%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO470^6 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 08:48:01 AM UTC 2026
% Result : Theorem 0.22s 0.36s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 17
% Syntax : Number of formulae : 153 ( 84 unt; 0 typ; 2 def)
% Number of atoms : 999 ( 135 equ; 0 cnn)
% Maximal formula atoms : 8 ( 6 avg)
% Number of connectives : 1917 ( 344 ~; 249 |; 14 &;1109 @)
% ( 2 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 136 ( 136 >; 0 *; 0 +; 0 <<)
% Number of symbols : 59 ( 55 usr; 9 con; 0-4 aty)
% ( 170 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 395 ( 0 sgn 46 !; 0 ?; 395 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mu: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
meq_ind: 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,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_11,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_12,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_13,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_14,type,
mtrue: $i > $o ).
thf(func_def_15,type,
mfalse: $i > $o ).
thf(func_def_16,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_17,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_18,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(func_def_19,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(func_def_20,type,
mserial: ( $i > $i > $o ) > $o ).
thf(func_def_21,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(func_def_22,type,
meuclidean: ( $i > $i > $o ) > $o ).
thf(func_def_23,type,
mpartially_functional: ( $i > $i > $o ) > $o ).
thf(func_def_24,type,
mfunctional: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
mweakly_dense: ( $i > $i > $o ) > $o ).
thf(func_def_26,type,
mweakly_connected: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
mweakly_directed: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
mvalid: ( $i > $o ) > $o ).
thf(func_def_29,type,
minvalid: ( $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,
rel_s5: $i > $i > $o ).
thf(func_def_33,type,
mbox_s5: ( $i > $o ) > $i > $o ).
thf(func_def_34,type,
mdia_s5: ( $i > $o ) > $i > $o ).
thf(func_def_35,type,
p: $i > $o ).
thf(func_def_38,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_39,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_40,type,
vIMP: $o > $o > $o ).
thf(func_def_41,type,
vAND: $o > $o > $o ).
thf(func_def_42,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_43,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_44,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_45,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_46,type,
vOR: $o > $o > $o ).
thf(func_def_47,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_48,type,
vNOT: $o > $o ).
thf(func_def_49,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_50,type,
db4:
!>[X0: $tType] : X0 ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mnot) ).
thf(f4,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mor) ).
thf(f5,axiom,
( mand
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mnot @ ( mor @ ( mnot @ X0 ) @ ( mnot @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mand) ).
thf(f6,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mimplies) ).
thf(f8,axiom,
( mequiv
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mand @ ( mimplies @ X0 @ X1 ) @ ( mimplies @ X1 @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mequiv) ).
thf(f18,axiom,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) )
= mreflexive ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mreflexive) ).
thf(f19,axiom,
( msymmetric
= ( ^ [X0: $i > $i > $o] :
! [X2: $i,X1: $i] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',msymmetric) ).
thf(f21,axiom,
( ( ^ [X0: $i > $i > $o] :
! [X2: $i,X1: $i,X3: $i] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X1 @ X3 ) ) )
= mtransitive ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mtransitive) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ~ ( rel_s5 @ X1 @ X2 )
| ( X0 @ X2 ) ) )
= mbox_s5 ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^6.ax',mbox_s5) ).
thf(f33,axiom,
( mdia_s5
= ( ^ [X0: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^6.ax',mdia_s5) ).
thf(f34,axiom,
mreflexive @ rel_s5,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^6.ax',a1) ).
thf(f35,axiom,
mtransitive @ rel_s5,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^6.ax',a2) ).
thf(f36,axiom,
msymmetric @ rel_s5,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^6.ax',a3) ).
thf(f37,conjecture,
mvalid @ ( mequiv @ ( mdia_s5 @ ( mdia_s5 @ ( mbox_s5 @ p ) ) ) @ ( mbox_s5 @ p ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove) ).
