%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG268^2 : TPTP v9.3.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 07:45:17 AM UTC 2026
% Result : Theorem 2.03s 0.58s
% Output : Refutation 2.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 49
% Number of leaves : 11
% Syntax : Number of formulae : 204 ( 63 unt; 0 typ; 5 def)
% Number of atoms : 1547 ( 450 equ; 0 cnn)
% Maximal formula atoms : 5 ( 7 avg)
% Number of connectives : 4907 ( 90 ~; 288 |; 0 &;4046 @)
% ( 5 <=>; 228 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 328 ( 328 >; 0 *; 0 +; 0 <<)
% Number of symbols : 156 ( 152 usr; 120 con; 0-4 aty)
% ( 250 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 554 ( 0 sgn 258 !; 0 ?; 554 :)
% 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,
vIMP: $o > $o > $o ).
thf(func_def_124,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_125,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_126,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_127,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_128,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_129,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_130,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_131,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_132,type,
vNOT: $o > $o ).
thf(func_def_133,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_136,type,
vIFF: $o > $o > $o ).
thf(func_def_137,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_138,type,
vAND: $o > $o > $o ).
thf(func_def_139,type,
sK0: subst > term > subst > $o ).
thf(func_def_140,type,
sK1: ( subst > term > term ) > term ).
thf(func_def_141,type,
sK2: ( subst > term > term ) > term ).
thf(func_def_142,type,
sK3: ( subst > term > term ) > subst ).
thf(func_def_143,type,
sK4: ( subst > term > term ) > subst ).
thf(func_def_144,type,
sK5: ( subst > term > term ) > subst ).
thf(func_def_145,type,
sK6: ( subst > term > term ) > subst ).
thf(func_def_146,type,
sK7: term ).
thf(func_def_147,type,
sK8: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_148,type,
sK9: ( subst > term > subst > $o ) > term > term ).
thf(f3,axiom,
! [X0: term] :
( ( ( sub @ X0 @ id )
= X0 )
= axvarid ),
file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',axvarid) ).
thf(f11,axiom,
( axvarshift
= ( ( push @ one @ sh )
= id ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',axvarshift) ).
thf(f96,axiom,
( hoasinduction_lem3aa
= ( ! [X0: subst > term > subst > $o] :
( ! [X1: subst > term > term] :
( ! [X2: subst,X3: term,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/sandbox2/benchmark/Axioms/ALG003^0.ax',hoasinduction_lem3aa) ).
thf(f99,axiom,
( hoasinduction_lem3
= ( ! [X0: subst > term > subst > $o] :
( ! [X4: subst,X2: term,X3: subst,X1: subst] :
( ( X0 @ X1 @ X2 @ ( comp @ X4 @ X3 ) )
=> ( X0 @ ( comp @ X1 @ X4 ) @ ( sub @ X2 @ X4 ) @ X3 ) )
=> ( ! [X1: subst,X3: subst,X2: term,X4: subst] :
( ( X0 @ ( comp @ X1 @ X4 ) @ ( sub @ X2 @ X4 ) @ X3 )
=> ( X0 @ X1 @ X2 @ ( comp @ X4 @ X3 ) ) )
=> ( ! [X5: subst > term > term] :
( ! [X1: subst,X3: subst,X2: term] :
( ( sub @ ( X5 @ X1 @ X2 ) @ X3 )
= ( X5 @ ( comp @ X1 @ X3 ) @ ( sub @ X2 @ X3 ) ) )
=> ( ! [X2: term] :
( ( X0 @ id @ X2 @ id )
=> ( X0 @ id @ ( X5 @ id @ X2 ) @ id ) )
=> ( X0 @ id
@ ( hoaslam @ id
@ ^ [X1: subst,X2: term] : ( X5 @ X1 @ X2 ) )
@ id ) ) )
=> ! [X2: term] :
( ! [X6: term] :
( ( X0 @ id @ X6 @ id )
=> ( X0 @ id @ ( sub @ X2 @ ( push @ X6 @ id ) ) @ id ) )
=> ( X0 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',hoasinduction_lem3) ).
thf(f101,axiom,
( ( hoasinduction_lem3_lthm = axvarid )
=> ( axvarshift
=> ( hoasinduction_lem3aa
=> hoasinduction_lem3 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',hoasinduction_lem3_lthm) ).
thf(f114,conjecture,
hoasinduction_lem3_lthm,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(f115,negated_conjecture,
~ hoasinduction_lem3_lthm,
inference(negated_conjecture,[status(cth)],[f114]) ).
thf(f122,plain,
( hoasinduction_lem3aa
= ( ! [X0: subst > term > subst > $o] :
( ! [X1: subst > term > term] :
( ! [X2: subst,X3: term,X4: subst] :
( ( sub @ ( X1 @ X2 @ X3 ) @ X4 )
= ( X1 @ ( comp @ X2 @ X4 ) @ ( sub @ X3 @ 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(f123,plain,
( hoasinduction_lem3aa
= ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y4 @ Y3 ) @ Y2 )
= ( Y1 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ 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,[],[f122]) ).
thf(f124,plain,
( axvarid
= ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f125,plain,
( hoasinduction_lem3
= ( ! [X0: subst > term > subst > $o] :
( ! [X1: subst,X2: term,X3: subst,X4: subst] :
( ( X0 @ X4 @ X2 @ ( comp @ X1 @ X3 ) )
=> ( X0 @ ( comp @ X4 @ X1 ) @ ( sub @ X2 @ X1 ) @ X3 ) )
=> ( ! [X5: subst,X6: subst,X7: term,X8: subst] :
( ( X0 @ ( comp @ X5 @ X8 ) @ ( sub @ X7 @ X8 ) @ X6 )
=> ( X0 @ X5 @ X7 @ ( comp @ X8 @ X6 ) ) )
=> ( ! [X9: subst > term > term] :
( ! [X10: subst,X11: subst,X12: term] :
( ( sub @ ( X9 @ X10 @ X12 ) @ X11 )
= ( X9 @ ( comp @ X10 @ X11 ) @ ( sub @ X12 @ X11 ) ) )
=> ( ! [X13: term] :
( ( X0 @ id @ X13 @ id )
=> ( X0 @ id @ ( X9 @ id @ X13 ) @ id ) )
=> ( X0 @ id
@ ( hoaslam @ id
@ ^ [X14: subst,X15: term] : ( X9 @ X14 @ X15 ) )
@ id ) ) )
=> ! [X16: term] :
( ! [X17: term] :
( ( X0 @ id @ X17 @ id )
=> ( X0 @ id @ ( sub @ X16 @ ( push @ X17 @ id ) ) @ id ) )
=> ( X0 @ id @ ( lam @ X16 ) @ id ) ) ) ) ) ) ),
inference(rectify,[],[f99]) ).
thf(f126,plain,
( hoasinduction_lem3
= ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y1 @ Y3 @ ( comp @ Y4 @ Y2 ) )
=> ( Y0 @ ( comp @ Y1 @ Y4 ) @ ( sub @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y4 @ Y1 ) @ ( sub @ Y2 @ Y1 ) @ Y3 )
=> ( Y0 @ Y4 @ Y2 @ ( comp @ Y1 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y4 @ Y2 ) @ Y3 )
= ( Y1 @ ( comp @ Y4 @ Y3 ) @ ( sub @ 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,[],[f125]) ).
thf(f134,plain,
( axvarshift
= ( id
= ( push @ one @ sh ) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f157,plain,
~ hoasinduction_lem3_lthm,
inference(rectify,[],[f115]) ).
thf(f158,plain,
hoasinduction_lem3_lthm != $true,
inference(fool_elimination,[],[f157]) ).
thf(f271,plain,
( ( hoasinduction_lem3_lthm = axvarid )
=> ( axvarshift
=> ( hoasinduction_lem3aa
=> hoasinduction_lem3 ) ) ),
inference(rectify,[],[f101]) ).
thf(f272,plain,
( hoasinduction_lem3_lthm
= ( axvarid
=> ( axvarshift
=> ( hoasinduction_lem3aa
=> hoasinduction_lem3 ) ) ) ),
inference(fool_elimination,[],[f271]) ).
thf(f315,plain,
hoasinduction_lem3_lthm != $true,
inference(flattening,[],[f158]) ).
thf(f316,plain,
( hoasinduction_lem3aa
= ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y4 @ Y3 ) @ Y2 )
= ( Y1 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ 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,[],[f123]) ).
thf(f317,plain,
hoasinduction_lem3_lthm != $true,
inference(cnf_transformation,[],[f315]) ).
thf(f318,plain,
( axvarshift
= ( id
= ( push @ one @ sh ) ) ),
inference(cnf_transformation,[],[f134]) ).
thf(f319,plain,
( hoasinduction_lem3
= ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y1 @ Y3 @ ( comp @ Y4 @ Y2 ) )
=> ( Y0 @ ( comp @ Y1 @ Y4 ) @ ( sub @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y4 @ Y1 ) @ ( sub @ Y2 @ Y1 ) @ Y3 )
=> ( Y0 @ Y4 @ Y2 @ ( comp @ Y1 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y4 @ Y2 ) @ Y3 )
= ( Y1 @ ( comp @ Y4 @ Y3 ) @ ( sub @ 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,[],[f126]) ).
thf(f320,plain,
( axvarid
= ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) ),
inference(cnf_transformation,[],[f124]) ).
thf(f321,plain,
( hoasinduction_lem3_lthm
= ( axvarid
=> ( axvarshift
=> ( hoasinduction_lem3aa
=> hoasinduction_lem3 ) ) ) ),
inference(cnf_transformation,[],[f272]) ).
thf(f323,plain,
( hoasinduction_lem3
= ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y1 @ Y3 @ ( comp @ Y4 @ Y2 ) )
=> ( Y0 @ ( comp @ Y1 @ Y4 ) @ ( sub @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y4 @ Y1 ) @ ( sub @ Y2 @ Y1 ) @ Y3 )
=> ( Y0 @ Y4 @ Y2 @ ( comp @ Y1 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y4 @ Y2 ) @ Y3 )
= ( Y1 @ ( comp @ Y4 @ Y3 ) @ ( sub @ 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,[],[f319]) ).
thf(f324,plain,
( hoasinduction_lem3aa
= ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y4 @ Y3 ) @ Y2 )
= ( Y1 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ 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,[],[f316]) ).
thf(f325,plain,
( ( $true != $true )
| ( hoasinduction_lem3_lthm = $false ) ),
inference(fool_paramodulation,[],[f317]) ).
thf(f326,plain,
hoasinduction_lem3_lthm = $false,
inference(trivial_inequality_removal,[],[f325]) ).
thf(f328,plain,
( $false
= ( axvarid
=> ( axvarshift
=> ( hoasinduction_lem3aa
=> hoasinduction_lem3 ) ) ) ),
inference(backward_demodulation,[],[f321,f326]) ).
thf(f329,plain,
( $false
= ( axvarshift
=> ( hoasinduction_lem3aa
=> hoasinduction_lem3 ) ) ),
inference(imp_proxy_clausification,[],[f328]) ).
thf(f330,plain,
axvarid = $true,
inference(imp_proxy_clausification,[],[f328]) ).
thf(f331,plain,
( $false
= ( hoasinduction_lem3aa
=> hoasinduction_lem3 ) ),
inference(imp_proxy_clausification,[],[f329]) ).
thf(f332,plain,
axvarshift = $true,
inference(imp_proxy_clausification,[],[f329]) ).
thf(f333,plain,
hoasinduction_lem3 = $false,
inference(imp_proxy_clausification,[],[f331]) ).
thf(f334,plain,
hoasinduction_lem3aa = $true,
inference(imp_proxy_clausification,[],[f331]) ).
thf(f335,plain,
( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
= $true ),
inference(backward_demodulation,[],[f320,f330]) ).
thf(f337,plain,
! [X1: term] :
( ( ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f335]) ).
thf(f338,plain,
! [X1: term] :
( ( ( sub @ X1 @ id )
= X1 )
= $true ),
inference(beta-eta_normalization,[],[f337]) ).
thf(f339,plain,
! [X1: term] :
( ( sub @ X1 @ id )
= X1 ),
inference(equality_proxy_clausification,[],[f338]) ).
thf(f340,plain,
( ( id
= ( push @ one @ sh ) )
= $true ),
inference(backward_demodulation,[],[f318,f332]) ).
thf(f342,plain,
( id
= ( push @ one @ sh ) ),
inference(equality_proxy_clausification,[],[f340]) ).
thf(f343,plain,
( $false
= ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y1 @ Y3 @ ( comp @ Y4 @ Y2 ) )
=> ( Y0 @ ( comp @ Y1 @ Y4 ) @ ( sub @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y4 @ Y1 ) @ ( sub @ Y2 @ Y1 ) @ Y3 )
=> ( Y0 @ Y4 @ Y2 @ ( comp @ Y1 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y4 @ Y2 ) @ Y3 )
= ( Y1 @ ( comp @ Y4 @ Y3 ) @ ( sub @ 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(backward_demodulation,[],[f323,f333]) ).
thf(f344,plain,
( $false
= ( ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y1 @ Y3 @ ( comp @ Y4 @ Y2 ) )
=> ( Y0 @ ( comp @ Y1 @ Y4 ) @ ( sub @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y4 @ Y1 ) @ ( sub @ Y2 @ Y1 ) @ Y3 )
=> ( Y0 @ Y4 @ Y2 @ ( comp @ Y1 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y4 @ Y2 ) @ Y3 )
= ( Y1 @ ( comp @ Y4 @ Y3 ) @ ( sub @ 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 ) ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f343]) ).
