TSTP Solution File: SET002^7 by LEO-II---1.7.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SET002^7 : TPTP v8.1.0. Released v5.5.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 02:57:38 EDT 2022
% Result : Theorem 0.39s 0.60s
% Output : CNFRefutation 0.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 98
% Syntax : Number of formulae : 430 ( 130 unt; 44 typ; 32 def)
% Number of atoms : 4048 (1012 equ; 0 cnn)
% Maximal formula atoms : 9 ( 10 avg)
% Number of connectives : 8022 (1212 ~;1435 |; 9 &;5356 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 195 ( 195 >; 0 *; 0 +; 0 <<)
% Number of symbols : 46 ( 43 usr; 4 con; 0-3 aty)
% Number of variables : 1271 ( 133 ^1131 !; 7 ?;1271 :)
% 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_X,type,
sK1_X: $i > mu ).
thf(tp_sK2_SX0,type,
sK2_SX0: $i ).
thf(tp_sK3_SY71,type,
sK3_SY71: mu ).
thf(tp_sK4_SY84,type,
sK4_SY84: mu > mu > $i > mu ).
thf(tp_sK5_SY86,type,
sK5_SY86: 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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',mbox_s4) ).
thf(mcountersatisfiable,definition,
( mcountersatisfiable
= ( ^ [Phi: $i > $o] :
? [W: $i] :
~ ( Phi @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mcountersatisfiable) ).
thf(mdia,definition,
( mdia
= ( ^ [R: $i > $i > $o,Phi: $i > $o] : ( mnot @ ( mbox @ R @ ( mnot @ Phi ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mdia) ).
thf(mdia_s4,definition,
( mdia_s4
= ( ^ [Phi: $i > $o] : ( mnot @ ( mbox_s4 @ ( mnot @ Phi ) ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',mexists_prop) ).
thf(mfalse,definition,
( mfalse
= ( mnot @ mtrue ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',mfunctional) ).
thf(mimplied,definition,
( mimplied
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Psi ) @ Phi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplied) ).
thf(mimplies,definition,
( mimplies
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Phi ) @ Psi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies) ).
thf(minvalid,definition,
( minvalid
= ( ^ [Phi: $i > $o] :
! [W: $i] :
~ ( Phi @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',minvalid) ).
thf(mnot,definition,
( mnot
= ( ^ [Phi: $i > $o,W: $i] :
~ ( Phi @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot) ).
thf(mor,definition,
( mor
= ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
( ( Phi @ W )
| ( Psi @ W ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',mpartially_functional) ).
thf(mreflexive,definition,
( mreflexive
= ( ^ [R: $i > $i > $o] :
! [S: $i] : ( R @ S @ S ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mreflexive) ).
thf(msatisfiable,definition,
( msatisfiable
= ( ^ [Phi: $i > $o] :
? [W: $i] : ( Phi @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',msatisfiable) ).
thf(mserial,definition,
( mserial
= ( ^ [R: $i > $i > $o] :
! [S: $i] :
? [T: $i] : ( R @ S @ T ) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',mtransitive) ).
thf(mtrue,definition,
( mtrue
= ( ^ [W: $i] : $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mtrue) ).
thf(mvalid,definition,
( mvalid
= ( ^ [Phi: $i > $o] :
! [W: $i] : ( Phi @ W ) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',mweakly_directed) ).
thf(mxor,definition,
( mxor
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mequiv @ Phi @ Psi ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',equal_member_defn) ).
thf(2,axiom,
( mvalid
@ ( mforall_ind
@ ^ [B: mu] : ( subset @ B @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_of_subset) ).
thf(3,axiom,
( mvalid
@ ( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] :
( mequiv @ ( subset @ B @ C )
@ ( mforall_ind
@ ^ [D: mu] : ( mimplies @ ( member @ D @ B ) @ ( member @ D @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
thf(4,axiom,
( mvalid
@ ( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( qmltpeq @ ( union @ B @ C ) @ ( union @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',symmetry) ).
thf(16,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X: mu] : ( qmltpeq @ X @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).
thf(17,axiom,
! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( union @ V2 @ V1 ) @ V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_union_ax) ).
thf(18,axiom,
! [X: mu,V: $i,W: $i] :
( ( ( exists_in_world @ X @ V )
& ( rel_s4 @ V @ W ) )
=> ( exists_in_world @ X @ W ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cumulative_ax) ).
thf(19,axiom,
mtransitive @ rel_s4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2) ).
thf(20,axiom,
mreflexive @ rel_s4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1) ).
thf(21,axiom,
! [V: $i] :
? [X: mu] : ( exists_in_world @ X @ V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonempty_ax) ).
thf(22,conjecture,
( mvalid
@ ( mforall_ind
@ ^ [B: mu] : ( qmltpeq @ ( union @ B @ B ) @ B ) ) ),
file('/export/starexec/sandbox/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,
( ( ~ ( mvalid
@ ( mforall_ind
@ ^ [B: mu] : ( qmltpeq @ ( union @ B @ B ) @ B ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[23]) ).
thf(25,plain,
( ( ! [X: mu,V: $i,W: $i] :
( ~ ( exists_in_world @ X @ V )
| ~ ( rel_s4 @ V @ W )
| ( exists_in_world @ X @ W ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[18]) ).
thf(26,plain,
( ( ! [V: $i] : ( exists_in_world @ ( sK1_X @ V ) @ V ) )
= $true ),
inference(extcnf_combined,[status(esa)],[21]) ).
thf(27,plain,
( ( ! [V: $i] : ( exists_in_world @ ( sK1_X @ V ) @ V ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(28,plain,
( ( mreflexive @ rel_s4 )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(29,plain,
( ( mtransitive @ rel_s4 )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(30,plain,
( ( ! [X: mu,V: $i,W: $i] :
( ~ ( exists_in_world @ X @ V )
| ~ ( rel_s4 @ V @ W )
| ( exists_in_world @ X @ W ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(31,plain,
( ( ! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( union @ V2 @ V1 ) @ V ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(32,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [X: mu] : ( qmltpeq @ X @ X ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(33,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [X: mu] :
( mforall_ind
@ ^ [Y: mu] : ( mimplies @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(34,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [X: mu] :
( mforall_ind
@ ^ [Y: mu] :
( mforall_ind
@ ^ [Z: mu] : ( mimplies @ ( mand @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ Z ) ) @ ( qmltpeq @ X @ Z ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(35,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( union @ A @ C ) @ ( union @ B @ C ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(36,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( union @ C @ A ) @ ( union @ C @ B ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(37,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( member @ A @ C ) ) @ ( member @ B @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(38,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( member @ C @ A ) ) @ ( member @ C @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(39,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( subset @ A @ C ) ) @ ( subset @ B @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(40,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( subset @ C @ A ) ) @ ( subset @ C @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(41,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mimplies @ ( subset @ B @ C ) @ ( qmltpeq @ ( union @ B @ C ) @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(42,plain,
( ( 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 ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(43,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mequiv @ ( qmltpeq @ B @ C ) @ ( mand @ ( subset @ B @ C ) @ ( subset @ C @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(44,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( qmltpeq @ ( union @ B @ C ) @ ( union @ C @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(45,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] :
( mequiv @ ( subset @ B @ C )
@ ( mforall_ind
@ ^ [D: mu] : ( mimplies @ ( member @ D @ B ) @ ( member @ D @ C ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[3]) ).
thf(46,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [B: mu] : ( subset @ B @ B ) ) )
= $true ),
inference(copy,[status(thm)],[2]) ).
thf(47,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] :
( mequiv @ ( qmltpeq @ B @ C )
@ ( mforall_ind
@ ^ [D: mu] : ( mequiv @ ( member @ D @ B ) @ ( member @ D @ C ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1]) ).
thf(48,plain,
( ( ~ ( mvalid
@ ( mforall_ind
@ ^ [B: mu] : ( qmltpeq @ ( union @ B @ B ) @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(49,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)],[43,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(50,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( rel_s4 @ SX0 @ SX1 )
| ~ ( rel_s4 @ SX1 @ SX2 ) )
| ( rel_s4 @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29,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(51,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)],[35,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(52,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)],[39,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(53,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ( subset @ SX1 @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46,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(54,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)],[42,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(55,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)],[41,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(56,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)],[36,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(57,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)],[37,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(58,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)],[33,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(59,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)],[44,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(60,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)],[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(61,plain,
( ( ! [SX0: $i] : ( rel_s4 @ SX0 @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[28,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(62,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ~ ( ~ ( ~ ( subset @ SX1 @ SX2 @ SX0 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX0 )
| ~ ( member @ SX3 @ SX1 @ SX0 )
| ( member @ SX3 @ SX2 @ SX0 ) ) )
| ~ ( ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX0 )
| ~ ( member @ SX3 @ SX1 @ SX0 )
| ( member @ SX3 @ SX2 @ SX0 ) )
| ( subset @ SX1 @ SX2 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45,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(63,plain,
( ( ~ ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ( qmltpeq @ ( union @ SX1 @ SX1 ) @ 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(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 @ SX2 @ SX3 @ SX0 ) )
| ( qmltpeq @ SX1 @ SX3 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34,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 )
| ~ ~ ( ~ ( qmltpeq @ SX1 @ SX2 @ SX0 )
| ~ ( member @ SX3 @ SX1 @ SX0 ) )
| ( member @ SX3 @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38,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 )
| ! [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)],[40,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 )
| ( qmltpeq @ SX1 @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32,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,