thf(f38,negated_conjecture,
~ ( mvalid @ ( mequiv @ ( mdia_s5 @ ( mdia_s5 @ ( mbox_s5 @ p ) ) ) @ ( mbox_s5 @ p ) ) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
thf(f44,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) )
= mreflexive ),
inference(rectify,[],[f18]) ).
thf(f45,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f44]) ).
thf(f48,plain,
msymmetric @ rel_s5,
inference(rectify,[],[f36]) ).
thf(f49,plain,
( ( msymmetric @ rel_s5 )
= $true ),
inference(fool_elimination,[],[f48]) ).
thf(f54,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f55,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f54]) ).
thf(f64,plain,
mtransitive @ rel_s5,
inference(rectify,[],[f35]) ).
thf(f65,plain,
( ( mtransitive @ rel_s5 )
= $true ),
inference(fool_elimination,[],[f64]) ).
thf(f67,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f68,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f67]) ).
thf(f69,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f70,plain,
~ ( mvalid @ ( mequiv @ ( mdia_s5 @ ( mdia_s5 @ ( mbox_s5 @ p ) ) ) @ ( mbox_s5 @ p ) ) ),
inference(rectify,[],[f38]) ).
thf(f71,plain,
( $true
= ( ~ ( mvalid @ ( mequiv @ ( mdia_s5 @ ( mdia_s5 @ ( mbox_s5 @ p ) ) ) @ ( mbox_s5 @ p ) ) ) ) ),
inference(fool_elimination,[],[f70]) ).
thf(f82,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X1 @ X3 )
& ( X0 @ X2 @ X1 ) )
=> ( X0 @ X2 @ X3 ) ) )
= mtransitive ),
inference(rectify,[],[f21]) ).
thf(f83,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f82]) ).
thf(f84,plain,
( mdia_s5
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f33]) ).
thf(f87,plain,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ~ ( rel_s5 @ X1 @ X2 )
| ( X0 @ X2 ) ) )
= mbox_s5 ),
inference(rectify,[],[f32]) ).
thf(f88,plain,
( mbox_s5
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f87]) ).
thf(f89,plain,
mreflexive @ rel_s5,
inference(rectify,[],[f34]) ).
thf(f90,plain,
( ( mreflexive @ rel_s5 )
= $true ),
inference(fool_elimination,[],[f89]) ).
thf(f91,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f92,plain,
( msymmetric
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X2 @ X1 )
=> ( X0 @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f19]) ).
thf(f93,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f92]) ).
thf(f99,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f100,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f101,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f100]) ).
thf(f105,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f99]) ).
thf(f106,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f45]) ).
thf(f107,plain,
( mdia_s5
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f84]) ).
thf(f110,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f93]) ).
thf(f113,plain,
( ( mreflexive @ rel_s5 )
= $true ),
inference(cnf_transformation,[],[f90]) ).
thf(f114,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f83]) ).
thf(f124,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f55]) ).
thf(f125,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f68]) ).
thf(f129,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f101]) ).
thf(f130,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f91]) ).
thf(f131,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f69]) ).
thf(f133,plain,
( $true
= ( ~ ( mvalid @ ( mequiv @ ( mdia_s5 @ ( mdia_s5 @ ( mbox_s5 @ p ) ) ) @ ( mbox_s5 @ p ) ) ) ) ),
inference(cnf_transformation,[],[f71]) ).
thf(f134,plain,
( ( mtransitive @ rel_s5 )
= $true ),
inference(cnf_transformation,[],[f65]) ).
thf(f136,plain,
( ( msymmetric @ rel_s5 )
= $true ),
inference(cnf_transformation,[],[f49]) ).
thf(f137,plain,
( mbox_s5
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f88]) ).
thf(f141,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f130,f124,f129,f124,f124]) ).
thf(f142,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 ) ) ),
inference(definition_unfolding,[],[f105,f129,f124]) ).
thf(f144,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y1
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f131,f141,f142,f142]) ).
thf(f150,plain,
( mdia_s5
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rel_s5 @ Y2 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f107,f124,f137,f124]) ).
