0_48
| ~ spl0_75 ),
inference(constrained_superposition,[],[f864,f1108]) ).
thf(f1123,plain,
( ( ( sK3 @ id @ ( lam @ sK10 ) @ id )
= $true )
| ( ( sK3 @ id @ ( hoaslam @ id @ ( sK1 @ sK3 ) ) @ id )
= $false )
| ~ spl0_48
| ~ spl0_75 ),
inference(trivial_inequality_removal,[],[f1121]) ).
thf(f1131,plain,
( ( $true = $false )
| ( ( sK3 @ id @ ( hoaslam @ id @ ( sK1 @ sK3 ) ) @ id )
= $false )
| ~ spl0_48
| ~ spl0_74
| ~ spl0_75 ),
inference(forward_demodulation,[],[f1123,f858]) ).
thf(f1132,plain,
( ( ( sK3 @ id @ ( hoaslam @ id @ ( sK1 @ sK3 ) ) @ id )
= $false )
| ~ spl0_48
| ~ spl0_74
| ~ spl0_75 ),
inference(trivial_inequality_removal,[],[f1131]) ).
thf(f1147,plain,
( spl0_76
| ~ spl0_48
| ~ spl0_74
| ~ spl0_75 ),
inference(avatar_split_clause,[],[f1132,f1106,f786,f656,f1110]) ).
thf(f1158,plain,
( ! [X0: term] :
( ( $true = $false )
| ( $true
= ( sK3 @ id @ ( sK1 @ sK3 @ id @ X0 ) @ id ) )
| ( ( sK3 @ id @ ( sK2 @ sK3 @ sK10 ) @ id )
= $false )
| ( ( sK3 @ id @ X0 @ id )
= $false )
| ( ( sK3 @ id @ ( lam @ sK10 ) @ id )
= $true ) )
| ~ spl0_48
| ~ spl0_74 ),
inference(constrained_superposition,[],[f872,f862]) ).
thf(f1196,plain,
( ! [X0: term] :
( ( ( sK3 @ id @ X0 @ id )
= $false )
| ( ( sK3 @ id @ ( sK2 @ sK3 @ sK10 ) @ id )
= $false )
| ( $true
= ( sK3 @ id @ ( sK1 @ sK3 @ id @ X0 ) @ id ) )
| ( ( sK3 @ id @ ( lam @ sK10 ) @ id )
= $true ) )
| ~ spl0_48
| ~ spl0_74 ),
inference(trivial_inequality_removal,[],[f1158]) ).
thf(f1204,plain,
( ! [X0: term] :
( ( ( sK3 @ id @ ( sK2 @ sK3 @ sK10 ) @ id )
= $false )
| ( $true
= ( sK3 @ id @ ( sK1 @ sK3 @ id @ X0 ) @ id ) )
| ( $true = $false )
| ( ( sK3 @ id @ X0 @ id )
= $false ) )
| ~ spl0_48
| ~ spl0_74 ),
inference(forward_demodulation,[],[f1196,f858]) ).
thf(f1205,plain,
( ! [X0: term] :
( ( $true
= ( sK3 @ id @ ( sK1 @ sK3 @ id @ X0 ) @ id ) )
| ( ( sK3 @ id @ ( sK2 @ sK3 @ sK10 ) @ id )
= $false )
| ( ( sK3 @ id @ X0 @ id )
= $false ) )
| ~ spl0_48
| ~ spl0_74 ),
inference(trivial_inequality_removal,[],[f1204]) ).
thf(f1207,definition,
( spl0_77
<=> ! [X0: term] :
( ( ( sK3 @ id @ X0 @ id )
= $false )
| ( $true
= ( sK3 @ id @ ( sK1 @ sK3 @ id @ X0 ) @ id ) ) ) ),
introduced(definition,[new_symbols(definition,[spl0_77])],[avatar_definition]) ).
thf(f1208,plain,
( ! [X0: term] :
( ( $true
= ( sK3 @ id @ ( sK1 @ sK3 @ id @ X0 ) @ id ) )
| ( ( sK3 @ id @ X0 @ id )
= $false ) )
| ~ spl0_77 ),
inference(avatar_component_clause,[],[f1207]) ).
thf(f1210,plain,
( spl0_77
| spl0_75
| ~ spl0_48
| ~ spl0_74 ),
inference(avatar_split_clause,[],[f1205,f786,f656,f1106,f1207]) ).
thf(f1220,plain,
( ! [X2: subst,X0: subst,X1: term] :
( ( ( sK3 @ id @ ( sK2 @ sK3 @ sK10 ) @ id )
= $false )
| ( $true = $false )
| ( ( sK3 @ id @ ( lam @ sK10 ) @ id )
= $true )
| ( ( sK1 @ sK3 @ ( comp @ X0 @ X2 ) @ ( sub @ X1 @ X2 ) )
= ( sub @ ( sK1 @ sK3 @ X0 @ X1 ) @ X2 ) ) )
| ~ spl0_48
| ~ spl0_74 ),
inference(constrained_superposition,[],[f874,f862]) ).
thf(f1250,plain,
( ! [X2: subst,X0: subst,X1: term] :
( ( ( sK1 @ sK3 @ ( comp @ X0 @ X2 ) @ ( sub @ X1 @ X2 ) )
= ( sub @ ( sK1 @ sK3 @ X0 @ X1 ) @ X2 ) )
| ( ( sK3 @ id @ ( sK2 @ sK3 @ sK10 ) @ id )
= $false )
| ( ( sK3 @ id @ ( lam @ sK10 ) @ id )
= $true ) )
| ~ spl0_48
| ~ spl0_74 ),
inference(trivial_inequality_removal,[],[f1220]) ).
thf(f1257,plain,
( ! [X2: subst,X0: subst,X1: term] :
( ( $true = $false )
| ( ( sK1 @ sK3 @ ( comp @ X0 @ X2 ) @ ( sub @ X1 @ X2 ) )
= ( sub @ ( sK1 @ sK3 @ X0 @ X1 ) @ X2 ) )
| ( ( sK3 @ id @ ( sK2 @ sK3 @ sK10 ) @ id )
= $false ) )
| ~ spl0_48
| ~ spl0_74 ),
inference(forward_demodulation,[],[f1250,f858]) ).
