%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET907^7 : 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 : n005.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 08:23:49 AM UTC 2026
% Result : Theorem 4.12s 0.98s
% Output : Refutation 4.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 11
% Syntax : Number of formulae : 122 ( 79 unt; 0 typ; 0 def)
% Number of atoms : 1078 ( 205 equ; 0 cnn)
% Maximal formula atoms : 9 ( 8 avg)
% Number of connectives : 2252 ( 265 ~; 217 |; 0 &;1634 @)
% ( 0 <=>; 73 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 3 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 135 ( 135 >; 0 *; 0 +; 0 <<)
% Number of symbols : 65 ( 61 usr; 7 con; 0-4 aty)
% ( 63 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 401 ( 297 ^; 104 !; 0 ?; 401 :)
% 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,
empty: mu > $i > $o ).
thf(func_def_37,type,
subset: mu > mu > $i > $o ).
thf(func_def_38,type,
in: mu > mu > $i > $o ).
thf(func_def_39,type,
unordered_pair: mu > mu > mu ).
thf(func_def_40,type,
set_union2: mu > mu > mu ).
thf(func_def_41,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_42,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_43,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_44,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_45,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_46,type,
vNOT: $o > $o ).
thf(func_def_47,type,
vOR: $o > $o > $o ).
thf(func_def_48,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_49,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_52,type,
vIMP: $o > $o > $o ).
thf(func_def_53,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_54,type,
vAND: $o > $o > $o ).
thf(func_def_55,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_56,type,
sK0: $i > mu ).
thf(func_def_58,type,
sK2: mu ).
thf(func_def_59,type,
sK3: mu ).
thf(func_def_60,type,
sK4: mu ).
thf(func_def_61,type,
sK5: $i > mu ).
thf(func_def_62,type,
sK6: $i > 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(f8,axiom,
( mand
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mnot @ ( mor @ ( mnot @ X0 ) @ ( mnot @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mand) ).
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(f11,axiom,
( mequiv
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mand @ ( mimplies @ X0 @ X1 ) @ ( mimplies @ X1 @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mequiv) ).
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(f37,axiom,
! [X0: $i,X1: mu,X2: mu] : ( exists_in_world @ ( unordered_pair @ X1 @ X2 ) @ X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_unordered_pair_ax) ).
thf(f60,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X0: mu] :
( mforall_ind
@ ^ [X1: mu] : ( mimplies @ ( subset @ X0 @ X1 ) @ ( qmltpeq @ ( set_union2 @ X0 @ X1 ) @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_xboole_1) ).
thf(f61,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X0: mu] :
( mforall_ind
@ ^ [X1: mu] :
( mforall_ind
@ ^ [X2: mu] : ( mequiv @ ( subset @ ( unordered_pair @ X0 @ X1 ) @ X2 ) @ ( mand @ ( in @ X0 @ X2 ) @ ( in @ X1 @ X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_zfmisc_1) ).
thf(f62,conjecture,
( mvalid
@ ( mforall_ind
@ ^ [X0: mu] :
( mforall_ind
@ ^ [X1: mu] :
( mforall_ind
@ ^ [X2: mu] : ( mimplies @ ( mand @ ( in @ X0 @ X1 ) @ ( in @ X2 @ X1 ) ) @ ( qmltpeq @ ( set_union2 @ ( unordered_pair @ X0 @ X2 ) @ X1 ) @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_zfmisc_1) ).
thf(f63,negated_conjecture,
~ ( mvalid
@ ( mforall_ind
@ ^ [X0: mu] :
( mforall_ind
@ ^ [X1: mu] :
( mforall_ind
@ ^ [X2: mu] : ( mimplies @ ( mand @ ( in @ X0 @ X1 ) @ ( in @ X2 @ X1 ) ) @ ( qmltpeq @ ( set_union2 @ ( unordered_pair @ X0 @ X2 ) @ X1 ) @ X1 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f62]) ).
thf(f65,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f2]) ).
thf(f66,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f65]) ).
thf(f67,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f68,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f67]) ).
thf(f74,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f75,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f77,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f82,plain,
( mforall_ind
= ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] :
( ( exists_in_world @ X2 @ X1 )
=> ( X0 @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f15]) ).
thf(f83,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f82]) ).
thf(f108,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f109,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f108]) ).
thf(f125,plain,
! [X0: $i,X1: mu,X2: mu] : ( exists_in_world @ ( unordered_pair @ X1 @ X2 ) @ X0 ),
inference(rectify,[],[f37]) ).
thf(f126,plain,
! [X0: $i,X1: mu,X2: mu] :
( ( exists_in_world @ ( unordered_pair @ X1 @ X2 ) @ X0 )
= $true ),
inference(fool_elimination,[],[f125]) ).
thf(f171,plain,
( mvalid
@ ( mforall_ind
@ ^ [X0: mu] :
( mforall_ind
@ ^ [X1: mu] : ( mimplies @ ( subset @ X0 @ X1 ) @ ( qmltpeq @ ( set_union2 @ X0 @ X1 ) @ X1 ) ) ) ) ),
inference(rectify,[],[f60]) ).
thf(f172,plain,
( $true
= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] :
( mforall_ind
@ ^ [Y1: mu] : ( mimplies @ ( subset @ Y0 @ Y1 ) @ ( qmltpeq @ ( set_union2 @ Y0 @ Y1 ) @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f171]) ).
thf(f173,plain,
( mvalid
@ ( mforall_ind
@ ^ [X0: mu] :
( mforall_ind
@ ^ [X1: mu] :
( mforall_ind
@ ^ [X2: mu] : ( mequiv @ ( subset @ ( unordered_pair @ X0 @ X1 ) @ X2 ) @ ( mand @ ( in @ X0 @ X2 ) @ ( in @ X1 @ X2 ) ) ) ) ) ) ),
inference(rectify,[],[f61]) ).
thf(f174,plain,
( $true
= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] :
( mforall_ind
@ ^ [Y1: mu] :
( mforall_ind
@ ^ [Y2: mu] : ( mequiv @ ( subset @ ( unordered_pair @ Y0 @ Y1 ) @ Y2 ) @ ( mand @ ( in @ Y0 @ Y2 ) @ ( in @ Y1 @ Y2 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f173]) ).
thf(f175,plain,
~ ( mvalid
@ ( mforall_ind
@ ^ [X0: mu] :
( mforall_ind
@ ^ [X1: mu] :
( mforall_ind
@ ^ [X2: mu] : ( mimplies @ ( mand @ ( in @ X0 @ X1 ) @ ( in @ X2 @ X1 ) ) @ ( qmltpeq @ ( set_union2 @ ( unordered_pair @ X0 @ X2 ) @ X1 ) @ X1 ) ) ) ) ) ),
inference(rectify,[],[f63]) ).