thf(f151,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ rel_s5 ) ),
inference(definition_unfolding,[],[f113,f106]) ).
thf(f152,plain,
( $true
= ( ~ ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y1
@ Y0 ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rel_s5 @ Y2 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rel_s5 @ Y2 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
@ p ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
@ p ) ) ) ) ),
inference(definition_unfolding,[],[f133,f125,f144,f150,f150,f137,f137]) ).
thf(f153,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
@ rel_s5 ) ),
inference(definition_unfolding,[],[f134,f114]) ).
thf(f154,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
@ rel_s5 ) ),
inference(definition_unfolding,[],[f136,f110]) ).
thf(f155,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( rel_s5 @ Y0 @ Y0 ) ) ),
inference(beta-eta_normalization,[],[f151]) ).
thf(f156,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel_s5 @ Y0 @ Y1 )
=> ( rel_s5 @ Y1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f154]) ).
thf(f157,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rel_s5 @ Y1 @ Y2 )
& ( rel_s5 @ Y2 @ Y0 ) )
=> ( rel_s5 @ Y1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f153]) ).
thf(f158,plain,
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
~ ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( p @ Y3 )
| ~ ( rel_s5 @ Y2 @ Y3 ) ) )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( p @ Y3 )
| ~ ( rel_s5 @ Y2 @ Y3 ) ) )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f152]) ).
thf(f159,plain,
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
~ ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( p @ Y3 )
| ~ ( rel_s5 @ Y2 @ Y3 ) ) )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( p @ Y3 )
| ~ ( rel_s5 @ Y2 @ Y3 ) ) )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) ) ) ) ) ) ),
inference(boolean_simplification,[],[f158]) ).
thf(f160,plain,
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
~ ( ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( p @ Y3 )
| ~ ( rel_s5 @ Y2 @ Y3 ) ) )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( p @ Y3 )
| ~ ( rel_s5 @ Y2 @ Y3 ) ) )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) ) ) ) ) ) ),
inference(boolean_simplification,[],[f159]) ).
thf(f161,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] : ( rel_s5 @ Y0 @ Y0 )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f155]) ).
thf(f162,plain,
! [X1: $i] :
( $true
= ( rel_s5 @ X1 @ X1 ) ),
inference(beta-eta_normalization,[],[f161]) ).
thf(f163,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
~ ( ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( p @ Y3 )
| ~ ( rel_s5 @ Y2 @ Y3 ) ) )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( p @ Y3 )
| ~ ( rel_s5 @ Y2 @ Y3 ) ) )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f160]) ).
thf(f164,plain,
( $false
= ( ^ [Y0: $i] :
~ ( ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( p @ Y3 )
| ~ ( rel_s5 @ Y2 @ Y3 ) ) )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( p @ Y3 )
| ~ ( rel_s5 @ Y2 @ Y3 ) ) )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f163]) ).
thf(f165,plain,
( $false
= ( ~ ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( p @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( p @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f164]) ).
thf(f166,plain,
( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( p @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( p @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f165]) ).
thf(f167,plain,
( ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( p @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) ) ) ) )
| ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( p @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f166]) ).
thf(f171,definition,
( spl1_1
<=> ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( p @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
thf(f173,plain,
( ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( p @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) ) ) ) )
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f171]) ).
thf(f175,definition,
( spl1_2
<=> ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( p @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
thf(f177,plain,
( ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( p @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) ) ) ) )
| ~ spl1_2 ),
inference(avatar_component_clause,[],[f175]) ).
thf(f178,plain,
( spl1_1
| spl1_2 ),
inference(avatar_split_clause,[],[f167,f175,f171]) ).
thf(f179,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( p @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) ) ) )
| ~ spl1_2 ),
inference(not_proxy_clausification,[],[f177]) ).
thf(f185,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( p @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) ) ) )
| ~ spl1_2 ),
inference(or_proxy_clausification,[],[f179]) ).