thf(f345,plain,
( $false
= ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sK0 @ Y0 @ Y2 @ ( comp @ Y3 @ Y1 ) )
=> ( sK0 @ ( comp @ Y0 @ Y3 ) @ ( sub @ Y2 @ Y3 ) @ Y1 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sK0 @ ( comp @ Y3 @ Y0 ) @ ( sub @ Y1 @ Y0 ) @ Y2 )
=> ( sK0 @ Y3 @ Y1 @ ( comp @ Y0 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 )
= ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( sK0 @ id @ Y1 @ id )
=> ( sK0 @ id @ ( Y0 @ id @ Y1 ) @ id ) ) )
=> ( sK0 @ id @ ( hoaslam @ id @ Y0 ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( sK0 @ id @ Y1 @ id )
=> ( sK0 @ id @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) @ id ) ) )
=> ( sK0 @ id @ ( lam @ Y0 ) @ id ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f344]) ).
thf(f346,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sK0 @ ( comp @ Y3 @ Y0 ) @ ( sub @ Y1 @ Y0 ) @ Y2 )
=> ( sK0 @ Y3 @ Y1 @ ( comp @ Y0 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 )
= ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( sK0 @ id @ Y1 @ id )
=> ( sK0 @ id @ ( Y0 @ id @ Y1 ) @ id ) ) )
=> ( sK0 @ id @ ( hoaslam @ id @ Y0 ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( sK0 @ id @ Y1 @ id )
=> ( sK0 @ id @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) @ id ) ) )
=> ( sK0 @ id @ ( lam @ Y0 ) @ id ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f345]) ).
thf(f357,plain,
( $false
= ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 )
= ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( sK0 @ id @ Y1 @ id )
=> ( sK0 @ id @ ( Y0 @ id @ Y1 ) @ id ) ) )
=> ( sK0 @ id @ ( hoaslam @ id @ Y0 ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( sK0 @ id @ Y1 @ id )
=> ( sK0 @ id @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) @ id ) ) )
=> ( sK0 @ id @ ( lam @ Y0 ) @ id ) ) ) ) ),
inference(imp_proxy_clausification,[],[f346]) ).
thf(f368,plain,
( ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( sK0 @ id @ Y1 @ id )
=> ( sK0 @ id @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) @ id ) ) )
=> ( sK0 @ id @ ( lam @ Y0 ) @ id ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f357]) ).
thf(f369,plain,
( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 )
= ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( sK0 @ id @ Y1 @ id )
=> ( sK0 @ id @ ( Y0 @ id @ Y1 ) @ id ) ) )
=> ( sK0 @ id @ ( hoaslam @ id @ Y0 ) @ id ) ) ) )
= $true ),
inference(imp_proxy_clausification,[],[f357]) ).
thf(f370,plain,
! [X1: subst > term > term] :
( ( ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 )
= ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( sK0 @ id @ Y1 @ id )
=> ( sK0 @ id @ ( Y0 @ id @ Y1 ) @ id ) ) )
=> ( sK0 @ id @ ( hoaslam @ id @ Y0 ) @ id ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f369]) ).
thf(f371,plain,
! [X1: subst > term > term] :
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( X1 @ Y2 @ Y0 ) @ Y1 )
= ( X1 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( sK0 @ id @ Y0 @ id )
=> ( sK0 @ id @ ( X1 @ id @ Y0 ) @ id ) ) )
=> ( sK0 @ id @ ( hoaslam @ id @ X1 ) @ id ) ) )
= $true ),
inference(beta-eta_normalization,[],[f370]) ).
thf(f372,plain,
! [X1: subst > term > term] :
( ( $false
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( X1 @ Y2 @ Y0 ) @ Y1 )
= ( X1 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y0 @ Y1 ) ) ) ) ) ) )
| ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sK0 @ id @ Y0 @ id )
=> ( sK0 @ id @ ( X1 @ id @ Y0 ) @ id ) ) )
=> ( sK0 @ id @ ( hoaslam @ id @ X1 ) @ id ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f371]) ).
thf(f373,plain,
! [X1: subst > term > term] :
( ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sK0 @ id @ Y0 @ id )
=> ( sK0 @ id @ ( X1 @ id @ Y0 ) @ id ) ) )
=> ( sK0 @ id @ ( hoaslam @ id @ X1 ) @ id ) )
= $true )
| ( $false
= ( ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( X1 @ Y2 @ Y0 ) @ Y1 )
= ( X1 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y0 @ Y1 ) ) ) ) )
@ ( sK1 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f372]) ).
thf(f374,plain,
! [X1: subst > term > term] :
( ( $false
= ( ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( X1 @ Y2 @ Y0 ) @ Y1 )
= ( X1 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y0 @ Y1 ) ) ) ) )
@ ( sK1 @ X1 ) ) )
| ( ( sK0 @ id @ ( hoaslam @ id @ X1 ) @ id )
= $true )
| ( ( !! @ term
@ ^ [Y0: term] :
( ( sK0 @ id @ Y0 @ id )
=> ( sK0 @ id @ ( X1 @ id @ Y0 ) @ id ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f373]) ).
thf(f375,plain,
! [X1: subst > term > term] :
( ( $false
= ( ^ [Y0: term] :
( ( sK0 @ id @ Y0 @ id )
=> ( sK0 @ id @ ( X1 @ id @ Y0 ) @ id ) )
@ ( sK2 @ X1 ) ) )
| ( ( sK0 @ id @ ( hoaslam @ id @ X1 ) @ id )
= $true )
| ( $false
= ( ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( X1 @ Y2 @ Y0 ) @ Y1 )
= ( X1 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y0 @ Y1 ) ) ) ) )
@ ( sK1 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f374]) ).
thf(f376,plain,
! [X1: subst > term > term] :
( ( ( sK0 @ id @ ( hoaslam @ id @ X1 ) @ id )
= $true )
| ( $false
= ( ( sK0 @ id @ ( sK2 @ X1 ) @ id )
=> ( sK0 @ id @ ( X1 @ id @ ( sK2 @ X1 ) ) @ id ) ) )
| ( $false
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ ( X1 @ Y1 @ ( sK1 @ X1 ) ) @ Y0 )
= ( X1 @ ( comp @ Y1 @ Y0 ) @ ( sub @ ( sK1 @ X1 ) @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f375]) ).
thf(f377,plain,
! [X1: subst > term > term] :
( ( ( sK0 @ id @ ( hoaslam @ id @ X1 ) @ id )
= $true )
| ( $false
= ( sK0 @ id @ ( X1 @ id @ ( sK2 @ X1 ) ) @ id ) )
| ( $false
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ ( X1 @ Y1 @ ( sK1 @ X1 ) ) @ Y0 )
= ( X1 @ ( comp @ Y1 @ Y0 ) @ ( sub @ ( sK1 @ X1 ) @ Y0 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f376]) ).
thf(f378,plain,
! [X1: subst > term > term] :
( ( ( sK0 @ id @ ( sK2 @ X1 ) @ id )
= $true )
| ( ( sK0 @ id @ ( hoaslam @ id @ X1 ) @ id )
= $true )
| ( $false
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ ( X1 @ Y1 @ ( sK1 @ X1 ) ) @ Y0 )
= ( X1 @ ( comp @ Y1 @ Y0 ) @ ( sub @ ( sK1 @ X1 ) @ Y0 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f376]) ).
thf(f379,plain,
! [X1: subst > term > term] :
( ( ( sK0 @ id @ ( sK2 @ X1 ) @ id )
= $true )
| ( ( ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ ( X1 @ Y1 @ ( sK1 @ X1 ) ) @ Y0 )
= ( X1 @ ( comp @ Y1 @ Y0 ) @ ( sub @ ( sK1 @ X1 ) @ Y0 ) ) ) )
@ ( sK3 @ X1 ) )
= $false )
| ( ( sK0 @ id @ ( hoaslam @ id @ X1 ) @ id )
= $true ) ),
inference(sigma_proxy_clausification,[],[f378]) ).
thf(f380,plain,
! [X1: subst > term > term] :
( ( ( sK0 @ id @ ( hoaslam @ id @ X1 ) @ id )
= $true )
| ( ( !! @ subst
@ ^ [Y0: subst] :
( ( sub @ ( X1 @ Y0 @ ( sK1 @ X1 ) ) @ ( sK3 @ X1 ) )
= ( X1 @ ( comp @ Y0 @ ( sK3 @ X1 ) ) @ ( sub @ ( sK1 @ X1 ) @ ( sK3 @ X1 ) ) ) ) )
= $false )
| ( ( sK0 @ id @ ( sK2 @ X1 ) @ id )
= $true ) ),
inference(beta-eta_normalization,[],[f379]) ).
thf(f381,plain,
! [X1: subst > term > term] :
( ( ( sK0 @ id @ ( sK2 @ X1 ) @ id )
= $true )
| ( ( sK0 @ id @ ( hoaslam @ id @ X1 ) @ id )
= $true )
| ( $false
= ( ^ [Y0: subst] :
( ( sub @ ( X1 @ Y0 @ ( sK1 @ X1 ) ) @ ( sK3 @ X1 ) )
= ( X1 @ ( comp @ Y0 @ ( sK3 @ X1 ) ) @ ( sub @ ( sK1 @ X1 ) @ ( sK3 @ X1 ) ) ) )
@ ( sK4 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f380]) ).
thf(f382,plain,
! [X1: subst > term > term] :
( ( ( sK0 @ id @ ( hoaslam @ id @ X1 ) @ id )
= $true )
| ( ( sK0 @ id @ ( sK2 @ X1 ) @ id )
= $true )
| ( $false
= ( ( sub @ ( X1 @ ( sK4 @ X1 ) @ ( sK1 @ X1 ) ) @ ( sK3 @ X1 ) )
= ( X1 @ ( comp @ ( sK4 @ X1 ) @ ( sK3 @ X1 ) ) @ ( sub @ ( sK1 @ X1 ) @ ( sK3 @ X1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f381]) ).
thf(f383,plain,
! [X1: subst > term > term] :
( ( ( sub @ ( X1 @ ( sK4 @ X1 ) @ ( sK1 @ X1 ) ) @ ( sK3 @ X1 ) )
!= ( X1 @ ( comp @ ( sK4 @ X1 ) @ ( sK3 @ X1 ) ) @ ( sub @ ( sK1 @ X1 ) @ ( sK3 @ X1 ) ) ) )
| ( ( sK0 @ id @ ( hoaslam @ id @ X1 ) @ id )
= $true )
| ( ( sK0 @ id @ ( sK2 @ X1 ) @ id )
= $true ) ),
inference(equality_proxy_clausification,[],[f382]) ).
thf(f384,plain,
! [X1: subst > term > term] :
( ( ( sK0 @ id @ ( hoaslam @ id @ X1 ) @ id )
= $true )
| ( $false
= ( sK0 @ id @ ( X1 @ id @ ( sK2 @ X1 ) ) @ id ) )
| ( ( ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ ( X1 @ Y1 @ ( sK1 @ X1 ) ) @ Y0 )
= ( X1 @ ( comp @ Y1 @ Y0 ) @ ( sub @ ( sK1 @ X1 ) @ Y0 ) ) ) )
@ ( sK5 @ X1 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f377]) ).
thf(f385,plain,
! [X1: subst > term > term] :
( ( $false
= ( sK0 @ id @ ( X1 @ id @ ( sK2 @ X1 ) ) @ id ) )
| ( $false
= ( !! @ subst
@ ^ [Y0: subst] :
( ( sub @ ( X1 @ Y0 @ ( sK1 @ X1 ) ) @ ( sK5 @ X1 ) )
= ( X1 @ ( comp @ Y0 @ ( sK5 @ X1 ) ) @ ( sub @ ( sK1 @ X1 ) @ ( sK5 @ X1 ) ) ) ) ) )
| ( ( sK0 @ id @ ( hoaslam @ id @ X1 ) @ id )
= $true ) ),
inference(beta-eta_normalization,[],[f384]) ).
thf(f386,plain,
! [X1: subst > term > term] :
( ( $false
= ( sK0 @ id @ ( X1 @ id @ ( sK2 @ X1 ) ) @ id ) )
| ( $false
= ( ^ [Y0: subst] :
( ( sub @ ( X1 @ Y0 @ ( sK1 @ X1 ) ) @ ( sK5 @ X1 ) )
= ( X1 @ ( comp @ Y0 @ ( sK5 @ X1 ) ) @ ( sub @ ( sK1 @ X1 ) @ ( sK5 @ X1 ) ) ) )
@ ( sK6 @ X1 ) ) )
| ( ( sK0 @ id @ ( hoaslam @ id @ X1 ) @ id )
= $true ) ),
inference(sigma_proxy_clausification,[],[f385]) ).
thf(f387,plain,
! [X1: subst > term > term] :
( ( ( sK0 @ id @ ( hoaslam @ id @ X1 ) @ id )
= $true )
| ( ( ( sub @ ( X1 @ ( sK6 @ X1 ) @ ( sK1 @ X1 ) ) @ ( sK5 @ X1 ) )
= ( X1 @ ( comp @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) ) @ ( sub @ ( sK1 @ X1 ) @ ( sK5 @ X1 ) ) ) )
= $false )
| ( $false
= ( sK0 @ id @ ( X1 @ id @ ( sK2 @ X1 ) ) @ id ) ) ),
inference(beta-eta_normalization,[],[f386]) ).
thf(f388,plain,
! [X1: subst > term > term] :
( ( ( sub @ ( X1 @ ( sK6 @ X1 ) @ ( sK1 @ X1 ) ) @ ( sK5 @ X1 ) )
!= ( X1 @ ( comp @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) ) @ ( sub @ ( sK1 @ X1 ) @ ( sK5 @ X1 ) ) ) )
| ( $false
= ( sK0 @ id @ ( X1 @ id @ ( sK2 @ X1 ) ) @ id ) )
| ( ( sK0 @ id @ ( hoaslam @ id @ X1 ) @ id )
= $true ) ),
inference(equality_proxy_clausification,[],[f387]) ).