! [SV1: $i] :
( ( exists_in_world @ ( sK1_X @ SV1 ) @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(69,plain,
! [SV2: mu] :
( ( ! [SY0: $i,SY1: $i] :
( ~ ( exists_in_world @ SV2 @ SY0 )
| ~ ( rel_s4 @ SY0 @ SY1 )
| ( exists_in_world @ SV2 @ SY1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(70,plain,
! [SV3: $i] :
( ( ! [SY2: mu,SY3: mu] : ( exists_in_world @ ( union @ SY2 @ SY3 ) @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(71,plain,
! [SV4: $i] :
( ( ! [SY4: mu] :
( ~ ( exists_in_world @ SY4 @ SV4 )
| ! [SY5: mu] :
( ~ ( exists_in_world @ SY5 @ SV4 )
| ~ ( ~ ( ~ ( qmltpeq @ SY4 @ SY5 @ SV4 )
| ~ ( ~ ( subset @ SY4 @ SY5 @ SV4 )
| ~ ( subset @ SY5 @ SY4 @ SV4 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SY4 @ SY5 @ SV4 )
| ~ ( subset @ SY5 @ SY4 @ SV4 ) )
| ( qmltpeq @ SY4 @ SY5 @ SV4 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(72,plain,
! [SV5: $i] :
( ( ! [SY6: $i,SY7: $i] :
( ~ ~ ( ~ ( rel_s4 @ SV5 @ SY6 )
| ~ ( rel_s4 @ SY6 @ SY7 ) )
| ( rel_s4 @ SV5 @ SY7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(73,plain,
! [SV6: $i] :
( ( ! [SY8: mu] :
( ~ ( exists_in_world @ SY8 @ SV6 )
| ! [SY9: mu] :
( ~ ( exists_in_world @ SY9 @ SV6 )
| ! [SY10: mu] :
( ~ ( exists_in_world @ SY10 @ SV6 )
| ~ ( qmltpeq @ SY8 @ SY9 @ SV6 )
| ( qmltpeq @ ( union @ SY8 @ SY10 ) @ ( union @ SY9 @ SY10 ) @ SV6 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(74,plain,
! [SV7: $i] :
( ( ! [SY11: mu] :
( ~ ( exists_in_world @ SY11 @ SV7 )
| ! [SY12: mu] :
( ~ ( exists_in_world @ SY12 @ SV7 )
| ! [SY13: mu] :
( ~ ( exists_in_world @ SY13 @ SV7 )
| ~ ~ ( ~ ( qmltpeq @ SY11 @ SY12 @ SV7 )
| ~ ( subset @ SY11 @ SY13 @ SV7 ) )
| ( subset @ SY12 @ SY13 @ SV7 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(75,plain,
! [SV8: $i] :
( ( ! [SY14: mu] :
( ~ ( exists_in_world @ SY14 @ SV8 )
| ( subset @ SY14 @ SY14 @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(76,plain,
! [SV9: $i] :
( ( ! [SY15: mu] :
( ~ ( exists_in_world @ SY15 @ SV9 )
| ! [SY16: mu] :
( ~ ( exists_in_world @ SY16 @ SV9 )
| ! [SY17: mu] :
( ~ ( exists_in_world @ SY17 @ SV9 )
| ~ ( ~ ( ~ ( member @ SY17 @ ( union @ SY15 @ SY16 ) @ SV9 )
| ( member @ SY17 @ SY15 @ SV9 )
| ( member @ SY17 @ SY16 @ SV9 ) )
| ~ ( ~ ( ( member @ SY17 @ SY15 @ SV9 )
| ( member @ SY17 @ SY16 @ SV9 ) )
| ( member @ SY17 @ ( union @ SY15 @ SY16 ) @ SV9 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(77,plain,
! [SV10: $i] :
( ( ! [SY18: mu] :
( ~ ( exists_in_world @ SY18 @ SV10 )
| ! [SY19: mu] :
( ~ ( exists_in_world @ SY19 @ SV10 )
| ~ ( subset @ SY18 @ SY19 @ SV10 )
| ( qmltpeq @ ( union @ SY18 @ SY19 ) @ SY19 @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(78,plain,
! [SV11: $i] :
( ( ! [SY20: mu] :
( ~ ( exists_in_world @ SY20 @ SV11 )
| ! [SY21: mu] :
( ~ ( exists_in_world @ SY21 @ SV11 )
| ! [SY22: mu] :
( ~ ( exists_in_world @ SY22 @ SV11 )
| ~ ( qmltpeq @ SY20 @ SY21 @ SV11 )
| ( qmltpeq @ ( union @ SY22 @ SY20 ) @ ( union @ SY22 @ SY21 ) @ SV11 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(79,plain,
! [SV12: $i] :
( ( ! [SY23: mu] :
( ~ ( exists_in_world @ SY23 @ SV12 )
| ! [SY24: mu] :
( ~ ( exists_in_world @ SY24 @ SV12 )
| ! [SY25: mu] :
( ~ ( exists_in_world @ SY25 @ SV12 )
| ~ ~ ( ~ ( qmltpeq @ SY23 @ SY24 @ SV12 )
| ~ ( member @ SY23 @ SY25 @ SV12 ) )
| ( member @ SY24 @ SY25 @ SV12 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(80,plain,
! [SV13: $i] :
( ( ! [SY26: mu] :
( ~ ( exists_in_world @ SY26 @ SV13 )
| ! [SY27: mu] :
( ~ ( exists_in_world @ SY27 @ SV13 )
| ~ ( qmltpeq @ SY26 @ SY27 @ SV13 )
| ( qmltpeq @ SY27 @ SY26 @ SV13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(81,plain,
! [SV14: $i] :
( ( ! [SY28: mu] :
( ~ ( exists_in_world @ SY28 @ SV14 )
| ! [SY29: mu] :
( ~ ( exists_in_world @ SY29 @ SV14 )
| ( qmltpeq @ ( union @ SY28 @ SY29 ) @ ( union @ SY29 @ SY28 ) @ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(82,plain,
! [SV15: $i] :
( ( ! [SY30: mu] :
( ~ ( exists_in_world @ SY30 @ SV15 )
| ! [SY31: mu] :
( ~ ( exists_in_world @ SY31 @ SV15 )
| ~ ( ~ ( ~ ( qmltpeq @ SY30 @ SY31 @ SV15 )
| ! [SY32: mu] :
( ~ ( exists_in_world @ SY32 @ SV15 )
| ~ ( ~ ( ~ ( member @ SY32 @ SY30 @ SV15 )
| ( member @ SY32 @ SY31 @ SV15 ) )
| ~ ( ~ ( member @ SY32 @ SY31 @ SV15 )
| ( member @ SY32 @ SY30 @ SV15 ) ) ) ) )
| ~ ( ~ ! [SY33: mu] :
( ~ ( exists_in_world @ SY33 @ SV15 )
| ~ ( ~ ( ~ ( member @ SY33 @ SY30 @ SV15 )
| ( member @ SY33 @ SY31 @ SV15 ) )
| ~ ( ~ ( member @ SY33 @ SY31 @ SV15 )
| ( member @ SY33 @ SY30 @ SV15 ) ) ) )
| ( qmltpeq @ SY30 @ SY31 @ SV15 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(83,plain,
! [SV16: $i] :
( ( rel_s4 @ SV16 @ SV16 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(84,plain,
! [SV17: $i] :
( ( ! [SY34: mu] :
( ~ ( exists_in_world @ SY34 @ SV17 )
| ! [SY35: mu] :
( ~ ( exists_in_world @ SY35 @ SV17 )
| ~ ( ~ ( ~ ( subset @ SY34 @ SY35 @ SV17 )
| ! [SY36: mu] :
( ~ ( exists_in_world @ SY36 @ SV17 )
| ~ ( member @ SY36 @ SY34 @ SV17 )
| ( member @ SY36 @ SY35 @ SV17 ) ) )
| ~ ( ~ ! [SY37: mu] :
( ~ ( exists_in_world @ SY37 @ SV17 )
| ~ ( member @ SY37 @ SY34 @ SV17 )
| ( member @ SY37 @ SY35 @ SV17 ) )
| ( subset @ SY34 @ SY35 @ SV17 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(85,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ( qmltpeq @ ( union @ SX1 @ SX1 ) @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(86,plain,
! [SV18: $i] :
( ( ! [SY38: mu] :
( ~ ( exists_in_world @ SY38 @ SV18 )
| ! [SY39: mu] :
( ~ ( exists_in_world @ SY39 @ SV18 )
| ! [SY40: mu] :
( ~ ( exists_in_world @ SY40 @ SV18 )
| ~ ~ ( ~ ( qmltpeq @ SY38 @ SY39 @ SV18 )
| ~ ( qmltpeq @ SY39 @ SY40 @ SV18 ) )
| ( qmltpeq @ SY38 @ SY40 @ SV18 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(87,plain,
! [SV19: $i] :
( ( ! [SY41: mu] :
( ~ ( exists_in_world @ SY41 @ SV19 )
| ! [SY42: mu] :
( ~ ( exists_in_world @ SY42 @ SV19 )
| ! [SY43: mu] :
( ~ ( exists_in_world @ SY43 @ SV19 )
| ~ ~ ( ~ ( qmltpeq @ SY41 @ SY42 @ SV19 )
| ~ ( member @ SY43 @ SY41 @ SV19 ) )
| ( member @ SY43 @ SY42 @ SV19 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(88,plain,
! [SV20: $i] :
( ( ! [SY44: mu] :
( ~ ( exists_in_world @ SY44 @ SV20 )
| ! [SY45: mu] :
( ~ ( exists_in_world @ SY45 @ SV20 )
| ! [SY46: mu] :
( ~ ( exists_in_world @ SY46 @ SV20 )
| ~ ~ ( ~ ( qmltpeq @ SY44 @ SY45 @ SV20 )
| ~ ( subset @ SY46 @ SY44 @ SV20 ) )
| ( subset @ SY46 @ SY45 @ SV20 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(89,plain,
! [SV21: $i] :
( ( ! [SY47: mu] :
( ~ ( exists_in_world @ SY47 @ SV21 )
| ( qmltpeq @ SY47 @ SY47 @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(90,plain,
! [SV22: $i,SV2: mu] :
( ( ! [SY48: $i] :
( ~ ( exists_in_world @ SV2 @ SV22 )
| ~ ( rel_s4 @ SV22 @ SY48 )
| ( exists_in_world @ SV2 @ SY48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(91,plain,
! [SV3: $i,SV23: mu] :
( ( ! [SY49: mu] : ( exists_in_world @ ( union @ SV23 @ SY49 ) @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(92,plain,
! [SV4: $i,SV24: mu] :
( ( ~ ( exists_in_world @ SV24 @ SV4 )
| ! [SY50: mu] :
( ~ ( exists_in_world @ SY50 @ SV4 )
| ~ ( ~ ( ~ ( qmltpeq @ SV24 @ SY50 @ SV4 )
| ~ ( ~ ( subset @ SV24 @ SY50 @ SV4 )
| ~ ( subset @ SY50 @ SV24 @ SV4 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV24 @ SY50 @ SV4 )
| ~ ( subset @ SY50 @ SV24 @ SV4 ) )
| ( qmltpeq @ SV24 @ SY50 @ SV4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(93,plain,
! [SV25: $i,SV5: $i] :
( ( ! [SY51: $i] :
( ~ ~ ( ~ ( rel_s4 @ SV5 @ SV25 )
| ~ ( rel_s4 @ SV25 @ SY51 ) )
| ( rel_s4 @ SV5 @ SY51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(94,plain,
! [SV6: $i,SV26: mu] :
( ( ~ ( exists_in_world @ SV26 @ SV6 )
| ! [SY52: mu] :
( ~ ( exists_in_world @ SY52 @ SV6 )
| ! [SY53: mu] :
( ~ ( exists_in_world @ SY53 @ SV6 )
| ~ ( qmltpeq @ SV26 @ SY52 @ SV6 )
| ( qmltpeq @ ( union @ SV26 @ SY53 ) @ ( union @ SY52 @ SY53 ) @ SV6 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(95,plain,
! [SV7: $i,SV27: mu] :
( ( ~ ( exists_in_world @ SV27 @ SV7 )
| ! [SY54: mu] :
( ~ ( exists_in_world @ SY54 @ SV7 )
| ! [SY55: mu] :
( ~ ( exists_in_world @ SY55 @ SV7 )
| ~ ~ ( ~ ( qmltpeq @ SV27 @ SY54 @ SV7 )
| ~ ( subset @ SV27 @ SY55 @ SV7 ) )
| ( subset @ SY54 @ SY55 @ SV7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(96,plain,
! [SV8: $i,SV28: mu] :
( ( ~ ( exists_in_world @ SV28 @ SV8 )
| ( subset @ SV28 @ SV28 @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(97,plain,
! [SV9: $i,SV29: mu] :
( ( ~ ( exists_in_world @ SV29 @ SV9 )
| ! [SY56: mu] :
( ~ ( exists_in_world @ SY56 @ SV9 )
| ! [SY57: mu] :
( ~ ( exists_in_world @ SY57 @ SV9 )
| ~ ( ~ ( ~ ( member @ SY57 @ ( union @ SV29 @ SY56 ) @ SV9 )
| ( member @ SY57 @ SV29 @ SV9 )
| ( member @ SY57 @ SY56 @ SV9 ) )
| ~ ( ~ ( ( member @ SY57 @ SV29 @ SV9 )
| ( member @ SY57 @ SY56 @ SV9 ) )
| ( member @ SY57 @ ( union @ SV29 @ SY56 ) @ SV9 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(98,plain,
! [SV10: $i,SV30: mu] :
( ( ~ ( exists_in_world @ SV30 @ SV10 )
| ! [SY58: mu] :
( ~ ( exists_in_world @ SY58 @ SV10 )
| ~ ( subset @ SV30 @ SY58 @ SV10 )
| ( qmltpeq @ ( union @ SV30 @ SY58 ) @ SY58 @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(99,plain,
! [SV11: $i,SV31: mu] :
( ( ~ ( exists_in_world @ SV31 @ SV11 )
| ! [SY59: mu] :
( ~ ( exists_in_world @ SY59 @ SV11 )
| ! [SY60: mu] :
( ~ ( exists_in_world @ SY60 @ SV11 )
| ~ ( qmltpeq @ SV31 @ SY59 @ SV11 )
| ( qmltpeq @ ( union @ SY60 @ SV31 ) @ ( union @ SY60 @ SY59 ) @ SV11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(100,plain,
! [SV12: $i,SV32: mu] :
( ( ~ ( exists_in_world @ SV32 @ SV12 )
| ! [SY61: mu] :
( ~ ( exists_in_world @ SY61 @ SV12 )
| ! [SY62: mu] :
( ~ ( exists_in_world @ SY62 @ SV12 )
| ~ ~ ( ~ ( qmltpeq @ SV32 @ SY61 @ SV12 )
| ~ ( member @ SV32 @ SY62 @ SV12 ) )
| ( member @ SY61 @ SY62 @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(101,plain,
! [SV13: $i,SV33: mu] :
( ( ~ ( exists_in_world @ SV33 @ SV13 )
| ! [SY63: mu] :
( ~ ( exists_in_world @ SY63 @ SV13 )
| ~ ( qmltpeq @ SV33 @ SY63 @ SV13 )
| ( qmltpeq @ SY63 @ SV33 @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(102,plain,
! [SV14: $i,SV34: mu] :
( ( ~ ( exists_in_world @ SV34 @ SV14 )
| ! [SY64: mu] :
( ~ ( exists_in_world @ SY64 @ SV14 )
| ( qmltpeq @ ( union @ SV34 @ SY64 ) @ ( union @ SY64 @ SV34 ) @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(103,plain,
! [SV15: $i,SV35: mu] :
( ( ~ ( exists_in_world @ SV35 @ SV15 )
| ! [SY65: mu] :
( ~ ( exists_in_world @ SY65 @ SV15 )
| ~ ( ~ ( ~ ( qmltpeq @ SV35 @ SY65 @ SV15 )
| ! [SY66: mu] :
( ~ ( exists_in_world @ SY66 @ SV15 )
| ~ ( ~ ( ~ ( member @ SY66 @ SV35 @ SV15 )
| ( member @ SY66 @ SY65 @ SV15 ) )
| ~ ( ~ ( member @ SY66 @ SY65 @ SV15 )
| ( member @ SY66 @ SV35 @ SV15 ) ) ) ) )
| ~ ( ~ ! [SY67: mu] :
( ~ ( exists_in_world @ SY67 @ SV15 )
| ~ ( ~ ( ~ ( member @ SY67 @ SV35 @ SV15 )
| ( member @ SY67 @ SY65 @ SV15 ) )
| ~ ( ~ ( member @ SY67 @ SY65 @ SV15 )
| ( member @ SY67 @ SV35 @ SV15 ) ) ) )
| ( qmltpeq @ SV35 @ SY65 @ SV15 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(104,plain,
! [SV17: $i,SV36: mu] :
( ( ~ ( exists_in_world @ SV36 @ SV17 )
| ! [SY68: mu] :
( ~ ( exists_in_world @ SY68 @ SV17 )
| ~ ( ~ ( ~ ( subset @ SV36 @ SY68 @ SV17 )
| ! [SY69: mu] :
( ~ ( exists_in_world @ SY69 @ SV17 )
| ~ ( member @ SY69 @ SV36 @ SV17 )
| ( member @ SY69 @ SY68 @ SV17 ) ) )
| ~ ( ~ ! [SY70: mu] :
( ~ ( exists_in_world @ SY70 @ SV17 )
| ~ ( member @ SY70 @ SV36 @ SV17 )
| ( member @ SY70 @ SY68 @ SV17 ) )
| ( subset @ SV36 @ SY68 @ SV17 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(105,plain,
( ( ! [SY71: mu] :
( ~ ( exists_in_world @ SY71 @ sK2_SX0 )
| ( qmltpeq @ ( union @ SY71 @ SY71 ) @ SY71 @ sK2_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[85]) ).
