%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL868^1 : 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 : n015.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 08:14:38 AM UTC 2026
% Result : Theorem 0.21s 0.31s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 12
% Syntax : Number of formulae : 142 ( 40 unt; 0 typ; 7 def)
% Number of atoms : 1083 ( 186 equ; 0 cnn)
% Maximal formula atoms : 5 ( 7 avg)
% Number of connectives : 1169 ( 74 ~; 169 |; 70 &; 718 @)
% ( 7 <=>; 48 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 54 ( 54 >; 0 *; 0 +; 0 <<)
% Number of symbols : 65 ( 60 usr; 18 con; 0-4 aty)
% ( 75 !!; 8 ??; 0 @@+; 0 @@-)
% Number of variables : 192 ( 0 sgn 73 !; 4 ?; 192 :)
% 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,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_33,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_34,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_35,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_36,type,
vIMP: $o > $o > $o ).
thf(func_def_37,type,
vAND: $o > $o > $o ).
thf(func_def_38,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_39,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_41,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_42,type,
vOR: $o > $o > $o ).
thf(func_def_43,type,
vNOT: $o > $o ).
thf(func_def_44,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_47,type,
sK0: $i > $i > $o ).
thf(f18,axiom,
( mreflexive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mreflexive) ).
thf(f20,axiom,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i] :
? [X2: $i] : ( X0 @ X1 @ X2 ) )
= mserial ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mserial) ).
thf(f21,axiom,
( mtransitive
= ( ^ [X0: $i > $i > $o] :
! [X3: $i,X1: $i,X2: $i] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mtransitive) ).
thf(f22,axiom,
( meuclidean
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X3: $i,X2: $i] :
( ( ( X0 @ X1 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',meuclidean) ).
thf(f32,conjecture,
! [X0: $i > $i > $o] :
( ( ( meuclidean @ X0 )
& ( mreflexive @ X0 ) )
=> ( ( mtransitive @ X0 )
& ( mserial @ X0 )
& ( meuclidean @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(f33,negated_conjecture,
~ ! [X0: $i > $i > $o] :
( ( ( meuclidean @ X0 )
& ( mreflexive @ X0 ) )
=> ( ( mtransitive @ X0 )
& ( mserial @ X0 )
& ( meuclidean @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
thf(f44,plain,
( mtransitive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X3 @ X1 )
& ( X0 @ X2 @ X3 ) )
=> ( X0 @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f21]) ).
thf(f45,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f44]) ).
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,
( meuclidean
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X1 @ X2 )
& ( X0 @ X1 @ X3 ) )
=> ( X0 @ X3 @ X2 ) ) ) ),
inference(rectify,[],[f22]) ).
thf(f71,plain,
( meuclidean
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f70]) ).
thf(f72,plain,
~ ! [X0: $i > $i > $o] :
( ( ( meuclidean @ X0 )
& ( mreflexive @ X0 ) )
=> ( ( mtransitive @ X0 )
& ( mserial @ X0 )
& ( meuclidean @ X0 ) ) ),
inference(rectify,[],[f33]) ).
thf(f73,plain,
~ ! [X0: $i > $i > $o] :
( ( ( ( mreflexive @ X0 )
= $true )
& ( ( meuclidean @ X0 )
= $true ) )
=> ( ( ( mserial @ X0 )
= $true )
& ( ( meuclidean @ X0 )
= $true )
& ( ( mtransitive @ X0 )
= $true ) ) ),
inference(fool_elimination,[],[f72]) ).
thf(f81,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i] :
? [X2: $i] : ( X0 @ X1 @ X2 ) )
= mserial ),
inference(rectify,[],[f20]) ).
thf(f82,plain,
( mserial
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f81]) ).
thf(f87,plain,
? [X0: $i > $i > $o] :
( ( ( ( mserial @ X0 )
!= $true )
| ( ( mtransitive @ X0 )
!= $true )
| ( ( meuclidean @ X0 )
!= $true ) )
& ( ( mreflexive @ X0 )
= $true )
& ( ( meuclidean @ X0 )
= $true ) ),
inference(ennf_transformation,[],[f73]) ).