thf(f1258,plain,
( ! [X2: subst,X0: subst,X1: term] :
( ( ( sK1 @ sK3 @ ( comp @ X0 @ X2 ) @ ( sub @ X1 @ X2 ) )
= ( sub @ ( sK1 @ sK3 @ X0 @ X1 ) @ X2 ) )
| ( ( sK3 @ id @ ( sK2 @ sK3 @ sK10 ) @ id )
= $false ) )
| ~ spl0_48
| ~ spl0_74 ),
inference(trivial_inequality_removal,[],[f1257]) ).
thf(f1260,definition,
( spl0_78
<=> ! [X2: subst,X0: subst,X1: term] :
( ( sK1 @ sK3 @ ( comp @ X0 @ X2 ) @ ( sub @ X1 @ X2 ) )
= ( sub @ ( sK1 @ sK3 @ X0 @ X1 ) @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[spl0_78])],[avatar_definition]) ).
thf(f1261,plain,
( ! [X2: subst,X0: subst,X1: term] :
( ( sK1 @ sK3 @ ( comp @ X0 @ X2 ) @ ( sub @ X1 @ X2 ) )
= ( sub @ ( sK1 @ sK3 @ X0 @ X1 ) @ X2 ) )
| ~ spl0_78 ),
inference(avatar_component_clause,[],[f1260]) ).
thf(f1263,plain,
( spl0_78
| spl0_75
| ~ spl0_48
| ~ spl0_74 ),
inference(avatar_split_clause,[],[f1258,f786,f656,f1106,f1260]) ).
thf(f1338,plain,
( ( ( sK3 @ id @ ( sK4 @ ( sK1 @ sK3 ) ) @ id )
= $true )
| ( $true
= ( sK3 @ id @ ( hoaslam @ id @ ( sK1 @ sK3 ) ) @ id ) )
| ( ( sub @ ( sK1 @ sK3 @ ( sK7 @ ( sK1 @ sK3 ) ) @ ( sK5 @ ( sK1 @ sK3 ) ) ) @ ( sK6 @ ( sK1 @ sK3 ) ) )
!= ( sub @ ( sK1 @ sK3 @ ( sK7 @ ( sK1 @ sK3 ) ) @ ( sK5 @ ( sK1 @ sK3 ) ) ) @ ( sK6 @ ( sK1 @ sK3 ) ) ) )
| ~ spl0_74
| ~ spl0_78 ),
inference(constrained_superposition,[],[f850,f1261]) ).
thf(f1341,plain,
( ( $true
= ( sK3 @ id @ ( hoaslam @ id @ ( sK1 @ sK3 ) ) @ id ) )
| ( ( sK3 @ id @ ( sK4 @ ( sK1 @ sK3 ) ) @ id )
= $true )
| ~ spl0_74
| ~ spl0_78 ),
inference(trivial_inequality_removal,[],[f1338]) ).
thf(f1356,plain,
( ( ( sK3 @ id @ ( sK4 @ ( sK1 @ sK3 ) ) @ id )
= $true )
| ( $true = $false )
| ~ spl0_74
| ~ spl0_76
| ~ spl0_78 ),
inference(forward_demodulation,[],[f1341,f1112]) ).
thf(f1357,plain,
( ( ( sK3 @ id @ ( sK4 @ ( sK1 @ sK3 ) ) @ id )
= $true )
| ~ spl0_74
| ~ spl0_76
| ~ spl0_78 ),
inference(trivial_inequality_removal,[],[f1356]) ).
thf(f1456,plain,
( ( $true
= ( sK3 @ id @ ( hoaslam @ id @ ( sK1 @ sK3 ) ) @ id ) )
| ( ( sub @ ( sK1 @ sK3 @ ( sK9 @ ( sK1 @ sK3 ) ) @ ( sK5 @ ( sK1 @ sK3 ) ) ) @ ( sK8 @ ( sK1 @ sK3 ) ) )
!= ( sub @ ( sK1 @ sK3 @ ( sK9 @ ( sK1 @ sK3 ) ) @ ( sK5 @ ( sK1 @ sK3 ) ) ) @ ( sK8 @ ( sK1 @ sK3 ) ) ) )
| ( ( sK3 @ id @ ( sK1 @ sK3 @ id @ ( sK4 @ ( sK1 @ sK3 ) ) ) @ id )
= $false )
| ~ spl0_74
| ~ spl0_78 ),
inference(constrained_superposition,[],[f855,f1261]) ).
thf(f1464,plain,
( ( $true
= ( sK3 @ id @ ( hoaslam @ id @ ( sK1 @ sK3 ) ) @ id ) )
| ( ( sK3 @ id @ ( sK1 @ sK3 @ id @ ( sK4 @ ( sK1 @ sK3 ) ) ) @ id )
= $false )
| ~ spl0_74
| ~ spl0_78 ),
inference(trivial_inequality_removal,[],[f1456]) ).
thf(f1467,plain,
( ( ( sK3 @ id @ ( sK1 @ sK3 @ id @ ( sK4 @ ( sK1 @ sK3 ) ) ) @ id )
= $false )
| ( $true = $false )
| ~ spl0_74
| ~ spl0_76
| ~ spl0_78 ),
inference(forward_demodulation,[],[f1464,f1112]) ).
thf(f1468,plain,
( ( ( sK3 @ id @ ( sK1 @ sK3 @ id @ ( sK4 @ ( sK1 @ sK3 ) ) ) @ id )
= $false )
| ~ spl0_74
| ~ spl0_76
| ~ spl0_78 ),
inference(trivial_inequality_removal,[],[f1467]) ).
thf(f1475,plain,
( ( ( sK3 @ id @ ( sK4 @ ( sK1 @ sK3 ) ) @ id )
= $false )
| ( $true = $false )
| ~ spl0_74
| ~ spl0_76
| ~ spl0_77
| ~ spl0_78 ),
inference(constrained_superposition,[],[f1468,f1208]) ).
