%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL721^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 0.20s 0.27s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 13
% Syntax : Number of formulae : 87 ( 48 unt; 0 typ; 4 def)
% Number of atoms : 445 ( 97 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 573 ( 89 ~; 83 |; 0 &; 360 @)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 92 ( 92 >; 0 *; 0 +; 0 <<)
% Number of symbols : 62 ( 57 usr; 9 con; 0-4 aty)
% ( 32 !!; 6 ??; 0 @@+; 0 @@-)
% Number of variables : 191 ( 0 sgn 22 !; 2 ?; 191 :)
% 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_d: $i > $i > $o ).
thf(func_def_33,type,
mbox_d: ( $i > $o ) > $i > $o ).
thf(func_def_34,type,
mdia_d: ( $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,
vAND: $o > $o > $o ).
thf(func_def_39,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_41,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_42,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_43,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_44,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_47,type,
vNOT: $o > $o ).
thf(func_def_48,type,
vOR: $o > $o > $o ).
thf(func_def_49,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_50,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_51,type,
sF0: $o ).
thf(func_def_52,type,
sK1: $i > $i ).
thf(func_def_54,type,
sK3: $i > $i ).
thf(func_def_55,type,
sK4: $i > $i ).
thf(f3,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mnot) ).
thf(f4,axiom,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mor) ).
thf(f6,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) )
= mimplies ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mimplies) ).
thf(f20,axiom,
( mserial
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] :
? [X2: $i] : ( X0 @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mserial) ).
thf(f28,axiom,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_d @ X1 @ X2 ) ) )
= mbox_d ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^2.ax',mbox_d) ).
thf(f33,axiom,
( ( ^ [X0: $i > $o] : ( mnot @ ( mbox_d @ ( mnot @ X0 ) ) ) )
= mdia_d ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^2.ax',mdia_d) ).
thf(f34,axiom,
mserial @ rel_d,
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^2.ax',a1) ).
thf(f35,conjecture,
mvalid @ ( mimplies @ ( mbox_d @ phi ) @ ( mdia_d @ phi ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(f36,negated_conjecture,
~ ( mvalid @ ( mimplies @ ( mbox_d @ phi ) @ ( mdia_d @ phi ) ) ),
inference(negated_conjecture,[status(cth)],[f35]) ).
thf(f41,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f42,plain,
mserial @ rel_d,
inference(rectify,[],[f34]) ).
thf(f43,plain,
( ( mserial @ rel_d )
= $true ),
inference(fool_elimination,[],[f42]) ).
thf(f48,plain,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f3]) ).
thf(f49,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f48]) ).
thf(f50,plain,
~ ( mvalid @ ( mimplies @ ( mbox_d @ phi ) @ ( mdia_d @ phi ) ) ),
inference(rectify,[],[f36]) ).
thf(f51,plain,
( ( mvalid @ ( mimplies @ ( mbox_d @ phi ) @ ( mdia_d @ phi ) ) )
!= $true ),
inference(fool_elimination,[],[f50]) ).
thf(f52,plain,
( mdia_d
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_d @ ( mnot @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f33]) ).
thf(f56,plain,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_d @ X1 @ X2 ) ) )
= mbox_d ),
inference(rectify,[],[f32]) ).
thf(f57,plain,
( mbox_d
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_d @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f56]) ).
thf(f60,plain,
( mserial
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] :
? [X2: $i] : ( X0 @ X1 @ X2 ) ) ),
inference(rectify,[],[f20]) ).
thf(f61,plain,
( mserial
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f60]) ).
thf(f62,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f63,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f62]) ).
thf(f90,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
inference(rectify,[],[f28]) ).
thf(f91,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f90]) ).
thf(f95,plain,
( ( mvalid @ ( mimplies @ ( mbox_d @ phi ) @ ( mdia_d @ phi ) ) )
!= $true ),
inference(flattening,[],[f51]) ).
thf(f98,plain,
( ( mvalid @ ( mimplies @ ( mbox_d @ phi ) @ ( mdia_d @ phi ) ) )
!= $true ),
inference(cnf_transformation,[],[f95]) ).
thf(f100,plain,
( mdia_d
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_d @ ( mnot @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f52]) ).
thf(f103,plain,
( ( mserial @ rel_d )
= $true ),
inference(cnf_transformation,[],[f43]) ).
thf(f110,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f41]) ).
thf(f117,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f91]) ).
thf(f118,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f63]) ).
thf(f119,plain,
( mbox_d
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_d @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f57]) ).
thf(f123,plain,
( mserial
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f61]) ).
thf(f124,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f49]) ).
thf(f134,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,[],[f110,f118,f124]) ).
thf(f142,plain,
( mdia_d
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_d @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f100,f124,f119,f124]) ).
thf(f143,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [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 )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_d @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ phi )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_d @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ phi ) ) ) ),
inference(definition_unfolding,[],[f98,f117,f134,f119,f142]) ).
thf(f144,plain,
( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y1 @ Y2 ) ) )
@ rel_d )
= $true ),
inference(definition_unfolding,[],[f103,f123]) ).
