%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET002^7 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 08:23:09 AM UTC 2026
% Result : Theorem 0.22s 0.32s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 12
% Syntax : Number of formulae : 91 ( 49 unt; 0 typ; 4 def)
% Number of atoms : 472 ( 99 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 729 ( 47 ~; 66 |; 0 &; 544 @)
% ( 3 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 60 ( 60 >; 0 *; 0 +; 0 <<)
% Number of symbols : 65 ( 61 usr; 9 con; 0-4 aty)
% ( 35 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 174 ( 0 sgn 35 !; 0 ?; 174 :)
% 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,
subset: mu > mu > $i > $o ).
thf(func_def_37,type,
member: mu > mu > $i > $o ).
thf(func_def_38,type,
union: mu > mu > mu ).
thf(func_def_39,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_41,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_42,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_43,type,
vIMP: $o > $o > $o ).
thf(func_def_44,type,
vAND: $o > $o > $o ).
thf(func_def_45,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_46,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_47,type,
vOR: $o > $o > $o ).
thf(func_def_48,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_51,type,
vNOT: $o > $o ).
thf(func_def_52,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_53,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_54,type,
sK0: $i > mu ).
thf(func_def_55,type,
sF1: $o ).
thf(func_def_56,type,
sK2: mu > $i > mu > mu ).
thf(func_def_57,type,
sK3: mu > $i > mu > mu ).
thf(func_def_59,type,
sK5: mu ).
thf(f2,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/LCL015^0.ax',mor) ).
thf(f9,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) )
= mimplies ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mimplies) ).
thf(f15,axiom,
( ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] :
( ( exists_in_world @ X2 @ X1 )
=> ( X0 @ X2 @ X1 ) ) )
= mforall_ind ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mforall_ind) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mvalid) ).
thf(f47,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X0: mu] :
( mforall_ind
@ ^ [X1: mu] : ( mimplies @ ( subset @ X0 @ X1 ) @ ( qmltpeq @ ( union @ X0 @ X1 ) @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_union) ).
thf(f52,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X0: mu] : ( subset @ X0 @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_of_subset) ).
thf(f54,conjecture,
( mvalid
@ ( mforall_ind
@ ^ [X0: mu] : ( qmltpeq @ ( union @ X0 @ X0 ) @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_idempotency_of_union) ).
thf(f55,negated_conjecture,
~ ( mvalid
@ ( mforall_ind
@ ^ [X0: mu] : ( qmltpeq @ ( union @ X0 @ X0 ) @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f54]) ).
thf(f66,plain,
( ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] :
( ( exists_in_world @ X2 @ X1 )
=> ( X0 @ X2 @ X1 ) ) )
= mforall_ind ),
inference(rectify,[],[f15]) ).
thf(f67,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f66]) ).
thf(f96,plain,
( mvalid
@ ( mforall_ind
@ ^ [X0: mu] :
( mforall_ind
@ ^ [X1: mu] : ( mimplies @ ( subset @ X0 @ X1 ) @ ( qmltpeq @ ( union @ X0 @ X1 ) @ X1 ) ) ) ) ),
inference(rectify,[],[f47]) ).
thf(f97,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] :
( mforall_ind
@ ^ [Y1: mu] : ( mimplies @ ( subset @ Y0 @ Y1 ) @ ( qmltpeq @ ( union @ Y0 @ Y1 ) @ Y1 ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f96]) ).
thf(f104,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f105,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f104]) ).
thf(f106,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f112,plain,
( mvalid
@ ( mforall_ind
@ ^ [X0: mu] : ( subset @ X0 @ X0 ) ) ),
inference(rectify,[],[f52]) ).
thf(f113,plain,
( $true
= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] : ( subset @ Y0 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f112]) ).
thf(f128,plain,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f2]) ).
thf(f129,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f128]) ).
thf(f135,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f136,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f135]) ).
thf(f145,plain,
~ ( mvalid
@ ( mforall_ind
@ ^ [X0: mu] : ( qmltpeq @ ( union @ X0 @ X0 ) @ X0 ) ) ),
inference(rectify,[],[f55]) ).
thf(f146,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] : ( qmltpeq @ ( union @ Y0 @ Y0 ) @ Y0 ) ) )
!= $true ),
inference(fool_elimination,[],[f145]) ).
thf(f153,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] : ( qmltpeq @ ( union @ Y0 @ Y0 ) @ Y0 ) ) )
!= $true ),
inference(flattening,[],[f146]) ).