thf(f1482,plain,
( ( ( sK3 @ id @ ( sK4 @ ( sK1 @ sK3 ) ) @ id )
= $false )
| ~ spl0_74
| ~ spl0_76
| ~ spl0_77
| ~ spl0_78 ),
inference(trivial_inequality_removal,[],[f1475]) ).
thf(f1495,plain,
( ( $true = $false )
| ~ spl0_74
| ~ spl0_76
| ~ spl0_77
| ~ spl0_78 ),
inference(backward_demodulation,[],[f1357,f1482]) ).
thf(f1496,plain,
( $false
| ~ spl0_74
| ~ spl0_76
| ~ spl0_77
| ~ spl0_78 ),
inference(trivial_inequality_removal,[],[f1495]) ).
thf(f1497,plain,
( ~ spl0_74
| ~ spl0_76
| ~ spl0_77
| ~ spl0_78 ),
inference(avatar_contradiction_clause,[],[f1496]) ).
thf(f1532,plain,
( ! [X2: subst,X0: subst,X1: term] :
( ( ( sK1 @ sK3 @ ( comp @ X0 @ X2 ) @ ( sub @ X1 @ X2 ) )
= ( sub @ ( sK1 @ sK3 @ X0 @ X1 ) @ X2 ) )
| ( $true = $false )
| ( ( sK3 @ id @ ( lam @ sK10 ) @ id )
= $true ) )
| ~ spl0_48
| ~ spl0_75 ),
inference(constrained_superposition,[],[f1108,f866]) ).
thf(f1534,plain,
( ! [X0: term] :
( ( $true
= ( sK3 @ id @ ( sK1 @ sK3 @ id @ X0 ) @ id ) )
| ( $true = $false )
| ( ( sK3 @ id @ X0 @ id )
= $false )
| ( ( sK3 @ id @ ( lam @ sK10 ) @ id )
= $true ) )
| ~ spl0_48
| ~ spl0_75 ),
inference(constrained_superposition,[],[f868,f1108]) ).
thf(f1538,plain,
( ! [X2: subst,X0: subst,X1: term] :
( ( ( sK1 @ sK3 @ ( comp @ X0 @ X2 ) @ ( sub @ X1 @ X2 ) )
= ( sub @ ( sK1 @ sK3 @ X0 @ X1 ) @ X2 ) )
| ( ( sK3 @ id @ ( lam @ sK10 ) @ id )
= $true ) )
| ~ spl0_48
| ~ spl0_75 ),
inference(trivial_inequality_removal,[],[f1532]) ).
thf(f1542,plain,
( ! [X0: term] :
( ( ( sK3 @ id @ ( lam @ sK10 ) @ id )
= $true )
| ( ( sK3 @ id @ X0 @ id )
= $false )
| ( $true
= ( sK3 @ id @ ( sK1 @ sK3 @ id @ X0 ) @ id ) ) )
| ~ spl0_48
| ~ spl0_75 ),
inference(trivial_inequality_removal,[],[f1534]) ).
thf(f1548,plain,
( ! [X2: subst,X0: subst,X1: term] :
( ( ( sK1 @ sK3 @ ( comp @ X0 @ X2 ) @ ( sub @ X1 @ X2 ) )
= ( sub @ ( sK1 @ sK3 @ X0 @ X1 ) @ X2 ) )
| ( $true = $false ) )
| ~ spl0_48
| ~ spl0_74
| ~ spl0_75 ),
inference(forward_demodulation,[],[f1538,f858]) ).
thf(f1549,plain,
( ! [X2: subst,X0: subst,X1: term] :
( ( sK1 @ sK3 @ ( comp @ X0 @ X2 ) @ ( sub @ X1 @ X2 ) )
= ( sub @ ( sK1 @ sK3 @ X0 @ X1 ) @ X2 ) )
| ~ spl0_48
| ~ spl0_74
| ~ spl0_75 ),
inference(trivial_inequality_removal,[],[f1548]) ).
thf(f1560,plain,
( spl0_78
| ~ spl0_48
| ~ spl0_74
| ~ spl0_75 ),
inference(avatar_split_clause,[],[f1549,f1106,f786,f656,f1260]) ).
thf(f1572,plain,
( ! [X0: term] :
( ( ( sK3 @ id @ X0 @ id )
= $false )
| ( $true = $false )
| ( $true
= ( sK3 @ id @ ( sK1 @ sK3 @ id @ X0 ) @ id ) ) )
| ~ spl0_48
| ~ spl0_74
| ~ spl0_75 ),
inference(forward_demodulation,[],[f1542,f858]) ).
thf(f1573,plain,
( ! [X0: term] :
( ( ( sK3 @ id @ X0 @ id )
= $false )
| ( $true
= ( sK3 @ id @ ( sK1 @ sK3 @ id @ X0 ) @ id ) ) )
| ~ spl0_48
| ~ spl0_74
| ~ spl0_75 ),
inference(trivial_inequality_removal,[],[f1572]) ).
thf(f1578,plain,
( spl0_77
| ~ spl0_48
| ~ spl0_74
| ~ spl0_75 ),
inference(avatar_split_clause,[],[f1573,f1106,f786,f656,f1207]) ).
cnf(s38,plain,
spl0_48,
inference(sat_conversion,[],[f790]) ).
cnf(s39,plain,
spl0_74,
inference(sat_conversion,[],[f791]) ).
cnf(s41,plain,
( ~ spl0_48
| ~ spl0_74
| spl0_75
| spl0_76 ),
inference(sat_conversion,[],[f1114]) ).
cnf(s42,plain,
( ~ spl0_48
| ~ spl0_74
| ~ spl0_75
| spl0_76 ),
inference(sat_conversion,[],[f1147]) ).
cnf(s45,plain,
( ~ spl0_48
| ~ spl0_74
| spl0_75
| spl0_77 ),
inference(sat_conversion,[],[f1210]) ).
cnf(s47,plain,
( ~ spl0_48
| ~ spl0_74
| spl0_75
| spl0_78 ),
inference(sat_conversion,[],[f1263]) ).
cnf(s53,plain,
( ~ spl0_74
| ~ spl0_76
| ~ spl0_77
| ~ spl0_78 ),
inference(sat_conversion,[],[f1497]) ).
