%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO570^7 : TPTP v9.3.1. Released v5.5.0.
% 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 08:48:26 AM UTC 2026
% Result : Theorem 0.22s 0.30s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 8
% Syntax : Number of formulae : 79 ( 53 unt; 0 typ; 0 def)
% Number of atoms : 589 ( 110 equ; 0 cnn)
% Maximal formula atoms : 10 ( 7 avg)
% Number of connectives : 860 ( 60 ~; 72 |; 3 &; 619 @)
% ( 0 <=>; 47 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 55 ( 55 >; 0 *; 0 +; 0 <<)
% Number of symbols : 59 ( 55 usr; 7 con; 0-4 aty)
% ( 59 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 218 ( 168 ^; 50 !; 0 ?; 218 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mu: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
qmltpeq: 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,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_7,type,
mtrue: $i > $o ).
thf(func_def_8,type,
mfalse: $i > $o ).
thf(func_def_9,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_11,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_12,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_13,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_14,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_15,type,
exists_in_world: mu > $i > $o ).
thf(func_def_16,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_17,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_18,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_19,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(func_def_20,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(func_def_21,type,
mserial: ( $i > $i > $o ) > $o ).
thf(func_def_22,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(func_def_23,type,
meuclidean: ( $i > $i > $o ) > $o ).
thf(func_def_24,type,
mpartially_functional: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
mfunctional: ( $i > $i > $o ) > $o ).
thf(func_def_26,type,
mweakly_dense: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
mweakly_connected: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
mweakly_directed: ( $i > $i > $o ) > $o ).
thf(func_def_29,type,
mvalid: ( $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,
minvalid: ( $i > $o ) > $o ).
thf(func_def_33,type,
rel_s4: $i > $i > $o ).
thf(func_def_34,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf(func_def_35,type,
mdia_s4: ( $i > $o ) > $i > $o ).
thf(func_def_36,type,
r: mu > 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_45,type,
vOR: $o > $o > $o ).
thf(func_def_46,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_47,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_48,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_51,type,
vNOT: $o > $o ).
thf(func_def_52,type,
sK0: $i > mu ).
thf(func_def_54,type,
sK2: mu ).
thf(func_def_55,type,
sK3: mu ).
thf(f2,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mnot) ).
thf(f3,axiom,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mor) ).
thf(f9,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) )
= mimplies ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mimplies) ).
thf(f15,axiom,
( mforall_ind
= ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] :
( ( exists_in_world @ X2 @ X1 )
=> ( X0 @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mforall_ind) ).
thf(f28,axiom,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mvalid) ).
thf(f32,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_s4 @ X1 @ X2 ) ) )
= mbox_s4 ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^5.ax',mbox_s4) ).
thf(f36,axiom,
! [X1: $i,X2: $i,X0: mu] :
( ( ( rel_s4 @ X1 @ X2 )
& ( exists_in_world @ X0 @ X1 ) )
=> ( exists_in_world @ X0 @ X2 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL015^1.ax',cumulative_ax) ).
thf(f37,conjecture,
( mvalid
@ ( mimplies
@ ( mforall_ind
@ ^ [X0: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [X1: mu] : ( r @ X0 @ X1 ) ) ) )
@ ( mforall_ind
@ ^ [X0: mu] :
( mforall_ind
@ ^ [X1: mu] : ( mbox_s4 @ ( r @ X0 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(f38,negated_conjecture,
~ ( mvalid
@ ( mimplies
@ ( mforall_ind
@ ^ [X0: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [X1: mu] : ( r @ X0 @ X1 ) ) ) )
@ ( mforall_ind
@ ^ [X0: mu] :
( mforall_ind
@ ^ [X1: mu] : ( mbox_s4 @ ( r @ X0 @ X1 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
thf(f44,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f49,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
inference(rectify,[],[f28]) ).
thf(f50,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f49]) ).
thf(f57,plain,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_s4 @ X1 @ X2 ) ) )
= mbox_s4 ),
inference(rectify,[],[f32]) ).
thf(f58,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f57]) ).
thf(f73,plain,
( mforall_ind
= ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] :
( ( exists_in_world @ X2 @ X1 )
=> ( X0 @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f15]) ).
thf(f74,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f73]) ).
thf(f76,plain,
~ ( mvalid
@ ( mimplies
@ ( mforall_ind
@ ^ [X0: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [X1: mu] : ( r @ X0 @ X1 ) ) ) )
@ ( mforall_ind
@ ^ [X2: mu] :
( mforall_ind
@ ^ [X3: mu] : ( mbox_s4 @ ( r @ X2 @ X3 ) ) ) ) ) ),
inference(rectify,[],[f38]) ).
