%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET002^7 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 Oct 7 10:38:48 AM UTC 2026
% Result : Theorem 0.66s 0.32s
% Output : CNFRefutation 0.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 49
% Syntax : Number of formulae : 341 ( 125 unt; 0 typ; 32 def)
% Number of atoms : 3564 ( 885 equ; 0 cnn)
% Maximal formula atoms : 9 ( 10 avg)
% Number of connectives : 7484 (1147 ~;1289 |; 8 &;4952 @)
% ( 0 <=>; 88 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 59 ( 59 >; 0 *; 0 +; 0 <<)
% Number of symbols : 44 ( 41 usr; 4 con; 0-3 aty)
% Number of variables : 1148 ( 88 ^;1054 !; 6 ?;1148 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_mu,type,
mu: $tType ).
thf(tp_exists_in_world,type,
exists_in_world: mu > $i > $o ).
thf(tp_mand,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mbox,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mbox_s4,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf(tp_mcountersatisfiable,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(tp_mdia,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mdia_s4,type,
mdia_s4: ( $i > $o ) > $i > $o ).
thf(tp_member,type,
member: mu > mu > $i > $o ).
thf(tp_meq_prop,type,
meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mequiv,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_meuclidean,type,
meuclidean: ( $i > $i > $o ) > $o ).
thf(tp_mexists_ind,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(tp_mexists_prop,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(tp_mfalse,type,
mfalse: $i > $o ).
thf(tp_mforall_ind,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(tp_mforall_prop,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(tp_mfunctional,type,
mfunctional: ( $i > $i > $o ) > $o ).
thf(tp_mimplied,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mimplies,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_minvalid,type,
minvalid: ( $i > $o ) > $o ).
thf(tp_mnot,type,
mnot: ( $i > $o ) > $i > $o ).
thf(tp_mor,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mpartially_functional,type,
mpartially_functional: ( $i > $i > $o ) > $o ).
thf(tp_mreflexive,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(tp_msatisfiable,type,
msatisfiable: ( $i > $o ) > $o ).
thf(tp_mserial,type,
mserial: ( $i > $i > $o ) > $o ).
thf(tp_msymmetric,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(tp_mtransitive,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(tp_mtrue,type,
mtrue: $i > $o ).
thf(tp_mvalid,type,
mvalid: ( $i > $o ) > $o ).
thf(tp_mweakly_connected,type,
mweakly_connected: ( $i > $i > $o ) > $o ).
thf(tp_mweakly_dense,type,
mweakly_dense: ( $i > $i > $o ) > $o ).
thf(tp_mweakly_directed,type,
mweakly_directed: ( $i > $i > $o ) > $o ).
thf(tp_mxor,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_qmltpeq,type,
qmltpeq: mu > mu > $i > $o ).
thf(tp_rel_s4,type,
rel_s4: $i > $i > $o ).
thf(tp_sK1_SY3,type,
sK1_SY3: $i ).
thf(tp_sK2_SY522,type,
sK2_SY522: mu ).
thf(tp_sK3_SY592,type,
sK3_SY592: mu > mu > $i > mu ).
thf(tp_subset,type,
subset: mu > mu > $i > $o ).
thf(tp_union,type,
union: mu > mu > mu ).
thf(mand,definition,
( mand
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mor @ ( mnot @ Phi ) @ ( mnot @ Psi ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mand) ).
thf(mbox,definition,
( mbox
= ( ^ [R: $i > $i > $o,Phi: $i > $o,W: $i] :
! [V: $i] :
( ~ ( R @ W @ V )
| ( Phi @ V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox) ).
thf(mbox_s4,definition,
( mbox_s4
= ( ^ [Phi: $i > $o,W: $i] :
! [V: $i] :
( ~ ( rel_s4 @ W @ V )
| ( Phi @ V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_s4) ).
thf(mcountersatisfiable,definition,
( mcountersatisfiable
= ( ^ [Phi: $i > $o] :
? [W: $i] :
~ ( Phi @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mcountersatisfiable) ).
thf(mdia,definition,
( mdia
= ( ^ [R: $i > $i > $o,Phi: $i > $o] : ( mnot @ ( mbox @ R @ ( mnot @ Phi ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia) ).
thf(mdia_s4,definition,
( mdia_s4
= ( ^ [Phi: $i > $o] : ( mnot @ ( mbox_s4 @ ( mnot @ Phi ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia_s4) ).
thf(meq_prop,definition,
( meq_prop
= ( ^ [X: $i > $o,Y: $i > $o,W: $i] :
( ( X @ W )
= ( Y @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',meq_prop) ).
thf(mequiv,definition,
( mequiv
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mand @ ( mimplies @ Phi @ Psi ) @ ( mimplies @ Psi @ Phi ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mequiv) ).
thf(meuclidean,definition,
( meuclidean
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ S @ U ) )
=> ( R @ T @ U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',meuclidean) ).
thf(mexists_ind,definition,
( mexists_ind
= ( ^ [Phi: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X: mu] : ( mnot @ ( Phi @ X ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mexists_ind) ).
thf(mexists_prop,definition,
( mexists_prop
= ( ^ [Phi: ( $i > $o ) > $i > $o] :
( mnot
@ ( mforall_prop
@ ^ [P: $i > $o] : ( mnot @ ( Phi @ P ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mexists_prop) ).
thf(mfalse,definition,
( mfalse
= ( mnot @ mtrue ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mfalse) ).
thf(mforall_ind,definition,
( mforall_ind
= ( ^ [Phi: mu > $i > $o,W: $i] :
! [X: mu] :
( ( exists_in_world @ X @ W )
=> ( Phi @ X @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mforall_ind) ).
thf(mforall_prop,definition,
( mforall_prop
= ( ^ [Phi: ( $i > $o ) > $i > $o,W: $i] :
! [P: $i > $o] : ( Phi @ P @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mforall_prop) ).
thf(mfunctional,definition,
( mfunctional
= ( ^ [R: $i > $i > $o] :
! [S: $i] :
? [T: $i] :
( ( R @ S @ T )
& ! [U: $i] :
( ( R @ S @ U )
=> ( T = U ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mfunctional) ).
thf(mimplied,definition,
( mimplied
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Psi ) @ Phi ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplied) ).
thf(mimplies,definition,
( mimplies
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Phi ) @ Psi ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies) ).
thf(minvalid,definition,
( minvalid
= ( ^ [Phi: $i > $o] :
! [W: $i] :
~ ( Phi @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',minvalid) ).
thf(mnot,definition,
( mnot
= ( ^ [Phi: $i > $o,W: $i] :
~ ( Phi @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot) ).
thf(mor,definition,
( mor
= ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
( ( Phi @ W )
| ( Psi @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor) ).
thf(mpartially_functional,definition,
( mpartially_functional
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ S @ U ) )
=> ( T = U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mpartially_functional) ).
thf(mreflexive,definition,
( mreflexive
= ( ^ [R: $i > $i > $o] :
! [S: $i] : ( R @ S @ S ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mreflexive) ).
thf(msatisfiable,definition,
( msatisfiable
= ( ^ [Phi: $i > $o] :
? [W: $i] : ( Phi @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',msatisfiable) ).
thf(mserial,definition,
( mserial
= ( ^ [R: $i > $i > $o] :
! [S: $i] :
? [T: $i] : ( R @ S @ T ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mserial) ).
thf(msymmetric,definition,
( msymmetric
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i] :
( ( R @ S @ T )
=> ( R @ T @ S ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',msymmetric) ).
thf(mtransitive,definition,
( mtransitive
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ T @ U ) )
=> ( R @ S @ U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mtransitive) ).
thf(mtrue,definition,
( mtrue
= ( ^ [W: $i] : $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mtrue) ).
thf(mvalid,definition,
( mvalid
= ( ^ [Phi: $i > $o] :
! [W: $i] : ( Phi @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mvalid) ).
thf(mweakly_connected,definition,
( mweakly_connected
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ S @ U ) )
=> ( ( R @ T @ U )
| ( T = U )
| ( R @ U @ T ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mweakly_connected) ).
thf(mweakly_dense,definition,
( mweakly_dense
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( R @ S @ T )
=> ? [U: $i] :
( ( R @ S @ U )
& ( R @ U @ T ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mweakly_dense) ).
thf(mweakly_directed,definition,
( mweakly_directed
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ S @ U ) )
=> ? [V: $i] :
( ( R @ T @ V )
& ( R @ U @ V ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mweakly_directed) ).
thf(mxor,definition,
( mxor
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mequiv @ Phi @ Psi ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mxor) ).
thf(1,axiom,
( mvalid
@ ( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] :
( mequiv @ ( qmltpeq @ B @ C )
@ ( mforall_ind
@ ^ [D: mu] : ( mequiv @ ( member @ D @ B ) @ ( member @ D @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_member_defn) ).
thf(2,axiom,
( mvalid
@ ( mforall_ind
@ ^ [B: mu] : ( subset @ B @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_of_subset) ).
thf(4,axiom,
( mvalid
@ ( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( qmltpeq @ ( union @ B @ C ) @ ( union @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_union) ).
thf(5,axiom,
( mvalid
@ ( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mequiv @ ( qmltpeq @ B @ C ) @ ( mand @ ( subset @ B @ C ) @ ( subset @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
thf(6,axiom,
( mvalid
@ ( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] :
( mforall_ind
@ ^ [D: mu] : ( mequiv @ ( member @ D @ ( union @ B @ C ) ) @ ( mor @ ( member @ D @ B ) @ ( member @ D @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_defn) ).
thf(7,axiom,
( mvalid
@ ( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mimplies @ ( subset @ B @ C ) @ ( qmltpeq @ ( union @ B @ C ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_union) ).
thf(8,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( subset @ C @ A ) ) @ ( subset @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_substitution_2) ).
thf(9,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( subset @ A @ C ) ) @ ( subset @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_substitution_1) ).
thf(10,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( member @ C @ A ) ) @ ( member @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_substitution_2) ).
thf(11,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( member @ A @ C ) ) @ ( member @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_substitution_1) ).
thf(12,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( union @ C @ A ) @ ( union @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_substitution_2) ).
thf(13,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( union @ A @ C ) @ ( union @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_substitution_1) ).
thf(14,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X: mu] :
( mforall_ind
@ ^ [Y: mu] :
( mforall_ind
@ ^ [Z: mu] : ( mimplies @ ( mand @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ Z ) ) @ ( qmltpeq @ X @ Z ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity) ).
thf(15,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X: mu] :
( mforall_ind
@ ^ [Y: mu] : ( mimplies @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ X ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry) ).
thf(16,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X: mu] : ( qmltpeq @ X @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).
thf(17,axiom,
! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( union @ V2 @ V1 ) @ V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_union_ax) ).
thf(22,conjecture,
( mvalid
@ ( mforall_ind
@ ^ [B: mu] : ( qmltpeq @ ( union @ B @ B ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_idempotency_of_union) ).
thf(23,negated_conjecture,
( ( mvalid
@ ( mforall_ind
@ ^ [B: mu] : ( qmltpeq @ ( union @ B @ B ) @ B ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[22]) ).
thf(24,plain,
( ( ! [SY3: $i,SY4: mu] :
( ( exists_in_world @ SY4 @ SY3 )
=> ( qmltpeq @ ( union @ SY4 @ SY4 ) @ SY4 @ SY3 ) ) )
= $false ),
inference(unfold_def,[status(thm)],[23,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(25,plain,
( ( ! [SY75: $i,SY76: mu] :
( ( exists_in_world @ SY76 @ SY75 )
=> ! [SY77: mu] :
( ( exists_in_world @ SY77 @ SY75 )
=> ~ ( ~ ( ~ ( qmltpeq @ SY76 @ SY77 @ SY75 )
| ! [SY78: mu] :
( ( exists_in_world @ SY78 @ SY75 )
=> ~ ( ~ ( ~ ( member @ SY78 @ SY76 @ SY75 )
| ( member @ SY78 @ SY77 @ SY75 ) )
| ~ ( ~ ( member @ SY78 @ SY77 @ SY75 )
| ( member @ SY78 @ SY76 @ SY75 ) ) ) ) )
| ~ ( ~ ! [SY79: mu] :
( ( exists_in_world @ SY79 @ SY75 )
=> ~ ( ~ ( ~ ( member @ SY79 @ SY76 @ SY75 )
| ( member @ SY79 @ SY77 @ SY75 ) )
| ~ ( ~ ( member @ SY79 @ SY77 @ SY75 )
| ( member @ SY79 @ SY76 @ SY75 ) ) ) )
| ( qmltpeq @ SY76 @ SY77 @ SY75 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(26,plain,
( ( ! [SY88: $i,SY89: mu] :
( ( exists_in_world @ SY89 @ SY88 )
=> ( subset @ SY89 @ SY89 @ SY88 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(27,plain,
( ( ! [SY101: $i,SY102: mu] :
( ( exists_in_world @ SY102 @ SY101 )
=> ! [SY103: mu] :
( ( exists_in_world @ SY103 @ SY101 )
=> ( qmltpeq @ ( union @ SY102 @ SY103 ) @ ( union @ SY103 @ SY102 ) @ SY101 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(28,plain,
( ( ! [SY147: $i,SY148: mu] :
( ( exists_in_world @ SY148 @ SY147 )
=> ! [SY149: mu] :
( ( exists_in_world @ SY149 @ SY147 )
=> ~ ( ~ ( ~ ( qmltpeq @ SY148 @ SY149 @ SY147 )
| ~ ( ~ ( subset @ SY148 @ SY149 @ SY147 )
| ~ ( subset @ SY149 @ SY148 @ SY147 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SY148 @ SY149 @ SY147 )
| ~ ( subset @ SY149 @ SY148 @ SY147 ) )
| ( qmltpeq @ SY148 @ SY149 @ SY147 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(29,plain,
( ( ! [SY196: $i,SY197: mu] :
( ( exists_in_world @ SY197 @ SY196 )
=> ! [SY198: mu] :
( ( exists_in_world @ SY198 @ SY196 )
=> ! [SY199: mu] :
( ( exists_in_world @ SY199 @ SY196 )
=> ~ ( ~ ( ~ ( member @ SY199 @ ( union @ SY197 @ SY198 ) @ SY196 )
| ( member @ SY199 @ SY197 @ SY196 )
| ( member @ SY199 @ SY198 @ SY196 ) )
| ~ ( ~ ( ( member @ SY199 @ SY197 @ SY196 )
| ( member @ SY199 @ SY198 @ SY196 ) )
| ( member @ SY199 @ ( union @ SY197 @ SY198 ) @ SY196 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(30,plain,
( ( ! [SY220: $i,SY221: mu] :
( ( exists_in_world @ SY221 @ SY220 )
=> ! [SY222: mu] :
( ( exists_in_world @ SY222 @ SY220 )
=> ( ~ ( subset @ SY221 @ SY222 @ SY220 )
| ( qmltpeq @ ( union @ SY221 @ SY222 ) @ SY222 @ SY220 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(31,plain,
( ( ! [SY258: $i,SY259: mu] :
( ( exists_in_world @ SY259 @ SY258 )
=> ! [SY260: mu] :
( ( exists_in_world @ SY260 @ SY258 )
=> ! [SY261: mu] :
( ( exists_in_world @ SY261 @ SY258 )
=> ( ~ ~ ( ~ ( qmltpeq @ SY259 @ SY260 @ SY258 )
| ~ ( subset @ SY261 @ SY259 @ SY258 ) )
| ( subset @ SY261 @ SY260 @ SY258 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(32,plain,
( ( ! [SY298: $i,SY299: mu] :
( ( exists_in_world @ SY299 @ SY298 )
=> ! [SY300: mu] :
( ( exists_in_world @ SY300 @ SY298 )
=> ! [SY301: mu] :
( ( exists_in_world @ SY301 @ SY298 )
=> ( ~ ~ ( ~ ( qmltpeq @ SY299 @ SY300 @ SY298 )
| ~ ( subset @ SY299 @ SY301 @ SY298 ) )
| ( subset @ SY300 @ SY301 @ SY298 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(33,plain,
( ( ! [SY338: $i,SY339: mu] :
( ( exists_in_world @ SY339 @ SY338 )
=> ! [SY340: mu] :
( ( exists_in_world @ SY340 @ SY338 )
=> ! [SY341: mu] :
( ( exists_in_world @ SY341 @ SY338 )
=> ( ~ ~ ( ~ ( qmltpeq @ SY339 @ SY340 @ SY338 )
| ~ ( member @ SY341 @ SY339 @ SY338 ) )
| ( member @ SY341 @ SY340 @ SY338 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(34,plain,
( ( ! [SY378: $i,SY379: mu] :
( ( exists_in_world @ SY379 @ SY378 )
=> ! [SY380: mu] :
( ( exists_in_world @ SY380 @ SY378 )
=> ! [SY381: mu] :
( ( exists_in_world @ SY381 @ SY378 )
=> ( ~ ~ ( ~ ( qmltpeq @ SY379 @ SY380 @ SY378 )
| ~ ( member @ SY379 @ SY381 @ SY378 ) )
| ( member @ SY380 @ SY381 @ SY378 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(35,plain,
( ( ! [SY410: $i,SY411: mu] :
( ( exists_in_world @ SY411 @ SY410 )
=> ! [SY412: mu] :
( ( exists_in_world @ SY412 @ SY410 )
=> ! [SY413: mu] :
( ( exists_in_world @ SY413 @ SY410 )
=> ( ~ ( qmltpeq @ SY411 @ SY412 @ SY410 )
| ( qmltpeq @ ( union @ SY413 @ SY411 ) @ ( union @ SY413 @ SY412 ) @ SY410 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(36,plain,
( ( ! [SY442: $i,SY443: mu] :
( ( exists_in_world @ SY443 @ SY442 )
=> ! [SY444: mu] :
( ( exists_in_world @ SY444 @ SY442 )
=> ! [SY445: mu] :
( ( exists_in_world @ SY445 @ SY442 )
=> ( ~ ( qmltpeq @ SY443 @ SY444 @ SY442 )
| ( qmltpeq @ ( union @ SY443 @ SY445 ) @ ( union @ SY444 @ SY445 ) @ SY442 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(37,plain,
( ( ! [SY482: $i,SY483: mu] :
( ( exists_in_world @ SY483 @ SY482 )
=> ! [SY484: mu] :
( ( exists_in_world @ SY484 @ SY482 )
=> ! [SY485: mu] :
( ( exists_in_world @ SY485 @ SY482 )
=> ( ~ ~ ( ~ ( qmltpeq @ SY483 @ SY484 @ SY482 )
| ~ ( qmltpeq @ SY484 @ SY485 @ SY482 ) )
| ( qmltpeq @ SY483 @ SY485 @ SY482 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(38,plain,
( ( ! [SY506: $i,SY507: mu] :
( ( exists_in_world @ SY507 @ SY506 )
=> ! [SY508: mu] :
( ( exists_in_world @ SY508 @ SY506 )
=> ( ~ ( qmltpeq @ SY507 @ SY508 @ SY506 )
| ( qmltpeq @ SY508 @ SY507 @ SY506 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(39,plain,
( ( ! [SY515: $i,SY516: mu] :
( ( exists_in_world @ SY516 @ SY515 )
=> ( qmltpeq @ SY516 @ SY516 @ SY515 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(40,plain,
( ( ! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( union @ V2 @ V1 ) @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[17,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(41,plain,
( ( ! [SY522: mu] :
( ( exists_in_world @ SY522 @ sK1_SY3 )
=> ( qmltpeq @ ( union @ SY522 @ SY522 ) @ SY522 @ sK1_SY3 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[24]) ).
thf(42,plain,
( ( ( exists_in_world @ sK2_SY522 @ sK1_SY3 )
=> ( qmltpeq @ ( union @ sK2_SY522 @ sK2_SY522 ) @ sK2_SY522 @ sK1_SY3 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[41]) ).
thf(43,plain,
( ( exists_in_world @ sK2_SY522 @ sK1_SY3 )
= $true ),
inference(standard_cnf,[status(thm)],[42]) ).
thf(44,plain,
( ( qmltpeq @ ( union @ sK2_SY522 @ sK2_SY522 ) @ sK2_SY522 @ sK1_SY3 )
= $false ),
inference(standard_cnf,[status(thm)],[42]) ).
thf(45,plain,
( ( ~ ( qmltpeq @ ( union @ sK2_SY522 @ sK2_SY522 ) @ sK2_SY522 @ sK1_SY3 ) )
= $true ),
inference(polarity_switch,[status(thm)],[44]) ).