cnf(s64,plain,
( ~ spl0_48
| ~ spl0_74
| ~ spl0_75
| spl0_78 ),
inference(sat_conversion,[],[f1560]) ).
cnf(s77,plain,
( ~ spl0_48
| ~ spl0_74
| ~ spl0_75
| spl0_77 ),
inference(sat_conversion,[],[f1578]) ).
cnf(s79,plain,
spl0_75,
inference(rat,[],[s53,s41,s45,s47,s39,s38]) ).
cnf(s80,plain,
spl0_77,
inference(rat,[],[s77,s38,s39,s79]) ).
cnf(s82,plain,
spl0_78,
inference(rat,[],[s64,s38,s39,s79]) ).
cnf(s83,plain,
spl0_76,
inference(rat,[],[s42,s38,s39,s79]) ).
cnf(s84,plain,
$false,
inference(rat,[],[s53,s80,s39,s82,s83]) ).
thf(f1579,plain,
$false,
inference(avatar_sat_refutation,[],[s84]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG266^2 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n020.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 17:35:35 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.22/0.26 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 % (1364272)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.61/0.39 % (1364277)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3988966894:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.61/0.39 % (1364283)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 % (1364283)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 % (1364278)lrs+10_16_si=on:nwc=1.5:random_seed=2152256444:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.61/0.39 % (1364279)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1855857735:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.61/0.39 % (1364281)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2033105682:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.61/0.39 % (1364280)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=2662872348: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 % (1364282)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=700357666:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.61/0.39 % (1364283)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=4209255871:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.61/0.39 % (1364279)Instruction limit reached!
% 0.61/0.39 % (1364279)------------------------------
% 0.61/0.39 % (1364279)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.39 % (1364279)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.39 % (1364279)CaDiCaL version: 2.1.3
% 0.61/0.39 % (1364279)Termination reason: Instruction limit
% 0.61/0.39 % (1364279)Termination phase: shuffling
% 0.61/0.39 % (1364279)Time elapsed: 0.002 s
% 0.61/0.39 % (1364279)Peak memory usage: 10 MB
% 0.61/0.39 % (1364279)Instructions burned: 4 (million)
% 0.61/0.39 % (1364278)Instruction limit reached!
% 0.61/0.39 % (1364278)------------------------------
% 0.61/0.39 % (1364278)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.39 % (1364278)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.39 % (1364278)CaDiCaL version: 2.1.3
% 0.61/0.39 % (1364278)Termination reason: Instruction limit
% 0.61/0.39 % (1364278)Termination phase: shuffling
% 0.61/0.39 % (1364278)Time elapsed: 0.008 s
% 0.61/0.39 % (1364278)Peak memory usage: 10 MB
% 0.61/0.39 % (1364278)Instructions burned: 19 (million)
% 0.61/0.39 % (1364281)Instruction limit reached!
% 0.61/0.39 % (1364281)------------------------------
% 0.61/0.39 % (1364281)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.39 % (1364281)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.39 % (1364281)CaDiCaL version: 2.1.3
% 0.61/0.39 % (1364281)Termination reason: Instruction limit
% 0.61/0.39 % (1364281)Termination phase: Naming
% 0.61/0.39 % (1364281)Time elapsed: 0.011 s
% 0.61/0.39 % (1364281)Peak memory usage: 11 MB
% 0.61/0.39 % (1364281)Instructions burned: 25 (million)
% 0.61/0.39 % (1364277)Instruction limit reached!
% 0.61/0.39 % (1364277)------------------------------
% 0.61/0.39 % (1364277)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.39 % (1364277)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.39 % (1364277)CaDiCaL version: 2.1.3
% 0.61/0.39 % (1364277)Termination reason: Instruction limit
% 0.61/0.39 % (1364277)Termination phase: Property scanning
% 0.61/0.39 % (1364277)Time elapsed: 0.021 s
% 0.61/0.39 % (1364277)Peak memory usage: 12 MB
% 0.61/0.39 % (1364277)Instructions burned: 92 (million)
% 0.61/0.39 % (1364291)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1332633958:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.61/0.39 % (1364294)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2040588536:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.61/0.41 % (1364291)Instruction limit reached!
% 0.61/0.41 % (1364291)------------------------------
% 0.61/0.41 % (1364291)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.41 % (1364291)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.41 % (1364291)CaDiCaL version: 2.1.3
% 0.61/0.41 % (1364291)Termination reason: Instruction limit
% 0.61/0.41 % (1364291)Termination phase: shuffling
% 0.61/0.41 % (1364291)Time elapsed: 0.002 s
% 0.61/0.41 % (1364291)Peak memory usage: 10 MB
% 0.61/0.41 % (1364291)Instructions burned: 3 (million)
% 0.61/0.41 % (1364293)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.61/0.41 % (1364294)Instruction limit reached!
% 0.61/0.41 % (1364294)------------------------------
% 0.61/0.41 % (1364294)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.41 % (1364294)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.41 % (1364294)CaDiCaL version: 2.1.3
% 0.61/0.41 % (1364294)Termination reason: Instruction limit
% 0.61/0.41 % (1364294)Termination phase: shuffling
% 0.61/0.41 % (1364294)Time elapsed: 0.004 s
% 0.61/0.41 % (1364294)Peak memory usage: 10 MB
% 0.61/0.41 % (1364294)Instructions burned: 16 (million)
% 0.61/0.41 % (1364293)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3495931238:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.61/0.41 % (1364292)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=334061654:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.61/0.41 % (1364293)Instruction limit reached!
% 0.61/0.41 % (1364293)------------------------------
% 0.61/0.41 % (1364293)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.41 % (1364293)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.41 % (1364293)CaDiCaL version: 2.1.3
% 0.61/0.41 % (1364293)Termination reason: Instruction limit
% 0.61/0.41 % (1364293)Termination phase: shuffling
% 0.61/0.41 % (1364293)Time elapsed: 0.004 s
% 0.61/0.41 % (1364293)Peak memory usage: 10 MB
% 0.61/0.41 % (1364293)Instructions burned: 8 (million)
% 0.61/0.41 % (1364282)Instruction limit reached!
