%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO495^6 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 08:48:07 AM UTC 2026
% Result : Theorem 0.23s 0.29s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 13
% Syntax : Number of formulae : 94 ( 38 unt; 0 typ; 6 def)
% Number of atoms : 696 ( 127 equ; 0 cnn)
% Maximal formula atoms : 13 ( 7 avg)
% Number of connectives : 951 ( 101 ~; 169 |; 0 &; 618 @)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 90 ( 90 >; 0 *; 0 +; 0 <<)
% Number of symbols : 66 ( 62 usr; 12 con; 0-4 aty)
% ( 58 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 249 ( 0 sgn 41 !; 0 ?; 249 :)
% 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,
g: mu > $i > $o ).
thf(func_def_37,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_38,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_39,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_40,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_41,type,
vIMP: $o > $o > $o ).
thf(func_def_42,type,
vAND: $o > $o > $o ).
thf(func_def_43,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_44,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_47,type,
vOR: $o > $o > $o ).
thf(func_def_48,type,
vNOT: $o > $o ).
thf(func_def_49,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_50,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_51,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_52,type,
sF0: $o ).
thf(func_def_53,type,
sK1: $i > mu ).
thf(func_def_54,type,
sK2: $i > $i ).
thf(func_def_55,type,
sK3: $i > $i ).
thf(func_def_58,type,
sK6: mu ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/LCL013^0.ax',mor) ).
thf(f6,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/LCL013^0.ax',mforall_ind) ).
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_s5 @ X1 @ X2 ) ) )
= mbox_s5 ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^6.ax',mbox_s5) ).
thf(f37,conjecture,
( mvalid
@ ( mimplies
@ ( mforall_ind
@ ^ [X0: mu] : ( mor @ ( mbox_s5 @ ( f @ X0 ) ) @ ( mbox_s5 @ ( g @ X0 ) ) ) )
@ ( mbox_s5
@ ( mforall_ind
@ ^ [X0: mu] : ( mor @ ( f @ X0 ) @ ( g @ X0 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove) ).
thf(f38,negated_conjecture,
~ ( mvalid
@ ( mimplies
@ ( mforall_ind
@ ^ [X0: mu] : ( mor @ ( mbox_s5 @ ( f @ X0 ) ) @ ( mbox_s5 @ ( g @ X0 ) ) ) )
@ ( mbox_s5
@ ( mforall_ind
@ ^ [X0: mu] : ( mor @ ( f @ X0 ) @ ( g @ X0 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
thf(f44,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
inference(rectify,[],[f28]) ).
thf(f45,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f44]) ).
thf(f73,plain,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_s5 @ X1 @ X2 ) ) )
= mbox_s5 ),
inference(rectify,[],[f32]) ).
thf(f74,plain,
( mbox_s5
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f73]) ).
thf(f78,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f81,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f82,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f81]) ).
thf(f90,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f91,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f90]) ).
thf(f94,plain,
~ ( mvalid
@ ( mimplies
@ ( mforall_ind
@ ^ [X0: mu] : ( mor @ ( mbox_s5 @ ( f @ X0 ) ) @ ( mbox_s5 @ ( g @ X0 ) ) ) )
@ ( mbox_s5
@ ( mforall_ind
@ ^ [X1: mu] : ( mor @ ( f @ X1 ) @ ( g @ X1 ) ) ) ) ) ),
inference(rectify,[],[f38]) ).
thf(f95,plain,
( ( mvalid
@ ( mimplies
@ ( mforall_ind
@ ^ [Y0: mu] : ( mor @ ( mbox_s5 @ ( f @ Y0 ) ) @ ( mbox_s5 @ ( g @ Y0 ) ) ) )
@ ( mbox_s5
@ ( mforall_ind
@ ^ [Y0: mu] : ( mor @ ( f @ Y0 ) @ ( g @ Y0 ) ) ) ) ) )
!= $true ),
inference(fool_elimination,[],[f94]) ).