thf(46,plain,
( ( ! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( union @ V2 @ V1 ) @ V ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(47,plain,
( ( ! [SY515: $i,SY516: mu] :
( ( exists_in_world @ SY516 @ SY515 )
=> ( qmltpeq @ SY516 @ SY516 @ SY515 ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(48,plain,
( ( ! [SY506: $i,SY507: mu] :
( ( exists_in_world @ SY507 @ SY506 )
=> ! [SY508: mu] :
( ( exists_in_world @ SY508 @ SY506 )
=> ( ~ ( qmltpeq @ SY507 @ SY508 @ SY506 )
| ( qmltpeq @ SY508 @ SY507 @ SY506 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(49,plain,
( ( ! [SY482: $i,SY483: mu] :
( ( exists_in_world @ SY483 @ SY482 )
=> ! [SY484: mu] :
( ( exists_in_world @ SY484 @ SY482 )
=> ! [SY485: mu] :
( ( exists_in_world @ SY485 @ SY482 )
=> ( ~ ~ ( ~ ( qmltpeq @ SY483 @ SY484 @ SY482 )
| ~ ( qmltpeq @ SY484 @ SY485 @ SY482 ) )
| ( qmltpeq @ SY483 @ SY485 @ SY482 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(50,plain,
( ( ! [SY442: $i,SY443: mu] :
( ( exists_in_world @ SY443 @ SY442 )
=> ! [SY444: mu] :
( ( exists_in_world @ SY444 @ SY442 )
=> ! [SY445: mu] :
( ( exists_in_world @ SY445 @ SY442 )
=> ( ~ ( qmltpeq @ SY443 @ SY444 @ SY442 )
| ( qmltpeq @ ( union @ SY443 @ SY445 ) @ ( union @ SY444 @ SY445 ) @ SY442 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(51,plain,
( ( ! [SY410: $i,SY411: mu] :
( ( exists_in_world @ SY411 @ SY410 )
=> ! [SY412: mu] :
( ( exists_in_world @ SY412 @ SY410 )
=> ! [SY413: mu] :
( ( exists_in_world @ SY413 @ SY410 )
=> ( ~ ( qmltpeq @ SY411 @ SY412 @ SY410 )
| ( qmltpeq @ ( union @ SY413 @ SY411 ) @ ( union @ SY413 @ SY412 ) @ SY410 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(52,plain,
( ( ! [SY378: $i,SY379: mu] :
( ( exists_in_world @ SY379 @ SY378 )
=> ! [SY380: mu] :
( ( exists_in_world @ SY380 @ SY378 )
=> ! [SY381: mu] :
( ( exists_in_world @ SY381 @ SY378 )
=> ( ~ ~ ( ~ ( qmltpeq @ SY379 @ SY380 @ SY378 )
| ~ ( member @ SY379 @ SY381 @ SY378 ) )
| ( member @ SY380 @ SY381 @ SY378 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(53,plain,
( ( ! [SY338: $i,SY339: mu] :
( ( exists_in_world @ SY339 @ SY338 )
=> ! [SY340: mu] :
( ( exists_in_world @ SY340 @ SY338 )
=> ! [SY341: mu] :
( ( exists_in_world @ SY341 @ SY338 )
=> ( ~ ~ ( ~ ( qmltpeq @ SY339 @ SY340 @ SY338 )
| ~ ( member @ SY341 @ SY339 @ SY338 ) )
| ( member @ SY341 @ SY340 @ SY338 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(54,plain,
( ( ! [SY298: $i,SY299: mu] :
( ( exists_in_world @ SY299 @ SY298 )
=> ! [SY300: mu] :
( ( exists_in_world @ SY300 @ SY298 )
=> ! [SY301: mu] :
( ( exists_in_world @ SY301 @ SY298 )
=> ( ~ ~ ( ~ ( qmltpeq @ SY299 @ SY300 @ SY298 )
| ~ ( subset @ SY299 @ SY301 @ SY298 ) )
| ( subset @ SY300 @ SY301 @ SY298 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(55,plain,
( ( ! [SY258: $i,SY259: mu] :
( ( exists_in_world @ SY259 @ SY258 )
=> ! [SY260: mu] :
( ( exists_in_world @ SY260 @ SY258 )
=> ! [SY261: mu] :
( ( exists_in_world @ SY261 @ SY258 )
=> ( ~ ~ ( ~ ( qmltpeq @ SY259 @ SY260 @ SY258 )
| ~ ( subset @ SY261 @ SY259 @ SY258 ) )
| ( subset @ SY261 @ SY260 @ SY258 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(56,plain,
( ( ! [SY220: $i,SY221: mu] :
( ( exists_in_world @ SY221 @ SY220 )
=> ! [SY222: mu] :
( ( exists_in_world @ SY222 @ SY220 )
=> ( ~ ( subset @ SY221 @ SY222 @ SY220 )
| ( qmltpeq @ ( union @ SY221 @ SY222 ) @ SY222 @ SY220 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(57,plain,
( ( ! [SY196: $i,SY197: mu] :
( ( exists_in_world @ SY197 @ SY196 )
=> ! [SY198: mu] :
( ( exists_in_world @ SY198 @ SY196 )
=> ! [SY199: mu] :
( ( exists_in_world @ SY199 @ SY196 )
=> ~ ( ~ ( ~ ( member @ SY199 @ ( union @ SY197 @ SY198 ) @ SY196 )
| ( member @ SY199 @ SY197 @ SY196 )
| ( member @ SY199 @ SY198 @ SY196 ) )
| ~ ( ~ ( ( member @ SY199 @ SY197 @ SY196 )
| ( member @ SY199 @ SY198 @ SY196 ) )
| ( member @ SY199 @ ( union @ SY197 @ SY198 ) @ SY196 ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(58,plain,
( ( ! [SY147: $i,SY148: mu] :
( ( exists_in_world @ SY148 @ SY147 )
=> ! [SY149: mu] :
( ( exists_in_world @ SY149 @ SY147 )
=> ~ ( ~ ( ~ ( qmltpeq @ SY148 @ SY149 @ SY147 )
| ~ ( ~ ( subset @ SY148 @ SY149 @ SY147 )
| ~ ( subset @ SY149 @ SY148 @ SY147 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SY148 @ SY149 @ SY147 )
| ~ ( subset @ SY149 @ SY148 @ SY147 ) )
| ( qmltpeq @ SY148 @ SY149 @ SY147 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(59,plain,
( ( ! [SY101: $i,SY102: mu] :
( ( exists_in_world @ SY102 @ SY101 )
=> ! [SY103: mu] :
( ( exists_in_world @ SY103 @ SY101 )
=> ( qmltpeq @ ( union @ SY102 @ SY103 ) @ ( union @ SY103 @ SY102 ) @ SY101 ) ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(60,plain,
( ( ! [SY88: $i,SY89: mu] :
( ( exists_in_world @ SY89 @ SY88 )
=> ( subset @ SY89 @ SY89 @ SY88 ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(61,plain,
( ( ! [SY75: $i,SY76: mu] :
( ( exists_in_world @ SY76 @ SY75 )
=> ! [SY77: mu] :
( ( exists_in_world @ SY77 @ SY75 )
=> ~ ( ~ ( ~ ( qmltpeq @ SY76 @ SY77 @ SY75 )
| ! [SY78: mu] :
( ( exists_in_world @ SY78 @ SY75 )
=> ~ ( ~ ( ~ ( member @ SY78 @ SY76 @ SY75 )
| ( member @ SY78 @ SY77 @ SY75 ) )
| ~ ( ~ ( member @ SY78 @ SY77 @ SY75 )
| ( member @ SY78 @ SY76 @ SY75 ) ) ) ) )
| ~ ( ~ ! [SY79: mu] :
( ( exists_in_world @ SY79 @ SY75 )
=> ~ ( ~ ( ~ ( member @ SY79 @ SY76 @ SY75 )
| ( member @ SY79 @ SY77 @ SY75 ) )
| ~ ( ~ ( member @ SY79 @ SY77 @ SY75 )
| ( member @ SY79 @ SY76 @ SY75 ) ) ) )
| ( qmltpeq @ SY76 @ SY77 @ SY75 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(62,plain,
( ( exists_in_world @ sK2_SY522 @ sK1_SY3 )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(63,plain,
( ( ~ ( qmltpeq @ ( union @ sK2_SY522 @ sK2_SY522 ) @ sK2_SY522 @ sK1_SY3 ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(64,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX0 )
| ~ ( qmltpeq @ SX1 @ SX2 @ SX0 )
| ( qmltpeq @ ( union @ SX3 @ SX1 ) @ ( union @ SX3 @ SX2 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(65,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX0 )
| ~ ( ~ ( ~ ( member @ SX3 @ ( union @ SX1 @ SX2 ) @ SX0 )
| ( member @ SX3 @ SX1 @ SX0 )
| ( member @ SX3 @ SX2 @ SX0 ) )
| ~ ( ~ ( ( member @ SX3 @ SX1 @ SX0 )
| ( member @ SX3 @ SX2 @ SX0 ) )
| ( member @ SX3 @ ( union @ SX1 @ SX2 ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(66,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ( qmltpeq @ SX1 @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(67,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX0 )
| ~ ~ ( ~ ( qmltpeq @ SX1 @ SX2 @ SX0 )
| ~ ( member @ SX3 @ SX1 @ SX0 ) )
| ( member @ SX3 @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(68,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX0 )
| ~ ~ ( ~ ( qmltpeq @ SX1 @ SX2 @ SX0 )
| ~ ( subset @ SX1 @ SX3 @ SX0 ) )
| ( subset @ SX2 @ SX3 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(69,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ~ ( qmltpeq @ SX1 @ SX2 @ SX0 )
| ( qmltpeq @ SX2 @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(70,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ~ ( ~ ( ~ ( qmltpeq @ SX1 @ SX2 @ SX0 )
| ~ ( ~ ( subset @ SX1 @ SX2 @ SX0 )
| ~ ( subset @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SX1 @ SX2 @ SX0 )
| ~ ( subset @ SX2 @ SX1 @ SX0 ) )
| ( qmltpeq @ SX1 @ SX2 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(71,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ~ ( ~ ( ~ ( qmltpeq @ SX1 @ SX2 @ SX0 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX0 )
| ~ ( ~ ( ~ ( member @ SX3 @ SX1 @ SX0 )
| ( member @ SX3 @ SX2 @ SX0 ) )
| ~ ( ~ ( member @ SX3 @ SX2 @ SX0 )
| ( member @ SX3 @ SX1 @ SX0 ) ) ) ) )
| ~ ( ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX0 )
| ~ ( ~ ( ~ ( member @ SX3 @ SX1 @ SX0 )
| ( member @ SX3 @ SX2 @ SX0 ) )
| ~ ( ~ ( member @ SX3 @ SX2 @ SX0 )
| ( member @ SX3 @ SX1 @ SX0 ) ) ) )
| ( qmltpeq @ SX1 @ SX2 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(72,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ~ ( subset @ SX1 @ SX2 @ SX0 )
| ( qmltpeq @ ( union @ SX1 @ SX2 ) @ SX2 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(73,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ( qmltpeq @ ( union @ SX1 @ SX2 ) @ ( union @ SX2 @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(74,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ( subset @ SX1 @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(75,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX0 )
| ~ ~ ( ~ ( qmltpeq @ SX1 @ SX2 @ SX0 )
| ~ ( subset @ SX3 @ SX1 @ SX0 ) )
| ( subset @ SX3 @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(76,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX0 )
| ~ ~ ( ~ ( qmltpeq @ SX1 @ SX2 @ SX0 )
| ~ ( member @ SX1 @ SX3 @ SX0 ) )
| ( member @ SX2 @ SX3 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(77,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX0 )
| ~ ~ ( ~ ( qmltpeq @ SX1 @ SX2 @ SX0 )
| ~ ( qmltpeq @ SX2 @ SX3 @ SX0 ) )
| ( qmltpeq @ SX1 @ SX3 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(78,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX0 )
| ~ ( qmltpeq @ SX1 @ SX2 @ SX0 )
| ( qmltpeq @ ( union @ SX1 @ SX3 ) @ ( union @ SX2 @ SX3 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(79,plain,
! [SV1: $i] :
( ( ! [SY523: mu,SY524: mu] : ( exists_in_world @ ( union @ SY523 @ SY524 ) @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(80,plain,
( ( qmltpeq @ ( union @ sK2_SY522 @ sK2_SY522 ) @ sK2_SY522 @ sK1_SY3 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(81,plain,
! [SV2: $i] :
( ( ! [SY525: mu] :
( ~ ( exists_in_world @ SY525 @ SV2 )
| ! [SY526: mu] :
( ~ ( exists_in_world @ SY526 @ SV2 )
| ! [SY527: mu] :
( ~ ( exists_in_world @ SY527 @ SV2 )
| ~ ( qmltpeq @ SY525 @ SY526 @ SV2 )
| ( qmltpeq @ ( union @ SY527 @ SY525 ) @ ( union @ SY527 @ SY526 ) @ SV2 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(82,plain,
! [SV3: $i] :
( ( ! [SY528: mu] :
( ~ ( exists_in_world @ SY528 @ SV3 )
| ! [SY529: mu] :
( ~ ( exists_in_world @ SY529 @ SV3 )
| ! [SY530: mu] :
( ~ ( exists_in_world @ SY530 @ SV3 )
| ~ ( ~ ( ~ ( member @ SY530 @ ( union @ SY528 @ SY529 ) @ SV3 )
| ( member @ SY530 @ SY528 @ SV3 )
| ( member @ SY530 @ SY529 @ SV3 ) )
| ~ ( ~ ( ( member @ SY530 @ SY528 @ SV3 )
| ( member @ SY530 @ SY529 @ SV3 ) )
| ( member @ SY530 @ ( union @ SY528 @ SY529 ) @ SV3 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(83,plain,
! [SV4: $i] :
( ( ! [SY531: mu] :
( ~ ( exists_in_world @ SY531 @ SV4 )
| ( qmltpeq @ SY531 @ SY531 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(84,plain,
! [SV5: $i] :
( ( ! [SY532: mu] :
( ~ ( exists_in_world @ SY532 @ SV5 )
| ! [SY533: mu] :
( ~ ( exists_in_world @ SY533 @ SV5 )
| ! [SY534: mu] :
( ~ ( exists_in_world @ SY534 @ SV5 )
| ~ ~ ( ~ ( qmltpeq @ SY532 @ SY533 @ SV5 )
| ~ ( member @ SY534 @ SY532 @ SV5 ) )
| ( member @ SY534 @ SY533 @ SV5 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(85,plain,
! [SV6: $i] :
( ( ! [SY535: mu] :
( ~ ( exists_in_world @ SY535 @ SV6 )
| ! [SY536: mu] :
( ~ ( exists_in_world @ SY536 @ SV6 )
| ! [SY537: mu] :
( ~ ( exists_in_world @ SY537 @ SV6 )
| ~ ~ ( ~ ( qmltpeq @ SY535 @ SY536 @ SV6 )
| ~ ( subset @ SY535 @ SY537 @ SV6 ) )
| ( subset @ SY536 @ SY537 @ SV6 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(86,plain,
! [SV7: $i] :
( ( ! [SY538: mu] :
( ~ ( exists_in_world @ SY538 @ SV7 )
| ! [SY539: mu] :
( ~ ( exists_in_world @ SY539 @ SV7 )
| ~ ( qmltpeq @ SY538 @ SY539 @ SV7 )
| ( qmltpeq @ SY539 @ SY538 @ SV7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(87,plain,
! [SV8: $i] :
( ( ! [SY540: mu] :
( ~ ( exists_in_world @ SY540 @ SV8 )
| ! [SY541: mu] :
( ~ ( exists_in_world @ SY541 @ SV8 )
| ~ ( ~ ( ~ ( qmltpeq @ SY540 @ SY541 @ SV8 )
| ~ ( ~ ( subset @ SY540 @ SY541 @ SV8 )
| ~ ( subset @ SY541 @ SY540 @ SV8 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SY540 @ SY541 @ SV8 )
| ~ ( subset @ SY541 @ SY540 @ SV8 ) )
| ( qmltpeq @ SY540 @ SY541 @ SV8 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(88,plain,
! [SV9: $i] :
( ( ! [SY542: mu] :
( ~ ( exists_in_world @ SY542 @ SV9 )
| ! [SY543: mu] :
( ~ ( exists_in_world @ SY543 @ SV9 )
| ~ ( ~ ( ~ ( qmltpeq @ SY542 @ SY543 @ SV9 )
| ! [SY544: mu] :
( ~ ( exists_in_world @ SY544 @ SV9 )
| ~ ( ~ ( ~ ( member @ SY544 @ SY542 @ SV9 )
| ( member @ SY544 @ SY543 @ SV9 ) )
| ~ ( ~ ( member @ SY544 @ SY543 @ SV9 )
| ( member @ SY544 @ SY542 @ SV9 ) ) ) ) )
| ~ ( ~ ! [SY545: mu] :
( ~ ( exists_in_world @ SY545 @ SV9 )
| ~ ( ~ ( ~ ( member @ SY545 @ SY542 @ SV9 )
| ( member @ SY545 @ SY543 @ SV9 ) )
| ~ ( ~ ( member @ SY545 @ SY543 @ SV9 )
| ( member @ SY545 @ SY542 @ SV9 ) ) ) )
| ( qmltpeq @ SY542 @ SY543 @ SV9 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(89,plain,
! [SV10: $i] :
( ( ! [SY546: mu] :
( ~ ( exists_in_world @ SY546 @ SV10 )
| ! [SY547: mu] :
( ~ ( exists_in_world @ SY547 @ SV10 )
| ~ ( subset @ SY546 @ SY547 @ SV10 )
| ( qmltpeq @ ( union @ SY546 @ SY547 ) @ SY547 @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(90,plain,
! [SV11: $i] :
( ( ! [SY548: mu] :
( ~ ( exists_in_world @ SY548 @ SV11 )
| ! [SY549: mu] :
( ~ ( exists_in_world @ SY549 @ SV11 )
| ( qmltpeq @ ( union @ SY548 @ SY549 ) @ ( union @ SY549 @ SY548 ) @ SV11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(91,plain,
! [SV12: $i] :
( ( ! [SY550: mu] :
( ~ ( exists_in_world @ SY550 @ SV12 )
| ( subset @ SY550 @ SY550 @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(92,plain,
! [SV13: $i] :
( ( ! [SY551: mu] :
( ~ ( exists_in_world @ SY551 @ SV13 )
| ! [SY552: mu] :
( ~ ( exists_in_world @ SY552 @ SV13 )
| ! [SY553: mu] :
( ~ ( exists_in_world @ SY553 @ SV13 )
| ~ ~ ( ~ ( qmltpeq @ SY551 @ SY552 @ SV13 )
| ~ ( subset @ SY553 @ SY551 @ SV13 ) )
| ( subset @ SY553 @ SY552 @ SV13 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(93,plain,
! [SV14: $i] :
( ( ! [SY554: mu] :
( ~ ( exists_in_world @ SY554 @ SV14 )
| ! [SY555: mu] :
( ~ ( exists_in_world @ SY555 @ SV14 )
| ! [SY556: mu] :
( ~ ( exists_in_world @ SY556 @ SV14 )
| ~ ~ ( ~ ( qmltpeq @ SY554 @ SY555 @ SV14 )
| ~ ( member @ SY554 @ SY556 @ SV14 ) )
| ( member @ SY555 @ SY556 @ SV14 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(94,plain,
! [SV15: $i] :
( ( ! [SY557: mu] :
( ~ ( exists_in_world @ SY557 @ SV15 )
| ! [SY558: mu] :
( ~ ( exists_in_world @ SY558 @ SV15 )
| ! [SY559: mu] :
( ~ ( exists_in_world @ SY559 @ SV15 )
| ~ ~ ( ~ ( qmltpeq @ SY557 @ SY558 @ SV15 )
| ~ ( qmltpeq @ SY558 @ SY559 @ SV15 ) )
| ( qmltpeq @ SY557 @ SY559 @ SV15 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(95,plain,
! [SV16: $i] :
( ( ! [SY560: mu] :
( ~ ( exists_in_world @ SY560 @ SV16 )
| ! [SY561: mu] :
( ~ ( exists_in_world @ SY561 @ SV16 )
| ! [SY562: mu] :
( ~ ( exists_in_world @ SY562 @ SV16 )