thf(f88,plain,
? [X0: $i > $i > $o] :
( ( ( ( mserial @ X0 )
!= $true )
| ( ( mtransitive @ X0 )
!= $true )
| ( ( meuclidean @ X0 )
!= $true ) )
& ( ( mreflexive @ X0 )
= $true )
& ( ( meuclidean @ X0 )
= $true ) ),
inference(flattening,[],[f87]) ).
thf(f89,plain,
( ( ( ( mserial @ sK0 )
!= $true )
| ( ( mtransitive @ sK0 )
!= $true )
| ( ( meuclidean @ sK0 )
!= $true ) )
& ( ( mreflexive @ sK0 )
= $true )
& ( ( meuclidean @ sK0 )
= $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f88]) ).
thf(f93,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f45]) ).
thf(f95,plain,
( mserial
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f82]) ).
thf(f101,plain,
( ( meuclidean @ sK0 )
= $true ),
inference(cnf_transformation,[],[f89]) ).
thf(f102,plain,
( ( mreflexive @ sK0 )
= $true ),
inference(cnf_transformation,[],[f89]) ).
thf(f103,plain,
( ( ( mserial @ sK0 )
!= $true )
| ( ( mtransitive @ sK0 )
!= $true )
| ( ( meuclidean @ sK0 )
!= $true ) ),
inference(cnf_transformation,[],[f89]) ).
thf(f112,plain,
( meuclidean
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f71]) ).
thf(f121,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f69]) ).
thf(f135,plain,
( ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y1 @ Y2 ) ) )
@ sK0 )
!= $true )
| ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
@ sK0 )
!= $true )
| ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
@ sK0 )
!= $true ) ),
inference(definition_unfolding,[],[f103,f95,f93,f112]) ).
thf(f136,plain,
( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ sK0 )
= $true ),
inference(definition_unfolding,[],[f102,f121]) ).
thf(f137,plain,
( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
@ sK0 )
= $true ),
inference(definition_unfolding,[],[f101,f112]) ).
thf(f138,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y0 )
& ( sK0 @ Y2 @ Y1 ) )
=> ( sK0 @ Y0 @ Y1 ) ) ) ) )
!= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] : ( ?? @ $i @ ( sK0 @ Y0 ) ) )
!= $true )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ Y2 ) )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f135]) ).
thf(f139,plain,
( ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ Y2 ) )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] : ( ?? @ $i @ ( sK0 @ Y0 ) ) )
!= $true )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y0 )
& ( sK0 @ Y2 @ Y1 ) )
=> ( sK0 @ Y0 @ Y1 ) ) ) )
@ sK1 ) ) ),
inference(sigma_proxy_clausification,[],[f138]) ).
thf(f140,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] : ( ?? @ $i @ ( sK0 @ Y0 ) ) )
!= $true )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ Y2 ) )
=> ( sK0 @ Y1 @ Y2 ) ) ) )
@ sK2 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y0 )
& ( sK0 @ Y2 @ Y1 ) )
=> ( sK0 @ Y0 @ Y1 ) ) ) )
@ sK1 ) ) ),
inference(sigma_proxy_clausification,[],[f139]) ).
thf(f141,plain,
( ( $false
= ( ^ [Y0: $i] : ( ?? @ $i @ ( sK0 @ Y0 ) )
@ sK3 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ Y2 ) )
=> ( sK0 @ Y1 @ Y2 ) ) ) )
@ sK2 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y0 )
& ( sK0 @ Y2 @ Y1 ) )
=> ( sK0 @ Y0 @ Y1 ) ) ) )
@ sK1 ) ) ),
inference(sigma_proxy_clausification,[],[f140]) ).
thf(f142,plain,
( ( $false
= ( ?? @ $i @ ( sK0 @ sK3 ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y0 @ sK2 )
& ( sK0 @ sK2 @ Y1 ) )
=> ( sK0 @ Y0 @ Y1 ) ) ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ sK1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ sK1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f141]) ).