thf(f389,plain,
( $false
= ( ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( sK0 @ id @ Y1 @ id )
=> ( sK0 @ id @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) @ id ) ) )
=> ( sK0 @ id @ ( lam @ Y0 ) @ id ) )
@ sK7 ) ),
inference(sigma_proxy_clausification,[],[f368]) ).
thf(f390,plain,
( $false
= ( ( !! @ term
@ ^ [Y0: term] :
( ( sK0 @ id @ Y0 @ id )
=> ( sK0 @ id @ ( sub @ sK7 @ ( push @ Y0 @ id ) ) @ id ) ) )
=> ( sK0 @ id @ ( lam @ sK7 ) @ id ) ) ),
inference(beta-eta_normalization,[],[f389]) ).
thf(f391,plain,
( $false
= ( sK0 @ id @ ( lam @ sK7 ) @ id ) ),
inference(imp_proxy_clausification,[],[f390]) ).
thf(f392,plain,
( ( !! @ term
@ ^ [Y0: term] :
( ( sK0 @ id @ Y0 @ id )
=> ( sK0 @ id @ ( sub @ sK7 @ ( push @ Y0 @ id ) ) @ id ) ) )
= $true ),
inference(imp_proxy_clausification,[],[f390]) ).
thf(f393,plain,
! [X1: term] :
( ( ^ [Y0: term] :
( ( sK0 @ id @ Y0 @ id )
=> ( sK0 @ id @ ( sub @ sK7 @ ( push @ Y0 @ id ) ) @ id ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f392]) ).
thf(f394,plain,
! [X1: term] :
( ( ( sK0 @ id @ X1 @ id )
=> ( sK0 @ id @ ( sub @ sK7 @ ( push @ X1 @ id ) ) @ id ) )
= $true ),
inference(beta-eta_normalization,[],[f393]) ).
thf(f395,plain,
! [X1: term] :
( ( ( sK0 @ id @ ( sub @ sK7 @ ( push @ X1 @ id ) ) @ id )
= $true )
| ( ( sK0 @ id @ X1 @ id )
= $false ) ),
inference(imp_proxy_clausification,[],[f394]) ).
thf(f396,plain,
( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y4 @ Y3 ) @ Y2 )
= ( Y1 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ 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,[],[f324,f334]) ).
thf(f398,plain,
! [X1: subst > term > subst > $o] :
( ( ^ [Y0: subst > term > subst > $o] :
( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y4 @ Y3 ) @ Y2 )
= ( Y1 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ 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 )
= $true ),
inference(pi_proxy_clausification,[],[f396]) ).
thf(f399,plain,
! [X1: subst > term > subst > $o] :
( ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ 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,[],[f398]) ).
thf(f400,plain,
! [X1: subst > term > subst > $o] :
( ( ( !! @ 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 )
| ( $false
= ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( X1 @ id @ Y1 @ id )
=> ( X1 @ id @ ( Y0 @ id @ Y1 ) @ id ) ) )
=> ( X1 @ id @ ( hoaslam @ id @ Y0 ) @ id ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f399]) ).
thf(f401,plain,
! [X2: term,X1: subst > term > subst > $o] :
( ( $false
= ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( X1 @ id @ Y1 @ id )
=> ( X1 @ id @ ( Y0 @ id @ Y1 ) @ id ) ) )
=> ( X1 @ id @ ( hoaslam @ id @ Y0 ) @ id ) ) ) ) )
| ( ( ^ [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 )
= $true ) ),
inference(pi_proxy_clausification,[],[f400]) ).
thf(f402,plain,
! [X2: term,X1: subst > term > subst > $o] :
( ( ( ^ [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 )
= $true )
| ( $false
= ( ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( X1 @ id @ Y1 @ id )
=> ( X1 @ id @ ( Y0 @ id @ Y1 ) @ id ) ) )
=> ( X1 @ id @ ( hoaslam @ id @ Y0 ) @ id ) ) )
@ ( sK8 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f401]) ).
thf(f403,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] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sK8 @ X1 @ Y2 @ Y1 ) @ Y0 )
= ( sK8 @ X1 @ ( comp @ Y2 @ Y0 ) @ ( sub @ Y1 @ Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( X1 @ id @ Y0 @ id )
=> ( X1 @ id @ ( sK8 @ X1 @ id @ Y0 ) @ id ) ) )
=> ( X1 @ id @ ( hoaslam @ id @ ( sK8 @ X1 ) ) @ id ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f402]) ).
thf(f404,plain,
! [X2: term,X1: subst > term > subst > $o] :
( ( $false
= ( !! @ 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] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sK8 @ X1 @ Y2 @ Y1 ) @ Y0 )
= ( sK8 @ X1 @ ( comp @ Y2 @ Y0 ) @ ( sub @ Y1 @ Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( X1 @ id @ Y0 @ id )
=> ( X1 @ id @ ( sK8 @ X1 @ id @ Y0 ) @ id ) ) )
=> ( X1 @ id @ ( hoaslam @ id @ ( sK8 @ X1 ) ) @ id ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f403]) ).
thf(f405,plain,
! [X2: term,X1: subst > term > subst > $o] :
( ( $false
= ( ^ [Y0: term] :
( ( X1 @ id @ Y0 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ Y0 @ id ) ) @ id ) )
@ ( sK9 @ X1 @ X2 ) ) )
| ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sK8 @ X1 @ Y2 @ Y1 ) @ Y0 )
= ( sK8 @ X1 @ ( comp @ Y2 @ Y0 ) @ ( sub @ Y1 @ Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( X1 @ id @ Y0 @ id )
=> ( X1 @ id @ ( sK8 @ X1 @ id @ Y0 ) @ id ) ) )
=> ( X1 @ id @ ( hoaslam @ id @ ( sK8 @ X1 ) ) @ id ) ) )
= $false )
| ( ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id )
= $true ) ),
inference(sigma_proxy_clausification,[],[f404]) ).
thf(f406,plain,
! [X2: term,X1: subst > term > subst > $o] :
( ( $false
= ( ^ [Y0: term] :
( ( X1 @ id @ Y0 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ Y0 @ id ) ) @ id ) )
@ ( sK9 @ X1 @ X2 ) ) )
| ( $false
= ( ( !! @ term
@ ^ [Y0: term] :
( ( X1 @ id @ Y0 @ id )
=> ( X1 @ id @ ( sK8 @ X1 @ id @ Y0 ) @ id ) ) )
=> ( X1 @ id @ ( hoaslam @ id @ ( sK8 @ X1 ) ) @ id ) ) )
| ( ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id )
= $true ) ),
inference(imp_proxy_clausification,[],[f405]) ).
thf(f407,plain,
! [X2: term,X1: subst > term > subst > $o] :
( ( ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sK8 @ X1 @ Y2 @ Y1 ) @ Y0 )
= ( sK8 @ X1 @ ( comp @ Y2 @ Y0 ) @ ( sub @ Y1 @ Y0 ) ) ) ) ) )
= $true )
| ( $false
= ( ^ [Y0: term] :
( ( X1 @ id @ Y0 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ Y0 @ id ) ) @ id ) )
@ ( sK9 @ X1 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f405]) ).
thf(f408,plain,
! [X2: term,X3: subst,X1: subst > term > subst > $o] :
( ( $true
= ( ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sK8 @ X1 @ Y2 @ Y1 ) @ Y0 )
= ( sK8 @ X1 @ ( comp @ Y2 @ Y0 ) @ ( sub @ Y1 @ Y0 ) ) ) ) )
@ X3 ) )
| ( $false
= ( ^ [Y0: term] :
( ( X1 @ id @ Y0 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ Y0 @ id ) ) @ id ) )
@ ( sK9 @ X1 @ X2 ) ) )
| ( ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id )
= $true ) ),
inference(pi_proxy_clausification,[],[f407]) ).
thf(f409,plain,
! [X2: term,X3: subst,X1: subst > term > subst > $o] :
( ( $false
= ( ( X1 @ id @ ( sK9 @ X1 @ X2 ) @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ ( sK9 @ X1 @ X2 ) @ id ) ) @ id ) ) )
| ( ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ( $true
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ ( sK8 @ X1 @ Y1 @ Y0 ) @ X3 )
= ( sK8 @ X1 @ ( comp @ Y1 @ X3 ) @ ( sub @ Y0 @ X3 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f408]) ).
thf(f410,plain,
! [X2: term,X3: subst,X1: subst > term > subst > $o] :
( ( $true
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ ( sK8 @ X1 @ Y1 @ Y0 ) @ X3 )
= ( sK8 @ X1 @ ( comp @ Y1 @ X3 ) @ ( sub @ Y0 @ X3 ) ) ) ) ) )
| ( ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ( ( X1 @ id @ ( sub @ X2 @ ( push @ ( sK9 @ X1 @ X2 ) @ id ) ) @ id )
= $false ) ),
inference(imp_proxy_clausification,[],[f409]) ).
thf(f411,plain,
! [X2: term,X3: subst,X1: subst > term > subst > $o] :
( ( ( X1 @ id @ ( sK9 @ X1 @ X2 ) @ id )
= $true )
| ( ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ( $true
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ ( sK8 @ X1 @ Y1 @ Y0 ) @ X3 )
= ( sK8 @ X1 @ ( comp @ Y1 @ X3 ) @ ( sub @ Y0 @ X3 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f409]) ).
thf(f412,plain,
! [X2: term,X3: subst,X1: subst > term > subst > $o,X4: term] :
( ( ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ( ( X1 @ id @ ( sK9 @ X1 @ X2 ) @ id )
= $true )
| ( $true
= ( ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ ( sK8 @ X1 @ Y1 @ Y0 ) @ X3 )
= ( sK8 @ X1 @ ( comp @ Y1 @ X3 ) @ ( sub @ Y0 @ X3 ) ) ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f411]) ).
thf(f413,plain,
! [X2: term,X3: subst,X1: subst > term > subst > $o,X4: term] :
( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( sub @ ( sK8 @ X1 @ Y0 @ X4 ) @ X3 )
= ( sK8 @ X1 @ ( comp @ Y0 @ X3 ) @ ( sub @ X4 @ X3 ) ) ) )
= $true )
| ( ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ( ( X1 @ id @ ( sK9 @ X1 @ X2 ) @ id )
= $true ) ),
inference(beta-eta_normalization,[],[f412]) ).
thf(f414,plain,
! [X2: term,X3: subst,X1: subst > term > subst > $o,X4: term,X5: subst] :
( ( ( X1 @ id @ ( sK9 @ X1 @ X2 ) @ id )
= $true )
| ( ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ( ( ^ [Y0: subst] :
( ( sub @ ( sK8 @ X1 @ Y0 @ X4 ) @ X3 )
= ( sK8 @ X1 @ ( comp @ Y0 @ X3 ) @ ( sub @ X4 @ X3 ) ) )
@ X5 )
= $true ) ),
inference(pi_proxy_clausification,[],[f413]) ).
thf(f415,plain,
! [X2: term,X3: subst,X1: subst > term > subst > $o,X4: term,X5: subst] :
( ( ( X1 @ id @ ( sK9 @ X1 @ X2 ) @ id )
= $true )
| ( ( ( sub @ ( sK8 @ X1 @ X5 @ X4 ) @ X3 )
= ( sK8 @ X1 @ ( comp @ X5 @ X3 ) @ ( sub @ X4 @ X3 ) ) )
= $true )
| ( ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id )
= $true ) ),
inference(beta-eta_normalization,[],[f414]) ).
thf(f416,plain,
! [X2: term,X3: subst,X1: subst > term > subst > $o,X4: term,X5: subst] :
( ( ( sub @ ( sK8 @ X1 @ X5 @ X4 ) @ X3 )
= ( sK8 @ X1 @ ( comp @ X5 @ X3 ) @ ( sub @ X4 @ X3 ) ) )
| ( ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ( ( X1 @ id @ ( sK9 @ X1 @ X2 ) @ id )
= $true ) ),
inference(equality_proxy_clausification,[],[f415]) ).
thf(f417,plain,
! [X2: term,X3: subst,X1: subst > term > subst > $o,X4: term] :
( ( ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ( $true
= ( ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ ( sK8 @ X1 @ Y1 @ Y0 ) @ X3 )
= ( sK8 @ X1 @ ( comp @ Y1 @ X3 ) @ ( sub @ Y0 @ X3 ) ) ) )
@ X4 ) )
| ( ( X1 @ id @ ( sub @ X2 @ ( push @ ( sK9 @ X1 @ X2 ) @ id ) ) @ id )
= $false ) ),
inference(pi_proxy_clausification,[],[f410]) ).
thf(f418,plain,
! [X2: term,X3: subst,X1: subst > term > subst > $o,X4: term] :
( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( sub @ ( sK8 @ X1 @ Y0 @ X4 ) @ X3 )
= ( sK8 @ X1 @ ( comp @ Y0 @ X3 ) @ ( sub @ X4 @ X3 ) ) ) )
= $true )
| ( ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ( ( X1 @ id @ ( sub @ X2 @ ( push @ ( sK9 @ X1 @ X2 ) @ id ) ) @ id )
= $false ) ),
inference(beta-eta_normalization,[],[f417]) ).
thf(f419,plain,
! [X2: term,X3: subst,X1: subst > term > subst > $o,X4: term,X5: subst] :
( ( ( ^ [Y0: subst] :
( ( sub @ ( sK8 @ X1 @ Y0 @ X4 ) @ X3 )
= ( sK8 @ X1 @ ( comp @ Y0 @ X3 ) @ ( sub @ X4 @ X3 ) ) )
@ X5 )
= $true )
| ( ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ( ( X1 @ id @ ( sub @ X2 @ ( push @ ( sK9 @ X1 @ X2 ) @ id ) ) @ id )
= $false ) ),
inference(pi_proxy_clausification,[],[f418]) ).