| ~ ( qmltpeq @ SY560 @ SY561 @ SV16 )
| ( qmltpeq @ ( union @ SY560 @ SY562 ) @ ( union @ SY561 @ SY562 ) @ SV16 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(96,plain,
! [SV1: $i,SV17: mu] :
( ( ! [SY563: mu] : ( exists_in_world @ ( union @ SV17 @ SY563 ) @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(97,plain,
! [SV2: $i,SV18: mu] :
( ( ~ ( exists_in_world @ SV18 @ SV2 )
| ! [SY564: mu] :
( ~ ( exists_in_world @ SY564 @ SV2 )
| ! [SY565: mu] :
( ~ ( exists_in_world @ SY565 @ SV2 )
| ~ ( qmltpeq @ SV18 @ SY564 @ SV2 )
| ( qmltpeq @ ( union @ SY565 @ SV18 ) @ ( union @ SY565 @ SY564 ) @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(98,plain,
! [SV3: $i,SV19: mu] :
( ( ~ ( exists_in_world @ SV19 @ SV3 )
| ! [SY566: mu] :
( ~ ( exists_in_world @ SY566 @ SV3 )
| ! [SY567: mu] :
( ~ ( exists_in_world @ SY567 @ SV3 )
| ~ ( ~ ( ~ ( member @ SY567 @ ( union @ SV19 @ SY566 ) @ SV3 )
| ( member @ SY567 @ SV19 @ SV3 )
| ( member @ SY567 @ SY566 @ SV3 ) )
| ~ ( ~ ( ( member @ SY567 @ SV19 @ SV3 )
| ( member @ SY567 @ SY566 @ SV3 ) )
| ( member @ SY567 @ ( union @ SV19 @ SY566 ) @ SV3 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(99,plain,
! [SV4: $i,SV20: mu] :
( ( ~ ( exists_in_world @ SV20 @ SV4 )
| ( qmltpeq @ SV20 @ SV20 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(100,plain,
! [SV5: $i,SV21: mu] :
( ( ~ ( exists_in_world @ SV21 @ SV5 )
| ! [SY568: mu] :
( ~ ( exists_in_world @ SY568 @ SV5 )
| ! [SY569: mu] :
( ~ ( exists_in_world @ SY569 @ SV5 )
| ~ ~ ( ~ ( qmltpeq @ SV21 @ SY568 @ SV5 )
| ~ ( member @ SY569 @ SV21 @ SV5 ) )
| ( member @ SY569 @ SY568 @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(101,plain,
! [SV6: $i,SV22: mu] :
( ( ~ ( exists_in_world @ SV22 @ SV6 )
| ! [SY570: mu] :
( ~ ( exists_in_world @ SY570 @ SV6 )
| ! [SY571: mu] :
( ~ ( exists_in_world @ SY571 @ SV6 )
| ~ ~ ( ~ ( qmltpeq @ SV22 @ SY570 @ SV6 )
| ~ ( subset @ SV22 @ SY571 @ SV6 ) )
| ( subset @ SY570 @ SY571 @ SV6 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(102,plain,
! [SV7: $i,SV23: mu] :
( ( ~ ( exists_in_world @ SV23 @ SV7 )
| ! [SY572: mu] :
( ~ ( exists_in_world @ SY572 @ SV7 )
| ~ ( qmltpeq @ SV23 @ SY572 @ SV7 )
| ( qmltpeq @ SY572 @ SV23 @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(103,plain,
! [SV8: $i,SV24: mu] :
( ( ~ ( exists_in_world @ SV24 @ SV8 )
| ! [SY573: mu] :
( ~ ( exists_in_world @ SY573 @ SV8 )
| ~ ( ~ ( ~ ( qmltpeq @ SV24 @ SY573 @ SV8 )
| ~ ( ~ ( subset @ SV24 @ SY573 @ SV8 )
| ~ ( subset @ SY573 @ SV24 @ SV8 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV24 @ SY573 @ SV8 )
| ~ ( subset @ SY573 @ SV24 @ SV8 ) )
| ( qmltpeq @ SV24 @ SY573 @ SV8 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(104,plain,
! [SV9: $i,SV25: mu] :
( ( ~ ( exists_in_world @ SV25 @ SV9 )
| ! [SY574: mu] :
( ~ ( exists_in_world @ SY574 @ SV9 )
| ~ ( ~ ( ~ ( qmltpeq @ SV25 @ SY574 @ SV9 )
| ! [SY575: mu] :
( ~ ( exists_in_world @ SY575 @ SV9 )
| ~ ( ~ ( ~ ( member @ SY575 @ SV25 @ SV9 )
| ( member @ SY575 @ SY574 @ SV9 ) )
| ~ ( ~ ( member @ SY575 @ SY574 @ SV9 )
| ( member @ SY575 @ SV25 @ SV9 ) ) ) ) )
| ~ ( ~ ! [SY576: mu] :
( ~ ( exists_in_world @ SY576 @ SV9 )
| ~ ( ~ ( ~ ( member @ SY576 @ SV25 @ SV9 )
| ( member @ SY576 @ SY574 @ SV9 ) )
| ~ ( ~ ( member @ SY576 @ SY574 @ SV9 )
| ( member @ SY576 @ SV25 @ SV9 ) ) ) )
| ( qmltpeq @ SV25 @ SY574 @ SV9 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(105,plain,
! [SV10: $i,SV26: mu] :
( ( ~ ( exists_in_world @ SV26 @ SV10 )
| ! [SY577: mu] :
( ~ ( exists_in_world @ SY577 @ SV10 )
| ~ ( subset @ SV26 @ SY577 @ SV10 )
| ( qmltpeq @ ( union @ SV26 @ SY577 ) @ SY577 @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(106,plain,
! [SV11: $i,SV27: mu] :
( ( ~ ( exists_in_world @ SV27 @ SV11 )
| ! [SY578: mu] :
( ~ ( exists_in_world @ SY578 @ SV11 )
| ( qmltpeq @ ( union @ SV27 @ SY578 ) @ ( union @ SY578 @ SV27 ) @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(107,plain,
! [SV12: $i,SV28: mu] :
( ( ~ ( exists_in_world @ SV28 @ SV12 )
| ( subset @ SV28 @ SV28 @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(108,plain,
! [SV13: $i,SV29: mu] :
( ( ~ ( exists_in_world @ SV29 @ SV13 )
| ! [SY579: mu] :
( ~ ( exists_in_world @ SY579 @ SV13 )
| ! [SY580: mu] :
( ~ ( exists_in_world @ SY580 @ SV13 )
| ~ ~ ( ~ ( qmltpeq @ SV29 @ SY579 @ SV13 )
| ~ ( subset @ SY580 @ SV29 @ SV13 ) )
| ( subset @ SY580 @ SY579 @ SV13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(109,plain,
! [SV14: $i,SV30: mu] :
( ( ~ ( exists_in_world @ SV30 @ SV14 )
| ! [SY581: mu] :
( ~ ( exists_in_world @ SY581 @ SV14 )
| ! [SY582: mu] :
( ~ ( exists_in_world @ SY582 @ SV14 )
| ~ ~ ( ~ ( qmltpeq @ SV30 @ SY581 @ SV14 )
| ~ ( member @ SV30 @ SY582 @ SV14 ) )
| ( member @ SY581 @ SY582 @ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(110,plain,
! [SV15: $i,SV31: mu] :
( ( ~ ( exists_in_world @ SV31 @ SV15 )
| ! [SY583: mu] :
( ~ ( exists_in_world @ SY583 @ SV15 )
| ! [SY584: mu] :
( ~ ( exists_in_world @ SY584 @ SV15 )
| ~ ~ ( ~ ( qmltpeq @ SV31 @ SY583 @ SV15 )
| ~ ( qmltpeq @ SY583 @ SY584 @ SV15 ) )
| ( qmltpeq @ SV31 @ SY584 @ SV15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(111,plain,
! [SV16: $i,SV32: mu] :
( ( ~ ( exists_in_world @ SV32 @ SV16 )
| ! [SY585: mu] :
( ~ ( exists_in_world @ SY585 @ SV16 )
| ! [SY586: mu] :
( ~ ( exists_in_world @ SY586 @ SV16 )
| ~ ( qmltpeq @ SV32 @ SY585 @ SV16 )
| ( qmltpeq @ ( union @ SV32 @ SY586 ) @ ( union @ SY585 @ SY586 ) @ SV16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(112,plain,
! [SV1: $i,SV33: mu,SV17: mu] :
( ( exists_in_world @ ( union @ SV17 @ SV33 ) @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(113,plain,
! [SV2: $i,SV18: mu] :
( ( ( ~ ( exists_in_world @ SV18 @ SV2 ) )
= $true )
| ( ( ! [SY564: mu] :
( ~ ( exists_in_world @ SY564 @ SV2 )
| ! [SY565: mu] :
( ~ ( exists_in_world @ SY565 @ SV2 )
| ~ ( qmltpeq @ SV18 @ SY564 @ SV2 )
| ( qmltpeq @ ( union @ SY565 @ SV18 ) @ ( union @ SY565 @ SY564 ) @ SV2 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[97]) ).
thf(114,plain,
! [SV3: $i,SV19: mu] :
( ( ( ~ ( exists_in_world @ SV19 @ SV3 ) )
= $true )
| ( ( ! [SY566: mu] :
( ~ ( exists_in_world @ SY566 @ SV3 )
| ! [SY567: mu] :
( ~ ( exists_in_world @ SY567 @ SV3 )
| ~ ( ~ ( ~ ( member @ SY567 @ ( union @ SV19 @ SY566 ) @ SV3 )
| ( member @ SY567 @ SV19 @ SV3 )
| ( member @ SY567 @ SY566 @ SV3 ) )
| ~ ( ~ ( ( member @ SY567 @ SV19 @ SV3 )
| ( member @ SY567 @ SY566 @ SV3 ) )
| ( member @ SY567 @ ( union @ SV19 @ SY566 ) @ SV3 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[98]) ).
thf(115,plain,
! [SV4: $i,SV20: mu] :
( ( ( ~ ( exists_in_world @ SV20 @ SV4 ) )
= $true )
| ( ( qmltpeq @ SV20 @ SV20 @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[99]) ).
thf(116,plain,
! [SV5: $i,SV21: mu] :
( ( ( ~ ( exists_in_world @ SV21 @ SV5 ) )
= $true )
| ( ( ! [SY568: mu] :
( ~ ( exists_in_world @ SY568 @ SV5 )
| ! [SY569: mu] :
( ~ ( exists_in_world @ SY569 @ SV5 )
| ~ ~ ( ~ ( qmltpeq @ SV21 @ SY568 @ SV5 )
| ~ ( member @ SY569 @ SV21 @ SV5 ) )
| ( member @ SY569 @ SY568 @ SV5 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[100]) ).
thf(117,plain,
! [SV6: $i,SV22: mu] :
( ( ( ~ ( exists_in_world @ SV22 @ SV6 ) )
= $true )
| ( ( ! [SY570: mu] :
( ~ ( exists_in_world @ SY570 @ SV6 )
| ! [SY571: mu] :
( ~ ( exists_in_world @ SY571 @ SV6 )
| ~ ~ ( ~ ( qmltpeq @ SV22 @ SY570 @ SV6 )
| ~ ( subset @ SV22 @ SY571 @ SV6 ) )
| ( subset @ SY570 @ SY571 @ SV6 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[101]) ).
thf(118,plain,
! [SV7: $i,SV23: mu] :
( ( ( ~ ( exists_in_world @ SV23 @ SV7 ) )
= $true )
| ( ( ! [SY572: mu] :
( ~ ( exists_in_world @ SY572 @ SV7 )
| ~ ( qmltpeq @ SV23 @ SY572 @ SV7 )
| ( qmltpeq @ SY572 @ SV23 @ SV7 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[102]) ).
thf(119,plain,
! [SV8: $i,SV24: mu] :
( ( ( ~ ( exists_in_world @ SV24 @ SV8 ) )
= $true )
| ( ( ! [SY573: mu] :
( ~ ( exists_in_world @ SY573 @ SV8 )
| ~ ( ~ ( ~ ( qmltpeq @ SV24 @ SY573 @ SV8 )
| ~ ( ~ ( subset @ SV24 @ SY573 @ SV8 )
| ~ ( subset @ SY573 @ SV24 @ SV8 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV24 @ SY573 @ SV8 )
| ~ ( subset @ SY573 @ SV24 @ SV8 ) )
| ( qmltpeq @ SV24 @ SY573 @ SV8 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[103]) ).
thf(120,plain,
! [SV9: $i,SV25: mu] :
( ( ( ~ ( exists_in_world @ SV25 @ SV9 ) )
= $true )
| ( ( ! [SY574: mu] :
( ~ ( exists_in_world @ SY574 @ SV9 )
| ~ ( ~ ( ~ ( qmltpeq @ SV25 @ SY574 @ SV9 )
| ! [SY575: mu] :
( ~ ( exists_in_world @ SY575 @ SV9 )
| ~ ( ~ ( ~ ( member @ SY575 @ SV25 @ SV9 )
| ( member @ SY575 @ SY574 @ SV9 ) )
| ~ ( ~ ( member @ SY575 @ SY574 @ SV9 )
| ( member @ SY575 @ SV25 @ SV9 ) ) ) ) )
| ~ ( ~ ! [SY576: mu] :
( ~ ( exists_in_world @ SY576 @ SV9 )
| ~ ( ~ ( ~ ( member @ SY576 @ SV25 @ SV9 )
| ( member @ SY576 @ SY574 @ SV9 ) )
| ~ ( ~ ( member @ SY576 @ SY574 @ SV9 )
| ( member @ SY576 @ SV25 @ SV9 ) ) ) )
| ( qmltpeq @ SV25 @ SY574 @ SV9 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[104]) ).
thf(121,plain,
! [SV10: $i,SV26: mu] :
( ( ( ~ ( exists_in_world @ SV26 @ SV10 ) )
= $true )
| ( ( ! [SY577: mu] :
( ~ ( exists_in_world @ SY577 @ SV10 )
| ~ ( subset @ SV26 @ SY577 @ SV10 )
| ( qmltpeq @ ( union @ SV26 @ SY577 ) @ SY577 @ SV10 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[105]) ).
thf(122,plain,
! [SV11: $i,SV27: mu] :
( ( ( ~ ( exists_in_world @ SV27 @ SV11 ) )
= $true )
| ( ( ! [SY578: mu] :
( ~ ( exists_in_world @ SY578 @ SV11 )
| ( qmltpeq @ ( union @ SV27 @ SY578 ) @ ( union @ SY578 @ SV27 ) @ SV11 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[106]) ).
thf(123,plain,
! [SV12: $i,SV28: mu] :
( ( ( ~ ( exists_in_world @ SV28 @ SV12 ) )
= $true )
| ( ( subset @ SV28 @ SV28 @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[107]) ).
thf(124,plain,
! [SV13: $i,SV29: mu] :
( ( ( ~ ( exists_in_world @ SV29 @ SV13 ) )
= $true )
| ( ( ! [SY579: mu] :
( ~ ( exists_in_world @ SY579 @ SV13 )
| ! [SY580: mu] :
( ~ ( exists_in_world @ SY580 @ SV13 )
| ~ ~ ( ~ ( qmltpeq @ SV29 @ SY579 @ SV13 )
| ~ ( subset @ SY580 @ SV29 @ SV13 ) )
| ( subset @ SY580 @ SY579 @ SV13 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[108]) ).
thf(125,plain,
! [SV14: $i,SV30: mu] :
( ( ( ~ ( exists_in_world @ SV30 @ SV14 ) )
= $true )
| ( ( ! [SY581: mu] :
( ~ ( exists_in_world @ SY581 @ SV14 )
| ! [SY582: mu] :
( ~ ( exists_in_world @ SY582 @ SV14 )
| ~ ~ ( ~ ( qmltpeq @ SV30 @ SY581 @ SV14 )
| ~ ( member @ SV30 @ SY582 @ SV14 ) )
| ( member @ SY581 @ SY582 @ SV14 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[109]) ).
thf(126,plain,
! [SV15: $i,SV31: mu] :
( ( ( ~ ( exists_in_world @ SV31 @ SV15 ) )
= $true )
| ( ( ! [SY583: mu] :
( ~ ( exists_in_world @ SY583 @ SV15 )
| ! [SY584: mu] :
( ~ ( exists_in_world @ SY584 @ SV15 )
| ~ ~ ( ~ ( qmltpeq @ SV31 @ SY583 @ SV15 )
| ~ ( qmltpeq @ SY583 @ SY584 @ SV15 ) )
| ( qmltpeq @ SV31 @ SY584 @ SV15 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[110]) ).
thf(127,plain,
! [SV16: $i,SV32: mu] :
( ( ( ~ ( exists_in_world @ SV32 @ SV16 ) )
= $true )
| ( ( ! [SY585: mu] :
( ~ ( exists_in_world @ SY585 @ SV16 )
| ! [SY586: mu] :
( ~ ( exists_in_world @ SY586 @ SV16 )
| ~ ( qmltpeq @ SV32 @ SY585 @ SV16 )
| ( qmltpeq @ ( union @ SV32 @ SY586 ) @ ( union @ SY585 @ SY586 ) @ SV16 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[111]) ).
thf(128,plain,
! [SV2: $i,SV18: mu] :
( ( ( exists_in_world @ SV18 @ SV2 )
= $false )
| ( ( ! [SY564: mu] :
( ~ ( exists_in_world @ SY564 @ SV2 )
| ! [SY565: mu] :
( ~ ( exists_in_world @ SY565 @ SV2 )
| ~ ( qmltpeq @ SV18 @ SY564 @ SV2 )
| ( qmltpeq @ ( union @ SY565 @ SV18 ) @ ( union @ SY565 @ SY564 ) @ SV2 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(129,plain,
! [SV3: $i,SV19: mu] :
( ( ( exists_in_world @ SV19 @ SV3 )
= $false )
| ( ( ! [SY566: mu] :
( ~ ( exists_in_world @ SY566 @ SV3 )
| ! [SY567: mu] :
( ~ ( exists_in_world @ SY567 @ SV3 )
| ~ ( ~ ( ~ ( member @ SY567 @ ( union @ SV19 @ SY566 ) @ SV3 )
| ( member @ SY567 @ SV19 @ SV3 )
| ( member @ SY567 @ SY566 @ SV3 ) )
| ~ ( ~ ( ( member @ SY567 @ SV19 @ SV3 )
| ( member @ SY567 @ SY566 @ SV3 ) )
| ( member @ SY567 @ ( union @ SV19 @ SY566 ) @ SV3 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[114]) ).
thf(130,plain,
! [SV4: $i,SV20: mu] :
( ( ( exists_in_world @ SV20 @ SV4 )
= $false )
| ( ( qmltpeq @ SV20 @ SV20 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(131,plain,
! [SV5: $i,SV21: mu] :
( ( ( exists_in_world @ SV21 @ SV5 )
= $false )
| ( ( ! [SY568: mu] :
( ~ ( exists_in_world @ SY568 @ SV5 )
| ! [SY569: mu] :
( ~ ( exists_in_world @ SY569 @ SV5 )
| ~ ~ ( ~ ( qmltpeq @ SV21 @ SY568 @ SV5 )
| ~ ( member @ SY569 @ SV21 @ SV5 ) )
| ( member @ SY569 @ SY568 @ SV5 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(132,plain,
! [SV6: $i,SV22: mu] :
( ( ( exists_in_world @ SV22 @ SV6 )
= $false )
| ( ( ! [SY570: mu] :
( ~ ( exists_in_world @ SY570 @ SV6 )
| ! [SY571: mu] :
( ~ ( exists_in_world @ SY571 @ SV6 )
| ~ ~ ( ~ ( qmltpeq @ SV22 @ SY570 @ SV6 )
| ~ ( subset @ SV22 @ SY571 @ SV6 ) )
| ( subset @ SY570 @ SY571 @ SV6 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(133,plain,
! [SV7: $i,SV23: mu] :
( ( ( exists_in_world @ SV23 @ SV7 )
= $false )
| ( ( ! [SY572: mu] :
( ~ ( exists_in_world @ SY572 @ SV7 )
| ~ ( qmltpeq @ SV23 @ SY572 @ SV7 )
| ( qmltpeq @ SY572 @ SV23 @ SV7 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(134,plain,
! [SV8: $i,SV24: mu] :
( ( ( exists_in_world @ SV24 @ SV8 )
= $false )
| ( ( ! [SY573: mu] :
( ~ ( exists_in_world @ SY573 @ SV8 )
| ~ ( ~ ( ~ ( qmltpeq @ SV24 @ SY573 @ SV8 )
| ~ ( ~ ( subset @ SV24 @ SY573 @ SV8 )
| ~ ( subset @ SY573 @ SV24 @ SV8 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV24 @ SY573 @ SV8 )
| ~ ( subset @ SY573 @ SV24 @ SV8 ) )
| ( qmltpeq @ SV24 @ SY573 @ SV8 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(135,plain,
! [SV9: $i,SV25: mu] :
( ( ( exists_in_world @ SV25 @ SV9 )
= $false )
| ( ( ! [SY574: mu] :
( ~ ( exists_in_world @ SY574 @ SV9 )
| ~ ( ~ ( ~ ( qmltpeq @ SV25 @ SY574 @ SV9 )
| ! [SY575: mu] :
( ~ ( exists_in_world @ SY575 @ SV9 )
| ~ ( ~ ( ~ ( member @ SY575 @ SV25 @ SV9 )
| ( member @ SY575 @ SY574 @ SV9 ) )
| ~ ( ~ ( member @ SY575 @ SY574 @ SV9 )
| ( member @ SY575 @ SV25 @ SV9 ) ) ) ) )
| ~ ( ~ ! [SY576: mu] :
( ~ ( exists_in_world @ SY576 @ SV9 )
| ~ ( ~ ( ~ ( member @ SY576 @ SV25 @ SV9 )
| ( member @ SY576 @ SY574 @ SV9 ) )
| ~ ( ~ ( member @ SY576 @ SY574 @ SV9 )
| ( member @ SY576 @ SV25 @ SV9 ) ) ) )
| ( qmltpeq @ SV25 @ SY574 @ SV9 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(136,plain,
! [SV10: $i,SV26: mu] :
( ( ( exists_in_world @ SV26 @ SV10 )
= $false )
| ( ( ! [SY577: mu] :
( ~ ( exists_in_world @ SY577 @ SV10 )
| ~ ( subset @ SV26 @ SY577 @ SV10 )
| ( qmltpeq @ ( union @ SV26 @ SY577 ) @ SY577 @ SV10 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[121]) ).