thf(f176,plain,
( $true
!= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] :
( mforall_ind
@ ^ [Y1: mu] :
( mforall_ind
@ ^ [Y2: mu] : ( mimplies @ ( mand @ ( in @ Y0 @ Y1 ) @ ( in @ Y2 @ Y1 ) ) @ ( qmltpeq @ ( set_union2 @ ( unordered_pair @ Y0 @ Y2 ) @ Y1 ) @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f175]) ).
thf(f177,plain,
( $true
!= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] :
( mforall_ind
@ ^ [Y1: mu] :
( mforall_ind
@ ^ [Y2: mu] : ( mimplies @ ( mand @ ( in @ Y0 @ Y1 ) @ ( in @ Y2 @ Y1 ) ) @ ( qmltpeq @ ( set_union2 @ ( unordered_pair @ Y0 @ Y2 ) @ Y1 ) @ Y1 ) ) ) ) ) ) ),
inference(flattening,[],[f176]) ).
thf(f182,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f66]) ).
thf(f183,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f68]) ).
thf(f188,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f74]) ).
thf(f189,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f75]) ).
thf(f191,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f77]) ).
thf(f195,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f83]) ).
thf(f208,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f109]) ).
thf(f217,plain,
! [X2: mu,X0: $i,X1: mu] :
( ( exists_in_world @ ( unordered_pair @ X1 @ X2 ) @ X0 )
= $true ),
inference(cnf_transformation,[],[f126]) ).
thf(f240,plain,
( $true
= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] :
( mforall_ind
@ ^ [Y1: mu] : ( mimplies @ ( subset @ Y0 @ Y1 ) @ ( qmltpeq @ ( set_union2 @ Y0 @ Y1 ) @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f172]) ).
thf(f241,plain,
( $true
= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] :
( mforall_ind
@ ^ [Y1: mu] :
( mforall_ind
@ ^ [Y2: mu] : ( mequiv @ ( subset @ ( unordered_pair @ Y0 @ Y1 ) @ Y2 ) @ ( mand @ ( in @ Y0 @ Y2 ) @ ( in @ Y1 @ Y2 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f174]) ).
thf(f242,plain,
( $true
!= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] :
( mforall_ind
@ ^ [Y1: mu] :
( mforall_ind
@ ^ [Y2: mu] : ( mimplies @ ( mand @ ( in @ Y0 @ Y1 ) @ ( in @ Y2 @ Y1 ) ) @ ( qmltpeq @ ( set_union2 @ ( unordered_pair @ Y0 @ Y2 ) @ Y1 ) @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f177]) ).
thf(f246,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f188,f182,f183,f182,f182]) ).
thf(f247,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,[],[f189,f183,f182]) ).
thf(f249,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ ( ^ [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 )
@ Y0
@ Y1 )
@ ( ^ [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 )
@ Y1
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f191,f246,f247,f247]) ).
thf(f278,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 @ ( set_union2 @ Y0 @ Y1 ) @ Y1 ) ) ) ) ) ),
inference(definition_unfolding,[],[f240,f208,f195,f195,f247]) ).
thf(f279,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: mu > $i > $o,Y3: $i] :
( !! @ mu
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) )
@ ^ [Y2: mu] :
( ^ [Y3: $i > $o,Y4: $i > $o] :
( ^ [Y5: $i > $o,Y6: $i > $o] :
( ^ [Y7: $i > $o,Y8: $i] :
~ ( Y7 @ Y8 )
@ ( ^ [Y7: $i > $o,Y8: $i > $o,Y9: $i] :
( ( Y7 @ Y9 )
| ( Y8 @ Y9 ) )
@ ( ^ [Y7: $i > $o,Y8: $i] :
~ ( Y7 @ Y8 )
@ Y5 )
@ ( ^ [Y7: $i > $o,Y8: $i] :
~ ( Y7 @ Y8 )
@ Y6 ) ) )
@ ( ^ [Y5: $i > $o,Y6: $i > $o] :
( ^ [Y7: $i > $o,Y8: $i > $o,Y9: $i] :
( ( Y7 @ Y9 )
| ( Y8 @ Y9 ) )
@ ( ^ [Y7: $i > $o,Y8: $i] :
~ ( Y7 @ Y8 )
@ Y5 )
@ Y6 )
@ Y3
@ Y4 )
@ ( ^ [Y5: $i > $o,Y6: $i > $o] :
( ^ [Y7: $i > $o,Y8: $i > $o,Y9: $i] :
( ( Y7 @ Y9 )
| ( Y8 @ Y9 ) )
@ ( ^ [Y7: $i > $o,Y8: $i] :
~ ( Y7 @ Y8 )
@ Y5 )
@ Y6 )
@ Y4
@ Y3 ) )
@ ( subset @ ( unordered_pair @ Y0 @ Y1 ) @ Y2 )
@ ( ^ [Y3: $i > $o,Y4: $i > $o] :
( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ ( ^ [Y5: $i > $o,Y6: $i > $o,Y7: $i] :
( ( Y5 @ Y7 )
| ( Y6 @ Y7 ) )
@ ( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ Y3 )
@ ( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ Y4 ) ) )
@ ( in @ Y0 @ Y2 )
@ ( in @ Y1 @ Y2 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f241,f208,f195,f195,f195,f249,f246]) ).
thf(f280,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: mu > $i > $o,Y3: $i] :
( !! @ mu
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) )
@ ^ [Y2: mu] :
( ^ [Y3: $i > $o,Y4: $i > $o] :
( ^ [Y5: $i > $o,Y6: $i > $o,Y7: $i] :
( ( Y5 @ Y7 )
| ( Y6 @ Y7 ) )
@ ( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ Y3 )
@ Y4 )
@ ( ^ [Y3: $i > $o,Y4: $i > $o] :
( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ ( ^ [Y5: $i > $o,Y6: $i > $o,Y7: $i] :
( ( Y5 @ Y7 )
| ( Y6 @ Y7 ) )
@ ( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ Y3 )
@ ( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ Y4 ) ) )
@ ( in @ Y0 @ Y1 )
@ ( in @ Y2 @ Y1 ) )
@ ( qmltpeq @ ( set_union2 @ ( unordered_pair @ Y0 @ Y2 ) @ Y1 ) @ Y1 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f242,f208,f195,f195,f195,f247,f246]) ).