% 0.61/0.41 % (1364282)------------------------------
% 0.61/0.41 % (1364282)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.41 % (1364282)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.41 % (1364282)CaDiCaL version: 2.1.3
% 0.61/0.41 % (1364282)Termination reason: Instruction limit
% 0.61/0.41 % (1364282)Termination phase: Property scanning
% 0.61/0.41 % (1364282)Time elapsed: 0.035 s
% 0.61/0.41 % (1364282)Peak memory usage: 12 MB
% 0.61/0.41 % (1364282)Instructions burned: 76 (million)
% 0.61/0.41 % (1364292)Instruction limit reached!
% 0.61/0.41 % (1364292)------------------------------
% 0.61/0.41 % (1364292)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.41 % (1364292)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.41 % (1364292)CaDiCaL version: 2.1.3
% 0.61/0.41 % (1364292)Termination reason: Instruction limit
% 0.61/0.41 % (1364292)Termination phase: shuffling
% 0.61/0.41 % (1364292)Time elapsed: 0.003 s
% 0.61/0.41 % (1364292)Peak memory usage: 10 MB
% 0.61/0.41 % (1364292)Instructions burned: 8 (million)
% 0.61/0.41 % (1364298)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=739882289:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.61/0.41 % (1364297)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
% 0.61/0.41 % (1364297)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.61/0.41 % (1364297)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3729896455:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.61/0.41 % (1364302)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.61/0.45 % (1364302)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=2706390469:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.61/0.45 % (1364301)lrs+10_1_si=on:cs=on:random_seed=3219689741:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.61/0.45 % (1364297)Instruction limit reached!
% 0.61/0.45 % (1364297)------------------------------
% 0.61/0.45 % (1364297)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.45 % (1364297)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.45 % (1364297)CaDiCaL version: 2.1.3
% 0.61/0.45 % (1364297)Termination reason: Instruction limit
% 0.61/0.45 % (1364297)Termination phase: Property scanning
% 0.61/0.45 % (1364297)Time elapsed: 0.013 s
% 0.61/0.45 % (1364297)Peak memory usage: 10 MB
% 0.61/0.45 % (1364297)Instructions burned: 30 (million)
% 0.61/0.45 % (1364304)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=2174938350:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.61/0.45 % (1364302)Instruction limit reached!
% 0.61/0.45 % (1364302)------------------------------
% 0.61/0.45 % (1364302)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.45 % (1364302)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.45 % (1364302)CaDiCaL version: 2.1.3
% 0.61/0.45 % (1364302)Termination reason: Instruction limit
% 0.61/0.45 % (1364302)Termination phase: shuffling
% 0.61/0.45 % (1364302)Time elapsed: 0.002 s
% 0.61/0.45 % (1364302)Peak memory usage: 10 MB
% 0.61/0.45 % (1364302)Instructions burned: 4 (million)
% 0.61/0.45 % (1364298)Instruction limit reached!
% 0.61/0.45 % (1364298)------------------------------
% 0.61/0.45 % (1364298)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.45 % (1364298)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.45 % (1364298)CaDiCaL version: 2.1.3
% 0.61/0.45 % (1364298)Termination reason: Instruction limit
% 0.61/0.45 % (1364298)Termination phase: Saturation
% 0.61/0.45 % (1364298)Time elapsed: 0.019 s
% 0.61/0.45 % (1364298)Peak memory usage: 12 MB
% 0.61/0.45 % (1364298)Instructions burned: 87 (million)
% 0.61/0.45 % (1364301)Instruction limit reached!
% 0.61/0.45 % (1364301)------------------------------
% 0.61/0.45 % (1364301)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.45 % (1364301)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.45 % (1364301)CaDiCaL version: 2.1.3
% 0.61/0.45 % (1364301)Termination reason: Instruction limit
% 0.61/0.45 % (1364301)Termination phase: shuffling
% 0.61/0.45 % (1364301)Time elapsed: 0.004 s
% 0.61/0.45 % (1364301)Peak memory usage: 10 MB
% 0.61/0.45 % (1364301)Instructions burned: 9 (million)
% 0.61/0.45 % (1364283)Instruction limit reached!
% 0.61/0.45 % (1364283)------------------------------
% 0.61/0.45 % (1364283)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.45 % (1364283)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.45 % (1364283)CaDiCaL version: 2.1.3
% 0.61/0.45 % (1364283)Termination reason: Instruction limit
% 0.61/0.45 % (1364283)Termination phase: Saturation
% 0.61/0.45 % (1364283)Time elapsed: 0.066 s
% 0.61/0.45 % (1364283)Peak memory usage: 13 MB
% 0.61/0.45 % (1364283)Instructions burned: 157 (million)
% 0.61/0.45 % (1364310)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2802296876:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.61/0.45 % (1364304)Instruction limit reached!
% 0.61/0.45 % (1364304)------------------------------
% 0.61/0.45 % (1364304)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.45 % (1364304)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.45 % (1364304)CaDiCaL version: 2.1.3
% 0.61/0.45 % (1364304)Termination reason: Instruction limit
% 0.61/0.45 % (1364304)Termination phase: Saturation
% 0.61/0.45 % (1364304)Time elapsed: 0.017 s
% 0.61/0.45 % (1364304)Peak memory usage: 12 MB
% 0.61/0.45 % (1364304)Instructions burned: 38 (million)
% 0.61/0.45 % (1364310)Instruction limit reached!
% 0.61/0.45 % (1364310)------------------------------
% 0.61/0.45 % (1364310)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.45 % (1364310)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.34/0.48 % (1364310)CaDiCaL version: 2.1.3
% 1.34/0.48 % (1364310)Termination reason: Instruction limit
% 1.34/0.48 % (1364310)Termination phase: Naming
% 1.34/0.48 % (1364310)Time elapsed: 0.006 s
% 1.34/0.48 % (1364310)Peak memory usage: 11 MB
% 1.34/0.48 % (1364310)Instructions burned: 27 (million)
% 1.34/0.48 % (1364309)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=396834698:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 1.34/0.48 % (1364311)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=2217924239:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.34/0.48 % (1364312)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=805049938:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 1.34/0.48 % (1364311)Instruction limit reached!