thf(f143,plain,
! [X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ sK1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ sK1 @ Y0 ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y0 @ sK2 )
& ( sK0 @ sK2 @ Y1 ) )
=> ( sK0 @ Y0 @ Y1 ) ) ) )
= $false )
| ( $false
= ( sK0 @ sK3 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f142]) ).
thf(f144,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK3 @ X1 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y0 @ sK2 )
& ( sK0 @ sK2 @ Y1 ) )
=> ( sK0 @ Y0 @ Y1 ) ) ) )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ sK1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ sK1 @ Y0 ) ) )
@ sK4 ) ) ),
inference(sigma_proxy_clausification,[],[f143]) ).
thf(f145,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ sK1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ sK1 @ Y0 ) ) )
@ sK4 ) )
| ( $false
= ( sK0 @ sK3 @ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y0 @ sK2 )
& ( sK0 @ sK2 @ Y1 ) )
=> ( sK0 @ Y0 @ Y1 ) ) )
@ sK5 ) ) ),
inference(sigma_proxy_clausification,[],[f144]) ).
thf(f146,plain,
! [X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ sK5 @ sK2 )
& ( sK0 @ sK2 @ Y0 ) )
=> ( sK0 @ sK5 @ Y0 ) ) ) )
| ( $false
= ( sK0 @ sK3 @ X1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK1 )
& ( sK0 @ Y0 @ sK4 ) )
=> ( sK0 @ sK1 @ sK4 ) ) ) ) ),
inference(beta-eta_normalization,[],[f145]) ).
thf(f147,plain,
! [X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK1 )
& ( sK0 @ Y0 @ sK4 ) )
=> ( sK0 @ sK1 @ sK4 ) ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ sK5 @ sK2 )
& ( sK0 @ sK2 @ Y0 ) )
=> ( sK0 @ sK5 @ Y0 ) )
@ sK6 ) )
| ( $false
= ( sK0 @ sK3 @ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f146]) ).
thf(f148,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ sK5 @ sK2 )
& ( sK0 @ sK2 @ Y0 ) )
=> ( sK0 @ sK5 @ Y0 ) )
@ sK6 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK1 )
& ( sK0 @ Y0 @ sK4 ) )
=> ( sK0 @ sK1 @ sK4 ) )
@ sK7 ) )
| ( $false
= ( sK0 @ sK3 @ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f147]) ).
thf(f149,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK3 @ X1 ) )
| ( $false
= ( ( ( sK0 @ sK7 @ sK1 )
& ( sK0 @ sK7 @ sK4 ) )
=> ( sK0 @ sK1 @ sK4 ) ) )
| ( $false
= ( ( ( sK0 @ sK5 @ sK2 )
& ( sK0 @ sK2 @ sK6 ) )
=> ( sK0 @ sK5 @ sK6 ) ) ) ),
inference(beta-eta_normalization,[],[f148]) ).
thf(f150,plain,
! [X1: $i] :
( ( ( sK0 @ sK1 @ sK4 )
= $false )
| ( $false
= ( ( ( sK0 @ sK5 @ sK2 )
& ( sK0 @ sK2 @ sK6 ) )
=> ( sK0 @ sK5 @ sK6 ) ) )
| ( $false
= ( sK0 @ sK3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f149]) ).
thf(f151,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK3 @ X1 ) )
| ( $false
= ( ( ( sK0 @ sK5 @ sK2 )
& ( sK0 @ sK2 @ sK6 ) )
=> ( sK0 @ sK5 @ sK6 ) ) )
| ( ( ( sK0 @ sK7 @ sK1 )
& ( sK0 @ sK7 @ sK4 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f149]) ).
thf(f152,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK3 @ X1 ) )
| ( ( ( sK0 @ sK7 @ sK1 )
& ( sK0 @ sK7 @ sK4 ) )
= $true )
| ( ( sK0 @ sK5 @ sK6 )
= $false ) ),
inference(imp_proxy_clausification,[],[f151]) ).
thf(f153,plain,
! [X1: $i] :
( ( ( ( sK0 @ sK7 @ sK1 )
& ( sK0 @ sK7 @ sK4 ) )
= $true )
| ( ( ( sK0 @ sK5 @ sK2 )
& ( sK0 @ sK2 @ sK6 ) )
= $true )
| ( $false
= ( sK0 @ sK3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f151]) ).