thf(f281,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y0 )
=> ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y0 )
=> ( ~ ~ ( ~ ( in @ Y1 @ Y2 @ Y0 )
| ~ ( in @ Y3 @ Y2 @ Y0 ) )
| ( qmltpeq @ ( set_union2 @ ( unordered_pair @ Y1 @ Y3 ) @ Y2 ) @ Y2 @ Y0 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f280]) ).
thf(f282,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y0 )
=> ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y0 )
=> ( ~ ~ ( ~ ( in @ Y1 @ Y2 @ Y0 )
| ~ ( in @ Y3 @ Y2 @ Y0 ) )
| ( qmltpeq @ ( set_union2 @ ( unordered_pair @ Y1 @ Y3 ) @ Y2 ) @ Y2 @ Y0 ) ) ) ) ) ) ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f281]) ).
thf(f283,plain,
( $false
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK1 )
=> ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ sK1 )
=> ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ sK1 )
=> ( ~ ~ ( ~ ( in @ Y0 @ Y1 @ sK1 )
| ~ ( in @ Y2 @ Y1 @ sK1 ) )
| ( qmltpeq @ ( set_union2 @ ( unordered_pair @ Y0 @ Y2 ) @ Y1 ) @ Y1 @ sK1 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f282]) ).
thf(f284,plain,
( $false
= ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK1 )
=> ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ sK1 )
=> ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ sK1 )
=> ( ~ ~ ( ~ ( in @ Y0 @ Y1 @ sK1 )
| ~ ( in @ Y2 @ Y1 @ sK1 ) )
| ( qmltpeq @ ( set_union2 @ ( unordered_pair @ Y0 @ Y2 ) @ Y1 ) @ Y1 @ sK1 ) ) ) ) ) ) )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f283]) ).
thf(f285,plain,
( $false
= ( ( exists_in_world @ sK2 @ sK1 )
=> ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK1 )
=> ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ sK1 )
=> ( ~ ~ ( ~ ( in @ sK2 @ Y0 @ sK1 )
| ~ ( in @ Y1 @ Y0 @ sK1 ) )
| ( qmltpeq @ ( set_union2 @ ( unordered_pair @ sK2 @ Y1 ) @ Y0 ) @ Y0 @ sK1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f284]) ).
thf(f286,plain,
( $false
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK1 )
=> ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ sK1 )
=> ( ~ ~ ( ~ ( in @ sK2 @ Y0 @ sK1 )
| ~ ( in @ Y1 @ Y0 @ sK1 ) )
| ( qmltpeq @ ( set_union2 @ ( unordered_pair @ sK2 @ Y1 ) @ Y0 ) @ Y0 @ sK1 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f285]) ).
thf(f287,plain,
( $true
= ( exists_in_world @ sK2 @ sK1 ) ),
inference(imp_proxy_clausification,[],[f285]) ).
thf(f288,plain,
( $false
= ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK1 )
=> ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ sK1 )
=> ( ~ ~ ( ~ ( in @ sK2 @ Y0 @ sK1 )
| ~ ( in @ Y1 @ Y0 @ sK1 ) )
| ( qmltpeq @ ( set_union2 @ ( unordered_pair @ sK2 @ Y1 ) @ Y0 ) @ Y0 @ sK1 ) ) ) ) )
@ sK3 ) ),
inference(sigma_proxy_clausification,[],[f286]) ).
thf(f289,plain,
( $false
= ( ( exists_in_world @ sK3 @ sK1 )
=> ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK1 )
=> ( ~ ~ ( ~ ( in @ sK2 @ sK3 @ sK1 )
| ~ ( in @ Y0 @ sK3 @ sK1 ) )
| ( qmltpeq @ ( set_union2 @ ( unordered_pair @ sK2 @ Y0 ) @ sK3 ) @ sK3 @ sK1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f288]) ).
thf(f290,plain,
( $false
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK1 )
=> ( ~ ~ ( ~ ( in @ sK2 @ sK3 @ sK1 )
| ~ ( in @ Y0 @ sK3 @ sK1 ) )
| ( qmltpeq @ ( set_union2 @ ( unordered_pair @ sK2 @ Y0 ) @ sK3 ) @ sK3 @ sK1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f289]) ).
thf(f291,plain,
( $true
= ( exists_in_world @ sK3 @ sK1 ) ),
inference(imp_proxy_clausification,[],[f289]) ).
thf(f292,plain,
( $false
= ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK1 )
=> ( ~ ~ ( ~ ( in @ sK2 @ sK3 @ sK1 )
| ~ ( in @ Y0 @ sK3 @ sK1 ) )
| ( qmltpeq @ ( set_union2 @ ( unordered_pair @ sK2 @ Y0 ) @ sK3 ) @ sK3 @ sK1 ) ) )
@ sK4 ) ),
inference(sigma_proxy_clausification,[],[f290]) ).
thf(f293,plain,
( $false
= ( ( exists_in_world @ sK4 @ sK1 )
=> ( ~ ~ ( ~ ( in @ sK2 @ sK3 @ sK1 )
| ~ ( in @ sK4 @ sK3 @ sK1 ) )
| ( qmltpeq @ ( set_union2 @ ( unordered_pair @ sK2 @ sK4 ) @ sK3 ) @ sK3 @ sK1 ) ) ) ),
inference(beta-eta_normalization,[],[f292]) ).
thf(f294,plain,
( $false
= ( ~ ~ ( ~ ( in @ sK2 @ sK3 @ sK1 )
| ~ ( in @ sK4 @ sK3 @ sK1 ) )
| ( qmltpeq @ ( set_union2 @ ( unordered_pair @ sK2 @ sK4 ) @ sK3 ) @ sK3 @ sK1 ) ) ),
inference(imp_proxy_clausification,[],[f293]) ).
thf(f295,plain,
( $true
= ( exists_in_world @ sK4 @ sK1 ) ),
inference(imp_proxy_clausification,[],[f293]) ).
thf(f296,plain,
( $false
= ( qmltpeq @ ( set_union2 @ ( unordered_pair @ sK2 @ sK4 ) @ sK3 ) @ sK3 @ sK1 ) ),
inference(or_proxy_clausification,[],[f294]) ).
thf(f297,plain,
( $false
= ( ~ ~ ( ~ ( in @ sK2 @ sK3 @ sK1 )
| ~ ( in @ sK4 @ sK3 @ sK1 ) ) ) ),
inference(or_proxy_clausification,[],[f294]) ).
