%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN741^7 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 08:41:44 AM UTC 2026
% Result : ContradictoryAxioms 10.72s 2.00s
% Output : Refutation 10.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 81
% Number of leaves : 18
% Syntax : Number of formulae : 447 ( 106 unt; 0 typ; 0 def)
% Number of atoms : 7210 (1790 equ; 0 cnn)
% Maximal formula atoms : 16 ( 16 avg)
% Number of connectives : 9321 (1062 ~;2128 |; 0 &;5557 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 164 ( 164 >; 0 *; 0 +; 0 <<)
% Number of symbols : 59 ( 55 usr; 3 con; 0-4 aty)
% ( 574 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 1810 ( 890 ^; 920 !; 0 ?;1810 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mu: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
qmltpeq: mu > mu > $i > $o ).
thf(func_def_1,type,
meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_3,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_4,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_5,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_7,type,
mtrue: $i > $o ).
thf(func_def_8,type,
mfalse: $i > $o ).
thf(func_def_9,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_11,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_12,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_13,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_14,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_15,type,
exists_in_world: mu > $i > $o ).
thf(func_def_16,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_17,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_18,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_19,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(func_def_20,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(func_def_21,type,
mserial: ( $i > $i > $o ) > $o ).
thf(func_def_22,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(func_def_23,type,
meuclidean: ( $i > $i > $o ) > $o ).
thf(func_def_24,type,
mpartially_functional: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
mfunctional: ( $i > $i > $o ) > $o ).
thf(func_def_26,type,
mweakly_dense: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
mweakly_connected: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
mweakly_directed: ( $i > $i > $o ) > $o ).
thf(func_def_29,type,
mvalid: ( $i > $o ) > $o ).
thf(func_def_30,type,
msatisfiable: ( $i > $o ) > $o ).
thf(func_def_31,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_32,type,
minvalid: ( $i > $o ) > $o ).
thf(func_def_33,type,
rel_s4: $i > $i > $o ).
thf(func_def_34,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf(func_def_35,type,
mdia_s4: ( $i > $o ) > $i > $o ).
thf(func_def_36,type,
v1: $i > $o ).
thf(func_def_37,type,
v3: $i > $o ).
thf(func_def_38,type,
v2: $i > $o ).
thf(func_def_39,type,
v4: $i > $o ).
thf(func_def_40,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_41,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_42,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_45,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_46,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_47,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_48,type,
vIMP: $o > $o > $o ).
thf(func_def_49,type,
vAND: $o > $o > $o ).
thf(func_def_50,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_51,type,
vOR: $o > $o > $o ).
thf(func_def_52,type,
vNOT: $o > $o ).
thf(func_def_53,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_54,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_56,type,
sK1: $i > mu ).
thf(func_def_57,type,
sK2: $i > $i ).
thf(f2,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mnot) ).
thf(f3,axiom,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mor) ).
thf(f6,axiom,
( mtrue
= ( ^ [X0: $i] : $true ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mtrue) ).
thf(f18,axiom,
( mreflexive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mreflexive) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mvalid) ).
thf(f32,axiom,
( mbox_s4
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_s4 @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^5.ax',mbox_s4) ).
thf(f33,axiom,
( mdia_s4
= ( ^ [X0: $i > $o] : ( mnot @ ( mbox_s4 @ ( mnot @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^5.ax',mdia_s4) ).
thf(f34,axiom,
mreflexive @ rel_s4,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^5.ax',a1) ).
thf(f41,axiom,
mvalid @ ( mor @ v1 @ ( mor @ ( mbox_s4 @ v1 ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ v4 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',persat5) ).
thf(f42,axiom,
mvalid @ ( mor @ v1 @ ( mor @ ( mbox_s4 @ ( mnot @ v2 ) ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ v2 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',persat6) ).
thf(f45,axiom,
mvalid @ ( mor @ v2 @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox_s4 @ ( mnot @ v3 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',persat9) ).
thf(f46,axiom,
mvalid @ ( mor @ v2 @ ( mor @ ( mnot @ v4 ) @ ( mor @ ( mbox_s4 @ ( mnot @ v4 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v4 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',persat10) ).
thf(f51,axiom,
mvalid @ ( mor @ v3 @ ( mor @ ( mnot @ v2 ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v2 ) ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v4 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',persat15) ).
thf(f52,axiom,
mvalid @ ( mor @ v3 @ ( mor @ ( mbox_s4 @ v4 ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ v2 ) ) @ ( mbox_s4 @ ( mbox_s4 @ v3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',persat16) ).
thf(f57,axiom,
mvalid @ ( mor @ v4 @ ( mor @ ( mnot @ v2 ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ v3 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',persat21) ).
thf(f61,axiom,
mvalid @ ( mor @ ( mnot @ v1 ) @ ( mor @ ( mbox_s4 @ ( mnot @ v1 ) ) @ ( mor @ ( mbox_s4 @ ( mnot @ v3 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',persat25) ).
thf(f62,axiom,
mvalid @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox_s4 @ ( mnot @ v2 ) ) @ ( mor @ ( mbox_s4 @ ( mnot @ v4 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',persat26) ).
thf(f67,axiom,
mvalid @ ( mdia_s4 @ mtrue ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',deontic1) ).
thf(f74,plain,
( mreflexive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
inference(rectify,[],[f18]) ).
thf(f75,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f74]) ).
thf(f76,plain,
mvalid @ ( mdia_s4 @ mtrue ),
inference(rectify,[],[f67]) ).
thf(f77,plain,
( ( mvalid @ ( mdia_s4 @ mtrue ) )
= $true ),
inference(fool_elimination,[],[f76]) ).
thf(f83,plain,
mvalid @ ( mor @ v3 @ ( mor @ ( mnot @ v2 ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v2 ) ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v4 ) ) ) ) ) ),
inference(rectify,[],[f51]) ).
thf(f84,plain,
( ( mvalid @ ( mor @ v3 @ ( mor @ ( mnot @ v2 ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v2 ) ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v4 ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f83]) ).
thf(f87,plain,
mvalid @ ( mor @ v1 @ ( mor @ ( mbox_s4 @ v1 ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ v4 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v2 ) ) ) ) ) ),
inference(rectify,[],[f41]) ).
thf(f88,plain,
( ( mvalid @ ( mor @ v1 @ ( mor @ ( mbox_s4 @ v1 ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ v4 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v2 ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f87]) ).
thf(f99,plain,
mvalid @ ( mor @ v3 @ ( mor @ ( mbox_s4 @ v4 ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ v2 ) ) @ ( mbox_s4 @ ( mbox_s4 @ v3 ) ) ) ) ),
inference(rectify,[],[f52]) ).
thf(f100,plain,
( ( mvalid @ ( mor @ v3 @ ( mor @ ( mbox_s4 @ v4 ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ v2 ) ) @ ( mbox_s4 @ ( mbox_s4 @ v3 ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f99]) ).
thf(f112,plain,
( mbox_s4
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_s4 @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f32]) ).
thf(f113,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f112]) ).
thf(f125,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f2]) ).
thf(f126,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f125]) ).
thf(f134,plain,
mvalid @ ( mor @ v4 @ ( mor @ ( mnot @ v2 ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ v3 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v1 ) ) ) ) ) ),
inference(rectify,[],[f57]) ).
thf(f135,plain,
( ( mvalid @ ( mor @ v4 @ ( mor @ ( mnot @ v2 ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ v3 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v1 ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f134]) ).
thf(f136,plain,
mvalid @ ( mor @ v2 @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox_s4 @ ( mnot @ v3 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v3 ) ) ) ) ) ),
inference(rectify,[],[f45]) ).
thf(f137,plain,
( ( mvalid @ ( mor @ v2 @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox_s4 @ ( mnot @ v3 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v3 ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f136]) ).
thf(f144,plain,
mvalid @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox_s4 @ ( mnot @ v2 ) ) @ ( mor @ ( mbox_s4 @ ( mnot @ v4 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v3 ) ) ) ) ) ),
inference(rectify,[],[f62]) ).
thf(f145,plain,
( ( mvalid @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox_s4 @ ( mnot @ v2 ) ) @ ( mor @ ( mbox_s4 @ ( mnot @ v4 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v3 ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f144]) ).
thf(f149,plain,
mvalid @ ( mor @ v2 @ ( mor @ ( mnot @ v4 ) @ ( mor @ ( mbox_s4 @ ( mnot @ v4 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v4 ) ) ) ) ) ),
inference(rectify,[],[f46]) ).
thf(f150,plain,
( ( mvalid @ ( mor @ v2 @ ( mor @ ( mnot @ v4 ) @ ( mor @ ( mbox_s4 @ ( mnot @ v4 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v4 ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f149]) ).
thf(f151,plain,
mvalid @ ( mor @ v1 @ ( mor @ ( mbox_s4 @ ( mnot @ v2 ) ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ v2 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v2 ) ) ) ) ) ),
inference(rectify,[],[f42]) ).
thf(f152,plain,
( ( mvalid @ ( mor @ v1 @ ( mor @ ( mbox_s4 @ ( mnot @ v2 ) ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ v2 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v2 ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f151]) ).
thf(f166,plain,
( mdia_s4
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s4 @ ( mnot @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f33]) ).
thf(f171,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f172,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f171]) ).
thf(f173,plain,
( mtrue
= ( ^ [Y0: $i] : $true ) ),
inference(fool_elimination,[],[f6]) ).
thf(f174,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f175,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f174]) ).
thf(f186,plain,
mreflexive @ rel_s4,
inference(rectify,[],[f34]) ).
thf(f187,plain,
( ( mreflexive @ rel_s4 )
= $true ),
inference(fool_elimination,[],[f186]) ).
thf(f194,plain,
mvalid @ ( mor @ ( mnot @ v1 ) @ ( mor @ ( mbox_s4 @ ( mnot @ v1 ) ) @ ( mor @ ( mbox_s4 @ ( mnot @ v3 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v1 ) ) ) ) ) ),
inference(rectify,[],[f61]) ).
thf(f195,plain,
( ( mvalid @ ( mor @ ( mnot @ v1 ) @ ( mor @ ( mbox_s4 @ ( mnot @ v1 ) ) @ ( mor @ ( mbox_s4 @ ( mnot @ v3 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v1 ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f194]) ).
thf(f201,plain,
( ( mvalid @ ( mor @ v1 @ ( mor @ ( mbox_s4 @ ( mnot @ v2 ) ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ v2 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v2 ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f152]) ).
thf(f203,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f113]) ).
thf(f206,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f175]) ).
thf(f210,plain,
( ( mvalid @ ( mor @ v2 @ ( mor @ ( mnot @ v4 ) @ ( mor @ ( mbox_s4 @ ( mnot @ v4 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v4 ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f150]) ).
thf(f215,plain,
( ( mvalid @ ( mor @ ( mnot @ v1 ) @ ( mor @ ( mbox_s4 @ ( mnot @ v1 ) ) @ ( mor @ ( mbox_s4 @ ( mnot @ v3 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v1 ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f195]) ).
thf(f216,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f75]) ).
thf(f218,plain,
( ( mvalid @ ( mor @ v4 @ ( mor @ ( mnot @ v2 ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ v3 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v1 ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f135]) ).
thf(f221,plain,
( ( mvalid @ ( mdia_s4 @ mtrue ) )
= $true ),
inference(cnf_transformation,[],[f77]) ).
thf(f225,plain,
( mdia_s4
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s4 @ ( mnot @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f166]) ).
thf(f227,plain,
( ( mvalid @ ( mor @ v1 @ ( mor @ ( mbox_s4 @ v1 ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ v4 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v2 ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f88]) ).
thf(f229,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f172]) ).
thf(f231,plain,
( ( mvalid @ ( mor @ v3 @ ( mor @ ( mnot @ v2 ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v2 ) ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v4 ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f84]) ).
thf(f234,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f126]) ).
thf(f235,plain,
( ( mreflexive @ rel_s4 )
= $true ),
inference(cnf_transformation,[],[f187]) ).
thf(f241,plain,
( ( mvalid @ ( mor @ v2 @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox_s4 @ ( mnot @ v3 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v3 ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f137]) ).
thf(f243,plain,
( mtrue
= ( ^ [Y0: $i] : $true ) ),
inference(cnf_transformation,[],[f173]) ).
thf(f258,plain,
( ( mvalid @ ( mor @ v3 @ ( mor @ ( mbox_s4 @ v4 ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ v2 ) ) @ ( mbox_s4 @ ( mbox_s4 @ v3 ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f100]) ).
thf(f262,plain,
( ( mvalid @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox_s4 @ ( mnot @ v2 ) ) @ ( mor @ ( mbox_s4 @ ( mnot @ v4 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v3 ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f145]) ).
thf(f275,plain,
( mdia_s4
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s4 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f225,f234,f203,f234]) ).
thf(f278,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ v1
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ v2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ v2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ v2 ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f201,f229,f206,f206,f203,f234,f206,f203,f203,f203,f203,f234]) ).
thf(f283,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ v2
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ v4 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ v4 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ v4 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f210,f229,f206,f206,f234,f206,f203,f234,f203,f203,f234]) ).
thf(f284,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ v1 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ v1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ v3 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ v1 ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f215,f229,f206,f234,f206,f203,f234,f206,f203,f234,f203,f203,f234]) ).
thf(f285,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ v4
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ v2 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ v3 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ v1 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f218,f229,f206,f206,f234,f206,f203,f203,f203,f203,f234]) ).
thf(f287,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s4 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ ^ [Y0: $i] : $true ) ) ),
inference(definition_unfolding,[],[f221,f229,f275,f243]) ).
thf(f290,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ v1
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ v1 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ v4 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ v2 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f227,f229,f206,f206,f203,f206,f203,f203,f203,f203,f234]) ).
thf(f292,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ v3
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ v2 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ v2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ v4 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f231,f229,f206,f206,f234,f206,f203,f203,f234,f203,f203,f234]) ).
thf(f293,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ rel_s4 ) ),
inference(definition_unfolding,[],[f235,f216]) ).
thf(f298,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ v2
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ v3 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ v3 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ v3 ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f241,f229,f206,f206,f234,f206,f203,f234,f203,f203,f234]) ).
thf(f305,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ v3
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ v4 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ v2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ v3 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f258,f229,f206,f206,f203,f206,f203,f203,f203,f203]) ).
thf(f309,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ v3 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ v2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ v4 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ v3 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f262,f229,f206,f234,f206,f203,f234,f206,f203,f234,f203,f203,f234]) ).
thf(f310,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( v3 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( v2 @ Y2 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( v3 @ Y2 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f305]) ).
thf(f311,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( v4 @ Y0 )
| ~ ( v2 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( v3 @ Y2 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ~ ( v1 @ Y2 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f285]) ).
thf(f312,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( v2 @ Y0 )
| ~ ( v4 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ~ ( v4 @ Y2 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f283]) ).
thf(f315,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( v1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( v4 @ Y2 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ~ ( v2 @ Y2 ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f290]) ).
thf(f317,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( v1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ~ ( v1 @ Y2 ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f284]) ).
thf(f318,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( v3 @ Y0 )
| ~ ( v2 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ~ ( v2 @ Y2 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ~ ( v4 @ Y2 ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f292]) ).
thf(f324,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ $true ) ) ) ),
inference(beta-eta_normalization,[],[f287]) ).
thf(f325,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| $false ) ) )
= $true ),
inference(boolean_simplification,[],[f324]) ).
thf(f326,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
~ ( !! @ $i
@ ^ [Y1: $i] :
~ ( rel_s4 @ Y0 @ Y1 ) ) )
= $true ),
inference(boolean_simplification,[],[f325]) ).
thf(f336,plain,
( ( !! @ $i
@ ^ [Y0: $i] : ( rel_s4 @ Y0 @ Y0 ) )
= $true ),
inference(beta-eta_normalization,[],[f293]) ).
thf(f337,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( v3 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ~ ( v3 @ Y2 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f309]) ).
thf(f338,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( v1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( v2 @ Y2 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ~ ( v2 @ Y2 ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f278]) ).
thf(f342,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( v2 @ Y0 )
| ~ ( v3 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ~ ( v3 @ Y2 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f298]) ).
thf(f359,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] : ( rel_s4 @ Y0 @ Y0 )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f336]) ).
thf(f360,plain,
! [X1: $i] :
( ( rel_s4 @ X1 @ X1 )
= $true ),
inference(beta-eta_normalization,[],[f359]) ).
thf(f365,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
~ ( !! @ $i
@ ^ [Y1: $i] :
~ ( rel_s4 @ Y0 @ Y1 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f326]) ).
thf(f366,plain,
! [X1: $i] :
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
~ ( rel_s4 @ X1 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f365]) ).
thf(f367,plain,
! [X1: $i] :
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
~ ( rel_s4 @ X1 @ Y0 ) ) ),
inference(not_proxy_clausification,[],[f366]) ).
thf(f368,plain,
! [X1: $i] :
( $false
= ( ^ [Y0: $i] :
~ ( rel_s4 @ X1 @ Y0 )
@ ( sK2 @ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f367]) ).
thf(f371,plain,
! [X1: $i] :
( $false
= ( ~ ( rel_s4 @ X1 @ ( sK2 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f368]) ).
thf(f372,plain,
! [X1: $i] :
( ( rel_s4 @ X1 @ ( sK2 @ X1 ) )
= $true ),
inference(not_proxy_clausification,[],[f371]) ).
thf(f658,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( v2 @ Y0 )
| ~ ( v4 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ~ ( v4 @ Y2 ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f312]) ).
thf(f659,plain,
! [X1: $i] :
( $true
= ( ( v2 @ X1 )
| ~ ( v4 @ X1 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v4 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v4 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f658]) ).
thf(f660,plain,
! [X1: $i] :
( ( ( ~ ( v4 @ X1 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v4 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v4 @ Y1 ) ) ) ) ) )
= $true )
| ( ( v2 @ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f659]) ).
thf(f661,plain,
! [X1: $i] :
( ( ( v2 @ X1 )
= $true )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v4 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v4 @ Y1 ) ) ) ) ) ) )
| ( ( ~ ( v4 @ X1 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f660]) ).
thf(f662,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v4 @ Y0 ) ) )
= $true )
| ( ( ~ ( v4 @ X1 ) )
= $true )
| ( ( v2 @ X1 )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v4 @ Y1 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f661]) ).
thf(f663,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v4 @ Y1 ) ) ) ) ) )
| ( $false
= ( v4 @ X1 ) )
| ( ( v2 @ X1 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v4 @ Y0 ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f662]) ).
thf(f664,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v4 @ Y0 ) ) )
= $true )
| ( ( v2 @ X1 )
= $true )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v4 @ Y1 ) ) ) )
@ X2 ) )
| ( $false
= ( v4 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f663]) ).
thf(f665,plain,
! [X2: $i,X1: $i] :
( ( ( v2 @ X1 )
= $true )
| ( $false
= ( v4 @ X1 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v4 @ Y0 ) ) )
= $true )
| ( ( ~ ( rel_s4 @ X1 @ X2 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v4 @ Y0 ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f664]) ).
thf(f666,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( v4 @ X1 ) )
| ( ( v2 @ X1 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v4 @ Y0 ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v4 @ Y0 ) ) )
= $true )
| ( ( ~ ( rel_s4 @ X1 @ X2 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f665]) ).
thf(f667,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v4 @ Y0 ) ) )
= $true )
| ( $false
= ( v4 @ X1 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( v2 @ X1 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v4 @ Y0 ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f666]) ).
thf(f668,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v4 @ Y0 ) )
@ X3 )
= $true )
| ( $false
= ( v4 @ X1 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v4 @ Y0 ) ) )
= $true )
| ( ( v2 @ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f667]) ).
thf(f669,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( v2 @ X1 )
= $true )
| ( ( ~ ( rel_s4 @ X2 @ X3 )
| ~ ( v4 @ X3 ) )
= $true )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v4 @ Y0 ) ) )
= $true )
| ( $false
= ( v4 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f668]) ).
thf(f670,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( v2 @ X1 )
= $true )
| ( $true
= ( ~ ( rel_s4 @ X2 @ X3 ) ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( v4 @ X1 ) )
| ( $true
= ( ~ ( v4 @ X3 ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v4 @ Y0 ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f669]) ).
thf(f671,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v4 @ Y0 ) ) )
= $true )
| ( ( rel_s4 @ X2 @ X3 )
= $false )
| ( $true
= ( ~ ( v4 @ X3 ) ) )
| ( $false
= ( v4 @ X1 ) )
| ( ( v2 @ X1 )
= $true )
| ( ( rel_s4 @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f670]) ).
thf(f672,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v4 @ Y0 ) ) )
= $true )
| ( ( rel_s4 @ X2 @ X3 )
= $false )
| ( $false
= ( v4 @ X1 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( v4 @ X3 ) )
| ( ( v2 @ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f671]) ).
thf(f673,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( v2 @ X1 )
= $true )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v4 @ Y0 ) )
@ X4 ) )
| ( ( rel_s4 @ X2 @ X3 )
= $false )
| ( $false
= ( v4 @ X3 ) )
| ( $false
= ( v4 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f672]) ).
thf(f674,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ~ ( rel_s4 @ X1 @ X4 )
| ~ ( v4 @ X4 ) )
= $true )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( v4 @ X1 ) )
| ( ( rel_s4 @ X2 @ X3 )
= $false )
| ( ( v2 @ X1 )
= $true )
| ( $false
= ( v4 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f673]) ).
thf(f675,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( v4 @ X3 ) )
| ( $false
= ( v4 @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X4 ) ) )
| ( ( v2 @ X1 )
= $true )
| ( ( rel_s4 @ X2 @ X3 )
= $false )
| ( ( ~ ( v4 @ X4 ) )
= $true )
| ( ( rel_s4 @ X1 @ X2 )
= $false ) ),
inference(or_proxy_clausification,[],[f674]) ).
thf(f676,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( rel_s4 @ X1 @ X4 ) )
| ( ( rel_s4 @ X2 @ X3 )
= $false )
| ( ( ~ ( v4 @ X4 ) )
= $true )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( v4 @ X1 ) )
| ( $false
= ( v4 @ X3 ) )
| ( ( v2 @ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f675]) ).
thf(f677,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( rel_s4 @ X1 @ X4 ) )
| ( $false
= ( v4 @ X3 ) )
| ( $false
= ( v4 @ X1 ) )
| ( ( rel_s4 @ X2 @ X3 )
= $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( v2 @ X1 )
= $true )
| ( $false
= ( v4 @ X4 ) ) ),
inference(not_proxy_clausification,[],[f676]) ).
thf(f699,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( v4 @ X0 ) )
| ( $false != $false )
| ( $false
= ( rel_s4 @ X0 @ X0 ) )
| ( $false
= ( v4 @ X1 ) )
| ( $false
= ( v4 @ X1 ) )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $true
= ( v2 @ X0 ) ) ),
inference(equality_factoring,[],[f677]) ).
thf(f708,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ X0 @ X0 ) )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $false != $false )
| ( $false
= ( v4 @ X0 ) )
| ( $true
= ( v2 @ X0 ) )
| ( $false
= ( v4 @ X1 ) ) ),
inference(duplicate_literal_removal,[],[f699]) ).
thf(f709,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( v4 @ X1 ) )
| ( $false
= ( rel_s4 @ X0 @ X0 ) )
| ( $false
= ( v4 @ X0 ) )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $true
= ( v2 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f708]) ).
thf(f713,plain,
! [X0: $i,X1: $i] :
( ( $false = $true )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $true
= ( v2 @ X0 ) )
| ( $false
= ( v4 @ X1 ) )
| ( $false
= ( v4 @ X0 ) ) ),
inference(forward_demodulation,[],[f709,f360]) ).
thf(f714,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $true
= ( v2 @ X0 ) )
| ( $false
= ( v4 @ X1 ) )
| ( $false
= ( v4 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f713]) ).
thf(f760,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( v2 @ Y0 )
| ~ ( v3 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ~ ( v3 @ Y2 ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f342]) ).
thf(f761,plain,
! [X1: $i] :
( ( ( v2 @ X1 )
| ~ ( v3 @ X1 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v3 @ Y1 ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f760]) ).
thf(f762,plain,
! [X1: $i] :
( ( ( v2 @ X1 )
= $true )
| ( ( ~ ( v3 @ X1 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v3 @ Y1 ) ) ) ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f761]) ).
thf(f763,plain,
! [X1: $i] :
( ( $true
= ( ~ ( v3 @ X1 ) ) )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v3 @ Y1 ) ) ) ) ) )
= $true )
| ( ( v2 @ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f762]) ).
thf(f764,plain,
! [X1: $i] :
( ( ( v3 @ X1 )
= $false )
| ( ( v2 @ X1 )
= $true )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v3 @ Y1 ) ) ) ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f763]) ).
thf(f765,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v3 @ Y1 ) ) ) ) ) )
| ( ( v2 @ X1 )
= $true )
| ( ( v3 @ X1 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v3 @ Y0 ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f764]) ).
thf(f766,plain,
! [X2: $i,X1: $i] :
( ( ( v2 @ X1 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v3 @ Y0 ) ) )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v3 @ Y1 ) ) ) )
@ X2 )
= $true )
| ( ( v3 @ X1 )
= $false ) ),
inference(pi_proxy_clausification,[],[f765]) ).
thf(f767,plain,
! [X2: $i,X1: $i] :
( ( ( v2 @ X1 )
= $true )
| ( ( v3 @ X1 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v3 @ Y0 ) ) )
= $true )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X2 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v3 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f766]) ).
thf(f768,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( rel_s4 @ X1 @ X2 ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v3 @ Y0 ) ) )
= $true )
| ( ( v2 @ X1 )
= $true )
| ( ( v3 @ X1 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v3 @ Y0 ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f767]) ).
thf(f769,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v3 @ Y0 ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v3 @ Y0 ) ) )
= $true )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( v3 @ X1 )
= $false )
| ( ( v2 @ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f768]) ).
thf(f770,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v3 @ Y0 ) )
@ X3 )
= $true )
| ( ( v2 @ X1 )
= $true )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v3 @ Y0 ) ) )
= $true )
| ( ( v3 @ X1 )
= $false ) ),
inference(pi_proxy_clausification,[],[f769]) ).
thf(f771,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ~ ( rel_s4 @ X2 @ X3 )
| ~ ( v3 @ X3 ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v3 @ Y0 ) ) )
= $true )
| ( ( v3 @ X1 )
= $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( v2 @ X1 )
= $true ) ),
inference(beta-eta_normalization,[],[f770]) ).
thf(f772,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( v2 @ X1 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v3 @ Y0 ) ) )
= $true )
| ( ( v3 @ X1 )
= $false )
| ( ( ~ ( v3 @ X3 ) )
= $true )
| ( $true
= ( ~ ( rel_s4 @ X2 @ X3 ) ) ) ),
inference(or_proxy_clausification,[],[f771]) ).
thf(f773,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( v2 @ X1 )
= $true )
| ( ( v3 @ X1 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v3 @ Y0 ) ) )
= $true )
| ( $false
= ( v3 @ X3 ) )
| ( $true
= ( ~ ( rel_s4 @ X2 @ X3 ) ) ) ),
inference(not_proxy_clausification,[],[f772]) ).
thf(f774,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v3 @ Y0 ) ) )
= $true )
| ( ( v2 @ X1 )
= $true )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( rel_s4 @ X2 @ X3 )
= $false )
| ( ( v3 @ X1 )
= $false )
| ( $false
= ( v3 @ X3 ) ) ),
inference(not_proxy_clausification,[],[f773]) ).
