%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO487^6 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : 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 08:48:06 AM UTC 2026
% Result : Theorem 0.10s 0.26s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 14
% Syntax : Number of formulae : 94 ( 46 unt; 0 typ; 5 def)
% Number of atoms : 535 ( 107 equ; 0 cnn)
% Maximal formula atoms : 8 ( 5 avg)
% Number of connectives : 800 ( 141 ~; 96 |; 0 &; 505 @)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 126 ( 126 >; 0 *; 0 +; 0 <<)
% Number of symbols : 63 ( 59 usr; 10 con; 0-4 aty)
% ( 54 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 280 ( 0 sgn 28 !; 0 ?; 280 :)
% 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,
f: mu > $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,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_41,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_42,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_43,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_44,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_45,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_46,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_47,type,
vNOT: $o > $o ).
thf(func_def_48,type,
vOR: $o > $o > $o ).
thf(func_def_51,type,
sF0: $o ).
thf(func_def_52,type,
sK1: $i > mu ).
thf(func_def_53,type,
sK2: $i > mu ).
thf(func_def_54,type,
sK3: $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,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mor) ).
thf(f6,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mimplies) ).
thf(f10,axiom,
( mforall_ind
= ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] : ( X0 @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mforall_ind) ).
thf(f12,axiom,
( ( ^ [X0: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X1: mu] : ( mnot @ ( X0 @ X1 ) ) ) ) )
= mexists_ind ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mexists_ind) ).
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_s5
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_s5 @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^6.ax',mbox_s5) ).
thf(f33,axiom,
( mdia_s5
= ( ^ [X0: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^6.ax',mdia_s5) ).
thf(f37,conjecture,
( mvalid
@ ( mimplies
@ ( mdia_s5
@ ( mforall_ind
@ ^ [X0: mu] : ( f @ X0 ) ) )
@ ( mexists_ind
@ ^ [X0: mu] : ( mdia_s5 @ ( f @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove) ).
thf(f38,negated_conjecture,
~ ( mvalid
@ ( mimplies
@ ( mdia_s5
@ ( mforall_ind
@ ^ [X0: mu] : ( f @ X0 ) ) )
@ ( mexists_ind
@ ^ [X0: mu] : ( mdia_s5 @ ( f @ X0 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
thf(f43,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f44,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f43]) ).
thf(f45,plain,
( ( ^ [X0: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X1: mu] : ( mnot @ ( X0 @ X1 ) ) ) ) )
= mexists_ind ),
inference(rectify,[],[f12]) ).
thf(f46,plain,
( mexists_ind
= ( ^ [Y0: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [Y1: mu] : ( mnot @ ( Y0 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f45]) ).
thf(f47,plain,
( mforall_ind
= ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f10]) ).
thf(f48,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f47]) ).
thf(f71,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f80,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f81,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f80]) ).
thf(f86,plain,
~ ( mvalid
@ ( mimplies
@ ( mdia_s5
@ ( mforall_ind
@ ^ [X0: mu] : ( f @ X0 ) ) )
@ ( mexists_ind
@ ^ [X1: mu] : ( mdia_s5 @ ( f @ X1 ) ) ) ) ),
inference(rectify,[],[f38]) ).
thf(f87,plain,
( ( mvalid
@ ( mimplies
@ ( mdia_s5
@ ( mforall_ind
@ ^ [Y0: mu] : ( f @ Y0 ) ) )
@ ( mexists_ind
@ ^ [Y0: mu] : ( mdia_s5 @ ( f @ Y0 ) ) ) ) )
!= $true ),
inference(fool_elimination,[],[f86]) ).
thf(f93,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
inference(rectify,[],[f28]) ).
thf(f94,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f93]) ).
thf(f96,plain,
( mdia_s5
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f33]) ).
thf(f99,plain,
( mbox_s5
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_s5 @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f32]) ).
thf(f100,plain,
( mbox_s5
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f99]) ).
thf(f101,plain,
( ( mvalid
@ ( mimplies
@ ( mdia_s5
@ ( mforall_ind
@ ^ [Y0: mu] : ( f @ Y0 ) ) )
@ ( mexists_ind
@ ^ [Y0: mu] : ( mdia_s5 @ ( f @ Y0 ) ) ) ) )
!= $true ),
inference(flattening,[],[f87]) ).
thf(f108,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f48]) ).
thf(f109,plain,
( ( mvalid
@ ( mimplies
@ ( mdia_s5
@ ( mforall_ind
@ ^ [Y0: mu] : ( f @ Y0 ) ) )
@ ( mexists_ind
@ ^ [Y0: mu] : ( mdia_s5 @ ( f @ Y0 ) ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f101]) ).
thf(f113,plain,
( mdia_s5
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f96]) ).
thf(f120,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f81]) ).
thf(f121,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f94]) ).
thf(f122,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f71]) ).
thf(f123,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f44]) ).
thf(f129,plain,
( mexists_ind
= ( ^ [Y0: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [Y1: mu] : ( mnot @ ( Y0 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f46]) ).
thf(f135,plain,
( mbox_s5
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f100]) ).