thf(f186,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) ) ) )
| ~ spl1_2 ),
inference(or_proxy_clausification,[],[f179]) ).
thf(f205,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( p @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) ) )
| ~ spl1_2 ),
inference(not_proxy_clausification,[],[f185]) ).
thf(f206,plain,
( ! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( p @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( rel_s5 @ sK0 @ Y0 ) )
@ X1 ) )
| ~ spl1_2 ),
inference(pi_proxy_clausification,[],[f205]) ).
thf(f207,plain,
( ! [X1: $i] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( rel_s5 @ X1 @ Y0 ) ) )
| ~ ( rel_s5 @ sK0 @ X1 ) ) )
| ~ spl1_2 ),
inference(beta-eta_normalization,[],[f206]) ).
thf(f209,plain,
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) )
| ~ $true ) )
| ~ spl1_2 ),
inference(constrained_superposition,[],[f207,f162]) ).
thf(f210,plain,
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) )
| $false ) )
| ~ spl1_2 ),
inference(boolean_simplification,[],[f209]) ).
thf(f211,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) ) )
| ~ spl1_2 ),
inference(boolean_simplification,[],[f210]) ).
thf(f212,plain,
( ! [X1: $i] :
( ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( rel_s5 @ sK0 @ Y0 ) )
@ X1 )
= $true )
| ~ spl1_2 ),
inference(pi_proxy_clausification,[],[f211]) ).
thf(f213,plain,
( ! [X1: $i] :
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s5 @ X1 @ Y0 ) ) )
| ~ ( rel_s5 @ sK0 @ X1 ) ) )
| ~ spl1_2 ),
inference(beta-eta_normalization,[],[f212]) ).
thf(f215,plain,
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) )
| ~ $true ) )
| ~ spl1_2 ),
inference(constrained_superposition,[],[f213,f162]) ).
thf(f216,plain,
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) )
| $false ) )
| ~ spl1_2 ),
inference(boolean_simplification,[],[f215]) ).
thf(f217,plain,
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) ) ) )
| ~ spl1_2 ),
inference(boolean_simplification,[],[f216]) ).
thf(f218,plain,
( ( $false = $true )
| ~ spl1_2 ),
inference(forward_demodulation,[],[f217,f186]) ).
thf(f219,plain,
( $false
| ~ spl1_2 ),
inference(trivial_inequality_removal,[],[f218]) ).
thf(f220,plain,
~ spl1_2,
inference(avatar_contradiction_clause,[],[f219]) ).
thf(f221,plain,
( ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( p @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) ) ) )
| ~ spl1_1 ),
inference(not_proxy_clausification,[],[f173]) ).
thf(f227,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) ) )
| ~ spl1_1 ),
inference(or_proxy_clausification,[],[f221]) ).
thf(f228,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( p @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) ) )
| ~ spl1_1 ),
inference(or_proxy_clausification,[],[f221]) ).
thf(f229,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) )
@ sK2 ) )
| ~ spl1_1 ),
inference(sigma_proxy_clausification,[],[f227]) ).
thf(f230,plain,
( ( $false
= ( ( p @ sK2 )
| ~ ( rel_s5 @ sK0 @ sK2 ) ) )
| ~ spl1_1 ),
inference(beta-eta_normalization,[],[f229]) ).
thf(f231,plain,
( ( $false
= ( ~ ( rel_s5 @ sK0 @ sK2 ) ) )
| ~ spl1_1 ),
inference(or_proxy_clausification,[],[f230]) ).
thf(f232,plain,
( ( $false
= ( p @ sK2 ) )
| ~ spl1_1 ),
inference(or_proxy_clausification,[],[f230]) ).
thf(f235,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK2 ) )
| ~ spl1_1 ),
inference(not_proxy_clausification,[],[f231]) ).
thf(f243,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( p @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( rel_s5 @ sK0 @ Y0 ) )
@ sK3 ) )
| ~ spl1_1 ),
inference(sigma_proxy_clausification,[],[f228]) ).