% 1.34/0.48 % (1364311)------------------------------
% 1.34/0.48 % (1364311)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.34/0.48 % (1364311)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.34/0.48 % (1364311)CaDiCaL version: 2.1.3
% 1.34/0.48 % (1364311)Termination reason: Instruction limit
% 1.34/0.48 % (1364311)Termination phase: shuffling
% 1.34/0.48 % (1364311)Time elapsed: 0.007 s
% 1.34/0.48 % (1364311)Peak memory usage: 10 MB
% 1.34/0.48 % (1364311)Instructions burned: 16 (million)
% 1.34/0.48 % (1364317)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=688249421:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.34/0.48 % (1364314)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=2007324856:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.34/0.48 % (1364317)Instruction limit reached!
% 1.34/0.48 % (1364317)------------------------------
% 1.34/0.48 % (1364317)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.34/0.48 % (1364317)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.34/0.48 % (1364317)CaDiCaL version: 2.1.3
% 1.34/0.48 % (1364317)Termination reason: Instruction limit
% 1.34/0.48 % (1364317)Termination phase: Property scanning
% 1.34/0.48 % (1364317)Time elapsed: 0.006 s
% 1.34/0.48 % (1364317)Peak memory usage: 10 MB
% 1.34/0.48 % (1364317)Instructions burned: 28 (million)
% 1.34/0.48 % (1364316)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=2606756402:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2998 on theBenchmark for (2998ds/2Mi)
% 1.34/0.48 % (1364314)Instruction limit reached!
% 1.34/0.48 % (1364314)------------------------------
% 1.34/0.48 % (1364314)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.34/0.48 % (1364314)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.34/0.48 % (1364314)CaDiCaL version: 2.1.3
% 1.34/0.48 % (1364314)Termination reason: Instruction limit
% 1.34/0.48 % (1364314)Termination phase: shuffling
% 1.34/0.48 % (1364314)Time elapsed: 0.007 s
% 1.34/0.48 % (1364314)Peak memory usage: 10 MB
% 1.34/0.48 % (1364314)Instructions burned: 16 (million)
% 1.34/0.48 % (1364316)Instruction limit reached!
% 1.34/0.48 % (1364316)------------------------------
% 1.34/0.48 % (1364316)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.34/0.48 % (1364316)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.34/0.48 % (1364316)CaDiCaL version: 2.1.3
% 1.34/0.48 % (1364316)Termination reason: Instruction limit
% 1.34/0.48 % (1364316)Termination phase: shuffling
% 1.34/0.48 % (1364316)Time elapsed: 0.002 s
% 1.34/0.48 % (1364316)Peak memory usage: 10 MB
% 1.34/0.48 % (1364316)Instructions burned: 4 (million)
% 1.34/0.48 % (1364309)Refutation not found, incomplete strategy
% 1.34/0.48 % (1364309)------------------------------
% 1.34/0.48 % (1364309)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.34/0.48 % (1364309)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.34/0.48 % (1364309)CaDiCaL version: 2.1.3
% 1.34/0.48 % (1364309)Termination reason: Refutation not found, incomplete strategy
% 1.34/0.48 % (1364309)Time elapsed: 0.022 s
% 1.34/0.48 % (1364309)Peak memory usage: 12 MB
% 1.34/0.48 % (1364309)Instructions burned: 50 (million)
% 1.34/0.48 % (1364309)------------------------------
% 1.34/0.48 % (1364309)------------------------------
% 1.34/0.48 % (1364323)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=257721731:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.34/0.55 % (1364320)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=611076695:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.34/0.55 % (1364325)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
% 1.34/0.55 % (1364325)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 1.34/0.55 % (1364326)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.34/0.55 % (1364325)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=1753473442:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.34/0.55 % (1364320)Instruction limit reached!
% 1.34/0.55 % (1364320)------------------------------
% 1.34/0.55 % (1364320)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.34/0.55 % (1364320)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.34/0.55 % (1364320)CaDiCaL version: 2.1.3
% 1.34/0.55 % (1364320)Termination reason: Instruction limit
% 1.34/0.55 % (1364320)Termination phase: Property scanning
% 1.34/0.55 % (1364320)Time elapsed: 0.011 s
% 1.34/0.55 % (1364320)Peak memory usage: 10 MB
% 1.34/0.55 % (1364320)Instructions burned: 25 (million)
% 1.34/0.55 % (1364326)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=2719937883:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.34/0.55 % (1364323)Instruction limit reached!
% 1.34/0.55 % (1364323)------------------------------
% 1.34/0.55 % (1364323)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.34/0.55 % (1364323)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.34/0.55 % (1364323)CaDiCaL version: 2.1.3
% 1.34/0.55 % (1364323)Termination reason: Instruction limit
% 1.34/0.55 % (1364323)Termination phase: Property scanning
% 1.34/0.55 % (1364323)Time elapsed: 0.015 s
% 1.34/0.55 % (1364323)Peak memory usage: 12 MB
% 1.34/0.55 % (1364323)Instructions burned: 61 (million)
% 1.34/0.55 % (1364327)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=3658725973:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 1.34/0.55 % (1364325)Instruction limit reached!
% 1.34/0.55 % (1364325)------------------------------
% 1.34/0.55 % (1364325)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.34/0.55 % (1364325)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.34/0.55 % (1364325)CaDiCaL version: 2.1.3
% 1.34/0.55 % (1364325)Termination reason: Instruction limit
% 1.34/0.55 % (1364325)Termination phase: shuffling
% 1.34/0.55 % (1364325)Time elapsed: 0.006 s
% 1.34/0.55 % (1364325)Peak memory usage: 10 MB
% 1.34/0.55 % (1364325)Instructions burned: 14 (million)
% 1.34/0.55 % (1364326)Instruction limit reached!
% 1.34/0.55 % (1364326)------------------------------
% 1.34/0.55 % (1364326)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.34/0.55 % (1364326)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.34/0.55 % (1364326)CaDiCaL version: 2.1.3
% 1.34/0.55 % (1364326)Termination reason: Instruction limit
% 1.34/0.55 % (1364326)Termination phase: shuffling
% 1.34/0.55 % (1364326)Time elapsed: 0.004 s
% 1.34/0.55 % (1364326)Peak memory usage: 10 MB
% 1.34/0.55 % (1364326)Instructions burned: 9 (million)
% 1.34/0.55 % (1364333)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=682022531:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.34/0.55 % (1364331)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=2992237643:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 1.34/0.55 % (1364327)Instruction limit reached!