thf(f420,plain,
! [X2: term,X3: subst,X1: subst > term > subst > $o,X4: term,X5: subst] :
( ( ( ( sub @ ( sK8 @ X1 @ X5 @ X4 ) @ X3 )
= ( sK8 @ X1 @ ( comp @ X5 @ X3 ) @ ( sub @ X4 @ X3 ) ) )
= $true )
| ( ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ( ( X1 @ id @ ( sub @ X2 @ ( push @ ( sK9 @ X1 @ X2 ) @ id ) ) @ id )
= $false ) ),
inference(beta-eta_normalization,[],[f419]) ).
thf(f421,plain,
! [X2: term,X3: subst,X1: subst > term > subst > $o,X4: term,X5: subst] :
( ( ( X1 @ id @ ( sub @ X2 @ ( push @ ( sK9 @ X1 @ X2 ) @ id ) ) @ id )
= $false )
| ( ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ( ( sub @ ( sK8 @ X1 @ X5 @ X4 ) @ X3 )
= ( sK8 @ X1 @ ( comp @ X5 @ X3 ) @ ( sub @ X4 @ X3 ) ) ) ),
inference(equality_proxy_clausification,[],[f420]) ).
thf(f422,plain,
! [X2: term,X1: subst > term > subst > $o] :
( ( $false
= ( ^ [Y0: term] :
( ( X1 @ id @ Y0 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ Y0 @ id ) ) @ id ) )
@ ( sK9 @ X1 @ X2 ) ) )
| ( $false
= ( X1 @ id @ ( hoaslam @ id @ ( sK8 @ X1 ) ) @ id ) )
| ( ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id )
= $true ) ),
inference(imp_proxy_clausification,[],[f406]) ).
thf(f423,plain,
! [X2: term,X1: subst > term > subst > $o] :
( ( ( !! @ term
@ ^ [Y0: term] :
( ( X1 @ id @ Y0 @ id )
=> ( X1 @ id @ ( sK8 @ X1 @ id @ Y0 ) @ id ) ) )
= $true )
| ( $false
= ( ^ [Y0: term] :
( ( X1 @ id @ Y0 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ Y0 @ id ) ) @ id ) )
@ ( sK9 @ X1 @ X2 ) ) )
| ( ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id )
= $true ) ),
inference(imp_proxy_clausification,[],[f406]) ).
thf(f424,plain,
! [X2: term,X3: term,X1: subst > term > subst > $o] :
( ( ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ( $false
= ( ^ [Y0: term] :
( ( X1 @ id @ Y0 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ Y0 @ id ) ) @ id ) )
@ ( sK9 @ X1 @ X2 ) ) )
| ( ( ^ [Y0: term] :
( ( X1 @ id @ Y0 @ id )
=> ( X1 @ id @ ( sK8 @ X1 @ id @ Y0 ) @ id ) )
@ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f423]) ).
thf(f425,plain,
! [X2: term,X3: term,X1: subst > term > subst > $o] :
( ( ( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sK8 @ X1 @ id @ X3 ) @ id ) )
= $true )
| ( ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ( $false
= ( ( X1 @ id @ ( sK9 @ X1 @ X2 ) @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ ( sK9 @ X1 @ X2 ) @ id ) ) @ id ) ) ) ),
inference(beta-eta_normalization,[],[f424]) ).
thf(f426,plain,
! [X2: term,X3: term,X1: subst > term > subst > $o] :
( ( ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ( $false
= ( ( X1 @ id @ ( sK9 @ X1 @ X2 ) @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ ( sK9 @ X1 @ X2 ) @ id ) ) @ id ) ) )
| ( $false
= ( X1 @ id @ X3 @ id ) )
| ( ( X1 @ id @ ( sK8 @ X1 @ id @ X3 ) @ id )
= $true ) ),
inference(imp_proxy_clausification,[],[f425]) ).
thf(f427,plain,
! [X2: term,X3: term,X1: subst > term > subst > $o] :
( ( ( X1 @ id @ ( sub @ X2 @ ( push @ ( sK9 @ X1 @ X2 ) @ id ) ) @ id )
= $false )
| ( $false
= ( X1 @ id @ X3 @ id ) )
| ( ( X1 @ id @ ( sK8 @ X1 @ id @ X3 ) @ id )
= $true )
| ( ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id )
= $true ) ),
inference(imp_proxy_clausification,[],[f426]) ).
thf(f428,plain,
! [X2: term,X3: term,X1: subst > term > subst > $o] :
( ( ( X1 @ id @ ( sK8 @ X1 @ id @ X3 ) @ id )
= $true )
| ( ( X1 @ id @ ( sK9 @ X1 @ X2 ) @ id )
= $true )
| ( ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ( $false
= ( X1 @ id @ X3 @ id ) ) ),
inference(imp_proxy_clausification,[],[f426]) ).
thf(f429,plain,
! [X2: term,X1: subst > term > subst > $o] :
( ( ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ( $false
= ( ( X1 @ id @ ( sK9 @ X1 @ X2 ) @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ ( sK9 @ X1 @ X2 ) @ id ) ) @ id ) ) )
| ( $false
= ( X1 @ id @ ( hoaslam @ id @ ( sK8 @ X1 ) ) @ id ) ) ),
inference(beta-eta_normalization,[],[f422]) ).
thf(f430,plain,
! [X2: term,X1: subst > term > subst > $o] :
( ( $false
= ( X1 @ id @ ( hoaslam @ id @ ( sK8 @ X1 ) ) @ id ) )
| ( ( X1 @ id @ ( sub @ X2 @ ( push @ ( sK9 @ X1 @ X2 ) @ id ) ) @ id )
= $false )
| ( ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id )
= $true ) ),
inference(imp_proxy_clausification,[],[f429]) ).
thf(f431,plain,
! [X2: term,X1: subst > term > subst > $o] :
( ( ( X1 @ id @ ( sK9 @ X1 @ X2 ) @ id )
= $true )
| ( $false
= ( X1 @ id @ ( hoaslam @ id @ ( sK8 @ X1 ) ) @ id ) )
| ( ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id )
= $true ) ),
inference(imp_proxy_clausification,[],[f429]) ).
thf(f450,plain,
! [X2: term,X1: subst > term > subst > $o] :
( ( ( X1 @ id @ ( lam @ ( sub @ X2 @ id ) ) @ id )
= $true )
| ( ( X1 @ id @ ( sK9 @ X1 @ X2 ) @ id )
= $true )
| ( $false
= ( X1 @ id @ ( hoaslam @ id @ ( sK8 @ X1 ) ) @ id ) ) ),
inference(forward_demodulation,[],[f431,f342]) ).
thf(f451,plain,
! [X2: term,X1: subst > term > subst > $o] :
( ( $false
= ( X1 @ id @ ( hoaslam @ id @ ( sK8 @ X1 ) ) @ id ) )
| ( ( X1 @ id @ ( sK9 @ X1 @ X2 ) @ id )
= $true )
| ( ( X1 @ id @ ( lam @ X2 ) @ id )
= $true ) ),
inference(forward_demodulation,[],[f450,f339]) ).
thf(f498,plain,
! [X2: term,X3: term,X1: subst > term > subst > $o] :
( ( $false
= ( X1 @ id @ X3 @ id ) )
| ( ( X1 @ id @ ( lam @ ( sub @ X2 @ id ) ) @ id )
= $true )
| ( ( X1 @ id @ ( sK8 @ X1 @ id @ X3 ) @ id )
= $true )
| ( ( X1 @ id @ ( sK9 @ X1 @ X2 ) @ id )
= $true ) ),
inference(forward_demodulation,[],[f428,f342]) ).
thf(f499,plain,
! [X2: term,X3: term,X1: subst > term > subst > $o] :
( ( ( X1 @ id @ ( sK8 @ X1 @ id @ X3 ) @ id )
= $true )
| ( ( X1 @ id @ ( sK9 @ X1 @ X2 ) @ id )
= $true )
| ( ( X1 @ id @ ( lam @ X2 ) @ id )
= $true )
| ( $false
= ( X1 @ id @ X3 @ id ) ) ),
inference(forward_demodulation,[],[f498,f339]) ).
thf(f549,plain,
! [X2: term,X1: subst > term > subst > $o] :
( ( ( X1 @ id @ ( sub @ X2 @ ( push @ ( sK9 @ X1 @ X2 ) @ id ) ) @ id )
= $false )
| ( $false
= ( X1 @ id @ ( hoaslam @ id @ ( sK8 @ X1 ) ) @ id ) )
| ( ( X1 @ id @ ( lam @ ( sub @ X2 @ id ) ) @ id )
= $true ) ),
inference(forward_demodulation,[],[f430,f342]) ).
thf(f550,plain,
! [X2: term,X1: subst > term > subst > $o] :
( ( ( X1 @ id @ ( sub @ X2 @ ( push @ ( sK9 @ X1 @ X2 ) @ id ) ) @ id )
= $false )
| ( $false
= ( X1 @ id @ ( hoaslam @ id @ ( sK8 @ X1 ) ) @ id ) )
| ( ( X1 @ id @ ( lam @ X2 ) @ id )
= $true ) ),
inference(forward_demodulation,[],[f549,f339]) ).
thf(f551,plain,
! [X2: term,X3: subst,X1: subst > term > subst > $o,X4: term,X5: subst] :
( ( ( sub @ ( sK8 @ X1 @ X5 @ X4 ) @ X3 )
= ( sK8 @ X1 @ ( comp @ X5 @ X3 ) @ ( sub @ X4 @ X3 ) ) )
| ( ( X1 @ id @ ( sK9 @ X1 @ X2 ) @ id )
= $true )
| ( ( X1 @ id @ ( lam @ ( sub @ X2 @ id ) ) @ id )
= $true ) ),
inference(forward_demodulation,[],[f416,f342]) ).
thf(f552,plain,
! [X2: term,X3: subst,X1: subst > term > subst > $o,X4: term,X5: subst] :
( ( ( sub @ ( sK8 @ X1 @ X5 @ X4 ) @ X3 )
= ( sK8 @ X1 @ ( comp @ X5 @ X3 ) @ ( sub @ X4 @ X3 ) ) )
| ( ( X1 @ id @ ( sK9 @ X1 @ X2 ) @ id )
= $true )
| ( ( X1 @ id @ ( lam @ X2 ) @ id )
= $true ) ),
inference(forward_demodulation,[],[f551,f339]) ).
thf(f559,plain,
( ( ( sK0 @ id @ ( lam @ sK7 ) @ id )
= $true )
| ( $false
= ( sK0 @ id @ ( hoaslam @ id @ ( sK8 @ sK0 ) ) @ id ) )
| ( $false
= ( sK0 @ id @ ( sK9 @ sK0 @ sK7 ) @ id ) )
| ( $false = $true ) ),
inference(constrained_superposition,[],[f395,f550]) ).
thf(f578,plain,
( ( ( sK0 @ id @ ( lam @ sK7 ) @ id )
= $true )
| ( $false
= ( sK0 @ id @ ( sK9 @ sK0 @ sK7 ) @ id ) )
| ( $false
= ( sK0 @ id @ ( hoaslam @ id @ ( sK8 @ sK0 ) ) @ id ) ) ),
inference(trivial_inequality_removal,[],[f559]) ).
thf(f580,plain,
( ( $false
= ( sK0 @ id @ ( hoaslam @ id @ ( sK8 @ sK0 ) ) @ id ) )
| ( $false
= ( sK0 @ id @ ( sK9 @ sK0 @ sK7 ) @ id ) )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f578,f391]) ).
thf(f581,plain,
( ( $false
= ( sK0 @ id @ ( hoaslam @ id @ ( sK8 @ sK0 ) ) @ id ) )
| ( $false
= ( sK0 @ id @ ( sK9 @ sK0 @ sK7 ) @ id ) ) ),
inference(trivial_inequality_removal,[],[f580]) ).
thf(f585,definition,
( spl10_1
<=> ( $false
= ( sK0 @ id @ ( hoaslam @ id @ ( sK8 @ sK0 ) ) @ id ) ) ),
introduced(definition,[new_symbols(definition,[spl10_1])],[avatar_definition]) ).
thf(f587,plain,
( ( $false
= ( sK0 @ id @ ( hoaslam @ id @ ( sK8 @ sK0 ) ) @ id ) )
| ~ spl10_1 ),
inference(avatar_component_clause,[],[f585]) ).
thf(f589,definition,
( spl10_2
<=> ( $false
= ( sK0 @ id @ ( sK9 @ sK0 @ sK7 ) @ id ) ) ),
introduced(definition,[new_symbols(definition,[spl10_2])],[avatar_definition]) ).
thf(f591,plain,
( ( $false
= ( sK0 @ id @ ( sK9 @ sK0 @ sK7 ) @ id ) )
| ~ spl10_2 ),
inference(avatar_component_clause,[],[f589]) ).
thf(f592,plain,
( spl10_1
| spl10_2 ),
inference(avatar_split_clause,[],[f581,f589,f585]) ).
thf(f596,plain,
( ! [X0: term] :
( ( ( sK0 @ id @ ( lam @ sK7 ) @ id )
= $true )
| ( $false = $true )
| ( $false
= ( sK0 @ id @ X0 @ id ) )
| ( ( sK0 @ id @ ( sK8 @ sK0 @ id @ X0 ) @ id )
= $true ) )
| ~ spl10_2 ),
inference(constrained_superposition,[],[f499,f591]) ).
thf(f597,plain,
( ( ( sK0 @ id @ ( lam @ sK7 ) @ id )
= $true )
| ( $false = $true )
| ( $false
= ( sK0 @ id @ ( hoaslam @ id @ ( sK8 @ sK0 ) ) @ id ) )
| ~ spl10_2 ),
inference(constrained_superposition,[],[f451,f591]) ).