thf(f98,plain,
( mforall_ind
= ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f10]) ).
thf(f99,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f98]) ).
thf(f101,plain,
( ( mvalid
@ ( mimplies
@ ( mforall_ind
@ ^ [Y0: mu] : ( mor @ ( mbox_s5 @ ( f @ Y0 ) ) @ ( mbox_s5 @ ( g @ Y0 ) ) ) )
@ ( mbox_s5
@ ( mforall_ind
@ ^ [Y0: mu] : ( mor @ ( f @ Y0 ) @ ( g @ Y0 ) ) ) ) ) )
!= $true ),
inference(flattening,[],[f95]) ).
thf(f106,plain,
( mbox_s5
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f74]) ).
thf(f110,plain,
( ( mvalid
@ ( mimplies
@ ( mforall_ind
@ ^ [Y0: mu] : ( mor @ ( mbox_s5 @ ( f @ Y0 ) ) @ ( mbox_s5 @ ( g @ Y0 ) ) ) )
@ ( mbox_s5
@ ( mforall_ind
@ ^ [Y0: mu] : ( mor @ ( f @ Y0 ) @ ( g @ Y0 ) ) ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f101]) ).
thf(f114,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f45]) ).
thf(f116,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f99]) ).
thf(f130,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f82]) ).
thf(f133,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f91]) ).
thf(f134,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f78]) ).
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,[],[f134,f130,f133]) ).
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: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: mu] :
( ^ [Y1: $i > $o,Y2: $i > $o,Y3: $i] :
( ( Y2 @ Y3 )
| ( Y1 @ Y3 ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( f @ Y0 ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( g @ Y0 ) ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: mu] :
( ^ [Y1: $i > $o,Y2: $i > $o,Y3: $i] :
( ( Y2 @ Y3 )
| ( Y1 @ Y3 ) )
@ ( f @ Y0 )
@ ( g @ Y0 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f110,f114,f142,f116,f130,f106,f106,f106,f116,f130]) ).
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: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: mu] :
( ^ [Y1: $i > $o,Y2: $i > $o,Y3: $i] :
( ( Y2 @ Y3 )
| ( Y1 @ Y3 ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( f @ Y0 ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( g @ Y0 ) ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: mu] :
( ^ [Y1: $i > $o,Y2: $i > $o,Y3: $i] :
( ( Y2 @ Y3 )
| ( Y1 @ Y3 ) )
@ ( f @ Y0 )
@ ( g @ Y0 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
thf(f156,plain,
sF0 != $true,
inference(definition_folding,[],[f151,f155]) ).
thf(f175,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: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: mu] :
( ^ [Y1: $i > $o,Y2: $i > $o,Y3: $i] :
( ( Y2 @ Y3 )
| ( Y1 @ Y3 ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( f @ Y0 ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( g @ Y0 ) ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: mu] :
( ^ [Y1: $i > $o,Y2: $i > $o,Y3: $i] :
( ( Y2 @ Y3 )
| ( Y1 @ Y3 ) )
@ ( f @ Y0 )
@ ( g @ Y0 ) ) ) ) ) ) )
| ( sF0 = $true ) ),
inference(iff_proxy_clausification,[],[f155]) ).
thf(f207,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( !! @ mu
@ ^ [Y2: mu] :
( ( g @ Y2 @ Y1 )
| ( f @ Y2 @ Y1 ) ) ) ) )
| ~ ( !! @ mu
@ ^ [Y1: mu] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y0 @ Y2 )
| ( g @ Y1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y0 @ Y2 )
| ( f @ Y1 @ Y2 ) ) ) ) ) ) ) )
| ( sF0 = $true ) ),
inference(beta-eta_normalization,[],[f175]) ).
