%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL725^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 08:14:34 AM UTC 2026
% Result : Theorem 0.22s 0.35s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 28
% Syntax : Number of formulae : 203 ( 71 unt; 0 typ; 15 def)
% Number of atoms : 1282 ( 247 equ; 0 cnn)
% Maximal formula atoms : 18 ( 6 avg)
% Number of connectives : 1583 ( 216 ~; 261 |; 21 &; 949 @)
% ( 12 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 156 ( 156 >; 0 *; 0 +; 0 <<)
% Number of symbols : 77 ( 73 usr; 24 con; 0-4 aty)
% ( 102 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 387 ( 0 sgn 67 !; 0 ?; 387 :)
% 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,
phi: $i > $o ).
thf(func_def_36,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_37,type,
vIMP: $o > $o > $o ).
thf(func_def_38,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_39,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_41,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_42,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_43,type,
vAND: $o > $o > $o ).
thf(func_def_44,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_45,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_46,type,
vOR: $o > $o > $o ).
thf(func_def_49,type,
vNOT: $o > $o ).
thf(func_def_50,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_51,type,
sF0: $o ).
thf(func_def_52,type,
sF1: $o ).
thf(func_def_53,type,
sF2: $o ).
thf(func_def_55,type,
sK4: $i > $i ).
thf(func_def_56,type,
sK5: $i > $i ).
thf(func_def_59,type,
sK8: $i > $i ).
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] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= mor ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mor) ).
thf(f6,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) )
= mimplies ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mimplies) ).
thf(f18,axiom,
( mreflexive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mreflexive) ).
thf(f19,axiom,
( ( ^ [X0: $i > $i > $o] :
! [X2: $i,X1: $i] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) ) )
= msymmetric ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',msymmetric) ).
thf(f21,axiom,
( mtransitive
= ( ^ [X0: $i > $i > $o] :
! [X2: $i,X3: $i,X1: $i] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X1 @ X3 ) ) ) ),
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,
( mbox_s5
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ~ ( rel_s5 @ X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^6.ax',mbox_s5) ).
thf(f33,axiom,
( ( ^ [X0: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ X0 ) ) ) )
= mdia_s5 ),
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 @ ( mimplies @ ( mbox_s5 @ phi ) @ ( mbox_s5 @ ( mbox_s5 @ phi ) ) ) )
& ( mvalid @ ( mimplies @ phi @ ( mbox_s5 @ ( mdia_s5 @ phi ) ) ) )
& ( mvalid @ ( mimplies @ ( mbox_s5 @ phi ) @ phi ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(f38,negated_conjecture,
~ ( ( mvalid @ ( mimplies @ ( mbox_s5 @ phi ) @ ( mbox_s5 @ ( mbox_s5 @ phi ) ) ) )
& ( mvalid @ ( mimplies @ phi @ ( mbox_s5 @ ( mdia_s5 @ phi ) ) ) )
& ( mvalid @ ( mimplies @ ( mbox_s5 @ phi ) @ phi ) ) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
thf(f39,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X2 @ X1 )
=> ( X0 @ X1 @ X2 ) ) )
= msymmetric ),
inference(rectify,[],[f19]) ).
thf(f40,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f39]) ).
thf(f43,plain,
( mdia_s5
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f33]) ).
thf(f44,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f45,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f44]) ).
thf(f54,plain,
mreflexive @ rel_s5,
inference(rectify,[],[f34]) ).
thf(f55,plain,
( ( mreflexive @ rel_s5 )
= $true ),
inference(fool_elimination,[],[f54]) ).
thf(f61,plain,
( mtransitive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X1 @ X2 )
& ( X0 @ X3 @ X1 ) )
=> ( X0 @ X3 @ X2 ) ) ) ),
inference(rectify,[],[f21]) ).
thf(f62,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f61]) ).
thf(f63,plain,
( mbox_s5
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ~ ( rel_s5 @ X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f32]) ).
thf(f64,plain,
( mbox_s5
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f63]) ).
thf(f68,plain,
( mreflexive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
inference(rectify,[],[f18]) ).
thf(f69,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f68]) ).
thf(f70,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f71,plain,
msymmetric @ rel_s5,
inference(rectify,[],[f36]) ).
thf(f72,plain,
( ( msymmetric @ rel_s5 )
= $true ),
inference(fool_elimination,[],[f71]) ).
thf(f87,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f88,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f87]) ).
thf(f93,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f94,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f93]) ).
thf(f96,plain,
mtransitive @ rel_s5,
inference(rectify,[],[f35]) ).
thf(f97,plain,
( ( mtransitive @ rel_s5 )
= $true ),
inference(fool_elimination,[],[f96]) ).
thf(f98,plain,
~ ( ( mvalid @ ( mimplies @ ( mbox_s5 @ phi ) @ ( mbox_s5 @ ( mbox_s5 @ phi ) ) ) )
& ( mvalid @ ( mimplies @ phi @ ( mbox_s5 @ ( mdia_s5 @ phi ) ) ) )
& ( mvalid @ ( mimplies @ ( mbox_s5 @ phi ) @ phi ) ) ),
inference(rectify,[],[f38]) ).