thf(f775,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( v2 @ X1 )
= $true )
| ( ( rel_s4 @ X2 @ X3 )
= $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v3 @ Y0 ) )
@ X4 ) )
| ( ( v3 @ X1 )
= $false )
| ( $false
= ( v3 @ X3 ) ) ),
inference(pi_proxy_clausification,[],[f774]) ).
thf(f776,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( v3 @ X3 ) )
| ( ( v3 @ X1 )
= $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( rel_s4 @ X2 @ X3 )
= $false )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X4 )
| ~ ( v3 @ X4 ) ) )
| ( ( v2 @ X1 )
= $true ) ),
inference(beta-eta_normalization,[],[f775]) ).
thf(f777,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ~ ( rel_s4 @ X1 @ X4 ) ) )
| ( ( rel_s4 @ X2 @ X3 )
= $false )
| ( ( v2 @ X1 )
= $true )
| ( $false
= ( v3 @ X3 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( v3 @ X1 )
= $false )
| ( ( ~ ( v3 @ X4 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f776]) ).
thf(f778,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( v2 @ X1 )
= $true )
| ( ( v3 @ X1 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X4 ) )
| ( ( ~ ( v3 @ X4 ) )
= $true )
| ( $false
= ( v3 @ X3 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( rel_s4 @ X2 @ X3 )
= $false ) ),
inference(not_proxy_clausification,[],[f777]) ).
thf(f779,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( rel_s4 @ X1 @ X4 ) )
| ( ( v3 @ X4 )
= $false )
| ( ( v2 @ X1 )
= $true )
| ( ( v3 @ X1 )
= $false )
| ( ( rel_s4 @ X2 @ X3 )
= $false )
| ( $false
= ( v3 @ X3 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f778]) ).
thf(f780,plain,
! [X0: $i] :
( ( $false = $true )
| ( $true
= ( v2 @ X0 ) )
| ( $false
= ( v4 @ X0 ) )
| ( $false
= ( v4 @ X0 ) ) ),
inference(superposition,[],[f714,f360]) ).
thf(f792,plain,
! [X0: $i] :
( ( $false = $true )
| ( $false
= ( v4 @ X0 ) )
| ( $true
= ( v2 @ X0 ) ) ),
inference(duplicate_literal_removal,[],[f780]) ).
thf(f793,plain,
! [X0: $i] :
( ( $true
= ( v2 @ X0 ) )
| ( $false
= ( v4 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f792]) ).
thf(f803,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( v2 @ X0 ) )
| ( ( v3 @ X0 )
= $false )
| ( ( v3 @ X1 )
= $false )
| ( $false != $false )
| ( $false
= ( rel_s4 @ X0 @ X0 ) )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( ( v3 @ X1 )
= $false ) ),
inference(equality_factoring,[],[f779]) ).
thf(f812,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $true
= ( v2 @ X0 ) )
| ( ( v3 @ X0 )
= $false )
| ( $false
= ( rel_s4 @ X0 @ X0 ) )
| ( ( v3 @ X1 )
= $false )
| ( $false != $false ) ),
inference(duplicate_literal_removal,[],[f803]) ).
thf(f813,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( ( v3 @ X0 )
= $false )
| ( $true
= ( v2 @ X0 ) )
| ( $false
= ( rel_s4 @ X0 @ X0 ) )
| ( ( v3 @ X1 )
= $false ) ),
inference(trivial_inequality_removal,[],[f812]) ).
thf(f817,plain,
! [X0: $i,X1: $i] :
( ( ( v3 @ X0 )
= $false )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $false = $true )
| ( ( v3 @ X1 )
= $false )
| ( $true
= ( v2 @ X0 ) ) ),
inference(forward_demodulation,[],[f813,f360]) ).
thf(f818,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $true
= ( v2 @ X0 ) )
| ( ( v3 @ X0 )
= $false )
| ( ( v3 @ X1 )
= $false ) ),
inference(trivial_inequality_removal,[],[f817]) ).
thf(f819,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( v4 @ Y0 )
| ~ ( v2 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( v3 @ Y2 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ~ ( v1 @ Y2 ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f311]) ).
thf(f820,plain,
! [X1: $i] :
( $true
= ( ( v4 @ X1 )
| ~ ( v2 @ X1 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v3 @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v1 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f819]) ).
thf(f821,plain,
! [X1: $i] :
( ( $true
= ( ~ ( v2 @ X1 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v3 @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v1 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( v4 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f820]) ).
thf(f822,plain,
! [X1: $i] :
( ( ( ~ ( v2 @ X1 ) )
= $true )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v3 @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v1 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( v4 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f821]) ).
thf(f823,plain,
! [X1: $i] :
( ( ( v2 @ X1 )
= $false )
| ( $true
= ( v4 @ X1 ) )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v3 @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v1 @ Y1 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f822]) ).
thf(f824,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v1 @ Y1 ) ) ) ) ) )
| ( ( v2 @ X1 )
= $false )
| ( $true
= ( v4 @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v3 @ Y1 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f823]) ).
thf(f825,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v1 @ Y1 ) ) ) )
@ X2 ) )
| ( $true
= ( v4 @ X1 ) )
| ( ( v2 @ X1 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v3 @ Y1 ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f824]) ).
thf(f826,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s4 @ X1 @ X2 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v1 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v3 @ Y1 ) ) ) ) ) )
| ( ( v2 @ X1 )
= $false )
| ( $true
= ( v4 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f825]) ).
thf(f827,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v1 @ Y0 ) ) )
= $true )
| ( ( ~ ( rel_s4 @ X1 @ X2 ) )
= $true )
| ( $true
= ( v4 @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v3 @ Y1 ) ) ) ) ) )
| ( ( v2 @ X1 )
= $false ) ),
inference(or_proxy_clausification,[],[f826]) ).
thf(f828,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v3 @ Y1 ) ) ) ) ) )
| ( $true
= ( v4 @ X1 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( v2 @ X1 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v1 @ Y0 ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f827]) ).
thf(f829,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v3 @ Y1 ) ) ) )
@ X3 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v1 @ Y0 ) ) )
= $true )
| ( $true
= ( v4 @ X1 ) )
| ( ( v2 @ X1 )
= $false ) ),
inference(pi_proxy_clausification,[],[f828]) ).
thf(f830,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( v4 @ X1 ) )
| ( ( v2 @ X1 )
= $false )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X3 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X3 @ Y0 )
| ( v3 @ Y0 ) ) ) ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v1 @ Y0 ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f829]) ).
thf(f831,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( v2 @ X1 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X3 @ Y0 )
| ( v3 @ Y0 ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v1 @ Y0 ) ) )
= $true )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $true
= ( v4 @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X3 ) ) ) ),
inference(or_proxy_clausification,[],[f830]) ).
thf(f832,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v1 @ Y0 ) ) )
= $true )
| ( $true
= ( v4 @ X1 ) )
| ( ( v2 @ X1 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X3 @ Y0 )
| ( v3 @ Y0 ) ) )
= $true )
| ( ( rel_s4 @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f831]) ).
thf(f833,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X3 @ Y0 )
| ( v3 @ Y0 ) ) )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v1 @ Y0 ) )
@ X4 )
= $true )
| ( $true
= ( v4 @ X1 ) )
| ( ( v2 @ X1 )
= $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f832]) ).
thf(f834,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( v2 @ X1 )
= $false )
| ( $true
= ( ~ ( rel_s4 @ X2 @ X4 )
| ~ ( v1 @ X4 ) ) )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X3 @ Y0 )
| ( v3 @ Y0 ) ) )
= $true )
| ( $true
= ( v4 @ X1 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f833]) ).
thf(f835,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( v4 @ X1 ) )
| ( ( ~ ( rel_s4 @ X2 @ X4 ) )
= $true )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X3 @ Y0 )
| ( v3 @ Y0 ) ) )
= $true )
| ( ( v2 @ X1 )
= $false )
| ( $true
= ( ~ ( v1 @ X4 ) ) ) ),
inference(or_proxy_clausification,[],[f834]) ).
thf(f836,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X3 @ Y0 )
| ( v3 @ Y0 ) ) )
= $true )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( $true
= ( v4 @ X1 ) )
| ( $true
= ( ~ ( v1 @ X4 ) ) )
| ( $false
= ( rel_s4 @ X2 @ X4 ) )
| ( ( v2 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f835]) ).
thf(f837,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X3 @ Y0 )
| ( v3 @ Y0 ) ) )
= $true )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $true
= ( v4 @ X1 ) )
| ( ( v2 @ X1 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( $false
= ( v1 @ X4 ) )
| ( $false
= ( rel_s4 @ X2 @ X4 ) ) ),
inference(not_proxy_clausification,[],[f836]) ).
thf(f838,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X3 @ Y0 )
| ( v3 @ Y0 ) )
@ X5 ) )
| ( ( v2 @ X1 )
= $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X2 @ X4 ) )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( $false
= ( v1 @ X4 ) )
| ( $true
= ( v4 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f837]) ).
thf(f839,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( ~ ( rel_s4 @ X3 @ X5 )
| ( v3 @ X5 ) ) )
| ( $true
= ( v4 @ X1 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X2 @ X4 ) )
| ( ( v2 @ X1 )
= $false )
| ( $false
= ( v1 @ X4 ) )
| ( $false
= ( rel_s4 @ X1 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f838]) ).
thf(f840,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( v3 @ X5 ) )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( $true
= ( v4 @ X1 ) )
| ( $false
= ( v1 @ X4 ) )
| ( ( v2 @ X1 )
= $false )
| ( $false
= ( rel_s4 @ X2 @ X4 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( ~ ( rel_s4 @ X3 @ X5 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f839]) ).
thf(f841,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( rel_s4 @ X2 @ X4 ) )
| ( $false
= ( v1 @ X4 ) )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( $true
= ( v4 @ X1 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $true
= ( v3 @ X5 ) )
| ( ( rel_s4 @ X3 @ X5 )
= $false )
| ( ( v2 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f840]) ).
thf(f851,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( v4 @ X2 ) )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( ( v3 @ X1 )
= $true )
| ( ( v2 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X2 @ X0 ) )
| ( ( v1 @ X1 )
= $false )
| ( $false
= ( rel_s4 @ X2 @ X0 ) )
| ( $false != $false ) ),
inference(equality_factoring,[],[f841]) ).
thf(f857,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( v2 @ X2 )
= $false )
| ( ( v1 @ X1 )
= $false )
| ( $false != $false )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( ( v3 @ X1 )
= $true )
| ( $false
= ( rel_s4 @ X2 @ X0 ) )
| ( $true
= ( v4 @ X2 ) ) ),
inference(duplicate_literal_removal,[],[f851]) ).
thf(f858,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ X2 @ X0 ) )
| ( $true
= ( v4 @ X2 ) )
| ( ( v3 @ X1 )
= $true )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( ( v2 @ X2 )
= $false )
| ( ( v1 @ X1 )
= $false ) ),
inference(trivial_inequality_removal,[],[f857]) ).
thf(f984,plain,
! [X0: $i] :
( ( ( v3 @ X0 )
= $false )
| ( ( v3 @ X0 )
= $false )
| ( $true
= ( v2 @ X0 ) )
| ( $false = $true ) ),
inference(superposition,[],[f360,f818]) ).
thf(f987,plain,
! [X0: $i] :
( ( ( v3 @ X0 )
= $false )
| ( $true
= ( v2 @ X0 ) )
| ( $false = $true ) ),
inference(duplicate_literal_removal,[],[f984]) ).
thf(f988,plain,
! [X0: $i] :
( ( $true
= ( v2 @ X0 ) )
| ( ( v3 @ X0 )
= $false ) ),
inference(trivial_inequality_removal,[],[f987]) ).
thf(f1207,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( v3 @ Y0 )
| ~ ( v2 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ~ ( v2 @ Y2 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ~ ( v4 @ Y2 ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f318]) ).
thf(f1208,plain,
! [X1: $i] :
( $true
= ( ( v3 @ X1 )
| ~ ( v2 @ X1 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v2 @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v4 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1207]) ).
thf(f1209,plain,
! [X1: $i] :
( ( ( ~ ( v2 @ X1 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v2 @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v4 @ Y1 ) ) ) ) ) )
= $true )
| ( ( v3 @ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f1208]) ).
thf(f1210,plain,
! [X1: $i] :
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v2 @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v4 @ Y1 ) ) ) ) ) )
= $true )
| ( ( ~ ( v2 @ X1 ) )
= $true )
| ( ( v3 @ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f1209]) ).
thf(f1211,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v4 @ Y1 ) ) ) ) ) )
| ( ( v3 @ X1 )
= $true )
| ( ( ~ ( v2 @ X1 ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v2 @ Y1 ) ) ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f1210]) ).
thf(f1212,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v4 @ Y1 ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v2 @ Y1 ) ) ) ) )
= $true )
| ( ( v3 @ X1 )
= $true )
| ( ( v2 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f1211]) ).
thf(f1215,plain,
! [X2: $i,X1: $i] :
( ( ( v3 @ X1 )
= $true )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v4 @ Y1 ) ) ) )
@ X2 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v2 @ Y1 ) ) ) ) )
= $true )
| ( ( v2 @ X1 )
= $false ) ),
inference(pi_proxy_clausification,[],[f1212]) ).
thf(f1216,plain,
! [X2: $i,X1: $i] :
( ( ( v3 @ X1 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v2 @ Y1 ) ) ) ) )
= $true )
| ( ( v2 @ X1 )
= $false )
| ( ( ~ ( rel_s4 @ X1 @ X2 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v4 @ Y0 ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f1215]) ).
thf(f1217,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v2 @ Y1 ) ) ) ) )
= $true )
| ( ( ~ ( rel_s4 @ X1 @ X2 ) )
= $true )
| ( ( v3 @ X1 )
= $true )
| ( ( v2 @ X1 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v4 @ Y0 ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f1216]) ).
thf(f1218,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v2 @ Y1 ) ) ) ) )
= $true )
| ( ( v2 @ X1 )
= $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( v3 @ X1 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v4 @ Y0 ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f1217]) ).
thf(f1219,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v4 @ Y0 ) ) )
= $true )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( v2 @ X1 )
= $false )
| ( ( v3 @ X1 )
= $true )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v2 @ Y1 ) ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f1218]) ).
thf(f1220,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X3 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X3 @ Y0 )
| ~ ( v2 @ Y0 ) ) ) ) )
| ( ( v2 @ X1 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v4 @ Y0 ) ) )
= $true )
| ( ( v3 @ X1 )
= $true ) ),
inference(beta-eta_normalization,[],[f1219]) ).
thf(f1221,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v4 @ Y0 ) ) )
= $true )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( v2 @ X1 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X3 @ Y0 )
| ~ ( v2 @ Y0 ) ) )
= $true )
| ( ( v3 @ X1 )
= $true )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X3 ) ) ) ),
inference(or_proxy_clausification,[],[f1220]) ).
thf(f1222,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X3 @ Y0 )
| ~ ( v2 @ Y0 ) ) )
= $true )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( v2 @ X1 )
= $false )
| ( ( v3 @ X1 )
= $true )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v4 @ Y0 ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f1221]) ).
thf(f1223,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( v2 @ X1 )
= $false )
| ( ( v3 @ X1 )
= $true )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v4 @ Y0 ) ) )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X3 @ Y0 )
| ~ ( v2 @ Y0 ) )
@ X4 )
= $true )
| ( $false
= ( rel_s4 @ X1 @ X3 ) ) ),
inference(pi_proxy_clausification,[],[f1222]) ).
thf(f1224,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( v2 @ X1 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( ( ~ ( rel_s4 @ X3 @ X4 )
| ~ ( v2 @ X4 ) )
= $true )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v4 @ Y0 ) ) )
= $true )
| ( ( v3 @ X1 )
= $true ) ),
inference(beta-eta_normalization,[],[f1223]) ).
thf(f1225,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ~ ( v2 @ X4 ) ) )
| ( ( ~ ( rel_s4 @ X3 @ X4 ) )
= $true )
| ( ( v3 @ X1 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v4 @ Y0 ) ) )
= $true )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( v2 @ X1 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) ) ),
inference(or_proxy_clausification,[],[f1224]) ).
thf(f1226,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v4 @ Y0 ) ) )
= $true )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( ( ~ ( rel_s4 @ X3 @ X4 ) )
= $true )
| ( ( v3 @ X1 )
= $true )
| ( ( v2 @ X1 )
= $false )
| ( $false
= ( v2 @ X4 ) ) ),
inference(not_proxy_clausification,[],[f1225]) ).
thf(f1227,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v4 @ Y0 ) ) )
= $true )
| ( ( rel_s4 @ X3 @ X4 )
= $false )
| ( $false
= ( v2 @ X4 ) )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( ( v3 @ X1 )
= $true )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( v2 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f1226]) ).
thf(f1228,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( ( rel_s4 @ X3 @ X4 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( ( v3 @ X1 )
= $true )
| ( $false
= ( v2 @ X4 ) )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v4 @ Y0 ) )
@ X5 )
= $true )
| ( ( v2 @ X1 )
= $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f1227]) ).
thf(f1229,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( ~ ( rel_s4 @ X2 @ X5 )
| ~ ( v4 @ X5 ) ) )
| ( ( rel_s4 @ X3 @ X4 )
= $false )
| ( ( v3 @ X1 )
= $true )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( v2 @ X1 )
= $false )
| ( $false
= ( v2 @ X4 ) ) ),
inference(beta-eta_normalization,[],[f1228]) ).
thf(f1230,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( v3 @ X1 )
= $true )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( ( v2 @ X1 )
= $false )
| ( ( ~ ( rel_s4 @ X2 @ X5 ) )
= $true )
| ( ( rel_s4 @ X3 @ X4 )
= $false )
| ( $false
= ( v2 @ X4 ) )
| ( ( ~ ( v4 @ X5 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f1229]) ).
thf(f1231,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( rel_s4 @ X2 @ X5 ) )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( ~ ( v4 @ X5 ) )
= $true )
| ( ( v3 @ X1 )
= $true )
| ( ( rel_s4 @ X3 @ X4 )
= $false )
| ( $false
= ( v2 @ X4 ) )
| ( ( v2 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f1230]) ).
thf(f1232,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( rel_s4 @ X2 @ X5 ) )
| ( $false
= ( v2 @ X4 ) )
| ( ( rel_s4 @ X3 @ X4 )
= $false )
| ( ( v2 @ X1 )
= $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( v4 @ X5 ) )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( ( v3 @ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f1231]) ).
thf(f1240,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ X2 @ X0 ) )
| ( $false
= ( rel_s4 @ X2 @ X0 ) )
| ( $false != $false )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( ( v2 @ X1 )
= $false )
| ( $false
= ( v4 @ X1 ) )
| ( ( v3 @ X2 )
= $true )
| ( ( v2 @ X2 )
= $false ) ),
inference(equality_factoring,[],[f1232]) ).
thf(f1244,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ X2 @ X0 ) )
| ( $false != $false )
| ( ( v2 @ X1 )
= $false )
| ( $false
= ( v4 @ X1 ) )
| ( ( v3 @ X2 )
= $true )
| ( ( v2 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X0 @ X1 ) ) ),
inference(duplicate_literal_removal,[],[f1240]) ).
thf(f1245,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ X2 @ X0 ) )
| ( ( v2 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( ( v2 @ X1 )
= $false )
| ( ( v3 @ X2 )
= $true )
| ( $false
= ( v4 @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f1244]) ).
thf(f1384,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ~ ( v1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ~ ( v1 @ Y2 ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f317]) ).
thf(f1385,plain,
! [X1: $i] :
( $true
= ( ~ ( v1 @ X1 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v1 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1384]) ).
thf(f1386,plain,
! [X1: $i] :
( ( $true
= ( ~ ( v1 @ X1 ) ) )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v1 @ Y1 ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f1385]) ).
thf(f1387,plain,
! [X1: $i] :
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v1 @ Y1 ) ) ) ) ) ) )
| ( ( v1 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f1386]) ).
thf(f1388,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v1 @ Y0 ) ) )
= $true )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v1 @ Y1 ) ) ) ) ) ) )
| ( ( v1 @ X1 )
= $false ) ),
inference(or_proxy_clausification,[],[f1387]) ).
thf(f1389,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v1 @ Y1 ) ) ) ) ) )
| ( ( v1 @ X1 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v1 @ Y0 ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v3 @ Y0 ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f1388]) ).
thf(f1392,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v1 @ Y0 ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v3 @ Y0 ) ) )
= $true )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v1 @ Y1 ) ) ) )
@ X2 ) )
| ( ( v1 @ X1 )
= $false ) ),
inference(pi_proxy_clausification,[],[f1389]) ).
thf(f1393,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v3 @ Y0 ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v1 @ Y0 ) ) )
= $true )
| ( ( v1 @ X1 )
= $false )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X2 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1392]) ).
thf(f1394,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( rel_s4 @ X1 @ X2 ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v1 @ Y0 ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v3 @ Y0 ) ) )
= $true )
| ( ( v1 @ X1 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v1 @ Y0 ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f1393]) ).
thf(f1395,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v1 @ Y0 ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v1 @ Y0 ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v3 @ Y0 ) ) )
= $true )
| ( ( v1 @ X1 )
= $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f1394]) ).
thf(f1396,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v3 @ Y0 ) ) )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v1 @ Y0 ) )
@ X3 )
= $true )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( v1 @ X1 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v1 @ Y0 ) ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f1395]) ).
thf(f1397,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( v1 @ X1 )
= $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( ~ ( rel_s4 @ X2 @ X3 )
| ~ ( v1 @ X3 ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v1 @ Y0 ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v3 @ Y0 ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f1396]) ).
thf(f1398,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s4 @ X2 @ X3 ) ) )
| ( ( ~ ( v1 @ X3 ) )
= $true )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v1 @ Y0 ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v3 @ Y0 ) ) )
= $true )
| ( ( v1 @ X1 )
= $false ) ),
inference(or_proxy_clausification,[],[f1397]) ).
thf(f1399,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( v1 @ X1 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v3 @ Y0 ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v1 @ Y0 ) ) )
= $true )
| ( ( ~ ( v1 @ X3 ) )
= $true )
| ( ( rel_s4 @ X2 @ X3 )
= $false ) ),
inference(not_proxy_clausification,[],[f1398]) ).
thf(f1400,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v3 @ Y0 ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v1 @ Y0 ) ) )
= $true )
| ( $false
= ( v1 @ X3 ) )
| ( ( rel_s4 @ X2 @ X3 )
= $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( v1 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f1399]) ).
thf(f1401,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v1 @ Y0 ) ) )
= $true )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v3 @ Y0 ) )
@ X4 ) )
| ( $false
= ( v1 @ X3 ) )
| ( ( rel_s4 @ X2 @ X3 )
= $false )
| ( ( v1 @ X1 )
= $false ) ),
inference(pi_proxy_clausification,[],[f1400]) ).
thf(f1402,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( rel_s4 @ X2 @ X3 )
= $false )
| ( $false
= ( v1 @ X3 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v1 @ Y0 ) ) )
= $true )
| ( ( v1 @ X1 )
= $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X4 )
| ~ ( v3 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1401]) ).
thf(f1403,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ~ ( rel_s4 @ X1 @ X4 ) ) )
| ( $false
= ( v1 @ X3 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v1 @ Y0 ) ) )
= $true )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( rel_s4 @ X2 @ X3 )
= $false )
| ( ( v1 @ X1 )
= $false )
| ( ( ~ ( v3 @ X4 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f1402]) ).
thf(f1404,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( rel_s4 @ X2 @ X3 )
= $false )
| ( ( ~ ( v3 @ X4 ) )
= $true )
| ( $false
= ( rel_s4 @ X1 @ X4 ) )
| ( ( v1 @ X1 )
= $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v1 @ Y0 ) ) )
= $true )
| ( $false
= ( v1 @ X3 ) ) ),
inference(not_proxy_clausification,[],[f1403]) ).
thf(f1405,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v1 @ Y0 ) ) )
= $true )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( v1 @ X3 ) )
| ( ( v1 @ X1 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X4 ) )
| ( ( rel_s4 @ X2 @ X3 )
= $false )
| ( ( v3 @ X4 )
= $false ) ),
inference(not_proxy_clausification,[],[f1404]) ).
thf(f1406,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( ( v1 @ X1 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X4 ) )
| ( $false
= ( v1 @ X3 ) )
| ( ( rel_s4 @ X2 @ X3 )
= $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v1 @ Y0 ) )
@ X5 )
= $true )
| ( ( v3 @ X4 )
= $false ) ),
inference(pi_proxy_clausification,[],[f1405]) ).
thf(f1407,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( ( ~ ( rel_s4 @ X1 @ X5 )
| ~ ( v1 @ X5 ) )
= $true )
| ( $false
= ( rel_s4 @ X1 @ X4 ) )
| ( ( v1 @ X1 )
= $false )
| ( ( v3 @ X4 )
= $false )
| ( $false
= ( v1 @ X3 ) )
| ( ( rel_s4 @ X2 @ X3 )
= $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f1406]) ).
thf(f1408,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( rel_s4 @ X1 @ X4 ) )
| ( ( v1 @ X1 )
= $false )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X5 ) ) )
| ( ( v3 @ X4 )
= $false )
| ( $false
= ( v1 @ X3 ) )
| ( $true
= ( ~ ( v1 @ X5 ) ) )
| ( ( rel_s4 @ X2 @ X3 )
= $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false ) ),
inference(or_proxy_clausification,[],[f1407]) ).
thf(f1409,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( rel_s4 @ X1 @ X5 ) )
| ( $true
= ( ~ ( v1 @ X5 ) ) )
| ( ( rel_s4 @ X2 @ X3 )
= $false )
| ( $false
= ( v1 @ X3 ) )
| ( $false
= ( rel_s4 @ X1 @ X4 ) )
| ( ( v3 @ X4 )
= $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( v1 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f1408]) ).
thf(f1410,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( rel_s4 @ X1 @ X5 ) )
| ( $false
= ( v1 @ X3 ) )
| ( ( rel_s4 @ X2 @ X3 )
= $false )
| ( ( v3 @ X4 )
= $false )
| ( $false
= ( v1 @ X5 ) )
| ( $false
= ( rel_s4 @ X1 @ X4 ) )
| ( ( v1 @ X1 )
= $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f1409]) ).
thf(f1432,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false != $false )
| ( $false
= ( rel_s4 @ X0 @ X0 ) )
| ( $false
= ( v3 @ X2 ) )
| ( ( v1 @ X1 )
= $false )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( ( v1 @ X1 )
= $false )
| ( ( v1 @ X0 )
= $false )
| ( $false
= ( rel_s4 @ X0 @ X2 ) ) ),
inference(equality_factoring,[],[f1410]) ).
thf(f1438,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( v1 @ X1 )
= $false )
| ( $false != $false )
| ( ( v1 @ X0 )
= $false )
| ( $false
= ( rel_s4 @ X0 @ X2 ) )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $false
= ( v3 @ X2 ) )
| ( $false
= ( rel_s4 @ X0 @ X0 ) ) ),
inference(duplicate_literal_removal,[],[f1432]) ).
thf(f1439,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ X0 @ X0 ) )
| ( $false
= ( rel_s4 @ X0 @ X2 ) )
| ( $false
= ( v3 @ X2 ) )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( ( v1 @ X1 )
= $false )
| ( ( v1 @ X0 )
= $false ) ),
inference(trivial_inequality_removal,[],[f1438]) ).
thf(f1448,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( v1 @ X0 )
= $false )
| ( $false = $true )
| ( $false
= ( v3 @ X2 ) )
| ( ( v1 @ X1 )
= $false )
| ( $false
= ( rel_s4 @ X0 @ X2 ) )
| ( $false
= ( rel_s4 @ X0 @ X1 ) ) ),
inference(forward_demodulation,[],[f1439,f360]) ).