thf(137,plain,
! [SV11: $i,SV27: mu] :
( ( ( exists_in_world @ SV27 @ SV11 )
= $false )
| ( ( ! [SY578: mu] :
( ~ ( exists_in_world @ SY578 @ SV11 )
| ( qmltpeq @ ( union @ SV27 @ SY578 ) @ ( union @ SY578 @ SV27 ) @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(138,plain,
! [SV12: $i,SV28: mu] :
( ( ( exists_in_world @ SV28 @ SV12 )
= $false )
| ( ( subset @ SV28 @ SV28 @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(139,plain,
! [SV13: $i,SV29: mu] :
( ( ( exists_in_world @ SV29 @ SV13 )
= $false )
| ( ( ! [SY579: mu] :
( ~ ( exists_in_world @ SY579 @ SV13 )
| ! [SY580: mu] :
( ~ ( exists_in_world @ SY580 @ SV13 )
| ~ ~ ( ~ ( qmltpeq @ SV29 @ SY579 @ SV13 )
| ~ ( subset @ SY580 @ SV29 @ SV13 ) )
| ( subset @ SY580 @ SY579 @ SV13 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(140,plain,
! [SV14: $i,SV30: mu] :
( ( ( exists_in_world @ SV30 @ SV14 )
= $false )
| ( ( ! [SY581: mu] :
( ~ ( exists_in_world @ SY581 @ SV14 )
| ! [SY582: mu] :
( ~ ( exists_in_world @ SY582 @ SV14 )
| ~ ~ ( ~ ( qmltpeq @ SV30 @ SY581 @ SV14 )
| ~ ( member @ SV30 @ SY582 @ SV14 ) )
| ( member @ SY581 @ SY582 @ SV14 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(141,plain,
! [SV15: $i,SV31: mu] :
( ( ( exists_in_world @ SV31 @ SV15 )
= $false )
| ( ( ! [SY583: mu] :
( ~ ( exists_in_world @ SY583 @ SV15 )
| ! [SY584: mu] :
( ~ ( exists_in_world @ SY584 @ SV15 )
| ~ ~ ( ~ ( qmltpeq @ SV31 @ SY583 @ SV15 )
| ~ ( qmltpeq @ SY583 @ SY584 @ SV15 ) )
| ( qmltpeq @ SV31 @ SY584 @ SV15 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[126]) ).
thf(142,plain,
! [SV16: $i,SV32: mu] :
( ( ( exists_in_world @ SV32 @ SV16 )
= $false )
| ( ( ! [SY585: mu] :
( ~ ( exists_in_world @ SY585 @ SV16 )
| ! [SY586: mu] :
( ~ ( exists_in_world @ SY586 @ SV16 )
| ~ ( qmltpeq @ SV32 @ SY585 @ SV16 )
| ( qmltpeq @ ( union @ SV32 @ SY586 ) @ ( union @ SY585 @ SY586 ) @ SV16 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[127]) ).
thf(143,plain,
! [SV18: mu,SV2: $i,SV34: mu] :
( ( ( ~ ( exists_in_world @ SV34 @ SV2 )
| ! [SY587: mu] :
( ~ ( exists_in_world @ SY587 @ SV2 )
| ~ ( qmltpeq @ SV18 @ SV34 @ SV2 )
| ( qmltpeq @ ( union @ SY587 @ SV18 ) @ ( union @ SY587 @ SV34 ) @ SV2 ) ) )
= $true )
| ( ( exists_in_world @ SV18 @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(144,plain,
! [SV19: mu,SV3: $i,SV35: mu] :
( ( ( ~ ( exists_in_world @ SV35 @ SV3 )
| ! [SY588: mu] :
( ~ ( exists_in_world @ SY588 @ SV3 )
| ~ ( ~ ( ~ ( member @ SY588 @ ( union @ SV19 @ SV35 ) @ SV3 )
| ( member @ SY588 @ SV19 @ SV3 )
| ( member @ SY588 @ SV35 @ SV3 ) )
| ~ ( ~ ( ( member @ SY588 @ SV19 @ SV3 )
| ( member @ SY588 @ SV35 @ SV3 ) )
| ( member @ SY588 @ ( union @ SV19 @ SV35 ) @ SV3 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV19 @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(145,plain,
! [SV21: mu,SV5: $i,SV36: mu] :
( ( ( ~ ( exists_in_world @ SV36 @ SV5 )
| ! [SY589: mu] :
( ~ ( exists_in_world @ SY589 @ SV5 )
| ~ ~ ( ~ ( qmltpeq @ SV21 @ SV36 @ SV5 )
| ~ ( member @ SY589 @ SV21 @ SV5 ) )
| ( member @ SY589 @ SV36 @ SV5 ) ) )
= $true )
| ( ( exists_in_world @ SV21 @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(146,plain,
! [SV22: mu,SV6: $i,SV37: mu] :
( ( ( ~ ( exists_in_world @ SV37 @ SV6 )
| ! [SY590: mu] :
( ~ ( exists_in_world @ SY590 @ SV6 )
| ~ ~ ( ~ ( qmltpeq @ SV22 @ SV37 @ SV6 )
| ~ ( subset @ SV22 @ SY590 @ SV6 ) )
| ( subset @ SV37 @ SY590 @ SV6 ) ) )
= $true )
| ( ( exists_in_world @ SV22 @ SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(147,plain,
! [SV23: mu,SV7: $i,SV38: mu] :
( ( ( ~ ( exists_in_world @ SV38 @ SV7 )
| ~ ( qmltpeq @ SV23 @ SV38 @ SV7 )
| ( qmltpeq @ SV38 @ SV23 @ SV7 ) )
= $true )
| ( ( exists_in_world @ SV23 @ SV7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(148,plain,
! [SV24: mu,SV8: $i,SV39: mu] :
( ( ( ~ ( exists_in_world @ SV39 @ SV8 )
| ~ ( ~ ( ~ ( qmltpeq @ SV24 @ SV39 @ SV8 )
| ~ ( ~ ( subset @ SV24 @ SV39 @ SV8 )
| ~ ( subset @ SV39 @ SV24 @ SV8 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV24 @ SV39 @ SV8 )
| ~ ( subset @ SV39 @ SV24 @ SV8 ) )
| ( qmltpeq @ SV24 @ SV39 @ SV8 ) ) ) )
= $true )
| ( ( exists_in_world @ SV24 @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(149,plain,
! [SV25: mu,SV9: $i,SV40: mu] :
( ( ( ~ ( exists_in_world @ SV40 @ SV9 )
| ~ ( ~ ( ~ ( qmltpeq @ SV25 @ SV40 @ SV9 )
| ! [SY591: mu] :
( ~ ( exists_in_world @ SY591 @ SV9 )
| ~ ( ~ ( ~ ( member @ SY591 @ SV25 @ SV9 )
| ( member @ SY591 @ SV40 @ SV9 ) )
| ~ ( ~ ( member @ SY591 @ SV40 @ SV9 )
| ( member @ SY591 @ SV25 @ SV9 ) ) ) ) )
| ~ ( ~ ! [SY592: mu] :
( ~ ( exists_in_world @ SY592 @ SV9 )
| ~ ( ~ ( ~ ( member @ SY592 @ SV25 @ SV9 )
| ( member @ SY592 @ SV40 @ SV9 ) )
| ~ ( ~ ( member @ SY592 @ SV40 @ SV9 )
| ( member @ SY592 @ SV25 @ SV9 ) ) ) )
| ( qmltpeq @ SV25 @ SV40 @ SV9 ) ) ) )
= $true )
| ( ( exists_in_world @ SV25 @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(150,plain,
! [SV26: mu,SV10: $i,SV41: mu] :
( ( ( ~ ( exists_in_world @ SV41 @ SV10 )
| ~ ( subset @ SV26 @ SV41 @ SV10 )
| ( qmltpeq @ ( union @ SV26 @ SV41 ) @ SV41 @ SV10 ) )
= $true )
| ( ( exists_in_world @ SV26 @ SV10 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(151,plain,
! [SV27: mu,SV11: $i,SV42: mu] :
( ( ( ~ ( exists_in_world @ SV42 @ SV11 )
| ( qmltpeq @ ( union @ SV27 @ SV42 ) @ ( union @ SV42 @ SV27 ) @ SV11 ) )
= $true )
| ( ( exists_in_world @ SV27 @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(152,plain,
! [SV29: mu,SV13: $i,SV43: mu] :
( ( ( ~ ( exists_in_world @ SV43 @ SV13 )
| ! [SY593: mu] :
( ~ ( exists_in_world @ SY593 @ SV13 )
| ~ ~ ( ~ ( qmltpeq @ SV29 @ SV43 @ SV13 )
| ~ ( subset @ SY593 @ SV29 @ SV13 ) )
| ( subset @ SY593 @ SV43 @ SV13 ) ) )
= $true )
| ( ( exists_in_world @ SV29 @ SV13 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(153,plain,
! [SV30: mu,SV14: $i,SV44: mu] :
( ( ( ~ ( exists_in_world @ SV44 @ SV14 )
| ! [SY594: mu] :
( ~ ( exists_in_world @ SY594 @ SV14 )
| ~ ~ ( ~ ( qmltpeq @ SV30 @ SV44 @ SV14 )
| ~ ( member @ SV30 @ SY594 @ SV14 ) )
| ( member @ SV44 @ SY594 @ SV14 ) ) )
= $true )
| ( ( exists_in_world @ SV30 @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(154,plain,
! [SV31: mu,SV15: $i,SV45: mu] :
( ( ( ~ ( exists_in_world @ SV45 @ SV15 )
| ! [SY595: mu] :
( ~ ( exists_in_world @ SY595 @ SV15 )
| ~ ~ ( ~ ( qmltpeq @ SV31 @ SV45 @ SV15 )
| ~ ( qmltpeq @ SV45 @ SY595 @ SV15 ) )
| ( qmltpeq @ SV31 @ SY595 @ SV15 ) ) )
= $true )
| ( ( exists_in_world @ SV31 @ SV15 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(155,plain,
! [SV32: mu,SV16: $i,SV46: mu] :
( ( ( ~ ( exists_in_world @ SV46 @ SV16 )
| ! [SY596: mu] :
( ~ ( exists_in_world @ SY596 @ SV16 )
| ~ ( qmltpeq @ SV32 @ SV46 @ SV16 )
| ( qmltpeq @ ( union @ SV32 @ SY596 ) @ ( union @ SV46 @ SY596 ) @ SV16 ) ) )
= $true )
| ( ( exists_in_world @ SV32 @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(156,plain,
! [SV18: mu,SV2: $i,SV34: mu] :
( ( ( ~ ( exists_in_world @ SV34 @ SV2 ) )
= $true )
| ( ( ! [SY587: mu] :
( ~ ( exists_in_world @ SY587 @ SV2 )
| ~ ( qmltpeq @ SV18 @ SV34 @ SV2 )
| ( qmltpeq @ ( union @ SY587 @ SV18 ) @ ( union @ SY587 @ SV34 ) @ SV2 ) ) )
= $true )
| ( ( exists_in_world @ SV18 @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[143]) ).
thf(157,plain,
! [SV19: mu,SV3: $i,SV35: mu] :
( ( ( ~ ( exists_in_world @ SV35 @ SV3 ) )
= $true )
| ( ( ! [SY588: mu] :
( ~ ( exists_in_world @ SY588 @ SV3 )
| ~ ( ~ ( ~ ( member @ SY588 @ ( union @ SV19 @ SV35 ) @ SV3 )
| ( member @ SY588 @ SV19 @ SV3 )
| ( member @ SY588 @ SV35 @ SV3 ) )
| ~ ( ~ ( ( member @ SY588 @ SV19 @ SV3 )
| ( member @ SY588 @ SV35 @ SV3 ) )
| ( member @ SY588 @ ( union @ SV19 @ SV35 ) @ SV3 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV19 @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[144]) ).
thf(158,plain,
! [SV21: mu,SV5: $i,SV36: mu] :
( ( ( ~ ( exists_in_world @ SV36 @ SV5 ) )
= $true )
| ( ( ! [SY589: mu] :
( ~ ( exists_in_world @ SY589 @ SV5 )
| ~ ~ ( ~ ( qmltpeq @ SV21 @ SV36 @ SV5 )
| ~ ( member @ SY589 @ SV21 @ SV5 ) )
| ( member @ SY589 @ SV36 @ SV5 ) ) )
= $true )
| ( ( exists_in_world @ SV21 @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[145]) ).
thf(159,plain,
! [SV22: mu,SV6: $i,SV37: mu] :
( ( ( ~ ( exists_in_world @ SV37 @ SV6 ) )
= $true )
| ( ( ! [SY590: mu] :
( ~ ( exists_in_world @ SY590 @ SV6 )
| ~ ~ ( ~ ( qmltpeq @ SV22 @ SV37 @ SV6 )
| ~ ( subset @ SV22 @ SY590 @ SV6 ) )
| ( subset @ SV37 @ SY590 @ SV6 ) ) )
= $true )
| ( ( exists_in_world @ SV22 @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[146]) ).
thf(160,plain,
! [SV23: mu,SV7: $i,SV38: mu] :
( ( ( ~ ( exists_in_world @ SV38 @ SV7 ) )
= $true )
| ( ( ~ ( qmltpeq @ SV23 @ SV38 @ SV7 )
| ( qmltpeq @ SV38 @ SV23 @ SV7 ) )
= $true )
| ( ( exists_in_world @ SV23 @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[147]) ).
thf(161,plain,
! [SV24: mu,SV8: $i,SV39: mu] :
( ( ( ~ ( exists_in_world @ SV39 @ SV8 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( qmltpeq @ SV24 @ SV39 @ SV8 )
| ~ ( ~ ( subset @ SV24 @ SV39 @ SV8 )
| ~ ( subset @ SV39 @ SV24 @ SV8 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV24 @ SV39 @ SV8 )
| ~ ( subset @ SV39 @ SV24 @ SV8 ) )
| ( qmltpeq @ SV24 @ SV39 @ SV8 ) ) ) )
= $true )
| ( ( exists_in_world @ SV24 @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[148]) ).
thf(162,plain,
! [SV25: mu,SV9: $i,SV40: mu] :
( ( ( ~ ( exists_in_world @ SV40 @ SV9 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( qmltpeq @ SV25 @ SV40 @ SV9 )
| ! [SY591: mu] :
( ~ ( exists_in_world @ SY591 @ SV9 )
| ~ ( ~ ( ~ ( member @ SY591 @ SV25 @ SV9 )
| ( member @ SY591 @ SV40 @ SV9 ) )
| ~ ( ~ ( member @ SY591 @ SV40 @ SV9 )
| ( member @ SY591 @ SV25 @ SV9 ) ) ) ) )
| ~ ( ~ ! [SY592: mu] :
( ~ ( exists_in_world @ SY592 @ SV9 )
| ~ ( ~ ( ~ ( member @ SY592 @ SV25 @ SV9 )
| ( member @ SY592 @ SV40 @ SV9 ) )
| ~ ( ~ ( member @ SY592 @ SV40 @ SV9 )
| ( member @ SY592 @ SV25 @ SV9 ) ) ) )
| ( qmltpeq @ SV25 @ SV40 @ SV9 ) ) ) )
= $true )
| ( ( exists_in_world @ SV25 @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[149]) ).
thf(163,plain,
! [SV26: mu,SV10: $i,SV41: mu] :
( ( ( ~ ( exists_in_world @ SV41 @ SV10 ) )
= $true )
| ( ( ~ ( subset @ SV26 @ SV41 @ SV10 )
| ( qmltpeq @ ( union @ SV26 @ SV41 ) @ SV41 @ SV10 ) )
= $true )
| ( ( exists_in_world @ SV26 @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[150]) ).
thf(164,plain,
! [SV27: mu,SV11: $i,SV42: mu] :
( ( ( ~ ( exists_in_world @ SV42 @ SV11 ) )
= $true )
| ( ( qmltpeq @ ( union @ SV27 @ SV42 ) @ ( union @ SV42 @ SV27 ) @ SV11 )
= $true )
| ( ( exists_in_world @ SV27 @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[151]) ).
thf(165,plain,
! [SV29: mu,SV13: $i,SV43: mu] :
( ( ( ~ ( exists_in_world @ SV43 @ SV13 ) )
= $true )
| ( ( ! [SY593: mu] :
( ~ ( exists_in_world @ SY593 @ SV13 )
| ~ ~ ( ~ ( qmltpeq @ SV29 @ SV43 @ SV13 )
| ~ ( subset @ SY593 @ SV29 @ SV13 ) )
| ( subset @ SY593 @ SV43 @ SV13 ) ) )
= $true )
| ( ( exists_in_world @ SV29 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[152]) ).
thf(166,plain,
! [SV30: mu,SV14: $i,SV44: mu] :
( ( ( ~ ( exists_in_world @ SV44 @ SV14 ) )
= $true )
| ( ( ! [SY594: mu] :
( ~ ( exists_in_world @ SY594 @ SV14 )
| ~ ~ ( ~ ( qmltpeq @ SV30 @ SV44 @ SV14 )
| ~ ( member @ SV30 @ SY594 @ SV14 ) )
| ( member @ SV44 @ SY594 @ SV14 ) ) )
= $true )
| ( ( exists_in_world @ SV30 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[153]) ).
thf(167,plain,
! [SV31: mu,SV15: $i,SV45: mu] :
( ( ( ~ ( exists_in_world @ SV45 @ SV15 ) )
= $true )
| ( ( ! [SY595: mu] :
( ~ ( exists_in_world @ SY595 @ SV15 )
| ~ ~ ( ~ ( qmltpeq @ SV31 @ SV45 @ SV15 )
| ~ ( qmltpeq @ SV45 @ SY595 @ SV15 ) )
| ( qmltpeq @ SV31 @ SY595 @ SV15 ) ) )
= $true )
| ( ( exists_in_world @ SV31 @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[154]) ).
thf(168,plain,
! [SV32: mu,SV16: $i,SV46: mu] :
( ( ( ~ ( exists_in_world @ SV46 @ SV16 ) )
= $true )
| ( ( ! [SY596: mu] :
( ~ ( exists_in_world @ SY596 @ SV16 )
| ~ ( qmltpeq @ SV32 @ SV46 @ SV16 )
| ( qmltpeq @ ( union @ SV32 @ SY596 ) @ ( union @ SV46 @ SY596 ) @ SV16 ) ) )
= $true )
| ( ( exists_in_world @ SV32 @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[155]) ).
thf(169,plain,
! [SV18: mu,SV2: $i,SV34: mu] :
( ( ( exists_in_world @ SV34 @ SV2 )
= $false )
| ( ( ! [SY587: mu] :
( ~ ( exists_in_world @ SY587 @ SV2 )
| ~ ( qmltpeq @ SV18 @ SV34 @ SV2 )
| ( qmltpeq @ ( union @ SY587 @ SV18 ) @ ( union @ SY587 @ SV34 ) @ SV2 ) ) )
= $true )
| ( ( exists_in_world @ SV18 @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(170,plain,
! [SV19: mu,SV3: $i,SV35: mu] :
( ( ( exists_in_world @ SV35 @ SV3 )
= $false )
| ( ( ! [SY588: mu] :
( ~ ( exists_in_world @ SY588 @ SV3 )
| ~ ( ~ ( ~ ( member @ SY588 @ ( union @ SV19 @ SV35 ) @ SV3 )
| ( member @ SY588 @ SV19 @ SV3 )
| ( member @ SY588 @ SV35 @ SV3 ) )
| ~ ( ~ ( ( member @ SY588 @ SV19 @ SV3 )
| ( member @ SY588 @ SV35 @ SV3 ) )
| ( member @ SY588 @ ( union @ SV19 @ SV35 ) @ SV3 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV19 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[157]) ).
thf(171,plain,
! [SV21: mu,SV5: $i,SV36: mu] :
( ( ( exists_in_world @ SV36 @ SV5 )
= $false )
| ( ( ! [SY589: mu] :
( ~ ( exists_in_world @ SY589 @ SV5 )
| ~ ~ ( ~ ( qmltpeq @ SV21 @ SV36 @ SV5 )
| ~ ( member @ SY589 @ SV21 @ SV5 ) )
| ( member @ SY589 @ SV36 @ SV5 ) ) )
= $true )
| ( ( exists_in_world @ SV21 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[158]) ).