thf(f162,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f129]) ).
thf(f164,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f105]) ).
thf(f169,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f67]) ).
thf(f181,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f136]) ).
thf(f187,plain,
( $true
= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] : ( subset @ Y0 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f113]) ).
thf(f196,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] :
( mforall_ind
@ ^ [Y1: mu] : ( mimplies @ ( subset @ Y0 @ Y1 ) @ ( qmltpeq @ ( union @ Y0 @ Y1 ) @ Y1 ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f97]) ).
thf(f200,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f106]) ).
thf(f201,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] : ( qmltpeq @ ( union @ Y0 @ Y0 ) @ Y0 ) ) )
!= $true ),
inference(cnf_transformation,[],[f153]) ).
thf(f217,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,[],[f200,f164,f162]) ).
thf(f234,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: mu] : ( subset @ Y0 @ Y0 ) ) )
= $true ),
inference(definition_unfolding,[],[f187,f181,f169]) ).
thf(f239,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( 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 > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( subset @ Y0 @ Y1 )
@ ( qmltpeq @ ( union @ Y0 @ Y1 ) @ Y1 ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f196,f181,f169,f169,f217]) ).
thf(f240,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: mu] : ( qmltpeq @ ( union @ Y0 @ Y0 ) @ Y0 ) ) )
!= $true ),
inference(definition_unfolding,[],[f201,f181,f169]) ).
thf(f244,definition,
( sF1
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: mu] : ( qmltpeq @ ( union @ Y0 @ Y0 ) @ Y0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
thf(f245,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: mu] : ( qmltpeq @ ( union @ Y0 @ Y0 ) @ Y0 ) ) )
= sF1 ),
inference(reorient_equations,[],[f244]) ).
thf(f246,plain,
sF1 != $true,
inference(definition_folding,[],[f240,f245]) ).
thf(f274,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y0 )
=> ( ~ ( subset @ Y1 @ Y2 @ Y0 )
| ( qmltpeq @ ( union @ Y1 @ Y2 ) @ Y2 @ Y0 ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f239]) ).
thf(f275,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y0 )
=> ( ~ ( subset @ Y1 @ Y2 @ Y0 )
| ( qmltpeq @ ( union @ Y1 @ Y2 ) @ Y2 @ Y0 ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f274]) ).
thf(f276,plain,
! [X1: $i] :
( ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X1 )
=> ( ~ ( subset @ Y0 @ Y1 @ X1 )
| ( qmltpeq @ ( union @ Y0 @ Y1 ) @ Y1 @ X1 ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f275]) ).
thf(f277,plain,
! [X2: mu,X1: $i] :
( ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X1 )
=> ( ~ ( subset @ Y0 @ Y1 @ X1 )
| ( qmltpeq @ ( union @ Y0 @ Y1 ) @ Y1 @ X1 ) ) ) ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f276]) ).
thf(f278,plain,
! [X2: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
=> ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( ~ ( subset @ X2 @ Y0 @ X1 )
| ( qmltpeq @ ( union @ X2 @ Y0 ) @ Y0 @ X1 ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f277]) ).
thf(f279,plain,
! [X2: mu,X1: $i] :
( ( ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( ~ ( subset @ X2 @ Y0 @ X1 )
| ( qmltpeq @ ( union @ X2 @ Y0 ) @ Y0 @ X1 ) ) ) )
= $true )
| ( ( exists_in_world @ X2 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f278]) ).
thf(f280,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( $true
= ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( ~ ( subset @ X2 @ Y0 @ X1 )
| ( qmltpeq @ ( union @ X2 @ Y0 ) @ Y0 @ X1 ) ) )
@ X3 ) )
| ( ( exists_in_world @ X2 @ X1 )
= $false ) ),
inference(pi_proxy_clausification,[],[f279]) ).
thf(f281,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( ( exists_in_world @ X3 @ X1 )
=> ( ~ ( subset @ X2 @ X3 @ X1 )
| ( qmltpeq @ ( union @ X2 @ X3 ) @ X3 @ X1 ) ) )
= $true )
| ( ( exists_in_world @ X2 @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f280]) ).
thf(f282,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( ( ~ ( subset @ X2 @ X3 @ X1 )
| ( qmltpeq @ ( union @ X2 @ X3 ) @ X3 @ X1 ) )
= $true )
| ( ( exists_in_world @ X3 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f281]) ).