thf(106,plain,
! [SV18: $i,SV37: mu] :
( ( ~ ( exists_in_world @ SV37 @ SV18 )
| ! [SY72: mu] :
( ~ ( exists_in_world @ SY72 @ SV18 )
| ! [SY73: mu] :
( ~ ( exists_in_world @ SY73 @ SV18 )
| ~ ~ ( ~ ( qmltpeq @ SV37 @ SY72 @ SV18 )
| ~ ( qmltpeq @ SY72 @ SY73 @ SV18 ) )
| ( qmltpeq @ SV37 @ SY73 @ SV18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(107,plain,
! [SV19: $i,SV38: mu] :
( ( ~ ( exists_in_world @ SV38 @ SV19 )
| ! [SY74: mu] :
( ~ ( exists_in_world @ SY74 @ SV19 )
| ! [SY75: mu] :
( ~ ( exists_in_world @ SY75 @ SV19 )
| ~ ~ ( ~ ( qmltpeq @ SV38 @ SY74 @ SV19 )
| ~ ( member @ SY75 @ SV38 @ SV19 ) )
| ( member @ SY75 @ SY74 @ SV19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(108,plain,
! [SV20: $i,SV39: mu] :
( ( ~ ( exists_in_world @ SV39 @ SV20 )
| ! [SY76: mu] :
( ~ ( exists_in_world @ SY76 @ SV20 )
| ! [SY77: mu] :
( ~ ( exists_in_world @ SY77 @ SV20 )
| ~ ~ ( ~ ( qmltpeq @ SV39 @ SY76 @ SV20 )
| ~ ( subset @ SY77 @ SV39 @ SV20 ) )
| ( subset @ SY77 @ SY76 @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(109,plain,
! [SV21: $i,SV40: mu] :
( ( ~ ( exists_in_world @ SV40 @ SV21 )
| ( qmltpeq @ SV40 @ SV40 @ SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(110,plain,
! [SV41: $i,SV22: $i,SV2: mu] :
( ( ~ ( exists_in_world @ SV2 @ SV22 )
| ~ ( rel_s4 @ SV22 @ SV41 )
| ( exists_in_world @ SV2 @ SV41 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(111,plain,
! [SV3: $i,SV42: mu,SV23: mu] :
( ( exists_in_world @ ( union @ SV23 @ SV42 ) @ SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(112,plain,
! [SV4: $i,SV24: mu] :
( ( ( ~ ( exists_in_world @ SV24 @ SV4 ) )
= $true )
| ( ( ! [SY50: mu] :
( ~ ( exists_in_world @ SY50 @ SV4 )
| ~ ( ~ ( ~ ( qmltpeq @ SV24 @ SY50 @ SV4 )
| ~ ( ~ ( subset @ SV24 @ SY50 @ SV4 )
| ~ ( subset @ SY50 @ SV24 @ SV4 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV24 @ SY50 @ SV4 )
| ~ ( subset @ SY50 @ SV24 @ SV4 ) )
| ( qmltpeq @ SV24 @ SY50 @ SV4 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[92]) ).
thf(113,plain,
! [SV43: $i,SV25: $i,SV5: $i] :
( ( ~ ~ ( ~ ( rel_s4 @ SV5 @ SV25 )
| ~ ( rel_s4 @ SV25 @ SV43 ) )
| ( rel_s4 @ SV5 @ SV43 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(114,plain,
! [SV6: $i,SV26: mu] :
( ( ( ~ ( exists_in_world @ SV26 @ SV6 ) )
= $true )
| ( ( ! [SY52: mu] :
( ~ ( exists_in_world @ SY52 @ SV6 )
| ! [SY53: mu] :
( ~ ( exists_in_world @ SY53 @ SV6 )
| ~ ( qmltpeq @ SV26 @ SY52 @ SV6 )
| ( qmltpeq @ ( union @ SV26 @ SY53 ) @ ( union @ SY52 @ SY53 ) @ SV6 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(115,plain,
! [SV7: $i,SV27: mu] :
( ( ( ~ ( exists_in_world @ SV27 @ SV7 ) )
= $true )
| ( ( ! [SY54: mu] :
( ~ ( exists_in_world @ SY54 @ SV7 )
| ! [SY55: mu] :
( ~ ( exists_in_world @ SY55 @ SV7 )
| ~ ~ ( ~ ( qmltpeq @ SV27 @ SY54 @ SV7 )
| ~ ( subset @ SV27 @ SY55 @ SV7 ) )
| ( subset @ SY54 @ SY55 @ SV7 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[95]) ).
thf(116,plain,
! [SV8: $i,SV28: mu] :
( ( ( ~ ( exists_in_world @ SV28 @ SV8 ) )
= $true )
| ( ( subset @ SV28 @ SV28 @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[96]) ).
thf(117,plain,
! [SV9: $i,SV29: mu] :
( ( ( ~ ( exists_in_world @ SV29 @ SV9 ) )
= $true )
| ( ( ! [SY56: mu] :
( ~ ( exists_in_world @ SY56 @ SV9 )
| ! [SY57: mu] :
( ~ ( exists_in_world @ SY57 @ SV9 )
| ~ ( ~ ( ~ ( member @ SY57 @ ( union @ SV29 @ SY56 ) @ SV9 )
| ( member @ SY57 @ SV29 @ SV9 )
| ( member @ SY57 @ SY56 @ SV9 ) )
| ~ ( ~ ( ( member @ SY57 @ SV29 @ SV9 )
| ( member @ SY57 @ SY56 @ SV9 ) )
| ( member @ SY57 @ ( union @ SV29 @ SY56 ) @ SV9 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[97]) ).
thf(118,plain,
! [SV10: $i,SV30: mu] :
( ( ( ~ ( exists_in_world @ SV30 @ SV10 ) )
= $true )
| ( ( ! [SY58: mu] :
( ~ ( exists_in_world @ SY58 @ SV10 )
| ~ ( subset @ SV30 @ SY58 @ SV10 )
| ( qmltpeq @ ( union @ SV30 @ SY58 ) @ SY58 @ SV10 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[98]) ).
thf(119,plain,
! [SV11: $i,SV31: mu] :
( ( ( ~ ( exists_in_world @ SV31 @ SV11 ) )
= $true )
| ( ( ! [SY59: mu] :
( ~ ( exists_in_world @ SY59 @ SV11 )
| ! [SY60: mu] :
( ~ ( exists_in_world @ SY60 @ SV11 )
| ~ ( qmltpeq @ SV31 @ SY59 @ SV11 )
| ( qmltpeq @ ( union @ SY60 @ SV31 ) @ ( union @ SY60 @ SY59 ) @ SV11 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[99]) ).
thf(120,plain,
! [SV12: $i,SV32: mu] :
( ( ( ~ ( exists_in_world @ SV32 @ SV12 ) )
= $true )
| ( ( ! [SY61: mu] :
( ~ ( exists_in_world @ SY61 @ SV12 )
| ! [SY62: mu] :
( ~ ( exists_in_world @ SY62 @ SV12 )
| ~ ~ ( ~ ( qmltpeq @ SV32 @ SY61 @ SV12 )
| ~ ( member @ SV32 @ SY62 @ SV12 ) )
| ( member @ SY61 @ SY62 @ SV12 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[100]) ).
thf(121,plain,
! [SV13: $i,SV33: mu] :
( ( ( ~ ( exists_in_world @ SV33 @ SV13 ) )
= $true )
| ( ( ! [SY63: mu] :
( ~ ( exists_in_world @ SY63 @ SV13 )
| ~ ( qmltpeq @ SV33 @ SY63 @ SV13 )
| ( qmltpeq @ SY63 @ SV33 @ SV13 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[101]) ).
thf(122,plain,
! [SV14: $i,SV34: mu] :
( ( ( ~ ( exists_in_world @ SV34 @ SV14 ) )
= $true )
| ( ( ! [SY64: mu] :
( ~ ( exists_in_world @ SY64 @ SV14 )
| ( qmltpeq @ ( union @ SV34 @ SY64 ) @ ( union @ SY64 @ SV34 ) @ SV14 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[102]) ).
thf(123,plain,
! [SV15: $i,SV35: mu] :
( ( ( ~ ( exists_in_world @ SV35 @ SV15 ) )
= $true )
| ( ( ! [SY65: mu] :
( ~ ( exists_in_world @ SY65 @ SV15 )
| ~ ( ~ ( ~ ( qmltpeq @ SV35 @ SY65 @ SV15 )
| ! [SY66: mu] :
( ~ ( exists_in_world @ SY66 @ SV15 )
| ~ ( ~ ( ~ ( member @ SY66 @ SV35 @ SV15 )
| ( member @ SY66 @ SY65 @ SV15 ) )
| ~ ( ~ ( member @ SY66 @ SY65 @ SV15 )
| ( member @ SY66 @ SV35 @ SV15 ) ) ) ) )
| ~ ( ~ ! [SY67: mu] :
( ~ ( exists_in_world @ SY67 @ SV15 )
| ~ ( ~ ( ~ ( member @ SY67 @ SV35 @ SV15 )
| ( member @ SY67 @ SY65 @ SV15 ) )
| ~ ( ~ ( member @ SY67 @ SY65 @ SV15 )
| ( member @ SY67 @ SV35 @ SV15 ) ) ) )
| ( qmltpeq @ SV35 @ SY65 @ SV15 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[103]) ).
thf(124,plain,
! [SV17: $i,SV36: mu] :
( ( ( ~ ( exists_in_world @ SV36 @ SV17 ) )
= $true )
| ( ( ! [SY68: mu] :
( ~ ( exists_in_world @ SY68 @ SV17 )
| ~ ( ~ ( ~ ( subset @ SV36 @ SY68 @ SV17 )
| ! [SY69: mu] :
( ~ ( exists_in_world @ SY69 @ SV17 )
| ~ ( member @ SY69 @ SV36 @ SV17 )
| ( member @ SY69 @ SY68 @ SV17 ) ) )
| ~ ( ~ ! [SY70: mu] :
( ~ ( exists_in_world @ SY70 @ SV17 )
| ~ ( member @ SY70 @ SV36 @ SV17 )
| ( member @ SY70 @ SY68 @ SV17 ) )
| ( subset @ SV36 @ SY68 @ SV17 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[104]) ).
thf(125,plain,
( ( ~ ( exists_in_world @ sK3_SY71 @ sK2_SX0 )
| ( qmltpeq @ ( union @ sK3_SY71 @ sK3_SY71 ) @ sK3_SY71 @ sK2_SX0 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[105]) ).
thf(126,plain,
! [SV18: $i,SV37: mu] :
( ( ( ~ ( exists_in_world @ SV37 @ SV18 ) )
= $true )
| ( ( ! [SY72: mu] :
( ~ ( exists_in_world @ SY72 @ SV18 )
| ! [SY73: mu] :
( ~ ( exists_in_world @ SY73 @ SV18 )
| ~ ~ ( ~ ( qmltpeq @ SV37 @ SY72 @ SV18 )
| ~ ( qmltpeq @ SY72 @ SY73 @ SV18 ) )
| ( qmltpeq @ SV37 @ SY73 @ SV18 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[106]) ).
thf(127,plain,
! [SV19: $i,SV38: mu] :
( ( ( ~ ( exists_in_world @ SV38 @ SV19 ) )
= $true )
| ( ( ! [SY74: mu] :
( ~ ( exists_in_world @ SY74 @ SV19 )
| ! [SY75: mu] :
( ~ ( exists_in_world @ SY75 @ SV19 )
| ~ ~ ( ~ ( qmltpeq @ SV38 @ SY74 @ SV19 )
| ~ ( member @ SY75 @ SV38 @ SV19 ) )
| ( member @ SY75 @ SY74 @ SV19 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[107]) ).
thf(128,plain,
! [SV20: $i,SV39: mu] :
( ( ( ~ ( exists_in_world @ SV39 @ SV20 ) )
= $true )
| ( ( ! [SY76: mu] :
( ~ ( exists_in_world @ SY76 @ SV20 )
| ! [SY77: mu] :
( ~ ( exists_in_world @ SY77 @ SV20 )
| ~ ~ ( ~ ( qmltpeq @ SV39 @ SY76 @ SV20 )
| ~ ( subset @ SY77 @ SV39 @ SV20 ) )
| ( subset @ SY77 @ SY76 @ SV20 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[108]) ).
thf(129,plain,
! [SV21: $i,SV40: mu] :
( ( ( ~ ( exists_in_world @ SV40 @ SV21 ) )
= $true )
| ( ( qmltpeq @ SV40 @ SV40 @ SV21 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[109]) ).