thf(172,plain,
! [SV22: mu,SV6: $i,SV37: mu] :
( ( ( exists_in_world @ SV37 @ SV6 )
= $false )
| ( ( ! [SY590: mu] :
( ~ ( exists_in_world @ SY590 @ SV6 )
| ~ ~ ( ~ ( qmltpeq @ SV22 @ SV37 @ SV6 )
| ~ ( subset @ SV22 @ SY590 @ SV6 ) )
| ( subset @ SV37 @ SY590 @ SV6 ) ) )
= $true )
| ( ( exists_in_world @ SV22 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(173,plain,
! [SV23: mu,SV7: $i,SV38: mu] :
( ( ( exists_in_world @ SV38 @ SV7 )
= $false )
| ( ( ~ ( qmltpeq @ SV23 @ SV38 @ SV7 )
| ( qmltpeq @ SV38 @ SV23 @ SV7 ) )
= $true )
| ( ( exists_in_world @ SV23 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(174,plain,
! [SV24: mu,SV8: $i,SV39: mu] :
( ( ( exists_in_world @ SV39 @ SV8 )
= $false )
| ( ( ~ ( ~ ( ~ ( qmltpeq @ SV24 @ SV39 @ SV8 )
| ~ ( ~ ( subset @ SV24 @ SV39 @ SV8 )
| ~ ( subset @ SV39 @ SV24 @ SV8 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV24 @ SV39 @ SV8 )
| ~ ( subset @ SV39 @ SV24 @ SV8 ) )
| ( qmltpeq @ SV24 @ SV39 @ SV8 ) ) ) )
= $true )
| ( ( exists_in_world @ SV24 @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[161]) ).
thf(175,plain,
! [SV25: mu,SV9: $i,SV40: mu] :
( ( ( exists_in_world @ SV40 @ SV9 )
= $false )
| ( ( ~ ( ~ ( ~ ( qmltpeq @ SV25 @ SV40 @ SV9 )
| ! [SY591: mu] :
( ~ ( exists_in_world @ SY591 @ SV9 )
| ~ ( ~ ( ~ ( member @ SY591 @ SV25 @ SV9 )
| ( member @ SY591 @ SV40 @ SV9 ) )
| ~ ( ~ ( member @ SY591 @ SV40 @ SV9 )
| ( member @ SY591 @ SV25 @ SV9 ) ) ) ) )
| ~ ( ~ ! [SY592: mu] :
( ~ ( exists_in_world @ SY592 @ SV9 )
| ~ ( ~ ( ~ ( member @ SY592 @ SV25 @ SV9 )
| ( member @ SY592 @ SV40 @ SV9 ) )
| ~ ( ~ ( member @ SY592 @ SV40 @ SV9 )
| ( member @ SY592 @ SV25 @ SV9 ) ) ) )
| ( qmltpeq @ SV25 @ SV40 @ SV9 ) ) ) )
= $true )
| ( ( exists_in_world @ SV25 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(176,plain,
! [SV26: mu,SV10: $i,SV41: mu] :
( ( ( exists_in_world @ SV41 @ SV10 )
= $false )
| ( ( ~ ( subset @ SV26 @ SV41 @ SV10 )
| ( qmltpeq @ ( union @ SV26 @ SV41 ) @ SV41 @ SV10 ) )
= $true )
| ( ( exists_in_world @ SV26 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[163]) ).
thf(177,plain,
! [SV27: mu,SV11: $i,SV42: mu] :
( ( ( exists_in_world @ SV42 @ SV11 )
= $false )
| ( ( qmltpeq @ ( union @ SV27 @ SV42 ) @ ( union @ SV42 @ SV27 ) @ SV11 )
= $true )
| ( ( exists_in_world @ SV27 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(178,plain,
! [SV29: mu,SV13: $i,SV43: mu] :
( ( ( exists_in_world @ SV43 @ SV13 )
= $false )
| ( ( ! [SY593: mu] :
( ~ ( exists_in_world @ SY593 @ SV13 )
| ~ ~ ( ~ ( qmltpeq @ SV29 @ SV43 @ SV13 )
| ~ ( subset @ SY593 @ SV29 @ SV13 ) )
| ( subset @ SY593 @ SV43 @ SV13 ) ) )
= $true )
| ( ( exists_in_world @ SV29 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[165]) ).
thf(179,plain,
! [SV30: mu,SV14: $i,SV44: mu] :
( ( ( exists_in_world @ SV44 @ SV14 )
= $false )
| ( ( ! [SY594: mu] :
( ~ ( exists_in_world @ SY594 @ SV14 )
| ~ ~ ( ~ ( qmltpeq @ SV30 @ SV44 @ SV14 )
| ~ ( member @ SV30 @ SY594 @ SV14 ) )
| ( member @ SV44 @ SY594 @ SV14 ) ) )
= $true )
| ( ( exists_in_world @ SV30 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(180,plain,
! [SV31: mu,SV15: $i,SV45: mu] :
( ( ( exists_in_world @ SV45 @ SV15 )
= $false )
| ( ( ! [SY595: mu] :
( ~ ( exists_in_world @ SY595 @ SV15 )
| ~ ~ ( ~ ( qmltpeq @ SV31 @ SV45 @ SV15 )
| ~ ( qmltpeq @ SV45 @ SY595 @ SV15 ) )
| ( qmltpeq @ SV31 @ SY595 @ SV15 ) ) )
= $true )
| ( ( exists_in_world @ SV31 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(181,plain,
! [SV32: mu,SV16: $i,SV46: mu] :
( ( ( exists_in_world @ SV46 @ SV16 )
= $false )
| ( ( ! [SY596: mu] :
( ~ ( exists_in_world @ SY596 @ SV16 )
| ~ ( qmltpeq @ SV32 @ SV46 @ SV16 )
| ( qmltpeq @ ( union @ SV32 @ SY596 ) @ ( union @ SV46 @ SY596 ) @ SV16 ) ) )
= $true )
| ( ( exists_in_world @ SV32 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[168]) ).
thf(182,plain,
! [SV34: mu,SV18: mu,SV2: $i,SV47: mu] :
( ( ( ~ ( exists_in_world @ SV47 @ SV2 )
| ~ ( qmltpeq @ SV18 @ SV34 @ SV2 )
| ( qmltpeq @ ( union @ SV47 @ SV18 ) @ ( union @ SV47 @ SV34 ) @ SV2 ) )
= $true )
| ( ( exists_in_world @ SV34 @ SV2 )
= $false )
| ( ( exists_in_world @ SV18 @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[169]) ).
thf(183,plain,
! [SV35: mu,SV19: mu,SV3: $i,SV48: mu] :
( ( ( ~ ( exists_in_world @ SV48 @ SV3 )
| ~ ( ~ ( ~ ( member @ SV48 @ ( union @ SV19 @ SV35 ) @ SV3 )
| ( member @ SV48 @ SV19 @ SV3 )
| ( member @ SV48 @ SV35 @ SV3 ) )
| ~ ( ~ ( ( member @ SV48 @ SV19 @ SV3 )
| ( member @ SV48 @ SV35 @ SV3 ) )
| ( member @ SV48 @ ( union @ SV19 @ SV35 ) @ SV3 ) ) ) )
= $true )
| ( ( exists_in_world @ SV35 @ SV3 )
= $false )
| ( ( exists_in_world @ SV19 @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(184,plain,
! [SV36: mu,SV21: mu,SV5: $i,SV49: mu] :
( ( ( ~ ( exists_in_world @ SV49 @ SV5 )
| ~ ~ ( ~ ( qmltpeq @ SV21 @ SV36 @ SV5 )
| ~ ( member @ SV49 @ SV21 @ SV5 ) )
| ( member @ SV49 @ SV36 @ SV5 ) )
= $true )
| ( ( exists_in_world @ SV36 @ SV5 )
= $false )
| ( ( exists_in_world @ SV21 @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(185,plain,
! [SV37: mu,SV22: mu,SV6: $i,SV50: mu] :
( ( ( ~ ( exists_in_world @ SV50 @ SV6 )
| ~ ~ ( ~ ( qmltpeq @ SV22 @ SV37 @ SV6 )
| ~ ( subset @ SV22 @ SV50 @ SV6 ) )
| ( subset @ SV37 @ SV50 @ SV6 ) )
= $true )
| ( ( exists_in_world @ SV37 @ SV6 )
= $false )
| ( ( exists_in_world @ SV22 @ SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(186,plain,
! [SV7: $i,SV38: mu,SV23: mu] :
( ( ( ~ ( qmltpeq @ SV23 @ SV38 @ SV7 ) )
= $true )
| ( ( qmltpeq @ SV38 @ SV23 @ SV7 )
= $true )
| ( ( exists_in_world @ SV38 @ SV7 )
= $false )
| ( ( exists_in_world @ SV23 @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[173]) ).
thf(187,plain,
! [SV8: $i,SV39: mu,SV24: mu] :
( ( ( ~ ( ~ ( qmltpeq @ SV24 @ SV39 @ SV8 )
| ~ ( ~ ( subset @ SV24 @ SV39 @ SV8 )
| ~ ( subset @ SV39 @ SV24 @ SV8 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV24 @ SV39 @ SV8 )
| ~ ( subset @ SV39 @ SV24 @ SV8 ) )
| ( qmltpeq @ SV24 @ SV39 @ SV8 ) ) )
= $false )
| ( ( exists_in_world @ SV39 @ SV8 )
= $false )
| ( ( exists_in_world @ SV24 @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[174]) ).
thf(188,plain,
! [SV9: $i,SV40: mu,SV25: mu] :
( ( ( ~ ( ~ ( qmltpeq @ SV25 @ SV40 @ SV9 )
| ! [SY591: mu] :
( ~ ( exists_in_world @ SY591 @ SV9 )
| ~ ( ~ ( ~ ( member @ SY591 @ SV25 @ SV9 )
| ( member @ SY591 @ SV40 @ SV9 ) )
| ~ ( ~ ( member @ SY591 @ SV40 @ SV9 )
| ( member @ SY591 @ SV25 @ SV9 ) ) ) ) )
| ~ ( ~ ! [SY592: mu] :
( ~ ( exists_in_world @ SY592 @ SV9 )
| ~ ( ~ ( ~ ( member @ SY592 @ SV25 @ SV9 )
| ( member @ SY592 @ SV40 @ SV9 ) )
| ~ ( ~ ( member @ SY592 @ SV40 @ SV9 )
| ( member @ SY592 @ SV25 @ SV9 ) ) ) )
| ( qmltpeq @ SV25 @ SV40 @ SV9 ) ) )
= $false )
| ( ( exists_in_world @ SV40 @ SV9 )
= $false )
| ( ( exists_in_world @ SV25 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[175]) ).
thf(189,plain,
! [SV10: $i,SV41: mu,SV26: mu] :
( ( ( ~ ( subset @ SV26 @ SV41 @ SV10 ) )
= $true )
| ( ( qmltpeq @ ( union @ SV26 @ SV41 ) @ SV41 @ SV10 )
= $true )
| ( ( exists_in_world @ SV41 @ SV10 )
= $false )
| ( ( exists_in_world @ SV26 @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[176]) ).
thf(190,plain,
! [SV43: mu,SV29: mu,SV13: $i,SV51: mu] :
( ( ( ~ ( exists_in_world @ SV51 @ SV13 )
| ~ ~ ( ~ ( qmltpeq @ SV29 @ SV43 @ SV13 )
| ~ ( subset @ SV51 @ SV29 @ SV13 ) )
| ( subset @ SV51 @ SV43 @ SV13 ) )
= $true )
| ( ( exists_in_world @ SV43 @ SV13 )
= $false )
| ( ( exists_in_world @ SV29 @ SV13 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(191,plain,
! [SV44: mu,SV30: mu,SV14: $i,SV52: mu] :
( ( ( ~ ( exists_in_world @ SV52 @ SV14 )
| ~ ~ ( ~ ( qmltpeq @ SV30 @ SV44 @ SV14 )
| ~ ( member @ SV30 @ SV52 @ SV14 ) )
| ( member @ SV44 @ SV52 @ SV14 ) )
= $true )
| ( ( exists_in_world @ SV44 @ SV14 )
= $false )
| ( ( exists_in_world @ SV30 @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(192,plain,
! [SV45: mu,SV31: mu,SV15: $i,SV53: mu] :
( ( ( ~ ( exists_in_world @ SV53 @ SV15 )
| ~ ~ ( ~ ( qmltpeq @ SV31 @ SV45 @ SV15 )
| ~ ( qmltpeq @ SV45 @ SV53 @ SV15 ) )
| ( qmltpeq @ SV31 @ SV53 @ SV15 ) )
= $true )
| ( ( exists_in_world @ SV45 @ SV15 )
= $false )
| ( ( exists_in_world @ SV31 @ SV15 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(193,plain,
! [SV46: mu,SV32: mu,SV16: $i,SV54: mu] :
( ( ( ~ ( exists_in_world @ SV54 @ SV16 )
| ~ ( qmltpeq @ SV32 @ SV46 @ SV16 )
| ( qmltpeq @ ( union @ SV32 @ SV54 ) @ ( union @ SV46 @ SV54 ) @ SV16 ) )
= $true )
| ( ( exists_in_world @ SV46 @ SV16 )
= $false )
| ( ( exists_in_world @ SV32 @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(194,plain,
! [SV34: mu,SV18: mu,SV2: $i,SV47: mu] :
( ( ( ~ ( exists_in_world @ SV47 @ SV2 ) )
= $true )
| ( ( ~ ( qmltpeq @ SV18 @ SV34 @ SV2 )
| ( qmltpeq @ ( union @ SV47 @ SV18 ) @ ( union @ SV47 @ SV34 ) @ SV2 ) )
= $true )
| ( ( exists_in_world @ SV34 @ SV2 )
= $false )
| ( ( exists_in_world @ SV18 @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[182]) ).
thf(195,plain,
! [SV35: mu,SV19: mu,SV3: $i,SV48: mu] :
( ( ( ~ ( exists_in_world @ SV48 @ SV3 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( member @ SV48 @ ( union @ SV19 @ SV35 ) @ SV3 )
| ( member @ SV48 @ SV19 @ SV3 )
| ( member @ SV48 @ SV35 @ SV3 ) )
| ~ ( ~ ( ( member @ SV48 @ SV19 @ SV3 )
| ( member @ SV48 @ SV35 @ SV3 ) )
| ( member @ SV48 @ ( union @ SV19 @ SV35 ) @ SV3 ) ) ) )
= $true )
| ( ( exists_in_world @ SV35 @ SV3 )
= $false )
| ( ( exists_in_world @ SV19 @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[183]) ).
thf(196,plain,
! [SV36: mu,SV21: mu,SV5: $i,SV49: mu] :
( ( ( ~ ( exists_in_world @ SV49 @ SV5 ) )
= $true )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV21 @ SV36 @ SV5 )
| ~ ( member @ SV49 @ SV21 @ SV5 ) )
| ( member @ SV49 @ SV36 @ SV5 ) )
= $true )
| ( ( exists_in_world @ SV36 @ SV5 )
= $false )
| ( ( exists_in_world @ SV21 @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[184]) ).
thf(197,plain,
! [SV37: mu,SV22: mu,SV6: $i,SV50: mu] :
( ( ( ~ ( exists_in_world @ SV50 @ SV6 ) )
= $true )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV22 @ SV37 @ SV6 )
| ~ ( subset @ SV22 @ SV50 @ SV6 ) )
| ( subset @ SV37 @ SV50 @ SV6 ) )
= $true )
| ( ( exists_in_world @ SV37 @ SV6 )
= $false )
| ( ( exists_in_world @ SV22 @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[185]) ).
thf(198,plain,
! [SV7: $i,SV38: mu,SV23: mu] :
( ( ( qmltpeq @ SV23 @ SV38 @ SV7 )
= $false )
| ( ( qmltpeq @ SV38 @ SV23 @ SV7 )
= $true )
| ( ( exists_in_world @ SV38 @ SV7 )
= $false )
| ( ( exists_in_world @ SV23 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[186]) ).
thf(199,plain,
! [SV8: $i,SV39: mu,SV24: mu] :
( ( ( ~ ( ~ ( qmltpeq @ SV24 @ SV39 @ SV8 )
| ~ ( ~ ( subset @ SV24 @ SV39 @ SV8 )
| ~ ( subset @ SV39 @ SV24 @ SV8 ) ) ) )
= $false )
| ( ( exists_in_world @ SV39 @ SV8 )
= $false )
| ( ( exists_in_world @ SV24 @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[187]) ).
thf(200,plain,
! [SV8: $i,SV39: mu,SV24: mu] :
( ( ( ~ ( ~ ~ ( ~ ( subset @ SV24 @ SV39 @ SV8 )
| ~ ( subset @ SV39 @ SV24 @ SV8 ) )
| ( qmltpeq @ SV24 @ SV39 @ SV8 ) ) )
= $false )
| ( ( exists_in_world @ SV39 @ SV8 )
= $false )
| ( ( exists_in_world @ SV24 @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[187]) ).
thf(201,plain,
! [SV9: $i,SV40: mu,SV25: mu] :
( ( ( ~ ( ~ ( qmltpeq @ SV25 @ SV40 @ SV9 )
| ! [SY591: mu] :
( ~ ( exists_in_world @ SY591 @ SV9 )
| ~ ( ~ ( ~ ( member @ SY591 @ SV25 @ SV9 )
| ( member @ SY591 @ SV40 @ SV9 ) )
| ~ ( ~ ( member @ SY591 @ SV40 @ SV9 )
| ( member @ SY591 @ SV25 @ SV9 ) ) ) ) ) )
= $false )
| ( ( exists_in_world @ SV40 @ SV9 )
= $false )
| ( ( exists_in_world @ SV25 @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[188]) ).
thf(202,plain,
! [SV40: mu,SV25: mu,SV9: $i] :
( ( ( ~ ( ~ ! [SY592: mu] :
( ~ ( exists_in_world @ SY592 @ SV9 )
| ~ ( ~ ( ~ ( member @ SY592 @ SV25 @ SV9 )
| ( member @ SY592 @ SV40 @ SV9 ) )
| ~ ( ~ ( member @ SY592 @ SV40 @ SV9 )
| ( member @ SY592 @ SV25 @ SV9 ) ) ) )
| ( qmltpeq @ SV25 @ SV40 @ SV9 ) ) )
= $false )
| ( ( exists_in_world @ SV40 @ SV9 )
= $false )
| ( ( exists_in_world @ SV25 @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[188]) ).
thf(203,plain,
! [SV10: $i,SV41: mu,SV26: mu] :
( ( ( subset @ SV26 @ SV41 @ SV10 )
= $false )
| ( ( qmltpeq @ ( union @ SV26 @ SV41 ) @ SV41 @ SV10 )
= $true )
| ( ( exists_in_world @ SV41 @ SV10 )
= $false )
| ( ( exists_in_world @ SV26 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[189]) ).
thf(204,plain,
! [SV43: mu,SV29: mu,SV13: $i,SV51: mu] :
( ( ( ~ ( exists_in_world @ SV51 @ SV13 ) )
= $true )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV29 @ SV43 @ SV13 )
| ~ ( subset @ SV51 @ SV29 @ SV13 ) )
| ( subset @ SV51 @ SV43 @ SV13 ) )
= $true )
| ( ( exists_in_world @ SV43 @ SV13 )
= $false )
| ( ( exists_in_world @ SV29 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[190]) ).
thf(205,plain,
! [SV44: mu,SV30: mu,SV14: $i,SV52: mu] :
( ( ( ~ ( exists_in_world @ SV52 @ SV14 ) )
= $true )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV30 @ SV44 @ SV14 )
| ~ ( member @ SV30 @ SV52 @ SV14 ) )
| ( member @ SV44 @ SV52 @ SV14 ) )
= $true )
| ( ( exists_in_world @ SV44 @ SV14 )
= $false )
| ( ( exists_in_world @ SV30 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[191]) ).
thf(206,plain,
! [SV45: mu,SV31: mu,SV15: $i,SV53: mu] :
( ( ( ~ ( exists_in_world @ SV53 @ SV15 ) )
= $true )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV31 @ SV45 @ SV15 )
| ~ ( qmltpeq @ SV45 @ SV53 @ SV15 ) )
| ( qmltpeq @ SV31 @ SV53 @ SV15 ) )
= $true )
| ( ( exists_in_world @ SV45 @ SV15 )
= $false )
| ( ( exists_in_world @ SV31 @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[192]) ).
thf(207,plain,
! [SV46: mu,SV32: mu,SV16: $i,SV54: mu] :
( ( ( ~ ( exists_in_world @ SV54 @ SV16 ) )
= $true )
| ( ( ~ ( qmltpeq @ SV32 @ SV46 @ SV16 )
| ( qmltpeq @ ( union @ SV32 @ SV54 ) @ ( union @ SV46 @ SV54 ) @ SV16 ) )
= $true )
| ( ( exists_in_world @ SV46 @ SV16 )
= $false )
| ( ( exists_in_world @ SV32 @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[193]) ).