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,[],[f122,f120,f123]) ).
thf(f146,plain,
( mexists_ind
= ( ^ [Y0: mu > $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: mu > $i > $o,Y2: $i] :
( !! @ mu
@ ^ [Y3: mu] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: mu] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( Y0 @ Y1 ) ) ) ) ) ),
inference(definition_unfolding,[],[f129,f123,f108,f123]) ).
thf(f150,plain,
( mdia_s5
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f113,f123,f135,f123]) ).
thf(f151,plain,
( $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 > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: mu] : ( f @ Y0 ) ) )
@ ( ^ [Y0: mu > $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: mu > $i > $o,Y2: $i] :
( !! @ mu
@ ^ [Y3: mu] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: mu] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( Y0 @ Y1 ) ) ) )
@ ^ [Y0: mu] :
( ^ [Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( rel_s5 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) )
@ ( f @ Y0 ) ) ) ) ) ),
inference(definition_unfolding,[],[f109,f121,f142,f150,f108,f146,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 > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: mu] : ( f @ Y0 ) ) )
@ ( ^ [Y0: mu > $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: mu > $i > $o,Y2: $i] :
( !! @ mu
@ ^ [Y3: mu] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: mu] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( Y0 @ Y1 ) ) ) )
@ ^ [Y0: mu] :
( ^ [Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( rel_s5 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) )
@ ( f @ Y0 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
thf(f156,plain,
sF0 != $true,
inference(definition_folding,[],[f151,f155]) ).
thf(f157,plain,
( ( $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 > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: mu] : ( f @ Y0 ) ) )
@ ( ^ [Y0: mu > $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: mu > $i > $o,Y2: $i] :
( !! @ mu
@ ^ [Y3: mu] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: mu] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( Y0 @ Y1 ) ) ) )
@ ^ [Y0: mu] :
( ^ [Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( rel_s5 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) )
@ ( f @ Y0 ) ) ) ) ) )
| ( sF0 = $true ) ),
inference(iff_proxy_clausification,[],[f155]) ).
thf(f181,plain,
( ( sF0 = $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ mu
@ ^ [Y1: mu] :
~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y0 @ Y2 )
| ~ ( f @ Y1 @ Y2 ) ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ mu
@ ^ [Y2: mu] : ( f @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f157]) ).
thf(f182,plain,
( ( sF0 = $true )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( !! @ mu
@ ^ [Y1: mu] :
~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y0 @ Y2 )
| ~ ( f @ Y1 @ Y2 ) ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ mu
@ ^ [Y2: mu] : ( f @ Y2 @ Y1 ) ) ) ) )
@ sK4 ) ) ),
inference(sigma_proxy_clausification,[],[f181]) ).
thf(f183,plain,
( ( sF0 = $true )
| ( $false
= ( ~ ( !! @ mu
@ ^ [Y0: mu] :
~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ sK4 @ Y1 )
| ~ ( f @ Y0 @ Y1 ) ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK4 @ Y0 )
| ~ ( !! @ mu
@ ^ [Y1: mu] : ( f @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f182]) ).
thf(f184,plain,
( ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK4 @ Y0 )
| ~ ( !! @ mu
@ ^ [Y1: mu] : ( f @ Y1 @ Y0 ) ) ) ) ) )
| ( sF0 = $true ) ),
inference(or_proxy_clausification,[],[f183]) ).
thf(f185,plain,
( ( $false
= ( ~ ( !! @ mu
@ ^ [Y0: mu] :
~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ sK4 @ Y1 )
| ~ ( f @ Y0 @ Y1 ) ) ) ) ) )
| ( sF0 = $true ) ),
inference(or_proxy_clausification,[],[f183]) ).
thf(f186,plain,
( ( $true
= ( !! @ mu
@ ^ [Y0: mu] :
~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ sK4 @ Y1 )
| ~ ( f @ Y0 @ Y1 ) ) ) ) )
| ( sF0 = $true ) ),
inference(not_proxy_clausification,[],[f185]) ).
thf(f187,plain,
! [X1: mu] :
( ( ( ^ [Y0: mu] :
~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ sK4 @ Y1 )
| ~ ( f @ Y0 @ Y1 ) ) )
@ X1 )
= $true )
| ( sF0 = $true ) ),
inference(pi_proxy_clausification,[],[f186]) ).
thf(f188,plain,
! [X1: mu] :
( ( ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK4 @ Y0 )
| ~ ( f @ X1 @ Y0 ) ) ) )
= $true )
| ( sF0 = $true ) ),
inference(beta-eta_normalization,[],[f187]) ).