thf(f77,plain,
( $true
!= ( mvalid
@ ( mimplies
@ ( mforall_ind
@ ^ [Y0: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [Y1: mu] : ( r @ Y0 @ Y1 ) ) ) )
@ ( mforall_ind
@ ^ [Y0: mu] :
( mforall_ind
@ ^ [Y1: mu] : ( mbox_s4 @ ( r @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f76]) ).
thf(f80,plain,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f2]) ).
thf(f81,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f80]) ).
thf(f87,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f88,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f87]) ).
thf(f91,plain,
! [X0: $i,X1: $i,X2: mu] :
( ( ( rel_s4 @ X0 @ X1 )
& ( exists_in_world @ X2 @ X0 ) )
=> ( exists_in_world @ X2 @ X1 ) ),
inference(rectify,[],[f36]) ).
thf(f92,plain,
! [X1: $i,X2: mu,X0: $i] :
( ( ( ( rel_s4 @ X0 @ X1 )
= $true )
& ( ( exists_in_world @ X2 @ X0 )
= $true ) )
=> ( ( exists_in_world @ X2 @ X1 )
= $true ) ),
inference(fool_elimination,[],[f91]) ).
thf(f102,plain,
( $true
!= ( mvalid
@ ( mimplies
@ ( mforall_ind
@ ^ [Y0: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [Y1: mu] : ( r @ Y0 @ Y1 ) ) ) )
@ ( mforall_ind
@ ^ [Y0: mu] :
( mforall_ind
@ ^ [Y1: mu] : ( mbox_s4 @ ( r @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(flattening,[],[f77]) ).
thf(f103,plain,
! [X1: $i,X2: mu,X0: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $true )
| ( ( rel_s4 @ X0 @ X1 )
!= $true )
| ( ( exists_in_world @ X2 @ X0 )
!= $true ) ),
inference(ennf_transformation,[],[f92]) ).
thf(f104,plain,
! [X2: mu,X0: $i,X1: $i] :
( ( ( rel_s4 @ X0 @ X1 )
!= $true )
| ( ( exists_in_world @ X2 @ X0 )
!= $true )
| ( ( exists_in_world @ X2 @ X1 )
= $true ) ),
inference(flattening,[],[f103]) ).
thf(f106,plain,
! [X0: mu,X1: $i,X2: $i] :
( ( ( rel_s4 @ X1 @ X2 )
!= $true )
| ( ( exists_in_world @ X0 @ X1 )
!= $true )
| ( ( exists_in_world @ X0 @ X2 )
= $true ) ),
inference(rectify,[],[f104]) ).
thf(f108,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f88]) ).
thf(f109,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f74]) ).
thf(f111,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f58]) ).
thf(f115,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f81]) ).
thf(f118,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f50]) ).
thf(f125,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f44]) ).
thf(f132,plain,
( $true
!= ( mvalid
@ ( mimplies
@ ( mforall_ind
@ ^ [Y0: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [Y1: mu] : ( r @ Y0 @ Y1 ) ) ) )
@ ( mforall_ind
@ ^ [Y0: mu] :
( mforall_ind
@ ^ [Y1: mu] : ( mbox_s4 @ ( r @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f102]) ).
thf(f133,plain,
! [X2: $i,X0: mu,X1: $i] :
( ( ( exists_in_world @ X0 @ X1 )
!= $true )
| ( ( rel_s4 @ X1 @ X2 )
!= $true )
| ( ( exists_in_world @ X0 @ X2 )
= $true ) ),
inference(cnf_transformation,[],[f106]) ).
thf(f148,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,[],[f125,f108,f115]) ).
thf(f157,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: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: mu] :
( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s4 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: mu > $i > $o,Y2: $i] :
( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) )
@ ^ [Y1: mu] : ( r @ Y0 @ Y1 ) ) ) )
@ ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: mu] :
( ^ [Y1: mu > $i > $o,Y2: $i] :
( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) )
@ ^ [Y1: mu] :
( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( rel_s4 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ ( r @ Y0 @ Y1 ) ) ) ) ) )
!= $true ),
inference(definition_unfolding,[],[f132,f118,f148,f109,f111,f109,f109,f109,f111]) ).
thf(f168,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y0 @ Y2 )
| ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( r @ Y1 @ Y3 @ Y2 ) ) ) ) ) ) )
| ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s4 @ Y0 @ Y3 )
| ( r @ Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f157]) ).
thf(f169,plain,
( ( ^ [Y0: $i] :
( ~ ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y0 @ Y2 )
| ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( r @ Y1 @ Y3 @ Y2 ) ) ) ) ) ) )
| ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s4 @ Y0 @ Y3 )
| ( r @ Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) )
@ sK1 )
= $false ),
inference(sigma_proxy_clausification,[],[f168]) ).