thf(130,plain,
! [SV41: $i,SV22: $i,SV2: mu] :
( ( ( ~ ( exists_in_world @ SV2 @ SV22 )
| ~ ( rel_s4 @ SV22 @ SV41 ) )
= $true )
| ( ( exists_in_world @ SV2 @ SV41 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[110]) ).
thf(131,plain,
! [SV4: $i,SV24: mu] :
( ( ( exists_in_world @ SV24 @ SV4 )
= $false )
| ( ( ! [SY50: mu] :
( ~ ( exists_in_world @ SY50 @ SV4 )
| ~ ( ~ ( ~ ( qmltpeq @ SV24 @ SY50 @ SV4 )
| ~ ( ~ ( subset @ SV24 @ SY50 @ SV4 )
| ~ ( subset @ SY50 @ SV24 @ SV4 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV24 @ SY50 @ SV4 )
| ~ ( subset @ SY50 @ SV24 @ SV4 ) )
| ( qmltpeq @ SV24 @ SY50 @ SV4 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(132,plain,
! [SV43: $i,SV25: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ( rel_s4 @ SV5 @ SV25 )
| ~ ( rel_s4 @ SV25 @ SV43 ) ) )
= $true )
| ( ( rel_s4 @ SV5 @ SV43 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[113]) ).
thf(133,plain,
! [SV6: $i,SV26: mu] :
( ( ( exists_in_world @ SV26 @ SV6 )
= $false )
| ( ( ! [SY52: mu] :
( ~ ( exists_in_world @ SY52 @ SV6 )
| ! [SY53: mu] :
( ~ ( exists_in_world @ SY53 @ SV6 )
| ~ ( qmltpeq @ SV26 @ SY52 @ SV6 )
| ( qmltpeq @ ( union @ SV26 @ SY53 ) @ ( union @ SY52 @ SY53 ) @ SV6 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[114]) ).
thf(134,plain,
! [SV7: $i,SV27: mu] :
( ( ( exists_in_world @ SV27 @ SV7 )
= $false )
| ( ( ! [SY54: mu] :
( ~ ( exists_in_world @ SY54 @ SV7 )
| ! [SY55: mu] :
( ~ ( exists_in_world @ SY55 @ SV7 )
| ~ ~ ( ~ ( qmltpeq @ SV27 @ SY54 @ SV7 )
| ~ ( subset @ SV27 @ SY55 @ SV7 ) )
| ( subset @ SY54 @ SY55 @ SV7 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(135,plain,
! [SV8: $i,SV28: mu] :
( ( ( exists_in_world @ SV28 @ SV8 )
= $false )
| ( ( subset @ SV28 @ SV28 @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(136,plain,
! [SV9: $i,SV29: mu] :
( ( ( exists_in_world @ SV29 @ SV9 )
= $false )
| ( ( ! [SY56: mu] :
( ~ ( exists_in_world @ SY56 @ SV9 )
| ! [SY57: mu] :
( ~ ( exists_in_world @ SY57 @ SV9 )
| ~ ( ~ ( ~ ( member @ SY57 @ ( union @ SV29 @ SY56 ) @ SV9 )
| ( member @ SY57 @ SV29 @ SV9 )
| ( member @ SY57 @ SY56 @ SV9 ) )
| ~ ( ~ ( ( member @ SY57 @ SV29 @ SV9 )
| ( member @ SY57 @ SY56 @ SV9 ) )
| ( member @ SY57 @ ( union @ SV29 @ SY56 ) @ SV9 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(137,plain,
! [SV10: $i,SV30: mu] :
( ( ( exists_in_world @ SV30 @ SV10 )
= $false )
| ( ( ! [SY58: mu] :
( ~ ( exists_in_world @ SY58 @ SV10 )
| ~ ( subset @ SV30 @ SY58 @ SV10 )
| ( qmltpeq @ ( union @ SV30 @ SY58 ) @ SY58 @ SV10 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(138,plain,
! [SV11: $i,SV31: mu] :
( ( ( exists_in_world @ SV31 @ SV11 )
= $false )
| ( ( ! [SY59: mu] :
( ~ ( exists_in_world @ SY59 @ SV11 )
| ! [SY60: mu] :
( ~ ( exists_in_world @ SY60 @ SV11 )
| ~ ( qmltpeq @ SV31 @ SY59 @ SV11 )
| ( qmltpeq @ ( union @ SY60 @ SV31 ) @ ( union @ SY60 @ SY59 ) @ SV11 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(139,plain,
! [SV12: $i,SV32: mu] :
( ( ( exists_in_world @ SV32 @ SV12 )
= $false )
| ( ( ! [SY61: mu] :
( ~ ( exists_in_world @ SY61 @ SV12 )
| ! [SY62: mu] :
( ~ ( exists_in_world @ SY62 @ SV12 )
| ~ ~ ( ~ ( qmltpeq @ SV32 @ SY61 @ SV12 )
| ~ ( member @ SV32 @ SY62 @ SV12 ) )
| ( member @ SY61 @ SY62 @ SV12 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(140,plain,
! [SV13: $i,SV33: mu] :
( ( ( exists_in_world @ SV33 @ SV13 )
= $false )
| ( ( ! [SY63: mu] :
( ~ ( exists_in_world @ SY63 @ SV13 )
| ~ ( qmltpeq @ SV33 @ SY63 @ SV13 )
| ( qmltpeq @ SY63 @ SV33 @ SV13 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[121]) ).
thf(141,plain,
! [SV14: $i,SV34: mu] :
( ( ( exists_in_world @ SV34 @ SV14 )
= $false )
| ( ( ! [SY64: mu] :
( ~ ( exists_in_world @ SY64 @ SV14 )
| ( qmltpeq @ ( union @ SV34 @ SY64 ) @ ( union @ SY64 @ SV34 ) @ SV14 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(142,plain,
! [SV15: $i,SV35: mu] :
( ( ( exists_in_world @ SV35 @ SV15 )
= $false )
| ( ( ! [SY65: mu] :
( ~ ( exists_in_world @ SY65 @ SV15 )
| ~ ( ~ ( ~ ( qmltpeq @ SV35 @ SY65 @ SV15 )
| ! [SY66: mu] :
( ~ ( exists_in_world @ SY66 @ SV15 )
| ~ ( ~ ( ~ ( member @ SY66 @ SV35 @ SV15 )
| ( member @ SY66 @ SY65 @ SV15 ) )
| ~ ( ~ ( member @ SY66 @ SY65 @ SV15 )
| ( member @ SY66 @ SV35 @ SV15 ) ) ) ) )
| ~ ( ~ ! [SY67: mu] :
( ~ ( exists_in_world @ SY67 @ SV15 )
| ~ ( ~ ( ~ ( member @ SY67 @ SV35 @ SV15 )
| ( member @ SY67 @ SY65 @ SV15 ) )
| ~ ( ~ ( member @ SY67 @ SY65 @ SV15 )
| ( member @ SY67 @ SV35 @ SV15 ) ) ) )
| ( qmltpeq @ SV35 @ SY65 @ SV15 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(143,plain,
! [SV17: $i,SV36: mu] :
( ( ( exists_in_world @ SV36 @ SV17 )
= $false )
| ( ( ! [SY68: mu] :
( ~ ( exists_in_world @ SY68 @ SV17 )
| ~ ( ~ ( ~ ( subset @ SV36 @ SY68 @ SV17 )
| ! [SY69: mu] :
( ~ ( exists_in_world @ SY69 @ SV17 )
| ~ ( member @ SY69 @ SV36 @ SV17 )
| ( member @ SY69 @ SY68 @ SV17 ) ) )
| ~ ( ~ ! [SY70: mu] :
( ~ ( exists_in_world @ SY70 @ SV17 )
| ~ ( member @ SY70 @ SV36 @ SV17 )
| ( member @ SY70 @ SY68 @ SV17 ) )
| ( subset @ SV36 @ SY68 @ SV17 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(144,plain,
( ( ~ ( exists_in_world @ sK3_SY71 @ sK2_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[125]) ).
thf(145,plain,
( ( qmltpeq @ ( union @ sK3_SY71 @ sK3_SY71 ) @ sK3_SY71 @ sK2_SX0 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[125]) ).
thf(146,plain,
! [SV18: $i,SV37: mu] :
( ( ( exists_in_world @ SV37 @ SV18 )
= $false )
| ( ( ! [SY72: mu] :
( ~ ( exists_in_world @ SY72 @ SV18 )
| ! [SY73: mu] :
( ~ ( exists_in_world @ SY73 @ SV18 )
| ~ ~ ( ~ ( qmltpeq @ SV37 @ SY72 @ SV18 )
| ~ ( qmltpeq @ SY72 @ SY73 @ SV18 ) )
| ( qmltpeq @ SV37 @ SY73 @ SV18 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[126]) ).
thf(147,plain,
! [SV19: $i,SV38: mu] :
( ( ( exists_in_world @ SV38 @ SV19 )
= $false )
| ( ( ! [SY74: mu] :
( ~ ( exists_in_world @ SY74 @ SV19 )
| ! [SY75: mu] :
( ~ ( exists_in_world @ SY75 @ SV19 )
| ~ ~ ( ~ ( qmltpeq @ SV38 @ SY74 @ SV19 )
| ~ ( member @ SY75 @ SV38 @ SV19 ) )
| ( member @ SY75 @ SY74 @ SV19 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[127]) ).
thf(148,plain,
! [SV20: $i,SV39: mu] :
( ( ( exists_in_world @ SV39 @ SV20 )
= $false )
| ( ( ! [SY76: mu] :
( ~ ( exists_in_world @ SY76 @ SV20 )
| ! [SY77: mu] :
( ~ ( exists_in_world @ SY77 @ SV20 )
| ~ ~ ( ~ ( qmltpeq @ SV39 @ SY76 @ SV20 )
| ~ ( subset @ SY77 @ SV39 @ SV20 ) )
| ( subset @ SY77 @ SY76 @ SV20 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(149,plain,
! [SV21: $i,SV40: mu] :
( ( ( exists_in_world @ SV40 @ SV21 )
= $false )
| ( ( qmltpeq @ SV40 @ SV40 @ SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[129]) ).
thf(150,plain,
! [SV41: $i,SV22: $i,SV2: mu] :
( ( ( ~ ( exists_in_world @ SV2 @ SV22 ) )
= $true )
| ( ( ~ ( rel_s4 @ SV22 @ SV41 ) )
= $true )
| ( ( exists_in_world @ SV2 @ SV41 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[130]) ).