thf(f99,plain,
~ ( ( ( mvalid @ ( mimplies @ ( mbox_s5 @ phi ) @ phi ) )
= $true )
& ( ( mvalid @ ( mimplies @ ( mbox_s5 @ phi ) @ ( mbox_s5 @ ( mbox_s5 @ phi ) ) ) )
= $true )
& ( ( mvalid @ ( mimplies @ phi @ ( mbox_s5 @ ( mdia_s5 @ phi ) ) ) )
= $true ) ),
inference(fool_elimination,[],[f98]) ).
thf(f101,plain,
( ( ( mvalid @ ( mimplies @ ( mbox_s5 @ phi ) @ phi ) )
!= $true )
| ( ( mvalid @ ( mimplies @ ( mbox_s5 @ phi ) @ ( mbox_s5 @ ( mbox_s5 @ phi ) ) ) )
!= $true )
| ( ( mvalid @ ( mimplies @ phi @ ( mbox_s5 @ ( mdia_s5 @ phi ) ) ) )
!= $true ) ),
inference(ennf_transformation,[],[f99]) ).
thf(f107,plain,
( ( msymmetric @ rel_s5 )
= $true ),
inference(cnf_transformation,[],[f72]) ).
thf(f108,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f45]) ).
thf(f110,plain,
( ( mreflexive @ rel_s5 )
= $true ),
inference(cnf_transformation,[],[f55]) ).
thf(f111,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f94]) ).
thf(f120,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f70]) ).
thf(f121,plain,
( ( mtransitive @ rel_s5 )
= $true ),
inference(cnf_transformation,[],[f97]) ).
thf(f124,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f88]) ).
thf(f125,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f40]) ).
thf(f126,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f69]) ).
thf(f133,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f62]) ).
thf(f136,plain,
( mbox_s5
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f64]) ).
thf(f137,plain,
( mdia_s5
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f43]) ).
thf(f138,plain,
( ( ( mvalid @ ( mimplies @ ( mbox_s5 @ phi ) @ phi ) )
!= $true )
| ( ( mvalid @ ( mimplies @ ( mbox_s5 @ phi ) @ ( mbox_s5 @ ( mbox_s5 @ phi ) ) ) )
!= $true )
| ( ( mvalid @ ( mimplies @ phi @ ( mbox_s5 @ ( mdia_s5 @ phi ) ) ) )
!= $true ) ),
inference(cnf_transformation,[],[f101]) ).
thf(f142,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 ) ) ),
inference(definition_unfolding,[],[f120,f108,f111]) ).
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,[],[f137,f111,f136,f111]) ).
thf(f151,plain,
( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
@ rel_s5 )
= $true ),
inference(definition_unfolding,[],[f107,f125]) ).
thf(f152,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ rel_s5 ) ),
inference(definition_unfolding,[],[f110,f126]) ).
thf(f153,plain,
( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
@ rel_s5 )
= $true ),
inference(definition_unfolding,[],[f121,f133]) ).
thf(f154,plain,
( ( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
@ phi )
@ phi ) )
!= $true )
| ( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
@ phi )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
@ phi ) ) ) ) )
| ( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 )
@ phi
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
@ ( ^ [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 ) ) )
@ phi ) ) ) ) ) ),
inference(definition_unfolding,[],[f138,f124,f142,f136,f124,f142,f136,f136,f136,f124,f142,f136,f150]) ).
thf(f155,definition,
( sF0
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
@ phi )
@ phi ) ) ),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
thf(f156,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
@ phi )
@ phi ) )
= sF0 ),
inference(reorient_equations,[],[f155]) ).
thf(f157,definition,
( sF1
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
@ phi )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
@ phi ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
thf(f158,definition,
( sF2
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 )
@ phi
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
@ ( ^ [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 ) ) )
@ phi ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
thf(f159,plain,
( ( sF0 != $true )
| ( sF1 != $true )
| ( sF2 != $true ) ),
inference(definition_folding,[],[f154,f158,f157,f156]) ).
thf(f160,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rel_s5 @ Y0 @ Y2 )
& ( rel_s5 @ Y2 @ Y1 ) )
=> ( rel_s5 @ Y0 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f153]) ).
thf(f161,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rel_s5 @ Y0 @ Y2 )
& ( rel_s5 @ Y2 @ Y1 ) )
=> ( rel_s5 @ Y0 @ Y1 ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f160]) ).
thf(f162,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rel_s5 @ X1 @ Y1 )
& ( rel_s5 @ Y1 @ Y0 ) )
=> ( rel_s5 @ X1 @ Y0 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f161]) ).
thf(f163,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rel_s5 @ X1 @ Y1 )
& ( rel_s5 @ Y1 @ Y0 ) )
=> ( rel_s5 @ X1 @ Y0 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f162]) ).
thf(f164,plain,
! [X2: $i,X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( rel_s5 @ X1 @ Y0 )
& ( rel_s5 @ Y0 @ X2 ) )
=> ( rel_s5 @ X1 @ X2 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f163]) ).