thf(f283,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( ( qmltpeq @ ( union @ X2 @ X3 ) @ X3 @ X1 )
= $true )
| ( ( ~ ( subset @ X2 @ X3 @ X1 ) )
= $true )
| ( ( exists_in_world @ X3 @ X1 )
= $false ) ),
inference(or_proxy_clausification,[],[f282]) ).
thf(f284,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( qmltpeq @ ( union @ X2 @ X3 ) @ X3 @ X1 )
= $true )
| ( ( subset @ X2 @ X3 @ X1 )
= $false )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( ( exists_in_world @ X3 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f283]) ).
thf(f424,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( subset @ Y1 @ Y1 @ Y0 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f234]) ).
thf(f425,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( subset @ Y1 @ Y1 @ Y0 ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f424]) ).
thf(f426,plain,
! [X1: $i] :
( ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( subset @ Y0 @ Y0 @ X1 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f425]) ).
thf(f427,plain,
! [X2: mu,X1: $i] :
( ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( subset @ Y0 @ Y0 @ X1 ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f426]) ).
thf(f428,plain,
! [X2: mu,X1: $i] :
( $true
= ( ( exists_in_world @ X2 @ X1 )
=> ( subset @ X2 @ X2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f427]) ).
thf(f429,plain,
! [X2: mu,X1: $i] :
( ( ( subset @ X2 @ X2 @ X1 )
= $true )
| ( ( exists_in_world @ X2 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f428]) ).
thf(f550,plain,
( ( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: mu] : ( qmltpeq @ ( union @ Y0 @ Y0 ) @ Y0 ) ) )
= $false )
| ( sF1 = $true ) ),
inference(iff_proxy_clausification,[],[f245]) ).
thf(f551,plain,
( ( sF1 = $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( qmltpeq @ ( union @ Y1 @ Y1 ) @ Y1 @ Y0 ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f550]) ).
thf(f552,plain,
( ( ( ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( qmltpeq @ ( union @ Y1 @ Y1 ) @ Y1 @ Y0 ) ) )
@ sK4 )
= $false )
| ( sF1 = $true ) ),
inference(sigma_proxy_clausification,[],[f551]) ).
thf(f553,plain,
( ( ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK4 )
=> ( qmltpeq @ ( union @ Y0 @ Y0 ) @ Y0 @ sK4 ) ) )
= $false )
| ( sF1 = $true ) ),
inference(beta-eta_normalization,[],[f552]) ).
thf(f554,plain,
( ( sF1 = $true )
| ( ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK4 )
=> ( qmltpeq @ ( union @ Y0 @ Y0 ) @ Y0 @ sK4 ) )
@ sK5 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f553]) ).
thf(f555,plain,
( ( sF1 = $true )
| ( ( ( exists_in_world @ sK5 @ sK4 )
=> ( qmltpeq @ ( union @ sK5 @ sK5 ) @ sK5 @ sK4 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f554]) ).
thf(f556,plain,
( ( ( qmltpeq @ ( union @ sK5 @ sK5 ) @ sK5 @ sK4 )
= $false )
| ( sF1 = $true ) ),
inference(imp_proxy_clausification,[],[f555]) ).
thf(f557,plain,
( ( sF1 = $true )
| ( $true
= ( exists_in_world @ sK5 @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f555]) ).
thf(f565,definition,
( spl6_1
<=> ( $true
= ( exists_in_world @ sK5 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
thf(f567,plain,
( ( $true
= ( exists_in_world @ sK5 @ sK4 ) )
| ~ spl6_1 ),
inference(avatar_component_clause,[],[f565]) ).
thf(f569,definition,
( spl6_2
<=> ( sF1 = $true ) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
thf(f572,plain,
( spl6_1
| spl6_2 ),
inference(avatar_split_clause,[],[f557,f569,f565]) ).
thf(f574,definition,
( spl6_3
<=> ( ( qmltpeq @ ( union @ sK5 @ sK5 ) @ sK5 @ sK4 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition]) ).
thf(f576,plain,
( ( ( qmltpeq @ ( union @ sK5 @ sK5 ) @ sK5 @ sK4 )
= $false )
| ~ spl6_3 ),
inference(avatar_component_clause,[],[f574]) ).
thf(f577,plain,
( spl6_2
| spl6_3 ),
inference(avatar_split_clause,[],[f556,f574,f569]) ).