thf(f244,plain,
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( rel_s5 @ sK3 @ Y0 ) ) )
| ~ ( rel_s5 @ sK0 @ sK3 ) )
= $false )
| ~ spl1_1 ),
inference(beta-eta_normalization,[],[f243]) ).
thf(f245,plain,
( ( $false
= ( ~ ( rel_s5 @ sK0 @ sK3 ) ) )
| ~ spl1_1 ),
inference(or_proxy_clausification,[],[f244]) ).
thf(f246,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( rel_s5 @ sK3 @ Y0 ) ) ) )
| ~ spl1_1 ),
inference(or_proxy_clausification,[],[f244]) ).
thf(f247,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK3 ) )
| ~ spl1_1 ),
inference(not_proxy_clausification,[],[f245]) ).
thf(f255,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( rel_s5 @ sK3 @ Y0 ) )
@ sK4 ) )
| ~ spl1_1 ),
inference(sigma_proxy_clausification,[],[f246]) ).
thf(f256,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s5 @ sK4 @ Y0 ) ) )
| ~ ( rel_s5 @ sK3 @ sK4 ) ) )
| ~ spl1_1 ),
inference(beta-eta_normalization,[],[f255]) ).
thf(f257,plain,
( ( $false
= ( ~ ( rel_s5 @ sK3 @ sK4 ) ) )
| ~ spl1_1 ),
inference(or_proxy_clausification,[],[f256]) ).
thf(f258,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s5 @ sK4 @ Y0 ) ) ) ) )
| ~ spl1_1 ),
inference(or_proxy_clausification,[],[f256]) ).
thf(f259,plain,
( ( $true
= ( rel_s5 @ sK3 @ sK4 ) )
| ~ spl1_1 ),
inference(not_proxy_clausification,[],[f257]) ).
thf(f267,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s5 @ sK4 @ Y0 ) ) ) )
| ~ spl1_1 ),
inference(not_proxy_clausification,[],[f258]) ).
thf(f268,plain,
( ! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s5 @ sK4 @ Y0 ) )
@ X1 ) )
| ~ spl1_1 ),
inference(pi_proxy_clausification,[],[f267]) ).
thf(f269,plain,
( ! [X1: $i] :
( $true
= ( ( p @ X1 )
| ~ ( rel_s5 @ sK4 @ X1 ) ) )
| ~ spl1_1 ),
inference(beta-eta_normalization,[],[f268]) ).
thf(f272,plain,
( ( $true
= ( $false
| ~ ( rel_s5 @ sK4 @ sK2 ) ) )
| ~ spl1_1 ),
inference(constrained_superposition,[],[f269,f232]) ).
thf(f273,plain,
( ( ( ~ ( rel_s5 @ sK4 @ sK2 ) )
= $true )
| ~ spl1_1 ),
inference(boolean_simplification,[],[f272]) ).
thf(f278,plain,
( ( $false
= ( rel_s5 @ sK4 @ sK2 ) )
| ~ spl1_1 ),
inference(not_proxy_clausification,[],[f273]) ).
thf(f290,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel_s5 @ Y0 @ Y1 )
=> ( rel_s5 @ Y1 @ Y0 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f156]) ).
thf(f291,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( rel_s5 @ X1 @ Y0 )
=> ( rel_s5 @ Y0 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f290]) ).
thf(f292,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( rel_s5 @ X1 @ Y0 )
=> ( rel_s5 @ Y0 @ X1 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f291]) ).
thf(f293,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( rel_s5 @ X1 @ X2 )
=> ( rel_s5 @ X2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f292]) ).
thf(f339,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rel_s5 @ Y1 @ Y2 )
& ( rel_s5 @ Y2 @ Y0 ) )
=> ( rel_s5 @ Y1 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f157]) ).