thf(151,plain,
! [SV24: mu,SV4: $i,SV44: mu] :
( ( ( ~ ( exists_in_world @ SV44 @ SV4 )
| ~ ( ~ ( ~ ( qmltpeq @ SV24 @ SV44 @ SV4 )
| ~ ( ~ ( subset @ SV24 @ SV44 @ SV4 )
| ~ ( subset @ SV44 @ SV24 @ SV4 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV24 @ SV44 @ SV4 )
| ~ ( subset @ SV44 @ SV24 @ SV4 ) )
| ( qmltpeq @ SV24 @ SV44 @ SV4 ) ) ) )
= $true )
| ( ( exists_in_world @ SV24 @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(152,plain,
! [SV43: $i,SV25: $i,SV5: $i] :
( ( ( ~ ( ~ ( rel_s4 @ SV5 @ SV25 )
| ~ ( rel_s4 @ SV25 @ SV43 ) ) )
= $false )
| ( ( rel_s4 @ SV5 @ SV43 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(153,plain,
! [SV26: mu,SV6: $i,SV45: mu] :
( ( ( ~ ( exists_in_world @ SV45 @ SV6 )
| ! [SY78: mu] :
( ~ ( exists_in_world @ SY78 @ SV6 )
| ~ ( qmltpeq @ SV26 @ SV45 @ SV6 )
| ( qmltpeq @ ( union @ SV26 @ SY78 ) @ ( union @ SV45 @ SY78 ) @ SV6 ) ) )
= $true )
| ( ( exists_in_world @ SV26 @ SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(154,plain,
! [SV27: mu,SV7: $i,SV46: mu] :
( ( ( ~ ( exists_in_world @ SV46 @ SV7 )
| ! [SY79: mu] :
( ~ ( exists_in_world @ SY79 @ SV7 )
| ~ ~ ( ~ ( qmltpeq @ SV27 @ SV46 @ SV7 )
| ~ ( subset @ SV27 @ SY79 @ SV7 ) )
| ( subset @ SV46 @ SY79 @ SV7 ) ) )
= $true )
| ( ( exists_in_world @ SV27 @ SV7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(155,plain,
! [SV29: mu,SV9: $i,SV47: mu] :
( ( ( ~ ( exists_in_world @ SV47 @ SV9 )
| ! [SY80: mu] :
( ~ ( exists_in_world @ SY80 @ SV9 )
| ~ ( ~ ( ~ ( member @ SY80 @ ( union @ SV29 @ SV47 ) @ SV9 )
| ( member @ SY80 @ SV29 @ SV9 )
| ( member @ SY80 @ SV47 @ SV9 ) )
| ~ ( ~ ( ( member @ SY80 @ SV29 @ SV9 )
| ( member @ SY80 @ SV47 @ SV9 ) )
| ( member @ SY80 @ ( union @ SV29 @ SV47 ) @ SV9 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV29 @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(156,plain,
! [SV30: mu,SV10: $i,SV48: mu] :
( ( ( ~ ( exists_in_world @ SV48 @ SV10 )
| ~ ( subset @ SV30 @ SV48 @ SV10 )
| ( qmltpeq @ ( union @ SV30 @ SV48 ) @ SV48 @ SV10 ) )
= $true )
| ( ( exists_in_world @ SV30 @ SV10 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(157,plain,
! [SV31: mu,SV11: $i,SV49: mu] :
( ( ( ~ ( exists_in_world @ SV49 @ SV11 )
| ! [SY81: mu] :
( ~ ( exists_in_world @ SY81 @ SV11 )
| ~ ( qmltpeq @ SV31 @ SV49 @ SV11 )
| ( qmltpeq @ ( union @ SY81 @ SV31 ) @ ( union @ SY81 @ SV49 ) @ SV11 ) ) )
= $true )
| ( ( exists_in_world @ SV31 @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(158,plain,
! [SV32: mu,SV12: $i,SV50: mu] :
( ( ( ~ ( exists_in_world @ SV50 @ SV12 )
| ! [SY82: mu] :
( ~ ( exists_in_world @ SY82 @ SV12 )
| ~ ~ ( ~ ( qmltpeq @ SV32 @ SV50 @ SV12 )
| ~ ( member @ SV32 @ SY82 @ SV12 ) )
| ( member @ SV50 @ SY82 @ SV12 ) ) )
= $true )
| ( ( exists_in_world @ SV32 @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(159,plain,
! [SV33: mu,SV13: $i,SV51: mu] :
( ( ( ~ ( exists_in_world @ SV51 @ SV13 )
| ~ ( qmltpeq @ SV33 @ SV51 @ SV13 )
| ( qmltpeq @ SV51 @ SV33 @ SV13 ) )
= $true )
| ( ( exists_in_world @ SV33 @ SV13 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(160,plain,
! [SV34: mu,SV14: $i,SV52: mu] :
( ( ( ~ ( exists_in_world @ SV52 @ SV14 )
| ( qmltpeq @ ( union @ SV34 @ SV52 ) @ ( union @ SV52 @ SV34 ) @ SV14 ) )
= $true )
| ( ( exists_in_world @ SV34 @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(161,plain,
! [SV35: mu,SV15: $i,SV53: mu] :
( ( ( ~ ( exists_in_world @ SV53 @ SV15 )
| ~ ( ~ ( ~ ( qmltpeq @ SV35 @ SV53 @ SV15 )
| ! [SY83: mu] :
( ~ ( exists_in_world @ SY83 @ SV15 )
| ~ ( ~ ( ~ ( member @ SY83 @ SV35 @ SV15 )
| ( member @ SY83 @ SV53 @ SV15 ) )
| ~ ( ~ ( member @ SY83 @ SV53 @ SV15 )
| ( member @ SY83 @ SV35 @ SV15 ) ) ) ) )
| ~ ( ~ ! [SY84: mu] :
( ~ ( exists_in_world @ SY84 @ SV15 )
| ~ ( ~ ( ~ ( member @ SY84 @ SV35 @ SV15 )
| ( member @ SY84 @ SV53 @ SV15 ) )
| ~ ( ~ ( member @ SY84 @ SV53 @ SV15 )
| ( member @ SY84 @ SV35 @ SV15 ) ) ) )
| ( qmltpeq @ SV35 @ SV53 @ SV15 ) ) ) )
= $true )
| ( ( exists_in_world @ SV35 @ SV15 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(162,plain,
! [SV36: mu,SV17: $i,SV54: mu] :
( ( ( ~ ( exists_in_world @ SV54 @ SV17 )
| ~ ( ~ ( ~ ( subset @ SV36 @ SV54 @ SV17 )
| ! [SY85: mu] :
( ~ ( exists_in_world @ SY85 @ SV17 )
| ~ ( member @ SY85 @ SV36 @ SV17 )
| ( member @ SY85 @ SV54 @ SV17 ) ) )
| ~ ( ~ ! [SY86: mu] :
( ~ ( exists_in_world @ SY86 @ SV17 )
| ~ ( member @ SY86 @ SV36 @ SV17 )
| ( member @ SY86 @ SV54 @ SV17 ) )
| ( subset @ SV36 @ SV54 @ SV17 ) ) ) )
= $true )
| ( ( exists_in_world @ SV36 @ SV17 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(163,plain,
( ( exists_in_world @ sK3_SY71 @ sK2_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[144]) ).
thf(164,plain,
! [SV37: mu,SV18: $i,SV55: mu] :
( ( ( ~ ( exists_in_world @ SV55 @ SV18 )
| ! [SY87: mu] :
( ~ ( exists_in_world @ SY87 @ SV18 )
| ~ ~ ( ~ ( qmltpeq @ SV37 @ SV55 @ SV18 )
| ~ ( qmltpeq @ SV55 @ SY87 @ SV18 ) )
| ( qmltpeq @ SV37 @ SY87 @ SV18 ) ) )
= $true )
| ( ( exists_in_world @ SV37 @ SV18 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(165,plain,
! [SV38: mu,SV19: $i,SV56: mu] :
( ( ( ~ ( exists_in_world @ SV56 @ SV19 )
| ! [SY88: mu] :
( ~ ( exists_in_world @ SY88 @ SV19 )
| ~ ~ ( ~ ( qmltpeq @ SV38 @ SV56 @ SV19 )
| ~ ( member @ SY88 @ SV38 @ SV19 ) )
| ( member @ SY88 @ SV56 @ SV19 ) ) )
= $true )
| ( ( exists_in_world @ SV38 @ SV19 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(166,plain,
! [SV39: mu,SV20: $i,SV57: mu] :
( ( ( ~ ( exists_in_world @ SV57 @ SV20 )
| ! [SY89: mu] :
( ~ ( exists_in_world @ SY89 @ SV20 )
| ~ ~ ( ~ ( qmltpeq @ SV39 @ SV57 @ SV20 )
| ~ ( subset @ SY89 @ SV39 @ SV20 ) )
| ( subset @ SY89 @ SV57 @ SV20 ) ) )
= $true )
| ( ( exists_in_world @ SV39 @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(167,plain,
! [SV41: $i,SV22: $i,SV2: mu] :
( ( ( exists_in_world @ SV2 @ SV22 )
= $false )
| ( ( ~ ( rel_s4 @ SV22 @ SV41 ) )
= $true )
| ( ( exists_in_world @ SV2 @ SV41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[150]) ).
thf(168,plain,
! [SV24: mu,SV4: $i,SV44: mu] :
( ( ( ~ ( exists_in_world @ SV44 @ SV4 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( qmltpeq @ SV24 @ SV44 @ SV4 )
| ~ ( ~ ( subset @ SV24 @ SV44 @ SV4 )
| ~ ( subset @ SV44 @ SV24 @ SV4 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV24 @ SV44 @ SV4 )
| ~ ( subset @ SV44 @ SV24 @ SV4 ) )
| ( qmltpeq @ SV24 @ SV44 @ SV4 ) ) ) )
= $true )
| ( ( exists_in_world @ SV24 @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[151]) ).
thf(169,plain,
! [SV43: $i,SV25: $i,SV5: $i] :
( ( ( ~ ( rel_s4 @ SV5 @ SV25 )
| ~ ( rel_s4 @ SV25 @ SV43 ) )
= $true )
| ( ( rel_s4 @ SV5 @ SV43 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[152]) ).
thf(170,plain,
! [SV26: mu,SV6: $i,SV45: mu] :
( ( ( ~ ( exists_in_world @ SV45 @ SV6 ) )
= $true )
| ( ( ! [SY78: mu] :
( ~ ( exists_in_world @ SY78 @ SV6 )
| ~ ( qmltpeq @ SV26 @ SV45 @ SV6 )
| ( qmltpeq @ ( union @ SV26 @ SY78 ) @ ( union @ SV45 @ SY78 ) @ SV6 ) ) )
= $true )
| ( ( exists_in_world @ SV26 @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[153]) ).
thf(171,plain,
! [SV27: mu,SV7: $i,SV46: mu] :
( ( ( ~ ( exists_in_world @ SV46 @ SV7 ) )
= $true )
| ( ( ! [SY79: mu] :
( ~ ( exists_in_world @ SY79 @ SV7 )
| ~ ~ ( ~ ( qmltpeq @ SV27 @ SV46 @ SV7 )
| ~ ( subset @ SV27 @ SY79 @ SV7 ) )
| ( subset @ SV46 @ SY79 @ SV7 ) ) )
= $true )
| ( ( exists_in_world @ SV27 @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[154]) ).
thf(172,plain,
! [SV29: mu,SV9: $i,SV47: mu] :
( ( ( ~ ( exists_in_world @ SV47 @ SV9 ) )
= $true )
| ( ( ! [SY80: mu] :
( ~ ( exists_in_world @ SY80 @ SV9 )
| ~ ( ~ ( ~ ( member @ SY80 @ ( union @ SV29 @ SV47 ) @ SV9 )
| ( member @ SY80 @ SV29 @ SV9 )
| ( member @ SY80 @ SV47 @ SV9 ) )
| ~ ( ~ ( ( member @ SY80 @ SV29 @ SV9 )
| ( member @ SY80 @ SV47 @ SV9 ) )
| ( member @ SY80 @ ( union @ SV29 @ SV47 ) @ SV9 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV29 @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[155]) ).
thf(173,plain,
! [SV30: mu,SV10: $i,SV48: mu] :
( ( ( ~ ( exists_in_world @ SV48 @ SV10 ) )
= $true )
| ( ( ~ ( subset @ SV30 @ SV48 @ SV10 )
| ( qmltpeq @ ( union @ SV30 @ SV48 ) @ SV48 @ SV10 ) )
= $true )
| ( ( exists_in_world @ SV30 @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[156]) ).
thf(174,plain,
! [SV31: mu,SV11: $i,SV49: mu] :
( ( ( ~ ( exists_in_world @ SV49 @ SV11 ) )
= $true )
| ( ( ! [SY81: mu] :
( ~ ( exists_in_world @ SY81 @ SV11 )
| ~ ( qmltpeq @ SV31 @ SV49 @ SV11 )
| ( qmltpeq @ ( union @ SY81 @ SV31 ) @ ( union @ SY81 @ SV49 ) @ SV11 ) ) )
= $true )
| ( ( exists_in_world @ SV31 @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[157]) ).
thf(175,plain,
! [SV32: mu,SV12: $i,SV50: mu] :
( ( ( ~ ( exists_in_world @ SV50 @ SV12 ) )
= $true )
| ( ( ! [SY82: mu] :
( ~ ( exists_in_world @ SY82 @ SV12 )
| ~ ~ ( ~ ( qmltpeq @ SV32 @ SV50 @ SV12 )
| ~ ( member @ SV32 @ SY82 @ SV12 ) )
| ( member @ SV50 @ SY82 @ SV12 ) ) )
= $true )
| ( ( exists_in_world @ SV32 @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[158]) ).
thf(176,plain,
! [SV33: mu,SV13: $i,SV51: mu] :
( ( ( ~ ( exists_in_world @ SV51 @ SV13 ) )
= $true )
| ( ( ~ ( qmltpeq @ SV33 @ SV51 @ SV13 )
| ( qmltpeq @ SV51 @ SV33 @ SV13 ) )
= $true )
| ( ( exists_in_world @ SV33 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[159]) ).
thf(177,plain,
! [SV34: mu,SV14: $i,SV52: mu] :
( ( ( ~ ( exists_in_world @ SV52 @ SV14 ) )
= $true )
| ( ( qmltpeq @ ( union @ SV34 @ SV52 ) @ ( union @ SV52 @ SV34 ) @ SV14 )
= $true )
| ( ( exists_in_world @ SV34 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[160]) ).
thf(178,plain,
! [SV35: mu,SV15: $i,SV53: mu] :
( ( ( ~ ( exists_in_world @ SV53 @ SV15 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( qmltpeq @ SV35 @ SV53 @ SV15 )
| ! [SY83: mu] :
( ~ ( exists_in_world @ SY83 @ SV15 )
| ~ ( ~ ( ~ ( member @ SY83 @ SV35 @ SV15 )
| ( member @ SY83 @ SV53 @ SV15 ) )
| ~ ( ~ ( member @ SY83 @ SV53 @ SV15 )
| ( member @ SY83 @ SV35 @ SV15 ) ) ) ) )
| ~ ( ~ ! [SY84: mu] :
( ~ ( exists_in_world @ SY84 @ SV15 )
| ~ ( ~ ( ~ ( member @ SY84 @ SV35 @ SV15 )
| ( member @ SY84 @ SV53 @ SV15 ) )
| ~ ( ~ ( member @ SY84 @ SV53 @ SV15 )
| ( member @ SY84 @ SV35 @ SV15 ) ) ) )
| ( qmltpeq @ SV35 @ SV53 @ SV15 ) ) ) )
= $true )
| ( ( exists_in_world @ SV35 @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[161]) ).
thf(179,plain,
! [SV36: mu,SV17: $i,SV54: mu] :
( ( ( ~ ( exists_in_world @ SV54 @ SV17 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( subset @ SV36 @ SV54 @ SV17 )
| ! [SY85: mu] :
( ~ ( exists_in_world @ SY85 @ SV17 )
| ~ ( member @ SY85 @ SV36 @ SV17 )
| ( member @ SY85 @ SV54 @ SV17 ) ) )
| ~ ( ~ ! [SY86: mu] :
( ~ ( exists_in_world @ SY86 @ SV17 )
| ~ ( member @ SY86 @ SV36 @ SV17 )
| ( member @ SY86 @ SV54 @ SV17 ) )
| ( subset @ SV36 @ SV54 @ SV17 ) ) ) )
= $true )
| ( ( exists_in_world @ SV36 @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[162]) ).