thf(208,plain,
! [SV34: mu,SV18: mu,SV2: $i,SV47: mu] :
( ( ( exists_in_world @ SV47 @ SV2 )
= $false )
| ( ( ~ ( qmltpeq @ SV18 @ SV34 @ SV2 )
| ( qmltpeq @ ( union @ SV47 @ SV18 ) @ ( union @ SV47 @ SV34 ) @ SV2 ) )
= $true )
| ( ( exists_in_world @ SV34 @ SV2 )
= $false )
| ( ( exists_in_world @ SV18 @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(209,plain,
! [SV35: mu,SV19: mu,SV3: $i,SV48: mu] :
( ( ( exists_in_world @ SV48 @ SV3 )
= $false )
| ( ( ~ ( ~ ( ~ ( member @ SV48 @ ( union @ SV19 @ SV35 ) @ SV3 )
| ( member @ SV48 @ SV19 @ SV3 )
| ( member @ SV48 @ SV35 @ SV3 ) )
| ~ ( ~ ( ( member @ SV48 @ SV19 @ SV3 )
| ( member @ SV48 @ SV35 @ SV3 ) )
| ( member @ SV48 @ ( union @ SV19 @ SV35 ) @ SV3 ) ) ) )
= $true )
| ( ( exists_in_world @ SV35 @ SV3 )
= $false )
| ( ( exists_in_world @ SV19 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(210,plain,
! [SV36: mu,SV21: mu,SV5: $i,SV49: mu] :
( ( ( exists_in_world @ SV49 @ SV5 )
= $false )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV21 @ SV36 @ SV5 )
| ~ ( member @ SV49 @ SV21 @ SV5 ) )
| ( member @ SV49 @ SV36 @ SV5 ) )
= $true )
| ( ( exists_in_world @ SV36 @ SV5 )
= $false )
| ( ( exists_in_world @ SV21 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(211,plain,
! [SV37: mu,SV22: mu,SV6: $i,SV50: mu] :
( ( ( exists_in_world @ SV50 @ SV6 )
= $false )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV22 @ SV37 @ SV6 )
| ~ ( subset @ SV22 @ SV50 @ SV6 ) )
| ( subset @ SV37 @ SV50 @ SV6 ) )
= $true )
| ( ( exists_in_world @ SV37 @ SV6 )
= $false )
| ( ( exists_in_world @ SV22 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[197]) ).
thf(212,plain,
! [SV8: $i,SV39: mu,SV24: mu] :
( ( ( ~ ( qmltpeq @ SV24 @ SV39 @ SV8 )
| ~ ( ~ ( subset @ SV24 @ SV39 @ SV8 )
| ~ ( subset @ SV39 @ SV24 @ SV8 ) ) )
= $true )
| ( ( exists_in_world @ SV39 @ SV8 )
= $false )
| ( ( exists_in_world @ SV24 @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[199]) ).
thf(213,plain,
! [SV8: $i,SV39: mu,SV24: mu] :
( ( ( ~ ~ ( ~ ( subset @ SV24 @ SV39 @ SV8 )
| ~ ( subset @ SV39 @ SV24 @ SV8 ) )
| ( qmltpeq @ SV24 @ SV39 @ SV8 ) )
= $true )
| ( ( exists_in_world @ SV39 @ SV8 )
= $false )
| ( ( exists_in_world @ SV24 @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[200]) ).
thf(214,plain,
! [SV9: $i,SV40: mu,SV25: mu] :
( ( ( ~ ( qmltpeq @ SV25 @ SV40 @ SV9 )
| ! [SY591: mu] :
( ~ ( exists_in_world @ SY591 @ SV9 )
| ~ ( ~ ( ~ ( member @ SY591 @ SV25 @ SV9 )
| ( member @ SY591 @ SV40 @ SV9 ) )
| ~ ( ~ ( member @ SY591 @ SV40 @ SV9 )
| ( member @ SY591 @ SV25 @ SV9 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV40 @ SV9 )
= $false )
| ( ( exists_in_world @ SV25 @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[201]) ).
thf(215,plain,
! [SV40: mu,SV25: mu,SV9: $i] :
( ( ( ~ ! [SY592: mu] :
( ~ ( exists_in_world @ SY592 @ SV9 )
| ~ ( ~ ( ~ ( member @ SY592 @ SV25 @ SV9 )
| ( member @ SY592 @ SV40 @ SV9 ) )
| ~ ( ~ ( member @ SY592 @ SV40 @ SV9 )
| ( member @ SY592 @ SV25 @ SV9 ) ) ) )
| ( qmltpeq @ SV25 @ SV40 @ SV9 ) )
= $true )
| ( ( exists_in_world @ SV40 @ SV9 )
= $false )
| ( ( exists_in_world @ SV25 @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[202]) ).
thf(216,plain,
! [SV43: mu,SV29: mu,SV13: $i,SV51: mu] :
( ( ( exists_in_world @ SV51 @ SV13 )
= $false )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV29 @ SV43 @ SV13 )
| ~ ( subset @ SV51 @ SV29 @ SV13 ) )
| ( subset @ SV51 @ SV43 @ SV13 ) )
= $true )
| ( ( exists_in_world @ SV43 @ SV13 )
= $false )
| ( ( exists_in_world @ SV29 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(217,plain,
! [SV44: mu,SV30: mu,SV14: $i,SV52: mu] :
( ( ( exists_in_world @ SV52 @ SV14 )
= $false )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV30 @ SV44 @ SV14 )
| ~ ( member @ SV30 @ SV52 @ SV14 ) )
| ( member @ SV44 @ SV52 @ SV14 ) )
= $true )
| ( ( exists_in_world @ SV44 @ SV14 )
= $false )
| ( ( exists_in_world @ SV30 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[205]) ).
thf(218,plain,
! [SV45: mu,SV31: mu,SV15: $i,SV53: mu] :
( ( ( exists_in_world @ SV53 @ SV15 )
= $false )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV31 @ SV45 @ SV15 )
| ~ ( qmltpeq @ SV45 @ SV53 @ SV15 ) )
| ( qmltpeq @ SV31 @ SV53 @ SV15 ) )
= $true )
| ( ( exists_in_world @ SV45 @ SV15 )
= $false )
| ( ( exists_in_world @ SV31 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[206]) ).
thf(219,plain,
! [SV46: mu,SV32: mu,SV16: $i,SV54: mu] :
( ( ( exists_in_world @ SV54 @ SV16 )
= $false )
| ( ( ~ ( qmltpeq @ SV32 @ SV46 @ SV16 )
| ( qmltpeq @ ( union @ SV32 @ SV54 ) @ ( union @ SV46 @ SV54 ) @ SV16 ) )
= $true )
| ( ( exists_in_world @ SV46 @ SV16 )
= $false )
| ( ( exists_in_world @ SV32 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[207]) ).
thf(220,plain,
! [SV47: mu,SV2: $i,SV34: mu,SV18: mu] :
( ( ( ~ ( qmltpeq @ SV18 @ SV34 @ SV2 ) )
= $true )
| ( ( qmltpeq @ ( union @ SV47 @ SV18 ) @ ( union @ SV47 @ SV34 ) @ SV2 )
= $true )
| ( ( exists_in_world @ SV47 @ SV2 )
= $false )
| ( ( exists_in_world @ SV34 @ SV2 )
= $false )
| ( ( exists_in_world @ SV18 @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[208]) ).
thf(221,plain,
! [SV3: $i,SV35: mu,SV19: mu,SV48: mu] :
( ( ( ~ ( ~ ( member @ SV48 @ ( union @ SV19 @ SV35 ) @ SV3 )
| ( member @ SV48 @ SV19 @ SV3 )
| ( member @ SV48 @ SV35 @ SV3 ) )
| ~ ( ~ ( ( member @ SV48 @ SV19 @ SV3 )
| ( member @ SV48 @ SV35 @ SV3 ) )
| ( member @ SV48 @ ( union @ SV19 @ SV35 ) @ SV3 ) ) )
= $false )
| ( ( exists_in_world @ SV48 @ SV3 )
= $false )
| ( ( exists_in_world @ SV35 @ SV3 )
= $false )
| ( ( exists_in_world @ SV19 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[209]) ).
thf(222,plain,
! [SV49: mu,SV5: $i,SV36: mu,SV21: mu] :
( ( ( ~ ~ ( ~ ( qmltpeq @ SV21 @ SV36 @ SV5 )
| ~ ( member @ SV49 @ SV21 @ SV5 ) ) )
= $true )
| ( ( member @ SV49 @ SV36 @ SV5 )
= $true )
| ( ( exists_in_world @ SV49 @ SV5 )
= $false )
| ( ( exists_in_world @ SV36 @ SV5 )
= $false )
| ( ( exists_in_world @ SV21 @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[210]) ).
thf(223,plain,
! [SV50: mu,SV6: $i,SV37: mu,SV22: mu] :
( ( ( ~ ~ ( ~ ( qmltpeq @ SV22 @ SV37 @ SV6 )
| ~ ( subset @ SV22 @ SV50 @ SV6 ) ) )
= $true )
| ( ( subset @ SV37 @ SV50 @ SV6 )
= $true )
| ( ( exists_in_world @ SV50 @ SV6 )
= $false )
| ( ( exists_in_world @ SV37 @ SV6 )
= $false )
| ( ( exists_in_world @ SV22 @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[211]) ).
thf(224,plain,
! [SV8: $i,SV39: mu,SV24: mu] :
( ( ( ~ ( qmltpeq @ SV24 @ SV39 @ SV8 ) )
= $true )
| ( ( ~ ( ~ ( subset @ SV24 @ SV39 @ SV8 )
| ~ ( subset @ SV39 @ SV24 @ SV8 ) ) )
= $true )
| ( ( exists_in_world @ SV39 @ SV8 )
= $false )
| ( ( exists_in_world @ SV24 @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[212]) ).
thf(225,plain,
! [SV8: $i,SV39: mu,SV24: mu] :
( ( ( ~ ~ ( ~ ( subset @ SV24 @ SV39 @ SV8 )
| ~ ( subset @ SV39 @ SV24 @ SV8 ) ) )
= $true )
| ( ( qmltpeq @ SV24 @ SV39 @ SV8 )
= $true )
| ( ( exists_in_world @ SV39 @ SV8 )
= $false )
| ( ( exists_in_world @ SV24 @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[213]) ).
thf(226,plain,
! [SV9: $i,SV40: mu,SV25: mu] :
( ( ( ~ ( qmltpeq @ SV25 @ SV40 @ SV9 ) )
= $true )
| ( ( ! [SY591: mu] :
( ~ ( exists_in_world @ SY591 @ SV9 )
| ~ ( ~ ( ~ ( member @ SY591 @ SV25 @ SV9 )
| ( member @ SY591 @ SV40 @ SV9 ) )
| ~ ( ~ ( member @ SY591 @ SV40 @ SV9 )
| ( member @ SY591 @ SV25 @ SV9 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV40 @ SV9 )
= $false )
| ( ( exists_in_world @ SV25 @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[214]) ).
thf(227,plain,
! [SV40: mu,SV25: mu,SV9: $i] :
( ( ( ~ ! [SY592: mu] :
( ~ ( exists_in_world @ SY592 @ SV9 )
| ~ ( ~ ( ~ ( member @ SY592 @ SV25 @ SV9 )
| ( member @ SY592 @ SV40 @ SV9 ) )
| ~ ( ~ ( member @ SY592 @ SV40 @ SV9 )
| ( member @ SY592 @ SV25 @ SV9 ) ) ) ) )
= $true )
| ( ( qmltpeq @ SV25 @ SV40 @ SV9 )
= $true )
| ( ( exists_in_world @ SV40 @ SV9 )
= $false )
| ( ( exists_in_world @ SV25 @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[215]) ).
thf(228,plain,
! [SV51: mu,SV13: $i,SV43: mu,SV29: mu] :
( ( ( ~ ~ ( ~ ( qmltpeq @ SV29 @ SV43 @ SV13 )
| ~ ( subset @ SV51 @ SV29 @ SV13 ) ) )
= $true )
| ( ( subset @ SV51 @ SV43 @ SV13 )
= $true )
| ( ( exists_in_world @ SV51 @ SV13 )
= $false )
| ( ( exists_in_world @ SV43 @ SV13 )
= $false )
| ( ( exists_in_world @ SV29 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[216]) ).
thf(229,plain,
! [SV52: mu,SV14: $i,SV44: mu,SV30: mu] :
( ( ( ~ ~ ( ~ ( qmltpeq @ SV30 @ SV44 @ SV14 )
| ~ ( member @ SV30 @ SV52 @ SV14 ) ) )
= $true )
| ( ( member @ SV44 @ SV52 @ SV14 )
= $true )
| ( ( exists_in_world @ SV52 @ SV14 )
= $false )
| ( ( exists_in_world @ SV44 @ SV14 )
= $false )
| ( ( exists_in_world @ SV30 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[217]) ).
thf(230,plain,
! [SV53: mu,SV15: $i,SV45: mu,SV31: mu] :
( ( ( ~ ~ ( ~ ( qmltpeq @ SV31 @ SV45 @ SV15 )
| ~ ( qmltpeq @ SV45 @ SV53 @ SV15 ) ) )
= $true )
| ( ( qmltpeq @ SV31 @ SV53 @ SV15 )
= $true )
| ( ( exists_in_world @ SV53 @ SV15 )
= $false )
| ( ( exists_in_world @ SV45 @ SV15 )
= $false )
| ( ( exists_in_world @ SV31 @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[218]) ).
thf(231,plain,
! [SV54: mu,SV16: $i,SV46: mu,SV32: mu] :
( ( ( ~ ( qmltpeq @ SV32 @ SV46 @ SV16 ) )
= $true )
| ( ( qmltpeq @ ( union @ SV32 @ SV54 ) @ ( union @ SV46 @ SV54 ) @ SV16 )
= $true )
| ( ( exists_in_world @ SV54 @ SV16 )
= $false )
| ( ( exists_in_world @ SV46 @ SV16 )
= $false )
| ( ( exists_in_world @ SV32 @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[219]) ).
thf(232,plain,
! [SV47: mu,SV2: $i,SV34: mu,SV18: mu] :
( ( ( qmltpeq @ SV18 @ SV34 @ SV2 )
= $false )
| ( ( qmltpeq @ ( union @ SV47 @ SV18 ) @ ( union @ SV47 @ SV34 ) @ SV2 )
= $true )
| ( ( exists_in_world @ SV47 @ SV2 )
= $false )
| ( ( exists_in_world @ SV34 @ SV2 )
= $false )
| ( ( exists_in_world @ SV18 @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[220]) ).
thf(233,plain,
! [SV3: $i,SV35: mu,SV19: mu,SV48: mu] :
( ( ( ~ ( ~ ( member @ SV48 @ ( union @ SV19 @ SV35 ) @ SV3 )
| ( member @ SV48 @ SV19 @ SV3 )
| ( member @ SV48 @ SV35 @ SV3 ) ) )
= $false )
| ( ( exists_in_world @ SV48 @ SV3 )
= $false )
| ( ( exists_in_world @ SV35 @ SV3 )
= $false )
| ( ( exists_in_world @ SV19 @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[221]) ).
thf(234,plain,
! [SV35: mu,SV3: $i,SV19: mu,SV48: mu] :
( ( ( ~ ( ~ ( ( member @ SV48 @ SV19 @ SV3 )
| ( member @ SV48 @ SV35 @ SV3 ) )
| ( member @ SV48 @ ( union @ SV19 @ SV35 ) @ SV3 ) ) )
= $false )
| ( ( exists_in_world @ SV48 @ SV3 )
= $false )
| ( ( exists_in_world @ SV35 @ SV3 )
= $false )
| ( ( exists_in_world @ SV19 @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[221]) ).
thf(235,plain,
! [SV49: mu,SV5: $i,SV36: mu,SV21: mu] :
( ( ( ~ ( ~ ( qmltpeq @ SV21 @ SV36 @ SV5 )
| ~ ( member @ SV49 @ SV21 @ SV5 ) ) )
= $false )
| ( ( member @ SV49 @ SV36 @ SV5 )
= $true )
| ( ( exists_in_world @ SV49 @ SV5 )
= $false )
| ( ( exists_in_world @ SV36 @ SV5 )
= $false )
| ( ( exists_in_world @ SV21 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[222]) ).
thf(236,plain,
! [SV50: mu,SV6: $i,SV37: mu,SV22: mu] :
( ( ( ~ ( ~ ( qmltpeq @ SV22 @ SV37 @ SV6 )
| ~ ( subset @ SV22 @ SV50 @ SV6 ) ) )
= $false )
| ( ( subset @ SV37 @ SV50 @ SV6 )
= $true )
| ( ( exists_in_world @ SV50 @ SV6 )
= $false )
| ( ( exists_in_world @ SV37 @ SV6 )
= $false )
| ( ( exists_in_world @ SV22 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[223]) ).
thf(237,plain,
! [SV8: $i,SV39: mu,SV24: mu] :
( ( ( qmltpeq @ SV24 @ SV39 @ SV8 )
= $false )
| ( ( ~ ( ~ ( subset @ SV24 @ SV39 @ SV8 )
| ~ ( subset @ SV39 @ SV24 @ SV8 ) ) )
= $true )
| ( ( exists_in_world @ SV39 @ SV8 )
= $false )
| ( ( exists_in_world @ SV24 @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[224]) ).
thf(238,plain,
! [SV8: $i,SV39: mu,SV24: mu] :
( ( ( ~ ( ~ ( subset @ SV24 @ SV39 @ SV8 )
| ~ ( subset @ SV39 @ SV24 @ SV8 ) ) )
= $false )
| ( ( qmltpeq @ SV24 @ SV39 @ SV8 )
= $true )
| ( ( exists_in_world @ SV39 @ SV8 )
= $false )
| ( ( exists_in_world @ SV24 @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[225]) ).
thf(239,plain,
! [SV9: $i,SV40: mu,SV25: mu] :
( ( ( qmltpeq @ SV25 @ SV40 @ SV9 )
= $false )
| ( ( ! [SY591: mu] :
( ~ ( exists_in_world @ SY591 @ SV9 )
| ~ ( ~ ( ~ ( member @ SY591 @ SV25 @ SV9 )
| ( member @ SY591 @ SV40 @ SV9 ) )
| ~ ( ~ ( member @ SY591 @ SV40 @ SV9 )
| ( member @ SY591 @ SV25 @ SV9 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV40 @ SV9 )
= $false )
| ( ( exists_in_world @ SV25 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[226]) ).
thf(240,plain,
! [SV40: mu,SV25: mu,SV9: $i] :
( ( ( ! [SY592: mu] :
( ~ ( exists_in_world @ SY592 @ SV9 )
| ~ ( ~ ( ~ ( member @ SY592 @ SV25 @ SV9 )
| ( member @ SY592 @ SV40 @ SV9 ) )
| ~ ( ~ ( member @ SY592 @ SV40 @ SV9 )
| ( member @ SY592 @ SV25 @ SV9 ) ) ) ) )
= $false )
| ( ( qmltpeq @ SV25 @ SV40 @ SV9 )
= $true )
| ( ( exists_in_world @ SV40 @ SV9 )
= $false )
| ( ( exists_in_world @ SV25 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[227]) ).
thf(241,plain,
! [SV51: mu,SV13: $i,SV43: mu,SV29: mu] :
( ( ( ~ ( ~ ( qmltpeq @ SV29 @ SV43 @ SV13 )
| ~ ( subset @ SV51 @ SV29 @ SV13 ) ) )
= $false )
| ( ( subset @ SV51 @ SV43 @ SV13 )
= $true )
| ( ( exists_in_world @ SV51 @ SV13 )
= $false )
| ( ( exists_in_world @ SV43 @ SV13 )
= $false )
| ( ( exists_in_world @ SV29 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[228]) ).
thf(242,plain,
! [SV52: mu,SV14: $i,SV44: mu,SV30: mu] :
( ( ( ~ ( ~ ( qmltpeq @ SV30 @ SV44 @ SV14 )
| ~ ( member @ SV30 @ SV52 @ SV14 ) ) )
= $false )
| ( ( member @ SV44 @ SV52 @ SV14 )
= $true )
| ( ( exists_in_world @ SV52 @ SV14 )
= $false )
| ( ( exists_in_world @ SV44 @ SV14 )
= $false )
| ( ( exists_in_world @ SV30 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[229]) ).
thf(243,plain,
! [SV53: mu,SV15: $i,SV45: mu,SV31: mu] :
( ( ( ~ ( ~ ( qmltpeq @ SV31 @ SV45 @ SV15 )
| ~ ( qmltpeq @ SV45 @ SV53 @ SV15 ) ) )
= $false )
| ( ( qmltpeq @ SV31 @ SV53 @ SV15 )
= $true )
| ( ( exists_in_world @ SV53 @ SV15 )
= $false )
| ( ( exists_in_world @ SV45 @ SV15 )
= $false )
| ( ( exists_in_world @ SV31 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[230]) ).
thf(244,plain,
! [SV54: mu,SV16: $i,SV46: mu,SV32: mu] :
( ( ( qmltpeq @ SV32 @ SV46 @ SV16 )
= $false )
| ( ( qmltpeq @ ( union @ SV32 @ SV54 ) @ ( union @ SV46 @ SV54 ) @ SV16 )
= $true )
| ( ( exists_in_world @ SV54 @ SV16 )
= $false )
| ( ( exists_in_world @ SV46 @ SV16 )
= $false )
| ( ( exists_in_world @ SV32 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[231]) ).