thf(f1449,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ X0 @ X2 ) )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( ( v1 @ X0 )
= $false )
| ( $false
= ( v3 @ X2 ) )
| ( ( v1 @ X1 )
= $false ) ),
inference(trivial_inequality_removal,[],[f1448]) ).
thf(f1450,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ~ ( v3 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ~ ( v3 @ Y2 ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f337]) ).
thf(f1451,plain,
! [X1: $i] :
( $true
= ( ~ ( v3 @ X1 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v4 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v3 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1450]) ).
thf(f1452,plain,
! [X1: $i] :
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v4 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v3 @ Y1 ) ) ) ) ) )
= $true )
| ( $true
= ( ~ ( v3 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f1451]) ).
thf(f1453,plain,
! [X1: $i] :
( ( $true
= ( ~ ( v3 @ X1 ) ) )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v4 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v3 @ Y1 ) ) ) ) ) )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v2 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f1452]) ).
thf(f1454,plain,
! [X1: $i] :
( ( ( v3 @ X1 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v2 @ Y0 ) ) ) )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v4 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v3 @ Y1 ) ) ) ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f1453]) ).
thf(f1455,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v3 @ Y1 ) ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v2 @ Y0 ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v4 @ Y0 ) ) )
= $true )
| ( ( v3 @ X1 )
= $false ) ),
inference(or_proxy_clausification,[],[f1454]) ).
thf(f1458,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v4 @ Y0 ) ) )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v2 @ Y0 ) ) ) )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v3 @ Y1 ) ) ) )
@ X2 )
= $true )
| ( ( v3 @ X1 )
= $false ) ),
inference(pi_proxy_clausification,[],[f1455]) ).
thf(f1459,plain,
! [X2: $i,X1: $i] :
( ( ( v3 @ X1 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v4 @ Y0 ) ) )
= $true )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X2 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v3 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v2 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f1458]) ).
thf(f1460,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( rel_s4 @ X1 @ X2 ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v3 @ Y0 ) ) )
= $true )
| ( ( v3 @ X1 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v4 @ Y0 ) ) )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v2 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f1459]) ).
thf(f1461,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v2 @ Y0 ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v4 @ Y0 ) ) )
= $true )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v3 @ Y0 ) ) )
= $true )
| ( ( v3 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f1460]) ).
thf(f1462,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v4 @ Y0 ) ) )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v2 @ Y0 ) )
@ X3 )
= $true )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v3 @ Y0 ) ) )
= $true )
| ( ( v3 @ X1 )
= $false ) ),
inference(pi_proxy_clausification,[],[f1461]) ).
thf(f1463,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v4 @ Y0 ) ) )
= $true )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( ~ ( rel_s4 @ X1 @ X3 )
| ~ ( v2 @ X3 ) )
= $true )
| ( ( v3 @ X1 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v3 @ Y0 ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f1462]) ).
thf(f1464,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ~ ( v2 @ X3 ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v4 @ Y0 ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v3 @ Y0 ) ) )
= $true )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X3 ) ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( v3 @ X1 )
= $false ) ),
inference(or_proxy_clausification,[],[f1463]) ).
thf(f1465,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v4 @ Y0 ) ) )
= $true )
| ( ( v3 @ X1 )
= $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v3 @ Y0 ) ) )
= $true )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X3 ) ) )
| ( ( v2 @ X3 )
= $false ) ),
inference(not_proxy_clausification,[],[f1464]) ).
thf(f1466,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v3 @ Y0 ) ) )
= $true )
| ( ( v2 @ X3 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v4 @ Y0 ) ) )
= $true )
| ( ( v3 @ X1 )
= $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) ) ),
inference(not_proxy_clausification,[],[f1465]) ).
thf(f1467,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v3 @ Y0 ) )
@ X4 )
= $true )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( ( v3 @ X1 )
= $false )
| ( ( v2 @ X3 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v4 @ Y0 ) ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f1466]) ).
thf(f1468,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v4 @ Y0 ) ) )
= $true )
| ( ( ~ ( rel_s4 @ X2 @ X4 )
| ~ ( v3 @ X4 ) )
= $true )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( ( v2 @ X3 )
= $false )
| ( ( v3 @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f1467]) ).
thf(f1469,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v4 @ Y0 ) ) )
= $true )
| ( ( ~ ( v3 @ X4 ) )
= $true )
| ( ( v2 @ X3 )
= $false )
| ( ( v3 @ X1 )
= $false )
| ( ( ~ ( rel_s4 @ X2 @ X4 ) )
= $true )
| ( ( rel_s4 @ X1 @ X2 )
= $false ) ),
inference(or_proxy_clausification,[],[f1468]) ).
thf(f1470,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v4 @ Y0 ) ) )
= $true )
| ( ( v3 @ X1 )
= $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( v2 @ X3 )
= $false )
| ( ( ~ ( rel_s4 @ X2 @ X4 ) )
= $true )
| ( ( v3 @ X4 )
= $false ) ),
inference(not_proxy_clausification,[],[f1469]) ).
thf(f1471,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v4 @ Y0 ) ) )
= $true )
| ( ( v3 @ X4 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( ( v2 @ X3 )
= $false )
| ( ( v3 @ X1 )
= $false )
| ( $false
= ( rel_s4 @ X2 @ X4 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f1470]) ).
thf(f1472,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( rel_s4 @ X2 @ X4 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v4 @ Y0 ) )
@ X5 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( ( v3 @ X1 )
= $false )
| ( ( v2 @ X3 )
= $false )
| ( ( v3 @ X4 )
= $false ) ),
inference(pi_proxy_clausification,[],[f1471]) ).
thf(f1473,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( ( v3 @ X4 )
= $false )
| ( ( v2 @ X3 )
= $false )
| ( ( ~ ( rel_s4 @ X1 @ X5 )
| ~ ( v4 @ X5 ) )
= $true )
| ( $false
= ( rel_s4 @ X2 @ X4 ) )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( v3 @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f1472]) ).
thf(f1474,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( ~ ( v4 @ X5 ) )
= $true )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( $false
= ( rel_s4 @ X2 @ X4 ) )
| ( ( v3 @ X4 )
= $false )
| ( ( v2 @ X3 )
= $false )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X5 ) ) )
| ( ( v3 @ X1 )
= $false ) ),
inference(or_proxy_clausification,[],[f1473]) ).
thf(f1475,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( ~ ( rel_s4 @ X1 @ X5 ) ) )
| ( $false
= ( v4 @ X5 ) )
| ( ( v3 @ X4 )
= $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( $false
= ( rel_s4 @ X2 @ X4 ) )
| ( ( v2 @ X3 )
= $false )
| ( ( v3 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f1474]) ).
thf(f1476,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( rel_s4 @ X2 @ X4 ) )
| ( $false
= ( rel_s4 @ X1 @ X5 ) )
| ( $false
= ( v4 @ X5 ) )
| ( ( v3 @ X1 )
= $false )
| ( ( v2 @ X3 )
= $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( ( v3 @ X4 )
= $false ) ),
inference(not_proxy_clausification,[],[f1475]) ).
thf(f1485,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ X0 @ X0 ) )
| ( $false
= ( v4 @ X1 ) )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( ( v3 @ X0 )
= $false )
| ( $false != $false )
| ( $false
= ( rel_s4 @ X0 @ X2 ) )
| ( ( v2 @ X2 )
= $false )
| ( ( v3 @ X0 )
= $false ) ),
inference(equality_factoring,[],[f1476]) ).
thf(f1488,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false != $false )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $false
= ( v4 @ X1 ) )
| ( $false
= ( rel_s4 @ X0 @ X2 ) )
| ( ( v2 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X0 @ X0 ) )
| ( ( v3 @ X0 )
= $false ) ),
inference(duplicate_literal_removal,[],[f1485]) ).
thf(f1489,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ X0 @ X0 ) )
| ( ( v3 @ X0 )
= $false )
| ( $false
= ( rel_s4 @ X0 @ X2 ) )
| ( $false
= ( v4 @ X1 ) )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( ( v2 @ X2 )
= $false ) ),
inference(trivial_inequality_removal,[],[f1488]) ).
thf(f1498,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ X0 @ X2 ) )
| ( ( v2 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $false
= ( v4 @ X1 ) )
| ( ( v3 @ X0 )
= $false )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f1489,f360]) ).
thf(f1499,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ X0 @ X2 ) )
| ( $false
= ( v4 @ X1 ) )
| ( ( v2 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( ( v3 @ X0 )
= $false ) ),
inference(trivial_inequality_removal,[],[f1498]) ).
thf(f1504,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( v3 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( v2 @ Y2 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( v3 @ Y2 ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f310]) ).
thf(f1505,plain,
! [X1: $i] :
( ( ( v3 @ X1 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( v4 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v2 @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v3 @ Y1 ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f1504]) ).
thf(f1506,plain,
! [X1: $i] :
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( v4 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v2 @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v3 @ Y1 ) ) ) ) ) ) )
| ( ( v3 @ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f1505]) ).
thf(f1507,plain,
! [X1: $i] :
( ( ( v3 @ X1 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( v4 @ Y0 ) ) )
= $true )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v2 @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v3 @ Y1 ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f1506]) ).
thf(f1508,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v3 @ Y1 ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v2 @ Y1 ) ) ) ) )
= $true )
| ( ( v3 @ X1 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( v4 @ Y0 ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f1507]) ).
thf(f1511,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v3 @ Y1 ) ) ) )
@ X2 )
= $true )
| ( ( v3 @ X1 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( v4 @ Y0 ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v2 @ Y1 ) ) ) ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f1508]) ).
thf(f1512,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( v4 @ Y0 ) ) )
= $true )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X2 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ( v3 @ Y0 ) ) ) ) )
| ( ( v3 @ X1 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v2 @ Y1 ) ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f1511]) ).
thf(f1513,plain,
! [X2: $i,X1: $i] :
( ( ( v3 @ X1 )
= $true )
| ( ( ~ ( rel_s4 @ X1 @ X2 ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ( v3 @ Y0 ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v2 @ Y1 ) ) ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( v4 @ Y0 ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f1512]) ).
thf(f1514,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v2 @ Y1 ) ) ) ) )
= $true )
| ( ( v3 @ X1 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ( v3 @ Y0 ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( v4 @ Y0 ) ) )
= $true )
| ( ( rel_s4 @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f1513]) ).
thf(f1515,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( v3 @ X1 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( v4 @ Y0 ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ( v3 @ Y0 ) ) )
= $true )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v2 @ Y1 ) ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f1514]) ).
thf(f1516,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s4 @ X1 @ X3 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X3 @ Y0 )
| ( v2 @ Y0 ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ( v3 @ Y0 ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( v4 @ Y0 ) ) )
= $true )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( v3 @ X1 )
= $true ) ),
inference(beta-eta_normalization,[],[f1515]) ).
thf(f1517,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X3 @ Y0 )
| ( v2 @ Y0 ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( v4 @ Y0 ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ( v3 @ Y0 ) ) )
= $true )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X3 ) ) )
| ( ( v3 @ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f1516]) ).
thf(f1518,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X3 @ Y0 )
| ( v2 @ Y0 ) ) )
= $true )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( v3 @ X1 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ( v3 @ Y0 ) ) )
= $true )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( v4 @ Y0 ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f1517]) ).
thf(f1519,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( v4 @ Y0 ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ( v3 @ Y0 ) ) )
= $true )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( v3 @ X1 )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X3 @ Y0 )
| ( v2 @ Y0 ) )
@ X4 )
= $true )
| ( $false
= ( rel_s4 @ X1 @ X3 ) ) ),
inference(pi_proxy_clausification,[],[f1518]) ).
thf(f1520,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( v3 @ X1 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( v4 @ Y0 ) ) )
= $true )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $true
= ( ~ ( rel_s4 @ X3 @ X4 )
| ( v2 @ X4 ) ) )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ( v3 @ Y0 ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f1519]) ).
thf(f1521,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ( v3 @ Y0 ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( v4 @ Y0 ) ) )
= $true )
| ( ( ~ ( rel_s4 @ X3 @ X4 ) )
= $true )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( v3 @ X1 )
= $true )
| ( $true
= ( v2 @ X4 ) )
| ( $false
= ( rel_s4 @ X1 @ X3 ) ) ),
inference(or_proxy_clausification,[],[f1520]) ).
thf(f1522,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ( v3 @ Y0 ) ) )
= $true )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( $true
= ( v2 @ X4 ) )
| ( ( rel_s4 @ X3 @ X4 )
= $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( v4 @ Y0 ) ) )
= $true )
| ( ( v3 @ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f1521]) ).
thf(f1523,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ( v3 @ Y0 ) )
@ X5 ) )
| ( ( rel_s4 @ X3 @ X4 )
= $false )
| ( $true
= ( v2 @ X4 ) )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( v4 @ Y0 ) ) )
= $true )
| ( ( v3 @ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f1522]) ).
thf(f1524,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( ( v3 @ X1 )
= $true )
| ( ( ~ ( rel_s4 @ X2 @ X5 )
| ( v3 @ X5 ) )
= $true )
| ( ( rel_s4 @ X3 @ X4 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( v4 @ Y0 ) ) )
= $true )
| ( $true
= ( v2 @ X4 ) ) ),
inference(beta-eta_normalization,[],[f1523]) ).
thf(f1525,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( v2 @ X4 ) )
| ( ( v3 @ X1 )
= $true )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( v4 @ Y0 ) ) )
= $true )
| ( ( ~ ( rel_s4 @ X2 @ X5 ) )
= $true )
| ( ( rel_s4 @ X3 @ X4 )
= $false )
| ( $true
= ( v3 @ X5 ) ) ),
inference(or_proxy_clausification,[],[f1524]) ).
thf(f1526,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( v4 @ Y0 ) ) )
= $true )
| ( ( rel_s4 @ X3 @ X4 )
= $false )
| ( $true
= ( v2 @ X4 ) )
| ( $true
= ( v3 @ X5 ) )
| ( ( v3 @ X1 )
= $true )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X2 @ X5 ) )
| ( $false
= ( rel_s4 @ X1 @ X3 ) ) ),
inference(not_proxy_clausification,[],[f1525]) ).
thf(f1529,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $false
= ( rel_s4 @ X2 @ X5 ) )
| ( ( v3 @ X1 )
= $true )
| ( $true
= ( v2 @ X4 ) )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( rel_s4 @ X3 @ X4 )
= $false )
| ( $true
= ( v3 @ X5 ) )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( v4 @ Y0 ) )
@ X6 )
= $true ) ),
inference(pi_proxy_clausification,[],[f1526]) ).
thf(f1530,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( ( v3 @ X1 )
= $true )
| ( $true
= ( v2 @ X4 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X2 @ X5 ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X6 )
| ( v4 @ X6 ) ) )
| ( ( rel_s4 @ X3 @ X4 )
= $false )
| ( $true
= ( v3 @ X5 ) )
| ( $false
= ( rel_s4 @ X1 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f1529]) ).
thf(f1531,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( ( rel_s4 @ X3 @ X4 )
= $false )
| ( $false
= ( rel_s4 @ X2 @ X5 ) )
| ( ( ~ ( rel_s4 @ X1 @ X6 ) )
= $true )
| ( $true
= ( v3 @ X5 ) )
| ( ( v3 @ X1 )
= $true )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $true
= ( v4 @ X6 ) )
| ( $true
= ( v2 @ X4 ) ) ),
inference(or_proxy_clausification,[],[f1530]) ).
thf(f1532,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $false
= ( rel_s4 @ X2 @ X5 ) )
| ( $true
= ( v2 @ X4 ) )
| ( $true
= ( v4 @ X6 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( ( rel_s4 @ X1 @ X6 )
= $false )
| ( $true
= ( v3 @ X5 ) )
| ( ( v3 @ X1 )
= $true )
| ( ( rel_s4 @ X3 @ X4 )
= $false ) ),
inference(not_proxy_clausification,[],[f1531]) ).
thf(f1540,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ X0 @ X2 ) )
| ( ( v3 @ X0 )
= $true )
| ( $false
= ( rel_s4 @ X3 @ X1 ) )
| ( $false
= ( rel_s4 @ X0 @ X0 ) )
| ( ( v2 @ X1 )
= $true )
| ( $false != $false )
| ( $false
= ( rel_s4 @ X0 @ X3 ) )
| ( $true
= ( v4 @ X2 ) )
| ( ( v3 @ X0 )
= $true ) ),
inference(equality_factoring,[],[f1532]) ).
thf(f1547,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
= ( v4 @ X2 ) )
| ( $false
= ( rel_s4 @ X0 @ X3 ) )
| ( $false
= ( rel_s4 @ X3 @ X1 ) )
| ( $false
= ( rel_s4 @ X0 @ X2 ) )
| ( $false
= ( rel_s4 @ X0 @ X0 ) )
| ( ( v2 @ X1 )
= $true )
| ( ( v3 @ X0 )
= $true )
| ( $false != $false ) ),
inference(duplicate_literal_removal,[],[f1540]) ).
thf(f1548,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ X0 @ X2 ) )
| ( $false
= ( rel_s4 @ X0 @ X0 ) )
| ( ( v2 @ X1 )
= $true )
| ( $false
= ( rel_s4 @ X3 @ X1 ) )
| ( $true
= ( v4 @ X2 ) )
| ( $false
= ( rel_s4 @ X0 @ X3 ) )
| ( ( v3 @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[],[f1547]) ).
thf(f1559,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $false = $true )
| ( ( v3 @ X0 )
= $true )
| ( ( v2 @ X1 )
= $true )
| ( $true
= ( v4 @ X2 ) )
| ( $false
= ( rel_s4 @ X0 @ X2 ) )
| ( $false
= ( rel_s4 @ X0 @ X3 ) )
| ( $false
= ( rel_s4 @ X3 @ X1 ) ) ),
inference(forward_demodulation,[],[f1548,f360]) ).
thf(f1560,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ X3 @ X1 ) )
| ( ( v3 @ X0 )
= $true )
| ( $false
= ( rel_s4 @ X0 @ X2 ) )
| ( ( v2 @ X1 )
= $true )
| ( $true
= ( v4 @ X2 ) )
| ( $false
= ( rel_s4 @ X0 @ X3 ) ) ),
inference(trivial_inequality_removal,[],[f1559]) ).
thf(f1563,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( v1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( v4 @ Y2 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ~ ( v2 @ Y2 ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f315]) ).
thf(f1564,plain,
! [X1: $i] :
( $true
= ( ( v1 @ X1 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( v1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v4 @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v2 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1563]) ).
thf(f1565,plain,
! [X1: $i] :
( ( ( v1 @ X1 )
= $true )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( v1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v4 @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v2 @ Y1 ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f1564]) ).
thf(f1566,plain,
! [X1: $i] :
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v4 @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v2 @ Y1 ) ) ) ) ) ) )
| ( ( v1 @ X1 )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( v1 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f1565]) ).
thf(f1567,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v2 @ Y1 ) ) ) ) )
= $true )
| ( ( v1 @ X1 )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( v1 @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v4 @ Y1 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f1566]) ).
thf(f1568,plain,
! [X2: $i,X1: $i] :
( ( ( v1 @ X1 )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( v1 @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v4 @ Y1 ) ) ) ) ) )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v2 @ Y1 ) ) ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f1567]) ).
thf(f1569,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( v1 @ Y0 ) ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X2 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v2 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v4 @ Y1 ) ) ) ) ) )
| ( ( v1 @ X1 )
= $true ) ),
inference(beta-eta_normalization,[],[f1568]) ).
thf(f1570,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v2 @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v4 @ Y1 ) ) ) ) ) )
| ( ( v1 @ X1 )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( v1 @ Y0 ) ) ) )
| ( ( ~ ( rel_s4 @ X1 @ X2 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f1569]) ).
thf(f1571,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v4 @ Y1 ) ) ) ) ) )
| ( ( v1 @ X1 )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v2 @ Y0 ) ) ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( v1 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f1570]) ).
thf(f1576,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v4 @ Y1 ) ) ) )
@ X3 )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( v1 @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v2 @ Y0 ) ) ) )
| ( ( v1 @ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f1571]) ).
thf(f1577,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ~ ( rel_s4 @ X1 @ X3 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X3 @ Y0 )
| ( v4 @ Y0 ) ) ) )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v2 @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( v1 @ Y0 ) ) ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( v1 @ X1 )
= $true ) ),
inference(beta-eta_normalization,[],[f1576]) ).
thf(f1578,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v2 @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( v1 @ Y0 ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X3 @ Y0 )
| ( v4 @ Y0 ) ) )
= $true )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( v1 @ X1 )
= $true )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X3 ) ) ) ),
inference(or_proxy_clausification,[],[f1577]) ).
thf(f1579,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v2 @ Y0 ) ) ) )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( ( v1 @ X1 )
= $true )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X3 @ Y0 )
| ( v4 @ Y0 ) ) )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( v1 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f1578]) ).
thf(f1580,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v2 @ Y0 ) )
@ X4 )
= $true )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( v1 @ X1 )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( v1 @ Y0 ) ) ) )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X3 @ Y0 )
| ( v4 @ Y0 ) ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f1579]) ).
thf(f1581,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X3 @ Y0 )
| ( v4 @ Y0 ) ) )
= $true )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( ~ ( rel_s4 @ X2 @ X4 )
| ~ ( v2 @ X4 ) )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( v1 @ Y0 ) ) ) )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( ( v1 @ X1 )
= $true ) ),
inference(beta-eta_normalization,[],[f1580]) ).
thf(f1582,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ~ ( v2 @ X4 ) ) )
| ( ( ~ ( rel_s4 @ X2 @ X4 ) )
= $true )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X3 @ Y0 )
| ( v4 @ Y0 ) ) )
= $true )
| ( ( v1 @ X1 )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( v1 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f1581]) ).
thf(f1583,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( v1 @ X1 )
= $true )
| ( ( ~ ( rel_s4 @ X2 @ X4 ) )
= $true )
| ( $false
= ( v2 @ X4 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X3 @ Y0 )
| ( v4 @ Y0 ) ) )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( v1 @ Y0 ) ) ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) ) ),
inference(not_proxy_clausification,[],[f1582]) ).
thf(f1584,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( v1 @ Y0 ) ) ) )
| ( ( v1 @ X1 )
= $true )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X3 @ Y0 )
| ( v4 @ Y0 ) ) )
= $true )
| ( $false
= ( v2 @ X4 ) )
| ( $false
= ( rel_s4 @ X2 @ X4 ) ) ),
inference(not_proxy_clausification,[],[f1583]) ).
thf(f1585,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( v1 @ Y0 ) )
@ X5 )
= $true )
| ( $false
= ( rel_s4 @ X2 @ X4 ) )
| ( ( v1 @ X1 )
= $true )
| ( $false
= ( v2 @ X4 ) )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X3 @ Y0 )
| ( v4 @ Y0 ) ) )
= $true )
| ( ( rel_s4 @ X1 @ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f1584]) ).
thf(f1586,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( $false
= ( v2 @ X4 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X3 @ Y0 )
| ( v4 @ Y0 ) ) )
= $true )
| ( ( v1 @ X1 )
= $true )
| ( ( ~ ( rel_s4 @ X1 @ X5 )
| ( v1 @ X5 ) )
= $true )
| ( $false
= ( rel_s4 @ X2 @ X4 ) ) ),
inference(beta-eta_normalization,[],[f1585]) ).
thf(f1587,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( ( v1 @ X1 )
= $true )
| ( $false
= ( v2 @ X4 ) )
| ( $true
= ( v1 @ X5 ) )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X5 ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X3 @ Y0 )
| ( v4 @ Y0 ) ) )
= $true )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X2 @ X4 ) ) ),
inference(or_proxy_clausification,[],[f1586]) ).
thf(f1588,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X3 @ Y0 )
| ( v4 @ Y0 ) ) )
= $true )
| ( ( v1 @ X1 )
= $true )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( v2 @ X4 ) )
| ( $false
= ( rel_s4 @ X2 @ X4 ) )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( $false
= ( rel_s4 @ X1 @ X5 ) )
| ( $true
= ( v1 @ X5 ) ) ),
inference(not_proxy_clausification,[],[f1587]) ).
thf(f1589,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( v1 @ X1 )
= $true )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( $false
= ( v2 @ X4 ) )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X3 @ Y0 )
| ( v4 @ Y0 ) )
@ X6 )
= $true )
| ( $false
= ( rel_s4 @ X1 @ X5 ) )
| ( $false
= ( rel_s4 @ X2 @ X4 ) )
| ( $true
= ( v1 @ X5 ) ) ),
inference(pi_proxy_clausification,[],[f1588]) ).
thf(f1590,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X2 @ X4 ) )
| ( ( ~ ( rel_s4 @ X3 @ X6 )
| ( v4 @ X6 ) )
= $true )
| ( ( v1 @ X1 )
= $true )
| ( $true
= ( v1 @ X5 ) )
| ( $false
= ( rel_s4 @ X1 @ X5 ) )
| ( $false
= ( v2 @ X4 ) )
| ( $false
= ( rel_s4 @ X1 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f1589]) ).
thf(f1591,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $true
= ( v1 @ X5 ) )
| ( $true
= ( v4 @ X6 ) )
| ( $false
= ( v2 @ X4 ) )
| ( ( ~ ( rel_s4 @ X3 @ X6 ) )
= $true )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X2 @ X4 ) )
| ( $false
= ( rel_s4 @ X1 @ X5 ) )
| ( ( v1 @ X1 )
= $true )
| ( $false
= ( rel_s4 @ X1 @ X3 ) ) ),
inference(or_proxy_clausification,[],[f1590]) ).
thf(f1592,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $false
= ( rel_s4 @ X2 @ X4 ) )
| ( $true
= ( v4 @ X6 ) )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( $true
= ( v1 @ X5 ) )
| ( $false
= ( rel_s4 @ X1 @ X5 ) )
| ( $false
= ( v2 @ X4 ) )
| ( ( rel_s4 @ X3 @ X6 )
= $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( v1 @ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f1591]) ).
thf(f1736,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
= ( v1 @ X2 ) )
| ( ( rel_s4 @ X2 @ X3 )
= $false )
| ( $false
= ( v2 @ ( sK2 @ X0 ) ) )
| ( $false
= ( rel_s4 @ X2 @ X4 ) )
| ( $true
= ( v1 @ X4 ) )
| ( $false
= ( rel_s4 @ X3 @ X1 ) )
| ( $false = $true )
| ( $true
= ( v4 @ X1 ) )
| ( $false
= ( rel_s4 @ X2 @ X0 ) ) ),
inference(superposition,[],[f372,f1592]) ).
thf(f1749,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
= ( v4 @ X1 ) )
| ( $false
= ( rel_s4 @ X2 @ X0 ) )
| ( $false
= ( rel_s4 @ X3 @ X1 ) )
| ( $false
= ( v2 @ ( sK2 @ X0 ) ) )
| ( $true
= ( v1 @ X2 ) )
| ( ( rel_s4 @ X2 @ X3 )
= $false )
| ( $false
= ( rel_s4 @ X2 @ X4 ) )
| ( $true
= ( v1 @ X4 ) ) ),
inference(trivial_inequality_removal,[],[f1736]) ).
thf(f1833,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( v1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( v2 @ Y2 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ~ ( v2 @ Y2 ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f338]) ).
thf(f1834,plain,
! [X1: $i] :
( ( ( v1 @ X1 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v2 @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v2 @ Y1 ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f1833]) ).