thf(f598,plain,
( ! [X0: term] :
( ( ( sK0 @ id @ ( sK8 @ sK0 @ id @ X0 ) @ id )
= $true )
| ( ( sK0 @ id @ ( lam @ sK7 ) @ id )
= $true )
| ( $false
= ( sK0 @ id @ X0 @ id ) ) )
| ~ spl10_2 ),
inference(trivial_inequality_removal,[],[f596]) ).
thf(f600,plain,
( ( ( sK0 @ id @ ( lam @ sK7 ) @ id )
= $true )
| ( $false
= ( sK0 @ id @ ( hoaslam @ id @ ( sK8 @ sK0 ) ) @ id ) )
| ~ spl10_2 ),
inference(trivial_inequality_removal,[],[f597]) ).
thf(f602,plain,
( ! [X0: term] :
( ( $false
= ( sK0 @ id @ X0 @ id ) )
| ( ( sK0 @ id @ ( sK8 @ sK0 @ id @ X0 ) @ id )
= $true )
| ( $false = $true ) )
| ~ spl10_2 ),
inference(forward_demodulation,[],[f598,f391]) ).
thf(f603,plain,
( ! [X0: term] :
( ( ( sK0 @ id @ ( sK8 @ sK0 @ id @ X0 ) @ id )
= $true )
| ( $false
= ( sK0 @ id @ X0 @ id ) ) )
| ~ spl10_2 ),
inference(trivial_inequality_removal,[],[f602]) ).
thf(f606,plain,
( ( $false
= ( sK0 @ id @ ( hoaslam @ id @ ( sK8 @ sK0 ) ) @ id ) )
| ( $false = $true )
| ~ spl10_2 ),
inference(forward_demodulation,[],[f600,f391]) ).
thf(f607,plain,
( ( $false
= ( sK0 @ id @ ( hoaslam @ id @ ( sK8 @ sK0 ) ) @ id ) )
| ~ spl10_2 ),
inference(trivial_inequality_removal,[],[f606]) ).
thf(f610,plain,
( spl10_1
| ~ spl10_2 ),
inference(avatar_split_clause,[],[f607,f589,f585]) ).
thf(f618,plain,
( ! [X2: subst,X0: subst,X1: term] :
( ( ( sK0 @ id @ ( lam @ sK7 ) @ id )
= $true )
| ( $false = $true )
| ( ( sK8 @ sK0 @ ( comp @ X0 @ X2 ) @ ( sub @ X1 @ X2 ) )
= ( sub @ ( sK8 @ sK0 @ X0 @ X1 ) @ X2 ) ) )
| ~ spl10_2 ),
inference(constrained_superposition,[],[f591,f552]) ).
thf(f628,plain,
( ! [X2: subst,X0: subst,X1: term] :
( ( ( sK0 @ id @ ( lam @ sK7 ) @ id )
= $true )
| ( ( sK8 @ sK0 @ ( comp @ X0 @ X2 ) @ ( sub @ X1 @ X2 ) )
= ( sub @ ( sK8 @ sK0 @ X0 @ X1 ) @ X2 ) ) )
| ~ spl10_2 ),
inference(trivial_inequality_removal,[],[f618]) ).
thf(f637,plain,
( ! [X2: subst,X0: subst,X1: term] :
( ( $false = $true )
| ( ( sK8 @ sK0 @ ( comp @ X0 @ X2 ) @ ( sub @ X1 @ X2 ) )
= ( sub @ ( sK8 @ sK0 @ X0 @ X1 ) @ X2 ) ) )
| ~ spl10_2 ),
inference(forward_demodulation,[],[f628,f391]) ).
thf(f638,plain,
( ! [X2: subst,X0: subst,X1: term] :
( ( sK8 @ sK0 @ ( comp @ X0 @ X2 ) @ ( sub @ X1 @ X2 ) )
= ( sub @ ( sK8 @ sK0 @ X0 @ X1 ) @ X2 ) )
| ~ spl10_2 ),
inference(trivial_inequality_removal,[],[f637]) ).
thf(f737,plain,
! [X2: term,X3: term,X1: subst > term > subst > $o] :
( ( $false
= ( X1 @ id @ X3 @ id ) )
| ( ( X1 @ id @ ( sK8 @ X1 @ id @ X3 ) @ id )
= $true )
| ( ( X1 @ id @ ( lam @ ( sub @ X2 @ id ) ) @ id )
= $true )
| ( ( X1 @ id @ ( sub @ X2 @ ( push @ ( sK9 @ X1 @ X2 ) @ id ) ) @ id )
= $false ) ),
inference(forward_demodulation,[],[f427,f342]) ).
thf(f738,plain,
! [X2: term,X3: term,X1: subst > term > subst > $o] :
( ( ( X1 @ id @ ( sub @ X2 @ ( push @ ( sK9 @ X1 @ X2 ) @ id ) ) @ id )
= $false )
| ( ( X1 @ id @ ( sK8 @ X1 @ id @ X3 ) @ id )
= $true )
| ( ( X1 @ id @ ( lam @ X2 ) @ id )
= $true )
| ( $false
= ( X1 @ id @ X3 @ id ) ) ),
inference(forward_demodulation,[],[f737,f339]) ).
thf(f749,plain,
! [X0: term] :
( ( $false
= ( sK0 @ id @ ( sK9 @ sK0 @ sK7 ) @ id ) )
| ( ( sK0 @ id @ ( lam @ sK7 ) @ id )
= $true )
| ( ( sK0 @ id @ ( sK8 @ sK0 @ id @ X0 ) @ id )
= $true )
| ( $false
= ( sK0 @ id @ X0 @ id ) )
| ( $false = $true ) ),
inference(constrained_superposition,[],[f738,f395]) ).
thf(f757,plain,
! [X0: term] :
( ( $false
= ( sK0 @ id @ X0 @ id ) )
| ( ( sK0 @ id @ ( lam @ sK7 ) @ id )
= $true )
| ( ( sK0 @ id @ ( sK8 @ sK0 @ id @ X0 ) @ id )
= $true )
| ( $false
= ( sK0 @ id @ ( sK9 @ sK0 @ sK7 ) @ id ) ) ),
inference(trivial_inequality_removal,[],[f749]) ).
thf(f821,plain,
( ( $true
= ( sK0 @ id @ ( hoaslam @ id @ ( sK8 @ sK0 ) ) @ id ) )
| ( ( sub @ ( sK8 @ sK0 @ ( sK4 @ ( sK8 @ sK0 ) ) @ ( sK1 @ ( sK8 @ sK0 ) ) ) @ ( sK3 @ ( sK8 @ sK0 ) ) )
!= ( sub @ ( sK8 @ sK0 @ ( sK4 @ ( sK8 @ sK0 ) ) @ ( sK1 @ ( sK8 @ sK0 ) ) ) @ ( sK3 @ ( sK8 @ sK0 ) ) ) )
| ( ( sK0 @ id @ ( sK2 @ ( sK8 @ sK0 ) ) @ id )
= $true )
| ~ spl10_2 ),
inference(constrained_superposition,[],[f383,f638]) ).
thf(f825,plain,
( ( ( sK0 @ id @ ( sK2 @ ( sK8 @ sK0 ) ) @ id )
= $true )
| ( $true
= ( sK0 @ id @ ( hoaslam @ id @ ( sK8 @ sK0 ) ) @ id ) )
| ~ spl10_2 ),
inference(trivial_inequality_removal,[],[f821]) ).
thf(f847,plain,
( ( ( sK0 @ id @ ( sK2 @ ( sK8 @ sK0 ) ) @ id )
= $true )
| ( $false = $true )
| ~ spl10_1
| ~ spl10_2 ),
inference(forward_demodulation,[],[f825,f587]) ).
thf(f848,plain,
( ( ( sK0 @ id @ ( sK2 @ ( sK8 @ sK0 ) ) @ id )
= $true )
| ~ spl10_1
| ~ spl10_2 ),
inference(trivial_inequality_removal,[],[f847]) ).
thf(f891,plain,
! [X2: term,X3: subst,X1: subst > term > subst > $o,X4: term,X5: subst] :
( ( ( X1 @ id @ ( lam @ ( sub @ X2 @ id ) ) @ id )
= $true )
| ( ( sub @ ( sK8 @ X1 @ X5 @ X4 ) @ X3 )
= ( sK8 @ X1 @ ( comp @ X5 @ X3 ) @ ( sub @ X4 @ X3 ) ) )
| ( ( X1 @ id @ ( sub @ X2 @ ( push @ ( sK9 @ X1 @ X2 ) @ id ) ) @ id )
= $false ) ),
inference(forward_demodulation,[],[f421,f342]) ).
thf(f892,plain,
! [X2: term,X3: subst,X1: subst > term > subst > $o,X4: term,X5: subst] :
( ( ( sub @ ( sK8 @ X1 @ X5 @ X4 ) @ X3 )
= ( sK8 @ X1 @ ( comp @ X5 @ X3 ) @ ( sub @ X4 @ X3 ) ) )
| ( ( X1 @ id @ ( sub @ X2 @ ( push @ ( sK9 @ X1 @ X2 ) @ id ) ) @ id )
= $false )
| ( ( X1 @ id @ ( lam @ X2 ) @ id )
= $true ) ),
inference(forward_demodulation,[],[f891,f339]) ).
thf(f904,plain,
! [X0: subst > term > subst > $o,X1: term] :
( ( ( X0 @ id @ ( lam @ X1 ) @ id )
= $true )
| ( ( sub @ ( sK8 @ X0 @ ( sK4 @ ( sK8 @ X0 ) ) @ ( sK1 @ ( sK8 @ X0 ) ) ) @ ( sK3 @ ( sK8 @ X0 ) ) )
!= ( sub @ ( sK8 @ X0 @ ( sK4 @ ( sK8 @ X0 ) ) @ ( sK1 @ ( sK8 @ X0 ) ) ) @ ( sK3 @ ( sK8 @ X0 ) ) ) )
| ( ( sK0 @ id @ ( hoaslam @ id @ ( sK8 @ X0 ) ) @ id )
= $true )
| ( ( sK0 @ id @ ( sK2 @ ( sK8 @ X0 ) ) @ id )
= $true )
| ( $false
= ( X0 @ id @ ( sub @ X1 @ ( push @ ( sK9 @ X0 @ X1 ) @ id ) ) @ id ) ) ),
inference(constrained_superposition,[],[f383,f892]) ).
thf(f909,plain,
! [X2: subst,X0: subst,X1: term] :
( ( $false = $true )
| ( $false
= ( sK0 @ id @ ( sK9 @ sK0 @ sK7 ) @ id ) )
| ( ( sK8 @ sK0 @ ( comp @ X0 @ X2 ) @ ( sub @ X1 @ X2 ) )
= ( sub @ ( sK8 @ sK0 @ X0 @ X1 ) @ X2 ) )
| ( ( sK0 @ id @ ( lam @ sK7 ) @ id )
= $true ) ),
inference(constrained_superposition,[],[f395,f892]) ).
thf(f911,plain,
! [X0: subst > term > subst > $o,X1: term] :
( ( $false
= ( X0 @ id @ ( sub @ X1 @ ( push @ ( sK9 @ X0 @ X1 ) @ id ) ) @ id ) )
| ( ( sK0 @ id @ ( sK2 @ ( sK8 @ X0 ) ) @ id )
= $true )
| ( ( X0 @ id @ ( lam @ X1 ) @ id )
= $true )
| ( ( sK0 @ id @ ( hoaslam @ id @ ( sK8 @ X0 ) ) @ id )
= $true ) ),
inference(trivial_inequality_removal,[],[f904]) ).
thf(f928,plain,
! [X2: subst,X0: subst,X1: term] :
( ( ( sK8 @ sK0 @ ( comp @ X0 @ X2 ) @ ( sub @ X1 @ X2 ) )
= ( sub @ ( sK8 @ sK0 @ X0 @ X1 ) @ X2 ) )
| ( $false
= ( sK0 @ id @ ( sK9 @ sK0 @ sK7 ) @ id ) )
| ( ( sK0 @ id @ ( lam @ sK7 ) @ id )
= $true ) ),
inference(trivial_inequality_removal,[],[f909]) ).
thf(f998,plain,
( ( ( sK0 @ id @ ( sK2 @ ( sK8 @ sK0 ) ) @ id )
= $true )
| ( $false = $true )
| ( $false
= ( sK0 @ id @ ( sK9 @ sK0 @ sK7 ) @ id ) )
| ( ( sK0 @ id @ ( lam @ sK7 ) @ id )
= $true )
| ( $true
= ( sK0 @ id @ ( hoaslam @ id @ ( sK8 @ sK0 ) ) @ id ) ) ),
inference(constrained_superposition,[],[f911,f395]) ).
thf(f1009,plain,
( ( $true
= ( sK0 @ id @ ( hoaslam @ id @ ( sK8 @ sK0 ) ) @ id ) )
| ( ( sK0 @ id @ ( lam @ sK7 ) @ id )
= $true )
| ( ( sK0 @ id @ ( sK2 @ ( sK8 @ sK0 ) ) @ id )
= $true )
| ( $false
= ( sK0 @ id @ ( sK9 @ sK0 @ sK7 ) @ id ) ) ),
inference(trivial_inequality_removal,[],[f998]) ).
thf(f1021,plain,
( ( $false
= ( sK0 @ id @ ( sK8 @ sK0 @ id @ ( sK2 @ ( sK8 @ sK0 ) ) ) @ id ) )
| ( $true
= ( sK0 @ id @ ( hoaslam @ id @ ( sK8 @ sK0 ) ) @ id ) )
| ( ( sub @ ( sK8 @ sK0 @ ( sK6 @ ( sK8 @ sK0 ) ) @ ( sK1 @ ( sK8 @ sK0 ) ) ) @ ( sK5 @ ( sK8 @ sK0 ) ) )
!= ( sub @ ( sK8 @ sK0 @ ( sK6 @ ( sK8 @ sK0 ) ) @ ( sK1 @ ( sK8 @ sK0 ) ) ) @ ( sK5 @ ( sK8 @ sK0 ) ) ) )
| ~ spl10_2 ),
inference(constrained_superposition,[],[f388,f638]) ).