thf(f154,plain,
! [X1: $i] :
( ( ( ( sK0 @ sK5 @ sK2 )
& ( sK0 @ sK2 @ sK6 ) )
= $true )
| ( $false
= ( sK0 @ sK3 @ X1 ) )
| ( ( sK0 @ sK7 @ sK4 )
= $true ) ),
inference(and_proxy_clausification,[],[f153]) ).
thf(f155,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK3 @ X1 ) )
| ( ( ( sK0 @ sK5 @ sK2 )
& ( sK0 @ sK2 @ sK6 ) )
= $true )
| ( ( sK0 @ sK7 @ sK1 )
= $true ) ),
inference(and_proxy_clausification,[],[f153]) ).
thf(f156,plain,
! [X1: $i] :
( ( ( sK0 @ sK7 @ sK1 )
= $true )
| ( $false
= ( sK0 @ sK3 @ X1 ) )
| ( ( sK0 @ sK2 @ sK6 )
= $true ) ),
inference(and_proxy_clausification,[],[f155]) ).
thf(f157,plain,
! [X1: $i] :
( ( ( sK0 @ sK7 @ sK1 )
= $true )
| ( $false
= ( sK0 @ sK3 @ X1 ) )
| ( ( sK0 @ sK5 @ sK2 )
= $true ) ),
inference(and_proxy_clausification,[],[f155]) ).
thf(f158,plain,
! [X1: $i] :
( ( ( sK0 @ sK7 @ sK4 )
= $true )
| ( ( sK0 @ sK2 @ sK6 )
= $true )
| ( $false
= ( sK0 @ sK3 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f154]) ).
thf(f159,plain,
! [X1: $i] :
( ( ( sK0 @ sK7 @ sK4 )
= $true )
| ( $false
= ( sK0 @ sK3 @ X1 ) )
| ( ( sK0 @ sK5 @ sK2 )
= $true ) ),
inference(and_proxy_clausification,[],[f154]) ).
thf(f160,plain,
! [X1: $i] :
( ( ( sK0 @ sK5 @ sK6 )
= $false )
| ( ( sK0 @ sK7 @ sK4 )
= $true )
| ( $false
= ( sK0 @ sK3 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f152]) ).
thf(f161,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK3 @ X1 ) )
| ( ( sK0 @ sK5 @ sK6 )
= $false )
| ( ( sK0 @ sK7 @ sK1 )
= $true ) ),
inference(and_proxy_clausification,[],[f152]) ).
thf(f162,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK3 @ X1 ) )
| ( ( sK0 @ sK5 @ sK6 )
= $false )
| ( ( sK0 @ sK1 @ sK4 )
= $false ) ),
inference(imp_proxy_clausification,[],[f150]) ).
thf(f163,plain,
! [X1: $i] :
( ( ( ( sK0 @ sK5 @ sK2 )
& ( sK0 @ sK2 @ sK6 ) )
= $true )
| ( $false
= ( sK0 @ sK3 @ X1 ) )
| ( ( sK0 @ sK1 @ sK4 )
= $false ) ),
inference(imp_proxy_clausification,[],[f150]) ).
thf(f164,plain,
! [X1: $i] :
( ( ( sK0 @ sK1 @ sK4 )
= $false )
| ( ( sK0 @ sK2 @ sK6 )
= $true )
| ( $false
= ( sK0 @ sK3 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f163]) ).
thf(f165,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK3 @ X1 ) )
| ( ( sK0 @ sK1 @ sK4 )
= $false )
| ( ( sK0 @ sK5 @ sK2 )
= $true ) ),
inference(and_proxy_clausification,[],[f163]) ).
thf(f166,plain,
( ( !! @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 ) )
= $true ),
inference(beta-eta_normalization,[],[f136]) ).
thf(f167,plain,
! [X1: $i] :
( ( ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f166]) ).
thf(f168,plain,
! [X1: $i] :
( ( sK0 @ X1 @ X1 )
= $true ),
inference(beta-eta_normalization,[],[f167]) ).