thf(f1835,plain,
! [X1: $i] :
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v2 @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v2 @ Y1 ) ) ) ) ) ) )
| ( ( v1 @ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f1834]) ).
thf(f1836,plain,
! [X1: $i] :
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v2 @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v2 @ Y1 ) ) ) ) ) )
= $true )
| ( ( v1 @ X1 )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v2 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f1835]) ).
thf(f1837,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v2 @ Y1 ) ) ) ) )
= $true )
| ( ( v1 @ X1 )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v2 @ Y0 ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v2 @ Y1 ) ) ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f1836]) ).
thf(f1838,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v2 @ Y1 ) ) ) )
@ X2 )
= $true )
| ( ( v1 @ X1 )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v2 @ Y0 ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v2 @ Y1 ) ) ) ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f1837]) ).
thf(f1839,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v2 @ Y0 ) ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X2 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v2 @ Y0 ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v2 @ Y1 ) ) ) ) )
= $true )
| ( ( v1 @ X1 )
= $true ) ),
inference(beta-eta_normalization,[],[f1838]) ).
thf(f1840,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v2 @ Y0 ) ) ) )
| ( ( v1 @ X1 )
= $true )
| ( ( ~ ( rel_s4 @ X1 @ X2 ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v2 @ Y1 ) ) ) ) )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v2 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f1839]) ).
thf(f1841,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v2 @ Y1 ) ) ) ) )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v2 @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v2 @ Y0 ) ) ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( v1 @ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f1840]) ).
thf(f1842,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v2 @ Y1 ) ) ) )
@ X3 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v2 @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v2 @ Y0 ) ) ) )
| ( ( v1 @ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f1841]) ).
thf(f1843,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v2 @ Y0 ) ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X3 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X3 @ Y0 )
| ( v2 @ Y0 ) ) ) ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( v1 @ X1 )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v2 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f1842]) ).
thf(f1844,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s4 @ X1 @ X3 ) ) )
| ( ( v1 @ X1 )
= $true )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X3 @ Y0 )
| ( v2 @ Y0 ) ) )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v2 @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v2 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f1843]) ).
thf(f1845,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v2 @ Y0 ) ) ) )
| ( ( v1 @ X1 )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v2 @ Y0 ) ) ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X3 @ Y0 )
| ( v2 @ Y0 ) ) )
= $true )
| ( $false
= ( rel_s4 @ X1 @ X3 ) ) ),
inference(not_proxy_clausification,[],[f1844]) ).
thf(f1846,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v2 @ Y0 ) )
@ X4 )
= $true )
| ( ( v1 @ X1 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X3 @ Y0 )
| ( v2 @ Y0 ) ) )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v2 @ Y0 ) ) ) )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f1845]) ).
thf(f1847,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ~ ( rel_s4 @ X2 @ X4 )
| ~ ( v2 @ X4 ) )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v2 @ Y0 ) ) ) )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( v1 @ X1 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X3 @ Y0 )
| ( v2 @ Y0 ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f1846]) ).
thf(f1848,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( $true
= ( ~ ( v2 @ X4 ) ) )
| ( ( ~ ( rel_s4 @ X2 @ X4 ) )
= $true )
| ( ( v1 @ X1 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X3 @ Y0 )
| ( v2 @ Y0 ) ) )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v2 @ Y0 ) ) ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false ) ),
inference(or_proxy_clausification,[],[f1847]) ).
thf(f1849,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( v1 @ X1 )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v2 @ Y0 ) ) ) )
| ( $false
= ( v2 @ X4 ) )
| ( ( ~ ( rel_s4 @ X2 @ X4 ) )
= $true )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X3 @ Y0 )
| ( v2 @ Y0 ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f1848]) ).
thf(f1850,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v2 @ Y0 ) ) ) )
| ( ( v1 @ X1 )
= $true )
| ( $false
= ( v2 @ X4 ) )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X3 @ Y0 )
| ( v2 @ Y0 ) ) )
= $true )
| ( $false
= ( rel_s4 @ X2 @ X4 ) ) ),
inference(not_proxy_clausification,[],[f1849]) ).
thf(f1851,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( $false
= ( v2 @ X4 ) )
| ( ( v1 @ X1 )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v2 @ Y0 ) )
@ X5 )
= $true )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X2 @ X4 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X3 @ Y0 )
| ( v2 @ Y0 ) ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f1850]) ).
thf(f1852,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X2 @ X4 ) )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X5 )
| ~ ( v2 @ X5 ) ) )
| ( $false
= ( v2 @ X4 ) )
| ( ( v1 @ X1 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X3 @ Y0 )
| ( v2 @ Y0 ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f1851]) ).
thf(f1853,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( ( v1 @ X1 )
= $true )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( $false
= ( rel_s4 @ X2 @ X4 ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X5 ) ) )
| ( ( ~ ( v2 @ X5 ) )
= $true )
| ( $false
= ( v2 @ X4 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X3 @ Y0 )
| ( v2 @ Y0 ) ) )
= $true )
| ( ( rel_s4 @ X1 @ X2 )
= $false ) ),
inference(or_proxy_clausification,[],[f1852]) ).
thf(f1854,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X3 @ Y0 )
| ( v2 @ Y0 ) ) )
= $true )
| ( $false
= ( rel_s4 @ X2 @ X4 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( v2 @ X4 ) )
| ( ( ~ ( v2 @ X5 ) )
= $true )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( ( v1 @ X1 )
= $true )
| ( $false
= ( rel_s4 @ X1 @ X5 ) ) ),
inference(not_proxy_clausification,[],[f1853]) ).
thf(f1855,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X3 @ Y0 )
| ( v2 @ Y0 ) ) )
= $true )
| ( ( v1 @ X1 )
= $true )
| ( $false
= ( v2 @ X5 ) )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( $false
= ( rel_s4 @ X2 @ X4 ) )
| ( $false
= ( v2 @ X4 ) )
| ( $false
= ( rel_s4 @ X1 @ X5 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f1854]) ).
thf(f1856,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( ( v1 @ X1 )
= $true )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X3 @ Y0 )
| ( v2 @ Y0 ) )
@ X6 ) )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( $false
= ( rel_s4 @ X1 @ X5 ) )
| ( $false
= ( v2 @ X4 ) )
| ( $false
= ( rel_s4 @ X2 @ X4 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( v2 @ X5 ) ) ),
inference(pi_proxy_clausification,[],[f1855]) ).
thf(f1857,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $false
= ( rel_s4 @ X1 @ X5 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( v1 @ X1 )
= $true )
| ( $false
= ( v2 @ X4 ) )
| ( $false
= ( v2 @ X5 ) )
| ( $false
= ( rel_s4 @ X2 @ X4 ) )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( ( ~ ( rel_s4 @ X3 @ X6 )
| ( v2 @ X6 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f1856]) ).
thf(f1858,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $true
= ( v2 @ X6 ) )
| ( ( v1 @ X1 )
= $true )
| ( ( ~ ( rel_s4 @ X3 @ X6 ) )
= $true )
| ( $false
= ( v2 @ X5 ) )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( $false
= ( rel_s4 @ X2 @ X4 ) )
| ( $false
= ( rel_s4 @ X1 @ X5 ) )
| ( $false
= ( v2 @ X4 ) ) ),
inference(or_proxy_clausification,[],[f1857]) ).
thf(f1859,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $false
= ( rel_s4 @ X2 @ X4 ) )
| ( ( v1 @ X1 )
= $true )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $true
= ( v2 @ X6 ) )
| ( ( rel_s4 @ X3 @ X6 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( $false
= ( rel_s4 @ X1 @ X5 ) )
| ( $false
= ( v2 @ X5 ) )
| ( $false
= ( v2 @ X4 ) ) ),
inference(not_proxy_clausification,[],[f1858]) ).
thf(f1872,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( v2 @ X1 )
= $false )
| ( ( v2 @ X2 )
= $true )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( ( v2 @ X1 )
= $false )
| ( $false
= ( rel_s4 @ X0 @ X3 ) )
| ( ( v1 @ X0 )
= $true )
| ( $false != $false )
| ( $false
= ( rel_s4 @ X3 @ X2 ) )
| ( $false
= ( rel_s4 @ X0 @ X0 ) ) ),
inference(equality_factoring,[],[f1859]) ).
thf(f1876,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( v2 @ X1 )
= $false )
| ( $false
= ( rel_s4 @ X3 @ X2 ) )
| ( $false
= ( rel_s4 @ X0 @ X0 ) )
| ( ( v1 @ X0 )
= $true )
| ( $false != $false )
| ( ( v2 @ X2 )
= $true )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $false
= ( rel_s4 @ X0 @ X3 ) ) ),
inference(duplicate_literal_removal,[],[f1872]) ).
thf(f1877,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( ( v1 @ X0 )
= $true )
| ( ( v2 @ X1 )
= $false )
| ( ( v2 @ X2 )
= $true )
| ( $false
= ( rel_s4 @ X0 @ X3 ) )
| ( $false
= ( rel_s4 @ X3 @ X2 ) )
| ( $false
= ( rel_s4 @ X0 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f1876]) ).
thf(f1888,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $false = $true )
| ( ( v1 @ X0 )
= $true )
| ( $false
= ( rel_s4 @ X3 @ X2 ) )
| ( $false
= ( rel_s4 @ X0 @ X3 ) )
| ( ( v2 @ X2 )
= $true )
| ( ( v2 @ X1 )
= $false )
| ( $false
= ( rel_s4 @ X0 @ X1 ) ) ),
inference(forward_demodulation,[],[f1877,f360]) ).
thf(f1889,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ X3 @ X2 ) )
| ( ( v1 @ X0 )
= $true )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( ( v2 @ X2 )
= $true )
| ( $false
= ( rel_s4 @ X0 @ X3 ) )
| ( ( v2 @ X1 )
= $false ) ),
inference(trivial_inequality_removal,[],[f1888]) ).
thf(f2441,plain,
! [X0: $i,X1: $i] :
( ( ( v1 @ X1 )
= $false )
| ( ( v1 @ X0 )
= $false )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( ( v3 @ X0 )
= $false )
| ( $false = $true ) ),
inference(superposition,[],[f360,f1449]) ).
thf(f2447,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( ( v3 @ X0 )
= $false )
| ( ( v1 @ X1 )
= $false )
| ( ( v1 @ X0 )
= $false ) ),
inference(trivial_inequality_removal,[],[f2441]) ).
thf(f2465,plain,
! [X0: $i,X1: $i] :
( ( $false != $false )
| ( $false
= ( v4 @ X1 ) )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( ( v3 @ X0 )
= $false )
| ( ( v2 @ X1 )
= $false ) ),
inference(equality_factoring,[],[f1499]) ).
thf(f2474,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $false
= ( v4 @ X1 ) )
| ( ( v2 @ X1 )
= $false )
| ( ( v3 @ X0 )
= $false ) ),
inference(trivial_inequality_removal,[],[f2465]) ).
thf(f2591,plain,
! [X0: $i] :
( ( ( v3 @ X0 )
= $true )
| ( ( v1 @ X0 )
= $false )
| ( $false != $false )
| ( $true
= ( v4 @ X0 ) )
| ( $false
= ( rel_s4 @ X0 @ X0 ) )
| ( $false
= ( v2 @ X0 ) ) ),
inference(equality_factoring,[],[f858]) ).
thf(f2597,plain,
! [X0: $i] :
( ( $false
= ( v2 @ X0 ) )
| ( ( v3 @ X0 )
= $true )
| ( $true
= ( v4 @ X0 ) )
| ( $false
= ( rel_s4 @ X0 @ X0 ) )
| ( ( v1 @ X0 )
= $false ) ),
inference(trivial_inequality_removal,[],[f2591]) ).
thf(f2602,plain,
! [X0: $i] :
( ( ( v1 @ X0 )
= $false )
| ( $true
= ( v4 @ X0 ) )
| ( $false
= ( v2 @ X0 ) )
| ( $false = $true )
| ( ( v3 @ X0 )
= $true ) ),
inference(forward_demodulation,[],[f2597,f360]) ).
thf(f2603,plain,
! [X0: $i] :
( ( $true
= ( v4 @ X0 ) )
| ( ( v1 @ X0 )
= $false )
| ( $false
= ( v2 @ X0 ) )
| ( ( v3 @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[],[f2602]) ).
thf(f2875,plain,
! [X0: $i] :
( ( $false = $true )
| ( ( v1 @ X0 )
= $false )
| ( ( v3 @ X0 )
= $false )
| ( ( v1 @ X0 )
= $false ) ),
inference(superposition,[],[f360,f2447]) ).
thf(f2881,plain,
! [X0: $i] :
( ( ( v3 @ X0 )
= $false )
| ( $false = $true )
| ( ( v1 @ X0 )
= $false ) ),
inference(duplicate_literal_removal,[],[f2875]) ).
thf(f2882,plain,
! [X0: $i] :
( ( ( v3 @ X0 )
= $false )
| ( ( v1 @ X0 )
= $false ) ),
inference(trivial_inequality_removal,[],[f2881]) ).
thf(f2899,plain,
! [X0: $i] :
( ( $false != $false )
| ( $false
= ( v2 @ X0 ) )
| ( ( v3 @ X0 )
= $true )
| ( $false
= ( v2 @ X0 ) )
| ( $false
= ( v4 @ X0 ) )
| ( $false
= ( rel_s4 @ X0 @ X0 ) ) ),
inference(equality_factoring,[],[f1245]) ).
thf(f2906,plain,
! [X0: $i] :
( ( $false != $false )
| ( $false
= ( v2 @ X0 ) )
| ( $false
= ( rel_s4 @ X0 @ X0 ) )
| ( $false
= ( v4 @ X0 ) )
| ( ( v3 @ X0 )
= $true ) ),
inference(duplicate_literal_removal,[],[f2899]) ).
thf(f2907,plain,
! [X0: $i] :
( ( $false
= ( rel_s4 @ X0 @ X0 ) )
| ( $false
= ( v2 @ X0 ) )
| ( ( v3 @ X0 )
= $true )
| ( $false
= ( v4 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f2906]) ).
thf(f2911,plain,
! [X0: $i] :
( ( ( v3 @ X0 )
= $true )
| ( $false
= ( v4 @ X0 ) )
| ( $false = $true )
| ( $false
= ( v2 @ X0 ) ) ),
inference(forward_demodulation,[],[f2907,f360]) ).
thf(f2912,plain,
! [X0: $i] :
( ( $false
= ( v4 @ X0 ) )
| ( ( v3 @ X0 )
= $true )
| ( $false
= ( v2 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f2911]) ).
thf(f3005,plain,
! [X0: $i] :
( ( $false = $true )
| ( ( v3 @ X0 )
= $true )
| ( $false
= ( v2 @ X0 ) )
| ( $false
= ( v2 @ X0 ) )
| ( ( v1 @ X0 )
= $false )
| ( ( v3 @ X0 )
= $true ) ),
inference(superposition,[],[f2912,f2603]) ).
thf(f3009,plain,
! [X0: $i] :
( ( ( v3 @ X0 )
= $true )
| ( $false
= ( v2 @ X0 ) )
| ( ( v1 @ X0 )
= $false )
| ( $false = $true ) ),
inference(duplicate_literal_removal,[],[f3005]) ).
thf(f3010,plain,
! [X0: $i] :
( ( $false
= ( v2 @ X0 ) )
| ( ( v3 @ X0 )
= $true )
| ( ( v1 @ X0 )
= $false ) ),
inference(trivial_inequality_removal,[],[f3009]) ).
thf(f3075,plain,
! [X0: $i] :
( ( $false
= ( v4 @ X0 ) )
| ( ( v1 @ X0 )
= $false )
| ( ( v3 @ X0 )
= $true )
| ( $false = $true ) ),
inference(superposition,[],[f3010,f793]) ).
thf(f3094,plain,
! [X0: $i] :
( ( $false
= ( v4 @ X0 ) )
| ( ( v1 @ X0 )
= $false )
| ( ( v3 @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[],[f3075]) ).
thf(f3177,plain,
! [X0: $i,X1: $i] :
( ( ( v3 @ X0 )
= $true )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $true
= ( v4 @ X1 ) )
| ( $true
= ( v2 @ X0 ) )
| ( $false
= ( rel_s4 @ X0 @ X0 ) )
| ( $false != $false ) ),
inference(equality_factoring,[],[f1560]) ).
thf(f3181,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ X0 @ X0 ) )
| ( $true
= ( v2 @ X0 ) )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( ( v3 @ X0 )
= $true )
| ( $true
= ( v4 @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f3177]) ).
thf(f3189,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $false = $true )
| ( ( v3 @ X0 )
= $true )
| ( $true
= ( v2 @ X0 ) )
| ( $true
= ( v4 @ X1 ) ) ),
inference(forward_demodulation,[],[f3181,f360]) ).
thf(f3190,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $true
= ( v4 @ X1 ) )
| ( ( v3 @ X0 )
= $true )
| ( $true
= ( v2 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f3189]) ).
thf(f3203,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ X0 @ X0 ) )
| ( $true
= ( v2 @ X0 ) )
| ( ( v1 @ X0 )
= $true )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( ( v2 @ X1 )
= $false )
| ( $false != $false ) ),
inference(equality_factoring,[],[f1889]) ).
thf(f3209,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( v2 @ X0 ) )
| ( ( v2 @ X1 )
= $false )
| ( ( v1 @ X0 )
= $true )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $false
= ( rel_s4 @ X0 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f3203]) ).
thf(f3215,plain,
! [X0: $i,X1: $i] :
( ( $false = $true )
| ( $true
= ( v2 @ X0 ) )
| ( ( v2 @ X1 )
= $false )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( ( v1 @ X0 )
= $true ) ),
inference(forward_demodulation,[],[f3209,f360]) ).
thf(f3216,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( v2 @ X0 ) )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( ( v1 @ X0 )
= $true )
| ( ( v2 @ X1 )
= $false ) ),
inference(trivial_inequality_removal,[],[f3215]) ).
thf(f3411,plain,
! [X0: $i] :
( ( $false = $true )
| ( ( v3 @ X0 )
= $false )
| ( $false
= ( v2 @ ( sK2 @ X0 ) ) )
| ( ( v4 @ ( sK2 @ X0 ) )
= $false ) ),
inference(superposition,[],[f2474,f372]) ).
thf(f3421,plain,
! [X0: $i] :
( ( $false
= ( v2 @ ( sK2 @ X0 ) ) )
| ( ( v3 @ X0 )
= $false )
| ( ( v4 @ ( sK2 @ X0 ) )
= $false ) ),
inference(trivial_inequality_removal,[],[f3411]) ).
thf(f3457,plain,
! [X0: $i] :
( ( ( v4 @ ( sK2 @ X0 ) )
= $false )
| ( $false = $true )
| ( ( v3 @ X0 )
= $false )
| ( ( v4 @ ( sK2 @ X0 ) )
= $false ) ),
inference(superposition,[],[f3421,f793]) ).
thf(f3482,plain,
! [X0: $i] :
( ( ( v4 @ ( sK2 @ X0 ) )
= $false )
| ( $false = $true )
| ( ( v3 @ X0 )
= $false ) ),
inference(duplicate_literal_removal,[],[f3457]) ).
thf(f3483,plain,
! [X0: $i] :
( ( ( v4 @ ( sK2 @ X0 ) )
= $false )
| ( ( v3 @ X0 )
= $false ) ),
inference(trivial_inequality_removal,[],[f3482]) ).
thf(f3625,plain,
! [X0: $i] :
( ( $false = $true )
| ( ( v3 @ X0 )
= $true )
| ( $true
= ( v2 @ X0 ) )
| ( ( v4 @ ( sK2 @ X0 ) )
= $true ) ),
inference(superposition,[],[f3190,f372]) ).
thf(f3629,plain,
! [X0: $i] :
( ( $true
= ( v4 @ X0 ) )
| ( ( v3 @ X0 )
= $true )
| ( $true
= ( v2 @ X0 ) )
| ( $false = $true ) ),
inference(superposition,[],[f360,f3190]) ).
thf(f3633,plain,
! [X0: $i] :
( ( $true
= ( v4 @ X0 ) )
| ( ( v3 @ X0 )
= $true )
| ( $true
= ( v2 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f3629]) ).
thf(f3634,plain,
! [X0: $i] :
( ( ( v4 @ ( sK2 @ X0 ) )
= $true )
| ( $true
= ( v2 @ X0 ) )
| ( ( v3 @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[],[f3625]) ).
thf(f3687,plain,
! [X0: $i] :
( ( ( v3 @ X0 )
= $true )
| ( ( v1 @ X0 )
= $false )
| ( ( v3 @ X0 )
= $true )
| ( $false = $true )
| ( $true
= ( v2 @ X0 ) ) ),
inference(superposition,[],[f3633,f3094]) ).
thf(f3721,plain,
! [X0: $i] :
( ( ( v1 @ X0 )
= $false )
| ( ( v3 @ X0 )
= $true )
| ( $false = $true )
| ( $true
= ( v2 @ X0 ) ) ),
inference(duplicate_literal_removal,[],[f3687]) ).
thf(f3722,plain,
! [X0: $i] :
( ( $true
= ( v2 @ X0 ) )
| ( ( v3 @ X0 )
= $true )
| ( ( v1 @ X0 )
= $false ) ),
inference(trivial_inequality_removal,[],[f3721]) ).
thf(f3811,plain,
! [X0: $i] :
( ( ( v3 @ X0 )
= $true )
| ( ( v3 @ X0 )
= $true )
| ( ( v1 @ X0 )
= $false )
| ( $false = $true )
| ( ( v1 @ X0 )
= $false ) ),
inference(superposition,[],[f3010,f3722]) ).
thf(f3817,plain,
! [X0: $i] :
( ( $false = $true )
| ( ( v3 @ X0 )
= $true )
| ( ( v1 @ X0 )
= $false ) ),
inference(duplicate_literal_removal,[],[f3811]) ).
thf(f3818,plain,
! [X0: $i] :
( ( ( v3 @ X0 )
= $true )
| ( ( v1 @ X0 )
= $false ) ),
inference(trivial_inequality_removal,[],[f3817]) ).
thf(f3854,plain,
! [X0: $i] :
( ( ( v1 @ X0 )
= $false )
| ( $false = $true )
| ( ( v1 @ X0 )
= $false ) ),
inference(superposition,[],[f2882,f3818]) ).
thf(f3862,plain,
! [X0: $i] :
( ( ( v1 @ X0 )
= $false )
| ( $false = $true ) ),
inference(duplicate_literal_removal,[],[f3854]) ).
thf(f3863,plain,
! [X0: $i] :
( ( v1 @ X0 )
= $false ),
inference(trivial_inequality_removal,[],[f3862]) ).
thf(f4177,plain,
! [X0: $i,X1: $i] :
( ( ( v2 @ X1 )
= $false )
| ( $false = $true )
| ( $true
= ( v2 @ X0 ) )
| ( $false
= ( rel_s4 @ X0 @ X1 ) ) ),
inference(forward_demodulation,[],[f3216,f3863]) ).
thf(f4178,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $true
= ( v2 @ X0 ) )
| ( ( v2 @ X1 )
= $false ) ),
inference(trivial_inequality_removal,[],[f4177]) ).
thf(f4187,plain,
! [X0: $i] :
( ( $false = $true )
| ( $true
= ( v2 @ X0 ) )
| ( $false
= ( v2 @ ( sK2 @ X0 ) ) ) ),
inference(superposition,[],[f372,f4178]) ).
thf(f4191,plain,
! [X0: $i] :
( ( $false
= ( v2 @ ( sK2 @ X0 ) ) )
| ( $true
= ( v2 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f4187]) ).
thf(f4237,plain,
! [X0: $i] :
( ( $true
= ( v2 @ X0 ) )
| ( $false
= ( v3 @ ( sK2 @ X0 ) ) )
| ( $false = $true ) ),
inference(superposition,[],[f4191,f988]) ).
thf(f4252,plain,
! [X0: $i] :
( ( ( v4 @ ( sK2 @ X0 ) )
= $false )
| ( $false = $true )
| ( $true
= ( v2 @ X0 ) ) ),
inference(superposition,[],[f793,f4191]) ).
thf(f4258,plain,
! [X0: $i] :
( ( ( v4 @ ( sK2 @ X0 ) )
= $false )
| ( $true
= ( v2 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f4252]) ).
thf(f4268,plain,
! [X0: $i] :
( ( $false
= ( v3 @ ( sK2 @ X0 ) ) )
| ( $true
= ( v2 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f4237]) ).
thf(f4342,plain,
! [X0: $i] :
( ( ( v3 @ X0 )
= $true )
| ( $true
= ( v2 @ X0 ) )
| ( $true
= ( v2 @ X0 ) )
| ( $false = $true ) ),
inference(superposition,[],[f3634,f4258]) ).
thf(f4349,plain,
! [X0: $i] :
( ( $true
= ( v2 @ X0 ) )
| ( ( v3 @ X0 )
= $true )
| ( $false = $true ) ),
inference(duplicate_literal_removal,[],[f4342]) ).
thf(f4350,plain,
! [X0: $i] :
( ( $true
= ( v2 @ X0 ) )
| ( ( v3 @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[],[f4349]) ).
thf(f4383,plain,
! [X0: $i] :
( ( $true
= ( v3 @ ( sK2 @ X0 ) ) )
| ( $false = $true )
| ( $true
= ( v2 @ X0 ) ) ),
inference(superposition,[],[f4350,f4191]) ).
thf(f4392,plain,
! [X0: $i] :
( ( $true
= ( v3 @ ( sK2 @ X0 ) ) )
| ( $true
= ( v2 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f4383]) ).
thf(f4524,plain,
! [X0: $i] :
( ( $true
= ( v2 @ X0 ) )
| ( $true
= ( v2 @ X0 ) )
| ( $false = $true ) ),
inference(superposition,[],[f4268,f4392]) ).
thf(f4540,plain,
! [X0: $i] :
( ( $false = $true )
| ( $true
= ( v2 @ X0 ) ) ),
inference(duplicate_literal_removal,[],[f4524]) ).
thf(f4541,plain,
! [X0: $i] :
( $true
= ( v2 @ X0 ) ),
inference(trivial_inequality_removal,[],[f4540]) ).
thf(f4555,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $false
= ( v2 @ ( sK2 @ X0 ) ) )
| ( ( rel_s4 @ X2 @ X3 )
= $false )
| ( $false
= ( rel_s4 @ X2 @ X4 ) )
| ( $false
= ( rel_s4 @ X2 @ X0 ) )
| ( $true
= ( v4 @ X1 ) )
| ( $true
= ( v1 @ X4 ) )
| ( $false
= ( rel_s4 @ X3 @ X1 ) )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f1749,f3863]) ).
thf(f4556,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
= ( v4 @ X1 ) )
| ( $true
= ( v1 @ X4 ) )
| ( $false
= ( rel_s4 @ X2 @ X0 ) )
| ( ( rel_s4 @ X2 @ X3 )
= $false )
| ( $false
= ( v2 @ ( sK2 @ X0 ) ) )
| ( $false
= ( rel_s4 @ X3 @ X1 ) )
| ( $false
= ( rel_s4 @ X2 @ X4 ) ) ),
inference(trivial_inequality_removal,[],[f4555]) ).