thf(180,plain,
! [SV37: mu,SV18: $i,SV55: mu] :
( ( ( ~ ( exists_in_world @ SV55 @ SV18 ) )
= $true )
| ( ( ! [SY87: mu] :
( ~ ( exists_in_world @ SY87 @ SV18 )
| ~ ~ ( ~ ( qmltpeq @ SV37 @ SV55 @ SV18 )
| ~ ( qmltpeq @ SV55 @ SY87 @ SV18 ) )
| ( qmltpeq @ SV37 @ SY87 @ SV18 ) ) )
= $true )
| ( ( exists_in_world @ SV37 @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[164]) ).
thf(181,plain,
! [SV38: mu,SV19: $i,SV56: mu] :
( ( ( ~ ( exists_in_world @ SV56 @ SV19 ) )
= $true )
| ( ( ! [SY88: mu] :
( ~ ( exists_in_world @ SY88 @ SV19 )
| ~ ~ ( ~ ( qmltpeq @ SV38 @ SV56 @ SV19 )
| ~ ( member @ SY88 @ SV38 @ SV19 ) )
| ( member @ SY88 @ SV56 @ SV19 ) ) )
= $true )
| ( ( exists_in_world @ SV38 @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[165]) ).
thf(182,plain,
! [SV39: mu,SV20: $i,SV57: mu] :
( ( ( ~ ( exists_in_world @ SV57 @ SV20 ) )
= $true )
| ( ( ! [SY89: mu] :
( ~ ( exists_in_world @ SY89 @ SV20 )
| ~ ~ ( ~ ( qmltpeq @ SV39 @ SV57 @ SV20 )
| ~ ( subset @ SY89 @ SV39 @ SV20 ) )
| ( subset @ SY89 @ SV57 @ SV20 ) ) )
= $true )
| ( ( exists_in_world @ SV39 @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[166]) ).
thf(183,plain,
! [SV2: mu,SV41: $i,SV22: $i] :
( ( ( rel_s4 @ SV22 @ SV41 )
= $false )
| ( ( exists_in_world @ SV2 @ SV22 )
= $false )
| ( ( exists_in_world @ SV2 @ SV41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(184,plain,
! [SV24: mu,SV4: $i,SV44: mu] :
( ( ( exists_in_world @ SV44 @ SV4 )
= $false )
| ( ( ~ ( ~ ( ~ ( qmltpeq @ SV24 @ SV44 @ SV4 )
| ~ ( ~ ( subset @ SV24 @ SV44 @ SV4 )
| ~ ( subset @ SV44 @ SV24 @ SV4 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV24 @ SV44 @ SV4 )
| ~ ( subset @ SV44 @ SV24 @ SV4 ) )
| ( qmltpeq @ SV24 @ SV44 @ SV4 ) ) ) )
= $true )
| ( ( exists_in_world @ SV24 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[168]) ).
thf(185,plain,
! [SV43: $i,SV25: $i,SV5: $i] :
( ( ( ~ ( rel_s4 @ SV5 @ SV25 ) )
= $true )
| ( ( ~ ( rel_s4 @ SV25 @ SV43 ) )
= $true )
| ( ( rel_s4 @ SV5 @ SV43 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[169]) ).
thf(186,plain,
! [SV26: mu,SV6: $i,SV45: mu] :
( ( ( exists_in_world @ SV45 @ SV6 )
= $false )
| ( ( ! [SY78: mu] :
( ~ ( exists_in_world @ SY78 @ SV6 )
| ~ ( qmltpeq @ SV26 @ SV45 @ SV6 )
| ( qmltpeq @ ( union @ SV26 @ SY78 ) @ ( union @ SV45 @ SY78 ) @ SV6 ) ) )
= $true )
| ( ( exists_in_world @ SV26 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(187,plain,
! [SV27: mu,SV7: $i,SV46: mu] :
( ( ( exists_in_world @ SV46 @ SV7 )
= $false )
| ( ( ! [SY79: mu] :
( ~ ( exists_in_world @ SY79 @ SV7 )
| ~ ~ ( ~ ( qmltpeq @ SV27 @ SV46 @ SV7 )
| ~ ( subset @ SV27 @ SY79 @ SV7 ) )
| ( subset @ SV46 @ SY79 @ SV7 ) ) )
= $true )
| ( ( exists_in_world @ SV27 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(188,plain,
! [SV29: mu,SV9: $i,SV47: mu] :
( ( ( exists_in_world @ SV47 @ SV9 )
= $false )
| ( ( ! [SY80: mu] :
( ~ ( exists_in_world @ SY80 @ SV9 )
| ~ ( ~ ( ~ ( member @ SY80 @ ( union @ SV29 @ SV47 ) @ SV9 )
| ( member @ SY80 @ SV29 @ SV9 )
| ( member @ SY80 @ SV47 @ SV9 ) )
| ~ ( ~ ( ( member @ SY80 @ SV29 @ SV9 )
| ( member @ SY80 @ SV47 @ SV9 ) )
| ( member @ SY80 @ ( union @ SV29 @ SV47 ) @ SV9 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV29 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(189,plain,
! [SV30: mu,SV10: $i,SV48: mu] :
( ( ( exists_in_world @ SV48 @ SV10 )
= $false )
| ( ( ~ ( subset @ SV30 @ SV48 @ SV10 )
| ( qmltpeq @ ( union @ SV30 @ SV48 ) @ SV48 @ SV10 ) )
= $true )
| ( ( exists_in_world @ SV30 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[173]) ).
thf(190,plain,
! [SV31: mu,SV11: $i,SV49: mu] :
( ( ( exists_in_world @ SV49 @ SV11 )
= $false )
| ( ( ! [SY81: mu] :
( ~ ( exists_in_world @ SY81 @ SV11 )
| ~ ( qmltpeq @ SV31 @ SV49 @ SV11 )
| ( qmltpeq @ ( union @ SY81 @ SV31 ) @ ( union @ SY81 @ SV49 ) @ SV11 ) ) )
= $true )
| ( ( exists_in_world @ SV31 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[174]) ).
thf(191,plain,
! [SV32: mu,SV12: $i,SV50: mu] :
( ( ( exists_in_world @ SV50 @ SV12 )
= $false )
| ( ( ! [SY82: mu] :
( ~ ( exists_in_world @ SY82 @ SV12 )
| ~ ~ ( ~ ( qmltpeq @ SV32 @ SV50 @ SV12 )
| ~ ( member @ SV32 @ SY82 @ SV12 ) )
| ( member @ SV50 @ SY82 @ SV12 ) ) )
= $true )
| ( ( exists_in_world @ SV32 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[175]) ).
thf(192,plain,
! [SV33: mu,SV13: $i,SV51: mu] :
( ( ( exists_in_world @ SV51 @ SV13 )
= $false )
| ( ( ~ ( qmltpeq @ SV33 @ SV51 @ SV13 )
| ( qmltpeq @ SV51 @ SV33 @ SV13 ) )
= $true )
| ( ( exists_in_world @ SV33 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[176]) ).
thf(193,plain,
! [SV34: mu,SV14: $i,SV52: mu] :
( ( ( exists_in_world @ SV52 @ SV14 )
= $false )
| ( ( qmltpeq @ ( union @ SV34 @ SV52 ) @ ( union @ SV52 @ SV34 ) @ SV14 )
= $true )
| ( ( exists_in_world @ SV34 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(194,plain,
! [SV35: mu,SV15: $i,SV53: mu] :
( ( ( exists_in_world @ SV53 @ SV15 )
= $false )
| ( ( ~ ( ~ ( ~ ( qmltpeq @ SV35 @ SV53 @ SV15 )
| ! [SY83: mu] :
( ~ ( exists_in_world @ SY83 @ SV15 )
| ~ ( ~ ( ~ ( member @ SY83 @ SV35 @ SV15 )
| ( member @ SY83 @ SV53 @ SV15 ) )
| ~ ( ~ ( member @ SY83 @ SV53 @ SV15 )
| ( member @ SY83 @ SV35 @ SV15 ) ) ) ) )
| ~ ( ~ ! [SY84: mu] :
( ~ ( exists_in_world @ SY84 @ SV15 )
| ~ ( ~ ( ~ ( member @ SY84 @ SV35 @ SV15 )
| ( member @ SY84 @ SV53 @ SV15 ) )
| ~ ( ~ ( member @ SY84 @ SV53 @ SV15 )
| ( member @ SY84 @ SV35 @ SV15 ) ) ) )
| ( qmltpeq @ SV35 @ SV53 @ SV15 ) ) ) )
= $true )
| ( ( exists_in_world @ SV35 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(195,plain,
! [SV36: mu,SV17: $i,SV54: mu] :
( ( ( exists_in_world @ SV54 @ SV17 )
= $false )
| ( ( ~ ( ~ ( ~ ( subset @ SV36 @ SV54 @ SV17 )
| ! [SY85: mu] :
( ~ ( exists_in_world @ SY85 @ SV17 )
| ~ ( member @ SY85 @ SV36 @ SV17 )
| ( member @ SY85 @ SV54 @ SV17 ) ) )
| ~ ( ~ ! [SY86: mu] :
( ~ ( exists_in_world @ SY86 @ SV17 )
| ~ ( member @ SY86 @ SV36 @ SV17 )
| ( member @ SY86 @ SV54 @ SV17 ) )
| ( subset @ SV36 @ SV54 @ SV17 ) ) ) )
= $true )
| ( ( exists_in_world @ SV36 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(196,plain,
! [SV37: mu,SV18: $i,SV55: mu] :
( ( ( exists_in_world @ SV55 @ SV18 )
= $false )
| ( ( ! [SY87: mu] :
( ~ ( exists_in_world @ SY87 @ SV18 )
| ~ ~ ( ~ ( qmltpeq @ SV37 @ SV55 @ SV18 )
| ~ ( qmltpeq @ SV55 @ SY87 @ SV18 ) )
| ( qmltpeq @ SV37 @ SY87 @ SV18 ) ) )
= $true )
| ( ( exists_in_world @ SV37 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[180]) ).
thf(197,plain,
! [SV38: mu,SV19: $i,SV56: mu] :
( ( ( exists_in_world @ SV56 @ SV19 )
= $false )
| ( ( ! [SY88: mu] :
( ~ ( exists_in_world @ SY88 @ SV19 )
| ~ ~ ( ~ ( qmltpeq @ SV38 @ SV56 @ SV19 )
| ~ ( member @ SY88 @ SV38 @ SV19 ) )
| ( member @ SY88 @ SV56 @ SV19 ) ) )
= $true )
| ( ( exists_in_world @ SV38 @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[181]) ).
thf(198,plain,
! [SV39: mu,SV20: $i,SV57: mu] :
( ( ( exists_in_world @ SV57 @ SV20 )
= $false )
| ( ( ! [SY89: mu] :
( ~ ( exists_in_world @ SY89 @ SV20 )
| ~ ~ ( ~ ( qmltpeq @ SV39 @ SV57 @ SV20 )
| ~ ( subset @ SY89 @ SV39 @ SV20 ) )
| ( subset @ SY89 @ SV57 @ SV20 ) ) )
= $true )
| ( ( exists_in_world @ SV39 @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[182]) ).
thf(199,plain,
! [SV4: $i,SV44: mu,SV24: mu] :
( ( ( ~ ( ~ ( qmltpeq @ SV24 @ SV44 @ SV4 )
| ~ ( ~ ( subset @ SV24 @ SV44 @ SV4 )
| ~ ( subset @ SV44 @ SV24 @ SV4 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV24 @ SV44 @ SV4 )
| ~ ( subset @ SV44 @ SV24 @ SV4 ) )
| ( qmltpeq @ SV24 @ SV44 @ SV4 ) ) )
= $false )
| ( ( exists_in_world @ SV44 @ SV4 )
= $false )
| ( ( exists_in_world @ SV24 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[184]) ).
thf(200,plain,
! [SV43: $i,SV25: $i,SV5: $i] :
( ( ( rel_s4 @ SV5 @ SV25 )
= $false )
| ( ( ~ ( rel_s4 @ SV25 @ SV43 ) )
= $true )
| ( ( rel_s4 @ SV5 @ SV43 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[185]) ).
thf(201,plain,
! [SV45: mu,SV26: mu,SV6: $i,SV58: mu] :
( ( ( ~ ( exists_in_world @ SV58 @ SV6 )
| ~ ( qmltpeq @ SV26 @ SV45 @ SV6 )
| ( qmltpeq @ ( union @ SV26 @ SV58 ) @ ( union @ SV45 @ SV58 ) @ SV6 ) )
= $true )
| ( ( exists_in_world @ SV45 @ SV6 )
= $false )
| ( ( exists_in_world @ SV26 @ SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(202,plain,
! [SV46: mu,SV27: mu,SV7: $i,SV59: mu] :
( ( ( ~ ( exists_in_world @ SV59 @ SV7 )
| ~ ~ ( ~ ( qmltpeq @ SV27 @ SV46 @ SV7 )
| ~ ( subset @ SV27 @ SV59 @ SV7 ) )
| ( subset @ SV46 @ SV59 @ SV7 ) )
= $true )
| ( ( exists_in_world @ SV46 @ SV7 )
= $false )
| ( ( exists_in_world @ SV27 @ SV7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[187]) ).