thf(f145,definition,
( sF0
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [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 )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_d @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ phi )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_d @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ phi ) ) ) ),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
thf(f146,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [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 )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_d @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ phi )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_d @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ phi ) ) )
= sF0 ),
inference(reorient_equations,[],[f145]) ).
thf(f147,plain,
$true != sF0,
inference(definition_folding,[],[f143,f146]) ).
thf(f148,plain,
( ( !! @ $i
@ ^ [Y0: $i] : ( ?? @ $i @ ( rel_d @ Y0 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f144]) ).
thf(f149,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] : ( ?? @ $i @ ( rel_d @ Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f148]) ).
thf(f150,plain,
! [X1: $i] :
( ( ?? @ $i @ ( rel_d @ X1 ) )
= $true ),
inference(beta-eta_normalization,[],[f149]) ).
thf(f151,plain,
! [X1: $i] :
( ( rel_d @ X1 @ ( sK1 @ X1 ) )
= $true ),
inference(sigma_proxy_clausification,[],[f150]) ).
thf(f153,plain,
( ( $false
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [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 )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_d @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ phi )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_d @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ phi ) ) ) )
| ( $true = sF0 ) ),
inference(iff_proxy_clausification,[],[f146]) ).
thf(f154,plain,
( ( $true = sF0 )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_d @ Y0 @ Y1 )
| ( phi @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_d @ Y0 @ Y1 )
| ~ ( phi @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f153]) ).
thf(f155,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_d @ Y0 @ Y1 )
| ( phi @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_d @ Y0 @ Y1 )
| ~ ( phi @ Y1 ) ) ) )
@ sK2 ) )
| ( $true = sF0 ) ),
inference(sigma_proxy_clausification,[],[f154]) ).
thf(f156,plain,
( ( $true = sF0 )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_d @ sK2 @ Y0 )
| ( phi @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_d @ sK2 @ Y0 )
| ~ ( phi @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f155]) ).
thf(f157,plain,
( ( $true = sF0 )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_d @ sK2 @ Y0 )
| ~ ( phi @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f156]) ).
thf(f158,plain,
( ( $true = sF0 )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_d @ sK2 @ Y0 )
| ( phi @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f156]) ).
thf(f159,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_d @ sK2 @ Y0 )
| ( phi @ Y0 ) ) )
= $true )
| ( $true = sF0 ) ),
inference(not_proxy_clausification,[],[f158]) ).
thf(f160,plain,
! [X1: $i] :
( ( $true = sF0 )
| ( ( ^ [Y0: $i] :
( ~ ( rel_d @ sK2 @ Y0 )
| ( phi @ Y0 ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f159]) ).
thf(f161,plain,
! [X1: $i] :
( ( $true = sF0 )
| ( $true
= ( ~ ( rel_d @ sK2 @ X1 )
| ( phi @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f160]) ).
thf(f162,plain,
! [X1: $i] :
( ( $true = sF0 )
| ( ( ~ ( rel_d @ sK2 @ X1 ) )
= $true )
| ( $true
= ( phi @ X1 ) ) ),
inference(or_proxy_clausification,[],[f161]) ).
thf(f163,plain,
! [X1: $i] :
( ( $true
= ( phi @ X1 ) )
| ( $true = sF0 )
| ( $false
= ( rel_d @ sK2 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f162]) ).
thf(f164,plain,
( ( $true = sF0 )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_d @ sK2 @ Y0 )
| ~ ( phi @ Y0 ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f157]) ).
thf(f165,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_d @ sK2 @ Y0 )
| ~ ( phi @ Y0 ) )
@ X1 ) )
| ( $true = sF0 ) ),
inference(pi_proxy_clausification,[],[f164]) ).
thf(f166,plain,
! [X1: $i] :
( ( $true
= ( ~ ( rel_d @ sK2 @ X1 )
| ~ ( phi @ X1 ) ) )
| ( $true = sF0 ) ),
inference(beta-eta_normalization,[],[f165]) ).
thf(f167,plain,
! [X1: $i] :
( ( ( ~ ( rel_d @ sK2 @ X1 ) )
= $true )
| ( $true = sF0 )
| ( ( ~ ( phi @ X1 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f166]) ).
thf(f168,plain,
! [X1: $i] :
( ( $false
= ( rel_d @ sK2 @ X1 ) )
| ( $true = sF0 )
| ( ( ~ ( phi @ X1 ) )
= $true ) ),
inference(not_proxy_clausification,[],[f167]) ).
thf(f169,plain,
! [X1: $i] :
( ( $false
= ( rel_d @ sK2 @ X1 ) )
| ( $true = sF0 )
| ( $false
= ( phi @ X1 ) ) ),
inference(not_proxy_clausification,[],[f168]) ).
thf(f191,definition,
( spl5_1
<=> ( $true = sF0 ) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
thf(f195,definition,
( spl5_2
<=> ! [X1: $i] :
( ( $true
= ( phi @ X1 ) )
| ( $false
= ( rel_d @ sK2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
thf(f196,plain,
( ! [X1: $i] :
( ( $false
= ( rel_d @ sK2 @ X1 ) )
| ( $true
= ( phi @ X1 ) ) )
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f195]) ).