thf(f4557,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $false
= ( v2 @ ( sK2 @ X0 ) ) )
| ( $true
= ( v4 @ X1 ) )
| ( $false
= ( rel_s4 @ X2 @ X0 ) )
| ( $false
= ( rel_s4 @ X2 @ X4 ) )
| ( $false = $true )
| ( $false
= ( rel_s4 @ X3 @ X1 ) )
| ( ( rel_s4 @ X2 @ X3 )
= $false ) ),
inference(forward_demodulation,[],[f4556,f3863]) ).
thf(f4558,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $false
= ( v2 @ ( sK2 @ X0 ) ) )
| ( $true
= ( v4 @ X1 ) )
| ( ( rel_s4 @ X2 @ X3 )
= $false )
| ( $false
= ( rel_s4 @ X2 @ X0 ) )
| ( $false
= ( rel_s4 @ X2 @ X4 ) )
| ( $false
= ( rel_s4 @ X3 @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f4557]) ).
thf(f4575,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $false
= ( rel_s4 @ X2 @ X4 ) )
| ( ( rel_s4 @ X2 @ X3 )
= $false )
| ( $false
= ( rel_s4 @ X3 @ X1 ) )
| ( $false = $true )
| ( $false
= ( rel_s4 @ X2 @ X0 ) )
| ( $true
= ( v4 @ X1 ) ) ),
inference(forward_demodulation,[],[f4558,f4541]) ).
thf(f4576,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $false
= ( rel_s4 @ X3 @ X1 ) )
| ( $false
= ( rel_s4 @ X2 @ X4 ) )
| ( ( rel_s4 @ X2 @ X3 )
= $false )
| ( $false
= ( rel_s4 @ X2 @ X0 ) )
| ( $true
= ( v4 @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f4575]) ).
thf(f4588,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( v4 @ X1 ) )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $false != $false )
| ( $false
= ( rel_s4 @ X0 @ X0 ) )
| ( $false
= ( rel_s4 @ X0 @ X2 ) ) ),
inference(equality_factoring,[],[f4576]) ).
thf(f4589,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ X0 @ X2 ) )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $true
= ( v4 @ X1 ) )
| ( $false
= ( rel_s4 @ X0 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f4588]) ).
thf(f4601,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ X0 @ X2 ) )
| ( $false = $true )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $true
= ( v4 @ X1 ) ) ),
inference(forward_demodulation,[],[f4589,f360]) ).
thf(f4602,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ X0 @ X2 ) )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $true
= ( v4 @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f4601]) ).
thf(f4645,plain,
! [X0: $i,X1: $i] :
( ( $false = $true )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $true
= ( v4 @ X1 ) ) ),
inference(superposition,[],[f360,f4602]) ).
thf(f4650,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $true
= ( v4 @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f4645]) ).
thf(f4660,plain,
! [X0: $i] :
( ( $false = $true )
| ( $true
= ( v4 @ X0 ) ) ),
inference(superposition,[],[f4650,f360]) ).
thf(f4673,plain,
! [X0: $i] :
( $true
= ( v4 @ X0 ) ),
inference(trivial_inequality_removal,[],[f4660]) ).
thf(f4679,plain,
! [X0: $i] :
( ( $false
= ( v2 @ X0 ) )
| ( ( v3 @ X0 )
= $true )
| ( $false = $true ) ),
inference(superposition,[],[f4673,f2912]) ).
thf(f4699,plain,
! [X0: $i] :
( ( $false = $true )
| ( ( v3 @ X0 )
= $false ) ),
inference(superposition,[],[f3483,f4673]) ).
thf(f4705,plain,
! [X0: $i] :
( ( v3 @ X0 )
= $false ),
inference(trivial_inequality_removal,[],[f4699]) ).
thf(f4710,plain,
! [X0: $i] :
( ( ( v3 @ X0 )
= $true )
| ( $false
= ( v2 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f4679]) ).
thf(f4732,plain,
! [X0: $i] :
( ( ( v3 @ X0 )
= $true )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f4710,f4541]) ).
thf(f4733,plain,
! [X0: $i] :
( ( v3 @ X0 )
= $true ),
inference(trivial_inequality_removal,[],[f4732]) ).
thf(f4803,plain,
$false = $true,
inference(forward_demodulation,[],[f4733,f4705]) ).
thf(f4804,plain,
$false,
inference(trivial_inequality_removal,[],[f4803]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN741^7 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n014.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 16:19:15 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.24 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
% 0.75/0.37 % (2865300)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.75/0.37 % (2865305)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3751705509:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.75/0.37 % (2865311)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.75/0.37 % (2865311)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
% 0.75/0.37 % (2865306)lrs+10_16_si=on:nwc=1.5:random_seed=1399579766:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.75/0.37 % (2865307)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=563086130:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.75/0.37 % (2865310)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2905723652:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.75/0.37 % (2865311)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=781271009:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.75/0.37 % (2865309)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=97374845:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.75/0.37 % (2865308)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=2622388275: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)
% 0.75/0.37 % (2865307)Instruction limit reached!
% 0.75/0.37 % (2865307)------------------------------
% 0.75/0.37 % (2865307)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.75/0.37 % (2865307)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.75/0.37 % (2865307)CaDiCaL version: 2.1.3
% 0.75/0.37 % (2865307)Termination reason: Instruction limit
% 0.75/0.37 % (2865307)Termination phase: shuffling
% 0.75/0.37 % (2865307)Time elapsed: 0.002 s
% 0.75/0.37 % (2865307)Peak memory usage: 9 MB
% 0.75/0.37 % (2865307)Instructions burned: 4 (million)
% 0.75/0.37 % (2865306)Instruction limit reached!
% 0.75/0.37 % (2865306)------------------------------
% 0.75/0.37 % (2865306)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.75/0.37 % (2865306)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.75/0.37 % (2865306)CaDiCaL version: 2.1.3
% 0.75/0.37 % (2865306)Termination reason: Instruction limit
% 0.75/0.37 % (2865306)Termination phase: Function definition elimination
% 0.75/0.37 % (2865306)Time elapsed: 0.007 s
% 0.75/0.37 % (2865306)Peak memory usage: 10 MB
% 0.75/0.37 % (2865306)Instructions burned: 18 (million)
% 0.75/0.37 % (2865309)Instruction limit reached!
% 0.75/0.37 % (2865309)------------------------------
% 0.75/0.37 % (2865309)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.75/0.37 % (2865309)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.75/0.37 % (2865309)CaDiCaL version: 2.1.3
% 0.75/0.37 % (2865309)Termination reason: Instruction limit
% 0.75/0.37 % (2865309)Termination phase: Saturation
% 0.75/0.37 % (2865309)Time elapsed: 0.012 s
% 0.75/0.37 % (2865309)Peak memory usage: 12 MB
% 0.75/0.37 % (2865309)Instructions burned: 24 (million)
% 0.75/0.37 % (2865305)Instruction limit reached!
% 0.75/0.37 % (2865305)------------------------------
% 0.75/0.37 % (2865305)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.75/0.37 % (2865305)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.75/0.37 % (2865305)CaDiCaL version: 2.1.3
% 0.75/0.37 % (2865305)Termination reason: Instruction limit
% 0.75/0.37 % (2865305)Termination phase: Saturation
% 0.75/0.37 % (2865305)Time elapsed: 0.022 s
% 0.75/0.37 % (2865305)Peak memory usage: 12 MB
% 0.75/0.37 % (2865305)Instructions burned: 89 (million)
% 0.75/0.37 % (2865319)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1686882253:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.75/0.37 % (2865319)Instruction limit reached!
% 0.75/0.37 % (2865319)------------------------------
% 0.75/0.37 % (2865319)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.75/0.39 % (2865319)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.75/0.39 % (2865319)CaDiCaL version: 2.1.3
% 0.75/0.39 % (2865319)Termination reason: Instruction limit
% 0.75/0.39 % (2865319)Termination phase: shuffling
% 0.75/0.39 % (2865319)Time elapsed: 0.001 s
% 0.75/0.39 % (2865319)Peak memory usage: 9 MB
% 0.75/0.39 % (2865319)Instructions burned: 2 (million)
% 0.75/0.39 % (2865322)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2804281638:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.75/0.39 % (2865320)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=917830429:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.75/0.39 % (2865322)Instruction limit reached!
% 0.75/0.39 % (2865322)------------------------------
% 0.75/0.39 % (2865322)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.75/0.39 % (2865322)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.75/0.39 % (2865322)CaDiCaL version: 2.1.3
% 0.75/0.39 % (2865322)Termination reason: Instruction limit
% 0.75/0.39 % (2865322)Termination phase: SInE selection
% 0.75/0.39 % (2865322)Time elapsed: 0.003 s
% 0.75/0.39 % (2865322)Peak memory usage: 10 MB
% 0.75/0.39 % (2865322)Instructions burned: 14 (million)
% 0.75/0.39 % (2865321)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.75/0.39 % (2865320)Instruction limit reached!
% 0.75/0.39 % (2865320)------------------------------
% 0.75/0.39 % (2865320)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.75/0.39 % (2865320)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.75/0.39 % (2865320)CaDiCaL version: 2.1.3
% 0.75/0.39 % (2865320)Termination reason: Instruction limit
% 0.75/0.39 % (2865320)Termination phase: shuffling
% 0.75/0.39 % (2865320)Time elapsed: 0.003 s
% 0.75/0.39 % (2865320)Peak memory usage: 9 MB
% 0.75/0.39 % (2865320)Instructions burned: 8 (million)
% 0.75/0.39 % (2865321)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3067022356:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.75/0.39 % (2865310)Instruction limit reached!
% 0.75/0.39 % (2865310)------------------------------
% 0.75/0.39 % (2865310)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.75/0.39 % (2865310)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.75/0.39 % (2865310)CaDiCaL version: 2.1.3
% 0.75/0.39 % (2865310)Termination reason: Instruction limit
% 0.75/0.39 % (2865310)Termination phase: Saturation
% 0.75/0.39 % (2865310)Time elapsed: 0.032 s
% 0.75/0.39 % (2865310)Peak memory usage: 12 MB
% 0.75/0.39 % (2865310)Instructions burned: 76 (million)
% 0.75/0.39 % (2865321)Instruction limit reached!
% 0.75/0.39 % (2865321)------------------------------
% 0.75/0.39 % (2865321)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.75/0.39 % (2865321)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.75/0.39 % (2865321)CaDiCaL version: 2.1.3
% 0.75/0.39 % (2865321)Termination reason: Instruction limit
% 0.75/0.39 % (2865321)Termination phase: Property scanning
% 0.75/0.39 % (2865321)Time elapsed: 0.003 s
% 0.75/0.39 % (2865321)Peak memory usage: 9 MB
% 0.75/0.39 % (2865321)Instructions burned: 7 (million)
% 0.75/0.39 % (2865327)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=2668338756:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.75/0.39 % (2865324)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
% 0.75/0.39 % (2865324)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.75/0.39 % (2865324)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2224231920:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.75/0.39 % (2865330)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.75/0.41 % (2865328)lrs+10_1_si=on:cs=on:random_seed=3587094418:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.75/0.41 % (2865330)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=2210999388:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.75/0.41 % (2865328)Instruction limit reached!
% 0.75/0.41 % (2865328)------------------------------
% 0.75/0.41 % (2865328)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.75/0.41 % (2865328)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.75/0.41 % (2865328)CaDiCaL version: 2.1.3
% 0.75/0.41 % (2865328)Termination reason: Instruction limit
% 0.75/0.41 % (2865328)Termination phase: Property scanning
% 0.75/0.41 % (2865328)Time elapsed: 0.004 s
% 0.75/0.41 % (2865328)Peak memory usage: 10 MB
% 0.75/0.41 % (2865328)Instructions burned: 10 (million)
% 0.75/0.41 % (2865331)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=2715650534:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.75/0.41 % (2865330)Instruction limit reached!
% 0.75/0.41 % (2865330)------------------------------
% 0.75/0.41 % (2865330)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.75/0.41 % (2865330)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.75/0.41 % (2865330)CaDiCaL version: 2.1.3
% 0.75/0.41 % (2865330)Termination reason: Instruction limit
% 0.75/0.41 % (2865330)Termination phase: Property scanning
% 0.75/0.41 % (2865330)Time elapsed: 0.003 s
% 0.75/0.41 % (2865330)Peak memory usage: 9 MB
% 0.75/0.41 % (2865330)Instructions burned: 7 (million)
% 0.75/0.41 % (2865324)Instruction limit reached!
% 0.75/0.41 % (2865324)------------------------------
% 0.75/0.41 % (2865324)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.75/0.41 % (2865324)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.75/0.41 % (2865324)CaDiCaL version: 2.1.3
% 0.75/0.41 % (2865324)Termination reason: Instruction limit
% 0.75/0.41 % (2865324)Termination phase: Saturation
% 0.75/0.41 % (2865324)Time elapsed: 0.013 s
% 0.75/0.41 % (2865324)Peak memory usage: 11 MB
% 0.75/0.41 % (2865324)Instructions burned: 29 (million)
% 0.75/0.41 % (2865327)Instruction limit reached!
% 0.75/0.41 % (2865327)------------------------------
% 0.75/0.41 % (2865327)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.75/0.41 % (2865327)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.75/0.41 % (2865327)CaDiCaL version: 2.1.3
% 0.75/0.41 % (2865327)Termination reason: Instruction limit
% 0.75/0.41 % (2865327)Termination phase: Saturation
% 0.75/0.41 % (2865327)Time elapsed: 0.021 s
% 0.75/0.41 % (2865327)Peak memory usage: 12 MB
% 0.75/0.41 % (2865327)Instructions burned: 87 (million)
% 0.75/0.41 % (2865331)Refutation not found, incomplete strategy
% 0.75/0.41 % (2865331)------------------------------
% 0.75/0.41 % (2865331)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.75/0.41 % (2865331)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.75/0.41 % (2865331)CaDiCaL version: 2.1.3
% 0.75/0.41 % (2865331)Termination reason: Refutation not found, incomplete strategy
% 0.75/0.41 % (2865331)Time elapsed: 0.006 s
% 0.75/0.41 % (2865331)Peak memory usage: 12 MB
% 0.75/0.41 % (2865331)Instructions burned: 14 (million)
% 0.75/0.41 % (2865331)------------------------------
% 0.75/0.41 % (2865331)------------------------------
% 0.75/0.41 % (2865340)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=1795415799:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/327Mi)
% 0.75/0.41 % (2865311)Instruction limit reached!
% 0.75/0.41 % (2865311)------------------------------
% 0.75/0.41 % (2865311)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.75/0.41 % (2865311)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.75/0.41 % (2865311)CaDiCaL version: 2.1.3
% 0.75/0.41 % (2865311)Termination reason: Instruction limit
% 0.75/0.41 % (2865311)Termination phase: Saturation
% 0.75/0.41 % (2865311)Time elapsed: 0.072 s
% 0.75/0.41 % (2865311)Peak memory usage: 12 MB
% 0.75/0.41 % (2865311)Instructions burned: 159 (million)
% 0.75/0.41 % (2865337)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=3411003989:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.75/0.41 % (2865338)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=1288029018:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/25Mi)
% 0.75/0.45 % (2865339)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=1005531632:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2999 on theBenchmark for (2999ds/14Mi)
% 0.75/0.45 % (2865340)Refutation not found, incomplete strategy
% 0.75/0.45 % (2865340)------------------------------
% 0.75/0.45 % (2865340)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.75/0.45 % (2865340)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.75/0.45 % (2865340)CaDiCaL version: 2.1.3
% 0.75/0.45 % (2865340)Termination reason: Refutation not found, incomplete strategy
% 0.75/0.45 % (2865340)Time elapsed: 0.010 s
% 0.75/0.45 % (2865340)Peak memory usage: 12 MB
% 0.75/0.45 % (2865340)Instructions burned: 40 (million)
% 0.75/0.45 % (2865340)------------------------------
% 0.75/0.45 % (2865340)------------------------------
% 0.75/0.45 % (2865337)Refutation not found, incomplete strategy
% 0.75/0.45 % (2865337)------------------------------
% 0.75/0.45 % (2865337)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.75/0.45 % (2865337)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.75/0.45 % (2865337)CaDiCaL version: 2.1.3
% 0.75/0.45 % (2865337)Termination reason: Refutation not found, incomplete strategy
% 0.75/0.45 % (2865337)Time elapsed: 0.011 s
% 0.75/0.45 % (2865337)Peak memory usage: 12 MB
% 0.75/0.45 % (2865337)Instructions burned: 25 (million)
% 0.75/0.45 % (2865339)Instruction limit reached!
% 0.75/0.45 % (2865339)------------------------------
% 0.75/0.45 % (2865339)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.75/0.45 % (2865339)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.75/0.45 % (2865339)CaDiCaL version: 2.1.3
% 0.75/0.45 % (2865339)Termination reason: Instruction limit
% 0.75/0.45 % (2865339)Termination phase: Function definition elimination
% 0.75/0.45 % (2865339)Time elapsed: 0.008 s
% 0.75/0.45 % (2865339)Peak memory usage: 11 MB
% 0.75/0.45 % (2865339)Instructions burned: 20 (million)
% 0.75/0.45 % (2865337)------------------------------
% 0.75/0.45 % (2865337)------------------------------
% 0.75/0.45 % (2865341)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=2644528950:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 0.75/0.45 % (2865338)Instruction limit reached!
% 0.75/0.45 % (2865338)------------------------------
% 0.75/0.45 % (2865338)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.75/0.45 % (2865338)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.75/0.45 % (2865338)CaDiCaL version: 2.1.3
% 0.75/0.45 % (2865338)Termination reason: Instruction limit
% 0.75/0.45 % (2865338)Termination phase: Saturation
% 0.75/0.45 % (2865338)Time elapsed: 0.012 s
% 0.75/0.45 % (2865338)Peak memory usage: 12 MB
% 0.75/0.45 % (2865338)Instructions burned: 25 (million)
% 0.75/0.45 % (2865343)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=3989115755: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)
% 0.75/0.45 % (2865341)Instruction limit reached!
% 0.75/0.45 % (2865341)------------------------------
% 0.75/0.45 % (2865341)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.75/0.45 % (2865341)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.75/0.45 % (2865341)CaDiCaL version: 2.1.3
% 0.75/0.45 % (2865341)Termination reason: Instruction limit
% 0.75/0.45 % (2865341)Termination phase: Property scanning
% 0.75/0.45 % (2865341)Time elapsed: 0.006 s
% 0.75/0.45 % (2865341)Peak memory usage: 10 MB
% 0.75/0.45 % (2865341)Instructions burned: 15 (million)
% 0.75/0.45 % (2865343)Instruction limit reached!
% 0.75/0.45 % (2865343)------------------------------
% 0.75/0.45 % (2865343)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.75/0.45 % (2865343)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.75/0.45 % (2865343)CaDiCaL version: 2.1.3
% 0.75/0.45 % (2865343)Termination reason: Instruction limit
% 0.75/0.45 % (2865343)Termination phase: shuffling
% 0.75/0.45 % (2865343)Time elapsed: 0.002 s
% 0.75/0.45 % (2865343)Peak memory usage: 10 MB
% 0.75/0.45 % (2865343)Instructions burned: 5 (million)
% 0.75/0.45 % (2865348)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=1079264085:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.47/0.48 % (2865347)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=713176528:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.47/0.48 % (2865348)Instruction limit reached!
% 1.47/0.48 % (2865348)------------------------------
% 1.47/0.48 % (2865348)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.47/0.48 % (2865348)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.47/0.48 % (2865348)CaDiCaL version: 2.1.3
% 1.47/0.48 % (2865348)Termination reason: Instruction limit
% 1.47/0.48 % (2865348)Termination phase: Property scanning
% 1.47/0.48 % (2865348)Time elapsed: 0.005 s
% 1.47/0.48 % (2865348)Peak memory usage: 11 MB
% 1.47/0.48 % (2865348)Instructions burned: 26 (million)
% 1.47/0.48 % (2865351)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
% 1.47/0.48 % (2865351)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 1.47/0.48 % (2865350)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=3630877818:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.47/0.48 % (2865351)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=2726842118:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.47/0.48 % (2865353)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.47/0.48 % (2865347)Instruction limit reached!
% 1.47/0.48 % (2865347)------------------------------
% 1.47/0.48 % (2865347)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.47/0.48 % (2865347)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.47/0.48 % (2865347)CaDiCaL version: 2.1.3
% 1.47/0.48 % (2865347)Termination reason: Instruction limit
% 1.47/0.48 % (2865347)Termination phase: Property scanning
% 1.47/0.48 % (2865347)Time elapsed: 0.010 s
% 1.47/0.48 % (2865347)Peak memory usage: 10 MB
% 1.47/0.48 % (2865347)Instructions burned: 26 (million)
% 1.47/0.48 % (2865353)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=525114077:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.47/0.48 % (2865357)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=1351928073:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 1.47/0.48 % (2865354)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=3681983924:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 1.47/0.48 % (2865351)Instruction limit reached!
% 1.47/0.48 % (2865351)------------------------------
% 1.47/0.48 % (2865351)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.47/0.48 % (2865351)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.47/0.48 % (2865351)CaDiCaL version: 2.1.3
% 1.47/0.48 % (2865351)Termination reason: Instruction limit
% 1.47/0.48 % (2865351)Termination phase: Function definition elimination
% 1.47/0.48 % (2865351)Time elapsed: 0.006 s
% 1.47/0.48 % (2865351)Peak memory usage: 10 MB
% 1.47/0.48 % (2865351)Instructions burned: 15 (million)
% 1.47/0.48 % (2865357)Instruction limit reached!
% 1.47/0.48 % (2865357)------------------------------
% 1.47/0.48 % (2865357)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.47/0.48 % (2865357)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.47/0.48 % (2865357)CaDiCaL version: 2.1.3
% 1.47/0.48 % (2865357)Termination reason: Instruction limit
% 1.47/0.48 % (2865357)Termination phase: Property scanning
% 1.47/0.48 % (2865357)Time elapsed: 0.002 s
% 1.47/0.48 % (2865357)Peak memory usage: 10 MB
% 1.47/0.48 % (2865357)Instructions burned: 10 (million)
% 1.47/0.48 % (2865353)Instruction limit reached!
% 1.47/0.48 % (2865353)------------------------------
% 1.47/0.48 % (2865353)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.47/0.53 % (2865353)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.47/0.53 % (2865353)CaDiCaL version: 2.1.3
% 1.47/0.53 % (2865353)Termination reason: Instruction limit
% 1.47/0.53 % (2865353)Termination phase: Property scanning
% 1.47/0.53 % (2865353)Time elapsed: 0.004 s
% 1.47/0.53 % (2865353)Peak memory usage: 10 MB
% 1.47/0.53 % (2865353)Instructions burned: 10 (million)
% 1.47/0.53 % (2865365)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=1774011484:i=1240:rtra=on:ixr=off_2998 on theBenchmark for (2998ds/1240Mi)
% 1.47/0.53 % (2865360)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=3688412972:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.47/0.53 % (2865354)Instruction limit reached!
% 1.47/0.53 % (2865354)------------------------------
% 1.47/0.53 % (2865354)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.47/0.53 % (2865354)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.47/0.53 % (2865354)CaDiCaL version: 2.1.3
% 1.47/0.53 % (2865354)Termination reason: Instruction limit
% 1.47/0.53 % (2865354)Termination phase: Saturation
% 1.47/0.53 % (2865354)Time elapsed: 0.016 s
% 1.47/0.53 % (2865354)Peak memory usage: 12 MB
% 1.47/0.53 % (2865354)Instructions burned: 32 (million)
% 1.47/0.53 % (2865364)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=1790157612:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/20Mi)
% 1.47/0.53 % (2865366)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=1467505318:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/143Mi)
% 1.47/0.53 % (2865350)Instruction limit reached!
% 1.47/0.53 % (2865350)------------------------------
% 1.47/0.53 % (2865350)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.47/0.53 % (2865350)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.47/0.53 % (2865350)CaDiCaL version: 2.1.3
% 1.47/0.53 % (2865350)Termination reason: Instruction limit
% 1.47/0.53 % (2865350)Termination phase: Saturation
% 1.47/0.53 % (2865350)Time elapsed: 0.030 s
% 1.47/0.53 % (2865350)Peak memory usage: 12 MB
% 1.47/0.53 % (2865350)Instructions burned: 61 (million)
% 1.47/0.53 % (2865360)Instruction limit reached!
% 1.47/0.53 % (2865360)------------------------------
% 1.47/0.53 % (2865360)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.47/0.53 % (2865360)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.47/0.53 % (2865360)CaDiCaL version: 2.1.3
% 1.47/0.53 % (2865360)Termination reason: Instruction limit
% 1.47/0.53 % (2865360)Termination phase: Property scanning
% 1.47/0.53 % (2865360)Time elapsed: 0.009 s
% 1.47/0.53 % (2865360)Peak memory usage: 10 MB
% 1.47/0.53 % (2865360)Instructions burned: 24 (million)
% 1.47/0.53 % (2865364)Instruction limit reached!
% 1.47/0.53 % (2865364)------------------------------
% 1.47/0.53 % (2865364)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.47/0.53 % (2865364)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.47/0.53 % (2865364)CaDiCaL version: 2.1.3
% 1.47/0.53 % (2865364)Termination reason: Instruction limit
% 1.47/0.53 % (2865364)Termination phase: Property scanning
% 1.47/0.53 % (2865364)Time elapsed: 0.008 s
% 1.47/0.53 % (2865364)Peak memory usage: 11 MB
% 1.47/0.53 % (2865364)Instructions burned: 21 (million)
% 1.47/0.53 % (2865369)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=3607739178:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/193Mi)
% 1.47/0.53 % (2865373)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.47/0.53 % (2865372)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3945553946:i=42:hud=10:rtra=on_2998 on theBenchmark for (2998ds/42Mi)
% 1.47/0.53 % (2865373)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=247559421:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2998 on theBenchmark for (2998ds/7Mi)
% 1.47/0.53 % (2865374)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=2727938029:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/181Mi)
% 1.47/0.53 % (2865373)Instruction limit reached!
% 1.47/0.53 % (2865373)------------------------------
% 2.15/0.61 % (2865373)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.15/0.61 % (2865373)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.15/0.61 % (2865373)CaDiCaL version: 2.1.3
% 2.15/0.61 % (2865373)Termination reason: Instruction limit
% 2.15/0.61 % (2865373)Termination phase: Property scanning
% 2.15/0.61 % (2865373)Time elapsed: 0.003 s
% 2.15/0.61 % (2865373)Peak memory usage: 9 MB
% 2.15/0.61 % (2865373)Instructions burned: 7 (million)
% 2.15/0.61 % (2865374)Refutation not found, incomplete strategy
% 2.15/0.61 % (2865374)------------------------------
% 2.15/0.61 % (2865374)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.15/0.61 % (2865374)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.15/0.61 % (2865374)CaDiCaL version: 2.1.3
% 2.15/0.61 % (2865374)Termination reason: Refutation not found, incomplete strategy
% 2.15/0.61 % (2865374)Time elapsed: 0.007 s
% 2.15/0.61 % (2865374)Peak memory usage: 12 MB
% 2.15/0.61 % (2865374)Instructions burned: 14 (million)
% 2.15/0.61 % (2865374)------------------------------
% 2.15/0.61 % (2865374)------------------------------
% 2.15/0.61 % (2865369)Refutation not found, incomplete strategy
% 2.15/0.61 % (2865369)------------------------------
% 2.15/0.61 % (2865369)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.15/0.61 % (2865369)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.15/0.61 % (2865369)CaDiCaL version: 2.1.3
% 2.15/0.61 % (2865369)Termination reason: Refutation not found, incomplete strategy
% 2.15/0.61 % (2865369)Time elapsed: 0.019 s
% 2.15/0.61 % (2865369)Peak memory usage: 12 MB
% 2.15/0.61 % (2865369)Instructions burned: 38 (million)
% 2.15/0.61 % (2865369)------------------------------
% 2.15/0.61 % (2865369)------------------------------
% 2.15/0.61 % (2865372)Instruction limit reached!