thf(203,plain,
! [SV47: mu,SV29: mu,SV9: $i,SV60: mu] :
( ( ( ~ ( exists_in_world @ SV60 @ SV9 )
| ~ ( ~ ( ~ ( member @ SV60 @ ( union @ SV29 @ SV47 ) @ SV9 )
| ( member @ SV60 @ SV29 @ SV9 )
| ( member @ SV60 @ SV47 @ SV9 ) )
| ~ ( ~ ( ( member @ SV60 @ SV29 @ SV9 )
| ( member @ SV60 @ SV47 @ SV9 ) )
| ( member @ SV60 @ ( union @ SV29 @ SV47 ) @ SV9 ) ) ) )
= $true )
| ( ( exists_in_world @ SV47 @ SV9 )
= $false )
| ( ( exists_in_world @ SV29 @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(204,plain,
! [SV10: $i,SV48: mu,SV30: mu] :
( ( ( ~ ( subset @ SV30 @ SV48 @ SV10 ) )
= $true )
| ( ( qmltpeq @ ( union @ SV30 @ SV48 ) @ SV48 @ SV10 )
= $true )
| ( ( exists_in_world @ SV48 @ SV10 )
= $false )
| ( ( exists_in_world @ SV30 @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[189]) ).
thf(205,plain,
! [SV49: mu,SV31: mu,SV11: $i,SV61: mu] :
( ( ( ~ ( exists_in_world @ SV61 @ SV11 )
| ~ ( qmltpeq @ SV31 @ SV49 @ SV11 )
| ( qmltpeq @ ( union @ SV61 @ SV31 ) @ ( union @ SV61 @ SV49 ) @ SV11 ) )
= $true )
| ( ( exists_in_world @ SV49 @ SV11 )
= $false )
| ( ( exists_in_world @ SV31 @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(206,plain,
! [SV50: mu,SV32: mu,SV12: $i,SV62: mu] :
( ( ( ~ ( exists_in_world @ SV62 @ SV12 )
| ~ ~ ( ~ ( qmltpeq @ SV32 @ SV50 @ SV12 )
| ~ ( member @ SV32 @ SV62 @ SV12 ) )
| ( member @ SV50 @ SV62 @ SV12 ) )
= $true )
| ( ( exists_in_world @ SV50 @ SV12 )
= $false )
| ( ( exists_in_world @ SV32 @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[191]) ).
thf(207,plain,
! [SV13: $i,SV51: mu,SV33: mu] :
( ( ( ~ ( qmltpeq @ SV33 @ SV51 @ SV13 ) )
= $true )
| ( ( qmltpeq @ SV51 @ SV33 @ SV13 )
= $true )
| ( ( exists_in_world @ SV51 @ SV13 )
= $false )
| ( ( exists_in_world @ SV33 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[192]) ).
thf(208,plain,
! [SV15: $i,SV53: mu,SV35: mu] :
( ( ( ~ ( ~ ( qmltpeq @ SV35 @ SV53 @ SV15 )
| ! [SY83: mu] :
( ~ ( exists_in_world @ SY83 @ SV15 )
| ~ ( ~ ( ~ ( member @ SY83 @ SV35 @ SV15 )
| ( member @ SY83 @ SV53 @ SV15 ) )
| ~ ( ~ ( member @ SY83 @ SV53 @ SV15 )
| ( member @ SY83 @ SV35 @ SV15 ) ) ) ) )
| ~ ( ~ ! [SY84: mu] :
( ~ ( exists_in_world @ SY84 @ SV15 )
| ~ ( ~ ( ~ ( member @ SY84 @ SV35 @ SV15 )
| ( member @ SY84 @ SV53 @ SV15 ) )
| ~ ( ~ ( member @ SY84 @ SV53 @ SV15 )
| ( member @ SY84 @ SV35 @ SV15 ) ) ) )
| ( qmltpeq @ SV35 @ SV53 @ SV15 ) ) )
= $false )
| ( ( exists_in_world @ SV53 @ SV15 )
= $false )
| ( ( exists_in_world @ SV35 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(209,plain,
! [SV17: $i,SV54: mu,SV36: mu] :
( ( ( ~ ( ~ ( subset @ SV36 @ SV54 @ SV17 )
| ! [SY85: mu] :
( ~ ( exists_in_world @ SY85 @ SV17 )
| ~ ( member @ SY85 @ SV36 @ SV17 )
| ( member @ SY85 @ SV54 @ SV17 ) ) )
| ~ ( ~ ! [SY86: mu] :
( ~ ( exists_in_world @ SY86 @ SV17 )
| ~ ( member @ SY86 @ SV36 @ SV17 )
| ( member @ SY86 @ SV54 @ SV17 ) )
| ( subset @ SV36 @ SV54 @ SV17 ) ) )
= $false )
| ( ( exists_in_world @ SV54 @ SV17 )
= $false )
| ( ( exists_in_world @ SV36 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(210,plain,
! [SV55: mu,SV37: mu,SV18: $i,SV63: mu] :
( ( ( ~ ( exists_in_world @ SV63 @ SV18 )
| ~ ~ ( ~ ( qmltpeq @ SV37 @ SV55 @ SV18 )
| ~ ( qmltpeq @ SV55 @ SV63 @ SV18 ) )
| ( qmltpeq @ SV37 @ SV63 @ SV18 ) )
= $true )
| ( ( exists_in_world @ SV55 @ SV18 )
= $false )
| ( ( exists_in_world @ SV37 @ SV18 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[196]) ).
thf(211,plain,
! [SV56: mu,SV38: mu,SV19: $i,SV64: mu] :
( ( ( ~ ( exists_in_world @ SV64 @ SV19 )
| ~ ~ ( ~ ( qmltpeq @ SV38 @ SV56 @ SV19 )
| ~ ( member @ SV64 @ SV38 @ SV19 ) )
| ( member @ SV64 @ SV56 @ SV19 ) )
= $true )
| ( ( exists_in_world @ SV56 @ SV19 )
= $false )
| ( ( exists_in_world @ SV38 @ SV19 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[197]) ).
thf(212,plain,
! [SV57: mu,SV39: mu,SV20: $i,SV65: mu] :
( ( ( ~ ( exists_in_world @ SV65 @ SV20 )
| ~ ~ ( ~ ( qmltpeq @ SV39 @ SV57 @ SV20 )
| ~ ( subset @ SV65 @ SV39 @ SV20 ) )
| ( subset @ SV65 @ SV57 @ SV20 ) )
= $true )
| ( ( exists_in_world @ SV57 @ SV20 )
= $false )
| ( ( exists_in_world @ SV39 @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(213,plain,
! [SV4: $i,SV44: mu,SV24: mu] :
( ( ( ~ ( ~ ( qmltpeq @ SV24 @ SV44 @ SV4 )
| ~ ( ~ ( subset @ SV24 @ SV44 @ SV4 )
| ~ ( subset @ SV44 @ SV24 @ SV4 ) ) ) )
= $false )
| ( ( exists_in_world @ SV44 @ SV4 )
= $false )
| ( ( exists_in_world @ SV24 @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[199]) ).
thf(214,plain,
! [SV4: $i,SV44: mu,SV24: mu] :
( ( ( ~ ( ~ ~ ( ~ ( subset @ SV24 @ SV44 @ SV4 )
| ~ ( subset @ SV44 @ SV24 @ SV4 ) )
| ( qmltpeq @ SV24 @ SV44 @ SV4 ) ) )
= $false )
| ( ( exists_in_world @ SV44 @ SV4 )
= $false )
| ( ( exists_in_world @ SV24 @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[199]) ).
thf(215,plain,
! [SV5: $i,SV43: $i,SV25: $i] :
( ( ( rel_s4 @ SV25 @ SV43 )
= $false )
| ( ( rel_s4 @ SV5 @ SV25 )
= $false )
| ( ( rel_s4 @ SV5 @ SV43 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[200]) ).
thf(216,plain,
! [SV45: mu,SV26: mu,SV6: $i,SV58: mu] :
( ( ( ~ ( exists_in_world @ SV58 @ SV6 ) )
= $true )
| ( ( ~ ( qmltpeq @ SV26 @ SV45 @ SV6 )
| ( qmltpeq @ ( union @ SV26 @ SV58 ) @ ( union @ SV45 @ SV58 ) @ SV6 ) )
= $true )
| ( ( exists_in_world @ SV45 @ SV6 )
= $false )
| ( ( exists_in_world @ SV26 @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[201]) ).
thf(217,plain,
! [SV46: mu,SV27: mu,SV7: $i,SV59: mu] :
( ( ( ~ ( exists_in_world @ SV59 @ SV7 ) )
= $true )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV27 @ SV46 @ SV7 )
| ~ ( subset @ SV27 @ SV59 @ SV7 ) )
| ( subset @ SV46 @ SV59 @ SV7 ) )
= $true )
| ( ( exists_in_world @ SV46 @ SV7 )
= $false )
| ( ( exists_in_world @ SV27 @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[202]) ).
thf(218,plain,
! [SV47: mu,SV29: mu,SV9: $i,SV60: mu] :
( ( ( ~ ( exists_in_world @ SV60 @ SV9 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( member @ SV60 @ ( union @ SV29 @ SV47 ) @ SV9 )
| ( member @ SV60 @ SV29 @ SV9 )
| ( member @ SV60 @ SV47 @ SV9 ) )
| ~ ( ~ ( ( member @ SV60 @ SV29 @ SV9 )
| ( member @ SV60 @ SV47 @ SV9 ) )
| ( member @ SV60 @ ( union @ SV29 @ SV47 ) @ SV9 ) ) ) )
= $true )
| ( ( exists_in_world @ SV47 @ SV9 )
= $false )
| ( ( exists_in_world @ SV29 @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[203]) ).
thf(219,plain,
! [SV10: $i,SV48: mu,SV30: mu] :
( ( ( subset @ SV30 @ SV48 @ SV10 )
= $false )
| ( ( qmltpeq @ ( union @ SV30 @ SV48 ) @ SV48 @ SV10 )
= $true )
| ( ( exists_in_world @ SV48 @ SV10 )
= $false )
| ( ( exists_in_world @ SV30 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(220,plain,
! [SV49: mu,SV31: mu,SV11: $i,SV61: mu] :
( ( ( ~ ( exists_in_world @ SV61 @ SV11 ) )
= $true )
| ( ( ~ ( qmltpeq @ SV31 @ SV49 @ SV11 )
| ( qmltpeq @ ( union @ SV61 @ SV31 ) @ ( union @ SV61 @ SV49 ) @ SV11 ) )
= $true )
| ( ( exists_in_world @ SV49 @ SV11 )
= $false )
| ( ( exists_in_world @ SV31 @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[205]) ).
thf(221,plain,
! [SV50: mu,SV32: mu,SV12: $i,SV62: mu] :
( ( ( ~ ( exists_in_world @ SV62 @ SV12 ) )
= $true )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV32 @ SV50 @ SV12 )
| ~ ( member @ SV32 @ SV62 @ SV12 ) )
| ( member @ SV50 @ SV62 @ SV12 ) )
= $true )
| ( ( exists_in_world @ SV50 @ SV12 )
= $false )
| ( ( exists_in_world @ SV32 @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[206]) ).
thf(222,plain,
! [SV13: $i,SV51: mu,SV33: mu] :
( ( ( qmltpeq @ SV33 @ SV51 @ SV13 )
= $false )
| ( ( qmltpeq @ SV51 @ SV33 @ SV13 )
= $true )
| ( ( exists_in_world @ SV51 @ SV13 )
= $false )
| ( ( exists_in_world @ SV33 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[207]) ).
thf(223,plain,
! [SV15: $i,SV53: mu,SV35: mu] :
( ( ( ~ ( ~ ( qmltpeq @ SV35 @ SV53 @ SV15 )
| ! [SY83: mu] :
( ~ ( exists_in_world @ SY83 @ SV15 )
| ~ ( ~ ( ~ ( member @ SY83 @ SV35 @ SV15 )
| ( member @ SY83 @ SV53 @ SV15 ) )
| ~ ( ~ ( member @ SY83 @ SV53 @ SV15 )
| ( member @ SY83 @ SV35 @ SV15 ) ) ) ) ) )
= $false )
| ( ( exists_in_world @ SV53 @ SV15 )
= $false )
| ( ( exists_in_world @ SV35 @ SV15 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[208]) ).
thf(224,plain,
! [SV53: mu,SV35: mu,SV15: $i] :
( ( ( ~ ( ~ ! [SY84: mu] :
( ~ ( exists_in_world @ SY84 @ SV15 )
| ~ ( ~ ( ~ ( member @ SY84 @ SV35 @ SV15 )
| ( member @ SY84 @ SV53 @ SV15 ) )
| ~ ( ~ ( member @ SY84 @ SV53 @ SV15 )
| ( member @ SY84 @ SV35 @ SV15 ) ) ) )
| ( qmltpeq @ SV35 @ SV53 @ SV15 ) ) )
= $false )
| ( ( exists_in_world @ SV53 @ SV15 )
= $false )
| ( ( exists_in_world @ SV35 @ SV15 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[208]) ).