thf(f1024,plain,
( ( $false
= ( sK0 @ id @ ( sK8 @ sK0 @ id @ ( sK2 @ ( sK8 @ sK0 ) ) ) @ id ) )
| ( $true
= ( sK0 @ id @ ( hoaslam @ id @ ( sK8 @ sK0 ) ) @ id ) )
| ~ spl10_2 ),
inference(trivial_inequality_removal,[],[f1021]) ).
thf(f1030,plain,
( ( $false = $true )
| ( $false
= ( sK0 @ id @ ( sK8 @ sK0 @ id @ ( sK2 @ ( sK8 @ sK0 ) ) ) @ id ) )
| ~ spl10_1
| ~ spl10_2 ),
inference(forward_demodulation,[],[f1024,f587]) ).
thf(f1031,plain,
( ( $false
= ( sK0 @ id @ ( sK8 @ sK0 @ id @ ( sK2 @ ( sK8 @ sK0 ) ) ) @ id ) )
| ~ spl10_1
| ~ spl10_2 ),
inference(trivial_inequality_removal,[],[f1030]) ).
thf(f1042,plain,
( ( $false = $true )
| ( ( sK0 @ id @ ( sK2 @ ( sK8 @ sK0 ) ) @ id )
= $false )
| ~ spl10_1
| ~ spl10_2 ),
inference(constrained_superposition,[],[f1031,f603]) ).
thf(f1048,plain,
( ( ( sK0 @ id @ ( sK2 @ ( sK8 @ sK0 ) ) @ id )
= $false )
| ~ spl10_1
| ~ spl10_2 ),
inference(trivial_inequality_removal,[],[f1042]) ).
thf(f1062,plain,
( ( $false = $true )
| ~ spl10_1
| ~ spl10_2 ),
inference(backward_demodulation,[],[f848,f1048]) ).
thf(f1063,plain,
( $false
| ~ spl10_1
| ~ spl10_2 ),
inference(trivial_inequality_removal,[],[f1062]) ).
thf(f1064,plain,
( ~ spl10_1
| ~ spl10_2 ),
inference(avatar_contradiction_clause,[],[f1063]) ).
thf(f1068,definition,
( spl10_11
<=> ( ( sK0 @ id @ ( sK2 @ ( sK8 @ sK0 ) ) @ id )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl10_11])],[avatar_definition]) ).
thf(f1070,plain,
( ( ( sK0 @ id @ ( sK2 @ ( sK8 @ sK0 ) ) @ id )
= $true )
| ~ spl10_11 ),
inference(avatar_component_clause,[],[f1068]) ).
thf(f1082,plain,
! [X2: subst,X0: subst,X1: term] :
( ( ( sK8 @ sK0 @ ( comp @ X0 @ X2 ) @ ( sub @ X1 @ X2 ) )
= ( sub @ ( sK8 @ sK0 @ X0 @ X1 ) @ X2 ) )
| ( $false = $true )
| ( $false
= ( sK0 @ id @ ( sK9 @ sK0 @ sK7 ) @ id ) ) ),
inference(forward_demodulation,[],[f928,f391]) ).
thf(f1083,plain,
! [X2: subst,X0: subst,X1: term] :
( ( ( sK8 @ sK0 @ ( comp @ X0 @ X2 ) @ ( sub @ X1 @ X2 ) )
= ( sub @ ( sK8 @ sK0 @ X0 @ X1 ) @ X2 ) )
| ( $false
= ( sK0 @ id @ ( sK9 @ sK0 @ sK7 ) @ id ) ) ),
inference(trivial_inequality_removal,[],[f1082]) ).
thf(f1088,plain,
( ( ( sK0 @ id @ ( sK2 @ ( sK8 @ sK0 ) ) @ id )
= $true )
| ( ( sK0 @ id @ ( lam @ sK7 ) @ id )
= $true )
| ( $false
= ( sK0 @ id @ ( sK9 @ sK0 @ sK7 ) @ id ) )
| ( $false = $true )
| ~ spl10_1 ),
inference(forward_demodulation,[],[f1009,f587]) ).
thf(f1089,plain,
( ( ( sK0 @ id @ ( lam @ sK7 ) @ id )
= $true )
| ( $false
= ( sK0 @ id @ ( sK9 @ sK0 @ sK7 ) @ id ) )
| ( ( sK0 @ id @ ( sK2 @ ( sK8 @ sK0 ) ) @ id )
= $true )
| ~ spl10_1 ),
inference(trivial_inequality_removal,[],[f1088]) ).
thf(f1090,plain,
! [X0: term] :
( ( $false
= ( sK0 @ id @ X0 @ id ) )
| ( ( sK0 @ id @ ( sK8 @ sK0 @ id @ X0 ) @ id )
= $true )
| ( $false = $true )
| ( $false
= ( sK0 @ id @ ( sK9 @ sK0 @ sK7 ) @ id ) ) ),
inference(forward_demodulation,[],[f757,f391]) ).
thf(f1091,plain,
! [X0: term] :
( ( $false
= ( sK0 @ id @ ( sK9 @ sK0 @ sK7 ) @ id ) )
| ( ( sK0 @ id @ ( sK8 @ sK0 @ id @ X0 ) @ id )
= $true )
| ( $false
= ( sK0 @ id @ X0 @ id ) ) ),
inference(trivial_inequality_removal,[],[f1090]) ).
thf(f1093,definition,
( spl10_13
<=> ! [X2: subst,X0: subst,X1: term] :
( ( sK8 @ sK0 @ ( comp @ X0 @ X2 ) @ ( sub @ X1 @ X2 ) )
= ( sub @ ( sK8 @ sK0 @ X0 @ X1 ) @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_13])],[avatar_definition]) ).
thf(f1094,plain,
( ! [X2: subst,X0: subst,X1: term] :
( ( sK8 @ sK0 @ ( comp @ X0 @ X2 ) @ ( sub @ X1 @ X2 ) )
= ( sub @ ( sK8 @ sK0 @ X0 @ X1 ) @ X2 ) )
| ~ spl10_13 ),
inference(avatar_component_clause,[],[f1093]) ).
thf(f1097,definition,
( spl10_14
<=> ! [X0: term] :
( ( $false
= ( sK0 @ id @ X0 @ id ) )
| ( ( sK0 @ id @ ( sK8 @ sK0 @ id @ X0 ) @ id )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl10_14])],[avatar_definition]) ).
thf(f1098,plain,
( ! [X0: term] :
( ( ( sK0 @ id @ ( sK8 @ sK0 @ id @ X0 ) @ id )
= $true )
| ( $false
= ( sK0 @ id @ X0 @ id ) ) )
| ~ spl10_14 ),
inference(avatar_component_clause,[],[f1097]) ).
thf(f1104,plain,
( spl10_2
| spl10_13 ),
inference(avatar_split_clause,[],[f1083,f1093,f589]) ).
thf(f1108,plain,
( ( $false = $true )
| ( ( sK0 @ id @ ( sK2 @ ( sK8 @ sK0 ) ) @ id )
= $true )
| ( $false
= ( sK0 @ id @ ( sK9 @ sK0 @ sK7 ) @ id ) )
| ~ spl10_1 ),
inference(forward_demodulation,[],[f1089,f391]) ).
thf(f1109,plain,
( ( $false
= ( sK0 @ id @ ( sK9 @ sK0 @ sK7 ) @ id ) )
| ( ( sK0 @ id @ ( sK2 @ ( sK8 @ sK0 ) ) @ id )
= $true )
| ~ spl10_1 ),
inference(trivial_inequality_removal,[],[f1108]) ).
thf(f1110,plain,
( spl10_14
| spl10_2 ),
inference(avatar_split_clause,[],[f1091,f589,f1097]) ).
thf(f1112,plain,
( spl10_11
| spl10_2
| ~ spl10_1 ),
inference(avatar_split_clause,[],[f1109,f585,f589,f1068]) ).
thf(f1131,plain,
( ( ( sub @ ( sK8 @ sK0 @ ( sK6 @ ( sK8 @ sK0 ) ) @ ( sK1 @ ( sK8 @ sK0 ) ) ) @ ( sK5 @ ( sK8 @ sK0 ) ) )
!= ( sub @ ( sK8 @ sK0 @ ( sK6 @ ( sK8 @ sK0 ) ) @ ( sK1 @ ( sK8 @ sK0 ) ) ) @ ( sK5 @ ( sK8 @ sK0 ) ) ) )
| ( $true
= ( sK0 @ id @ ( hoaslam @ id @ ( sK8 @ sK0 ) ) @ id ) )
| ( $false
= ( sK0 @ id @ ( sK8 @ sK0 @ id @ ( sK2 @ ( sK8 @ sK0 ) ) ) @ id ) )
| ~ spl10_13 ),
inference(constrained_superposition,[],[f388,f1094]) ).
thf(f1135,plain,
( ( $true
= ( sK0 @ id @ ( hoaslam @ id @ ( sK8 @ sK0 ) ) @ id ) )
| ( $false
= ( sK0 @ id @ ( sK8 @ sK0 @ id @ ( sK2 @ ( sK8 @ sK0 ) ) ) @ id ) )
| ~ spl10_13 ),
inference(trivial_inequality_removal,[],[f1131]) ).
thf(f1139,plain,
( ( $false
= ( sK0 @ id @ ( sK8 @ sK0 @ id @ ( sK2 @ ( sK8 @ sK0 ) ) ) @ id ) )
| ( $false = $true )
| ~ spl10_1
| ~ spl10_13 ),
inference(forward_demodulation,[],[f1135,f587]) ).
thf(f1140,plain,
( ( $false
= ( sK0 @ id @ ( sK8 @ sK0 @ id @ ( sK2 @ ( sK8 @ sK0 ) ) ) @ id ) )
| ~ spl10_1
| ~ spl10_13 ),
inference(trivial_inequality_removal,[],[f1139]) ).
thf(f1272,plain,
( ( $false = $true )
| ( ( sK0 @ id @ ( sK2 @ ( sK8 @ sK0 ) ) @ id )
= $false )
| ~ spl10_1
| ~ spl10_13
| ~ spl10_14 ),
inference(constrained_superposition,[],[f1140,f1098]) ).
thf(f1276,plain,
( ( ( sK0 @ id @ ( sK2 @ ( sK8 @ sK0 ) ) @ id )
= $false )
| ~ spl10_1
| ~ spl10_13
| ~ spl10_14 ),
inference(trivial_inequality_removal,[],[f1272]) ).
thf(f1287,plain,
( ( $false = $true )
| ~ spl10_1
| ~ spl10_11
| ~ spl10_13
| ~ spl10_14 ),
inference(backward_demodulation,[],[f1070,f1276]) ).
thf(f1288,plain,
( $false
| ~ spl10_1
| ~ spl10_11
| ~ spl10_13
| ~ spl10_14 ),
inference(trivial_inequality_removal,[],[f1287]) ).
thf(f1289,plain,
( ~ spl10_1
| ~ spl10_11
| ~ spl10_13
| ~ spl10_14 ),
inference(avatar_contradiction_clause,[],[f1288]) ).
cnf(s1,plain,
( spl10_1
| spl10_2 ),
inference(sat_conversion,[],[f592]) ).
cnf(s3,plain,
( spl10_1
| ~ spl10_2 ),
inference(sat_conversion,[],[f610]) ).
cnf(s10,plain,
( ~ spl10_1
| ~ spl10_2 ),
inference(sat_conversion,[],[f1064]) ).
cnf(s20,plain,
( spl10_2
| spl10_13 ),
inference(sat_conversion,[],[f1104]) ).
cnf(s22,plain,
( spl10_2
| spl10_14 ),
inference(sat_conversion,[],[f1110]) ).
cnf(s24,plain,
( ~ spl10_1
| spl10_2
| spl10_11 ),
inference(sat_conversion,[],[f1112]) ).
cnf(s35,plain,
( ~ spl10_1
| ~ spl10_11
| ~ spl10_13
| ~ spl10_14 ),
inference(sat_conversion,[],[f1289]) ).
cnf(s36,plain,
spl10_1,
inference(rat,[],[s1,s3]) ).
cnf(s37,plain,
~ spl10_2,
inference(rat,[],[s10,s36]) ).
cnf(s38,plain,
spl10_11,
inference(rat,[],[s24,s36,s37]) ).
cnf(s39,plain,
spl10_14,
inference(rat,[],[s22,s37]) ).
cnf(s41,plain,
spl10_13,
inference(rat,[],[s20,s37]) ).
cnf(s42,plain,
$false,
inference(rat,[],[s35,s39,s36,s41,s38]) ).
thf(f1290,plain,
$false,
inference(avatar_sat_refutation,[],[s42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG268^2 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 % Computer : n019.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 17:35:03 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 Running higher-order theorem proving
% 0.21/0.27 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.60/0.38 % (1127796)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.60/0.38 % (1127801)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2548468113:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.60/0.38 % (1127807)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.60/0.38 % (1127807)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
% 0.60/0.38 % (1127802)lrs+10_16_si=on:nwc=1.5:random_seed=1528072845:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.60/0.38 % (1127805)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2538017484:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.60/0.38 % (1127804)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=496020617: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)
% 0.60/0.38 % (1127803)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3131420853:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.60/0.38 % (1127806)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2423741329:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.60/0.38 % (1127807)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=2623100838:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.60/0.38 % (1127803)Instruction limit reached!