% 1.34/0.55 % (1364327)------------------------------
% 1.34/0.55 % (1364327)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.34/0.55 % (1364327)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.02/0.58 % (1364333)Instruction limit reached!
% 2.02/0.58 % (1364333)------------------------------
% 2.02/0.58 % (1364333)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.02/0.58 % (1364327)CaDiCaL version: 2.1.3
% 2.02/0.58 % (1364327)Termination reason: Instruction limit
% 2.02/0.58 % (1364327)Termination phase: Property scanning
% 2.02/0.58 % (1364327)Time elapsed: 0.015 s
% 2.02/0.58 % (1364333)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.02/0.58 % (1364327)Peak memory usage: 10 MB
% 2.02/0.58 % (1364333)CaDiCaL version: 2.1.3
% 2.02/0.58 % (1364327)Instructions burned: 33 (million)
% 2.02/0.58 % (1364333)Termination reason: Instruction limit
% 2.02/0.58 % (1364333)Termination phase: Property scanning
% 2.02/0.58 % (1364333)Time elapsed: 0.006 s
% 2.02/0.58 % (1364333)Peak memory usage: 10 MB
% 2.02/0.58 % (1364333)Instructions burned: 27 (million)
% 2.02/0.58 % (1364331)Instruction limit reached!
% 2.02/0.58 % (1364331)------------------------------
% 2.02/0.58 % (1364331)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.02/0.58 % (1364331)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.02/0.58 % (1364331)CaDiCaL version: 2.1.3
% 2.02/0.58 % (1364331)Termination reason: Instruction limit
% 2.02/0.58 % (1364331)Termination phase: shuffling
% 2.02/0.58 % (1364331)Time elapsed: 0.004 s
% 2.02/0.58 % (1364331)Peak memory usage: 10 MB
% 2.02/0.58 % (1364331)Instructions burned: 8 (million)
% 2.02/0.58 % (1364335)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=2644797892:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/20Mi)
% 2.02/0.58 % (1364336)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=2408615655:i=1240:rtra=on:ixr=off_2998 on theBenchmark for (2998ds/1240Mi)
% 2.02/0.58 % (1364340)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=2416628696:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/193Mi)
% 2.02/0.58 % (1364335)Instruction limit reached!
% 2.02/0.58 % (1364335)------------------------------
% 2.02/0.58 % (1364335)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.02/0.58 % (1364335)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.02/0.58 % (1364335)CaDiCaL version: 2.1.3
% 2.02/0.58 % (1364335)Termination reason: Instruction limit
% 2.02/0.58 % (1364335)Termination phase: shuffling
% 2.02/0.58 % (1364335)Time elapsed: 0.009 s
% 2.02/0.58 % (1364335)Peak memory usage: 10 MB
% 2.02/0.58 % (1364335)Instructions burned: 20 (million)
% 2.02/0.58 % (1364339)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=620668381:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/143Mi)
% 2.02/0.58 % (1364341)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=4211408065:i=42:hud=10:rtra=on_2998 on theBenchmark for (2998ds/42Mi)
% 2.02/0.58 % (1364340)Refutation not found, incomplete strategy
% 2.02/0.58 % (1364340)------------------------------
% 2.02/0.58 % (1364340)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.02/0.58 % (1364340)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.02/0.58 % (1364340)CaDiCaL version: 2.1.3
% 2.02/0.58 % (1364340)Termination reason: Refutation not found, incomplete strategy
% 2.02/0.58 % (1364340)Time elapsed: 0.014 s
% 2.02/0.58 % (1364340)Peak memory usage: 13 MB
% 2.02/0.58 % (1364340)Instructions burned: 59 (million)
% 2.02/0.58 % (1364340)------------------------------
% 2.02/0.58 % (1364340)------------------------------
% 2.02/0.58 % (1364345)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 2.02/0.58 % (1364345)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1471086053:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2998 on theBenchmark for (2998ds/7Mi)
% 2.02/0.58 % (1364348)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=900954071:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/181Mi)
% 2.02/0.58 % (1364345)Instruction limit reached!
% 2.02/0.58 % (1364345)------------------------------
% 2.02/0.58 % (1364345)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.02/0.58 % (1364345)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.02/0.58 % (1364345)CaDiCaL version: 2.1.3
% 2.02/0.58 % (1364345)Termination reason: Instruction limit
% 2.02/0.58 % (1364345)Termination phase: shuffling
% 2.02/0.58 % (1364345)Time elapsed: 0.004 s
% 2.02/0.58 % (1364345)Peak memory usage: 10 MB
% 2.02/0.58 % (1364345)Instructions burned: 9 (million)
% 2.02/0.58 % (1364341)Instruction limit reached!
% 2.02/0.58 % (1364341)------------------------------
% 2.02/0.58 % (1364341)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.02/0.58 % (1364341)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.02/0.58 % (1364341)CaDiCaL version: 2.1.3
% 2.02/0.58 % (1364341)Termination reason: Instruction limit
% 2.02/0.58 % (1364341)Termination phase: Property scanning
% 2.02/0.58 % (1364341)Time elapsed: 0.018 s
% 2.02/0.58 % (1364341)Peak memory usage: 11 MB
% 2.02/0.58 % (1364341)Instructions burned: 44 (million)
% 2.02/0.58 % (1364352)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 2.02/0.58 % (1364351)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=1852350122:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2997 on theBenchmark for (2997ds/169Mi)
% 2.02/0.58 % (1364352)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=2657926698:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2997 on theBenchmark for (2997ds/6Mi)
% 2.02/0.58 % (1364352)Instruction limit reached!