thf(f165,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( ( rel_s5 @ X1 @ Y0 )
& ( rel_s5 @ Y0 @ X2 ) )
=> ( rel_s5 @ X1 @ X2 ) )
@ X3 )
= $true ),
inference(pi_proxy_clausification,[],[f164]) ).
thf(f166,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( rel_s5 @ X1 @ X3 )
& ( rel_s5 @ X3 @ X2 ) )
=> ( rel_s5 @ X1 @ X2 ) )
= $true ),
inference(beta-eta_normalization,[],[f165]) ).
thf(f167,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( rel_s5 @ X1 @ X3 )
& ( rel_s5 @ X3 @ X2 ) )
= $false )
| ( ( rel_s5 @ X1 @ X2 )
= $true ) ),
inference(imp_proxy_clausification,[],[f166]) ).
thf(f168,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( rel_s5 @ X3 @ X2 )
= $false )
| ( ( rel_s5 @ X1 @ X3 )
= $false )
| ( ( rel_s5 @ X1 @ X2 )
= $true ) ),
inference(and_proxy_clausification,[],[f167]) ).
thf(f169,plain,
( ( !! @ $i
@ ^ [Y0: $i] : ( rel_s5 @ Y0 @ Y0 ) )
= $true ),
inference(beta-eta_normalization,[],[f152]) ).
thf(f170,plain,
! [X1: $i] :
( ( ^ [Y0: $i] : ( rel_s5 @ Y0 @ Y0 )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f169]) ).
thf(f171,plain,
! [X1: $i] :
( ( rel_s5 @ X1 @ X1 )
= $true ),
inference(beta-eta_normalization,[],[f170]) ).
thf(f173,plain,
( ( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
@ phi )
@ phi ) )
= $false )
| ( sF0 = $true ) ),
inference(iff_proxy_clausification,[],[f156]) ).
thf(f174,plain,
( ( sF0 = $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( phi @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( phi @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f173]) ).
thf(f175,plain,
( ( sF0 = $true )
| ( ( ^ [Y0: $i] :
( ( phi @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( phi @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) ) )
@ sK3 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f174]) ).
thf(f176,plain,
( ( sF0 = $true )
| ( ( ( phi @ sK3 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( phi @ Y0 )
| ~ ( rel_s5 @ sK3 @ Y0 ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f175]) ).
thf(f177,plain,
( ( sF0 = $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( phi @ Y0 )
| ~ ( rel_s5 @ sK3 @ Y0 ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f176]) ).
thf(f178,plain,
( ( ( phi @ sK3 )
= $false )
| ( sF0 = $true ) ),
inference(or_proxy_clausification,[],[f176]) ).
thf(f179,plain,
( ( sF0 = $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( phi @ Y0 )
| ~ ( rel_s5 @ sK3 @ Y0 ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f177]) ).
thf(f180,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( phi @ Y0 )
| ~ ( rel_s5 @ sK3 @ Y0 ) )
@ X1 ) )
| ( sF0 = $true ) ),
inference(pi_proxy_clausification,[],[f179]) ).
thf(f181,plain,
! [X1: $i] :
( ( ( ( phi @ X1 )
| ~ ( rel_s5 @ sK3 @ X1 ) )
= $true )
| ( sF0 = $true ) ),
inference(beta-eta_normalization,[],[f180]) ).
thf(f182,plain,
! [X1: $i] :
( ( ( phi @ X1 )
= $true )
| ( ( ~ ( rel_s5 @ sK3 @ X1 ) )
= $true )
| ( sF0 = $true ) ),
inference(or_proxy_clausification,[],[f181]) ).
thf(f183,plain,
! [X1: $i] :
( ( ( rel_s5 @ sK3 @ X1 )
= $false )
| ( sF0 = $true )
| ( ( phi @ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f182]) ).
thf(f194,plain,
( ( sF2 = $true )
| ( $false
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 )
@ phi
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
@ ( ^ [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 ) ) )
@ phi ) ) ) ) ) ),
inference(iff_proxy_clausification,[],[f158]) ).
thf(f212,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( phi @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( phi @ Y0 ) ) )
= $false )
| ( sF2 = $true ) ),
inference(beta-eta_normalization,[],[f194]) ).
thf(f213,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( phi @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( phi @ Y0 ) )
@ sK6 ) )
| ( sF2 = $true ) ),
inference(sigma_proxy_clausification,[],[f212]) ).
thf(f214,plain,
( ( sF2 = $true )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( phi @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( rel_s5 @ sK6 @ Y0 ) ) )
| ~ ( phi @ sK6 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f213]) ).
thf(f215,plain,
( ( ( ~ ( phi @ sK6 ) )
= $false )
| ( sF2 = $true ) ),
inference(or_proxy_clausification,[],[f214]) ).
thf(f216,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( phi @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( rel_s5 @ sK6 @ Y0 ) ) )
= $false )
| ( sF2 = $true ) ),
inference(or_proxy_clausification,[],[f214]) ).
thf(f217,plain,
( ( ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( phi @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( rel_s5 @ sK6 @ Y0 ) )
@ sK7 )
= $false )
| ( sF2 = $true ) ),
inference(sigma_proxy_clausification,[],[f216]) ).
