%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL720^1 : 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 : n003.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 08:14:33 AM UTC 2026
% Result : Theorem 0.10s 0.24s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 12
% Syntax : Number of formulae : 90 ( 35 unt; 0 typ; 6 def)
% Number of atoms : 601 ( 112 equ; 0 cnn)
% Maximal formula atoms : 11 ( 6 avg)
% Number of connectives : 779 ( 121 ~; 155 |; 0 &; 461 @)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 107 ( 107 >; 0 *; 0 +; 0 <<)
% Number of symbols : 64 ( 60 usr; 11 con; 0-4 aty)
% ( 37 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 216 ( 0 sgn 18 !; 0 ?; 216 :)
% 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_k: $i > $i > $o ).
thf(func_def_33,type,
mbox_k: ( $i > $o ) > $i > $o ).
thf(func_def_34,type,
mdia_k: ( $i > $o ) > $i > $o ).
thf(func_def_35,type,
phi: $i > $o ).
thf(func_def_36,type,
psi: $i > $o ).
thf(func_def_37,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_38,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_39,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_41,type,
vIMP: $o > $o > $o ).
thf(func_def_42,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_43,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_46,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_47,type,
vAND: $o > $o > $o ).
thf(func_def_48,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_49,type,
vOR: $o > $o > $o ).
thf(func_def_50,type,
vNOT: $o > $o ).
thf(func_def_51,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_52,type,
sF0: $o ).
thf(func_def_55,type,
sK3: $i > $i ).
thf(func_def_56,type,
sK4: $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(f28,axiom,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,axiom,
( mbox_k
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ~ ( rel_k @ X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^1.ax',mbox_k) ).
thf(f34,conjecture,
mvalid @ ( mimplies @ ( mbox_k @ ( mimplies @ phi @ psi ) ) @ ( mimplies @ ( mbox_k @ phi ) @ ( mbox_k @ psi ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(f35,negated_conjecture,
~ ( mvalid @ ( mimplies @ ( mbox_k @ ( mimplies @ phi @ psi ) ) @ ( mimplies @ ( mbox_k @ phi ) @ ( mbox_k @ psi ) ) ) ),
inference(negated_conjecture,[status(cth)],[f34]) ).
thf(f36,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
inference(rectify,[],[f28]) ).
thf(f37,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f36]) ).
thf(f45,plain,
~ ( mvalid @ ( mimplies @ ( mbox_k @ ( mimplies @ phi @ psi ) ) @ ( mimplies @ ( mbox_k @ phi ) @ ( mbox_k @ psi ) ) ) ),
inference(rectify,[],[f35]) ).
thf(f46,plain,
( ( mvalid @ ( mimplies @ ( mbox_k @ ( mimplies @ phi @ psi ) ) @ ( mimplies @ ( mbox_k @ phi ) @ ( mbox_k @ psi ) ) ) )
!= $true ),
inference(fool_elimination,[],[f45]) ).
thf(f65,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f66,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f65]) ).
thf(f75,plain,
( mbox_k
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ~ ( rel_k @ X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f32]) ).
thf(f76,plain,
( mbox_k
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_k @ Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f75]) ).
thf(f83,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f88,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f89,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f88]) ).
thf(f92,plain,
( ( mvalid @ ( mimplies @ ( mbox_k @ ( mimplies @ phi @ psi ) ) @ ( mimplies @ ( mbox_k @ phi ) @ ( mbox_k @ psi ) ) ) )
!= $true ),
inference(flattening,[],[f46]) ).
thf(f109,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f66]) ).
thf(f118,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f89]) ).
thf(f121,plain,
( ( mvalid @ ( mimplies @ ( mbox_k @ ( mimplies @ phi @ psi ) ) @ ( mimplies @ ( mbox_k @ phi ) @ ( mbox_k @ psi ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f92]) ).
thf(f123,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f37]) ).
thf(f124,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f83]) ).
thf(f125,plain,
( mbox_k
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_k @ Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f76]) ).
thf(f130,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,[],[f124,f109,f118]) ).
thf(f139,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_k @ Y1 @ Y2 ) ) )
@ ( ^ [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
@ psi ) )
@ ( ^ [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_k @ Y1 @ Y2 ) ) )
@ phi )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_k @ Y1 @ Y2 ) ) )
@ psi ) ) ) )
!= $true ),
inference(definition_unfolding,[],[f121,f123,f130,f125,f130,f130,f125,f125]) ).