thf(f170,plain,
( $false
= ( ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ sK1 @ Y1 )
| ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( r @ Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
| ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK1 )
=> ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ sK1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ sK1 @ Y2 )
| ( r @ Y0 @ Y1 @ Y2 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f169]) ).
thf(f171,plain,
( ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK1 )
=> ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ sK1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ sK1 @ Y2 )
| ( r @ Y0 @ Y1 @ Y2 ) ) ) ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f170]) ).
thf(f172,plain,
( $false
= ( ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ sK1 @ Y1 )
| ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( r @ Y0 @ Y2 @ Y1 ) ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f170]) ).
thf(f173,plain,
( $true
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ sK1 @ Y1 )
| ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( r @ Y0 @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f172]) ).
thf(f174,plain,
! [X1: mu] :
( $true
= ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ sK1 @ Y1 )
| ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( r @ Y0 @ Y2 @ Y1 ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f173]) ).
thf(f175,plain,
! [X1: mu] :
( $true
= ( ( exists_in_world @ X1 @ sK1 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( r @ X1 @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f174]) ).
thf(f176,plain,
! [X1: mu] :
( ( ( exists_in_world @ X1 @ sK1 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( r @ X1 @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f175]) ).
thf(f177,plain,
! [X2: $i,X1: mu] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( r @ X1 @ Y1 @ Y0 ) ) ) )
@ X2 ) )
| ( ( exists_in_world @ X1 @ sK1 )
= $false ) ),
inference(pi_proxy_clausification,[],[f176]) ).
thf(f178,plain,
! [X2: $i,X1: mu] :
( ( ( exists_in_world @ X1 @ sK1 )
= $false )
| ( ( ~ ( rel_s4 @ sK1 @ X2 )
| ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ( r @ X1 @ Y0 @ X2 ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f177]) ).
thf(f179,plain,
! [X2: $i,X1: mu] :
( ( ( exists_in_world @ X1 @ sK1 )
= $false )
| ( $true
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ( r @ X1 @ Y0 @ X2 ) ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f178]) ).
thf(f180,plain,
! [X2: $i,X3: mu,X1: mu] :
( ( ( exists_in_world @ X1 @ sK1 )
= $false )
| ( $true
= ( ~ ( rel_s4 @ sK1 @ X2 ) ) )
| ( ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ( r @ X1 @ Y0 @ X2 ) )
@ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f179]) ).
thf(f181,plain,
! [X2: $i,X3: mu,X1: mu] :
( ( ( rel_s4 @ sK1 @ X2 )
= $false )
| ( ( exists_in_world @ X1 @ sK1 )
= $false )
| ( ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ( r @ X1 @ Y0 @ X2 ) )
@ X3 )
= $true ) ),
inference(not_proxy_clausification,[],[f180]) ).
thf(f182,plain,
! [X2: $i,X3: mu,X1: mu] :
( ( ( rel_s4 @ sK1 @ X2 )
= $false )
| ( ( ( exists_in_world @ X3 @ X2 )
=> ( r @ X1 @ X3 @ X2 ) )
= $true )
| ( ( exists_in_world @ X1 @ sK1 )
= $false ) ),
inference(beta-eta_normalization,[],[f181]) ).
thf(f183,plain,
! [X2: $i,X3: mu,X1: mu] :
( ( $true
= ( r @ X1 @ X3 @ X2 ) )
| ( ( exists_in_world @ X3 @ X2 )
= $false )
| ( ( exists_in_world @ X1 @ sK1 )
= $false )
| ( ( rel_s4 @ sK1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f182]) ).
thf(f184,plain,
( ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK1 )
=> ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ sK1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ sK1 @ Y2 )
| ( r @ Y0 @ Y1 @ Y2 ) ) ) ) ) )
@ sK2 )
= $false ),
inference(sigma_proxy_clausification,[],[f171]) ).
thf(f185,plain,
( ( ( exists_in_world @ sK2 @ sK1 )
=> ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ sK1 @ Y1 )
| ( r @ sK2 @ Y0 @ Y1 ) ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f184]) ).
thf(f186,plain,
( $false
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ sK1 @ Y1 )
| ( r @ sK2 @ Y0 @ Y1 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f185]) ).
thf(f187,plain,
( $true
= ( exists_in_world @ sK2 @ sK1 ) ),
inference(imp_proxy_clausification,[],[f185]) ).
thf(f188,plain,
( ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ sK1 @ Y1 )
| ( r @ sK2 @ Y0 @ Y1 ) ) ) )
@ sK3 )
= $false ),
inference(sigma_proxy_clausification,[],[f186]) ).
thf(f189,plain,
( $false
= ( ( exists_in_world @ sK3 @ sK1 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( r @ sK2 @ sK3 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f188]) ).