thf(f298,plain,
( $true
= ( ~ ( ~ ( in @ sK2 @ sK3 @ sK1 )
| ~ ( in @ sK4 @ sK3 @ sK1 ) ) ) ),
inference(not_proxy_clausification,[],[f297]) ).
thf(f299,plain,
( $false
= ( ~ ( in @ sK2 @ sK3 @ sK1 )
| ~ ( in @ sK4 @ sK3 @ sK1 ) ) ),
inference(not_proxy_clausification,[],[f298]) ).
thf(f300,plain,
( $false
= ( ~ ( in @ sK4 @ sK3 @ sK1 ) ) ),
inference(or_proxy_clausification,[],[f299]) ).
thf(f301,plain,
( $false
= ( ~ ( in @ sK2 @ sK3 @ sK1 ) ) ),
inference(or_proxy_clausification,[],[f299]) ).
thf(f302,plain,
( $true
= ( in @ sK2 @ sK3 @ sK1 ) ),
inference(not_proxy_clausification,[],[f301]) ).
thf(f303,plain,
( $true
= ( in @ sK4 @ sK3 @ sK1 ) ),
inference(not_proxy_clausification,[],[f300]) ).
thf(f304,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y0 )
=> ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y0 )
=> ~ ( ~ ( ~ ( subset @ ( unordered_pair @ Y1 @ Y2 ) @ Y3 @ Y0 )
| ~ ( ~ ( in @ Y1 @ Y3 @ Y0 )
| ~ ( in @ Y2 @ Y3 @ Y0 ) ) )
| ~ ( ~ ~ ( ~ ( in @ Y1 @ Y3 @ Y0 )
| ~ ( in @ Y2 @ Y3 @ Y0 ) )
| ( subset @ ( unordered_pair @ Y1 @ Y2 ) @ Y3 @ Y0 ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f279]) ).
thf(f305,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y0 )
=> ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y0 )
=> ~ ( ~ ( ~ ( subset @ ( unordered_pair @ Y1 @ Y2 ) @ Y3 @ Y0 )
| ~ ( ~ ( in @ Y1 @ Y3 @ Y0 )
| ~ ( in @ Y2 @ Y3 @ Y0 ) ) )
| ~ ( ~ ~ ( ~ ( in @ Y1 @ Y3 @ Y0 )
| ~ ( in @ Y2 @ Y3 @ Y0 ) )
| ( subset @ ( unordered_pair @ Y1 @ Y2 ) @ Y3 @ Y0 ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f304]) ).
thf(f306,plain,
! [X1: $i] :
( $true
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X1 )
=> ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ X1 )
=> ~ ( ~ ( ~ ( subset @ ( unordered_pair @ Y0 @ Y1 ) @ Y2 @ X1 )
| ~ ( ~ ( in @ Y0 @ Y2 @ X1 )
| ~ ( in @ Y1 @ Y2 @ X1 ) ) )
| ~ ( ~ ~ ( ~ ( in @ Y0 @ Y2 @ X1 )
| ~ ( in @ Y1 @ Y2 @ X1 ) )
| ( subset @ ( unordered_pair @ Y0 @ Y1 ) @ Y2 @ X1 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f305]) ).
thf(f307,plain,
! [X2: mu,X1: $i] :
( $true
= ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X1 )
=> ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ X1 )
=> ~ ( ~ ( ~ ( subset @ ( unordered_pair @ Y0 @ Y1 ) @ Y2 @ X1 )
| ~ ( ~ ( in @ Y0 @ Y2 @ X1 )
| ~ ( in @ Y1 @ Y2 @ X1 ) ) )
| ~ ( ~ ~ ( ~ ( in @ Y0 @ Y2 @ X1 )
| ~ ( in @ Y1 @ Y2 @ X1 ) )
| ( subset @ ( unordered_pair @ Y0 @ Y1 ) @ Y2 @ X1 ) ) ) ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f306]) ).
thf(f308,plain,
! [X2: mu,X1: $i] :
( $true
= ( ( exists_in_world @ X2 @ X1 )
=> ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X1 )
=> ~ ( ~ ( ~ ( subset @ ( unordered_pair @ X2 @ Y0 ) @ Y1 @ X1 )
| ~ ( ~ ( in @ X2 @ Y1 @ X1 )
| ~ ( in @ Y0 @ Y1 @ X1 ) ) )
| ~ ( ~ ~ ( ~ ( in @ X2 @ Y1 @ X1 )
| ~ ( in @ Y0 @ Y1 @ X1 ) )
| ( subset @ ( unordered_pair @ X2 @ Y0 ) @ Y1 @ X1 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f307]) ).
thf(f309,plain,
! [X2: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $true
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X1 )
=> ~ ( ~ ( ~ ( subset @ ( unordered_pair @ X2 @ Y0 ) @ Y1 @ X1 )
| ~ ( ~ ( in @ X2 @ Y1 @ X1 )
| ~ ( in @ Y0 @ Y1 @ X1 ) ) )
| ~ ( ~ ~ ( ~ ( in @ X2 @ Y1 @ X1 )
| ~ ( in @ Y0 @ Y1 @ X1 ) )
| ( subset @ ( unordered_pair @ X2 @ Y0 ) @ Y1 @ X1 ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f308]) ).
thf(f310,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $true
= ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X1 )
=> ~ ( ~ ( ~ ( subset @ ( unordered_pair @ X2 @ Y0 ) @ Y1 @ X1 )
| ~ ( ~ ( in @ X2 @ Y1 @ X1 )
| ~ ( in @ Y0 @ Y1 @ X1 ) ) )
| ~ ( ~ ~ ( ~ ( in @ X2 @ Y1 @ X1 )
| ~ ( in @ Y0 @ Y1 @ X1 ) )
| ( subset @ ( unordered_pair @ X2 @ Y0 ) @ Y1 @ X1 ) ) ) ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f309]) ).
thf(f311,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $true
= ( ( exists_in_world @ X3 @ X1 )
=> ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ~ ( ~ ( ~ ( subset @ ( unordered_pair @ X2 @ X3 ) @ Y0 @ X1 )
| ~ ( ~ ( in @ X2 @ Y0 @ X1 )
| ~ ( in @ X3 @ Y0 @ X1 ) ) )
| ~ ( ~ ~ ( ~ ( in @ X2 @ Y0 @ X1 )
| ~ ( in @ X3 @ Y0 @ X1 ) )
| ( subset @ ( unordered_pair @ X2 @ X3 ) @ Y0 @ X1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f310]) ).