% 0.60/0.38 % (1127803)------------------------------
% 0.60/0.38 % (1127803)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.60/0.38 % (1127803)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.60/0.38 % (1127803)CaDiCaL version: 2.1.3
% 0.60/0.38 % (1127803)Termination reason: Instruction limit
% 0.60/0.38 % (1127803)Termination phase: shuffling
% 0.60/0.38 % (1127803)Time elapsed: 0.002 s
% 0.60/0.38 % (1127803)Peak memory usage: 10 MB
% 0.60/0.38 % (1127803)Instructions burned: 3 (million)
% 0.60/0.38 % (1127802)Instruction limit reached!
% 0.60/0.38 % (1127802)------------------------------
% 0.60/0.38 % (1127802)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.60/0.38 % (1127802)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.60/0.38 % (1127802)CaDiCaL version: 2.1.3
% 0.60/0.38 % (1127802)Termination reason: Instruction limit
% 0.60/0.38 % (1127802)Termination phase: shuffling
% 0.60/0.38 % (1127802)Time elapsed: 0.008 s
% 0.60/0.38 % (1127802)Peak memory usage: 10 MB
% 0.60/0.38 % (1127802)Instructions burned: 19 (million)
% 0.60/0.38 % (1127805)Instruction limit reached!
% 0.60/0.38 % (1127805)------------------------------
% 0.60/0.38 % (1127805)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.60/0.38 % (1127805)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.60/0.38 % (1127805)CaDiCaL version: 2.1.3
% 0.60/0.38 % (1127805)Termination reason: Instruction limit
% 0.60/0.38 % (1127805)Termination phase: Naming
% 0.60/0.38 % (1127805)Time elapsed: 0.011 s
% 0.60/0.38 % (1127805)Peak memory usage: 11 MB
% 0.60/0.38 % (1127805)Instructions burned: 25 (million)
% 0.60/0.38 % (1127801)Instruction limit reached!
% 0.60/0.38 % (1127801)------------------------------
% 0.60/0.38 % (1127801)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.60/0.38 % (1127801)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.60/0.38 % (1127801)CaDiCaL version: 2.1.3
% 0.60/0.38 % (1127801)Termination reason: Instruction limit
% 0.60/0.38 % (1127801)Termination phase: Function definition elimination
% 0.60/0.38 % (1127801)Time elapsed: 0.021 s
% 0.60/0.38 % (1127801)Peak memory usage: 12 MB
% 0.60/0.38 % (1127801)Instructions burned: 88 (million)
% 0.60/0.38 % (1127815)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3056736181:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.60/0.38 % (1127818)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=7887370:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.60/0.41 % (1127815)Instruction limit reached!
% 0.60/0.41 % (1127815)------------------------------
% 0.60/0.41 % (1127815)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.60/0.41 % (1127815)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.60/0.41 % (1127815)CaDiCaL version: 2.1.3
% 0.60/0.41 % (1127815)Termination reason: Instruction limit
% 0.60/0.41 % (1127815)Termination phase: shuffling
% 0.60/0.41 % (1127815)Time elapsed: 0.002 s
% 0.60/0.41 % (1127815)Peak memory usage: 10 MB
% 0.60/0.41 % (1127815)Instructions burned: 3 (million)
% 0.60/0.41 % (1127817)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.60/0.41 % (1127818)Instruction limit reached!
% 0.60/0.41 % (1127818)------------------------------
% 0.60/0.41 % (1127818)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.60/0.41 % (1127818)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.60/0.41 % (1127818)CaDiCaL version: 2.1.3
% 0.60/0.41 % (1127818)Termination reason: Instruction limit
% 0.60/0.41 % (1127818)Termination phase: shuffling
% 0.60/0.41 % (1127818)Time elapsed: 0.003 s
% 0.60/0.41 % (1127818)Peak memory usage: 10 MB
% 0.60/0.41 % (1127818)Instructions burned: 14 (million)
% 0.60/0.41 % (1127816)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2416938232:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.60/0.41 % (1127817)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2509895731:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.60/0.41 % (1127816)Instruction limit reached!
% 0.60/0.41 % (1127816)------------------------------
% 0.60/0.41 % (1127816)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.60/0.41 % (1127816)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.60/0.41 % (1127816)CaDiCaL version: 2.1.3
% 0.60/0.41 % (1127816)Termination reason: Instruction limit
% 0.60/0.41 % (1127816)Termination phase: shuffling
% 0.60/0.41 % (1127816)Time elapsed: 0.003 s
% 0.60/0.41 % (1127816)Peak memory usage: 10 MB
% 0.60/0.41 % (1127816)Instructions burned: 6 (million)
% 0.60/0.41 % (1127817)Instruction limit reached!
% 0.60/0.41 % (1127817)------------------------------
% 0.60/0.41 % (1127817)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.60/0.41 % (1127817)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.60/0.41 % (1127817)CaDiCaL version: 2.1.3
% 0.60/0.41 % (1127817)Termination reason: Instruction limit
% 0.60/0.41 % (1127817)Termination phase: shuffling
% 0.60/0.41 % (1127817)Time elapsed: 0.004 s
% 0.60/0.41 % (1127817)Peak memory usage: 10 MB
% 0.60/0.41 % (1127817)Instructions burned: 8 (million)
% 0.60/0.41 % (1127806)Instruction limit reached!
% 0.60/0.41 % (1127806)------------------------------
% 0.60/0.41 % (1127806)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.60/0.41 % (1127806)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.60/0.41 % (1127806)CaDiCaL version: 2.1.3
% 0.60/0.41 % (1127806)Termination reason: Instruction limit
% 0.60/0.41 % (1127806)Termination phase: Property scanning
% 0.60/0.41 % (1127806)Time elapsed: 0.035 s
% 0.60/0.41 % (1127806)Peak memory usage: 12 MB
% 0.60/0.41 % (1127806)Instructions burned: 77 (million)
% 0.60/0.41 % (1127822)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=1611429790:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.60/0.41 % (1127821)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
% 0.60/0.41 % (1127821)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.60/0.41 % (1127821)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1231808040:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.60/0.41 % (1127826)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.60/0.44 % (1127825)lrs+10_1_si=on:cs=on:random_seed=648876414:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.60/0.44 % (1127826)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=840704946:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.60/0.44 % (1127827)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=16229343:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.60/0.44 % (1127825)Instruction limit reached!
% 0.60/0.44 % (1127825)------------------------------
% 0.60/0.44 % (1127825)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.60/0.44 % (1127825)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.60/0.44 % (1127825)CaDiCaL version: 2.1.3
% 0.60/0.44 % (1127825)Termination reason: Instruction limit
% 0.60/0.44 % (1127825)Termination phase: shuffling
% 0.60/0.44 % (1127825)Time elapsed: 0.004 s
% 0.60/0.44 % (1127825)Peak memory usage: 10 MB
% 0.60/0.44 % (1127825)Instructions burned: 9 (million)
% 0.60/0.44 % (1127822)Instruction limit reached!
% 0.60/0.44 % (1127822)------------------------------
% 0.60/0.44 % (1127822)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.60/0.44 % (1127822)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.60/0.44 % (1127822)CaDiCaL version: 2.1.3
% 0.60/0.44 % (1127822)Termination reason: Instruction limit
% 0.60/0.44 % (1127822)Termination phase: Saturation
% 0.60/0.44 % (1127822)Time elapsed: 0.018 s
% 0.60/0.44 % (1127822)Peak memory usage: 11 MB
% 0.60/0.44 % (1127822)Instructions burned: 86 (million)
% 0.60/0.44 % (1127826)Instruction limit reached!
% 0.60/0.44 % (1127826)------------------------------
% 0.60/0.44 % (1127826)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.60/0.44 % (1127826)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.60/0.44 % (1127826)CaDiCaL version: 2.1.3
% 0.60/0.44 % (1127826)Termination reason: Instruction limit
% 0.60/0.44 % (1127826)Termination phase: shuffling
% 0.60/0.44 % (1127826)Time elapsed: 0.002 s
% 0.60/0.44 % (1127826)Peak memory usage: 10 MB
% 0.60/0.44 % (1127826)Instructions burned: 4 (million)
% 0.60/0.44 % (1127821)Instruction limit reached!
% 0.60/0.44 % (1127821)------------------------------
% 0.60/0.44 % (1127821)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.60/0.44 % (1127821)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.60/0.44 % (1127821)CaDiCaL version: 2.1.3
% 0.60/0.44 % (1127821)Termination reason: Instruction limit
% 0.60/0.44 % (1127821)Termination phase: Property scanning
% 0.60/0.44 % (1127821)Time elapsed: 0.013 s
% 0.60/0.44 % (1127821)Peak memory usage: 10 MB
% 0.60/0.44 % (1127821)Instructions burned: 30 (million)
% 0.60/0.44 % (1127834)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2788513777:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/25Mi)
% 0.60/0.44 % (1127807)Instruction limit reached!
% 0.60/0.44 % (1127807)------------------------------
% 0.60/0.44 % (1127807)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.60/0.44 % (1127807)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.60/0.44 % (1127807)CaDiCaL version: 2.1.3
% 0.60/0.44 % (1127807)Termination reason: Instruction limit
% 0.60/0.44 % (1127807)Termination phase: Saturation
% 0.60/0.44 % (1127807)Time elapsed: 0.067 s
% 0.60/0.44 % (1127807)Peak memory usage: 13 MB
% 0.60/0.44 % (1127807)Instructions burned: 159 (million)
% 0.60/0.44 % (1127834)Instruction limit reached!
% 0.60/0.44 % (1127834)------------------------------
% 0.60/0.44 % (1127834)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.60/0.44 % (1127834)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.60/0.44 % (1127834)CaDiCaL version: 2.1.3
% 0.60/0.44 % (1127834)Termination reason: Instruction limit
% 0.60/0.44 % (1127834)Termination phase: Preprocessing 2
% 0.60/0.44 % (1127834)Time elapsed: 0.006 s
% 0.60/0.44 % (1127834)Peak memory usage: 10 MB
% 0.60/0.44 % (1127834)Instructions burned: 26 (million)
% 0.60/0.44 % (1127827)Instruction limit reached!
% 0.60/0.44 % (1127827)------------------------------
% 0.60/0.44 % (1127827)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.60/0.44 % (1127827)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.33/0.48 % (1127827)CaDiCaL version: 2.1.3
% 1.33/0.48 % (1127827)Termination reason: Instruction limit
% 1.33/0.48 % (1127827)Termination phase: Property scanning
% 1.33/0.48 % (1127827)Time elapsed: 0.018 s
% 1.33/0.48 % (1127827)Peak memory usage: 12 MB
% 1.33/0.48 % (1127827)Instructions burned: 40 (million)
% 1.33/0.48 % (1127833)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=159684582:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 1.33/0.48 % (1127835)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=2476052390:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2999 on theBenchmark for (2999ds/14Mi)
% 1.33/0.48 % (1127836)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=924575664:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/327Mi)
% 1.33/0.48 % (1127835)Instruction limit reached!
% 1.33/0.48 % (1127835)------------------------------
% 1.33/0.48 % (1127835)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.33/0.48 % (1127835)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.33/0.48 % (1127835)CaDiCaL version: 2.1.3
% 1.33/0.48 % (1127835)Termination reason: Instruction limit
% 1.33/0.48 % (1127835)Termination phase: shuffling
% 1.33/0.48 % (1127835)Time elapsed: 0.007 s
% 1.33/0.48 % (1127835)Peak memory usage: 10 MB
% 1.33/0.48 % (1127835)Instructions burned: 15 (million)
% 1.33/0.48 % (1127845)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=222429831:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.33/0.48 % (1127842)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=637196023:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/14Mi)
% 1.33/0.48 % (1127845)Instruction limit reached!
% 1.33/0.48 % (1127845)------------------------------
% 1.33/0.48 % (1127845)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.33/0.48 % (1127845)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.33/0.48 % (1127845)CaDiCaL version: 2.1.3
% 1.33/0.48 % (1127845)Termination reason: Instruction limit
% 1.33/0.48 % (1127845)Termination phase: Property scanning
% 1.33/0.48 % (1127845)Time elapsed: 0.007 s
% 1.33/0.48 % (1127845)Peak memory usage: 10 MB
% 1.33/0.48 % (1127845)Instructions burned: 30 (million)
% 1.33/0.48 % (1127844)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=1988176713: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)
% 1.33/0.48 % (1127842)Instruction limit reached!
% 1.33/0.48 % (1127842)------------------------------
% 1.33/0.48 % (1127842)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.33/0.48 % (1127842)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.33/0.48 % (1127842)CaDiCaL version: 2.1.3
% 1.33/0.48 % (1127842)Termination reason: Instruction limit
% 1.33/0.48 % (1127842)Termination phase: shuffling
% 1.33/0.48 % (1127842)Time elapsed: 0.007 s
% 1.33/0.48 % (1127842)Peak memory usage: 10 MB
% 1.33/0.48 % (1127842)Instructions burned: 15 (million)
% 1.33/0.48 % (1127844)Instruction limit reached!
% 1.33/0.48 % (1127844)------------------------------
% 1.33/0.48 % (1127844)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.33/0.48 % (1127844)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.33/0.48 % (1127844)CaDiCaL version: 2.1.3
% 1.33/0.48 % (1127844)Termination reason: Instruction limit
% 1.33/0.48 % (1127844)Termination phase: shuffling
% 1.33/0.48 % (1127844)Time elapsed: 0.002 s
% 1.33/0.48 % (1127844)Peak memory usage: 10 MB
% 1.33/0.48 % (1127844)Instructions burned: 4 (million)
% 1.33/0.48 % (1127833)Refutation not found, incomplete strategy
% 1.33/0.48 % (1127833)------------------------------
% 1.33/0.48 % (1127833)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.33/0.48 % (1127833)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.33/0.48 % (1127833)CaDiCaL version: 2.1.3
% 1.33/0.48 % (1127833)Termination reason: Refutation not found, incomplete strategy
% 1.33/0.48 % (1127833)Time elapsed: 0.021 s
% 1.33/0.48 % (1127833)Peak memory usage: 12 MB
% 1.33/0.48 % (1127833)Instructions burned: 50 (million)
% 1.33/0.48 % (1127833)------------------------------
% 1.33/0.48 % (1127833)------------------------------
% 1.33/0.48 % (1127849)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=3866954463:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.33/0.54 % (1127855)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=2071418862:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.33/0.54 % (1127857)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
% 1.33/0.54 % (1127857)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 1.33/0.54 % (1127858)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.33/0.54 % (1127849)Instruction limit reached!