% 2.15/0.61 % (2865372)------------------------------
% 2.15/0.61 % (2865372)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.15/0.61 % (2865372)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.15/0.61 % (2865372)CaDiCaL version: 2.1.3
% 2.15/0.61 % (2865372)Termination reason: Instruction limit
% 2.15/0.61 % (2865372)Termination phase: Saturation
% 2.15/0.61 % (2865372)Time elapsed: 0.017 s
% 2.15/0.61 % (2865372)Peak memory usage: 11 MB
% 2.15/0.61 % (2865372)Instructions burned: 43 (million)
% 2.15/0.61 % (2865379)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=3175635251: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)
% 2.15/0.61 % (2865380)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 2.15/0.61 % (2865380)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=1830426374:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2997 on theBenchmark for (2997ds/6Mi)
% 2.15/0.61 % (2865381)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=981625340:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2997 on theBenchmark for (2997ds/22Mi)
% 2.15/0.61 % (2865380)Instruction limit reached!
% 2.15/0.61 % (2865380)------------------------------
% 2.15/0.61 % (2865380)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.15/0.61 % (2865380)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.15/0.61 % (2865380)CaDiCaL version: 2.1.3
% 2.15/0.61 % (2865380)Termination reason: Instruction limit
% 2.15/0.61 % (2865380)Termination phase: Property scanning
% 2.15/0.61 % (2865380)Time elapsed: 0.003 s
% 2.15/0.61 % (2865380)Peak memory usage: 10 MB
% 2.15/0.61 % (2865380)Instructions burned: 7 (million)
% 2.15/0.61 % (2865382)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=4085665396:i=19:add=on:rtra=on_2997 on theBenchmark for (2997ds/19Mi)
% 2.15/0.61 % (2865379)Refutation not found, incomplete strategy
% 2.15/0.61 % (2865379)------------------------------
% 2.15/0.61 % (2865379)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.15/0.61 % (2865379)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.15/0.61 % (2865379)CaDiCaL version: 2.1.3
% 2.15/0.61 % (2865379)Termination reason: Refutation not found, incomplete strategy
% 2.15/0.61 % (2865379)Time elapsed: 0.013 s
% 2.60/0.68 % (2865379)Peak memory usage: 12 MB
% 2.60/0.68 % (2865379)Instructions burned: 30 (million)
% 2.60/0.68 % (2865379)------------------------------
% 2.60/0.68 % (2865379)------------------------------
% 2.60/0.68 % (2865381)Instruction limit reached!
% 2.60/0.68 % (2865381)------------------------------
% 2.60/0.68 % (2865381)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.60/0.68 % (2865381)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.60/0.68 % (2865381)CaDiCaL version: 2.1.3
% 2.60/0.68 % (2865381)Termination reason: Instruction limit
% 2.60/0.68 % (2865381)Termination phase: Property scanning
% 2.60/0.68 % (2865381)Time elapsed: 0.010 s
% 2.60/0.68 % (2865381)Peak memory usage: 11 MB
% 2.60/0.68 % (2865381)Instructions burned: 24 (million)
% 2.60/0.68 % (2865382)Instruction limit reached!
% 2.60/0.68 % (2865382)------------------------------
% 2.60/0.68 % (2865382)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.60/0.68 % (2865382)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.60/0.68 % (2865382)CaDiCaL version: 2.1.3
% 2.60/0.68 % (2865382)Termination reason: Instruction limit
% 2.60/0.68 % (2865382)Termination phase: Property scanning
% 2.60/0.68 % (2865382)Time elapsed: 0.008 s
% 2.60/0.68 % (2865382)Peak memory usage: 10 MB
% 2.60/0.68 % (2865382)Instructions burned: 21 (million)
% 2.60/0.68 % (2865366)Instruction limit reached!
% 2.60/0.68 % (2865366)------------------------------
% 2.60/0.68 % (2865366)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.60/0.68 % (2865366)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.60/0.68 % (2865366)CaDiCaL version: 2.1.3
% 2.60/0.68 % (2865366)Termination reason: Instruction limit
% 2.60/0.68 % (2865366)Termination phase: Saturation
% 2.60/0.68 % (2865366)Time elapsed: 0.066 s
% 2.60/0.68 % (2865366)Peak memory usage: 12 MB
% 2.60/0.68 % (2865366)Instructions burned: 145 (million)
% 2.60/0.68 % (2865387)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=3879205679:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/316Mi)
% 2.60/0.68 % (2865388)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=2467875372: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)
% 2.60/0.68 % (2865389)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=3769420255: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)
% 2.60/0.68 % (2865390)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=1165254191:i=480:rtra=on_2997 on theBenchmark for (2997ds/480Mi)
% 2.60/0.68 % (2865391)dis+1010_40_sil=128000:si=on:uwa=off:nwc=1:sac=on:chr=on:avsqc=3:random_seed=4251443976:avsq=on:i=21:avsqr=8,1:kws=frequency:fgj=on:bd=all:rtra=on:fe=axiom:ntd=on_2997 on theBenchmark for (2997ds/21Mi)
% 2.60/0.68 % (2865391)Instruction limit reached!
% 2.60/0.68 % (2865391)------------------------------
% 2.60/0.68 % (2865391)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.60/0.68 % (2865391)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.60/0.68 % (2865391)CaDiCaL version: 2.1.3
% 2.60/0.68 % (2865391)Termination reason: Instruction limit
% 2.60/0.68 % (2865391)Termination phase: Property scanning
% 2.60/0.68 % (2865391)Time elapsed: 0.008 s
% 2.60/0.68 % (2865391)Peak memory usage: 10 MB
% 2.60/0.68 % (2865391)Instructions burned: 21 (million)
% 2.60/0.68 % (2865390)Refutation not found, incomplete strategy
% 2.60/0.68 % (2865390)------------------------------
% 2.60/0.68 % (2865390)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.60/0.68 % (2865390)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.60/0.68 % (2865390)CaDiCaL version: 2.1.3
% 2.60/0.68 % (2865390)Termination reason: Refutation not found, incomplete strategy
% 2.60/0.68 % (2865390)Time elapsed: 0.011 s
% 2.60/0.68 % (2865390)Peak memory usage: 12 MB
% 2.60/0.68 % (2865390)Instructions burned: 26 (million)
% 2.60/0.68 % (2865390)------------------------------
% 2.60/0.68 % (2865390)------------------------------
% 2.60/0.68 % (2865389)Instruction limit reached!
% 3.01/0.72 % (2865389)------------------------------
% 3.01/0.72 % (2865389)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.01/0.72 % (2865389)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.01/0.72 % (2865389)CaDiCaL version: 2.1.3
% 3.01/0.72 % (2865389)Termination reason: Instruction limit
% 3.01/0.72 % (2865389)Termination phase: Saturation
% 3.01/0.72 % (2865389)Time elapsed: 0.019 s
% 3.01/0.72 % (2865389)Peak memory usage: 11 MB
% 3.01/0.72 % (2865389)Instructions burned: 47 (million)
% 3.01/0.72 % (2865397)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 3.01/0.72 % (2865397)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=3620545066:cts=off:uwa_fpi=on:i=200:av=off:fsr=off:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/200Mi)
% 3.01/0.72 % (2865398)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=677879882:s2a=on:i=13:kws=inv_frequency:bd=all:rtra=on_2997 on theBenchmark for (2997ds/13Mi)
% 3.01/0.72 % (2865398)Instruction limit reached!
% 3.01/0.72 % (2865398)------------------------------
% 3.01/0.72 % (2865398)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.01/0.72 % (2865398)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.01/0.72 % (2865398)CaDiCaL version: 2.1.3
% 3.01/0.72 % (2865398)Termination reason: Instruction limit
% 3.01/0.72 % (2865398)Termination phase: Property scanning
% 3.01/0.72 % (2865398)Time elapsed: 0.006 s
% 3.01/0.72 % (2865398)Peak memory usage: 10 MB
% 3.01/0.72 % (2865398)Instructions burned: 14 (million)
% 3.01/0.72 % (2865399)lrs+1010_1_anc=none:slsqr=1,2:sil=128000:cnfonf=conj_eager:sas=cadical:si=on:hi=on:uwa=one_side_interpreted:rp=on:nwc=2:slsqc=3:slsq=on:random_seed=2225320469:i=66:s2at=3:nm=2:rtra=on:rawr=on_2997 on theBenchmark for (2997ds/66Mi)
% 3.01/0.72 % (2865402)lrs+1004_128_si=on:sos=all:uwa=off:random_seed=315472771:i=51:fsr=off:rtra=on_2997 on theBenchmark for (2997ds/51Mi)
% 3.01/0.72 % (2865399)Instruction limit reached!
% 3.01/0.72 % (2865399)------------------------------
% 3.01/0.72 % (2865399)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.01/0.72 % (2865399)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.01/0.72 % (2865399)CaDiCaL version: 2.1.3
% 3.01/0.72 % (2865399)Termination reason: Instruction limit
% 3.01/0.72 % (2865399)Termination phase: Saturation
% 3.01/0.72 % (2865399)Time elapsed: 0.029 s
% 3.01/0.72 % (2865399)Peak memory usage: 12 MB
% 3.01/0.72 % (2865399)Instructions burned: 68 (million)
% 3.01/0.72 % (2865402)Instruction limit reached!
% 3.01/0.72 % (2865402)------------------------------
% 3.01/0.72 % (2865402)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.01/0.72 % (2865402)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.01/0.72 % (2865402)CaDiCaL version: 2.1.3
% 3.01/0.72 % (2865402)Termination reason: Instruction limit
% 3.01/0.72 % (2865402)Termination phase: Saturation
% 3.01/0.72 % (2865402)Time elapsed: 0.021 s
% 3.01/0.72 % (2865402)Peak memory usage: 12 MB
% 3.01/0.72 % (2865402)Instructions burned: 52 (million)
% 3.01/0.72 % (2865405)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=1204781823:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/31Mi)
% 3.01/0.72 % (2865308)Instruction limit reached!
% 3.01/0.72 % (2865308)------------------------------
% 3.01/0.72 % (2865308)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.01/0.72 % (2865308)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.01/0.72 % (2865308)CaDiCaL version: 2.1.3
% 3.01/0.72 % (2865308)Termination reason: Instruction limit
% 3.01/0.72 % (2865308)Termination phase: Saturation
% 3.01/0.72 % (2865308)Time elapsed: 0.307 s
% 3.01/0.72 % (2865308)Peak memory usage: 15 MB
% 3.01/0.72 % (2865308)Instructions burned: 634 (million)
% 3.01/0.72 % (2865406)dis+1010_40_to=kbo:tgt=full:fde=unused:si=on:sp=const_frequency:lma=off:cbe=off:uwa=interpreted_only:random_seed=3502317692:i=137:kws=precedence:bd=all:rtra=on:c=on:ntd=on_2996 on theBenchmark for (2996ds/137Mi)
% 3.01/0.72 % (2865405)Instruction limit reached!
% 3.01/0.72 % (2865405)------------------------------
% 3.01/0.72 % (2865405)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.01/0.72 % (2865405)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.01/0.77 % (2865405)CaDiCaL version: 2.1.3
% 3.01/0.77 % (2865405)Termination reason: Instruction limit
% 3.01/0.77 % (2865405)Termination phase: Saturation
% 3.01/0.77 % (2865405)Time elapsed: 0.013 s
% 3.01/0.77 % (2865405)Peak memory usage: 11 MB
% 3.01/0.77 % (2865405)Instructions burned: 32 (million)
% 3.01/0.77 % (2865408)dis+10_2_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_pi_sigma_gen:si=on:sp=occurrence:plsqr=5,1:bsr=on:plsql=on:random_seed=4162911124:cond=on:i=34:hud=10:nm=10:rtra=on_2996 on theBenchmark for (2996ds/34Mi)
% 3.01/0.77 % (2865397)Instruction limit reached!
% 3.01/0.77 % (2865397)------------------------------
% 3.01/0.77 % (2865397)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.01/0.77 % (2865397)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.01/0.77 % (2865397)CaDiCaL version: 2.1.3
% 3.01/0.77 % (2865397)Termination reason: Instruction limit
% 3.01/0.77 % (2865397)Termination phase: Saturation
% 3.01/0.77 % (2865397)Time elapsed: 0.085 s
% 3.01/0.77 % (2865397)Peak memory usage: 12 MB
% 3.01/0.77 % (2865397)Instructions burned: 200 (million)
% 3.01/0.77 % (2865410)lrs+1010_1_sil=128000:hsqc=4:si=on:sos=on:random_seed=3258027396:hsq=on:i=67:hsqaw=5:rtra=on:fe=abstraction:ntd=on_2996 on theBenchmark for (2996ds/67Mi)
% 3.01/0.77 % (2865408)Instruction limit reached!
% 3.01/0.77 % (2865408)------------------------------
% 3.01/0.77 % (2865408)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.01/0.77 % (2865408)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.01/0.77 % (2865408)CaDiCaL version: 2.1.3
% 3.01/0.77 % (2865408)Termination reason: Instruction limit
% 3.01/0.77 % (2865408)Termination phase: Saturation
% 3.01/0.77 % (2865408)Time elapsed: 0.015 s
% 3.01/0.77 % (2865408)Peak memory usage: 11 MB
% 3.01/0.77 % (2865408)Instructions burned: 36 (million)
% 3.01/0.77 % (2865412)WARNING Broken Constraint: if sine_generality_threshold(60) has been set then sine_selection(off) is not equal to off
% 3.01/0.77 % (2865412)dis+21_1_to=lpo:sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:bsr=on:random_seed=3058503978:i=180:hud=16:bd=all:fsr=off:rtra=on:sgt=60:ntd=on_2996 on theBenchmark for (2996ds/180Mi)
% 3.01/0.77 % (2865414)lrs+1002_1_sil=128000:si=on:uwa=off:random_seed=2115480899:st=2:i=246:sd=3:rtra=on:ss=axioms_2996 on theBenchmark for (2996ds/246Mi)
% 3.01/0.77 % (2865410)Refutation not found, incomplete strategy
% 3.01/0.77 % (2865410)------------------------------
% 3.01/0.77 % (2865410)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.01/0.77 % (2865410)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.01/0.77 % (2865410)CaDiCaL version: 2.1.3
% 3.01/0.77 % (2865410)Termination reason: Refutation not found, incomplete strategy
% 3.01/0.77 % (2865410)Time elapsed: 0.023 s
% 3.01/0.77 % (2865410)Peak memory usage: 12 MB
% 3.01/0.77 % (2865410)Instructions burned: 57 (million)
% 3.01/0.77 % (2865410)------------------------------
% 3.01/0.77 % (2865410)------------------------------
% 3.01/0.77 % (2865387)Instruction limit reached!
% 3.01/0.77 % (2865387)------------------------------
% 3.01/0.77 % (2865387)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.01/0.77 % (2865387)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.01/0.77 % (2865387)CaDiCaL version: 2.1.3
% 3.01/0.77 % (2865387)Termination reason: Instruction limit
% 3.01/0.77 % (2865387)Termination phase: Saturation
% 3.01/0.77 % (2865387)Time elapsed: 0.156 s
% 3.01/0.77 % (2865387)Peak memory usage: 14 MB
% 3.01/0.77 % (2865387)Instructions burned: 318 (million)
% 3.01/0.77 % (2865414)Refutation not found, incomplete strategy
% 3.01/0.77 % (2865414)------------------------------
% 3.01/0.77 % (2865414)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.01/0.77 % (2865414)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.01/0.77 % (2865414)CaDiCaL version: 2.1.3
% 3.01/0.77 % (2865414)Termination reason: Refutation not found, incomplete strategy
% 3.01/0.77 % (2865414)Time elapsed: 0.017 s
% 3.01/0.77 % (2865414)Peak memory usage: 12 MB
% 3.01/0.77 % (2865414)Instructions burned: 37 (million)
% 3.01/0.77 % (2865414)------------------------------
% 3.01/0.77 % (2865414)------------------------------
% 3.01/0.77 % (2865417)lrs+10_7_sil=128000:tgt=full:si=on:lma=off:uwa=off:nwc=1:sac=on:random_seed=3070704373:cond=on:i=96:bd=all:rtra=on_2995 on theBenchmark for (2995ds/96Mi)
% 3.01/0.77 % (2865418)lrs+10_1_sil=128000:si=on:sos=on:urr=on:random_seed=857510322:i=427:sd=1:rtra=on:ss=axioms_2995 on theBenchmark for (2995ds/427Mi)
% 3.62/0.82 % (2865406)Instruction limit reached!
% 3.62/0.82 % (2865406)------------------------------
% 3.62/0.82 % (2865406)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.62/0.82 % (2865406)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.62/0.82 % (2865406)CaDiCaL version: 2.1.3
% 3.62/0.82 % (2865406)Termination reason: Instruction limit
% 3.62/0.82 % (2865406)Termination phase: Saturation
% 3.62/0.82 % (2865406)Time elapsed: 0.071 s
% 3.62/0.82 % (2865406)Peak memory usage: 13 MB
% 3.62/0.82 % (2865406)Instructions burned: 139 (million)
% 3.62/0.82 % (2865418)Refutation not found, incomplete strategy
% 3.62/0.82 % (2865418)------------------------------
% 3.62/0.82 % (2865418)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.62/0.82 % (2865418)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.62/0.82 % (2865418)CaDiCaL version: 2.1.3
% 3.62/0.82 % (2865418)Termination reason: Refutation not found, incomplete strategy
% 3.62/0.82 % (2865418)Time elapsed: 0.006 s
% 3.62/0.82 % (2865418)Peak memory usage: 12 MB
% 3.62/0.82 % (2865418)Instructions burned: 14 (million)
% 3.62/0.82 % (2865418)------------------------------
% 3.62/0.82 % (2865418)------------------------------
% 3.62/0.82 % (2865419)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=1400433565:st=3:s2a=on:i=874:sd=3:rtra=on:ss=axioms_2995 on theBenchmark for (2995ds/874Mi)
% 3.62/0.82 % (2865422)dis+1010_4_sas=cadical:si=on:cbe=off:nwc=20:random_seed=3159088761:st=6:s2a=on:i=515:sd=2:nm=2:rtra=on:ss=axioms_2995 on theBenchmark for (2995ds/515Mi)
% 3.62/0.82 % (2865423)lrs+1002_1_cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:random_seed=2236774254:st=1.5:i=130:rtra=on:ss=axioms_2995 on theBenchmark for (2995ds/130Mi)
% 3.62/0.82 % (2865419)Refutation not found, incomplete strategy
% 3.62/0.82 % (2865419)------------------------------
% 3.62/0.82 % (2865419)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.62/0.82 % (2865419)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.62/0.82 % (2865419)CaDiCaL version: 2.1.3
% 3.62/0.82 % (2865419)Termination reason: Refutation not found, incomplete strategy
% 3.62/0.82 % (2865419)Time elapsed: 0.018 s
% 3.62/0.82 % (2865419)Peak memory usage: 12 MB
% 3.62/0.82 % (2865419)Instructions burned: 40 (million)
% 3.62/0.82 % (2865419)------------------------------
% 3.62/0.82 % (2865419)------------------------------
% 3.62/0.82 % (2865423)Refutation not found, incomplete strategy
% 3.62/0.82 % (2865423)------------------------------
% 3.62/0.82 % (2865423)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.62/0.82 % (2865423)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.62/0.82 % (2865423)CaDiCaL version: 2.1.3
% 3.62/0.82 % (2865423)Termination reason: Refutation not found, incomplete strategy
% 3.62/0.82 % (2865423)Time elapsed: 0.008 s
% 3.62/0.82 % (2865423)Peak memory usage: 12 MB
% 3.62/0.82 % (2865423)Instructions burned: 15 (million)
% 3.62/0.82 % (2865423)------------------------------
% 3.62/0.82 % (2865423)------------------------------
% 3.62/0.82 % (2865417)Instruction limit reached!
% 3.62/0.82 % (2865417)------------------------------
% 3.62/0.82 % (2865417)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.62/0.82 % (2865417)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.62/0.82 % (2865417)CaDiCaL version: 2.1.3
% 3.62/0.82 % (2865417)Termination reason: Instruction limit
% 3.62/0.82 % (2865417)Termination phase: Saturation
% 3.62/0.82 % (2865417)Time elapsed: 0.041 s
% 3.62/0.82 % (2865417)Peak memory usage: 12 MB
% 3.62/0.82 % (2865417)Instructions burned: 97 (million)
% 3.62/0.82 % (2865365)Instruction limit reached!
% 3.62/0.82 % (2865365)------------------------------
% 3.62/0.82 % (2865365)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.62/0.82 % (2865365)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.62/0.82 % (2865365)CaDiCaL version: 2.1.3
% 3.62/0.82 % (2865365)Termination reason: Instruction limit
% 3.62/0.82 % (2865365)Termination phase: Saturation
% 3.62/0.82 % (2865365)Time elapsed: 0.301 s
% 3.62/0.82 % (2865365)Peak memory usage: 14 MB
% 3.62/0.82 % (2865365)Instructions burned: 1242 (million)
% 3.62/0.82 % (2865412)Instruction limit reached!
% 3.62/0.82 % (2865412)------------------------------
% 3.62/0.82 % (2865412)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.62/0.82 % (2865412)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/0.93 % (2865412)CaDiCaL version: 2.1.3
% 3.91/0.93 % (2865412)Termination reason: Instruction limit
% 3.91/0.93 % (2865412)Termination phase: Saturation
% 3.91/0.93 % (2865412)Time elapsed: 0.079 s
% 3.91/0.93 % (2865412)Peak memory usage: 12 MB
% 3.91/0.93 % (2865412)Instructions burned: 181 (million)
% 3.91/0.93 % (2865430)lrs+10_5:1_to=lpo:sil=128000:si=on:uwa=one_side_interpreted:random_seed=1391363693:cts=off:i=95:piset=pi_sigma:bd=all:rtra=on:ntd=on_2995 on theBenchmark for (2995ds/95Mi)
% 3.91/0.93 % (2865427)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=1933915490:i=44:ep=R:rtra=on:ntd=on_2995 on theBenchmark for (2995ds/44Mi)
% 3.91/0.93 % (2865428)lrs+1010_8:1_sil=128000:fde=unused:e2e=on:si=on:sos=on:urr=on:uwa=one_side_constant:fd=off:random_seed=997360544:s2a=on:i=571:nm=16:rtra=on_2995 on theBenchmark for (2995ds/571Mi)
% 3.91/0.93 % (2865429)dis+1010_8_to=lpo:sil=128000:tgt=ground:si=on:sp=reverse_frequency:cbe=off:uwa=off:random_seed=1082920372:i=450:rtra=on:ixr=off:ntd=on_2995 on theBenchmark for (2995ds/450Mi)
% 3.91/0.93 % (2865431)lrs+1003_1_sil=128000:drc=off:cnfonf=lazy_pi_sigma_gen:si=on:uwa=one_side_interpreted:fd=off:rp=on:sac=on:random_seed=3163636178:s2a=on:i=65:add=on:bd=preordered:ins=10:rtra=on_2995 on theBenchmark for (2995ds/65Mi)
% 3.91/0.93 % (2865428)Refutation not found, incomplete strategy
% 3.91/0.93 % (2865428)------------------------------
% 3.91/0.93 % (2865428)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.91/0.93 % (2865428)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/0.93 % (2865428)CaDiCaL version: 2.1.3
% 3.91/0.93 % (2865428)Termination reason: Refutation not found, incomplete strategy
% 3.91/0.93 % (2865428)Time elapsed: 0.012 s
% 3.91/0.93 % (2865428)Peak memory usage: 12 MB
% 3.91/0.93 % (2865428)Instructions burned: 27 (million)
% 3.91/0.93 % (2865428)------------------------------
% 3.91/0.93 % (2865428)------------------------------
% 3.91/0.93 % (2865427)Instruction limit reached!
% 3.91/0.93 % (2865427)------------------------------
% 3.91/0.93 % (2865427)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.91/0.93 % (2865427)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/0.93 % (2865427)CaDiCaL version: 2.1.3
% 3.91/0.93 % (2865427)Termination reason: Instruction limit
% 3.91/0.93 % (2865427)Termination phase: Saturation
% 3.91/0.93 % (2865427)Time elapsed: 0.018 s
% 3.91/0.93 % (2865427)Peak memory usage: 11 MB
% 3.91/0.93 % (2865427)Instructions burned: 45 (million)
% 3.91/0.93 % (2865430)Instruction limit reached!
% 3.91/0.93 % (2865430)------------------------------
% 3.91/0.93 % (2865430)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.91/0.93 % (2865430)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/0.93 % (2865430)CaDiCaL version: 2.1.3
% 3.91/0.93 % (2865430)Termination reason: Instruction limit
% 3.91/0.93 % (2865430)Termination phase: Saturation
% 3.91/0.93 % (2865430)Time elapsed: 0.021 s
% 3.91/0.93 % (2865430)Peak memory usage: 12 MB
% 3.91/0.93 % (2865430)Instructions burned: 100 (million)
% 3.91/0.93 % (2865422)Refutation not found, incomplete strategy
% 3.91/0.93 % (2865422)------------------------------
% 3.91/0.93 % (2865422)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.91/0.93 % (2865422)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/0.93 % (2865422)CaDiCaL version: 2.1.3
% 3.91/0.93 % (2865422)Termination reason: Refutation not found, incomplete strategy
% 3.91/0.93 % (2865422)Time elapsed: 0.051 s
% 3.91/0.93 % (2865422)Peak memory usage: 13 MB
% 3.91/0.93 % (2865422)Instructions burned: 119 (million)
% 3.91/0.93 % (2865422)------------------------------
% 3.91/0.93 % (2865422)------------------------------
% 3.91/0.93 % (2865439)lrs+10_1_sil=128000:drc=off:si=on:fs=off:urr=on:uwa=one_side_constant:random_seed=2092459460:st=10:i=375:sd=1:bd=all:fsr=off:rtra=on:ss=axioms_2995 on theBenchmark for (2995ds/375Mi)
% 3.91/0.93 % (2865437)dis+1010_2:1_slsqr=2,1:to=lpo:plsq=on:cnfonf=lazy_pi_sigma_gen:si=on:sp=reverse_arity:acc=on:uwa=hol:fd=preordered:s2agt=16:flr=on:pe=on:slsq=on:random_seed=2248482369:uwa_fpi=on:avsq=on:s2a=on:cond=fast:i=105:s2at=1.5:aac=none:fgj=on:piset=and:hud=3:fsr=off:rtra=on:er=filter:rawr=on_2995 on theBenchmark for (2995ds/105Mi)
% 3.91/0.93 % (2865438)dis+10_4:1_sfv=off:to=kbo:fde=unused:cnfonf=off:sas=cadical:e2e=on:si=on:sp=occurrence:acc=on:uwa=off:fd=preordered:foolp=on:random_seed=1534559245:hsq=on:hsqr=16,1:s2a=on:i=5755:piset=or:nm=32:rtra=on:ss=axioms:c=on:sgt=8:rawr=on_2995 on theBenchmark for (2995ds/5755Mi)
% 3.91/1.00 % (2865439)Refutation not found, incomplete strategy
% 3.91/1.00 % (2865439)------------------------------
% 3.91/1.00 % (2865439)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.91/1.00 % (2865439)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/1.00 % (2865439)CaDiCaL version: 2.1.3
% 3.91/1.00 % (2865439)Termination reason: Refutation not found, incomplete strategy
% 3.91/1.00 % (2865439)Time elapsed: 0.008 s
% 3.91/1.00 % (2865439)Peak memory usage: 12 MB
% 3.91/1.00 % (2865439)Instructions burned: 35 (million)
% 3.91/1.00 % (2865439)------------------------------
% 3.91/1.00 % (2865439)------------------------------
% 3.91/1.00 % (2865440)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3478395376:s2a=on:i=495:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2995 on theBenchmark for (2995ds/495Mi)
% 3.91/1.00 % (2865431)Instruction limit reached!