thf(f340,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rel_s5 @ Y0 @ Y1 )
& ( rel_s5 @ Y1 @ X1 ) )
=> ( rel_s5 @ Y0 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f339]) ).
thf(f341,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rel_s5 @ Y0 @ Y1 )
& ( rel_s5 @ Y1 @ X1 ) )
=> ( rel_s5 @ Y0 @ X1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f340]) ).
thf(f342,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( rel_s5 @ X2 @ Y0 )
& ( rel_s5 @ Y0 @ X1 ) )
=> ( rel_s5 @ X2 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f341]) ).
thf(f343,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ( rel_s5 @ X2 @ Y0 )
& ( rel_s5 @ Y0 @ X1 ) )
=> ( rel_s5 @ X2 @ X1 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f342]) ).
thf(f344,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( rel_s5 @ X2 @ X3 )
& ( rel_s5 @ X3 @ X1 ) )
=> ( rel_s5 @ X2 @ X1 ) )
= $true ),
inference(beta-eta_normalization,[],[f343]) ).
thf(f358,plain,
( ! [X0: $i] :
( $true
= ( ( ( rel_s5 @ X0 @ sK0 )
& $true )
=> ( rel_s5 @ X0 @ sK2 ) ) )
| ~ spl1_1 ),
inference(constrained_superposition,[],[f344,f235]) ).
thf(f369,plain,
( ! [X0: $i] :
( $true
= ( ( $true
& ( rel_s5 @ sK3 @ X0 ) )
=> ( rel_s5 @ sK0 @ X0 ) ) )
| ~ spl1_1 ),
inference(constrained_superposition,[],[f344,f247]) ).
thf(f375,plain,
( ! [X0: $i] :
( $true
= ( ( rel_s5 @ sK3 @ X0 )
=> ( rel_s5 @ sK0 @ X0 ) ) )
| ~ spl1_1 ),
inference(boolean_simplification,[],[f369]) ).
thf(f400,plain,
( ! [X0: $i] :
( $true
= ( ( rel_s5 @ X0 @ sK0 )
=> ( rel_s5 @ X0 @ sK2 ) ) )
| ~ spl1_1 ),
inference(boolean_simplification,[],[f358]) ).
thf(f412,plain,
( ( $true
= ( $true
=> ( rel_s5 @ sK0 @ sK4 ) ) )
| ~ spl1_1 ),
inference(constrained_superposition,[],[f375,f259]) ).
thf(f414,plain,
( ( ( rel_s5 @ sK0 @ sK4 )
= $true )
| ~ spl1_1 ),
inference(boolean_simplification,[],[f412]) ).
thf(f423,plain,
( ( $true
= ( $true
=> ( rel_s5 @ sK4 @ sK0 ) ) )
| ~ spl1_1 ),
inference(constrained_superposition,[],[f293,f414]) ).
thf(f428,plain,
( ( $true
= ( rel_s5 @ sK4 @ sK0 ) )
| ~ spl1_1 ),
inference(boolean_simplification,[],[f423]) ).
thf(f463,plain,
( ( $true
= ( ( rel_s5 @ sK4 @ sK0 )
=> $false ) )
| ~ spl1_1 ),
inference(constrained_superposition,[],[f400,f278]) ).
thf(f475,plain,
( ( $true
= ( ~ ( rel_s5 @ sK4 @ sK0 ) ) )
| ~ spl1_1 ),
inference(boolean_simplification,[],[f463]) ).
thf(f479,plain,
( ( $true = ( ~ $true ) )
| ~ spl1_1 ),
inference(forward_demodulation,[],[f475,f428]) ).
thf(f480,plain,
( ( $false = $true )
| ~ spl1_1 ),
inference(boolean_simplification,[],[f479]) ).
thf(f481,plain,
( $false
| ~ spl1_1 ),
inference(trivial_inequality_removal,[],[f480]) ).
thf(f482,plain,
~ spl1_1,
inference(avatar_contradiction_clause,[],[f481]) ).
cnf(s1,plain,
( spl1_1
| spl1_2 ),
inference(sat_conversion,[],[f178]) ).
cnf(s2,plain,
~ spl1_2,
inference(sat_conversion,[],[f220]) ).
cnf(s4,plain,
~ spl1_1,
inference(sat_conversion,[],[f482]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s2,s4]) ).
thf(f483,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO470^6 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n013.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 17:02:51 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.24 Running higher-order theorem proving
% 0.08/0.25 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
% 0.22/0.36 % (2388176)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.36 % (2388183)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=4119604001:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.36 % (2388183)Instruction limit reached!