% 1.33/0.54 % (1127849)------------------------------
% 1.33/0.54 % (1127849)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.33/0.54 % (1127849)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.33/0.54 % (1127849)CaDiCaL version: 2.1.3
% 1.33/0.54 % (1127849)Termination reason: Instruction limit
% 1.33/0.54 % (1127849)Termination phase: Property scanning
% 1.33/0.54 % (1127849)Time elapsed: 0.011 s
% 1.33/0.54 % (1127849)Peak memory usage: 10 MB
% 1.33/0.54 % (1127849)Instructions burned: 24 (million)
% 1.33/0.54 % (1127857)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=4016799865:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.33/0.54 % (1127858)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=3336413813:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.33/0.54 % (1127860)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=792704394:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 1.33/0.54 % (1127855)Instruction limit reached!
% 1.33/0.54 % (1127855)------------------------------
% 1.33/0.54 % (1127855)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.33/0.54 % (1127855)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.33/0.54 % (1127855)CaDiCaL version: 2.1.3
% 1.33/0.54 % (1127855)Termination reason: Instruction limit
% 1.33/0.54 % (1127855)Termination phase: Property scanning
% 1.33/0.54 % (1127855)Time elapsed: 0.015 s
% 1.33/0.54 % (1127855)Peak memory usage: 12 MB
% 1.33/0.54 % (1127855)Instructions burned: 61 (million)
% 1.33/0.54 % (1127858)Instruction limit reached!
% 1.33/0.54 % (1127858)------------------------------
% 1.33/0.54 % (1127858)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.33/0.54 % (1127858)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.33/0.54 % (1127858)CaDiCaL version: 2.1.3
% 1.33/0.54 % (1127858)Termination reason: Instruction limit
% 1.33/0.54 % (1127858)Termination phase: shuffling
% 1.33/0.54 % (1127858)Time elapsed: 0.004 s
% 1.33/0.54 % (1127858)Peak memory usage: 10 MB
% 1.33/0.54 % (1127858)Instructions burned: 9 (million)
% 1.33/0.54 % (1127857)Instruction limit reached!
% 1.33/0.54 % (1127857)------------------------------
% 1.33/0.54 % (1127857)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.33/0.54 % (1127857)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.33/0.54 % (1127857)CaDiCaL version: 2.1.3
% 1.33/0.54 % (1127857)Termination reason: Instruction limit
% 1.33/0.54 % (1127857)Termination phase: shuffling
% 1.33/0.54 % (1127857)Time elapsed: 0.008 s
% 1.33/0.54 % (1127857)Peak memory usage: 10 MB
% 1.33/0.54 % (1127857)Instructions burned: 19 (million)
% 1.33/0.54 % (1127879)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=2089241903:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.33/0.54 % (1127860)Instruction limit reached!
% 1.33/0.54 % (1127860)------------------------------
% 1.33/0.54 % (1127860)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.33/0.54 % (1127860)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.33/0.54 % (1127860)CaDiCaL version: 2.1.3
% 1.33/0.54 % (1127860)Termination reason: Instruction limit
% 2.03/0.58 % (1127860)Termination phase: Property scanning
% 2.03/0.58 % (1127860)Time elapsed: 0.013 s
% 2.03/0.58 % (1127860)Peak memory usage: 10 MB
% 2.03/0.58 % (1127860)Instructions burned: 31 (million)
% 2.03/0.58 % (1127872)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=173069671:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 2.03/0.58 % (1127879)Instruction limit reached!
% 2.03/0.58 % (1127879)------------------------------
% 2.03/0.58 % (1127879)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.03/0.58 % (1127879)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.03/0.58 % (1127879)CaDiCaL version: 2.1.3
% 2.03/0.58 % (1127879)Termination reason: Instruction limit
% 2.03/0.58 % (1127879)Termination phase: Property scanning
% 2.03/0.58 % (1127879)Time elapsed: 0.006 s
% 2.03/0.58 % (1127879)Peak memory usage: 10 MB
% 2.03/0.58 % (1127879)Instructions burned: 27 (million)
% 2.03/0.58 % (1127872)Instruction limit reached!
% 2.03/0.58 % (1127872)------------------------------
% 2.03/0.58 % (1127872)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.03/0.58 % (1127872)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.03/0.58 % (1127872)CaDiCaL version: 2.1.3
% 2.03/0.58 % (1127872)Termination reason: Instruction limit
% 2.03/0.58 % (1127872)Termination phase: shuffling
% 2.03/0.58 % (1127872)Time elapsed: 0.004 s
% 2.03/0.58 % (1127872)Peak memory usage: 10 MB
% 2.03/0.58 % (1127872)Instructions burned: 8 (million)
% 2.03/0.58 % (1127881)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=2026000:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/20Mi)
% 2.03/0.58 % (1127886)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=2787162985:i=1240:rtra=on:ixr=off_2998 on theBenchmark for (2998ds/1240Mi)
% 2.03/0.58 % (1127896)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=635409207:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/193Mi)
% 2.03/0.58 % (1127881)Instruction limit reached!
% 2.03/0.58 % (1127881)------------------------------
% 2.03/0.58 % (1127881)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.03/0.58 % (1127881)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.03/0.58 % (1127881)CaDiCaL version: 2.1.3
% 2.03/0.58 % (1127881)Termination reason: Instruction limit
% 2.03/0.58 % (1127881)Termination phase: Property scanning
% 2.03/0.58 % (1127881)Time elapsed: 0.010 s
% 2.03/0.58 % (1127881)Peak memory usage: 10 MB
% 2.03/0.58 % (1127881)Instructions burned: 22 (million)
% 2.03/0.58 % (1127893)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=1793893851:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/143Mi)
% 2.03/0.58 % (1127898)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1504300316:i=42:hud=10:rtra=on_2998 on theBenchmark for (2998ds/42Mi)
% 2.03/0.58 % (1127896)Refutation not found, incomplete strategy
% 2.03/0.58 % (1127896)------------------------------
% 2.03/0.58 % (1127896)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.03/0.58 % (1127896)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.03/0.58 % (1127896)CaDiCaL version: 2.1.3
% 2.03/0.58 % (1127896)Termination reason: Refutation not found, incomplete strategy
% 2.03/0.58 % (1127896)Time elapsed: 0.014 s
% 2.03/0.58 % (1127896)Peak memory usage: 13 MB
% 2.03/0.58 % (1127896)Instructions burned: 60 (million)
% 2.03/0.58 % (1127896)------------------------------
% 2.03/0.58 % (1127896)------------------------------
% 2.03/0.58 % (1127911)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 2.03/0.58 % (1127911)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3613757665:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2998 on theBenchmark for (2998ds/7Mi)
% 2.03/0.58 % (1127911)Instruction limit reached!
% 2.03/0.58 % (1127911)------------------------------
% 2.03/0.58 % (1127911)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.03/0.58 % (1127911)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.03/0.58 % (1127911)CaDiCaL version: 2.1.3
% 2.03/0.58 % (1127911)Termination reason: Instruction limit
% 2.03/0.58 % (1127911)Termination phase: shuffling
% 2.03/0.58 % (1127911)Time elapsed: 0.004 s
% 2.03/0.58 % (1127911)Peak memory usage: 10 MB
% 2.03/0.58 % (1127911)Instructions burned: 9 (million)
% 2.03/0.58 % (1127898)Instruction limit reached!
% 2.03/0.58 % (1127898)------------------------------
% 2.03/0.58 % (1127898)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.03/0.58 % (1127898)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.03/0.58 % (1127898)CaDiCaL version: 2.1.3
% 2.03/0.58 % (1127898)Termination reason: Instruction limit
% 2.03/0.58 % (1127898)Termination phase: Property scanning
% 2.03/0.58 % (1127898)Time elapsed: 0.018 s
% 2.03/0.58 % (1127898)Peak memory usage: 11 MB
% 2.03/0.58 % (1127898)Instructions burned: 43 (million)
% 2.03/0.58 % (1127915)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=1185781543:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/181Mi)
% 2.03/0.58 % (1127921)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 2.03/0.58 % (1127920)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=2852244961: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)
% 2.03/0.58 % (1127921)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=970789085:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2997 on theBenchmark for (2997ds/6Mi)
% 2.03/0.58 % (1127921)Instruction limit reached!
% 2.03/0.58 % (1127921)------------------------------
% 2.03/0.58 % (1127921)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.03/0.58 % (1127921)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.03/0.58 % (1127921)CaDiCaL version: 2.1.3
% 2.03/0.58 % (1127921)Termination reason: Instruction limit
% 2.03/0.58 % (1127921)Termination phase: shuffling
% 2.03/0.58 % (1127921)Time elapsed: 0.003 s
% 2.03/0.58 % (1127921)Peak memory usage: 10 MB
% 2.03/0.58 % (1127921)Instructions burned: 6 (million)
% 2.03/0.58 % (1127893)Instruction limit reached!
% 2.03/0.58 % (1127893)------------------------------
% 2.03/0.58 % (1127893)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.03/0.58 % (1127893)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.03/0.58 % (1127893)CaDiCaL version: 2.1.3
% 2.03/0.58 % (1127893)Termination reason: Instruction limit
% 2.03/0.58 % (1127893)Termination phase: Saturation
% 2.03/0.58 % (1127893)Time elapsed: 0.060 s
% 2.03/0.58 % (1127893)Peak memory usage: 13 MB
% 2.03/0.58 % (1127893)Instructions burned: 144 (million)
% 2.03/0.58 % (1127926)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=3305167200:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2997 on theBenchmark for (2997ds/22Mi)
% 2.03/0.58 % (1127926)Instruction limit reached!
% 2.03/0.58 % (1127926)------------------------------
% 2.03/0.58 % (1127926)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.03/0.58 % (1127926)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.03/0.58 % (1127926)CaDiCaL version: 2.1.3
% 2.03/0.58 % (1127926)Termination reason: Instruction limit
% 2.03/0.58 % (1127926)Termination phase: Property scanning
% 2.03/0.58 % (1127926)Time elapsed: 0.010 s
% 2.03/0.58 % (1127926)Peak memory usage: 10 MB
% 2.03/0.58 % (1127926)Instructions burned: 24 (million)
% 2.03/0.58 % (1127927)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=189084838:i=19:add=on:rtra=on_2997 on theBenchmark for (2997ds/19Mi)
% 2.03/0.58 % (1127836)Instruction limit reached!
% 2.03/0.58 % (1127836)------------------------------
% 2.03/0.58 % (1127836)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.03/0.58 % (1127836)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.03/0.58 % (1127836)CaDiCaL version: 2.1.3
% 2.03/0.58 % (1127836)Termination reason: Instruction limit
% 2.03/0.58 % (1127836)Termination phase: Saturation
% 2.03/0.58 % (1127836)Time elapsed: 0.156 s
% 2.03/0.58 % (1127836)Peak memory usage: 15 MB
% 2.03/0.58 % (1127836)Instructions burned: 328 (million)
% 2.03/0.58 % (1127929)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=1164175116:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/316Mi)
% 2.03/0.58 % (1127927)Instruction limit reached!
% 2.03/0.58 % (1127927)------------------------------
% 2.03/0.58 % (1127927)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.03/0.58 % (1127927)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.03/0.58 % (1127927)CaDiCaL version: 2.1.3
% 2.03/0.58 % (1127927)Termination reason: Instruction limit
% 2.03/0.58 % (1127927)Termination phase: shuffling
% 2.03/0.58 % (1127927)Time elapsed: 0.009 s
% 2.03/0.58 % (1127927)Peak memory usage: 10 MB
% 2.03/0.58 % (1127927)Instructions burned: 19 (million)
% 2.03/0.58 % (1127931)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=735197817: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)
% 2.03/0.58 % (1127933)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=1201162358: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)
% 2.03/0.58 % (1127920) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1127796-1127920"...
% 2.03/0.58 % (1127915)Instruction limit reached!
% 2.03/0.58 % (1127915)------------------------------
% 2.03/0.58 % (1127915)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.03/0.58 % (1127915)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.03/0.58 % (1127915)CaDiCaL version: 2.1.3
% 2.03/0.58 % (1127915)Termination reason: Instruction limit
% 2.03/0.58 % (1127915)Termination phase: Saturation
% 2.03/0.58 % (1127915)Time elapsed: 0.088 s
% 2.03/0.58 % (1127915)Peak memory usage: 14 MB
% 2.03/0.58 % (1127915)Instructions burned: 182 (million)
% 2.03/0.58 % (1127920)...printing done.
% 2.03/0.58 % (1127920)Refutation found. Thanks to Tanya!
% 2.03/0.58 % SZS status Theorem for theBenchmark
% 2.03/0.58 % SZS output start Proof for theBenchmark
% See solution above
% 2.03/0.59 % (1127920)------------------------------
% 2.03/0.59 % (1127920)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.03/0.59 % (1127920)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.03/0.59 % (1127920)CaDiCaL version: 2.1.3
% 2.03/0.59 % (1127920)Termination reason: Refutation
% 2.03/0.59 % (1127920)Time elapsed: 0.078 s
% 2.03/0.59 % (1127920)Peak memory usage: 14 MB
% 2.03/0.59 % (1127920)Instructions burned: 159 (million)
% 2.03/0.59 % (1127796)Success in time 0.302 s
% 2.03/0.59 % Vampire exiting
%------------------------------------------------------------------------------