% 3.91/1.00 % (2865431)------------------------------
% 3.91/1.00 % (2865431)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.91/1.00 % (2865431)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/1.00 % (2865431)CaDiCaL version: 2.1.3
% 3.91/1.00 % (2865431)Termination reason: Instruction limit
% 3.91/1.00 % (2865431)Termination phase: Saturation
% 3.91/1.00 % (2865431)Time elapsed: 0.029 s
% 3.91/1.00 % (2865431)Peak memory usage: 12 MB
% 3.91/1.00 % (2865431)Instructions burned: 66 (million)
% 3.91/1.00 % (2865444)dis+10_2_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_pi_sigma_gen:si=on:sp=occurrence:plsqr=5,1:bsr=on:plsql=on:random_seed=1421881113:cond=on:i=34:hud=10:nm=10:rtra=on_2994 on theBenchmark for (2994ds/34Mi)
% 3.91/1.00 % (2865444)Instruction limit reached!
% 3.91/1.00 % (2865444)------------------------------
% 3.91/1.00 % (2865444)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.91/1.00 % (2865444)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/1.00 % (2865444)CaDiCaL version: 2.1.3
% 3.91/1.00 % (2865444)Termination reason: Instruction limit
% 3.91/1.00 % (2865444)Termination phase: Saturation
% 3.91/1.00 % (2865444)Time elapsed: 0.007 s
% 3.91/1.00 % (2865444)Peak memory usage: 11 MB
% 3.91/1.00 % (2865444)Instructions burned: 34 (million)
% 3.91/1.00 % (2865446)ott+1002_4_tgt=ground:si=on:tsa=off:nwc=1:random_seed=2349982287:s2a=on:i=91:piset=or:hud=5:rtra=on:fe=abstraction_2994 on theBenchmark for (2994ds/91Mi)
% 3.91/1.00 % (2865448)dis+2_1_sil=128000:tgt=ground:e2e=on:si=on:sos=on:urr=on:uwa=off:nwc=2:random_seed=2518850790:i=66:sd=50:kws=inv_arity:bd=preordered:nm=64:rtra=on:ss=axioms:c=on:ntd=on_2994 on theBenchmark for (2994ds/66Mi)
% 3.91/1.00 % (2865448)Refutation not found, incomplete strategy
% 3.91/1.00 % (2865448)------------------------------
% 3.91/1.00 % (2865448)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.91/1.00 % (2865448)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/1.00 % (2865448)CaDiCaL version: 2.1.3
% 3.91/1.00 % (2865448)Termination reason: Refutation not found, incomplete strategy
% 3.91/1.00 % (2865448)Time elapsed: 0.003 s
% 3.91/1.00 % (2865448)Peak memory usage: 12 MB
% 3.91/1.00 % (2865448)Instructions burned: 14 (million)
% 3.91/1.00 % (2865448)------------------------------
% 3.91/1.00 % (2865448)------------------------------
% 3.91/1.00 % (2865451)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=3784217624:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2994 on theBenchmark for (2994ds/22Mi)
% 3.91/1.00 % (2865437)Instruction limit reached!
% 3.91/1.00 % (2865437)------------------------------
% 3.91/1.00 % (2865437)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.91/1.00 % (2865437)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/1.00 % (2865437)CaDiCaL version: 2.1.3
% 3.91/1.00 % (2865437)Termination reason: Instruction limit
% 3.91/1.00 % (2865437)Termination phase: Saturation
% 3.91/1.00 % (2865437)Time elapsed: 0.048 s
% 3.91/1.00 % (2865437)Peak memory usage: 12 MB
% 3.91/1.00 % (2865437)Instructions burned: 106 (million)
% 3.91/1.00 % (2865451)Instruction limit reached!
% 3.91/1.00 % (2865451)------------------------------
% 3.91/1.00 % (2865451)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.46/1.04 % (2865451)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.46/1.04 % (2865451)CaDiCaL version: 2.1.3
% 5.46/1.04 % (2865451)Termination reason: Instruction limit
% 5.46/1.04 % (2865451)Termination phase: Property scanning
% 5.46/1.04 % (2865451)Time elapsed: 0.005 s
% 5.46/1.04 % (2865451)Peak memory usage: 10 MB
% 5.46/1.04 % (2865451)Instructions burned: 25 (million)
% 5.46/1.04 % (2865454)lrs+10_1_sil=128000:si=on:urr=on:random_seed=2311111976:i=28:sd=1:rtra=on:ss=axioms:sgt=64_2994 on theBenchmark for (2994ds/28Mi)
% 5.46/1.04 % (2865446)Instruction limit reached!
% 5.46/1.04 % (2865446)------------------------------
% 5.46/1.04 % (2865446)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.46/1.04 % (2865446)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.46/1.04 % (2865446)CaDiCaL version: 2.1.3
% 5.46/1.04 % (2865446)Termination reason: Instruction limit
% 5.46/1.04 % (2865446)Termination phase: Saturation
% 5.46/1.04 % (2865446)Time elapsed: 0.042 s
% 5.46/1.04 % (2865446)Peak memory usage: 12 MB
% 5.46/1.04 % (2865446)Instructions burned: 93 (million)
% 5.46/1.04 % (2865453)lrs+21_16_anc=none:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:sas=cadical:si=on:plsqr=32,1:uwa=interpreted_only:foolp=on:nwc=3:random_seed=1768945840:i=338:bd=all:ins=4:rtra=on_2994 on theBenchmark for (2994ds/338Mi)
% 5.46/1.04 % (2865454)Instruction limit reached!
% 5.46/1.04 % (2865454)------------------------------
% 5.46/1.04 % (2865454)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.46/1.04 % (2865454)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.46/1.04 % (2865454)CaDiCaL version: 2.1.3
% 5.46/1.04 % (2865454)Termination reason: Instruction limit
% 5.46/1.04 % (2865454)Termination phase: Saturation
% 5.46/1.04 % (2865454)Time elapsed: 0.007 s
% 5.46/1.04 % (2865454)Peak memory usage: 12 MB
% 5.46/1.04 % (2865454)Instructions burned: 31 (million)
% 5.46/1.04 % (2865458)dis+10_32_sil=128000:tgt=ground:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=32,1:uwa=one_side_interpreted:nwc=1:random_seed=4180887723:hsq=on:hsqr=1,8:i=340:hsql=off:bd=preordered:av=off:rtra=on_2994 on theBenchmark for (2994ds/340Mi)
% 5.46/1.04 % (2865457)WARNING Broken Constraint: if avatar_split_queue_ratios(1,16) has been set then avatar_split_queue(off) is equal to on
% 5.46/1.04 % (2865457)lrs+1010_2:13_to=kbo:sil=128000:cnfonf=lazy_not_gen:si=on:sp=const_min:uwa=interpreted_only:random_seed=3885120768:i=137:add=off:avsqr=1,16:kws=inv_arity:bd=preordered:nm=0:rtra=on:ntd=on:rawr=on_2994 on theBenchmark for (2994ds/137Mi)
% 5.46/1.04 % (2865457)Instruction limit reached!
% 5.46/1.04 % (2865457)------------------------------
% 5.46/1.04 % (2865457)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.46/1.04 % (2865457)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.46/1.04 % (2865457)CaDiCaL version: 2.1.3
% 5.46/1.04 % (2865457)Termination reason: Instruction limit
% 5.46/1.04 % (2865457)Termination phase: Saturation
% 5.46/1.04 % (2865457)Time elapsed: 0.056 s
% 5.46/1.04 % (2865457)Peak memory usage: 12 MB
% 5.46/1.04 % (2865457)Instructions burned: 138 (million)
% 5.46/1.04 % (2865461)dis+1004_1_sil=128000:si=on:sos=on:uwa=one_side_interpreted:random_seed=3528683324:i=227:sd=1:bd=all:rtra=on:ss=axioms_2993 on theBenchmark for (2993ds/227Mi)
% 5.46/1.04 % (2865458)Instruction limit reached!
% 5.46/1.04 % (2865458)------------------------------
% 5.46/1.04 % (2865458)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.46/1.04 % (2865458)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.46/1.04 % (2865458)CaDiCaL version: 2.1.3
% 5.46/1.04 % (2865458)Termination reason: Instruction limit
% 5.46/1.04 % (2865458)Termination phase: Saturation
% 5.46/1.04 % (2865458)Time elapsed: 0.085 s
% 5.46/1.04 % (2865458)Peak memory usage: 13 MB
% 5.46/1.04 % (2865458)Instructions burned: 341 (million)
% 5.46/1.04 % (2865461)Refutation not found, incomplete strategy
% 5.46/1.04 % (2865461)------------------------------
% 5.46/1.04 % (2865461)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.46/1.04 % (2865461)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.46/1.04 % (2865461)CaDiCaL version: 2.1.3
% 5.46/1.04 % (2865461)Termination reason: Refutation not found, incomplete strategy
% 5.46/1.04 % (2865461)Time elapsed: 0.006 s
% 5.46/1.04 % (2865461)Peak memory usage: 12 MB
% 5.46/1.04 % (2865461)Instructions burned: 14 (million)
% 5.46/1.11 % (2865461)------------------------------
% 5.46/1.11 % (2865461)------------------------------
% 5.46/1.11 % (2865463)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(1) has been set then sine_level_split_queue(off) is equal to on
% 5.46/1.11 % (2865463)dis+1010_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:nwc=2:slsqc=1:random_seed=806862850:i=373:hud=10:nm=16:av=off:rtra=on:ntd=on_2993 on theBenchmark for (2993ds/373Mi)
% 5.46/1.11 % (2865429)Instruction limit reached!
% 5.46/1.11 % (2865429)------------------------------
% 5.46/1.11 % (2865429)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.46/1.11 % (2865429)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.46/1.11 % (2865429)CaDiCaL version: 2.1.3
% 5.46/1.11 % (2865429)Termination reason: Instruction limit
% 5.46/1.11 % (2865429)Termination phase: Saturation
% 5.46/1.11 % (2865429)Time elapsed: 0.205 s
% 5.46/1.11 % (2865429)Peak memory usage: 12 MB
% 5.46/1.11 % (2865429)Instructions burned: 450 (million)
% 5.46/1.11 % (2865388)Instruction limit reached!
% 5.46/1.11 % (2865388)------------------------------
% 5.46/1.11 % (2865388)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.46/1.11 % (2865388)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.46/1.11 % (2865388)CaDiCaL version: 2.1.3
% 5.46/1.11 % (2865388)Termination reason: Instruction limit
% 5.46/1.11 % (2865388)Termination phase: Saturation
% 5.46/1.11 % (2865388)Time elapsed: 0.444 s
% 5.46/1.11 % (2865388)Peak memory usage: 16 MB
% 5.46/1.11 % (2865388)Instructions burned: 853 (million)
% 5.46/1.11 % (2865464)lrs+10_64_anc=all_dependent:sil=128000:e2e=on:si=on:cbe=off:uwa=off:random_seed=3833737839:i=116:ep=RSTC:rtra=on:ntd=on_2993 on theBenchmark for (2993ds/116Mi)
% 5.46/1.11 % (2865466)lrs+10_1_sil=128000:drc=off:si=on:sos=on:erd=off:urr=on:uwa=interpreted_only:random_seed=2383456156:i=575:rtra=on_2993 on theBenchmark for (2993ds/575Mi)
% 5.46/1.11 % (2865467)dis+2_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:fdtod=off:sp=const_max:lma=off:random_seed=4000783889:cts=off:i=270:doe=on:hud=5:bs=unit_only:bd=preordered:nm=30:ins=25:rtra=on_2993 on theBenchmark for (2993ds/270Mi)
% 5.46/1.11 % (2865440)Instruction limit reached!
% 5.46/1.11 % (2865440)------------------------------
% 5.46/1.11 % (2865440)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.46/1.11 % (2865440)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.46/1.11 % (2865440)CaDiCaL version: 2.1.3
% 5.46/1.11 % (2865440)Termination reason: Instruction limit
% 5.46/1.11 % (2865440)Termination phase: Saturation
% 5.46/1.11 % (2865440)Time elapsed: 0.211 s
% 5.46/1.11 % (2865440)Peak memory usage: 13 MB
% 5.46/1.11 % (2865440)Instructions burned: 496 (million)
% 5.46/1.11 % (2865466)Refutation not found, incomplete strategy
% 5.46/1.11 % (2865466)------------------------------
% 5.46/1.11 % (2865466)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.46/1.11 % (2865466)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.46/1.11 % (2865466)CaDiCaL version: 2.1.3
% 5.46/1.11 % (2865466)Termination reason: Refutation not found, incomplete strategy
% 5.46/1.11 % (2865466)Time elapsed: 0.024 s
% 5.46/1.11 % (2865466)Peak memory usage: 12 MB
% 5.46/1.11 % (2865466)Instructions burned: 57 (million)
% 5.46/1.11 % (2865466)------------------------------
% 5.46/1.11 % (2865466)------------------------------
% 5.46/1.11 % (2865453)Instruction limit reached!
% 5.46/1.11 % (2865453)------------------------------
% 5.46/1.11 % (2865453)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.46/1.11 % (2865453)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.46/1.11 % (2865453)CaDiCaL version: 2.1.3
% 5.46/1.11 % (2865453)Termination reason: Instruction limit
% 5.46/1.11 % (2865453)Termination phase: Saturation
% 5.46/1.11 % (2865453)Time elapsed: 0.159 s
% 5.46/1.11 % (2865453)Peak memory usage: 14 MB
% 5.46/1.11 % (2865453)Instructions burned: 340 (million)
% 5.46/1.11 % (2865471)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=3706143646:hsq=on:hsqr=16,1:s2a=on:i=9840:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2992 on theBenchmark for (2992ds/9840Mi)
% 5.46/1.11 % (2865472)lrs+1010_1_sil=128000:si=on:sos=all:uwa=off:nwc=1:random_seed=1437147844:i=421:rtra=on:ss=axioms_2992 on theBenchmark for (2992ds/421Mi)
% 6.26/1.21 % (2865464)Instruction limit reached!
% 6.26/1.21 % (2865464)------------------------------
% 6.26/1.21 % (2865464)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.26/1.21 % (2865464)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.26/1.21 % (2865464)CaDiCaL version: 2.1.3
% 6.26/1.21 % (2865464)Termination reason: Instruction limit
% 6.26/1.21 % (2865464)Termination phase: Saturation
% 6.26/1.21 % (2865464)Time elapsed: 0.053 s
% 6.26/1.21 % (2865464)Peak memory usage: 12 MB
% 6.26/1.21 % (2865464)Instructions burned: 117 (million)
% 6.26/1.21 % (2865473)WARNING Broken Constraint: if sine_to_age_tolerance(3) 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
% 6.26/1.21 % (2865472)Refutation not found, incomplete strategy
% 6.26/1.21 % (2865472)------------------------------
% 6.26/1.21 % (2865472)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.26/1.21 % (2865472)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.26/1.21 % (2865472)CaDiCaL version: 2.1.3
% 6.26/1.21 % (2865472)Termination reason: Refutation not found, incomplete strategy
% 6.26/1.21 % (2865472)Time elapsed: 0.006 s
% 6.26/1.21 % (2865472)Peak memory usage: 12 MB
% 6.26/1.21 % (2865472)Instructions burned: 14 (million)
% 6.26/1.21 % (2865473)lrs+10_40_sil=128000:tgt=full:cnfonf=off:si=on:sp=reverse_frequency:spb=goal_then_units:uwa=off:fd=preordered:nwc=1:random_seed=3770311566:avsq=on:i=270:s2at=3:avsqr=1,16:rtra=on:ntd=on_2992 on theBenchmark for (2992ds/270Mi)
% 6.26/1.21 % (2865472)------------------------------
% 6.26/1.21 % (2865472)------------------------------
% 6.26/1.21 % (2865476)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=391228700:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_2992 on theBenchmark for (2992ds/31Mi)
% 6.26/1.21 % (2865478)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 6.26/1.21 % (2865478)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
% 6.26/1.21 % (2865478)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=2345075339:hsqr=1,8:i=1440:s2at=5:add=on:nm=2:rtra=on_2992 on theBenchmark for (2992ds/1440Mi)
% 6.26/1.21 % (2865463)Instruction limit reached!
% 6.26/1.21 % (2865463)------------------------------
% 6.26/1.21 % (2865463)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.26/1.21 % (2865463)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.26/1.21 % (2865463)CaDiCaL version: 2.1.3
% 6.26/1.21 % (2865463)Termination reason: Instruction limit
% 6.26/1.21 % (2865463)Termination phase: Saturation
% 6.26/1.21 % (2865463)Time elapsed: 0.093 s
% 6.26/1.21 % (2865463)Peak memory usage: 12 MB
% 6.26/1.21 % (2865463)Instructions burned: 375 (million)
% 6.26/1.21 % (2865473)Refutation not found, incomplete strategy
% 6.26/1.21 % (2865473)------------------------------
% 6.26/1.21 % (2865473)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.26/1.21 % (2865473)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.26/1.21 % (2865473)CaDiCaL version: 2.1.3
% 6.26/1.21 % (2865473)Termination reason: Refutation not found, incomplete strategy
% 6.26/1.21 % (2865473)Time elapsed: 0.026 s
% 6.26/1.21 % (2865473)Peak memory usage: 12 MB
% 6.26/1.21 % (2865473)Instructions burned: 62 (million)
% 6.26/1.21 % (2865473)------------------------------
% 6.26/1.21 % (2865473)------------------------------
% 6.26/1.21 % (2865476)Instruction limit reached!
% 6.26/1.21 % (2865476)------------------------------
% 6.26/1.21 % (2865476)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.26/1.21 % (2865476)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.26/1.21 % (2865476)CaDiCaL version: 2.1.3
% 6.26/1.21 % (2865476)Termination reason: Instruction limit
% 6.26/1.21 % (2865476)Termination phase: Saturation
% 6.26/1.21 % (2865476)Time elapsed: 0.013 s
% 6.26/1.21 % (2865476)Peak memory usage: 12 MB
% 6.26/1.21 % (2865476)Instructions burned: 32 (million)
% 6.26/1.21 % (2865481)dis+10_2_sil=128000:si=on:random_seed=3019397917:s2a=on:i=339:av=off:rtra=on:fe=abstraction:ss=axioms:fsd=on:ntd=on_2992 on theBenchmark for (2992ds/339Mi)
% 6.82/1.36 % (2865481)Refutation not found, incomplete strategy
% 6.82/1.36 % (2865481)------------------------------
% 6.82/1.36 % (2865481)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.82/1.36 % (2865481)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.82/1.36 % (2865481)CaDiCaL version: 2.1.3
% 6.82/1.36 % (2865481)Termination reason: Refutation not found, incomplete strategy
% 6.82/1.36 % (2865481)Time elapsed: 0.003 s
% 6.82/1.36 % (2865481)Peak memory usage: 12 MB
% 6.82/1.36 % (2865481)Instructions burned: 15 (million)
% 6.82/1.36 % (2865481)------------------------------
% 6.82/1.36 % (2865481)------------------------------
% 6.82/1.36 % (2865482)lrs+2_16:1_si=on:cbe=off:uwa=interpreted_only:random_seed=134735540:i=111:add=on:fgj=on:rtra=on:fdi=1024_2992 on theBenchmark for (2992ds/111Mi)
% 6.82/1.36 % (2865483)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=3854690233:st=3:avsq=on:i=122:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2992 on theBenchmark for (2992ds/122Mi)
% 6.82/1.36 % (2865485)dis+1010_3:2_anc=all_dependent:sil=128000:si=on:sos=on:lma=off:spb=goal_then_units:bce=on:fd=off:random_seed=379619267:uwa_fpi=on:avsq=on:i=136:avsqr=1,32:hud=15:nm=0:rtra=on:ntd=on_2992 on theBenchmark for (2992ds/136Mi)
% 6.82/1.36 % (2865483)Refutation not found, incomplete strategy
% 6.82/1.36 % (2865483)------------------------------
% 6.82/1.36 % (2865483)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.82/1.36 % (2865483)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.82/1.36 % (2865483)CaDiCaL version: 2.1.3
% 6.82/1.36 % (2865483)Termination reason: Refutation not found, incomplete strategy
% 6.82/1.36 % (2865483)Time elapsed: 0.013 s
% 6.82/1.36 % (2865483)Peak memory usage: 12 MB
% 6.82/1.36 % (2865483)Instructions burned: 30 (million)
% 6.82/1.36 % (2865485)Refutation not found, incomplete strategy
% 6.82/1.36 % (2865485)------------------------------
% 6.82/1.36 % (2865485)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.82/1.36 % (2865485)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.82/1.36 % (2865485)CaDiCaL version: 2.1.3
% 6.82/1.36 % (2865485)Termination reason: Refutation not found, incomplete strategy
% 6.82/1.36 % (2865485)Time elapsed: 0.012 s
% 6.82/1.36 % (2865485)Peak memory usage: 12 MB
% 6.82/1.36 % (2865485)Instructions burned: 56 (million)
% 6.82/1.36 % (2865485)------------------------------
% 6.82/1.36 % (2865485)------------------------------
% 6.82/1.36 % (2865483)------------------------------
% 6.82/1.36 % (2865483)------------------------------
% 6.82/1.36 % (2865489)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=1529656240:hsq=on:st=2:i=232:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2991 on theBenchmark for (2991ds/232Mi)
% 6.82/1.36 % (2865490)lrs+1010_8:1_sil=128000:tgt=ground:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sos=on:plsqr=256,1:uwa=off:random_seed=2527761440:i=1254:kws=precedence:bd=preordered:av=off:rtra=on_2991 on theBenchmark for (2991ds/1254Mi)
% 6.82/1.36 % (2865467)Instruction limit reached!
% 6.82/1.36 % (2865467)------------------------------
% 6.82/1.36 % (2865467)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.82/1.36 % (2865467)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.82/1.36 % (2865467)CaDiCaL version: 2.1.3
% 6.82/1.36 % (2865467)Termination reason: Instruction limit
% 6.82/1.36 % (2865467)Termination phase: Saturation
% 6.82/1.36 % (2865467)Time elapsed: 0.124 s
% 6.82/1.36 % (2865467)Peak memory usage: 12 MB
% 6.82/1.36 % (2865467)Instructions burned: 271 (million)
% 6.82/1.36 % (2865482)Instruction limit reached!
% 6.82/1.36 % (2865482)------------------------------
% 6.82/1.36 % (2865482)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.82/1.36 % (2865482)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.82/1.36 % (2865482)CaDiCaL version: 2.1.3
% 6.82/1.36 % (2865482)Termination reason: Instruction limit
% 6.82/1.36 % (2865482)Termination phase: Saturation
% 6.82/1.36 % (2865482)Time elapsed: 0.049 s
% 6.82/1.36 % (2865482)Peak memory usage: 12 MB
% 6.82/1.36 % (2865482)Instructions burned: 112 (million)
% 6.82/1.36 % (2865493)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(discount) is equal to lrs
% 7.77/1.53 % (2865493)dis+1002_5:4_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_simp:si=on:plsqr=878,253:plsql=on:uwa=interpreted_only:lwlo=on:random_seed=1798107736:s2a=on:i=281:add=on:rtra=on:fe=axiom:fdi=1024_2991 on theBenchmark for (2991ds/281Mi)
% 7.77/1.53 % (2865490)Refutation not found, incomplete strategy
% 7.77/1.53 % (2865490)------------------------------
% 7.77/1.53 % (2865490)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.77/1.53 % (2865490)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.77/1.53 % (2865490)CaDiCaL version: 2.1.3
% 7.77/1.53 % (2865490)Termination reason: Refutation not found, incomplete strategy
% 7.77/1.53 % (2865490)Time elapsed: 0.023 s
% 7.77/1.53 % (2865490)Peak memory usage: 12 MB
% 7.77/1.53 % (2865490)Instructions burned: 55 (million)
% 7.77/1.53 % (2865490)------------------------------
% 7.77/1.53 % (2865490)------------------------------
% 7.77/1.53 % (2865494)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=863759160:i=619:add=on:rtra=on_2991 on theBenchmark for (2991ds/619Mi)
% 7.77/1.53 % (2865496)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=2306437720:i=865:bs=unit_only:ins=25:rtra=on:ntd=on_2991 on theBenchmark for (2991ds/865Mi)
% 7.77/1.53 % (2865489)Instruction limit reached!
% 7.77/1.53 % (2865489)------------------------------
% 7.77/1.53 % (2865489)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.77/1.53 % (2865489)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.77/1.53 % (2865489)CaDiCaL version: 2.1.3
% 7.77/1.53 % (2865489)Termination reason: Instruction limit
% 7.77/1.53 % (2865489)Termination phase: Saturation
% 7.77/1.53 % (2865489)Time elapsed: 0.060 s
% 7.77/1.53 % (2865489)Peak memory usage: 13 MB
% 7.77/1.53 % (2865489)Instructions burned: 233 (million)
% 7.77/1.53 % (2865494)Refutation not found, incomplete strategy
% 7.77/1.53 % (2865494)------------------------------
% 7.77/1.53 % (2865494)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.77/1.53 % (2865494)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.77/1.53 % (2865494)CaDiCaL version: 2.1.3
% 7.77/1.53 % (2865494)Termination reason: Refutation not found, incomplete strategy
% 7.77/1.53 % (2865494)Time elapsed: 0.022 s
% 7.77/1.53 % (2865494)Peak memory usage: 12 MB
% 7.77/1.53 % (2865494)Instructions burned: 53 (million)
% 7.77/1.53 % (2865494)------------------------------
% 7.77/1.53 % (2865494)------------------------------
% 7.77/1.53 % (2865499)lrs+10_1_sil=128000:si=on:urr=on:random_seed=1164028859:i=212:sd=1:rtra=on:ss=axioms:sgt=64_2991 on theBenchmark for (2991ds/212Mi)
% 7.77/1.53 % (2865500)lrs+1010_64_sil=128000:si=on:avsql=on:uwa=off:random_seed=3780207933:hsq=on:st=3:avsq=on:i=130:avsqr=1,16:sd=1:rtra=on:ss=axioms_2991 on theBenchmark for (2991ds/130Mi)
% 7.77/1.53 % (2865500)Refutation not found, incomplete strategy
% 7.77/1.53 % (2865500)------------------------------
% 7.77/1.53 % (2865500)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.77/1.53 % (2865500)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.77/1.53 % (2865500)CaDiCaL version: 2.1.3
% 7.77/1.53 % (2865500)Termination reason: Refutation not found, incomplete strategy
% 7.77/1.53 % (2865500)Time elapsed: 0.016 s
% 7.77/1.53 % (2865500)Peak memory usage: 12 MB
% 7.77/1.53 % (2865500)Instructions burned: 37 (million)
% 7.77/1.53 % (2865500)------------------------------
% 7.77/1.53 % (2865500)------------------------------
% 7.77/1.53 % (2865503)lrs+1002_1_cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:random_seed=3604045751:st=1.5:i=346:rtra=on:ss=axioms_2990 on theBenchmark for (2990ds/346Mi)
% 7.77/1.53 % (2865499)Instruction limit reached!
