%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n017.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 08:23:31 AM UTC 2026
% Result : Theorem 0.48s 0.40s
% Output : Refutation 0.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 8
% Syntax : Number of formulae : 70 ( 51 unt; 0 typ; 0 def)
% Number of atoms : 370 ( 82 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 603 ( 23 ~; 35 |; 0 &; 485 @)
% ( 0 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 51 ( 51 >; 0 *; 0 +; 0 <<)
% Number of symbols : 61 ( 57 usr; 5 con; 0-4 aty)
% ( 29 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 156 ( 121 ^; 35 !; 0 ?; 156 :)
% 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,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_41,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_42,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_43,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_44,type,
vNOT: $o > $o ).
thf(func_def_45,type,
vOR: $o > $o > $o ).
thf(func_def_46,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_47,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_50,type,
vIMP: $o > $o > $o ).
thf(func_def_51,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_52,type,
vAND: $o > $o > $o ).
thf(func_def_53,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_54,type,
sK0: $i > mu ).
thf(func_def_56,type,
sK2: mu ).
thf(func_def_57,type,
sK3: mu > $i > mu > mu ).
thf(func_def_58,type,
sK4: mu > $i > mu > mu ).
thf(f2,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
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,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox2/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/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(f57,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f2]) ).
thf(f58,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f57]) ).
thf(f59,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f60,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f59]) ).
thf(f67,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f74,plain,
( mforall_ind
= ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] :
( ( exists_in_world @ X2 @ X1 )
=> ( X0 @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f15]) ).
thf(f75,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f74]) ).
thf(f100,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f101,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f100]) ).
thf(f137,plain,
( mvalid
@ ( mforall_ind
@ ^ [X0: mu] :
( mforall_ind
@ ^ [X1: mu] : ( mimplies @ ( subset @ X0 @ X1 ) @ ( qmltpeq @ ( union @ X0 @ X1 ) @ X1 ) ) ) ) ),
inference(rectify,[],[f47]) ).
thf(f138,plain,
( $true
= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] :
( mforall_ind
@ ^ [Y1: mu] : ( mimplies @ ( subset @ Y0 @ Y1 ) @ ( qmltpeq @ ( union @ Y0 @ Y1 ) @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f137]) ).
thf(f147,plain,
( mvalid
@ ( mforall_ind
@ ^ [X0: mu] : ( subset @ X0 @ X0 ) ) ),
inference(rectify,[],[f52]) ).
thf(f148,plain,
( $true
= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] : ( subset @ Y0 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f147]) ).
thf(f151,plain,
~ ( mvalid
@ ( mforall_ind
@ ^ [X0: mu] : ( qmltpeq @ ( union @ X0 @ X0 ) @ X0 ) ) ),
inference(rectify,[],[f55]) ).
thf(f152,plain,
( $true
!= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] : ( qmltpeq @ ( union @ Y0 @ Y0 ) @ Y0 ) ) ) ),
inference(fool_elimination,[],[f151]) ).
thf(f153,plain,
( $true
!= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] : ( qmltpeq @ ( union @ Y0 @ Y0 ) @ Y0 ) ) ) ),
inference(flattening,[],[f152]) ).
thf(f158,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f58]) ).
thf(f159,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f60]) ).
thf(f165,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f67]) ).
thf(f171,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f75]) ).
thf(f184,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f101]) ).
thf(f203,plain,
( $true
= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] :
( mforall_ind
@ ^ [Y1: mu] : ( mimplies @ ( subset @ Y0 @ Y1 ) @ ( qmltpeq @ ( union @ Y0 @ Y1 ) @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f138]) ).
thf(f208,plain,
( $true
= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] : ( subset @ Y0 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f148]) ).
thf(f210,plain,
( $true
!= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] : ( qmltpeq @ ( union @ Y0 @ Y0 ) @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f153]) ).
thf(f215,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,[],[f165,f159,f158]) ).
thf(f234,plain,
( $true
= ( ^ [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 ) ) ) ) ) ),
inference(definition_unfolding,[],[f203,f184,f171,f171,f215]) ).
thf(f239,plain,
( $true
= ( ^ [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 ) ) ) ),
inference(definition_unfolding,[],[f208,f184,f171]) ).