thf(f218,plain,
( ( sF2 = $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( phi @ Y0 )
| ~ ( rel_s5 @ sK7 @ Y0 ) ) )
| ~ ( rel_s5 @ sK6 @ sK7 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f217]) ).
thf(f219,plain,
( ( sF2 = $true )
| ( ( ~ ( rel_s5 @ sK6 @ sK7 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f218]) ).
thf(f220,plain,
( ( sF2 = $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( phi @ Y0 )
| ~ ( rel_s5 @ sK7 @ Y0 ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f218]) ).
thf(f221,plain,
( ( sF2 = $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( phi @ Y0 )
| ~ ( rel_s5 @ sK7 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f220]) ).
thf(f222,plain,
! [X1: $i] :
( ( sF2 = $true )
| ( ( ^ [Y0: $i] :
( ~ ( phi @ Y0 )
| ~ ( rel_s5 @ sK7 @ Y0 ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f221]) ).
thf(f223,plain,
! [X1: $i] :
( ( ( ~ ( phi @ X1 )
| ~ ( rel_s5 @ sK7 @ X1 ) )
= $true )
| ( sF2 = $true ) ),
inference(beta-eta_normalization,[],[f222]) ).
thf(f224,plain,
! [X1: $i] :
( ( sF2 = $true )
| ( ( ~ ( rel_s5 @ sK7 @ X1 ) )
= $true )
| ( $true
= ( ~ ( phi @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f223]) ).
thf(f225,plain,
! [X1: $i] :
( ( sF2 = $true )
| ( $true
= ( ~ ( phi @ X1 ) ) )
| ( ( rel_s5 @ sK7 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f224]) ).
thf(f226,plain,
! [X1: $i] :
( ( ( phi @ X1 )
= $false )
| ( sF2 = $true )
| ( ( rel_s5 @ sK7 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f225]) ).
thf(f227,plain,
( ( sF2 = $true )
| ( ( rel_s5 @ sK6 @ sK7 )
= $true ) ),
inference(not_proxy_clausification,[],[f219]) ).
thf(f228,plain,
( ( sF2 = $true )
| ( ( phi @ sK6 )
= $true ) ),
inference(not_proxy_clausification,[],[f215]) ).
thf(f229,plain,
( ( sF1 = $true )
| ( $false
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
@ phi )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
@ phi ) ) ) ) ) ),
inference(iff_proxy_clausification,[],[f157]) ).
thf(f254,plain,
( ( sF1 = $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( phi @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( phi @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f229]) ).
thf(f255,plain,
( ( ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( phi @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( phi @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) ) )
@ sK9 )
= $false )
| ( sF1 = $true ) ),
inference(sigma_proxy_clausification,[],[f254]) ).
thf(f256,plain,
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( phi @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( rel_s5 @ sK9 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( phi @ Y0 )
| ~ ( rel_s5 @ sK9 @ Y0 ) ) ) )
= $false )
| ( sF1 = $true ) ),
inference(beta-eta_normalization,[],[f255]) ).
thf(f257,plain,
( ( sF1 = $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( phi @ Y0 )
| ~ ( rel_s5 @ sK9 @ Y0 ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f256]) ).
thf(f258,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( phi @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( rel_s5 @ sK9 @ Y0 ) ) )
= $false )
| ( sF1 = $true ) ),
inference(or_proxy_clausification,[],[f256]) ).
thf(f259,plain,
( ( ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( phi @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( rel_s5 @ sK9 @ Y0 ) )
@ sK10 )
= $false )
| ( sF1 = $true ) ),
inference(sigma_proxy_clausification,[],[f258]) ).
thf(f260,plain,
( ( sF1 = $true )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( phi @ Y0 )
| ~ ( rel_s5 @ sK10 @ Y0 ) ) )
| ~ ( rel_s5 @ sK9 @ sK10 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f259]) ).
thf(f261,plain,
( ( sF1 = $true )
| ( ( ~ ( rel_s5 @ sK9 @ sK10 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f260]) ).
thf(f262,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( phi @ Y0 )
| ~ ( rel_s5 @ sK10 @ Y0 ) ) )
= $false )
| ( sF1 = $true ) ),
inference(or_proxy_clausification,[],[f260]) ).
thf(f263,plain,
( ( ( ^ [Y0: $i] :
( ( phi @ Y0 )
| ~ ( rel_s5 @ sK10 @ Y0 ) )
@ sK11 )
= $false )
| ( sF1 = $true ) ),
inference(sigma_proxy_clausification,[],[f262]) ).
thf(f264,plain,
( ( sF1 = $true )
| ( ( ( phi @ sK11 )
| ~ ( rel_s5 @ sK10 @ sK11 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f263]) ).
thf(f265,plain,
( ( ( ~ ( rel_s5 @ sK10 @ sK11 ) )
= $false )
| ( sF1 = $true ) ),
inference(or_proxy_clausification,[],[f264]) ).
thf(f266,plain,
( ( sF1 = $true )
| ( ( phi @ sK11 )
= $false ) ),
inference(or_proxy_clausification,[],[f264]) ).