thf(f208,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( !! @ mu
@ ^ [Y2: mu] :
( ( g @ Y2 @ Y1 )
| ( f @ Y2 @ Y1 ) ) ) ) )
| ~ ( !! @ mu
@ ^ [Y1: mu] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y0 @ Y2 )
| ( g @ Y1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y0 @ Y2 )
| ( f @ Y1 @ Y2 ) ) ) ) ) )
@ sK4 ) )
| ( sF0 = $true ) ),
inference(sigma_proxy_clausification,[],[f207]) ).
thf(f209,plain,
( ( sF0 = $true )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK4 @ Y0 )
| ( !! @ mu
@ ^ [Y1: mu] :
( ( g @ Y1 @ Y0 )
| ( f @ Y1 @ Y0 ) ) ) ) )
| ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ sK4 @ Y1 )
| ( g @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ sK4 @ Y1 )
| ( f @ Y0 @ Y1 ) ) ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f208]) ).
thf(f210,plain,
( ( $false
= ( ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ sK4 @ Y1 )
| ( g @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ sK4 @ Y1 )
| ( f @ Y0 @ Y1 ) ) ) ) ) ) )
| ( sF0 = $true ) ),
inference(or_proxy_clausification,[],[f209]) ).
thf(f211,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK4 @ Y0 )
| ( !! @ mu
@ ^ [Y1: mu] :
( ( g @ Y1 @ Y0 )
| ( f @ Y1 @ Y0 ) ) ) ) ) )
| ( sF0 = $true ) ),
inference(or_proxy_clausification,[],[f209]) ).
thf(f212,plain,
( ( sF0 = $true )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK4 @ Y0 )
| ( !! @ mu
@ ^ [Y1: mu] :
( ( g @ Y1 @ Y0 )
| ( f @ Y1 @ Y0 ) ) ) )
@ sK5 ) ) ),
inference(sigma_proxy_clausification,[],[f211]) ).
thf(f213,plain,
( ( $false
= ( ~ ( rel_s5 @ sK4 @ sK5 )
| ( !! @ mu
@ ^ [Y0: mu] :
( ( g @ Y0 @ sK5 )
| ( f @ Y0 @ sK5 ) ) ) ) )
| ( sF0 = $true ) ),
inference(beta-eta_normalization,[],[f212]) ).
thf(f214,plain,
( ( $false
= ( !! @ mu
@ ^ [Y0: mu] :
( ( g @ Y0 @ sK5 )
| ( f @ Y0 @ sK5 ) ) ) )
| ( sF0 = $true ) ),
inference(or_proxy_clausification,[],[f213]) ).
thf(f215,plain,
( ( sF0 = $true )
| ( $false
= ( ~ ( rel_s5 @ sK4 @ sK5 ) ) ) ),
inference(or_proxy_clausification,[],[f213]) ).
thf(f216,plain,
( ( sF0 = $true )
| ( ( rel_s5 @ sK4 @ sK5 )
= $true ) ),
inference(not_proxy_clausification,[],[f215]) ).
thf(f217,plain,
( ( ( ^ [Y0: mu] :
( ( g @ Y0 @ sK5 )
| ( f @ Y0 @ sK5 ) )
@ sK6 )
= $false )
| ( sF0 = $true ) ),
inference(sigma_proxy_clausification,[],[f214]) ).
thf(f218,plain,
( ( sF0 = $true )
| ( ( ( g @ sK6 @ sK5 )
| ( f @ sK6 @ sK5 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f217]) ).
thf(f219,plain,
( ( sF0 = $true )
| ( $false
= ( f @ sK6 @ sK5 ) ) ),
inference(or_proxy_clausification,[],[f218]) ).
thf(f220,plain,
( ( sF0 = $true )
| ( $false
= ( g @ sK6 @ sK5 ) ) ),
inference(or_proxy_clausification,[],[f218]) ).
thf(f221,plain,
( ( ( !! @ mu
@ ^ [Y0: mu] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ sK4 @ Y1 )
| ( g @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ sK4 @ Y1 )
| ( f @ Y0 @ Y1 ) ) ) ) )
= $true )
| ( sF0 = $true ) ),
inference(not_proxy_clausification,[],[f210]) ).