thf(f140,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_k @ Y1 @ Y2 ) ) )
@ ( ^ [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
@ psi ) )
@ ( ^ [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_k @ Y1 @ Y2 ) ) )
@ phi )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_k @ Y1 @ Y2 ) ) )
@ psi ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
thf(f141,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_k @ Y1 @ Y2 ) ) )
@ ( ^ [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
@ psi ) )
@ ( ^ [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_k @ Y1 @ Y2 ) ) )
@ phi )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_k @ Y1 @ Y2 ) ) )
@ psi ) ) ) )
= sF0 ),
inference(reorient_equations,[],[f140]) ).
thf(f142,plain,
$true != sF0,
inference(definition_folding,[],[f139,f141]) ).
thf(f144,plain,
( ( $true = 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_k @ Y1 @ Y2 ) ) )
@ ( ^ [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
@ psi ) )
@ ( ^ [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_k @ Y1 @ Y2 ) ) )
@ phi )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_k @ Y1 @ Y2 ) ) )
@ psi ) ) ) )
= $false ) ),
inference(iff_proxy_clausification,[],[f141]) ).
thf(f145,plain,
( ( $true = sF0 )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( psi @ Y1 )
| ~ ( rel_k @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( phi @ Y1 )
| ~ ( rel_k @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( psi @ Y1 )
| ~ ( phi @ Y1 )
| ~ ( rel_k @ Y0 @ Y1 ) ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f144]) ).
thf(f146,plain,
( ( ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( psi @ Y1 )
| ~ ( rel_k @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( phi @ Y1 )
| ~ ( rel_k @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( psi @ Y1 )
| ~ ( phi @ Y1 )
| ~ ( rel_k @ Y0 @ Y1 ) ) ) )
@ sK1 )
= $false )
| ( $true = sF0 ) ),
inference(sigma_proxy_clausification,[],[f145]) ).
thf(f147,plain,
( ( $true = sF0 )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( psi @ Y0 )
| ~ ( rel_k @ sK1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( phi @ Y0 )
| ~ ( rel_k @ sK1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( psi @ Y0 )
| ~ ( phi @ Y0 )
| ~ ( rel_k @ sK1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f146]) ).
thf(f148,plain,
( ( $true = sF0 )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( psi @ Y0 )
| ~ ( phi @ Y0 )
| ~ ( rel_k @ sK1 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f147]) ).
thf(f149,plain,
( ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( psi @ Y0 )
| ~ ( rel_k @ sK1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( phi @ Y0 )
| ~ ( rel_k @ sK1 @ Y0 ) ) ) ) )
| ( $true = sF0 ) ),
inference(or_proxy_clausification,[],[f147]) ).
thf(f150,plain,
( ( $true = sF0 )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( phi @ Y0 )
| ~ ( rel_k @ sK1 @ Y0 ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f149]) ).
thf(f151,plain,
( ( $true = sF0 )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( psi @ Y0 )
| ~ ( rel_k @ sK1 @ Y0 ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f149]) ).
thf(f152,plain,
( ( $true = sF0 )
| ( ( ^ [Y0: $i] :
( ( psi @ Y0 )
| ~ ( rel_k @ sK1 @ Y0 ) )
@ sK2 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f151]) ).
thf(f153,plain,
( ( ( ( psi @ sK2 )
| ~ ( rel_k @ sK1 @ sK2 ) )
= $false )
| ( $true = sF0 ) ),
inference(beta-eta_normalization,[],[f152]) ).
thf(f154,plain,
( ( $true = sF0 )
| ( $false
= ( ~ ( rel_k @ sK1 @ sK2 ) ) ) ),
inference(or_proxy_clausification,[],[f153]) ).
thf(f155,plain,
( ( $true = sF0 )
| ( $false
= ( psi @ sK2 ) ) ),
inference(or_proxy_clausification,[],[f153]) ).
thf(f156,plain,
( ( $true
= ( rel_k @ sK1 @ sK2 ) )
| ( $true = sF0 ) ),
inference(not_proxy_clausification,[],[f154]) ).
thf(f157,plain,
( ( $true = sF0 )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( phi @ Y0 )
| ~ ( rel_k @ sK1 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f150]) ).
thf(f158,plain,
! [X1: $i] :
( ( $true = sF0 )
| ( $true
= ( ^ [Y0: $i] :
( ( phi @ Y0 )
| ~ ( rel_k @ sK1 @ Y0 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f157]) ).
thf(f159,plain,
! [X1: $i] :
( ( $true = sF0 )
| ( $true
= ( ( phi @ X1 )
| ~ ( rel_k @ sK1 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f158]) ).
thf(f160,plain,
! [X1: $i] :
( ( $true
= ( phi @ X1 ) )
| ( ( ~ ( rel_k @ sK1 @ X1 ) )
= $true )
| ( $true = sF0 ) ),
inference(or_proxy_clausification,[],[f159]) ).