thf(f586,plain,
~ spl6_2,
inference(avatar_split_clause,[],[f246,f569]) ).
thf(f641,plain,
( ( ( exists_in_world @ sK5 @ sK4 )
= $false )
| ( ( exists_in_world @ sK5 @ sK4 )
= $false )
| ( ( subset @ sK5 @ sK5 @ sK4 )
= $false )
| ( $true = $false )
| ~ spl6_3 ),
inference(constrained_superposition,[],[f284,f576]) ).
thf(f643,plain,
( ( ( exists_in_world @ sK5 @ sK4 )
= $false )
| ( ( subset @ sK5 @ sK5 @ sK4 )
= $false )
| ( $true = $false )
| ~ spl6_3 ),
inference(duplicate_literal_removal,[],[f641]) ).
thf(f644,plain,
( ( ( subset @ sK5 @ sK5 @ sK4 )
= $false )
| ( ( exists_in_world @ sK5 @ sK4 )
= $false )
| ~ spl6_3 ),
inference(trivial_inequality_removal,[],[f643]) ).
thf(f647,plain,
( ( $true = $false )
| ( ( subset @ sK5 @ sK5 @ sK4 )
= $false )
| ~ spl6_1
| ~ spl6_3 ),
inference(forward_demodulation,[],[f644,f567]) ).
thf(f648,plain,
( ( ( subset @ sK5 @ sK5 @ sK4 )
= $false )
| ~ spl6_1
| ~ spl6_3 ),
inference(trivial_inequality_removal,[],[f647]) ).
thf(f651,plain,
( ( ( exists_in_world @ sK5 @ sK4 )
= $false )
| ( $true = $false )
| ~ spl6_1
| ~ spl6_3 ),
inference(constrained_superposition,[],[f648,f429]) ).
thf(f656,plain,
( ( ( exists_in_world @ sK5 @ sK4 )
= $false )
| ~ spl6_1
| ~ spl6_3 ),
inference(trivial_inequality_removal,[],[f651]) ).
thf(f660,plain,
( ( $true = $false )
| ~ spl6_1
| ~ spl6_3 ),
inference(forward_demodulation,[],[f656,f567]) ).
thf(f661,plain,
( $false
| ~ spl6_1
| ~ spl6_3 ),
inference(trivial_inequality_removal,[],[f660]) ).
thf(f662,plain,
( ~ spl6_1
| ~ spl6_3 ),
inference(avatar_contradiction_clause,[],[f661]) ).
cnf(s1,plain,
( spl6_1
| spl6_2 ),
inference(sat_conversion,[],[f572]) ).
cnf(s2,plain,
( spl6_2
| spl6_3 ),
inference(sat_conversion,[],[f577]) ).
cnf(s4,plain,
~ spl6_2,
inference(sat_conversion,[],[f586]) ).
cnf(s9,plain,
( ~ spl6_1
| ~ spl6_3 ),
inference(sat_conversion,[],[f662]) ).
cnf(s11,plain,
spl6_3,
inference(rat,[],[s2,s4]) ).
cnf(s12,plain,
~ spl6_1,
inference(rat,[],[s9,s11]) ).
cnf(s13,plain,
$false,
inference(rat,[],[s1,s4,s12]) ).
thf(f663,plain,
$false,
inference(avatar_sat_refutation,[],[s13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET002^7 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n002.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 13:38:23 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.25 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
% 0.22/0.32 % (1285300)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.32 % (1285307)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2897361007:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.32 % (1285314)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.32 % (1285314)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
% 0.22/0.32 % (1285308)lrs+10_16_si=on:nwc=1.5:random_seed=648869074:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.32 % (1285312)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3787509931:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.32 % (1285310)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2169910491:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.32 % (1285313)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1693837107:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.32 % (1285311)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=146349685: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)
% 0.22/0.32 % (1285314)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=2312484979:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.32 % (1285310)Instruction limit reached!
% 0.22/0.32 % (1285310)------------------------------
% 0.22/0.32 % (1285310)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.32 % (1285310)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.32 % (1285310)CaDiCaL version: 2.1.3
% 0.22/0.32 % (1285310)Termination reason: Instruction limit
% 0.22/0.32 % (1285310)Termination phase: shuffling
% 0.22/0.32 % (1285310)Time elapsed: 0.002 s
% 0.22/0.32 % (1285310)Peak memory usage: 9 MB
% 0.22/0.32 % (1285310)Instructions burned: 4 (million)
% 0.22/0.32 % (1285308)Instruction limit reached!