thf(f169,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y0 )
& ( sK0 @ Y2 @ Y1 ) )
=> ( sK0 @ Y0 @ Y1 ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f137]) ).
thf(f170,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y0 )
& ( sK0 @ Y2 @ Y1 ) )
=> ( sK0 @ Y0 @ Y1 ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f169]) ).
thf(f171,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ X1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ X1 @ Y0 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f170]) ).
thf(f172,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ X1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ X1 @ Y0 ) ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f171]) ).
thf(f173,plain,
! [X2: $i,X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ X1 )
& ( sK0 @ Y0 @ X2 ) )
=> ( sK0 @ X1 @ X2 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f172]) ).
thf(f174,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ X1 )
& ( sK0 @ Y0 @ X2 ) )
=> ( sK0 @ X1 @ X2 ) )
@ X3 )
= $true ),
inference(pi_proxy_clausification,[],[f173]) ).
thf(f175,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( sK0 @ X3 @ X1 )
& ( sK0 @ X3 @ X2 ) )
=> ( sK0 @ X1 @ X2 ) )
= $true ),
inference(beta-eta_normalization,[],[f174]) ).
thf(f176,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ( sK0 @ X3 @ X1 )
& ( sK0 @ X3 @ X2 ) ) )
| ( ( sK0 @ X1 @ X2 )
= $true ) ),
inference(imp_proxy_clausification,[],[f175]) ).
thf(f177,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( sK0 @ X1 @ X2 )
= $true )
| ( $false
= ( sK0 @ X3 @ X1 ) )
| ( $false
= ( sK0 @ X3 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f176]) ).
thf(f179,definition,
( spl8_1
<=> ( ( sK0 @ sK5 @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl8_1])],[avatar_definition]) ).
thf(f181,plain,
( ( ( sK0 @ sK5 @ sK2 )
= $true )
| ~ spl8_1 ),
inference(avatar_component_clause,[],[f179]) ).
thf(f183,definition,
( spl8_2
<=> ( ( sK0 @ sK7 @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl8_2])],[avatar_definition]) ).
thf(f185,plain,
( ( ( sK0 @ sK7 @ sK1 )
= $true )
| ~ spl8_2 ),
inference(avatar_component_clause,[],[f183]) ).
thf(f187,definition,
( spl8_3
<=> ! [X1: $i] :
( $false
= ( sK0 @ sK3 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_3])],[avatar_definition]) ).
thf(f188,plain,
( ! [X1: $i] :
( $false
= ( sK0 @ sK3 @ X1 ) )
| ~ spl8_3 ),
inference(avatar_component_clause,[],[f187]) ).
thf(f189,plain,
( spl8_1
| spl8_2
| spl8_3 ),
inference(avatar_split_clause,[],[f157,f187,f183,f179]) ).
thf(f191,definition,
( spl8_4
<=> ( ( sK0 @ sK2 @ sK6 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl8_4])],[avatar_definition]) ).
thf(f193,plain,
( ( ( sK0 @ sK2 @ sK6 )
= $true )
| ~ spl8_4 ),
inference(avatar_component_clause,[],[f191]) ).
thf(f194,plain,
( spl8_3
| spl8_2
| spl8_4 ),
inference(avatar_split_clause,[],[f156,f191,f183,f187]) ).
thf(f196,definition,
( spl8_5
<=> ( ( sK0 @ sK7 @ sK4 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl8_5])],[avatar_definition]) ).
thf(f198,plain,
( ( ( sK0 @ sK7 @ sK4 )
= $true )
| ~ spl8_5 ),
inference(avatar_component_clause,[],[f196]) ).
thf(f199,plain,
( spl8_3
| spl8_1
| spl8_5 ),
inference(avatar_split_clause,[],[f159,f196,f179,f187]) ).
thf(f200,plain,
( spl8_4
| spl8_5
| spl8_3 ),
inference(avatar_split_clause,[],[f158,f187,f196,f191]) ).
thf(f202,definition,
( spl8_6
<=> ( ( sK0 @ sK5 @ sK6 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl8_6])],[avatar_definition]) ).