thf(f312,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ X1 ) )
| ( $true
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ~ ( ~ ( ~ ( subset @ ( unordered_pair @ X2 @ X3 ) @ Y0 @ X1 )
| ~ ( ~ ( in @ X2 @ Y0 @ X1 )
| ~ ( in @ X3 @ Y0 @ X1 ) ) )
| ~ ( ~ ~ ( ~ ( in @ X2 @ Y0 @ X1 )
| ~ ( in @ X3 @ Y0 @ X1 ) )
| ( subset @ ( unordered_pair @ X2 @ X3 ) @ Y0 @ X1 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f311]) ).
thf(f313,plain,
! [X2: mu,X3: mu,X1: $i,X4: mu] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ X1 ) )
| ( $true
= ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ~ ( ~ ( ~ ( subset @ ( unordered_pair @ X2 @ X3 ) @ Y0 @ X1 )
| ~ ( ~ ( in @ X2 @ Y0 @ X1 )
| ~ ( in @ X3 @ Y0 @ X1 ) ) )
| ~ ( ~ ~ ( ~ ( in @ X2 @ Y0 @ X1 )
| ~ ( in @ X3 @ Y0 @ X1 ) )
| ( subset @ ( unordered_pair @ X2 @ X3 ) @ Y0 @ X1 ) ) ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f312]) ).
thf(f314,plain,
! [X2: mu,X3: mu,X1: $i,X4: mu] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ X1 ) )
| ( $true
= ( ( exists_in_world @ X4 @ X1 )
=> ~ ( ~ ( ~ ( subset @ ( unordered_pair @ X2 @ X3 ) @ X4 @ X1 )
| ~ ( ~ ( in @ X2 @ X4 @ X1 )
| ~ ( in @ X3 @ X4 @ X1 ) ) )
| ~ ( ~ ~ ( ~ ( in @ X2 @ X4 @ X1 )
| ~ ( in @ X3 @ X4 @ X1 ) )
| ( subset @ ( unordered_pair @ X2 @ X3 ) @ X4 @ X1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f313]) ).
thf(f315,plain,
! [X2: mu,X3: mu,X1: $i,X4: mu] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ X1 ) )
| ( $false
= ( exists_in_world @ X4 @ X1 ) )
| ( $true
= ( ~ ( ~ ( ~ ( subset @ ( unordered_pair @ X2 @ X3 ) @ X4 @ X1 )
| ~ ( ~ ( in @ X2 @ X4 @ X1 )
| ~ ( in @ X3 @ X4 @ X1 ) ) )
| ~ ( ~ ~ ( ~ ( in @ X2 @ X4 @ X1 )
| ~ ( in @ X3 @ X4 @ X1 ) )
| ( subset @ ( unordered_pair @ X2 @ X3 ) @ X4 @ X1 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f314]) ).
thf(f316,plain,
! [X2: mu,X3: mu,X1: $i,X4: mu] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ X1 ) )
| ( $false
= ( exists_in_world @ X4 @ X1 ) )
| ( $false
= ( ~ ( ~ ( subset @ ( unordered_pair @ X2 @ X3 ) @ X4 @ X1 )
| ~ ( ~ ( in @ X2 @ X4 @ X1 )
| ~ ( in @ X3 @ X4 @ X1 ) ) )
| ~ ( ~ ~ ( ~ ( in @ X2 @ X4 @ X1 )
| ~ ( in @ X3 @ X4 @ X1 ) )
| ( subset @ ( unordered_pair @ X2 @ X3 ) @ X4 @ X1 ) ) ) ) ),
inference(not_proxy_clausification,[],[f315]) ).
thf(f317,plain,
! [X2: mu,X3: mu,X1: $i,X4: mu] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ X1 ) )
| ( $false
= ( exists_in_world @ X4 @ X1 ) )
| ( $false
= ( ~ ( ~ ~ ( ~ ( in @ X2 @ X4 @ X1 )
| ~ ( in @ X3 @ X4 @ X1 ) )
| ( subset @ ( unordered_pair @ X2 @ X3 ) @ X4 @ X1 ) ) ) ) ),
inference(or_proxy_clausification,[],[f316]) ).
thf(f328,plain,
! [X2: mu,X3: mu,X1: $i,X4: mu] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ X1 ) )
| ( $false
= ( exists_in_world @ X4 @ X1 ) )
| ( $true
= ( ~ ~ ( ~ ( in @ X2 @ X4 @ X1 )
| ~ ( in @ X3 @ X4 @ X1 ) )
| ( subset @ ( unordered_pair @ X2 @ X3 ) @ X4 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f317]) ).
thf(f329,plain,
! [X2: mu,X3: mu,X1: $i,X4: mu] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ X1 ) )
| ( $false
= ( exists_in_world @ X4 @ X1 ) )
| ( $true
= ( subset @ ( unordered_pair @ X2 @ X3 ) @ X4 @ X1 ) )
| ( $true
= ( ~ ~ ( ~ ( in @ X2 @ X4 @ X1 )
| ~ ( in @ X3 @ X4 @ X1 ) ) ) ) ),
inference(or_proxy_clausification,[],[f328]) ).
thf(f330,plain,
! [X2: mu,X3: mu,X1: $i,X4: mu] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ X1 ) )
| ( $false
= ( exists_in_world @ X4 @ X1 ) )
| ( $true
= ( subset @ ( unordered_pair @ X2 @ X3 ) @ X4 @ X1 ) )
| ( $false
= ( ~ ( ~ ( in @ X2 @ X4 @ X1 )
| ~ ( in @ X3 @ X4 @ X1 ) ) ) ) ),
inference(not_proxy_clausification,[],[f329]) ).
thf(f331,plain,
! [X2: mu,X3: mu,X1: $i,X4: mu] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ X1 ) )
| ( $false
= ( exists_in_world @ X4 @ X1 ) )
| ( $true
= ( subset @ ( unordered_pair @ X2 @ X3 ) @ X4 @ X1 ) )
| ( $true
= ( ~ ( in @ X2 @ X4 @ X1 )
| ~ ( in @ X3 @ X4 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f330]) ).
thf(f332,plain,
! [X2: mu,X3: mu,X1: $i,X4: mu] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ X1 ) )
| ( $false
= ( exists_in_world @ X4 @ X1 ) )
| ( $true
= ( subset @ ( unordered_pair @ X2 @ X3 ) @ X4 @ X1 ) )
| ( $true
= ( ~ ( in @ X3 @ X4 @ X1 ) ) )
| ( $true
= ( ~ ( in @ X2 @ X4 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f331]) ).