thf(f241,plain,
( $true
!= ( ^ [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 ) ) ) ),
inference(definition_unfolding,[],[f210,f184,f171]) ).
thf(f242,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( qmltpeq @ ( union @ Y1 @ Y1 ) @ Y1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f241]) ).
thf(f243,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( qmltpeq @ ( union @ Y1 @ Y1 ) @ Y1 @ Y0 ) ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f242]) ).
thf(f244,plain,
( $false
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK1 )
=> ( qmltpeq @ ( union @ Y0 @ Y0 ) @ Y0 @ sK1 ) ) ) ),
inference(beta-eta_normalization,[],[f243]) ).
thf(f245,plain,
( $false
= ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK1 )
=> ( qmltpeq @ ( union @ Y0 @ Y0 ) @ Y0 @ sK1 ) )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f244]) ).
thf(f246,plain,
( $false
= ( ( exists_in_world @ sK2 @ sK1 )
=> ( qmltpeq @ ( union @ sK2 @ sK2 ) @ sK2 @ sK1 ) ) ),
inference(beta-eta_normalization,[],[f245]) ).
thf(f247,plain,
( $false
= ( qmltpeq @ ( union @ sK2 @ sK2 ) @ sK2 @ sK1 ) ),
inference(imp_proxy_clausification,[],[f246]) ).
thf(f248,plain,
( $true
= ( exists_in_world @ sK2 @ sK1 ) ),
inference(imp_proxy_clausification,[],[f246]) ).
thf(f297,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( subset @ Y1 @ Y1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f239]) ).
thf(f298,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( subset @ Y1 @ Y1 @ Y0 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f297]) ).
thf(f299,plain,
! [X1: $i] :
( $true
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( subset @ Y0 @ Y0 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f298]) ).
thf(f300,plain,
! [X2: mu,X1: $i] :
( $true
= ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( subset @ Y0 @ Y0 @ X1 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f299]) ).
thf(f301,plain,
! [X2: mu,X1: $i] :
( $true
= ( ( exists_in_world @ X2 @ X1 )
=> ( subset @ X2 @ X2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f300]) ).
thf(f302,plain,
! [X2: mu,X1: $i] :
( ( $true
= ( subset @ X2 @ X2 @ X1 ) )
| ( ( exists_in_world @ X2 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f301]) ).
thf(f394,plain,
( $true
= ( !! @ $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 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f234]) ).
thf(f395,plain,
! [X1: $i] :
( $true
= ( ^ [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 ) ),
inference(pi_proxy_clausification,[],[f394]) ).
thf(f396,plain,
! [X1: $i] :
( $true
= ( !! @ 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 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f395]) ).
thf(f397,plain,
! [X2: mu,X1: $i] :
( $true
= ( ^ [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 ) ),
inference(pi_proxy_clausification,[],[f396]) ).
thf(f398,plain,
! [X2: mu,X1: $i] :
( $true
= ( ( exists_in_world @ X2 @ X1 )
=> ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( ~ ( subset @ X2 @ Y0 @ X1 )
| ( qmltpeq @ ( union @ X2 @ Y0 ) @ Y0 @ X1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f397]) ).
thf(f399,plain,
! [X2: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $true
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( ~ ( subset @ X2 @ Y0 @ X1 )
| ( qmltpeq @ ( union @ X2 @ Y0 ) @ Y0 @ X1 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f398]) ).
thf(f400,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $true
= ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( ~ ( subset @ X2 @ Y0 @ X1 )
| ( qmltpeq @ ( union @ X2 @ Y0 ) @ Y0 @ X1 ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f399]) ).
thf(f401,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $true
= ( ( exists_in_world @ X3 @ X1 )
=> ( ~ ( subset @ X2 @ X3 @ X1 )
| ( qmltpeq @ ( union @ X2 @ X3 ) @ X3 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f400]) ).
thf(f402,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ X1 ) )
| ( $true
= ( ~ ( subset @ X2 @ X3 @ X1 )
| ( qmltpeq @ ( union @ X2 @ X3 ) @ X3 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f401]) ).
thf(f403,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( union @ X2 @ X3 ) @ X3 @ X1 ) )
| ( $true
= ( ~ ( subset @ X2 @ X3 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f402]) ).