thf(f204,plain,
( ( ( sK0 @ sK5 @ sK6 )
= $false )
| ~ spl8_6 ),
inference(avatar_component_clause,[],[f202]) ).
thf(f205,plain,
( spl8_6
| spl8_2
| spl8_3 ),
inference(avatar_split_clause,[],[f161,f187,f183,f202]) ).
thf(f206,plain,
( spl8_5
| spl8_3
| spl8_6 ),
inference(avatar_split_clause,[],[f160,f202,f187,f196]) ).
thf(f208,definition,
( spl8_7
<=> ( ( sK0 @ sK1 @ sK4 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl8_7])],[avatar_definition]) ).
thf(f210,plain,
( ( ( sK0 @ sK1 @ sK4 )
= $false )
| ~ spl8_7 ),
inference(avatar_component_clause,[],[f208]) ).
thf(f211,plain,
( spl8_7
| spl8_3
| spl8_1 ),
inference(avatar_split_clause,[],[f165,f179,f187,f208]) ).
thf(f212,plain,
( spl8_7
| spl8_3
| spl8_4 ),
inference(avatar_split_clause,[],[f164,f191,f187,f208]) ).
thf(f213,plain,
( spl8_6
| spl8_3
| spl8_7 ),
inference(avatar_split_clause,[],[f162,f208,f187,f202]) ).
thf(f221,plain,
! [X0: $i,X1: $i] :
( ( ( sK0 @ X1 @ X0 )
= $true )
| ( $false = $true )
| ( $false
= ( sK0 @ X0 @ X1 ) ) ),
inference(constrained_superposition,[],[f168,f177]) ).
thf(f226,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( sK0 @ X0 @ X1 ) )
| ( ( sK0 @ X1 @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[],[f221]) ).
thf(f235,plain,
( ( $false = $true )
| ~ spl8_3 ),
inference(constrained_superposition,[],[f188,f168]) ).
thf(f242,plain,
( $false
| ~ spl8_3 ),
inference(trivial_inequality_removal,[],[f235]) ).
thf(f243,plain,
~ spl8_3,
inference(avatar_contradiction_clause,[],[f242]) ).
thf(f245,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ X0 @ sK5 ) )
| ( $false = $true )
| ( $false
= ( sK0 @ X0 @ sK6 ) ) )
| ~ spl8_6 ),
inference(constrained_superposition,[],[f204,f177]) ).
thf(f247,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ X0 @ sK6 ) )
| ( $false
= ( sK0 @ X0 @ sK5 ) ) )
| ~ spl8_6 ),
inference(trivial_inequality_removal,[],[f245]) ).
thf(f268,plain,
( ( $false = $true )
| ( ( sK0 @ sK2 @ sK5 )
= $true )
| ~ spl8_1 ),
inference(constrained_superposition,[],[f181,f226]) ).
thf(f277,plain,
( ( ( sK0 @ sK2 @ sK5 )
= $true )
| ~ spl8_1 ),
inference(trivial_inequality_removal,[],[f268]) ).
thf(f287,plain,
( ( $false = $true )
| ( ( sK0 @ sK2 @ sK5 )
= $false )
| ~ spl8_4
| ~ spl8_6 ),
inference(constrained_superposition,[],[f247,f193]) ).
thf(f298,plain,
( ( ( sK0 @ sK2 @ sK5 )
= $false )
| ~ spl8_4
| ~ spl8_6 ),
inference(trivial_inequality_removal,[],[f287]) ).
thf(f303,plain,
( ( $false = $true )
| ~ spl8_1
| ~ spl8_4
| ~ spl8_6 ),
inference(forward_demodulation,[],[f298,f277]) ).
thf(f304,plain,
( $false
| ~ spl8_1
| ~ spl8_4
| ~ spl8_6 ),
inference(trivial_inequality_removal,[],[f303]) ).
thf(f305,plain,
( ~ spl8_1
| ~ spl8_4
| ~ spl8_6 ),
inference(avatar_contradiction_clause,[],[f304]) ).