thf(f189,plain,
! [X1: mu] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK4 @ Y0 )
| ~ ( f @ X1 @ Y0 ) ) ) )
= $false )
| ( sF0 = $true ) ),
inference(not_proxy_clausification,[],[f188]) ).
thf(f190,plain,
! [X1: mu] :
( ( sF0 = $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK4 @ Y0 )
| ~ ( f @ X1 @ Y0 ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f189]) ).
thf(f191,plain,
! [X2: $i,X1: mu] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK4 @ Y0 )
| ~ ( f @ X1 @ Y0 ) )
@ X2 ) )
| ( sF0 = $true ) ),
inference(pi_proxy_clausification,[],[f190]) ).
thf(f192,plain,
! [X2: $i,X1: mu] :
( ( sF0 = $true )
| ( $true
= ( ~ ( rel_s5 @ sK4 @ X2 )
| ~ ( f @ X1 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f191]) ).
thf(f193,plain,
! [X2: $i,X1: mu] :
( ( sF0 = $true )
| ( $true
= ( ~ ( f @ X1 @ X2 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK4 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f192]) ).
thf(f194,plain,
! [X2: $i,X1: mu] :
( ( sF0 = $true )
| ( $false
= ( f @ X1 @ X2 ) )
| ( $true
= ( ~ ( rel_s5 @ sK4 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f193]) ).
thf(f195,plain,
! [X2: $i,X1: mu] :
( ( sF0 = $true )
| ( $false
= ( rel_s5 @ sK4 @ X2 ) )
| ( $false
= ( f @ X1 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f194]) ).
thf(f196,plain,
( ( sF0 = $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK4 @ Y0 )
| ~ ( !! @ mu
@ ^ [Y1: mu] : ( f @ Y1 @ Y0 ) ) ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f184]) ).
thf(f197,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK4 @ Y0 )
| ~ ( !! @ mu
@ ^ [Y1: mu] : ( f @ Y1 @ Y0 ) ) ) )
= $false )
| ( sF0 = $true ) ),
inference(not_proxy_clausification,[],[f196]) ).
thf(f198,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK4 @ Y0 )
| ~ ( !! @ mu
@ ^ [Y1: mu] : ( f @ Y1 @ Y0 ) ) )
@ sK5 ) )
| ( sF0 = $true ) ),
inference(sigma_proxy_clausification,[],[f197]) ).
thf(f199,plain,
( ( ( ~ ( rel_s5 @ sK4 @ sK5 )
| ~ ( !! @ mu
@ ^ [Y0: mu] : ( f @ Y0 @ sK5 ) ) )
= $false )
| ( sF0 = $true ) ),
inference(beta-eta_normalization,[],[f198]) ).
thf(f200,plain,
( ( ( ~ ( !! @ mu
@ ^ [Y0: mu] : ( f @ Y0 @ sK5 ) ) )
= $false )
| ( sF0 = $true ) ),
inference(or_proxy_clausification,[],[f199]) ).
thf(f201,plain,
( ( $false
= ( ~ ( rel_s5 @ sK4 @ sK5 ) ) )
| ( sF0 = $true ) ),
inference(or_proxy_clausification,[],[f199]) ).
thf(f202,plain,
( ( sF0 = $true )
| ( $true
= ( rel_s5 @ sK4 @ sK5 ) ) ),
inference(not_proxy_clausification,[],[f201]) ).
thf(f203,plain,
( ( sF0 = $true )
| ( $true
= ( !! @ mu
@ ^ [Y0: mu] : ( f @ Y0 @ sK5 ) ) ) ),
inference(not_proxy_clausification,[],[f200]) ).
thf(f204,plain,
! [X1: mu] :
( ( $true
= ( ^ [Y0: mu] : ( f @ Y0 @ sK5 )
@ X1 ) )
| ( sF0 = $true ) ),
inference(pi_proxy_clausification,[],[f203]) ).
thf(f205,plain,
! [X1: mu] :
( ( sF0 = $true )
| ( ( f @ X1 @ sK5 )
= $true ) ),
inference(beta-eta_normalization,[],[f204]) ).
thf(f237,definition,
( spl6_4
<=> ( sF0 = $true ) ),
introduced(definition,[new_symbols(definition,[spl6_4])],[avatar_definition]) ).
thf(f241,definition,
( spl6_5
<=> ! [X2: $i,X1: mu] :
( ( $false
= ( rel_s5 @ sK4 @ X2 ) )
| ( $false
= ( f @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl6_5])],[avatar_definition]) ).
thf(f242,plain,
( ! [X2: $i,X1: mu] :
( ( $false
= ( f @ X1 @ X2 ) )
| ( $false
= ( rel_s5 @ sK4 @ X2 ) ) )
| ~ spl6_5 ),
inference(avatar_component_clause,[],[f241]) ).