thf(f197,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f163,f195,f191]) ).
thf(f199,definition,
( spl5_3
<=> ! [X1: $i] :
( ( $false
= ( rel_d @ sK2 @ X1 ) )
| ( $false
= ( phi @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition]) ).
thf(f200,plain,
( ! [X1: $i] :
( ( $false
= ( rel_d @ sK2 @ X1 ) )
| ( $false
= ( phi @ X1 ) ) )
| ~ spl5_3 ),
inference(avatar_component_clause,[],[f199]) ).
thf(f201,plain,
( spl5_1
| spl5_3 ),
inference(avatar_split_clause,[],[f169,f199,f191]) ).
thf(f222,plain,
~ spl5_1,
inference(avatar_split_clause,[],[f147,f191]) ).
thf(f238,plain,
( ( $false = $true )
| ( ( phi @ ( sK1 @ sK2 ) )
= $true )
| ~ spl5_2 ),
inference(constrained_superposition,[],[f151,f196]) ).
thf(f239,plain,
( ( ( phi @ ( sK1 @ sK2 ) )
= $true )
| ~ spl5_2 ),
inference(trivial_inequality_removal,[],[f238]) ).
thf(f244,plain,
( ( $false
= ( phi @ ( sK1 @ sK2 ) ) )
| ( $false = $true )
| ~ spl5_3 ),
inference(constrained_superposition,[],[f151,f200]) ).
thf(f247,plain,
( ( $false
= ( phi @ ( sK1 @ sK2 ) ) )
| ~ spl5_3 ),
inference(trivial_inequality_removal,[],[f244]) ).
thf(f251,plain,
( ( $false = $true )
| ~ spl5_2
| ~ spl5_3 ),
inference(forward_demodulation,[],[f247,f239]) ).
thf(f252,plain,
( $false
| ~ spl5_2
| ~ spl5_3 ),
inference(trivial_inequality_removal,[],[f251]) ).
thf(f253,plain,
( ~ spl5_2
| ~ spl5_3 ),
inference(avatar_contradiction_clause,[],[f252]) ).
cnf(s1,plain,
( spl5_1
| spl5_2 ),
inference(sat_conversion,[],[f197]) ).
cnf(s2,plain,
( spl5_1
| spl5_3 ),
inference(sat_conversion,[],[f201]) ).
cnf(s7,plain,
~ spl5_1,
inference(sat_conversion,[],[f222]) ).
cnf(s10,plain,
( ~ spl5_2
| ~ spl5_3 ),
inference(sat_conversion,[],[f253]) ).
cnf(s12,plain,
spl5_3,
inference(rat,[],[s2,s7]) ).
cnf(s13,plain,
~ spl5_2,
inference(rat,[],[s10,s12]) ).
cnf(s14,plain,
$false,
inference(rat,[],[s1,s13,s7]) ).
thf(f254,plain,
$false,
inference(avatar_sat_refutation,[],[s14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL721^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n020.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 09:56:34 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running higher-order theorem proving
% 0.07/0.23 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.27 % (850983)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.27 % (850989)lrs+10_16_si=on:nwc=1.5:random_seed=1632033100:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.27 % (850992)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2633272898:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.27 % (850994)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.27 % (850994)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
% 0.20/0.27 % (850990)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2862683543:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.27 % (850988)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=123985578:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.27 % (850991)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=2915440025: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)
% 0.20/0.27 % (850994)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=2135948576:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.27 % (850990)Instruction limit reached!
% 0.20/0.27 % (850990)------------------------------
% 0.20/0.27 % (850990)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (850990)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (850990)CaDiCaL version: 2.1.3
% 0.20/0.27 % (850990)Termination reason: Instruction limit
% 0.20/0.27 % (850990)Termination phase: Preprocessing 3
% 0.20/0.27 % (850990)Time elapsed: 0.002 s
% 0.20/0.27 % (850990)Peak memory usage: 10 MB
% 0.20/0.27 % (850990)Instructions burned: 4 (million)
% 0.20/0.27 % (850993)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=627806945:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.27 % (850989) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-850983-850989"...
% 0.20/0.27 % (850994) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-850983-850994"...
% 0.20/0.27 % (850988) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-850983-850988"...
% 0.20/0.27 % (850994)...printing done.
% 0.20/0.27 % (850994)Refutation found. Thanks to Tanya!
% 0.20/0.27 % SZS status Theorem for theBenchmark
% 0.20/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.28 % (850994)------------------------------
% 0.20/0.28 % (850994)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (850994)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (850994)CaDiCaL version: 2.1.3
% 0.20/0.28 % (850994)Termination reason: Refutation
% 0.20/0.28 % (850994)Time elapsed: 0.004 s
% 0.20/0.28 % (850994)Peak memory usage: 13 MB
% 0.20/0.28 % (850994)Instructions burned: 14 (million)
% 0.20/0.28 % (850983)Success in time 0.038 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------