thf(f310,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ X0 @ sK4 ) )
| ( $false = $true )
| ( ( sK0 @ X0 @ sK1 )
= $false ) )
| ~ spl8_7 ),
inference(constrained_superposition,[],[f177,f210]) ).
thf(f311,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ X0 @ sK4 ) )
| ( ( sK0 @ X0 @ sK1 )
= $false ) )
| ~ spl8_7 ),
inference(trivial_inequality_removal,[],[f310]) ).
thf(f377,plain,
( ( ( sK0 @ sK7 @ sK1 )
= $false )
| ( $false = $true )
| ~ spl8_5
| ~ spl8_7 ),
inference(constrained_superposition,[],[f198,f311]) ).
thf(f385,plain,
( ( ( sK0 @ sK7 @ sK1 )
= $false )
| ~ spl8_5
| ~ spl8_7 ),
inference(trivial_inequality_removal,[],[f377]) ).
thf(f389,plain,
( ( $false = $true )
| ~ spl8_2
| ~ spl8_5
| ~ spl8_7 ),
inference(forward_demodulation,[],[f385,f185]) ).
thf(f390,plain,
( $false
| ~ spl8_2
| ~ spl8_5
| ~ spl8_7 ),
inference(trivial_inequality_removal,[],[f389]) ).
thf(f391,plain,
( ~ spl8_2
| ~ spl8_5
| ~ spl8_7 ),
inference(avatar_contradiction_clause,[],[f390]) ).
cnf(s1,plain,
( spl8_1
| spl8_2
| spl8_3 ),
inference(sat_conversion,[],[f189]) ).
cnf(s2,plain,
( spl8_2
| spl8_3
| spl8_4 ),
inference(sat_conversion,[],[f194]) ).
cnf(s3,plain,
( spl8_1
| spl8_3
| spl8_5 ),
inference(sat_conversion,[],[f199]) ).
cnf(s4,plain,
( spl8_3
| spl8_4
| spl8_5 ),
inference(sat_conversion,[],[f200]) ).
cnf(s5,plain,
( spl8_2
| spl8_3
| spl8_6 ),
inference(sat_conversion,[],[f205]) ).
cnf(s6,plain,
( spl8_3
| spl8_5
| spl8_6 ),
inference(sat_conversion,[],[f206]) ).
cnf(s7,plain,
( spl8_1
| spl8_3
| spl8_7 ),
inference(sat_conversion,[],[f211]) ).
cnf(s8,plain,
( spl8_3
| spl8_4
| spl8_7 ),
inference(sat_conversion,[],[f212]) ).
cnf(s9,plain,
( spl8_3
| spl8_6
| spl8_7 ),
inference(sat_conversion,[],[f213]) ).
cnf(s11,plain,
~ spl8_3,
inference(sat_conversion,[],[f243]) ).
cnf(s13,plain,
( ~ spl8_1
| ~ spl8_4
| ~ spl8_6 ),
inference(sat_conversion,[],[f305]) ).
cnf(s15,plain,
( ~ spl8_2
| ~ spl8_5
| ~ spl8_7 ),
inference(sat_conversion,[],[f391]) ).
cnf(s16,plain,
( spl8_6
| spl8_7 ),
inference(rat,[],[s9,s11]) ).
cnf(s17,plain,
( spl8_4
| spl8_7 ),
inference(rat,[],[s8,s11]) ).
cnf(s18,plain,
( spl8_1
| spl8_7 ),
inference(rat,[],[s7,s11]) ).
cnf(s19,plain,
( spl8_5
| spl8_6 ),
inference(rat,[],[s6,s11]) ).
cnf(s20,plain,
( spl8_2
| spl8_6 ),
inference(rat,[],[s5,s11]) ).
cnf(s21,plain,
( spl8_4
| spl8_5 ),
inference(rat,[],[s4,s11]) ).
cnf(s22,plain,
( spl8_1
| spl8_5 ),
inference(rat,[],[s3,s11]) ).
cnf(s23,plain,
( spl8_2
| spl8_4 ),
inference(rat,[],[s2,s11]) ).