thf(f222,plain,
! [X1: mu] :
( ( sF0 = $true )
| ( ( ^ [Y0: mu] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ sK4 @ Y1 )
| ( g @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ sK4 @ Y1 )
| ( f @ Y0 @ Y1 ) ) ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f221]) ).
thf(f223,plain,
! [X1: mu] :
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK4 @ Y0 )
| ( g @ X1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK4 @ Y0 )
| ( f @ X1 @ Y0 ) ) ) )
= $true )
| ( sF0 = $true ) ),
inference(beta-eta_normalization,[],[f222]) ).
thf(f224,plain,
! [X1: mu] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK4 @ Y0 )
| ( f @ X1 @ Y0 ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK4 @ Y0 )
| ( g @ X1 @ Y0 ) ) )
= $true )
| ( sF0 = $true ) ),
inference(or_proxy_clausification,[],[f223]) ).
thf(f225,plain,
! [X2: $i,X1: mu] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK4 @ Y0 )
| ( g @ X1 @ Y0 ) ) )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK4 @ Y0 )
| ( f @ X1 @ Y0 ) )
@ X2 )
= $true )
| ( sF0 = $true ) ),
inference(pi_proxy_clausification,[],[f224]) ).
thf(f226,plain,
! [X2: $i,X3: $i,X1: mu] :
( ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK4 @ Y0 )
| ( g @ X1 @ Y0 ) )
@ X3 )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK4 @ Y0 )
| ( f @ X1 @ Y0 ) )
@ X2 )
= $true )
| ( sF0 = $true ) ),
inference(pi_proxy_clausification,[],[f225]) ).
thf(f227,plain,
! [X2: $i,X3: $i,X1: mu] :
( ( $true
= ( ~ ( rel_s5 @ sK4 @ X2 )
| ( f @ X1 @ X2 ) ) )
| ( ( ~ ( rel_s5 @ sK4 @ X3 )
| ( g @ X1 @ X3 ) )
= $true )
| ( sF0 = $true ) ),
inference(beta-eta_normalization,[],[f226]) ).
thf(f228,plain,
! [X2: $i,X3: $i,X1: mu] :
( ( ( ~ ( rel_s5 @ sK4 @ X2 ) )
= $true )
| ( ( f @ X1 @ X2 )
= $true )
| ( sF0 = $true )
| ( ( ~ ( rel_s5 @ sK4 @ X3 )
| ( g @ X1 @ X3 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f227]) ).
thf(f229,plain,
! [X2: $i,X3: $i,X1: mu] :
( ( sF0 = $true )
| ( ( ~ ( rel_s5 @ sK4 @ X3 )
| ( g @ X1 @ X3 ) )
= $true )
| ( ( f @ X1 @ X2 )
= $true )
| ( ( rel_s5 @ sK4 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f228]) ).
thf(f230,plain,
! [X2: $i,X3: $i,X1: mu] :
( ( ( rel_s5 @ sK4 @ X2 )
= $false )
| ( ( g @ X1 @ X3 )
= $true )
| ( ( f @ X1 @ X2 )
= $true )
| ( ( ~ ( rel_s5 @ sK4 @ X3 ) )
= $true )
| ( sF0 = $true ) ),
inference(or_proxy_clausification,[],[f229]) ).
thf(f231,plain,
! [X2: $i,X3: $i,X1: mu] :
( ( ( g @ X1 @ X3 )
= $true )
| ( ( f @ X1 @ X2 )
= $true )
| ( $false
= ( rel_s5 @ sK4 @ X3 ) )
| ( sF0 = $true )
| ( ( rel_s5 @ sK4 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f230]) ).
thf(f253,definition,
( spl7_6
<=> ( ( rel_s5 @ sK4 @ sK5 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl7_6])],[avatar_definition]) ).