% 0.22/0.36 % (2388183)------------------------------
% 0.22/0.36 % (2388183)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.36 % (2388183)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.36 % (2388183)CaDiCaL version: 2.1.3
% 0.22/0.36 % (2388183)Termination reason: Instruction limit
% 0.22/0.36 % (2388183)Termination phase: Property scanning
% 0.22/0.36 % (2388183)Time elapsed: 0.002 s
% 0.22/0.36 % (2388183)Peak memory usage: 10 MB
% 0.22/0.36 % (2388183)Instructions burned: 7 (million)
% 0.22/0.36 % (2388187)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.36 % (2388187)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
% 0.22/0.36 % (2388182)lrs+10_16_si=on:nwc=1.5:random_seed=393369698:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.36 % (2388184)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=902730578: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)
% 0.22/0.36 % (2388181)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1452662557:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.36 % (2388185)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1292879045:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.36 % (2388186)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2442418413:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.36 % (2388187)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=2506704643:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.36 % (2388189)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3336153163:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.22/0.36 % (2388189)Instruction limit reached!
% 0.22/0.36 % (2388189)------------------------------
% 0.22/0.36 % (2388189)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.36 % (2388189)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.36 % (2388189)CaDiCaL version: 2.1.3
% 0.22/0.36 % (2388189)Termination reason: Instruction limit
% 0.22/0.36 % (2388189)Termination phase: Function definition elimination
% 0.22/0.36 % (2388189)Time elapsed: 0.001 s
% 0.22/0.36 % (2388189)Peak memory usage: 10 MB
% 0.22/0.36 % (2388189)Instructions burned: 6 (million)
% 0.22/0.36 % (2388182)Instruction limit reached!
% 0.22/0.36 % (2388182)------------------------------
% 0.22/0.36 % (2388182)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.36 % (2388182)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.36 % (2388182)CaDiCaL version: 2.1.3
% 0.22/0.36 % (2388182)Termination reason: Instruction limit
% 0.22/0.36 % (2388182)Termination phase: Saturation
% 0.22/0.36 % (2388182)Time elapsed: 0.009 s
% 0.22/0.36 % (2388182)Peak memory usage: 12 MB
% 0.22/0.36 % (2388182)Instructions burned: 18 (million)
% 0.22/0.36 % (2388185)Instruction limit reached!
% 0.22/0.36 % (2388185)------------------------------
% 0.22/0.36 % (2388185)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.36 % (2388185)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.36 % (2388185)CaDiCaL version: 2.1.3
% 0.22/0.36 % (2388185)Termination reason: Instruction limit
% 0.22/0.36 % (2388185)Termination phase: Saturation
% 0.22/0.36 % (2388185)Time elapsed: 0.014 s
% 0.22/0.36 % (2388185)Peak memory usage: 11 MB
% 0.22/0.36 % (2388185)Instructions burned: 25 (million)
% 0.22/0.36 % (2388197)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1200238360:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.22/0.36 % (2388197)Instruction limit reached!