% 2.02/0.58 % (1364352)------------------------------
% 2.02/0.58 % (1364352)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.02/0.58 % (1364352)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.02/0.58 % (1364352)CaDiCaL version: 2.1.3
% 2.02/0.58 % (1364352)Termination reason: Instruction limit
% 2.02/0.58 % (1364352)Termination phase: shuffling
% 2.02/0.58 % (1364352)Time elapsed: 0.003 s
% 2.02/0.58 % (1364352)Peak memory usage: 10 MB
% 2.02/0.58 % (1364352)Instructions burned: 6 (million)
% 2.02/0.58 % (1364339)Instruction limit reached!
% 2.02/0.58 % (1364339)------------------------------
% 2.02/0.58 % (1364339)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.02/0.58 % (1364339)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.02/0.58 % (1364339)CaDiCaL version: 2.1.3
% 2.02/0.58 % (1364339)Termination reason: Instruction limit
% 2.02/0.58 % (1364339)Termination phase: Saturation
% 2.02/0.58 % (1364339)Time elapsed: 0.060 s
% 2.02/0.58 % (1364339)Peak memory usage: 13 MB
% 2.02/0.58 % (1364339)Instructions burned: 143 (million)
% 2.02/0.58 % (1364355)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=1992811081:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2997 on theBenchmark for (2997ds/22Mi)
% 2.02/0.58 % (1364348)Instruction limit reached!
% 2.02/0.58 % (1364348)------------------------------
% 2.02/0.58 % (1364348)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.02/0.58 % (1364348)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.02/0.58 % (1364348)CaDiCaL version: 2.1.3
% 2.02/0.58 % (1364348)Termination reason: Instruction limit
% 2.02/0.58 % (1364348)Termination phase: Saturation
% 2.02/0.58 % (1364348)Time elapsed: 0.048 s
% 2.02/0.58 % (1364348)Peak memory usage: 14 MB
% 2.02/0.58 % (1364348)Instructions burned: 195 (million)
% 2.02/0.58 % (1364355)Instruction limit reached!
% 2.02/0.58 % (1364355)------------------------------
% 2.02/0.58 % (1364355)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.02/0.58 % (1364355)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.02/0.58 % (1364355)CaDiCaL version: 2.1.3
% 2.02/0.58 % (1364355)Termination reason: Instruction limit
% 2.02/0.58 % (1364355)Termination phase: Property scanning
% 2.02/0.58 % (1364355)Time elapsed: 0.011 s
% 2.02/0.58 % (1364355)Peak memory usage: 10 MB
% 2.02/0.58 % (1364355)Instructions burned: 24 (million)
% 2.02/0.58 % (1364358)ott+10_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:lma=off:plsqr=128,1:urr=ec_only:uwa=off:rp=on:nwc=20:br=off:random_seed=2975090610:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/316Mi)
% 2.02/0.58 % (1364356)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=2417912059:i=19:add=on:rtra=on_2997 on theBenchmark for (2997ds/19Mi)
% 2.02/0.58 % (1364312)Instruction limit reached!
% 2.02/0.58 % (1364312)------------------------------
% 2.02/0.58 % (1364312)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.02/0.58 % (1364312)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.02/0.58 % (1364312)CaDiCaL version: 2.1.3
% 2.02/0.58 % (1364312)Termination reason: Instruction limit
% 2.02/0.58 % (1364312)Termination phase: Saturation
% 2.02/0.58 % (1364312)Time elapsed: 0.155 s
% 2.02/0.58 % (1364312)Peak memory usage: 15 MB
% 2.02/0.58 % (1364312)Instructions burned: 328 (million)
% 2.02/0.58 % (1364356)Instruction limit reached!
% 2.02/0.58 % (1364356)------------------------------
% 2.02/0.58 % (1364356)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.02/0.58 % (1364356)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.02/0.58 % (1364356)CaDiCaL version: 2.1.3
% 2.02/0.58 % (1364356)Termination reason: Instruction limit
% 2.02/0.58 % (1364356)Termination phase: shuffling
% 2.02/0.58 % (1364356)Time elapsed: 0.009 s
% 2.02/0.58 % (1364356)Peak memory usage: 10 MB
% 2.02/0.58 % (1364356)Instructions burned: 20 (million)
% 2.02/0.58 % (1364359)dis+1004_4:1_slsqr=1,2:to=lpo:plsq=on:fde=unused:e2e=on:si=on:spb=goal_then_units:acc=on:urr=on:uwa=off:fd=preordered:s2agt=16:slsqc=1:slsq=on:random_seed=1732591881:hsq=on:hsqr=16,1:s2a=on:i=853:add=off:bd=all:nm=64:rtra=on:gtg=position:c=on:ntd=on_2997 on theBenchmark for (2997ds/853Mi)
% 2.02/0.58 % (1364351) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1364272-1364351"...
% 2.02/0.58 % (1364362)dis+1003_3:4_to=kbo:plsq=on:prc=on:sims=off:e2e=on:si=on:spb=intro:acc=on:urr=on:uwa=off:foolp=on:s2agt=32:slsqc=3:slsq=on:random_seed=2440759305:hsq=on:hsqr=16,1:s2a=on:i=45:erml=3:slsql=off:rtra=on:gtg=exists_top:er=filter:ntd=on_2997 on theBenchmark for (2997ds/45Mi)
% 2.02/0.58 % (1364363)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=2516380757:i=480:rtra=on_2997 on theBenchmark for (2997ds/480Mi)
% 2.02/0.58 % (1364351)...printing done.
% 2.02/0.58 % (1364351)Refutation found. Thanks to Tanya!
% 2.02/0.58 % SZS status Theorem for theBenchmark
% 2.02/0.58 % SZS output start Proof for theBenchmark
% See solution above
% 2.02/0.58 % (1364351)------------------------------
% 2.02/0.58 % (1364351)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.02/0.58 % (1364351)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.02/0.58 % (1364351)CaDiCaL version: 2.1.3
% 2.02/0.58 % (1364351)Termination reason: Refutation
% 2.02/0.58 % (1364351)Time elapsed: 0.070 s
% 2.02/0.58 % (1364351)Peak memory usage: 14 MB
% 2.02/0.58 % (1364351)Instructions burned: 144 (million)
% 2.02/0.58 % (1364272)Success in time 0.31 s
% 2.02/0.58 % Vampire exiting
%------------------------------------------------------------------------------