thf(f267,plain,
( ( ( rel_s5 @ sK10 @ sK11 )
= $true )
| ( sF1 = $true ) ),
inference(not_proxy_clausification,[],[f265]) ).
thf(f268,plain,
( ( sF1 = $true )
| ( $true
= ( rel_s5 @ sK9 @ sK10 ) ) ),
inference(not_proxy_clausification,[],[f261]) ).
thf(f269,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( phi @ Y0 )
| ~ ( rel_s5 @ sK9 @ Y0 ) ) )
= $true )
| ( sF1 = $true ) ),
inference(not_proxy_clausification,[],[f257]) ).
thf(f270,plain,
! [X1: $i] :
( ( sF1 = $true )
| ( ( ^ [Y0: $i] :
( ( phi @ Y0 )
| ~ ( rel_s5 @ sK9 @ Y0 ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f269]) ).
thf(f271,plain,
! [X1: $i] :
( ( ( ( phi @ X1 )
| ~ ( rel_s5 @ sK9 @ X1 ) )
= $true )
| ( sF1 = $true ) ),
inference(beta-eta_normalization,[],[f270]) ).
thf(f272,plain,
! [X1: $i] :
( ( ( phi @ X1 )
= $true )
| ( ( ~ ( rel_s5 @ sK9 @ X1 ) )
= $true )
| ( sF1 = $true ) ),
inference(or_proxy_clausification,[],[f271]) ).
thf(f273,plain,
! [X1: $i] :
( ( ( rel_s5 @ sK9 @ X1 )
= $false )
| ( sF1 = $true )
| ( ( phi @ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f272]) ).
thf(f274,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel_s5 @ Y0 @ Y1 )
=> ( rel_s5 @ Y1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f151]) ).
thf(f275,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel_s5 @ Y0 @ Y1 )
=> ( rel_s5 @ Y1 @ Y0 ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f274]) ).
thf(f276,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( rel_s5 @ X1 @ Y0 )
=> ( rel_s5 @ Y0 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f275]) ).
thf(f277,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( rel_s5 @ X1 @ Y0 )
=> ( rel_s5 @ Y0 @ X1 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f276]) ).
thf(f278,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( rel_s5 @ X1 @ X2 )
=> ( rel_s5 @ X2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f277]) ).
thf(f279,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s5 @ X2 @ X1 )
= $true )
| ( ( rel_s5 @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f278]) ).
thf(f281,definition,
( spl12_1
<=> ( sF1 = $true ) ),
introduced(definition,[new_symbols(definition,[spl12_1])],[avatar_definition]) ).
thf(f285,definition,
( spl12_2
<=> ( sF2 = $true ) ),
introduced(definition,[new_symbols(definition,[spl12_2])],[avatar_definition]) ).
thf(f289,definition,
( spl12_3
<=> ( sF0 = $true ) ),
introduced(definition,[new_symbols(definition,[spl12_3])],[avatar_definition]) ).
thf(f292,plain,
( ~ spl12_1
| ~ spl12_2
| ~ spl12_3 ),
inference(avatar_split_clause,[],[f159,f289,f285,f281]) ).
thf(f294,definition,
( spl12_4
<=> ( ( phi @ sK3 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl12_4])],[avatar_definition]) ).
thf(f296,plain,
( ( ( phi @ sK3 )
= $false )
| ~ spl12_4 ),
inference(avatar_component_clause,[],[f294]) ).
thf(f297,plain,
( spl12_4
| spl12_3 ),
inference(avatar_split_clause,[],[f178,f289,f294]) ).
thf(f299,definition,
( spl12_5
<=> ! [X1: $i] :
( ( ( rel_s5 @ sK3 @ X1 )
= $false )
| ( ( phi @ X1 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl12_5])],[avatar_definition]) ).
thf(f300,plain,
( ! [X1: $i] :
( ( ( rel_s5 @ sK3 @ X1 )
= $false )
| ( ( phi @ X1 )
= $true ) )
| ~ spl12_5 ),
inference(avatar_component_clause,[],[f299]) ).
thf(f301,plain,
( spl12_5
| spl12_3 ),
inference(avatar_split_clause,[],[f183,f289,f299]) ).
thf(f327,definition,
( spl12_12
<=> ! [X1: $i] :
( ( ( phi @ X1 )
= $false )
| ( ( rel_s5 @ sK7 @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl12_12])],[avatar_definition]) ).
thf(f328,plain,
( ! [X1: $i] :
( ( ( rel_s5 @ sK7 @ X1 )
= $false )
| ( ( phi @ X1 )
= $false ) )
| ~ spl12_12 ),
inference(avatar_component_clause,[],[f327]) ).
thf(f329,plain,
( spl12_2
| spl12_12 ),
inference(avatar_split_clause,[],[f226,f327,f285]) ).
thf(f331,definition,
( spl12_13
<=> ( ( rel_s5 @ sK6 @ sK7 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl12_13])],[avatar_definition]) ).