thf(f333,plain,
! [X2: mu,X3: mu,X1: $i,X4: mu] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ X1 ) )
| ( $false
= ( exists_in_world @ X4 @ X1 ) )
| ( $true
= ( subset @ ( unordered_pair @ X2 @ X3 ) @ X4 @ X1 ) )
| ( $false
= ( in @ X3 @ X4 @ X1 ) )
| ( $true
= ( ~ ( in @ X2 @ X4 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f332]) ).
thf(f334,plain,
! [X2: mu,X3: mu,X1: $i,X4: mu] :
( ( $true
= ( subset @ ( unordered_pair @ X2 @ X3 ) @ X4 @ X1 ) )
| ( $false
= ( exists_in_world @ X3 @ X1 ) )
| ( $false
= ( exists_in_world @ X4 @ X1 ) )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( in @ X3 @ X4 @ X1 ) )
| ( $false
= ( in @ X2 @ X4 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f333]) ).
thf(f335,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 @ ( set_union2 @ Y1 @ Y2 ) @ Y2 @ Y0 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f278]) ).
thf(f336,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 @ ( set_union2 @ Y1 @ Y2 ) @ Y2 @ Y0 ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f335]) ).
thf(f337,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 @ ( set_union2 @ Y0 @ Y1 ) @ Y1 @ X1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f336]) ).
thf(f338,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 @ ( set_union2 @ Y0 @ Y1 ) @ Y1 @ X1 ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f337]) ).
thf(f339,plain,
! [X2: mu,X1: $i] :
( $true
= ( ( exists_in_world @ X2 @ X1 )
=> ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( ~ ( subset @ X2 @ Y0 @ X1 )
| ( qmltpeq @ ( set_union2 @ X2 @ Y0 ) @ Y0 @ X1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f338]) ).
thf(f340,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 @ ( set_union2 @ X2 @ Y0 ) @ Y0 @ X1 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f339]) ).
thf(f341,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 @ ( set_union2 @ X2 @ Y0 ) @ Y0 @ X1 ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f340]) ).
thf(f342,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $true
= ( ( exists_in_world @ X3 @ X1 )
=> ( ~ ( subset @ X2 @ X3 @ X1 )
| ( qmltpeq @ ( set_union2 @ X2 @ X3 ) @ X3 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f341]) ).
thf(f343,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 @ ( set_union2 @ X2 @ X3 ) @ X3 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f342]) ).
thf(f344,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( set_union2 @ X2 @ X3 ) @ X3 @ X1 ) )
| ( $true
= ( ~ ( subset @ X2 @ X3 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f343]) ).
thf(f345,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( $true
= ( qmltpeq @ ( set_union2 @ 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,[],[f344]) ).
thf(f861,plain,
( ( $true = $false )
| ( $false
= ( exists_in_world @ sK3 @ sK1 ) )
| ( $false
= ( exists_in_world @ ( unordered_pair @ sK2 @ sK4 ) @ sK1 ) )
| ( $false
= ( subset @ ( unordered_pair @ sK2 @ sK4 ) @ sK3 @ sK1 ) ) ),
inference(constrained_superposition,[],[f296,f345]) ).
thf(f862,plain,
( ( $false
= ( exists_in_world @ sK3 @ sK1 ) )
| ( $false
= ( exists_in_world @ ( unordered_pair @ sK2 @ sK4 ) @ sK1 ) )
| ( $false
= ( subset @ ( unordered_pair @ sK2 @ sK4 ) @ sK3 @ sK1 ) ) ),
inference(trivial_inequality_removal,[],[f861]) ).
thf(f872,plain,
( ( $true = $false )
| ( $false
= ( exists_in_world @ ( unordered_pair @ sK2 @ sK4 ) @ sK1 ) )
| ( $false
= ( subset @ ( unordered_pair @ sK2 @ sK4 ) @ sK3 @ sK1 ) ) ),
inference(forward_demodulation,[],[f862,f291]) ).
thf(f873,plain,
( ( $false
= ( exists_in_world @ ( unordered_pair @ sK2 @ sK4 ) @ sK1 ) )
| ( $false
= ( subset @ ( unordered_pair @ sK2 @ sK4 ) @ sK3 @ sK1 ) ) ),
inference(trivial_inequality_removal,[],[f872]) ).
thf(f880,plain,
( ( $true = $false )
| ( $false
= ( subset @ ( unordered_pair @ sK2 @ sK4 ) @ sK3 @ sK1 ) ) ),
inference(forward_demodulation,[],[f873,f217]) ).
thf(f881,plain,
( $false
= ( subset @ ( unordered_pair @ sK2 @ sK4 ) @ sK3 @ sK1 ) ),
inference(trivial_inequality_removal,[],[f880]) ).
thf(f13936,plain,
( ( $true = $false )
| ( $false
= ( exists_in_world @ sK4 @ sK1 ) )
| ( $false
= ( exists_in_world @ sK3 @ sK1 ) )
| ( $false
= ( exists_in_world @ sK2 @ sK1 ) )
| ( $false
= ( in @ sK4 @ sK3 @ sK1 ) )
| ( $false
= ( in @ sK2 @ sK3 @ sK1 ) ) ),
inference(constrained_superposition,[],[f881,f334]) ).
thf(f13937,plain,
( ( $false
= ( exists_in_world @ sK4 @ sK1 ) )
| ( $false
= ( exists_in_world @ sK3 @ sK1 ) )
| ( $false
= ( exists_in_world @ sK2 @ sK1 ) )
| ( $false
= ( in @ sK4 @ sK3 @ sK1 ) )
| ( $false
= ( in @ sK2 @ sK3 @ sK1 ) ) ),
inference(trivial_inequality_removal,[],[f13936]) ).
thf(f13965,plain,
( ( $true = $false )
| ( $false
= ( exists_in_world @ sK3 @ sK1 ) )
| ( $false
= ( exists_in_world @ sK2 @ sK1 ) )
| ( $false
= ( in @ sK4 @ sK3 @ sK1 ) )
| ( $false
= ( in @ sK2 @ sK3 @ sK1 ) ) ),
inference(forward_demodulation,[],[f13937,f295]) ).
thf(f13966,plain,
( ( $false
= ( exists_in_world @ sK3 @ sK1 ) )
| ( $false
= ( exists_in_world @ sK2 @ sK1 ) )
| ( $false
= ( in @ sK4 @ sK3 @ sK1 ) )
| ( $false
= ( in @ sK2 @ sK3 @ sK1 ) ) ),
inference(trivial_inequality_removal,[],[f13965]) ).