% 7.77/1.53 % (2865499)------------------------------
% 7.77/1.53 % (2865499)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.77/1.53 % (2865499)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.77/1.53 % (2865499)CaDiCaL version: 2.1.3
% 7.77/1.53 % (2865499)Termination reason: Instruction limit
% 7.77/1.53 % (2865499)Termination phase: Saturation
% 7.77/1.53 % (2865499)Time elapsed: 0.051 s
% 7.77/1.53 % (2865499)Peak memory usage: 12 MB
% 7.77/1.53 % (2865499)Instructions burned: 217 (million)
% 7.77/1.53 % (2865503)Refutation not found, incomplete strategy
% 7.77/1.53 % (2865503)------------------------------
% 9.69/1.73 % (2865503)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.69/1.73 % (2865503)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.69/1.73 % (2865503)CaDiCaL version: 2.1.3
% 9.69/1.73 % (2865503)Termination reason: Refutation not found, incomplete strategy
% 9.69/1.73 % (2865503)Time elapsed: 0.008 s
% 9.69/1.73 % (2865503)Peak memory usage: 12 MB
% 9.69/1.73 % (2865503)Instructions burned: 15 (million)
% 9.69/1.73 % (2865503)------------------------------
% 9.69/1.73 % (2865503)------------------------------
% 9.69/1.73 % (2865505)lrs+1010_3_sil=128000:si=on:slsq=on:random_seed=1148907352:avsq=on:i=152:avsqr=8,1:hud=5:ins=1:fsr=off:rtra=on_2990 on theBenchmark for (2990ds/152Mi)
% 9.69/1.73 % (2865506)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=557339329:i=75:ep=R:rtra=on:ntd=on_2990 on theBenchmark for (2990ds/75Mi)
% 9.69/1.73 % (2865493)Instruction limit reached!
% 9.69/1.73 % (2865493)------------------------------
% 9.69/1.73 % (2865493)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.69/1.73 % (2865493)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.69/1.73 % (2865493)CaDiCaL version: 2.1.3
% 9.69/1.73 % (2865493)Termination reason: Instruction limit
% 9.69/1.73 % (2865493)Termination phase: Saturation
% 9.69/1.73 % (2865493)Time elapsed: 0.132 s
% 9.69/1.73 % (2865493)Peak memory usage: 13 MB
% 9.69/1.73 % (2865493)Instructions burned: 281 (million)
% 9.69/1.73 % (2865505)Instruction limit reached!
% 9.69/1.73 % (2865505)------------------------------
% 9.69/1.73 % (2865505)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.69/1.73 % (2865505)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.69/1.73 % (2865505)CaDiCaL version: 2.1.3
% 9.69/1.73 % (2865505)Termination reason: Instruction limit
% 9.69/1.73 % (2865505)Termination phase: Saturation
% 9.69/1.73 % (2865505)Time elapsed: 0.038 s
% 9.69/1.73 % (2865505)Peak memory usage: 12 MB
% 9.69/1.73 % (2865505)Instructions burned: 156 (million)
% 9.69/1.73 % (2865509)dis+10_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=one_side_interpreted:nwc=5:random_seed=2249385165:st=2.5:i=387:sd=2:rtra=on:ss=axioms_2990 on theBenchmark for (2990ds/387Mi)
% 9.69/1.73 % (2865510)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=3155954080:uwa_fpi=on:i=148:doe=on:bd=preordered:rtra=on:fsd=on_2989 on theBenchmark for (2989ds/148Mi)
% 9.69/1.73 % (2865506)Instruction limit reached!
% 9.69/1.73 % (2865506)------------------------------
% 9.69/1.73 % (2865506)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.69/1.73 % (2865506)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.69/1.73 % (2865506)CaDiCaL version: 2.1.3
% 9.69/1.73 % (2865506)Termination reason: Instruction limit
% 9.69/1.73 % (2865506)Termination phase: Saturation
% 9.69/1.73 % (2865506)Time elapsed: 0.034 s
% 9.69/1.73 % (2865506)Peak memory usage: 12 MB
% 9.69/1.73 % (2865506)Instructions burned: 75 (million)
% 9.69/1.73 % (2865513)dis+1010_3_si=on:uwa=one_side_interpreted:random_seed=1073818850:i=161:piset=and:rtra=on:ntd=on_2989 on theBenchmark for (2989ds/161Mi)
% 9.69/1.73 % (2865510)Instruction limit reached!
% 9.69/1.73 % (2865510)------------------------------
% 9.69/1.73 % (2865510)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.69/1.73 % (2865510)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.69/1.73 % (2865510)CaDiCaL version: 2.1.3
% 9.69/1.73 % (2865510)Termination reason: Instruction limit
% 9.69/1.73 % (2865510)Termination phase: Saturation
% 9.69/1.73 % (2865510)Time elapsed: 0.042 s
% 9.69/1.73 % (2865510)Peak memory usage: 13 MB
% 9.69/1.73 % (2865510)Instructions burned: 150 (million)
% 9.69/1.73 % (2865515)lrs+10_1_sil=128000:si=on:random_seed=974826722:st=5:i=888:sd=3:bd=preordered:rtra=on:ss=axioms_2989 on theBenchmark for (2989ds/888Mi)
% 9.69/1.73 % (2865513)Instruction limit reached!
% 9.69/1.73 % (2865513)------------------------------
% 9.69/1.73 % (2865513)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.69/1.73 % (2865513)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.69/1.73 % (2865513)CaDiCaL version: 2.1.3
% 9.69/1.73 % (2865513)Termination reason: Instruction limit
% 9.69/1.73 % (2865513)Termination phase: Saturation
% 9.69/1.73 % (2865513)Time elapsed: 0.072 s
% 10.72/1.90 % (2865513)Peak memory usage: 12 MB
% 10.72/1.90 % (2865513)Instructions burned: 161 (million)
% 10.72/1.90 % (2865517)ott-1003_1_sil=128000:plsq=on:plsqc=1:si=on:sp=weighted_frequency:lma=off:plsqr=1,32:urr=on:cbe=off:random_seed=2669067398:i=136:add=on:ins=4:rtra=on:sup=off_2988 on theBenchmark for (2988ds/136Mi)
% 10.72/1.90 % (2865509)Instruction limit reached!
% 10.72/1.90 % (2865509)------------------------------
% 10.72/1.90 % (2865509)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.72/1.90 % (2865509)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.72/1.90 % (2865509)CaDiCaL version: 2.1.3
% 10.72/1.90 % (2865509)Termination reason: Instruction limit
% 10.72/1.90 % (2865509)Termination phase: Saturation
% 10.72/1.90 % (2865509)Time elapsed: 0.170 s
% 10.72/1.90 % (2865509)Peak memory usage: 12 MB
% 10.72/1.90 % (2865509)Instructions burned: 388 (million)
% 10.72/1.90 % (2865517)Instruction limit reached!
% 10.72/1.90 % (2865517)------------------------------
% 10.72/1.90 % (2865517)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.72/1.90 % (2865517)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.72/1.90 % (2865517)CaDiCaL version: 2.1.3
% 10.72/1.90 % (2865517)Termination reason: Instruction limit
% 10.72/1.90 % (2865517)Termination phase: Saturation
% 10.72/1.90 % (2865517)Time elapsed: 0.062 s
% 10.72/1.90 % (2865517)Peak memory usage: 13 MB
% 10.72/1.90 % (2865517)Instructions burned: 138 (million)
% 10.72/1.90 % (2865519)lrs+1010_1_anc=none:slsqr=1,2:sil=128000:cnfonf=conj_eager:sas=cadical:si=on:hi=on:uwa=one_side_interpreted:rp=on:nwc=2:slsqc=3:slsq=on:random_seed=346456679:i=88:s2at=3:nm=2:rtra=on:rawr=on_2988 on theBenchmark for (2988ds/88Mi)
% 10.72/1.90 % (2865520)dis+1002_5:4_to=kbo:sil=128000:cnfonf=conj_eager:si=on:sp=reverse_arity:lma=off:hi=on:nwc=20:random_seed=2558157023:s2a=on:cond=on:i=93:add=on:bd=preordered:rtra=on:er=filter_2988 on theBenchmark for (2988ds/93Mi)
% 10.72/1.90 % (2865519)Instruction limit reached!
% 10.72/1.90 % (2865519)------------------------------
% 10.72/1.90 % (2865519)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.72/1.90 % (2865519)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.72/1.90 % (2865519)CaDiCaL version: 2.1.3
% 10.72/1.90 % (2865519)Termination reason: Instruction limit
% 10.72/1.90 % (2865519)Termination phase: Saturation
% 10.72/1.90 % (2865519)Time elapsed: 0.036 s
% 10.72/1.90 % (2865519)Peak memory usage: 12 MB
% 10.72/1.90 % (2865519)Instructions burned: 89 (million)
% 10.72/1.90 % (2865520)Instruction limit reached!
% 10.72/1.90 % (2865520)------------------------------
% 10.72/1.90 % (2865520)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.72/1.90 % (2865520)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.72/1.90 % (2865520)CaDiCaL version: 2.1.3
% 10.72/1.90 % (2865520)Termination reason: Instruction limit
% 10.72/1.90 % (2865520)Termination phase: Saturation
% 10.72/1.90 % (2865520)Time elapsed: 0.038 s
% 10.72/1.90 % (2865520)Peak memory usage: 12 MB
% 10.72/1.90 % (2865520)Instructions burned: 93 (million)
% 10.72/1.90 % (2865523)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=3695571569:i=2186:rtra=on:ixr=off_2987 on theBenchmark for (2987ds/2186Mi)
% 10.72/1.90 % (2865524)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=4022413523:s2a=on:i=240:rtra=on:ntd=on_2987 on theBenchmark for (2987ds/240Mi)
% 10.72/1.90 % (2865515)Instruction limit reached!
% 10.72/1.90 % (2865515)------------------------------
% 10.72/1.90 % (2865515)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.72/1.90 % (2865515)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.72/1.90 % (2865515)CaDiCaL version: 2.1.3
% 10.72/1.90 % (2865515)Termination reason: Instruction limit
% 10.72/1.90 % (2865515)Termination phase: Saturation
% 10.72/1.90 % (2865515)Time elapsed: 0.207 s
% 10.72/1.90 % (2865515)Peak memory usage: 13 MB
% 10.72/1.90 % (2865515)Instructions burned: 892 (million)
% 10.72/1.90 % (2865496)Instruction limit reached!
% 10.72/1.90 % (2865496)------------------------------
% 10.72/1.90 % (2865496)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.72/1.90 % (2865496)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.72/1.90 % (2865496)CaDiCaL version: 2.1.3
% 10.72/1.90 % (2865496)Termination reason: Instruction limit
% 10.72/1.90 % (2865496)Termination phase: Saturation
% 10.72/1.90 % (2865496)Time elapsed: 0.396 s
% 10.72/1.99 % (2865496)Peak memory usage: 15 MB
% 10.72/1.99 % (2865496)Instructions burned: 867 (million)
% 10.72/1.99 % (2865527)dis+10_1_to=lpo:sil=128000:tgt=ground:si=on:urr=on:cbe=off:uwa=one_side_constant:nwc=5:random_seed=2311779244:i=805:aac=none:doe=on:piset=not:bd=all:rtra=on:fe=abstraction_2987 on theBenchmark for (2987ds/805Mi)
% 10.72/1.99 % (2865528)WARNING Broken Constraint: if avatar_split_queue_cutoffs(1) has been set then avatar_split_queue(off) is equal to on
% 10.72/1.99 % (2865528)dis+1002_1_to=lpo:sil=128000:cnfonf=conj_eager:si=on:sp=unary_first:spb=intro:urr=on:cbe=off:uwa=one_side_interpreted:rp=on:avsqc=1:random_seed=3659435294:st=2:s2a=on:i=391:sd=4:bd=preordered:nm=16:rtra=on:ss=axioms:rawr=on_2987 on theBenchmark for (2987ds/391Mi)
% 10.72/1.99 % (2865528)Refutation not found, incomplete strategy
% 10.72/1.99 % (2865528)------------------------------
% 10.72/1.99 % (2865528)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.72/1.99 % (2865528)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.72/1.99 % (2865528)CaDiCaL version: 2.1.3
% 10.72/1.99 % (2865528)Termination reason: Refutation not found, incomplete strategy
% 10.72/1.99 % (2865528)Time elapsed: 0.019 s
% 10.72/1.99 % (2865528)Peak memory usage: 12 MB
% 10.72/1.99 % (2865528)Instructions burned: 40 (million)
% 10.72/1.99 % (2865528)------------------------------
% 10.72/1.99 % (2865528)------------------------------
% 10.72/1.99 % (2865531)dis+10_1_sil=128000:si=on:urr=on:uwa=off:random_seed=1338485625:i=355:av=off:fsr=off:rtra=on:ixr=off_2986 on theBenchmark for (2986ds/355Mi)
% 10.72/1.99 % (2865524)Instruction limit reached!
% 10.72/1.99 % (2865524)------------------------------
% 10.72/1.99 % (2865524)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.72/1.99 % (2865524)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.72/1.99 % (2865524)CaDiCaL version: 2.1.3
% 10.72/1.99 % (2865524)Termination reason: Instruction limit
% 10.72/1.99 % (2865524)Termination phase: Saturation
% 10.72/1.99 % (2865524)Time elapsed: 0.110 s
% 10.72/1.99 % (2865524)Peak memory usage: 13 MB
% 10.72/1.99 % (2865524)Instructions burned: 241 (million)
% 10.72/1.99 % (2865533)lrs+1010_5:1_sil=128000:si=on:uwa=interpreted_only:sac=on:slsq=on:random_seed=1708572681:lrd=on:i=314:sd=1:rtra=on:ss=axioms_2986 on theBenchmark for (2986ds/314Mi)
% 10.72/1.99 % (2865533)Refutation not found, incomplete strategy
% 10.72/1.99 % (2865533)------------------------------
% 10.72/1.99 % (2865533)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.72/1.99 % (2865533)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.72/1.99 % (2865533)CaDiCaL version: 2.1.3
% 10.72/1.99 % (2865533)Termination reason: Refutation not found, incomplete strategy
% 10.72/1.99 % (2865533)Time elapsed: 0.007 s
% 10.72/1.99 % (2865533)Peak memory usage: 12 MB
% 10.72/1.99 % (2865533)Instructions burned: 16 (million)
% 10.72/1.99 % (2865533)------------------------------
% 10.72/1.99 % (2865533)------------------------------
% 10.72/1.99 % (2865478)Instruction limit reached!
% 10.72/1.99 % (2865478)------------------------------
% 10.72/1.99 % (2865478)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.72/1.99 % (2865478)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.72/1.99 % (2865478)CaDiCaL version: 2.1.3
% 10.72/1.99 % (2865478)Termination reason: Instruction limit
% 10.72/1.99 % (2865478)Termination phase: Saturation
% 10.72/1.99 % (2865478)Time elapsed: 0.633 s
% 10.72/1.99 % (2865478)Peak memory usage: 13 MB
% 10.72/1.99 % (2865478)Instructions burned: 1440 (million)
% 10.72/1.99 % (2865535)lrs+10_1_sil=128000:e2e=on:si=on:cbe=off:uwa=interpreted_only:cs=on:random_seed=3101251109:s2a=on:i=251:fsr=off:rtra=on_2985 on theBenchmark for (2985ds/251Mi)
% 10.72/1.99 % (2865536)dis+1010_2:1_slsqr=2,1:to=lpo:plsq=on:cnfonf=lazy_pi_sigma_gen:si=on:sp=reverse_arity:acc=on:uwa=hol:fd=preordered:s2agt=16:flr=on:pe=on:slsq=on:random_seed=3896411482:uwa_fpi=on:avsq=on:s2a=on:cond=fast:i=2470:s2at=1.5:aac=none:fgj=on:piset=and:hud=3:fsr=off:rtra=on:er=filter:rawr=on_2985 on theBenchmark for (2985ds/2470Mi)
% 10.72/1.99 % (2865527)Instruction limit reached!
% 10.72/1.99 % (2865527)------------------------------
% 10.72/1.99 % (2865527)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.72/1.99 % (2865527)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.72/1.99 % (2865527)CaDiCaL version: 2.1.3
% 10.72/2.00 % (2865527)Termination reason: Instruction limit
% 10.72/2.00 % (2865527)Termination phase: Saturation
% 10.72/2.00 % (2865527)Time elapsed: 0.193 s
% 10.72/2.00 % (2865527)Peak memory usage: 13 MB
% 10.72/2.00 % (2865527)Instructions burned: 807 (million)
% 10.72/2.00 % (2865531)Instruction limit reached!
% 10.72/2.00 % (2865531)------------------------------
% 10.72/2.00 % (2865531)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.72/2.00 % (2865531)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.72/2.00 % (2865531)CaDiCaL version: 2.1.3
% 10.72/2.00 % (2865531)Termination reason: Instruction limit
% 10.72/2.00 % (2865531)Termination phase: Saturation
% 10.72/2.00 % (2865531)Time elapsed: 0.153 s
% 10.72/2.00 % (2865531)Peak memory usage: 13 MB
% 10.72/2.00 % (2865531)Instructions burned: 356 (million)
% 10.72/2.00 % (2865539)dis+10_6_sil=128000:si=on:sp=arity:bce=on:cbe=off:uwa=interpreted_only:slsqc=4:slsq=on:random_seed=97338543:i=673:doe=on:fgj=on:piset=and:slsql=off:rtra=on:fdi=1024:ntd=on_2985 on theBenchmark for (2985ds/673Mi)
% 10.72/2.00 % (2865540)lrs+10_64_anc=all_dependent:sil=128000:e2e=on:si=on:cbe=off:uwa=off:random_seed=4240335422:i=116:ep=RSTC:rtra=on:ntd=on_2985 on theBenchmark for (2985ds/116Mi)
% 10.72/2.00 % (2865535)Instruction limit reached!
% 10.72/2.00 % (2865535)------------------------------
% 10.72/2.00 % (2865535)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.72/2.00 % (2865535)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.72/2.00 % (2865535)CaDiCaL version: 2.1.3
% 10.72/2.00 % (2865535)Termination reason: Instruction limit
% 10.72/2.00 % (2865535)Termination phase: Saturation
% 10.72/2.00 % (2865535)Time elapsed: 0.097 s
% 10.72/2.00 % (2865535)Peak memory usage: 12 MB
% 10.72/2.00 % (2865535)Instructions burned: 251 (million)
% 10.72/2.00 % (2865543)dis+2_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:fdtod=off:sp=const_max:lma=off:random_seed=3864380611:cts=off:i=270:doe=on:hud=5:bs=unit_only:bd=preordered:nm=30:ins=25:rtra=on_2984 on theBenchmark for (2984ds/270Mi)
% 10.72/2.00 % (2865540)Instruction limit reached!
% 10.72/2.00 % (2865540)------------------------------
% 10.72/2.00 % (2865540)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.72/2.00 % (2865540)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.72/2.00 % (2865540)CaDiCaL version: 2.1.3
% 10.72/2.00 % (2865540)Termination reason: Instruction limit
% 10.72/2.00 % (2865540)Termination phase: Saturation
% 10.72/2.00 % (2865540)Time elapsed: 0.052 s
% 10.72/2.00 % (2865540)Peak memory usage: 12 MB
% 10.72/2.00 % (2865540)Instructions burned: 117 (million)
% 10.72/2.00 % (2865545)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=3337852041:hsq=on:hsqr=16,1:s2a=on:i=30:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2984 on theBenchmark for (2984ds/30Mi)
% 10.72/2.00 % (2865545)Instruction limit reached!
% 10.72/2.00 % (2865545)------------------------------
% 10.72/2.00 % (2865545)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.72/2.00 % (2865545)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.72/2.00 % (2865545)CaDiCaL version: 2.1.3
% 10.72/2.00 % (2865545)Termination reason: Instruction limit
% 10.72/2.00 % (2865545)Termination phase: Saturation
% 10.72/2.00 % (2865545)Time elapsed: 0.014 s
% 10.72/2.00 % (2865545)Peak memory usage: 12 MB
% 10.72/2.00 % (2865545)Instructions burned: 31 (million)
% 10.72/2.00 % (2865547)WARNING Broken Constraint: if sine_tolerance(12) has been set then sine_selection(off) is not equal to off
% 10.72/2.00 % (2865547)dis+1010_128_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=hol:nwc=2:flr=on:random_seed=3841046961:st=12:uwa_fpi=on:i=39:nm=40:ins=7:rtra=on_2984 on theBenchmark for (2984ds/39Mi)
% 10.72/2.00 % (2865547)Instruction limit reached!
% 10.72/2.00 % (2865547)------------------------------
% 10.72/2.00 % (2865547)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.72/2.00 % (2865547)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.72/2.00 % (2865547)CaDiCaL version: 2.1.3
% 10.72/2.00 % (2865547)Termination reason: Instruction limit
% 10.72/2.00 % (2865547)Termination phase: Saturation
% 10.72/2.00 % (2865547)Time elapsed: 0.016 s
% 10.72/2.00 % (2865547)Peak memory usage: 11 MB
% 10.72/2.00 % (2865547)Instructions burned: 40 (million)
% 10.72/2.00 % (2865549)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=3063411267:i=365:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2983 on theBenchmark for (2983ds/365Mi)
% 10.72/2.00 % (2865543)Instruction limit reached!
% 10.72/2.00 % (2865543)------------------------------
% 10.72/2.00 % (2865543)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.72/2.00 % (2865543)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.72/2.00 % (2865543)CaDiCaL version: 2.1.3
% 10.72/2.00 % (2865543)Termination reason: Instruction limit
% 10.72/2.00 % (2865543)Termination phase: Saturation
% 10.72/2.00 % (2865543)Time elapsed: 0.122 s
% 10.72/2.00 % (2865543)Peak memory usage: 12 MB
% 10.72/2.00 % (2865543)Instructions burned: 271 (million)
% 10.72/2.00 % (2865551)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=155479913:i=158:av=off:rtra=on_2983 on theBenchmark for (2983ds/158Mi)
% 10.72/2.00 % (2865539)Instruction limit reached!
% 10.72/2.00 % (2865539)------------------------------
% 10.72/2.00 % (2865539)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.72/2.00 % (2865539)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.72/2.00 % (2865539)CaDiCaL version: 2.1.3
% 10.72/2.00 % (2865539)Termination reason: Instruction limit
% 10.72/2.00 % (2865539)Termination phase: Saturation
% 10.72/2.00 % (2865539)Time elapsed: 0.186 s
% 10.72/2.00 % (2865539)Peak memory usage: 13 MB
% 10.72/2.00 % (2865539)Instructions burned: 676 (million)
% 10.72/2.00 % (2865553)WARNING Broken Constraint: if sine_to_age_tolerance(3) 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
% 10.72/2.00 % (2865553)lrs+10_40_sil=128000:tgt=full:cnfonf=off:si=on:sp=reverse_frequency:spb=goal_then_units:uwa=off:fd=preordered:nwc=1:random_seed=1049491589:avsq=on:i=252:s2at=3:avsqr=1,16:rtra=on:ntd=on_2983 on theBenchmark for (2983ds/252Mi)
% 10.72/2.00 % (2865553)Refutation not found, incomplete strategy
% 10.72/2.00 % (2865553)------------------------------
% 10.72/2.00 % (2865553)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.72/2.00 % (2865553)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.72/2.00 % (2865553)CaDiCaL version: 2.1.3
% 10.72/2.00 % (2865553)Termination reason: Refutation not found, incomplete strategy
% 10.72/2.00 % (2865553)Time elapsed: 0.013 s
% 10.72/2.00 % (2865553)Peak memory usage: 12 MB
% 10.72/2.00 % (2865553)Instructions burned: 62 (million)
% 10.72/2.00 % (2865553)------------------------------
% 10.72/2.00 % (2865553)------------------------------
% 10.72/2.00 % (2865555)lrs+10_1_cnfonf=off:si=on:sos=on:uwa=off:random_seed=1514822036:i=213:rtra=on:ss=axioms_2982 on theBenchmark for (2982ds/213Mi)
% 10.72/2.00 % (2865555)Refutation not found, incomplete strategy
% 10.72/2.00 % (2865555)------------------------------
% 10.72/2.00 % (2865555)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.72/2.00 % (2865555)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.72/2.00 % (2865555)CaDiCaL version: 2.1.3
% 10.72/2.00 % (2865555)Termination reason: Refutation not found, incomplete strategy
% 10.72/2.00 % (2865555)Time elapsed: 0.003 s
% 10.72/2.00 % (2865555)Peak memory usage: 12 MB
% 10.72/2.00 % (2865555)Instructions burned: 14 (million)
% 10.72/2.00 % (2865523) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2865300-2865523"...
% 10.72/2.00 % (2865555)------------------------------
% 10.72/2.00 % (2865555)------------------------------
% 10.72/2.00 % (2865557)dis+1010_28_sil=128000:tgt=full:plsq=on:plsqc=1:cnfonf=off:si=on:plsqr=128,1:uwa=off:slsqc=2:sac=on:slsq=on:random_seed=842276201:st=3:i=160:s2at=3:bd=preordered:nm=16:rtra=on:ss=axioms:ntd=on_2982 on theBenchmark for (2982ds/160Mi)
% 10.72/2.00 % (2865557)Refutation not found, incomplete strategy
% 10.72/2.00 % (2865557)------------------------------
% 10.72/2.00 % (2865557)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.72/2.00 % (2865557)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.72/2.00 % (2865557)CaDiCaL version: 2.1.3
% 10.72/2.00 % (2865557)Termination reason: Refutation not found, incomplete strategy
% 10.72/2.00 % (2865557)Time elapsed: 0.011 s
% 10.72/2.00 % (2865557)Peak memory usage: 12 MB
% 10.72/2.00 % (2865557)Instructions burned: 44 (million)
% 10.72/2.00 % (2865557)------------------------------
% 10.72/2.00 % (2865557)------------------------------
% 10.72/2.00 % (2865523)...printing done.
% 10.72/2.00 % (2865523)Refutation found. Thanks to Tanya!
% 10.72/2.00 % SZS status ContradictoryAxioms for theBenchmark
% 10.72/2.00 % SZS output start Proof for theBenchmark
% See solution above
% 10.72/2.01 % (2865523)------------------------------
% 10.72/2.01 % (2865523)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.72/2.01 % (2865523)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.72/2.01 % (2865523)CaDiCaL version: 2.1.3
% 10.72/2.01 % (2865523)Termination reason: Refutation
% 10.72/2.01 % (2865523)Time elapsed: 0.485 s
% 10.72/2.01 % (2865523)Peak memory usage: 14 MB
% 10.72/2.01 % (2865523)Instructions burned: 1068 (million)
% 10.72/2.01 % (2865300)Success in time 1.746 s
% 10.72/2.01 % Vampire exiting
%------------------------------------------------------------------------------