thf(f333,plain,
( ( ( rel_s5 @ sK6 @ sK7 )
= $true )
| ~ spl12_13 ),
inference(avatar_component_clause,[],[f331]) ).
thf(f334,plain,
( spl12_13
| spl12_2 ),
inference(avatar_split_clause,[],[f227,f285,f331]) ).
thf(f336,definition,
( spl12_14
<=> ( ( phi @ sK6 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl12_14])],[avatar_definition]) ).
thf(f338,plain,
( ( ( phi @ sK6 )
= $true )
| ~ spl12_14 ),
inference(avatar_component_clause,[],[f336]) ).
thf(f339,plain,
( spl12_14
| spl12_2 ),
inference(avatar_split_clause,[],[f228,f285,f336]) ).
thf(f353,definition,
( spl12_18
<=> ( ( phi @ sK11 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl12_18])],[avatar_definition]) ).
thf(f355,plain,
( ( ( phi @ sK11 )
= $false )
| ~ spl12_18 ),
inference(avatar_component_clause,[],[f353]) ).
thf(f356,plain,
( spl12_18
| spl12_1 ),
inference(avatar_split_clause,[],[f266,f281,f353]) ).
thf(f358,definition,
( spl12_19
<=> ( ( rel_s5 @ sK10 @ sK11 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl12_19])],[avatar_definition]) ).
thf(f360,plain,
( ( ( rel_s5 @ sK10 @ sK11 )
= $true )
| ~ spl12_19 ),
inference(avatar_component_clause,[],[f358]) ).
thf(f361,plain,
( spl12_19
| spl12_1 ),
inference(avatar_split_clause,[],[f267,f281,f358]) ).
thf(f363,definition,
( spl12_20
<=> ( $true
= ( rel_s5 @ sK9 @ sK10 ) ) ),
introduced(definition,[new_symbols(definition,[spl12_20])],[avatar_definition]) ).
thf(f365,plain,
( ( $true
= ( rel_s5 @ sK9 @ sK10 ) )
| ~ spl12_20 ),
inference(avatar_component_clause,[],[f363]) ).
thf(f366,plain,
( spl12_20
| spl12_1 ),
inference(avatar_split_clause,[],[f268,f281,f363]) ).
thf(f368,definition,
( spl12_21
<=> ! [X1: $i] :
( ( ( rel_s5 @ sK9 @ X1 )
= $false )
| ( ( phi @ X1 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl12_21])],[avatar_definition]) ).
thf(f369,plain,
( ! [X1: $i] :
( ( ( rel_s5 @ sK9 @ X1 )
= $false )
| ( ( phi @ X1 )
= $true ) )
| ~ spl12_21 ),
inference(avatar_component_clause,[],[f368]) ).
thf(f370,plain,
( spl12_1
| spl12_21 ),
inference(avatar_split_clause,[],[f273,f368,f281]) ).
thf(f413,plain,
( ! [X0: $i] :
( ( ( rel_s5 @ X0 @ sK10 )
= $false )
| ( $true = $false )
| ( $true
= ( rel_s5 @ X0 @ sK11 ) ) )
| ~ spl12_19 ),
inference(constrained_superposition,[],[f168,f360]) ).
thf(f428,plain,
( ! [X0: $i] :
( ( $true
= ( rel_s5 @ X0 @ sK11 ) )
| ( ( rel_s5 @ X0 @ sK10 )
= $false ) )
| ~ spl12_19 ),
inference(trivial_inequality_removal,[],[f413]) ).
thf(f460,plain,
( ( $true = $false )
| ( $true
= ( phi @ sK11 ) )
| ( $false
= ( rel_s5 @ sK9 @ sK10 ) )
| ~ spl12_19
| ~ spl12_21 ),
inference(constrained_superposition,[],[f369,f428]) ).
thf(f464,plain,
( ( $true
= ( phi @ sK11 ) )
| ( $false
= ( rel_s5 @ sK9 @ sK10 ) )
| ~ spl12_19
| ~ spl12_21 ),
inference(trivial_inequality_removal,[],[f460]) ).
thf(f467,plain,
( ( $false
= ( rel_s5 @ sK9 @ sK10 ) )
| ( $true = $false )
| ~ spl12_18
| ~ spl12_19
| ~ spl12_21 ),
inference(forward_demodulation,[],[f464,f355]) ).
thf(f468,plain,
( ( $false
= ( rel_s5 @ sK9 @ sK10 ) )
| ~ spl12_18
| ~ spl12_19
| ~ spl12_21 ),
inference(trivial_inequality_removal,[],[f467]) ).
thf(f472,plain,
( ( $true = $false )
| ~ spl12_18
| ~ spl12_19
| ~ spl12_20
| ~ spl12_21 ),
inference(forward_demodulation,[],[f468,f365]) ).
thf(f473,plain,
( $false
| ~ spl12_18
| ~ spl12_19
| ~ spl12_20
| ~ spl12_21 ),
inference(trivial_inequality_removal,[],[f472]) ).
thf(f474,plain,
( ~ spl12_18
| ~ spl12_19
| ~ spl12_20
| ~ spl12_21 ),
inference(avatar_contradiction_clause,[],[f473]) ).