thf(f161,plain,
! [X1: $i] :
( ( $true
= ( phi @ X1 ) )
| ( $true = sF0 )
| ( ( rel_k @ sK1 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f160]) ).
thf(f162,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( psi @ Y0 )
| ~ ( phi @ Y0 )
| ~ ( rel_k @ sK1 @ Y0 ) ) )
= $true )
| ( $true = sF0 ) ),
inference(not_proxy_clausification,[],[f148]) ).
thf(f163,plain,
! [X1: $i] :
( ( $true = sF0 )
| ( $true
= ( ^ [Y0: $i] :
( ( psi @ Y0 )
| ~ ( phi @ Y0 )
| ~ ( rel_k @ sK1 @ Y0 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f162]) ).
thf(f164,plain,
! [X1: $i] :
( ( $true
= ( ( psi @ X1 )
| ~ ( phi @ X1 )
| ~ ( rel_k @ sK1 @ X1 ) ) )
| ( $true = sF0 ) ),
inference(beta-eta_normalization,[],[f163]) ).
thf(f165,plain,
! [X1: $i] :
( ( $true = sF0 )
| ( ( ~ ( rel_k @ sK1 @ X1 ) )
= $true )
| ( $true
= ( ( psi @ X1 )
| ~ ( phi @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f164]) ).
thf(f166,plain,
! [X1: $i] :
( ( $true
= ( ( psi @ X1 )
| ~ ( phi @ X1 ) ) )
| ( ( rel_k @ sK1 @ X1 )
= $false )
| ( $true = sF0 ) ),
inference(not_proxy_clausification,[],[f165]) ).
thf(f167,plain,
! [X1: $i] :
( ( $true
= ( psi @ X1 ) )
| ( ( ~ ( phi @ X1 ) )
= $true )
| ( $true = sF0 )
| ( ( rel_k @ sK1 @ X1 )
= $false ) ),
inference(or_proxy_clausification,[],[f166]) ).
thf(f168,plain,
! [X1: $i] :
( ( $false
= ( phi @ X1 ) )
| ( $true = sF0 )
| ( ( rel_k @ sK1 @ X1 )
= $false )
| ( $true
= ( psi @ X1 ) ) ),
inference(not_proxy_clausification,[],[f167]) ).
thf(f205,definition,
( spl5_1
<=> ( $false
= ( psi @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
thf(f207,plain,
( ( $false
= ( psi @ sK2 ) )
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f205]) ).
thf(f209,definition,
( spl5_2
<=> ( $true = sF0 ) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
thf(f212,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f155,f209,f205]) ).
thf(f214,definition,
( spl5_3
<=> ( $true
= ( rel_k @ sK1 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition]) ).
thf(f216,plain,
( ( $true
= ( rel_k @ sK1 @ sK2 ) )
| ~ spl5_3 ),
inference(avatar_component_clause,[],[f214]) ).
thf(f217,plain,
( spl5_2
| spl5_3 ),
inference(avatar_split_clause,[],[f156,f214,f209]) ).
thf(f219,definition,
( spl5_4
<=> ! [X1: $i] :
( ( $true
= ( phi @ X1 ) )
| ( ( rel_k @ sK1 @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition]) ).
thf(f220,plain,
( ! [X1: $i] :
( ( ( rel_k @ sK1 @ X1 )
= $false )
| ( $true
= ( phi @ X1 ) ) )
| ~ spl5_4 ),
inference(avatar_component_clause,[],[f219]) ).
thf(f221,plain,
( spl5_2
| spl5_4 ),
inference(avatar_split_clause,[],[f161,f219,f209]) ).
thf(f223,definition,
( spl5_5
<=> ! [X1: $i] :
( ( $false
= ( phi @ X1 ) )
| ( $true
= ( psi @ X1 ) )
| ( ( rel_k @ sK1 @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition]) ).
thf(f224,plain,
( ! [X1: $i] :
( ( ( rel_k @ sK1 @ X1 )
= $false )
| ( $false
= ( phi @ X1 ) )
| ( $true
= ( psi @ X1 ) ) )
| ~ spl5_5 ),
inference(avatar_component_clause,[],[f223]) ).
thf(f225,plain,
( spl5_2
| spl5_5 ),
inference(avatar_split_clause,[],[f168,f223,f209]) ).
thf(f254,plain,
~ spl5_2,
inference(avatar_split_clause,[],[f142,f209]) ).
thf(f270,plain,
( ( ( phi @ sK2 )
= $true )
| ( $true = $false )
| ~ spl5_3
| ~ spl5_4 ),
inference(constrained_superposition,[],[f220,f216]) ).
thf(f273,plain,
( ( ( phi @ sK2 )
= $true )
| ~ spl5_3
| ~ spl5_4 ),
inference(trivial_inequality_removal,[],[f270]) ).