thf(f255,plain,
( ( ( rel_s5 @ sK4 @ sK5 )
= $true )
| ~ spl7_6 ),
inference(avatar_component_clause,[],[f253]) ).
thf(f257,definition,
( spl7_7
<=> ( sF0 = $true ) ),
introduced(definition,[new_symbols(definition,[spl7_7])],[avatar_definition]) ).
thf(f260,plain,
( spl7_6
| spl7_7 ),
inference(avatar_split_clause,[],[f216,f257,f253]) ).
thf(f262,definition,
( spl7_8
<=> ( $false
= ( g @ sK6 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_8])],[avatar_definition]) ).
thf(f264,plain,
( ( $false
= ( g @ sK6 @ sK5 ) )
| ~ spl7_8 ),
inference(avatar_component_clause,[],[f262]) ).
thf(f265,plain,
( spl7_7
| spl7_8 ),
inference(avatar_split_clause,[],[f220,f262,f257]) ).
thf(f267,definition,
( spl7_9
<=> ( $false
= ( f @ sK6 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_9])],[avatar_definition]) ).
thf(f269,plain,
( ( $false
= ( f @ sK6 @ sK5 ) )
| ~ spl7_9 ),
inference(avatar_component_clause,[],[f267]) ).
thf(f270,plain,
( spl7_7
| spl7_9 ),
inference(avatar_split_clause,[],[f219,f267,f257]) ).
thf(f272,definition,
( spl7_10
<=> ! [X2: $i,X1: mu,X3: $i] :
( ( ( g @ X1 @ X3 )
= $true )
| ( ( rel_s5 @ sK4 @ X2 )
= $false )
| ( $false
= ( rel_s5 @ sK4 @ X3 ) )
| ( ( f @ X1 @ X2 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl7_10])],[avatar_definition]) ).
thf(f273,plain,
( ! [X2: $i,X3: $i,X1: mu] :
( ( $false
= ( rel_s5 @ sK4 @ X3 ) )
| ( ( g @ X1 @ X3 )
= $true )
| ( ( rel_s5 @ sK4 @ X2 )
= $false )
| ( ( f @ X1 @ X2 )
= $true ) )
| ~ spl7_10 ),
inference(avatar_component_clause,[],[f272]) ).
thf(f274,plain,
( spl7_7
| spl7_10 ),
inference(avatar_split_clause,[],[f231,f272,f257]) ).
thf(f275,plain,
~ spl7_7,
inference(avatar_split_clause,[],[f156,f257]) ).
thf(f348,plain,
( ! [X0: $i,X1: mu] :
( ( ( g @ X1 @ X0 )
= $true )
| ( ( f @ X1 @ X0 )
= $true )
| ( $false != $false )
| ( $false
= ( rel_s5 @ sK4 @ X0 ) ) )
| ~ spl7_10 ),
inference(equality_factoring,[],[f273]) ).
thf(f351,plain,
( ! [X0: $i,X1: mu] :
( ( $false
= ( rel_s5 @ sK4 @ X0 ) )
| ( ( g @ X1 @ X0 )
= $true )
| ( ( f @ X1 @ X0 )
= $true ) )
| ~ spl7_10 ),
inference(trivial_inequality_removal,[],[f348]) ).
thf(f368,plain,
( ! [X0: mu] :
( ( $true
= ( g @ X0 @ sK5 ) )
| ( $false = $true )
| ( ( f @ X0 @ sK5 )
= $true ) )
| ~ spl7_6
| ~ spl7_10 ),
inference(constrained_superposition,[],[f255,f351]) ).
thf(f370,plain,
( ! [X0: mu] :
( ( $true
= ( g @ X0 @ sK5 ) )
| ( ( f @ X0 @ sK5 )
= $true ) )
| ~ spl7_6
| ~ spl7_10 ),
inference(trivial_inequality_removal,[],[f368]) ).