thf(f13997,plain,
( ( $true = $false )
| ( $false
= ( exists_in_world @ sK2 @ sK1 ) )
| ( $false
= ( in @ sK4 @ sK3 @ sK1 ) )
| ( $false
= ( in @ sK2 @ sK3 @ sK1 ) ) ),
inference(forward_demodulation,[],[f13966,f291]) ).
thf(f13998,plain,
( ( $false
= ( exists_in_world @ sK2 @ sK1 ) )
| ( $false
= ( in @ sK4 @ sK3 @ sK1 ) )
| ( $false
= ( in @ sK2 @ sK3 @ sK1 ) ) ),
inference(trivial_inequality_removal,[],[f13997]) ).
thf(f14013,plain,
( ( $true = $false )
| ( $false
= ( in @ sK4 @ sK3 @ sK1 ) )
| ( $false
= ( in @ sK2 @ sK3 @ sK1 ) ) ),
inference(forward_demodulation,[],[f13998,f287]) ).
thf(f14014,plain,
( ( $false
= ( in @ sK4 @ sK3 @ sK1 ) )
| ( $false
= ( in @ sK2 @ sK3 @ sK1 ) ) ),
inference(trivial_inequality_removal,[],[f14013]) ).
thf(f14017,plain,
( ( $true = $false )
| ( $false
= ( in @ sK4 @ sK3 @ sK1 ) ) ),
inference(forward_demodulation,[],[f14014,f302]) ).
thf(f14018,plain,
( $false
= ( in @ sK4 @ sK3 @ sK1 ) ),
inference(trivial_inequality_removal,[],[f14017]) ).
thf(f14381,plain,
$true = $false,
inference(constrained_superposition,[],[f303,f14018]) ).
thf(f14386,plain,
$false,
inference(trivial_inequality_removal,[],[f14381]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET907^7 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.18 % Computer : n005.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 13:40:46 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.21 Running first-order model finding
% 0.08/0.21 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
% 4.12/0.98 % (1681416)Will run a generic schedule for satisfiability detection.
% 4.12/0.98 % (1681424)dis+10_1_sil=32000:sp=arity:random_seed=4226163400:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 4.12/0.98 % (1681422)% WARNING: option uhcvi not known.
% 4.12/0.98 % (1681425)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1087654394:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 4.12/0.98 % (1681422)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=654949175:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 4.12/0.98 % (1681423)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1424454209:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 4.12/0.98 % (1681421)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=997614509_2999 on theBenchmark for (2999ds/0Mi)
% 4.12/0.98 % (1681425)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.12/0.98 % (1681422)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.12/0.98 % (1681426)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2390886847:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 4.12/0.98 % (1681422)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 4.12/0.98 % Exception at run slice level
% 4.12/0.98 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.12/0.98 % (1681427)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3138197878:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 4.12/0.98 % (1681424)Instruction limit reached!
% 4.12/0.98 % (1681424)------------------------------
% 4.12/0.98 % (1681424)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.12/0.98 % (1681424)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.12/0.98 % (1681424)CaDiCaL version: 2.1.3
% 4.12/0.98 % (1681424)Termination reason: Instruction limit
% 4.12/0.98 % (1681424)Termination phase: Saturation
% 4.12/0.98 % (1681424)Time elapsed: 0.033 s
% 4.12/0.98 % (1681424)Peak memory usage: 12 MB
% 4.12/0.98 % (1681424)Instructions burned: 104 (million)
% 4.12/0.98 % (1681434)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=4284123228:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 4.12/0.98 % (1681436)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=483499228:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 4.12/0.98 % Exception at run slice level
% 4.12/0.98 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.12/0.98 % (1681425)Instruction limit reached!
% 4.12/0.98 % (1681425)------------------------------
% 4.12/0.98 % (1681425)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.12/0.98 % (1681425)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.12/0.98 % (1681425)CaDiCaL version: 2.1.3
% 4.12/0.98 % (1681425)Termination reason: Instruction limit
% 4.12/0.98 % (1681425)Termination phase: Saturation
% 4.12/0.98 % (1681425)Time elapsed: 0.055 s
% 4.12/0.98 % (1681425)Peak memory usage: 12 MB
% 4.12/0.98 % (1681425)Instructions burned: 118 (million)
% 4.12/0.98 % (1681439)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=2122428522:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 4.12/0.98 % (1681426)Instruction limit reached!
% 4.12/0.98 % (1681426)------------------------------
% 4.12/0.98 % (1681426)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.12/0.98 % (1681426)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.12/0.98 % (1681426)CaDiCaL version: 2.1.3
% 4.12/0.98 % (1681426)Termination reason: Instruction limit
% 4.12/0.98 % (1681426)Termination phase: Saturation
% 4.12/0.98 % (1681426)Time elapsed: 0.062 s
% 4.12/0.98 % (1681426)Peak memory usage: 13 MB
% 4.12/0.98 % (1681426)Instructions burned: 133 (million)
% 4.12/0.98 % (1681439)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.12/0.98 % (1681440)ott-21_1_sil=16000:fs=off:random_seed=1472054782:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 4.12/0.98 % (1681436)Instruction limit reached!
% 4.12/0.98 % (1681436)------------------------------
% 4.12/0.98 % (1681436)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.12/0.98 % (1681436)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.12/0.98 % (1681436)CaDiCaL version: 2.1.3
% 4.12/0.98 % (1681436)Termination reason: Instruction limit
% 4.12/0.98 % (1681436)Termination phase: Saturation
% 4.12/0.98 % (1681436)Time elapsed: 0.037 s
% 4.12/0.98 % (1681436)Peak memory usage: 12 MB
% 4.12/0.98 % (1681436)Instructions burned: 132 (million)
% 4.12/0.98 % (1681439)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 4.12/0.98 % (1681442)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3351752370:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 4.12/0.98 % (1681444)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=1897772705:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 4.12/0.98 % Exception at run slice level
% 4.12/0.98 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.12/0.98 % (1681447)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=2765483116:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 4.12/0.98 % (1681427)Instruction limit reached!
% 4.12/0.98 % (1681427)------------------------------
% 4.12/0.98 % (1681427)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.12/0.98 % (1681427)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.12/0.98 % (1681427)CaDiCaL version: 2.1.3
% 4.12/0.98 % (1681427)Termination reason: Instruction limit
% 4.12/0.98 % (1681427)Termination phase: Saturation
% 4.12/0.98 % (1681427)Time elapsed: 0.130 s
% 4.12/0.98 % (1681427)Peak memory usage: 12 MB
% 4.12/0.98 % (1681427)Instructions burned: 159 (million)
% 4.12/0.98 % (1681440)Instruction limit reached!