thf(245,plain,
! [SV3: $i,SV35: mu,SV19: mu,SV48: mu] :
( ( ( ~ ( member @ SV48 @ ( union @ SV19 @ SV35 ) @ SV3 )
| ( member @ SV48 @ SV19 @ SV3 )
| ( member @ SV48 @ SV35 @ SV3 ) )
= $true )
| ( ( exists_in_world @ SV48 @ SV3 )
= $false )
| ( ( exists_in_world @ SV35 @ SV3 )
= $false )
| ( ( exists_in_world @ SV19 @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[233]) ).
thf(246,plain,
! [SV35: mu,SV3: $i,SV19: mu,SV48: mu] :
( ( ( ~ ( ( member @ SV48 @ SV19 @ SV3 )
| ( member @ SV48 @ SV35 @ SV3 ) )
| ( member @ SV48 @ ( union @ SV19 @ SV35 ) @ SV3 ) )
= $true )
| ( ( exists_in_world @ SV48 @ SV3 )
= $false )
| ( ( exists_in_world @ SV35 @ SV3 )
= $false )
| ( ( exists_in_world @ SV19 @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[234]) ).
thf(247,plain,
! [SV49: mu,SV5: $i,SV36: mu,SV21: mu] :
( ( ( ~ ( qmltpeq @ SV21 @ SV36 @ SV5 )
| ~ ( member @ SV49 @ SV21 @ SV5 ) )
= $true )
| ( ( member @ SV49 @ SV36 @ SV5 )
= $true )
| ( ( exists_in_world @ SV49 @ SV5 )
= $false )
| ( ( exists_in_world @ SV36 @ SV5 )
= $false )
| ( ( exists_in_world @ SV21 @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[235]) ).
thf(248,plain,
! [SV50: mu,SV6: $i,SV37: mu,SV22: mu] :
( ( ( ~ ( qmltpeq @ SV22 @ SV37 @ SV6 )
| ~ ( subset @ SV22 @ SV50 @ SV6 ) )
= $true )
| ( ( subset @ SV37 @ SV50 @ SV6 )
= $true )
| ( ( exists_in_world @ SV50 @ SV6 )
= $false )
| ( ( exists_in_world @ SV37 @ SV6 )
= $false )
| ( ( exists_in_world @ SV22 @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[236]) ).
thf(249,plain,
! [SV8: $i,SV39: mu,SV24: mu] :
( ( ( ~ ( subset @ SV24 @ SV39 @ SV8 )
| ~ ( subset @ SV39 @ SV24 @ SV8 ) )
= $false )
| ( ( qmltpeq @ SV24 @ SV39 @ SV8 )
= $false )
| ( ( exists_in_world @ SV39 @ SV8 )
= $false )
| ( ( exists_in_world @ SV24 @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[237]) ).
thf(250,plain,
! [SV8: $i,SV39: mu,SV24: mu] :
( ( ( ~ ( subset @ SV24 @ SV39 @ SV8 )
| ~ ( subset @ SV39 @ SV24 @ SV8 ) )
= $true )
| ( ( qmltpeq @ SV24 @ SV39 @ SV8 )
= $true )
| ( ( exists_in_world @ SV39 @ SV8 )
= $false )
| ( ( exists_in_world @ SV24 @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[238]) ).
thf(251,plain,
! [SV40: mu,SV25: mu,SV9: $i,SV55: mu] :
( ( ( ~ ( exists_in_world @ SV55 @ SV9 )
| ~ ( ~ ( ~ ( member @ SV55 @ SV25 @ SV9 )
| ( member @ SV55 @ SV40 @ SV9 ) )
| ~ ( ~ ( member @ SV55 @ SV40 @ SV9 )
| ( member @ SV55 @ SV25 @ SV9 ) ) ) )
= $true )
| ( ( qmltpeq @ SV25 @ SV40 @ SV9 )
= $false )
| ( ( exists_in_world @ SV40 @ SV9 )
= $false )
| ( ( exists_in_world @ SV25 @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[239]) ).
thf(252,plain,
! [SV9: $i,SV25: mu,SV40: mu] :
( ( ( ~ ( exists_in_world @ ( sK3_SY592 @ SV40 @ SV25 @ SV9 ) @ SV9 )
| ~ ( ~ ( ~ ( member @ ( sK3_SY592 @ SV40 @ SV25 @ SV9 ) @ SV25 @ SV9 )
| ( member @ ( sK3_SY592 @ SV40 @ SV25 @ SV9 ) @ SV40 @ SV9 ) )
| ~ ( ~ ( member @ ( sK3_SY592 @ SV40 @ SV25 @ SV9 ) @ SV40 @ SV9 )
| ( member @ ( sK3_SY592 @ SV40 @ SV25 @ SV9 ) @ SV25 @ SV9 ) ) ) )
= $false )
| ( ( qmltpeq @ SV25 @ SV40 @ SV9 )
= $true )
| ( ( exists_in_world @ SV40 @ SV9 )
= $false )
| ( ( exists_in_world @ SV25 @ SV9 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[240]) ).
thf(253,plain,
! [SV51: mu,SV13: $i,SV43: mu,SV29: mu] :
( ( ( ~ ( qmltpeq @ SV29 @ SV43 @ SV13 )
| ~ ( subset @ SV51 @ SV29 @ SV13 ) )
= $true )
| ( ( subset @ SV51 @ SV43 @ SV13 )
= $true )
| ( ( exists_in_world @ SV51 @ SV13 )
= $false )
| ( ( exists_in_world @ SV43 @ SV13 )
= $false )
| ( ( exists_in_world @ SV29 @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[241]) ).
thf(254,plain,
! [SV52: mu,SV14: $i,SV44: mu,SV30: mu] :
( ( ( ~ ( qmltpeq @ SV30 @ SV44 @ SV14 )
| ~ ( member @ SV30 @ SV52 @ SV14 ) )
= $true )
| ( ( member @ SV44 @ SV52 @ SV14 )
= $true )
| ( ( exists_in_world @ SV52 @ SV14 )
= $false )
| ( ( exists_in_world @ SV44 @ SV14 )
= $false )
| ( ( exists_in_world @ SV30 @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[242]) ).
thf(255,plain,
! [SV53: mu,SV15: $i,SV45: mu,SV31: mu] :
( ( ( ~ ( qmltpeq @ SV31 @ SV45 @ SV15 )
| ~ ( qmltpeq @ SV45 @ SV53 @ SV15 ) )
= $true )
| ( ( qmltpeq @ SV31 @ SV53 @ SV15 )
= $true )
| ( ( exists_in_world @ SV53 @ SV15 )
= $false )
| ( ( exists_in_world @ SV45 @ SV15 )
= $false )
| ( ( exists_in_world @ SV31 @ SV15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[243]) ).
thf(256,plain,
! [SV3: $i,SV35: mu,SV19: mu,SV48: mu] :
( ( ( ~ ( member @ SV48 @ ( union @ SV19 @ SV35 ) @ SV3 ) )
= $true )
| ( ( ( member @ SV48 @ SV19 @ SV3 )
| ( member @ SV48 @ SV35 @ SV3 ) )
= $true )
| ( ( exists_in_world @ SV48 @ SV3 )
= $false )
| ( ( exists_in_world @ SV35 @ SV3 )
= $false )
| ( ( exists_in_world @ SV19 @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[245]) ).
thf(257,plain,
! [SV35: mu,SV3: $i,SV19: mu,SV48: mu] :
( ( ( ~ ( ( member @ SV48 @ SV19 @ SV3 )
| ( member @ SV48 @ SV35 @ SV3 ) ) )
= $true )
| ( ( member @ SV48 @ ( union @ SV19 @ SV35 ) @ SV3 )
= $true )
| ( ( exists_in_world @ SV48 @ SV3 )
= $false )
| ( ( exists_in_world @ SV35 @ SV3 )
= $false )
| ( ( exists_in_world @ SV19 @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[246]) ).
thf(258,plain,
! [SV49: mu,SV5: $i,SV36: mu,SV21: mu] :
( ( ( ~ ( qmltpeq @ SV21 @ SV36 @ SV5 ) )
= $true )
| ( ( ~ ( member @ SV49 @ SV21 @ SV5 ) )
= $true )
| ( ( member @ SV49 @ SV36 @ SV5 )
= $true )
| ( ( exists_in_world @ SV49 @ SV5 )
= $false )
| ( ( exists_in_world @ SV36 @ SV5 )
= $false )
| ( ( exists_in_world @ SV21 @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[247]) ).
thf(259,plain,
! [SV50: mu,SV6: $i,SV37: mu,SV22: mu] :
( ( ( ~ ( qmltpeq @ SV22 @ SV37 @ SV6 ) )
= $true )
| ( ( ~ ( subset @ SV22 @ SV50 @ SV6 ) )
= $true )
| ( ( subset @ SV37 @ SV50 @ SV6 )
= $true )
| ( ( exists_in_world @ SV50 @ SV6 )
= $false )
| ( ( exists_in_world @ SV37 @ SV6 )
= $false )
| ( ( exists_in_world @ SV22 @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[248]) ).
thf(260,plain,
! [SV8: $i,SV39: mu,SV24: mu] :
( ( ( ~ ( subset @ SV24 @ SV39 @ SV8 ) )
= $false )
| ( ( qmltpeq @ SV24 @ SV39 @ SV8 )
= $false )
| ( ( exists_in_world @ SV39 @ SV8 )
= $false )
| ( ( exists_in_world @ SV24 @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[249]) ).
thf(261,plain,
! [SV8: $i,SV24: mu,SV39: mu] :
( ( ( ~ ( subset @ SV39 @ SV24 @ SV8 ) )
= $false )
| ( ( qmltpeq @ SV24 @ SV39 @ SV8 )
= $false )
| ( ( exists_in_world @ SV39 @ SV8 )
= $false )
| ( ( exists_in_world @ SV24 @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[249]) ).
thf(262,plain,
! [SV8: $i,SV39: mu,SV24: mu] :
( ( ( ~ ( subset @ SV24 @ SV39 @ SV8 ) )
= $true )
| ( ( ~ ( subset @ SV39 @ SV24 @ SV8 ) )
= $true )
| ( ( qmltpeq @ SV24 @ SV39 @ SV8 )
= $true )
| ( ( exists_in_world @ SV39 @ SV8 )
= $false )
| ( ( exists_in_world @ SV24 @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[250]) ).
thf(263,plain,
! [SV40: mu,SV25: mu,SV9: $i,SV55: mu] :
( ( ( ~ ( exists_in_world @ SV55 @ SV9 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( member @ SV55 @ SV25 @ SV9 )
| ( member @ SV55 @ SV40 @ SV9 ) )
| ~ ( ~ ( member @ SV55 @ SV40 @ SV9 )
| ( member @ SV55 @ SV25 @ SV9 ) ) ) )
= $true )
| ( ( qmltpeq @ SV25 @ SV40 @ SV9 )
= $false )
| ( ( exists_in_world @ SV40 @ SV9 )
= $false )
| ( ( exists_in_world @ SV25 @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[251]) ).
thf(264,plain,
! [SV9: $i,SV25: mu,SV40: mu] :
( ( ( ~ ( exists_in_world @ ( sK3_SY592 @ SV40 @ SV25 @ SV9 ) @ SV9 ) )
= $false )
| ( ( qmltpeq @ SV25 @ SV40 @ SV9 )
= $true )
| ( ( exists_in_world @ SV40 @ SV9 )
= $false )
| ( ( exists_in_world @ SV25 @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[252]) ).
thf(265,plain,
! [SV9: $i,SV25: mu,SV40: mu] :
( ( ( ~ ( ~ ( ~ ( member @ ( sK3_SY592 @ SV40 @ SV25 @ SV9 ) @ SV25 @ SV9 )
| ( member @ ( sK3_SY592 @ SV40 @ SV25 @ SV9 ) @ SV40 @ SV9 ) )
| ~ ( ~ ( member @ ( sK3_SY592 @ SV40 @ SV25 @ SV9 ) @ SV40 @ SV9 )
| ( member @ ( sK3_SY592 @ SV40 @ SV25 @ SV9 ) @ SV25 @ SV9 ) ) ) )
= $false )
| ( ( qmltpeq @ SV25 @ SV40 @ SV9 )
= $true )
| ( ( exists_in_world @ SV40 @ SV9 )
= $false )
| ( ( exists_in_world @ SV25 @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[252]) ).
thf(266,plain,
! [SV51: mu,SV13: $i,SV43: mu,SV29: mu] :
( ( ( ~ ( qmltpeq @ SV29 @ SV43 @ SV13 ) )
= $true )
| ( ( ~ ( subset @ SV51 @ SV29 @ SV13 ) )
= $true )
| ( ( subset @ SV51 @ SV43 @ SV13 )
= $true )
| ( ( exists_in_world @ SV51 @ SV13 )
= $false )
| ( ( exists_in_world @ SV43 @ SV13 )
= $false )
| ( ( exists_in_world @ SV29 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[253]) ).
thf(267,plain,
! [SV52: mu,SV14: $i,SV44: mu,SV30: mu] :
( ( ( ~ ( qmltpeq @ SV30 @ SV44 @ SV14 ) )
= $true )
| ( ( ~ ( member @ SV30 @ SV52 @ SV14 ) )
= $true )
| ( ( member @ SV44 @ SV52 @ SV14 )
= $true )
| ( ( exists_in_world @ SV52 @ SV14 )
= $false )
| ( ( exists_in_world @ SV44 @ SV14 )
= $false )
| ( ( exists_in_world @ SV30 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[254]) ).
thf(268,plain,
! [SV53: mu,SV15: $i,SV45: mu,SV31: mu] :
( ( ( ~ ( qmltpeq @ SV31 @ SV45 @ SV15 ) )
= $true )
| ( ( ~ ( qmltpeq @ SV45 @ SV53 @ SV15 ) )
= $true )
| ( ( qmltpeq @ SV31 @ SV53 @ SV15 )
= $true )
| ( ( exists_in_world @ SV53 @ SV15 )
= $false )
| ( ( exists_in_world @ SV45 @ SV15 )
= $false )
| ( ( exists_in_world @ SV31 @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[255]) ).
thf(269,plain,
! [SV3: $i,SV35: mu,SV19: mu,SV48: mu] :
( ( ( member @ SV48 @ ( union @ SV19 @ SV35 ) @ SV3 )
= $false )
| ( ( ( member @ SV48 @ SV19 @ SV3 )
| ( member @ SV48 @ SV35 @ SV3 ) )
= $true )
| ( ( exists_in_world @ SV48 @ SV3 )
= $false )
| ( ( exists_in_world @ SV35 @ SV3 )
= $false )
| ( ( exists_in_world @ SV19 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[256]) ).
thf(270,plain,
! [SV35: mu,SV3: $i,SV19: mu,SV48: mu] :
( ( ( ( member @ SV48 @ SV19 @ SV3 )
| ( member @ SV48 @ SV35 @ SV3 ) )
= $false )
| ( ( member @ SV48 @ ( union @ SV19 @ SV35 ) @ SV3 )
= $true )
| ( ( exists_in_world @ SV48 @ SV3 )
= $false )
| ( ( exists_in_world @ SV35 @ SV3 )
= $false )
| ( ( exists_in_world @ SV19 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[257]) ).
thf(271,plain,
! [SV49: mu,SV5: $i,SV36: mu,SV21: mu] :
( ( ( qmltpeq @ SV21 @ SV36 @ SV5 )
= $false )
| ( ( ~ ( member @ SV49 @ SV21 @ SV5 ) )
= $true )
| ( ( member @ SV49 @ SV36 @ SV5 )
= $true )
| ( ( exists_in_world @ SV49 @ SV5 )
= $false )
| ( ( exists_in_world @ SV36 @ SV5 )
= $false )
| ( ( exists_in_world @ SV21 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[258]) ).
thf(272,plain,
! [SV50: mu,SV6: $i,SV37: mu,SV22: mu] :
( ( ( qmltpeq @ SV22 @ SV37 @ SV6 )
= $false )
| ( ( ~ ( subset @ SV22 @ SV50 @ SV6 ) )
= $true )
| ( ( subset @ SV37 @ SV50 @ SV6 )
= $true )
| ( ( exists_in_world @ SV50 @ SV6 )
= $false )
| ( ( exists_in_world @ SV37 @ SV6 )
= $false )
| ( ( exists_in_world @ SV22 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[259]) ).
thf(273,plain,
! [SV8: $i,SV39: mu,SV24: mu] :
( ( ( subset @ SV24 @ SV39 @ SV8 )
= $true )
| ( ( qmltpeq @ SV24 @ SV39 @ SV8 )
= $false )
| ( ( exists_in_world @ SV39 @ SV8 )
= $false )
| ( ( exists_in_world @ SV24 @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[260]) ).
thf(274,plain,
! [SV8: $i,SV24: mu,SV39: mu] :
( ( ( subset @ SV39 @ SV24 @ SV8 )
= $true )
| ( ( qmltpeq @ SV24 @ SV39 @ SV8 )
= $false )
| ( ( exists_in_world @ SV39 @ SV8 )
= $false )
| ( ( exists_in_world @ SV24 @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[261]) ).
thf(275,plain,
! [SV8: $i,SV39: mu,SV24: mu] :
( ( ( subset @ SV24 @ SV39 @ SV8 )
= $false )
| ( ( ~ ( subset @ SV39 @ SV24 @ SV8 ) )
= $true )
| ( ( qmltpeq @ SV24 @ SV39 @ SV8 )
= $true )
| ( ( exists_in_world @ SV39 @ SV8 )
= $false )
| ( ( exists_in_world @ SV24 @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[262]) ).
thf(276,plain,
! [SV40: mu,SV25: mu,SV9: $i,SV55: mu] :
( ( ( exists_in_world @ SV55 @ SV9 )
= $false )
| ( ( ~ ( ~ ( ~ ( member @ SV55 @ SV25 @ SV9 )
| ( member @ SV55 @ SV40 @ SV9 ) )
| ~ ( ~ ( member @ SV55 @ SV40 @ SV9 )
| ( member @ SV55 @ SV25 @ SV9 ) ) ) )
= $true )
| ( ( qmltpeq @ SV25 @ SV40 @ SV9 )
= $false )
| ( ( exists_in_world @ SV40 @ SV9 )
= $false )
| ( ( exists_in_world @ SV25 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[263]) ).
thf(277,plain,
! [SV9: $i,SV25: mu,SV40: mu] :
( ( ( exists_in_world @ ( sK3_SY592 @ SV40 @ SV25 @ SV9 ) @ SV9 )
= $true )
| ( ( qmltpeq @ SV25 @ SV40 @ SV9 )
= $true )
| ( ( exists_in_world @ SV40 @ SV9 )
= $false )
| ( ( exists_in_world @ SV25 @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[264]) ).
thf(278,plain,
! [SV9: $i,SV25: mu,SV40: mu] :
( ( ( ~ ( ~ ( member @ ( sK3_SY592 @ SV40 @ SV25 @ SV9 ) @ SV25 @ SV9 )
| ( member @ ( sK3_SY592 @ SV40 @ SV25 @ SV9 ) @ SV40 @ SV9 ) )
| ~ ( ~ ( member @ ( sK3_SY592 @ SV40 @ SV25 @ SV9 ) @ SV40 @ SV9 )
| ( member @ ( sK3_SY592 @ SV40 @ SV25 @ SV9 ) @ SV25 @ SV9 ) ) )
= $true )
| ( ( qmltpeq @ SV25 @ SV40 @ SV9 )
= $true )
| ( ( exists_in_world @ SV40 @ SV9 )
= $false )
| ( ( exists_in_world @ SV25 @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[265]) ).
thf(279,plain,
! [SV51: mu,SV13: $i,SV43: mu,SV29: mu] :
( ( ( qmltpeq @ SV29 @ SV43 @ SV13 )
= $false )
| ( ( ~ ( subset @ SV51 @ SV29 @ SV13 ) )
= $true )
| ( ( subset @ SV51 @ SV43 @ SV13 )
= $true )
| ( ( exists_in_world @ SV51 @ SV13 )
= $false )
| ( ( exists_in_world @ SV43 @ SV13 )
= $false )
| ( ( exists_in_world @ SV29 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[266]) ).
thf(280,plain,
! [SV52: mu,SV14: $i,SV44: mu,SV30: mu] :
( ( ( qmltpeq @ SV30 @ SV44 @ SV14 )
= $false )
| ( ( ~ ( member @ SV30 @ SV52 @ SV14 ) )
= $true )
| ( ( member @ SV44 @ SV52 @ SV14 )
= $true )
| ( ( exists_in_world @ SV52 @ SV14 )
= $false )
| ( ( exists_in_world @ SV44 @ SV14 )
= $false )
| ( ( exists_in_world @ SV30 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[267]) ).