thf(f494,plain,
( ( ( phi @ sK3 )
= $true )
| ( $true = $false )
| ~ spl12_5 ),
inference(constrained_superposition,[],[f300,f171]) ).
thf(f514,plain,
( ( ( phi @ sK3 )
= $true )
| ~ spl12_5 ),
inference(trivial_inequality_removal,[],[f494]) ).
thf(f531,plain,
( ( $true = $false )
| ~ spl12_4
| ~ spl12_5 ),
inference(forward_demodulation,[],[f514,f296]) ).
thf(f532,plain,
( $false
| ~ spl12_4
| ~ spl12_5 ),
inference(trivial_inequality_removal,[],[f531]) ).
thf(f533,plain,
( ~ spl12_4
| ~ spl12_5 ),
inference(avatar_contradiction_clause,[],[f532]) ).
thf(f557,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( ( rel_s5 @ X0 @ sK7 )
= $false )
| ( ( phi @ X0 )
= $false ) )
| ~ spl12_12 ),
inference(constrained_superposition,[],[f328,f279]) ).
thf(f568,plain,
( ! [X0: $i] :
( ( ( rel_s5 @ X0 @ sK7 )
= $false )
| ( ( phi @ X0 )
= $false ) )
| ~ spl12_12 ),
inference(trivial_inequality_removal,[],[f557]) ).
thf(f684,plain,
( ( $true = $false )
| ( ( phi @ sK6 )
= $false )
| ~ spl12_12
| ~ spl12_13 ),
inference(constrained_superposition,[],[f568,f333]) ).
thf(f695,plain,
( ( ( phi @ sK6 )
= $false )
| ~ spl12_12
| ~ spl12_13 ),
inference(trivial_inequality_removal,[],[f684]) ).
thf(f702,plain,
( ( $true = $false )
| ~ spl12_12
| ~ spl12_13
| ~ spl12_14 ),
inference(forward_demodulation,[],[f695,f338]) ).
thf(f703,plain,
( $false
| ~ spl12_12
| ~ spl12_13
| ~ spl12_14 ),
inference(trivial_inequality_removal,[],[f702]) ).
thf(f704,plain,
( ~ spl12_12
| ~ spl12_13
| ~ spl12_14 ),
inference(avatar_contradiction_clause,[],[f703]) ).
cnf(s1,plain,
( ~ spl12_1
| ~ spl12_2
| ~ spl12_3 ),
inference(sat_conversion,[],[f292]) ).
cnf(s2,plain,
( spl12_3
| spl12_4 ),
inference(sat_conversion,[],[f297]) ).
cnf(s3,plain,
( spl12_3
| spl12_5 ),
inference(sat_conversion,[],[f301]) ).
cnf(s8,plain,
( spl12_2
| spl12_12 ),
inference(sat_conversion,[],[f329]) ).
cnf(s9,plain,
( spl12_2
| spl12_13 ),
inference(sat_conversion,[],[f334]) ).
cnf(s10,plain,
( spl12_2
| spl12_14 ),
inference(sat_conversion,[],[f339]) ).
cnf(s13,plain,
( spl12_1
| spl12_18 ),
inference(sat_conversion,[],[f356]) ).
cnf(s14,plain,
( spl12_1
| spl12_19 ),
inference(sat_conversion,[],[f361]) ).
cnf(s15,plain,
( spl12_1
| spl12_20 ),
inference(sat_conversion,[],[f366]) ).
cnf(s16,plain,
( spl12_1
| spl12_21 ),
inference(sat_conversion,[],[f370]) ).
cnf(s20,plain,
( ~ spl12_18
| ~ spl12_19
| ~ spl12_20
| ~ spl12_21 ),
inference(sat_conversion,[],[f474]) ).
cnf(s24,plain,
( ~ spl12_4
| ~ spl12_5 ),
inference(sat_conversion,[],[f533]) ).
cnf(s39,plain,
( ~ spl12_12
| ~ spl12_13
| ~ spl12_14 ),
inference(sat_conversion,[],[f704]) ).
cnf(s40,plain,
spl12_1,
inference(rat,[],[s20,s13,s14,s15,s16]) ).
cnf(s44,plain,
spl12_2,
inference(rat,[],[s39,s8,s9,s10]) ).
cnf(s46,plain,
~ spl12_3,
inference(rat,[],[s1,s40,s44]) ).
cnf(s50,plain,
spl12_5,
inference(rat,[],[s3,s46]) ).
cnf(s51,plain,
spl12_4,
inference(rat,[],[s2,s46]) ).
cnf(s52,plain,
$false,
inference(rat,[],[s24,s50,s51]) ).
thf(f705,plain,
$false,
inference(avatar_sat_refutation,[],[s52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL725^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 % Computer : n011.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Tue Sep 29 09:57:01 UTC 2026
% 0.09/0.22 % CPUTime :
% 0.09/0.22 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.25 Running higher-order theorem proving
% 0.22/0.27 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.35 % (4077649)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.35 % (4077660)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.35 % (4077660)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
% 0.22/0.35 % (4077656)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1017095355:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.35 % (4077655)lrs+10_16_si=on:nwc=1.5:random_seed=1709826913:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.35 % (4077654)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=332670872:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.35 % (4077658)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1852718668:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.35 % (4077657)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=2995854802: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)
% 0.22/0.35 % (4077659)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=429096323:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.35 % (4077660)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=3182750296:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.35 % (4077656)Instruction limit reached!