% 0.22/0.32 % (1285308)------------------------------
% 0.22/0.32 % (1285308)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.32 % (1285308)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.32 % (1285308)CaDiCaL version: 2.1.3
% 0.22/0.32 % (1285308)Termination reason: Instruction limit
% 0.22/0.32 % (1285308)Termination phase: Property scanning
% 0.22/0.32 % (1285308)Time elapsed: 0.008 s
% 0.22/0.32 % (1285308)Peak memory usage: 10 MB
% 0.22/0.32 % (1285308)Instructions burned: 20 (million)
% 0.22/0.32 % (1285312)Instruction limit reached!
% 0.22/0.32 % (1285312)------------------------------
% 0.22/0.32 % (1285312)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.32 % (1285312)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.32 % (1285312)CaDiCaL version: 2.1.3
% 0.22/0.32 % (1285312)Termination reason: Instruction limit
% 0.22/0.32 % (1285312)Termination phase: Saturation
% 0.22/0.32 % (1285312)Time elapsed: 0.013 s
% 0.22/0.32 % (1285312)Peak memory usage: 12 MB
% 0.22/0.32 % (1285312)Instructions burned: 24 (million)
% 0.22/0.32 % (1285307)Instruction limit reached!
% 0.22/0.32 % (1285307)------------------------------
% 0.22/0.32 % (1285307)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.32 % (1285307)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.32 % (1285307)CaDiCaL version: 2.1.3
% 0.22/0.32 % (1285307)Termination reason: Instruction limit
% 0.22/0.32 % (1285307)Termination phase: Saturation
% 0.22/0.32 % (1285307)Time elapsed: 0.022 s
% 0.22/0.32 % (1285307)Peak memory usage: 12 MB
% 0.22/0.32 % (1285307)Instructions burned: 92 (million)
% 0.22/0.32 % (1285327)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=276689413:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.22/0.32 % (1285327)Instruction limit reached!
% 0.22/0.32 % (1285327)------------------------------
% 0.22/0.32 % (1285327)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.32 % (1285327)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.32 % (1285327)CaDiCaL version: 2.1.3
% 0.22/0.32 % (1285327)Termination reason: Instruction limit
% 0.22/0.32 % (1285327)Termination phase: shuffling
% 0.22/0.32 % (1285327)Time elapsed: 0.002 s
% 0.22/0.32 % (1285327)Peak memory usage: 9 MB
% 0.22/0.32 % (1285327)Instructions burned: 4 (million)
% 0.22/0.32 % (1285328)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=4065689943:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.22/0.32 % (1285314) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1285300-1285314"...
% 0.22/0.32 % (1285329)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.22/0.32 % (1285328)Instruction limit reached!
% 0.22/0.32 % (1285328)------------------------------
% 0.22/0.32 % (1285328)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.32 % (1285328)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.32 % (1285328)CaDiCaL version: 2.1.3
% 0.22/0.32 % (1285328)Termination reason: Instruction limit
% 0.22/0.32 % (1285328)Termination phase: Property scanning
% 0.22/0.32 % (1285328)Time elapsed: 0.003 s
% 0.22/0.32 % (1285328)Peak memory usage: 10 MB
% 0.22/0.32 % (1285328)Instructions burned: 7 (million)
% 0.22/0.32 % (1285313) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1285300-1285313"...
% 0.22/0.32 % (1285329)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=543938565:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.22/0.32 % (1285314)...printing done.
% 0.22/0.32 % (1285330)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1145237056:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.22/0.32 % (1285314)Refutation found. Thanks to Tanya!
% 0.22/0.32 % SZS status Theorem for theBenchmark
% 0.22/0.32 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.32 % (1285314)------------------------------
% 0.22/0.32 % (1285314)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.32 % (1285314)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.32 % (1285314)CaDiCaL version: 2.1.3
% 0.22/0.32 % (1285314)Termination reason: Refutation
% 0.22/0.32 % (1285314)Time elapsed: 0.030 s
% 0.22/0.32 % (1285314)Peak memory usage: 13 MB
% 0.22/0.32 % (1285314)Instructions burned: 64 (million)
% 0.22/0.32 % (1285300)Success in time 0.057 s
% 0.22/0.32 % Vampire exiting
%------------------------------------------------------------------------------