thf(f243,plain,
( spl6_4
| spl6_5 ),
inference(avatar_split_clause,[],[f195,f241,f237]) ).
thf(f245,definition,
( spl6_6
<=> ( $true
= ( rel_s5 @ sK4 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_6])],[avatar_definition]) ).
thf(f247,plain,
( ( $true
= ( rel_s5 @ sK4 @ sK5 ) )
| ~ spl6_6 ),
inference(avatar_component_clause,[],[f245]) ).
thf(f248,plain,
( spl6_4
| spl6_6 ),
inference(avatar_split_clause,[],[f202,f245,f237]) ).
thf(f250,definition,
( spl6_7
<=> ! [X1: mu] :
( ( f @ X1 @ sK5 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl6_7])],[avatar_definition]) ).
thf(f251,plain,
( ! [X1: mu] :
( ( f @ X1 @ sK5 )
= $true )
| ~ spl6_7 ),
inference(avatar_component_clause,[],[f250]) ).
thf(f252,plain,
( spl6_7
| spl6_4 ),
inference(avatar_split_clause,[],[f205,f237,f250]) ).
thf(f253,plain,
~ spl6_4,
inference(avatar_split_clause,[],[f156,f237]) ).
thf(f270,plain,
( ( $false
= ( rel_s5 @ sK4 @ sK5 ) )
| ( $false = $true )
| ~ spl6_5
| ~ spl6_7 ),
inference(constrained_superposition,[],[f251,f242]) ).
thf(f273,plain,
( ( $false
= ( rel_s5 @ sK4 @ sK5 ) )
| ~ spl6_5
| ~ spl6_7 ),
inference(trivial_inequality_removal,[],[f270]) ).
thf(f277,plain,
( ( $false = $true )
| ~ spl6_5
| ~ spl6_6
| ~ spl6_7 ),
inference(forward_demodulation,[],[f273,f247]) ).
thf(f278,plain,
( $false
| ~ spl6_5
| ~ spl6_6
| ~ spl6_7 ),
inference(trivial_inequality_removal,[],[f277]) ).
thf(f279,plain,
( ~ spl6_5
| ~ spl6_6
| ~ spl6_7 ),
inference(avatar_contradiction_clause,[],[f278]) ).
cnf(s3,plain,
( spl6_4
| spl6_5 ),
inference(sat_conversion,[],[f243]) ).
cnf(s4,plain,
( spl6_4
| spl6_6 ),
inference(sat_conversion,[],[f248]) ).
cnf(s5,plain,
( spl6_4
| spl6_7 ),
inference(sat_conversion,[],[f252]) ).
cnf(s6,plain,
~ spl6_4,
inference(sat_conversion,[],[f253]) ).
cnf(s9,plain,
( ~ spl6_5
| ~ spl6_6
| ~ spl6_7 ),
inference(sat_conversion,[],[f279]) ).
cnf(s11,plain,
spl6_7,
inference(rat,[],[s5,s6]) ).
cnf(s12,plain,
spl6_6,
inference(rat,[],[s4,s6]) ).
cnf(s13,plain,
~ spl6_5,
inference(rat,[],[s9,s11,s12]) ).
cnf(s14,plain,
$false,
inference(rat,[],[s3,s13,s6]) ).
thf(f280,plain,
$false,
inference(avatar_sat_refutation,[],[s14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO487^6 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.17 % Computer : n015.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Tue Sep 29 17:12:19 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.21 Running higher-order theorem proving
% 0.10/0.22 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
% 0.10/0.26 % (3824281)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.10/0.26 % (3824292)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.10/0.26 % (3824292)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
% 0.10/0.26 % (3824292)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=1490603881:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.10/0.26 % (3824292) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3824281-3824292"...
% 0.10/0.26 % (3824286)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=4085255313:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.10/0.26 % (3824288)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=863751359:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.10/0.26 % (3824292)...printing done.
% 0.10/0.26 % (3824292)Refutation found. Thanks to Tanya!
% 0.10/0.26 % SZS status Theorem for theBenchmark
% 0.10/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.26 % (3824292)------------------------------
% 0.10/0.26 % (3824292)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.26 % (3824292)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.26 % (3824292)CaDiCaL version: 2.1.3
% 0.10/0.26 % (3824292)Termination reason: Refutation
% 0.10/0.27 % (3824292)Time elapsed: 0.005 s
% 0.10/0.27 % (3824292)Peak memory usage: 13 MB
% 0.10/0.27 % (3824292)Instructions burned: 18 (million)
% 0.10/0.27 % (3824281)Success in time 0.032 s
% 0.10/0.27 % Vampire exiting
%------------------------------------------------------------------------------