% 0.22/0.35 % (4077656)------------------------------
% 0.22/0.35 % (4077656)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.35 % (4077656)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.35 % (4077656)CaDiCaL version: 2.1.3
% 0.22/0.35 % (4077656)Termination reason: Instruction limit
% 0.22/0.35 % (4077656)Termination phase: Property scanning
% 0.22/0.35 % (4077656)Time elapsed: 0.002 s
% 0.22/0.35 % (4077656)Peak memory usage: 10 MB
% 0.22/0.35 % (4077656)Instructions burned: 3 (million)
% 0.22/0.35 % (4077655)Instruction limit reached!
% 0.22/0.35 % (4077655)------------------------------
% 0.22/0.35 % (4077655)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.35 % (4077655)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.35 % (4077655)CaDiCaL version: 2.1.3
% 0.22/0.35 % (4077655)Termination reason: Instruction limit
% 0.22/0.35 % (4077655)Termination phase: Saturation
% 0.22/0.35 % (4077655)Time elapsed: 0.010 s
% 0.22/0.35 % (4077655)Peak memory usage: 12 MB
% 0.22/0.35 % (4077655)Instructions burned: 19 (million)
% 0.22/0.35 % (4077658)Instruction limit reached!
% 0.22/0.35 % (4077658)------------------------------
% 0.22/0.35 % (4077658)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.35 % (4077658)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.35 % (4077658)CaDiCaL version: 2.1.3
% 0.22/0.35 % (4077658)Termination reason: Instruction limit
% 0.22/0.35 % (4077658)Termination phase: Saturation
% 0.22/0.35 % (4077658)Time elapsed: 0.013 s
% 0.22/0.35 % (4077658)Peak memory usage: 12 MB
% 0.22/0.35 % (4077658)Instructions burned: 24 (million)
% 0.22/0.35 % (4077668)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=351576796:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.22/0.35 % (4077668)Instruction limit reached!
% 0.22/0.35 % (4077668)------------------------------
% 0.22/0.35 % (4077668)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.35 % (4077668)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.35 % (4077668)CaDiCaL version: 2.1.3
% 0.22/0.35 % (4077668)Termination reason: Instruction limit
% 0.22/0.35 % (4077668)Termination phase: Property scanning
% 0.22/0.35 % (4077668)Time elapsed: 0.002 s
% 0.22/0.35 % (4077668)Peak memory usage: 10 MB
% 0.22/0.35 % (4077668)Instructions burned: 4 (million)
% 0.22/0.35 % (4077660) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4077649-4077660"...
% 0.22/0.35 % (4077670)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.22/0.35 % (4077670)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=286497615:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.22/0.35 % (4077660)...printing done.
% 0.22/0.35 % (4077659)Instruction limit reached!
% 0.22/0.35 % (4077659)------------------------------
% 0.22/0.35 % (4077659)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.35 % (4077659)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.35 % (4077659)CaDiCaL version: 2.1.3
% 0.22/0.35 % (4077659)Termination reason: Instruction limit
% 0.22/0.35 % (4077659)Termination phase: Saturation
% 0.22/0.35 % (4077659)Time elapsed: 0.035 s
% 0.22/0.35 % (4077659)Peak memory usage: 12 MB
% 0.22/0.35 % (4077659)Instructions burned: 75 (million)
% 0.22/0.35 % (4077670)Instruction limit reached!
% 0.22/0.35 % (4077670)------------------------------
% 0.22/0.35 % (4077670)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.35 % (4077670)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.35 % (4077670)CaDiCaL version: 2.1.3
% 0.22/0.35 % (4077670)Termination reason: Instruction limit
% 0.22/0.35 % (4077670)Termination phase: Saturation
% 0.22/0.35 % (4077670)Time elapsed: 0.004 s
% 0.22/0.35 % (4077670)Peak memory usage: 10 MB
% 0.22/0.35 % (4077670)Instructions burned: 8 (million)
% 0.22/0.35 % (4077660)Refutation found. Thanks to Tanya!
% 0.22/0.35 % SZS status Theorem for theBenchmark
% 0.22/0.35 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.36 % (4077660)------------------------------
% 0.22/0.36 % (4077660)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.36 % (4077660)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.36 % (4077660)CaDiCaL version: 2.1.3
% 0.22/0.36 % (4077660)Termination reason: Refutation
% 0.22/0.36 % (4077660)Time elapsed: 0.033 s
% 0.22/0.36 % (4077660)Peak memory usage: 13 MB
% 0.22/0.36 % (4077660)Instructions burned: 39 (million)
% 0.22/0.36 % (4077649)Success in time 0.075 s
% 0.22/0.36 % Vampire exiting
%------------------------------------------------------------------------------