% 4.12/0.98 % (1681440)------------------------------
% 4.12/0.98 % (1681440)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.12/0.98 % (1681440)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.12/0.98 % (1681440)CaDiCaL version: 2.1.3
% 4.12/0.98 % (1681440)Termination reason: Instruction limit
% 4.12/0.98 % (1681440)Termination phase: Saturation
% 4.12/0.98 % (1681440)Time elapsed: 0.081 s
% 4.12/0.98 % (1681440)Peak memory usage: 12 MB
% 4.12/0.98 % (1681440)Instructions burned: 182 (million)
% 4.12/0.98 % (1681449)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=739777556:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 4.12/0.98 % (1681450)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=3732154000:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2998 on theBenchmark for (2998ds/692Mi)
% 4.12/0.98 % Exception at run slice level
% 4.12/0.98 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.12/0.98 % (1681450)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.12/0.98 % (1681453)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=2154379096:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 4.12/0.98 % (1681453)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.12/0.98 % (1681442)Instruction limit reached!
% 4.12/0.98 % (1681442)------------------------------
% 4.12/0.98 % (1681442)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.12/0.98 % (1681442)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.12/0.98 % (1681442)CaDiCaL version: 2.1.3
% 4.12/0.98 % (1681442)Termination reason: Instruction limit
% 4.12/0.98 % (1681442)Termination phase: Saturation
% 4.12/0.98 % (1681442)Time elapsed: 0.282 s
% 4.12/0.98 % (1681442)Peak memory usage: 13 MB
% 4.12/0.98 % (1681442)Instructions burned: 477 (million)
% 4.12/0.98 % (1681456)fmb+10_1_sil=64000:random_seed=3531565905:i=22061:nm=2:gsp=on_2995 on theBenchmark for (2995ds/22061Mi)
% 4.12/0.98 % (1681456)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 4.12/0.98 % Exception at run slice level
% 4.12/0.98 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.12/0.98 % (1681458)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=3778912017:i=9515:nm=5_2995 on theBenchmark for (2995ds/9515Mi)
% 4.12/0.98 % Exception at run slice level
% 4.12/0.98 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.12/0.98 % (1681447)Instruction limit reached!
% 4.12/0.98 % (1681447)------------------------------
% 4.12/0.98 % (1681447)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.12/0.98 % (1681447)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.12/0.98 % (1681447)CaDiCaL version: 2.1.3
% 4.12/0.98 % (1681447)Termination reason: Instruction limit
% 4.12/0.98 % (1681447)Termination phase: Saturation
% 4.12/0.98 % (1681447)Time elapsed: 0.328 s
% 4.12/0.98 % (1681447)Peak memory usage: 15 MB
% 4.12/0.98 % (1681447)Instructions burned: 1180 (million)
% 4.12/0.98 % (1681460)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=1666321242:fmbsr=1.7:i=920_2995 on theBenchmark for (2995ds/920Mi)
% 4.12/0.98 % (1681461)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=197552365:i=5131_2995 on theBenchmark for (2995ds/5131Mi)
% 4.12/0.98 % (1681461)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.12/0.98 % Exception at run slice level
% 4.12/0.98 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.12/0.98 % (1681450)Instruction limit reached!
% 4.12/0.98 % (1681450)------------------------------
% 4.12/0.98 % (1681450)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.12/0.98 % (1681450)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.12/0.98 % (1681450)CaDiCaL version: 2.1.3
% 4.12/0.98 % (1681450)Termination reason: Instruction limit
% 4.12/0.98 % (1681450)Termination phase: Saturation
% 4.12/0.98 % (1681450)Time elapsed: 0.290 s
% 4.12/0.98 % (1681450)Peak memory usage: 13 MB
% 4.12/0.98 % (1681450)Instructions burned: 695 (million)
% 4.12/0.98 % (1681439)Instruction limit reached!
% 4.12/0.98 % (1681439)------------------------------
% 4.12/0.98 % (1681439)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.12/0.98 % (1681439)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.12/0.98 % (1681439)CaDiCaL version: 2.1.3
% 4.12/0.98 % (1681439)Termination reason: Instruction limit
% 4.12/0.98 % (1681439)Termination phase: Saturation
% 4.12/0.98 % (1681439)Time elapsed: 0.405 s
% 4.12/0.98 % (1681439)Peak memory usage: 14 MB
% 4.12/0.98 % (1681439)Instructions burned: 684 (million)
% 4.12/0.98 % (1681464)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=386892094:i=1472:ins=7:fdi=8:gsp=on_2995 on theBenchmark for (2995ds/1472Mi)
% 4.12/0.98 % (1681464)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 4.12/0.98 % (1681464)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 4.12/0.98 % (1681465)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=3483857812:i=6324_2994 on theBenchmark for (2994ds/6324Mi)
% 4.12/0.98 % (1681466)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=4059408648:fmbsr=2.30978:i=2174_2994 on theBenchmark for (2994ds/2174Mi)
% 4.12/0.98 % Exception at run slice level
% 4.12/0.98 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.12/0.98 % Exception at run slice level
% 4.12/0.98 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.12/0.98 % (1681470)ott-2_1_sil=16000:newcnf=on:random_seed=974677320:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2994 on theBenchmark for (2994ds/869Mi)
% 4.12/0.98 % (1681470)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.12/0.98 % (1681471)ott+10_1_sil=32000:tgt=ground:random_seed=1625739551:i=5114:av=off_2994 on theBenchmark for (2994ds/5114Mi)
% 4.12/0.98 % (1681422) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1681416-1681422"...
% 4.12/0.98 % (1681422)...printing done.
% 4.12/0.98 % (1681422)Refutation found. Thanks to Tanya!
% 4.12/0.98 % SZS status Theorem for theBenchmark
% 4.12/0.98 % SZS output start Proof for theBenchmark
% See solution above
% 4.12/0.98 % (1681422)------------------------------
% 4.12/0.98 % (1681422)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.12/0.98 % (1681422)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.12/0.98 % (1681422)CaDiCaL version: 2.1.3
% 4.12/0.98 % (1681422)Termination reason: Refutation
% 4.12/0.98 % (1681422)Time elapsed: 0.713 s
% 4.12/0.98 % (1681422)Peak memory usage: 15 MB
% 4.12/0.98 % (1681422)Instructions burned: 1668 (million)
% 4.12/0.98 % (1681416)Success in time 0.756 s
% 4.12/0.98 % Vampire exiting
%------------------------------------------------------------------------------