% 0.22/0.36 % (2388197)------------------------------
% 0.22/0.36 % (2388197)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.36 % (2388197)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.36 % (2388197)CaDiCaL version: 2.1.3
% 0.22/0.36 % (2388197)Termination reason: Instruction limit
% 0.22/0.36 % (2388197)Termination phase: Saturation
% 0.22/0.36 % (2388197)Time elapsed: 0.002 s
% 0.22/0.36 % (2388197)Peak memory usage: 10 MB
% 0.22/0.36 % (2388197)Instructions burned: 8 (million)
% 0.22/0.36 % (2388198)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.22/0.36 % (2388198)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2328504740:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.22/0.36 % (2388198)Instruction limit reached!
% 0.22/0.36 % (2388198)------------------------------
% 0.22/0.36 % (2388198)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.36 % (2388198)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.36 % (2388198)CaDiCaL version: 2.1.3
% 0.22/0.36 % (2388198)Termination reason: Instruction limit
% 0.22/0.36 % (2388198)Termination phase: Saturation
% 0.22/0.36 % (2388198)Time elapsed: 0.002 s
% 0.22/0.36 % (2388198)Peak memory usage: 11 MB
% 0.22/0.36 % (2388198)Instructions burned: 9 (million)
% 0.22/0.36 % (2388199)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=4277231301:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.22/0.36 % (2388186)Instruction limit reached!
% 0.22/0.36 % (2388186)------------------------------
% 0.22/0.36 % (2388186)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.36 % (2388186)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.36 % (2388186)CaDiCaL version: 2.1.3
% 0.22/0.36 % (2388186)Termination reason: Instruction limit
% 0.22/0.36 % (2388186)Termination phase: Saturation
% 0.22/0.36 % (2388186)Time elapsed: 0.035 s
% 0.22/0.36 % (2388186)Peak memory usage: 12 MB
% 0.22/0.36 % (2388186)Instructions burned: 75 (million)
% 0.22/0.36 % (2388203)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=183684760:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.22/0.36 % (2388199)Instruction limit reached!
% 0.22/0.36 % (2388199)------------------------------
% 0.22/0.36 % (2388199)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.36 % (2388199)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.36 % (2388199)CaDiCaL version: 2.1.3
% 0.22/0.36 % (2388199)Termination reason: Instruction limit
% 0.22/0.36 % (2388199)Termination phase: Saturation
% 0.22/0.36 % (2388199)Time elapsed: 0.006 s
% 0.22/0.36 % (2388199)Peak memory usage: 11 MB
% 0.22/0.36 % (2388199)Instructions burned: 13 (million)
% 0.22/0.36 % (2388201)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
% 0.22/0.36 % (2388201)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.22/0.36 % (2388181)Instruction limit reached!
% 0.22/0.36 % (2388181)------------------------------
% 0.22/0.36 % (2388181)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.36 % (2388181)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.36 % (2388181)CaDiCaL version: 2.1.3
% 0.22/0.36 % (2388181)Termination reason: Instruction limit
% 0.22/0.36 % (2388181)Termination phase: Saturation
% 0.22/0.36 % (2388181)Time elapsed: 0.045 s
% 0.22/0.36 % (2388181)Peak memory usage: 12 MB
% 0.22/0.36 % (2388181)Instructions burned: 87 (million)
% 0.22/0.36 % (2388203) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2388176-2388203"...
% 0.22/0.36 % (2388201)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=824426934:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.22/0.36 % (2388203)...printing done.
% 0.22/0.36 % (2388203)Refutation found. Thanks to Tanya!
% 0.22/0.36 % SZS status Theorem for theBenchmark
% 0.22/0.36 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.36 % (2388203)------------------------------
% 0.22/0.36 % (2388203)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.36 % (2388203)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.36 % (2388203)CaDiCaL version: 2.1.3
% 0.22/0.36 % (2388203)Termination reason: Refutation
% 0.22/0.36 % (2388203)Time elapsed: 0.014 s
% 0.22/0.36 % (2388203)Peak memory usage: 13 MB
% 0.22/0.36 % (2388203)Instructions burned: 48 (million)
% 0.22/0.36 % (2388176)Success in time 0.093 s
% 0.22/0.36 % Vampire exiting
%------------------------------------------------------------------------------