thf(f276,plain,
( ( ( phi @ sK2 )
= $false )
| ( $true = $false )
| ( $true
= ( psi @ sK2 ) )
| ~ spl5_3
| ~ spl5_5 ),
inference(constrained_superposition,[],[f224,f216]) ).
thf(f281,plain,
( ( ( phi @ sK2 )
= $false )
| ( $true
= ( psi @ sK2 ) )
| ~ spl5_3
| ~ spl5_5 ),
inference(trivial_inequality_removal,[],[f276]) ).
thf(f284,plain,
( ( $true = $false )
| ( $true
= ( psi @ sK2 ) )
| ~ spl5_3
| ~ spl5_4
| ~ spl5_5 ),
inference(forward_demodulation,[],[f281,f273]) ).
thf(f285,plain,
( ( $true
= ( psi @ sK2 ) )
| ~ spl5_3
| ~ spl5_4
| ~ spl5_5 ),
inference(trivial_inequality_removal,[],[f284]) ).
thf(f289,plain,
( ( $true = $false )
| ~ spl5_1
| ~ spl5_3
| ~ spl5_4
| ~ spl5_5 ),
inference(forward_demodulation,[],[f285,f207]) ).
thf(f290,plain,
( $false
| ~ spl5_1
| ~ spl5_3
| ~ spl5_4
| ~ spl5_5 ),
inference(trivial_inequality_removal,[],[f289]) ).
thf(f291,plain,
( ~ spl5_1
| ~ spl5_3
| ~ spl5_4
| ~ spl5_5 ),
inference(avatar_contradiction_clause,[],[f290]) ).
cnf(s1,plain,
( spl5_1
| spl5_2 ),
inference(sat_conversion,[],[f212]) ).
cnf(s2,plain,
( spl5_2
| spl5_3 ),
inference(sat_conversion,[],[f217]) ).
cnf(s3,plain,
( spl5_2
| spl5_4 ),
inference(sat_conversion,[],[f221]) ).
cnf(s4,plain,
( spl5_2
| spl5_5 ),
inference(sat_conversion,[],[f225]) ).
cnf(s11,plain,
~ spl5_2,
inference(sat_conversion,[],[f254]) ).
cnf(s14,plain,
( ~ spl5_1
| ~ spl5_3
| ~ spl5_4
| ~ spl5_5 ),
inference(sat_conversion,[],[f291]) ).
cnf(s16,plain,
spl5_5,
inference(rat,[],[s4,s11]) ).
cnf(s17,plain,
spl5_4,
inference(rat,[],[s3,s11]) ).
cnf(s18,plain,
spl5_3,
inference(rat,[],[s2,s11]) ).
cnf(s19,plain,
~ spl5_1,
inference(rat,[],[s14,s16,s17,s18]) ).
cnf(s20,plain,
$false,
inference(rat,[],[s1,s11,s19]) ).
thf(f292,plain,
$false,
inference(avatar_sat_refutation,[],[s20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL720^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.16 % Computer : n003.cluster.edu
% 0.10/0.16 % Model : x86_64 x86_64
% 0.10/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.16 % Memory : 8046.5625MB
% 0.10/0.16 % OS : Linux 6.8.0-71-generic
% 0.10/0.16 % CPULimit : 300
% 0.10/0.16 % WCLimit : 300
% 0.10/0.16 % DateTime : Tue Sep 29 09:56:58 UTC 2026
% 0.10/0.16 % CPUTime :
% 0.10/0.16 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 Running higher-order theorem proving
% 0.10/0.21 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
% 0.10/0.24 % (2309545)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.10/0.24 % (2309556)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.10/0.24 % (2309556)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
% 0.10/0.24 % (2309556)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=1330031235:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.10/0.24 % (2309556) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2309545-2309556"...
% 0.10/0.24 % (2309556)...printing done.
% 0.10/0.24 % (2309556)Refutation found. Thanks to Tanya!
% 0.10/0.24 % SZS status Theorem for theBenchmark
% 0.10/0.24 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.25 % (2309556)------------------------------
% 0.10/0.25 % (2309556)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.25 % (2309556)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.25 % (2309556)CaDiCaL version: 2.1.3
% 0.10/0.25 % (2309556)Termination reason: Refutation
% 0.10/0.25 % (2309556)Time elapsed: 0.005 s
% 0.10/0.25 % (2309556)Peak memory usage: 13 MB
% 0.10/0.25 % (2309556)Instructions burned: 17 (million)
% 0.10/0.25 % (2309545)Success in time 0.029 s
% 0.10/0.25 % Vampire exiting
%------------------------------------------------------------------------------