thf(281,plain,
! [SV53: mu,SV15: $i,SV45: mu,SV31: mu] :
( ( ( qmltpeq @ SV31 @ SV45 @ SV15 )
= $false )
| ( ( ~ ( qmltpeq @ SV45 @ SV53 @ SV15 ) )
= $true )
| ( ( qmltpeq @ SV31 @ SV53 @ SV15 )
= $true )
| ( ( exists_in_world @ SV53 @ SV15 )
= $false )
| ( ( exists_in_world @ SV45 @ SV15 )
= $false )
| ( ( exists_in_world @ SV31 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[268]) ).
thf(282,plain,
! [SV35: mu,SV3: $i,SV19: mu,SV48: mu] :
( ( ( member @ SV48 @ SV19 @ SV3 )
= $true )
| ( ( member @ SV48 @ SV35 @ SV3 )
= $true )
| ( ( member @ SV48 @ ( union @ SV19 @ SV35 ) @ SV3 )
= $false )
| ( ( exists_in_world @ SV48 @ SV3 )
= $false )
| ( ( exists_in_world @ SV35 @ SV3 )
= $false )
| ( ( exists_in_world @ SV19 @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[269]) ).
thf(283,plain,
! [SV35: mu,SV3: $i,SV19: mu,SV48: mu] :
( ( ( member @ SV48 @ SV19 @ SV3 )
= $false )
| ( ( member @ SV48 @ ( union @ SV19 @ SV35 ) @ SV3 )
= $true )
| ( ( exists_in_world @ SV48 @ SV3 )
= $false )
| ( ( exists_in_world @ SV35 @ SV3 )
= $false )
| ( ( exists_in_world @ SV19 @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[270]) ).
thf(284,plain,
! [SV19: mu,SV3: $i,SV35: mu,SV48: mu] :
( ( ( member @ SV48 @ SV35 @ SV3 )
= $false )
| ( ( member @ SV48 @ ( union @ SV19 @ SV35 ) @ SV3 )
= $true )
| ( ( exists_in_world @ SV48 @ SV3 )
= $false )
| ( ( exists_in_world @ SV35 @ SV3 )
= $false )
| ( ( exists_in_world @ SV19 @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[270]) ).
thf(285,plain,
! [SV36: mu,SV5: $i,SV21: mu,SV49: mu] :
( ( ( member @ SV49 @ SV21 @ SV5 )
= $false )
| ( ( qmltpeq @ SV21 @ SV36 @ SV5 )
= $false )
| ( ( member @ SV49 @ SV36 @ SV5 )
= $true )
| ( ( exists_in_world @ SV49 @ SV5 )
= $false )
| ( ( exists_in_world @ SV36 @ SV5 )
= $false )
| ( ( exists_in_world @ SV21 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[271]) ).
thf(286,plain,
! [SV37: mu,SV6: $i,SV50: mu,SV22: mu] :
( ( ( subset @ SV22 @ SV50 @ SV6 )
= $false )
| ( ( qmltpeq @ SV22 @ SV37 @ SV6 )
= $false )
| ( ( subset @ SV37 @ SV50 @ SV6 )
= $true )
| ( ( exists_in_world @ SV50 @ SV6 )
= $false )
| ( ( exists_in_world @ SV37 @ SV6 )
= $false )
| ( ( exists_in_world @ SV22 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[272]) ).
thf(287,plain,
! [SV8: $i,SV24: mu,SV39: mu] :
( ( ( subset @ SV39 @ SV24 @ SV8 )
= $false )
| ( ( subset @ SV24 @ SV39 @ SV8 )
= $false )
| ( ( qmltpeq @ SV24 @ SV39 @ SV8 )
= $true )
| ( ( exists_in_world @ SV39 @ SV8 )
= $false )
| ( ( exists_in_world @ SV24 @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[275]) ).
thf(288,plain,
! [SV40: mu,SV9: $i,SV25: mu,SV55: mu] :
( ( ( ~ ( ~ ( member @ SV55 @ SV25 @ SV9 )
| ( member @ SV55 @ SV40 @ SV9 ) )
| ~ ( ~ ( member @ SV55 @ SV40 @ SV9 )
| ( member @ SV55 @ SV25 @ SV9 ) ) )
= $false )
| ( ( exists_in_world @ SV55 @ SV9 )
= $false )
| ( ( qmltpeq @ SV25 @ SV40 @ SV9 )
= $false )
| ( ( exists_in_world @ SV40 @ SV9 )
= $false )
| ( ( exists_in_world @ SV25 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[276]) ).
thf(289,plain,
! [SV9: $i,SV25: mu,SV40: mu] :
( ( ( ~ ( ~ ( member @ ( sK3_SY592 @ SV40 @ SV25 @ SV9 ) @ SV25 @ SV9 )
| ( member @ ( sK3_SY592 @ SV40 @ SV25 @ SV9 ) @ SV40 @ SV9 ) ) )
= $true )
| ( ( ~ ( ~ ( member @ ( sK3_SY592 @ SV40 @ SV25 @ SV9 ) @ SV40 @ SV9 )
| ( member @ ( sK3_SY592 @ SV40 @ SV25 @ SV9 ) @ SV25 @ SV9 ) ) )
= $true )
| ( ( qmltpeq @ SV25 @ SV40 @ SV9 )
= $true )
| ( ( exists_in_world @ SV40 @ SV9 )
= $false )
| ( ( exists_in_world @ SV25 @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[278]) ).
thf(290,plain,
! [SV43: mu,SV13: $i,SV29: mu,SV51: mu] :
( ( ( subset @ SV51 @ SV29 @ SV13 )
= $false )
| ( ( qmltpeq @ SV29 @ SV43 @ SV13 )
= $false )
| ( ( subset @ SV51 @ SV43 @ SV13 )
= $true )
| ( ( exists_in_world @ SV51 @ SV13 )
= $false )
| ( ( exists_in_world @ SV43 @ SV13 )
= $false )
| ( ( exists_in_world @ SV29 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[279]) ).
thf(291,plain,
! [SV44: mu,SV14: $i,SV52: mu,SV30: mu] :
( ( ( member @ SV30 @ SV52 @ SV14 )
= $false )
| ( ( qmltpeq @ SV30 @ SV44 @ SV14 )
= $false )
| ( ( member @ SV44 @ SV52 @ SV14 )
= $true )
| ( ( exists_in_world @ SV52 @ SV14 )
= $false )
| ( ( exists_in_world @ SV44 @ SV14 )
= $false )
| ( ( exists_in_world @ SV30 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[280]) ).
thf(292,plain,
! [SV31: mu,SV15: $i,SV53: mu,SV45: mu] :
( ( ( qmltpeq @ SV45 @ SV53 @ SV15 )
= $false )
| ( ( qmltpeq @ SV31 @ SV45 @ SV15 )
= $false )
| ( ( qmltpeq @ SV31 @ SV53 @ SV15 )
= $true )
| ( ( exists_in_world @ SV53 @ SV15 )
= $false )
| ( ( exists_in_world @ SV45 @ SV15 )
= $false )
| ( ( exists_in_world @ SV31 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[281]) ).
thf(293,plain,
! [SV40: mu,SV9: $i,SV25: mu,SV55: mu] :
( ( ( ~ ( ~ ( member @ SV55 @ SV25 @ SV9 )
| ( member @ SV55 @ SV40 @ SV9 ) ) )
= $false )
| ( ( exists_in_world @ SV55 @ SV9 )
= $false )
| ( ( qmltpeq @ SV25 @ SV40 @ SV9 )
= $false )
| ( ( exists_in_world @ SV40 @ SV9 )
= $false )
| ( ( exists_in_world @ SV25 @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[288]) ).
thf(294,plain,
! [SV25: mu,SV9: $i,SV40: mu,SV55: mu] :
( ( ( ~ ( ~ ( member @ SV55 @ SV40 @ SV9 )
| ( member @ SV55 @ SV25 @ SV9 ) ) )
= $false )
| ( ( exists_in_world @ SV55 @ SV9 )
= $false )
| ( ( qmltpeq @ SV25 @ SV40 @ SV9 )
= $false )
| ( ( exists_in_world @ SV40 @ SV9 )
= $false )
| ( ( exists_in_world @ SV25 @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[288]) ).
thf(295,plain,
! [SV9: $i,SV25: mu,SV40: mu] :
( ( ( ~ ( member @ ( sK3_SY592 @ SV40 @ SV25 @ SV9 ) @ SV25 @ SV9 )
| ( member @ ( sK3_SY592 @ SV40 @ SV25 @ SV9 ) @ SV40 @ SV9 ) )
= $false )
| ( ( ~ ( ~ ( member @ ( sK3_SY592 @ SV40 @ SV25 @ SV9 ) @ SV40 @ SV9 )
| ( member @ ( sK3_SY592 @ SV40 @ SV25 @ SV9 ) @ SV25 @ SV9 ) ) )
= $true )
| ( ( qmltpeq @ SV25 @ SV40 @ SV9 )
= $true )
| ( ( exists_in_world @ SV40 @ SV9 )
= $false )
| ( ( exists_in_world @ SV25 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[289]) ).
thf(296,plain,
! [SV40: mu,SV9: $i,SV25: mu,SV55: mu] :
( ( ( ~ ( member @ SV55 @ SV25 @ SV9 )
| ( member @ SV55 @ SV40 @ SV9 ) )
= $true )
| ( ( exists_in_world @ SV55 @ SV9 )
= $false )
| ( ( qmltpeq @ SV25 @ SV40 @ SV9 )
= $false )
| ( ( exists_in_world @ SV40 @ SV9 )
= $false )
| ( ( exists_in_world @ SV25 @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[293]) ).
thf(297,plain,
! [SV25: mu,SV9: $i,SV40: mu,SV55: mu] :
( ( ( ~ ( member @ SV55 @ SV40 @ SV9 )
| ( member @ SV55 @ SV25 @ SV9 ) )
= $true )
| ( ( exists_in_world @ SV55 @ SV9 )
= $false )
| ( ( qmltpeq @ SV25 @ SV40 @ SV9 )
= $false )
| ( ( exists_in_world @ SV40 @ SV9 )
= $false )
| ( ( exists_in_world @ SV25 @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[294]) ).
thf(298,plain,
! [SV9: $i,SV25: mu,SV40: mu] :
( ( ( ~ ( member @ ( sK3_SY592 @ SV40 @ SV25 @ SV9 ) @ SV25 @ SV9 ) )
= $false )
| ( ( ~ ( ~ ( member @ ( sK3_SY592 @ SV40 @ SV25 @ SV9 ) @ SV40 @ SV9 )
| ( member @ ( sK3_SY592 @ SV40 @ SV25 @ SV9 ) @ SV25 @ SV9 ) ) )
= $true )
| ( ( qmltpeq @ SV25 @ SV40 @ SV9 )
= $true )
| ( ( exists_in_world @ SV40 @ SV9 )
= $false )
| ( ( exists_in_world @ SV25 @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[295]) ).
thf(299,plain,
! [SV9: $i,SV25: mu,SV40: mu] :
( ( ( member @ ( sK3_SY592 @ SV40 @ SV25 @ SV9 ) @ SV40 @ SV9 )
= $false )
| ( ( ~ ( ~ ( member @ ( sK3_SY592 @ SV40 @ SV25 @ SV9 ) @ SV40 @ SV9 )
| ( member @ ( sK3_SY592 @ SV40 @ SV25 @ SV9 ) @ SV25 @ SV9 ) ) )
= $true )
| ( ( qmltpeq @ SV25 @ SV40 @ SV9 )
= $true )
| ( ( exists_in_world @ SV40 @ SV9 )
= $false )
| ( ( exists_in_world @ SV25 @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[295]) ).
thf(300,plain,
! [SV40: mu,SV9: $i,SV25: mu,SV55: mu] :
( ( ( ~ ( member @ SV55 @ SV25 @ SV9 ) )
= $true )
| ( ( member @ SV55 @ SV40 @ SV9 )
= $true )
| ( ( exists_in_world @ SV55 @ SV9 )
= $false )
| ( ( qmltpeq @ SV25 @ SV40 @ SV9 )
= $false )
| ( ( exists_in_world @ SV40 @ SV9 )
= $false )
| ( ( exists_in_world @ SV25 @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[296]) ).
thf(301,plain,
! [SV25: mu,SV9: $i,SV40: mu,SV55: mu] :
( ( ( ~ ( member @ SV55 @ SV40 @ SV9 ) )
= $true )
| ( ( member @ SV55 @ SV25 @ SV9 )
= $true )
| ( ( exists_in_world @ SV55 @ SV9 )
= $false )
| ( ( qmltpeq @ SV25 @ SV40 @ SV9 )
= $false )
| ( ( exists_in_world @ SV40 @ SV9 )
= $false )
| ( ( exists_in_world @ SV25 @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[297]) ).
thf(302,plain,
! [SV9: $i,SV25: mu,SV40: mu] :
( ( ( member @ ( sK3_SY592 @ SV40 @ SV25 @ SV9 ) @ SV25 @ SV9 )
= $true )
| ( ( ~ ( ~ ( member @ ( sK3_SY592 @ SV40 @ SV25 @ SV9 ) @ SV40 @ SV9 )
| ( member @ ( sK3_SY592 @ SV40 @ SV25 @ SV9 ) @ SV25 @ SV9 ) ) )
= $true )
| ( ( qmltpeq @ SV25 @ SV40 @ SV9 )
= $true )
| ( ( exists_in_world @ SV40 @ SV9 )
= $false )
| ( ( exists_in_world @ SV25 @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[298]) ).
thf(303,plain,
! [SV9: $i,SV25: mu,SV40: mu] :
( ( ( ~ ( member @ ( sK3_SY592 @ SV40 @ SV25 @ SV9 ) @ SV40 @ SV9 )
| ( member @ ( sK3_SY592 @ SV40 @ SV25 @ SV9 ) @ SV25 @ SV9 ) )
= $false )
| ( ( member @ ( sK3_SY592 @ SV40 @ SV25 @ SV9 ) @ SV40 @ SV9 )
= $false )
| ( ( qmltpeq @ SV25 @ SV40 @ SV9 )
= $true )
| ( ( exists_in_world @ SV40 @ SV9 )
= $false )
| ( ( exists_in_world @ SV25 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[299]) ).
thf(304,plain,
! [SV40: mu,SV9: $i,SV25: mu,SV55: mu] :
( ( ( member @ SV55 @ SV25 @ SV9 )
= $false )
| ( ( member @ SV55 @ SV40 @ SV9 )
= $true )
| ( ( exists_in_world @ SV55 @ SV9 )
= $false )
| ( ( qmltpeq @ SV25 @ SV40 @ SV9 )
= $false )
| ( ( exists_in_world @ SV40 @ SV9 )
= $false )
| ( ( exists_in_world @ SV25 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[300]) ).
thf(305,plain,
! [SV25: mu,SV9: $i,SV40: mu,SV55: mu] :
( ( ( member @ SV55 @ SV40 @ SV9 )
= $false )
| ( ( member @ SV55 @ SV25 @ SV9 )
= $true )
| ( ( exists_in_world @ SV55 @ SV9 )
= $false )
| ( ( qmltpeq @ SV25 @ SV40 @ SV9 )
= $false )
| ( ( exists_in_world @ SV40 @ SV9 )
= $false )
| ( ( exists_in_world @ SV25 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[301]) ).
thf(306,plain,
! [SV9: $i,SV25: mu,SV40: mu] :
( ( ( ~ ( member @ ( sK3_SY592 @ SV40 @ SV25 @ SV9 ) @ SV40 @ SV9 )
| ( member @ ( sK3_SY592 @ SV40 @ SV25 @ SV9 ) @ SV25 @ SV9 ) )
= $false )
| ( ( member @ ( sK3_SY592 @ SV40 @ SV25 @ SV9 ) @ SV25 @ SV9 )
= $true )
| ( ( qmltpeq @ SV25 @ SV40 @ SV9 )
= $true )
| ( ( exists_in_world @ SV40 @ SV9 )
= $false )
| ( ( exists_in_world @ SV25 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[302]) ).
thf(307,plain,
! [SV9: $i,SV25: mu,SV40: mu] :
( ( ( ~ ( member @ ( sK3_SY592 @ SV40 @ SV25 @ SV9 ) @ SV40 @ SV9 ) )
= $false )
| ( ( member @ ( sK3_SY592 @ SV40 @ SV25 @ SV9 ) @ SV40 @ SV9 )
= $false )
| ( ( qmltpeq @ SV25 @ SV40 @ SV9 )
= $true )
| ( ( exists_in_world @ SV40 @ SV9 )
= $false )
| ( ( exists_in_world @ SV25 @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[303]) ).
thf(308,plain,
! [SV9: $i,SV25: mu,SV40: mu] :
( ( ( member @ ( sK3_SY592 @ SV40 @ SV25 @ SV9 ) @ SV25 @ SV9 )
= $false )
| ( ( member @ ( sK3_SY592 @ SV40 @ SV25 @ SV9 ) @ SV40 @ SV9 )
= $false )
| ( ( qmltpeq @ SV25 @ SV40 @ SV9 )
= $true )
| ( ( exists_in_world @ SV40 @ SV9 )
= $false )
| ( ( exists_in_world @ SV25 @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[303]) ).
thf(309,plain,
! [SV9: $i,SV25: mu,SV40: mu] :
( ( ( ~ ( member @ ( sK3_SY592 @ SV40 @ SV25 @ SV9 ) @ SV40 @ SV9 ) )
= $false )
| ( ( member @ ( sK3_SY592 @ SV40 @ SV25 @ SV9 ) @ SV25 @ SV9 )
= $true )
| ( ( qmltpeq @ SV25 @ SV40 @ SV9 )
= $true )
| ( ( exists_in_world @ SV40 @ SV9 )
= $false )
| ( ( exists_in_world @ SV25 @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[306]) ).
thf(310,plain,
! [SV9: $i,SV25: mu,SV40: mu] :
( ( ( member @ ( sK3_SY592 @ SV40 @ SV25 @ SV9 ) @ SV25 @ SV9 )
= $false )
| ( ( member @ ( sK3_SY592 @ SV40 @ SV25 @ SV9 ) @ SV25 @ SV9 )
= $true )
| ( ( qmltpeq @ SV25 @ SV40 @ SV9 )
= $true )
| ( ( exists_in_world @ SV40 @ SV9 )
= $false )
| ( ( exists_in_world @ SV25 @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[306]) ).
thf(311,plain,
! [SV9: $i,SV25: mu,SV40: mu] :
( ( ( member @ ( sK3_SY592 @ SV40 @ SV25 @ SV9 ) @ SV40 @ SV9 )
= $true )
| ( ( member @ ( sK3_SY592 @ SV40 @ SV25 @ SV9 ) @ SV40 @ SV9 )
= $false )
| ( ( qmltpeq @ SV25 @ SV40 @ SV9 )
= $true )
| ( ( exists_in_world @ SV40 @ SV9 )
= $false )
| ( ( exists_in_world @ SV25 @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[307]) ).
thf(312,plain,
! [SV9: $i,SV25: mu,SV40: mu] :
( ( ( member @ ( sK3_SY592 @ SV40 @ SV25 @ SV9 ) @ SV40 @ SV9 )
= $true )
| ( ( member @ ( sK3_SY592 @ SV40 @ SV25 @ SV9 ) @ SV25 @ SV9 )
= $true )
| ( ( qmltpeq @ SV25 @ SV40 @ SV9 )
= $true )
| ( ( exists_in_world @ SV40 @ SV9 )
= $false )
| ( ( exists_in_world @ SV25 @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[309]) ).
thf(313,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[62,312,311,310,308,305,304,292,291,290,287,286,285,284,283,282,277,274,273,244,232,203,198,177,138,130,112,80]) ).
thf(314,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[313]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET002^7 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.15 % Computer : n018.cluster.edu
% 0.10/0.15 % Model : x86_64 x86_64
% 0.10/0.15 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.15 % Memory : 8046.5625MB
% 0.10/0.15 % OS : Linux 6.8.0-71-generic
% 0.10/0.15 % CPULimit : 300
% 0.10/0.15 % WCLimit : 300
% 0.10/0.15 % DateTime : Tue Oct 6 14:28:22 UTC 2026
% 0.10/0.15 % CPUTime :
% 0.10/0.15 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.66/0.32
% 0.66/0.32 No.of.Axioms: 16
% 0.66/0.32
% 0.66/0.32 Length.of.Defs: 5540
% 0.66/0.32
% 0.66/0.32 Contains.Choice.Funs: false
% 0.66/0.32 ......................
% 0.66/0.32
% 0.66/0.32 ********************************
% 0.66/0.32 * All subproblems solved! *
% 0.66/0.32 ********************************
% 0.66/0.32 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:17,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:313,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.66/0.32
% 0.66/0.32 %**** Beginning of derivation protocol ****
% 0.66/0.32 % SZS output start CNFRefutation
% See solution above
% 0.66/0.33
% 0.66/0.33 %**** End of derivation protocol ****
% 0.66/0.33 %**** no. of clauses in derivation: 309 ****
% 0.66/0.33 %**** clause counter: 313 ****
% 0.66/0.33
% 0.66/0.33 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:17,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:313,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------