cnf(s24,plain,
( spl8_1
| spl8_2 ),
inference(rat,[],[s1,s11]) ).
cnf(s25,plain,
spl8_1,
inference(rat,[],[s15,s24,s22,s18]) ).
cnf(s26,plain,
spl8_2,
inference(rat,[],[s13,s23,s20,s25]) ).
cnf(s27,plain,
spl8_6,
inference(rat,[],[s15,s19,s16,s26]) ).
cnf(s28,plain,
~ spl8_4,
inference(rat,[],[s13,s25,s27]) ).
cnf(s29,plain,
spl8_7,
inference(rat,[],[s17,s28]) ).
cnf(s30,plain,
spl8_5,
inference(rat,[],[s21,s28]) ).
cnf(s31,plain,
$false,
inference(rat,[],[s15,s26,s29,s30]) ).
thf(f392,plain,
$false,
inference(avatar_sat_refutation,[],[s31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL868^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n015.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 10:20:03 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running higher-order theorem proving
% 0.07/0.25 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.31 % (3346348)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.31 % (3346355)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=36943785:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.31 % (3346355)Instruction limit reached!
% 0.21/0.31 % (3346355)------------------------------
% 0.21/0.31 % (3346355)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (3346355)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (3346355)CaDiCaL version: 2.1.3
% 0.21/0.31 % (3346355)Termination reason: Instruction limit
% 0.21/0.31 % (3346355)Termination phase: Property scanning
% 0.21/0.31 % (3346355)Time elapsed: 0.001 s
% 0.21/0.31 % (3346355)Peak memory usage: 10 MB
% 0.21/0.31 % (3346355)Instructions burned: 5 (million)
% 0.21/0.31 % (3346354)lrs+10_16_si=on:nwc=1.5:random_seed=3837965331:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.31 % (3346353)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2586295863:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.31 % (3346356)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=610779801: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)
% 0.21/0.31 % (3346357)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=478780921:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.31 % (3346358)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1970697089:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.31 % (3346354)Instruction limit reached!
% 0.21/0.31 % (3346354)------------------------------
% 0.21/0.31 % (3346354)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (3346354)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (3346354)CaDiCaL version: 2.1.3
% 0.21/0.31 % (3346354)Termination reason: Instruction limit
% 0.21/0.31 % (3346354)Termination phase: Saturation
% 0.21/0.31 % (3346354)Time elapsed: 0.010 s
% 0.21/0.31 % (3346354)Peak memory usage: 12 MB
% 0.21/0.31 % (3346354)Instructions burned: 18 (million)
% 0.21/0.31 % (3346359)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.31 % (3346359)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
% 0.21/0.31 % (3346353) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3346348-3346353"...
% 0.21/0.31 % (3346357)Instruction limit reached!
% 0.21/0.31 % (3346357)------------------------------
% 0.21/0.31 % (3346357)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (3346357)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (3346357)CaDiCaL version: 2.1.3
% 0.21/0.31 % (3346357)Termination reason: Instruction limit
% 0.21/0.31 % (3346357)Termination phase: Saturation
% 0.21/0.31 % (3346357)Time elapsed: 0.013 s
% 0.21/0.31 % (3346357)Peak memory usage: 12 MB
% 0.21/0.31 % (3346357)Instructions burned: 24 (million)
% 0.21/0.31 % (3346353)...printing done.
% 0.21/0.31 % (3346353)Refutation found. Thanks to Tanya!
% 0.21/0.31 % SZS status Theorem for theBenchmark
% 0.21/0.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.31 % (3346353)------------------------------
% 0.21/0.31 % (3346353)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (3346353)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (3346353)CaDiCaL version: 2.1.3
% 0.21/0.31 % (3346353)Termination reason: Refutation
% 0.21/0.31 % (3346353)Time elapsed: 0.015 s
% 0.21/0.31 % (3346353)Peak memory usage: 13 MB
% 0.21/0.31 % (3346353)Instructions burned: 26 (million)
% 0.21/0.31 % (3346348)Success in time 0.052 s
% 0.21/0.31 % Vampire exiting
%------------------------------------------------------------------------------