thf(f404,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( $true
= ( qmltpeq @ ( union @ X2 @ X3 ) @ X3 @ X1 ) )
| ( $false
= ( exists_in_world @ X3 @ X1 ) )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( subset @ X2 @ X3 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f403]) ).
thf(f982,plain,
( ( $true = $false )
| ( $false
= ( exists_in_world @ sK2 @ sK1 ) )
| ( $false
= ( exists_in_world @ sK2 @ sK1 ) )
| ( $false
= ( subset @ sK2 @ sK2 @ sK1 ) ) ),
inference(constrained_superposition,[],[f247,f404]) ).
thf(f983,plain,
( ( $true = $false )
| ( $false
= ( exists_in_world @ sK2 @ sK1 ) )
| ( $false
= ( subset @ sK2 @ sK2 @ sK1 ) ) ),
inference(duplicate_literal_removal,[],[f982]) ).
thf(f984,plain,
( ( $false
= ( exists_in_world @ sK2 @ sK1 ) )
| ( $false
= ( subset @ sK2 @ sK2 @ sK1 ) ) ),
inference(trivial_inequality_removal,[],[f983]) ).
thf(f995,plain,
( ( $true = $false )
| ( $false
= ( subset @ sK2 @ sK2 @ sK1 ) ) ),
inference(forward_demodulation,[],[f984,f248]) ).
thf(f996,plain,
( $false
= ( subset @ sK2 @ sK2 @ sK1 ) ),
inference(trivial_inequality_removal,[],[f995]) ).
thf(f1011,plain,
( ( $true = $false )
| ( $false
= ( exists_in_world @ sK2 @ sK1 ) ) ),
inference(constrained_superposition,[],[f302,f996]) ).
thf(f1018,plain,
( $false
= ( exists_in_world @ sK2 @ sK1 ) ),
inference(trivial_inequality_removal,[],[f1011]) ).
thf(f1065,plain,
$true = $false,
inference(constrained_superposition,[],[f248,f1018]) ).
thf(f1066,plain,
$false,
inference(trivial_inequality_removal,[],[f1065]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET002^7 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.23/0.27 % Computer : n017.cluster.edu
% 0.23/0.27 % Model : x86_64 x86_64
% 0.23/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.27 % Memory : 8046.5625MB
% 0.23/0.27 % OS : Linux 6.8.0-71-generic
% 0.23/0.27 % CPULimit : 300
% 0.23/0.27 % WCLimit : 300
% 0.23/0.27 % DateTime : Tue Sep 29 13:31:07 UTC 2026
% 0.23/0.28 % CPUTime :
% 0.23/0.28 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.23/0.32 Running first-order model finding
% 0.23/0.32 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.48/0.40 % (334351)Will run a generic schedule for satisfiability detection.
% 0.48/0.40 % (334358)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3670943847:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.48/0.40 % (334357)% WARNING: option uhcvi not known.
% 0.48/0.40 % (334359)dis+10_1_sil=32000:sp=arity:random_seed=4038534884:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.48/0.40 % (334357)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=697086181:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.48/0.40 % (334356)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3084498718_2999 on theBenchmark for (2999ds/0Mi)
% 0.48/0.40 % (334361)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=522034949:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.48/0.40 % (334362)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1335405082:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.48/0.40 % (334360)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2548458762:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.48/0.40 % (334357)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.48/0.40 % (334360)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.48/0.40 % (334357)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.48/0.40 % Exception at run slice level
% 0.48/0.40 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.48/0.40 % (334358) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-334351-334358"...
% 0.48/0.40 % (334358)...printing done.
% 0.48/0.40 % (334358)Refutation found. Thanks to Tanya!
% 0.48/0.40 % SZS status Theorem for theBenchmark
% 0.48/0.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.48/0.40 % (334358)------------------------------
% 0.48/0.40 % (334358)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.40 % (334358)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.40 % (334358)CaDiCaL version: 2.1.3
% 0.48/0.40 % (334358)Termination reason: Refutation
% 0.48/0.40 % (334358)Time elapsed: 0.043 s
% 0.48/0.40 % (334358)Peak memory usage: 13 MB
% 0.48/0.40 % (334358)Instructions burned: 93 (million)
% 0.48/0.40 % (334351)Success in time 0.071 s
% 0.48/0.40 % Vampire exiting
%------------------------------------------------------------------------------