thf(f190,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( r @ sK2 @ sK3 @ Y0 ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f189]) ).
thf(f191,plain,
( $true
= ( exists_in_world @ sK3 @ sK1 ) ),
inference(imp_proxy_clausification,[],[f189]) ).
thf(f192,plain,
( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( r @ sK2 @ sK3 @ Y0 ) )
@ sK4 )
= $false ),
inference(sigma_proxy_clausification,[],[f190]) ).
thf(f193,plain,
( ( ~ ( rel_s4 @ sK1 @ sK4 )
| ( r @ sK2 @ sK3 @ sK4 ) )
= $false ),
inference(beta-eta_normalization,[],[f192]) ).
thf(f194,plain,
( ( r @ sK2 @ sK3 @ sK4 )
= $false ),
inference(or_proxy_clausification,[],[f193]) ).
thf(f195,plain,
( $false
= ( ~ ( rel_s4 @ sK1 @ sK4 ) ) ),
inference(or_proxy_clausification,[],[f193]) ).
thf(f196,plain,
( ( rel_s4 @ sK1 @ sK4 )
= $true ),
inference(not_proxy_clausification,[],[f195]) ).
thf(f201,plain,
( ( $false
= ( exists_in_world @ sK3 @ sK4 ) )
| ( ( rel_s4 @ sK1 @ sK4 )
= $false )
| ( $true = $false )
| ( $false
= ( exists_in_world @ sK2 @ sK1 ) ) ),
inference(constrained_superposition,[],[f183,f194]) ).
thf(f202,plain,
( ( $false
= ( exists_in_world @ sK2 @ sK1 ) )
| ( ( rel_s4 @ sK1 @ sK4 )
= $false )
| ( $false
= ( exists_in_world @ sK3 @ sK4 ) ) ),
inference(trivial_inequality_removal,[],[f201]) ).
thf(f204,plain,
( ( ( rel_s4 @ sK1 @ sK4 )
= $false )
| ( $false
= ( exists_in_world @ sK3 @ sK4 ) )
| ( $true = $false ) ),
inference(forward_demodulation,[],[f202,f187]) ).
thf(f205,plain,
( ( $false
= ( exists_in_world @ sK3 @ sK4 ) )
| ( ( rel_s4 @ sK1 @ sK4 )
= $false ) ),
inference(trivial_inequality_removal,[],[f204]) ).
thf(f208,plain,
( ( $true = $false )
| ( $false
= ( exists_in_world @ sK3 @ sK4 ) ) ),
inference(forward_demodulation,[],[f205,f196]) ).
thf(f209,plain,
( $false
= ( exists_in_world @ sK3 @ sK4 ) ),
inference(trivial_inequality_removal,[],[f208]) ).
thf(f213,plain,
! [X0: $i] :
( ( $true
!= ( rel_s4 @ sK1 @ X0 ) )
| ( ( exists_in_world @ sK3 @ X0 )
= $true )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f133,f191]) ).
thf(f216,plain,
! [X0: $i] :
( ( $true
!= ( rel_s4 @ sK1 @ X0 ) )
| ( ( exists_in_world @ sK3 @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[],[f213]) ).
thf(f225,plain,
( ( $true != $true )
| ( $true
= ( exists_in_world @ sK3 @ sK4 ) ) ),
inference(constrained_superposition,[],[f216,f196]) ).
thf(f228,plain,
( $true
= ( exists_in_world @ sK3 @ sK4 ) ),
inference(trivial_inequality_removal,[],[f225]) ).
thf(f229,plain,
$true = $false,
inference(forward_demodulation,[],[f228,f209]) ).
thf(f230,plain,
$false,
inference(trivial_inequality_removal,[],[f229]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO570^7 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.06 % 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 17:18:13 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
% 0.09/0.24 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
% 0.22/0.30 % (896924)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.30 % (896929)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2368130141:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.30 % (896929) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-896924-896929"...
% 0.22/0.30 % (896935)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.30 % (896935)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
% 0.22/0.30 % (896929)...printing done.
% 0.22/0.30 % (896929)Refutation found. Thanks to Tanya!
% 0.22/0.30 % SZS status Theorem for theBenchmark
% 0.22/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.30 % (896929)------------------------------
% 0.22/0.30 % (896929)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.30 % (896929)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.30 % (896929)CaDiCaL version: 2.1.3
% 0.22/0.30 % (896929)Termination reason: Refutation
% 0.22/0.30 % (896929)Time elapsed: 0.005 s
% 0.22/0.30 % (896929)Peak memory usage: 12 MB
% 0.22/0.30 % (896929)Instructions burned: 18 (million)
% 0.22/0.30 % (896924)Success in time 0.044 s
% 0.22/0.30 % Vampire exiting
%------------------------------------------------------------------------------