thf(f376,plain,
( ( $false = $true )
| ( ( f @ sK6 @ sK5 )
= $true )
| ~ spl7_6
| ~ spl7_8
| ~ spl7_10 ),
inference(constrained_superposition,[],[f264,f370]) ).
thf(f378,plain,
( ( ( f @ sK6 @ sK5 )
= $true )
| ~ spl7_6
| ~ spl7_8
| ~ spl7_10 ),
inference(trivial_inequality_removal,[],[f376]) ).
thf(f382,plain,
( ( $false = $true )
| ~ spl7_6
| ~ spl7_8
| ~ spl7_9
| ~ spl7_10 ),
inference(forward_demodulation,[],[f378,f269]) ).
thf(f383,plain,
( $false
| ~ spl7_6
| ~ spl7_8
| ~ spl7_9
| ~ spl7_10 ),
inference(trivial_inequality_removal,[],[f382]) ).
thf(f384,plain,
( ~ spl7_6
| ~ spl7_8
| ~ spl7_9
| ~ spl7_10 ),
inference(avatar_contradiction_clause,[],[f383]) ).
cnf(s5,plain,
( spl7_6
| spl7_7 ),
inference(sat_conversion,[],[f260]) ).
cnf(s6,plain,
( spl7_7
| spl7_8 ),
inference(sat_conversion,[],[f265]) ).
cnf(s7,plain,
( spl7_7
| spl7_9 ),
inference(sat_conversion,[],[f270]) ).
cnf(s8,plain,
( spl7_7
| spl7_10 ),
inference(sat_conversion,[],[f274]) ).
cnf(s9,plain,
~ spl7_7,
inference(sat_conversion,[],[f275]) ).
cnf(s12,plain,
( ~ spl7_6
| ~ spl7_8
| ~ spl7_9
| ~ spl7_10 ),
inference(sat_conversion,[],[f384]) ).
cnf(s14,plain,
spl7_10,
inference(rat,[],[s8,s9]) ).
cnf(s15,plain,
spl7_9,
inference(rat,[],[s7,s9]) ).
cnf(s16,plain,
spl7_8,
inference(rat,[],[s6,s9]) ).
cnf(s17,plain,
~ spl7_6,
inference(rat,[],[s12,s14,s15,s16]) ).
cnf(s18,plain,
$false,
inference(rat,[],[s5,s9,s17]) ).
thf(f385,plain,
$false,
inference(avatar_sat_refutation,[],[s18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO495^6 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n026.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 17:13:29 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.25 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
% 0.23/0.29 % (885440)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.29 % (885451)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.23/0.29 % (885451)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
% 0.23/0.29 % (885451)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=2748083117:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.23/0.29 % (885451) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-885440-885451"...
% 0.23/0.29 % (885445)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2722229957:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.23/0.29 % (885446)lrs+10_16_si=on:nwc=1.5:random_seed=562484947:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.23/0.29 % (885449)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1318899299:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.23/0.29 % (885447)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=4263467788:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.23/0.29 % (885448)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=2480164794: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)
% 0.23/0.29 % (885450)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1143169985:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.23/0.29 % (885451)...printing done.
% 0.23/0.29 % (885451)Refutation found. Thanks to Tanya!
% 0.23/0.29 % SZS status Theorem for theBenchmark
% 0.23/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.29 % (885451)------------------------------
% 0.23/0.29 % (885451)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.29 % (885451)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.29 % (885451)CaDiCaL version: 2.1.3
% 0.23/0.29 % (885451)Termination reason: Refutation
% 0.23/0.29 % (885451)Time elapsed: 0.007 s
% 0.23/0.29 % (885451)Peak memory usage: 13 MB
% 0.23/0.29 % (885451)Instructions burned: 24 (million)
% 0.23/0.29 % (885440)Success in time 0.037 s
% 0.23/0.29 % Vampire exiting
%------------------------------------------------------------------------------