thf(225,plain,
! [SV17: $i,SV54: mu,SV36: mu] :
( ( ( ~ ( ~ ( subset @ SV36 @ SV54 @ SV17 )
| ! [SY85: mu] :
( ~ ( exists_in_world @ SY85 @ SV17 )
| ~ ( member @ SY85 @ SV36 @ SV17 )
| ( member @ SY85 @ SV54 @ SV17 ) ) ) )
= $false )
| ( ( exists_in_world @ SV54 @ SV17 )
= $false )
| ( ( exists_in_world @ SV36 @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[209]) ).
thf(226,plain,
! [SV54: mu,SV36: mu,SV17: $i] :
( ( ( ~ ( ~ ! [SY86: mu] :
( ~ ( exists_in_world @ SY86 @ SV17 )
| ~ ( member @ SY86 @ SV36 @ SV17 )
| ( member @ SY86 @ SV54 @ SV17 ) )
| ( subset @ SV36 @ SV54 @ SV17 ) ) )
= $false )
| ( ( exists_in_world @ SV54 @ SV17 )
= $false )
| ( ( exists_in_world @ SV36 @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[209]) ).
thf(227,plain,
! [SV55: mu,SV37: mu,SV18: $i,SV63: mu] :
( ( ( ~ ( exists_in_world @ SV63 @ SV18 ) )
= $true )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV37 @ SV55 @ SV18 )
| ~ ( qmltpeq @ SV55 @ SV63 @ SV18 ) )
| ( qmltpeq @ SV37 @ SV63 @ SV18 ) )
= $true )
| ( ( exists_in_world @ SV55 @ SV18 )
= $false )
| ( ( exists_in_world @ SV37 @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[210]) ).
thf(228,plain,
! [SV56: mu,SV38: mu,SV19: $i,SV64: mu] :
( ( ( ~ ( exists_in_world @ SV64 @ SV19 ) )
= $true )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV38 @ SV56 @ SV19 )
| ~ ( member @ SV64 @ SV38 @ SV19 ) )
| ( member @ SV64 @ SV56 @ SV19 ) )
= $true )
| ( ( exists_in_world @ SV56 @ SV19 )
= $false )
| ( ( exists_in_world @ SV38 @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[211]) ).
thf(229,plain,
! [SV57: mu,SV39: mu,SV20: $i,SV65: mu] :
( ( ( ~ ( exists_in_world @ SV65 @ SV20 ) )
= $true )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV39 @ SV57 @ SV20 )
| ~ ( subset @ SV65 @ SV39 @ SV20 ) )
| ( subset @ SV65 @ SV57 @ SV20 ) )
= $true )
| ( ( exists_in_world @ SV57 @ SV20 )
= $false )
| ( ( exists_in_world @ SV39 @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[212]) ).
thf(230,plain,
! [SV4: $i,SV44: mu,SV24: mu] :
( ( ( ~ ( qmltpeq @ SV24 @ SV44 @ SV4 )
| ~ ( ~ ( subset @ SV24 @ SV44 @ SV4 )
| ~ ( subset @ SV44 @ SV24 @ SV4 ) ) )
= $true )
| ( ( exists_in_world @ SV44 @ SV4 )
= $false )
| ( ( exists_in_world @ SV24 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[213]) ).
thf(231,plain,
! [SV4: $i,SV44: mu,SV24: mu] :
( ( ( ~ ~ ( ~ ( subset @ SV24 @ SV44 @ SV4 )
| ~ ( subset @ SV44 @ SV24 @ SV4 ) )
| ( qmltpeq @ SV24 @ SV44 @ SV4 ) )
= $true )
| ( ( exists_in_world @ SV44 @ SV4 )
= $false )
| ( ( exists_in_world @ SV24 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[214]) ).
thf(232,plain,
! [SV45: mu,SV26: mu,SV6: $i,SV58: mu] :
( ( ( exists_in_world @ SV58 @ SV6 )
= $false )
| ( ( ~ ( qmltpeq @ SV26 @ SV45 @ SV6 )
| ( qmltpeq @ ( union @ SV26 @ SV58 ) @ ( union @ SV45 @ SV58 ) @ SV6 ) )
= $true )
| ( ( exists_in_world @ SV45 @ SV6 )
= $false )
| ( ( exists_in_world @ SV26 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[216]) ).
thf(233,plain,
! [SV46: mu,SV27: mu,SV7: $i,SV59: mu] :
( ( ( exists_in_world @ SV59 @ SV7 )
= $false )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV27 @ SV46 @ SV7 )
| ~ ( subset @ SV27 @ SV59 @ SV7 ) )
| ( subset @ SV46 @ SV59 @ SV7 ) )
= $true )
| ( ( exists_in_world @ SV46 @ SV7 )
= $false )
| ( ( exists_in_world @ SV27 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[217]) ).
thf(234,plain,
! [SV47: mu,SV29: mu,SV9: $i,SV60: mu] :
( ( ( exists_in_world @ SV60 @ SV9 )
= $false )
| ( ( ~ ( ~ ( ~ ( member @ SV60 @ ( union @ SV29 @ SV47 ) @ SV9 )
| ( member @ SV60 @ SV29 @ SV9 )
| ( member @ SV60 @ SV47 @ SV9 ) )
| ~ ( ~ ( ( member @ SV60 @ SV29 @ SV9 )
| ( member @ SV60 @ SV47 @ SV9 ) )
| ( member @ SV60 @ ( union @ SV29 @ SV47 ) @ SV9 ) ) ) )
= $true )
| ( ( exists_in_world @ SV47 @ SV9 )
= $false )
| ( ( exists_in_world @ SV29 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[218]) ).
thf(235,plain,
! [SV49: mu,SV31: mu,SV11: $i,SV61: mu] :
( ( ( exists_in_world @ SV61 @ SV11 )
= $false )
| ( ( ~ ( qmltpeq @ SV31 @ SV49 @ SV11 )
| ( qmltpeq @ ( union @ SV61 @ SV31 ) @ ( union @ SV61 @ SV49 ) @ SV11 ) )
= $true )
| ( ( exists_in_world @ SV49 @ SV11 )
= $false )
| ( ( exists_in_world @ SV31 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[220]) ).
thf(236,plain,
! [SV50: mu,SV32: mu,SV12: $i,SV62: mu] :
( ( ( exists_in_world @ SV62 @ SV12 )
= $false )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV32 @ SV50 @ SV12 )
| ~ ( member @ SV32 @ SV62 @ SV12 ) )
| ( member @ SV50 @ SV62 @ SV12 ) )
= $true )
| ( ( exists_in_world @ SV50 @ SV12 )
= $false )
| ( ( exists_in_world @ SV32 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[221]) ).
thf(237,plain,
! [SV15: $i,SV53: mu,SV35: mu] :
( ( ( ~ ( qmltpeq @ SV35 @ SV53 @ SV15 )
| ! [SY83: mu] :
( ~ ( exists_in_world @ SY83 @ SV15 )
| ~ ( ~ ( ~ ( member @ SY83 @ SV35 @ SV15 )
| ( member @ SY83 @ SV53 @ SV15 ) )
| ~ ( ~ ( member @ SY83 @ SV53 @ SV15 )
| ( member @ SY83 @ SV35 @ SV15 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV53 @ SV15 )
= $false )
| ( ( exists_in_world @ SV35 @ SV15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[223]) ).
thf(238,plain,
! [SV53: mu,SV35: mu,SV15: $i] :
( ( ( ~ ! [SY84: mu] :
( ~ ( exists_in_world @ SY84 @ SV15 )
| ~ ( ~ ( ~ ( member @ SY84 @ SV35 @ SV15 )
| ( member @ SY84 @ SV53 @ SV15 ) )
| ~ ( ~ ( member @ SY84 @ SV53 @ SV15 )
| ( member @ SY84 @ SV35 @ SV15 ) ) ) )
| ( qmltpeq @ SV35 @ SV53 @ SV15 ) )
= $true )
| ( ( exists_in_world @ SV53 @ SV15 )
= $false )
| ( ( exists_in_world @ SV35 @ SV15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[224]) ).
thf(239,plain,
! [SV17: $i,SV54: mu,SV36: mu] :
( ( ( ~ ( subset @ SV36 @ SV54 @ SV17 )
| ! [SY85: mu] :
( ~ ( exists_in_world @ SY85 @ SV17 )
| ~ ( member @ SY85 @ SV36 @ SV17 )
| ( member @ SY85 @ SV54 @ SV17 ) ) )
= $true )
| ( ( exists_in_world @ SV54 @ SV17 )
= $false )
| ( ( exists_in_world @ SV36 @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[225]) ).
thf(240,plain,
! [SV54: mu,SV36: mu,SV17: $i] :
( ( ( ~ ! [SY86: mu] :
( ~ ( exists_in_world @ SY86 @ SV17 )
| ~ ( member @ SY86 @ SV36 @ SV17 )
| ( member @ SY86 @ SV54 @ SV17 ) )
| ( subset @ SV36 @ SV54 @ SV17 ) )
= $true )
| ( ( exists_in_world @ SV54 @ SV17 )
= $false )
| ( ( exists_in_world @ SV36 @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[226]) ).
thf(241,plain,
! [SV55: mu,SV37: mu,SV18: $i,SV63: mu] :
( ( ( exists_in_world @ SV63 @ SV18 )
= $false )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV37 @ SV55 @ SV18 )
| ~ ( qmltpeq @ SV55 @ SV63 @ SV18 ) )
| ( qmltpeq @ SV37 @ SV63 @ SV18 ) )
= $true )
| ( ( exists_in_world @ SV55 @ SV18 )
= $false )
| ( ( exists_in_world @ SV37 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[227]) ).
thf(242,plain,
! [SV56: mu,SV38: mu,SV19: $i,SV64: mu] :
( ( ( exists_in_world @ SV64 @ SV19 )
= $false )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV38 @ SV56 @ SV19 )
| ~ ( member @ SV64 @ SV38 @ SV19 ) )
| ( member @ SV64 @ SV56 @ SV19 ) )
= $true )
| ( ( exists_in_world @ SV56 @ SV19 )
= $false )
| ( ( exists_in_world @ SV38 @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[228]) ).
thf(243,plain,
! [SV57: mu,SV39: mu,SV20: $i,SV65: mu] :
( ( ( exists_in_world @ SV65 @ SV20 )
= $false )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV39 @ SV57 @ SV20 )
| ~ ( subset @ SV65 @ SV39 @ SV20 ) )
| ( subset @ SV65 @ SV57 @ SV20 ) )
= $true )
| ( ( exists_in_world @ SV57 @ SV20 )
= $false )
| ( ( exists_in_world @ SV39 @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[229]) ).
thf(244,plain,
! [SV4: $i,SV44: mu,SV24: mu] :
( ( ( ~ ( qmltpeq @ SV24 @ SV44 @ SV4 ) )
= $true )
| ( ( ~ ( ~ ( subset @ SV24 @ SV44 @ SV4 )
| ~ ( subset @ SV44 @ SV24 @ SV4 ) ) )
= $true )
| ( ( exists_in_world @ SV44 @ SV4 )
= $false )
| ( ( exists_in_world @ SV24 @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[230]) ).
thf(245,plain,
! [SV4: $i,SV44: mu,SV24: mu] :
( ( ( ~ ~ ( ~ ( subset @ SV24 @ SV44 @ SV4 )
| ~ ( subset @ SV44 @ SV24 @ SV4 ) ) )
= $true )
| ( ( qmltpeq @ SV24 @ SV44 @ SV4 )
= $true )
| ( ( exists_in_world @ SV44 @ SV4 )
= $false )
| ( ( exists_in_world @ SV24 @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[231]) ).
thf(246,plain,
! [SV58: mu,SV6: $i,SV45: mu,SV26: mu] :
( ( ( ~ ( qmltpeq @ SV26 @ SV45 @ SV6 ) )
= $true )
| ( ( qmltpeq @ ( union @ SV26 @ SV58 ) @ ( union @ SV45 @ SV58 ) @ SV6 )
= $true )
| ( ( exists_in_world @ SV58 @ SV6 )
= $false )
| ( ( exists_in_world @ SV45 @ SV6 )
= $false )
| ( ( exists_in_world @ SV26 @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[232]) ).
thf(247,plain,
! [SV59: mu,SV7: $i,SV46: mu,SV27: mu] :
( ( ( ~ ~ ( ~ ( qmltpeq @ SV27 @ SV46 @ SV7 )
| ~ ( subset @ SV27 @ SV59 @ SV7 ) ) )
= $true )
| ( ( subset @ SV46 @ SV59 @ SV7 )
= $true )
| ( ( exists_in_world @ SV59 @ SV7 )
= $false )
| ( ( exists_in_world @ SV46 @ SV7 )
= $false )
| ( ( exists_in_world @ SV27 @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[233]) ).
thf(248,plain,
! [SV9: $i,SV47: mu,SV29: mu,SV60: mu] :
( ( ( ~ ( ~ ( member @ SV60 @ ( union @ SV29 @ SV47 ) @ SV9 )
| ( member @ SV60 @ SV29 @ SV9 )
| ( member @ SV60 @ SV47 @ SV9 ) )
| ~ ( ~ ( ( member @ SV60 @ SV29 @ SV9 )
| ( member @ SV60 @ SV47 @ SV9 ) )
| ( member @ SV60 @ ( union @ SV29 @ SV47 ) @ SV9 ) ) )
= $false )
| ( ( exists_in_world @ SV60 @ SV9 )
= $false )
| ( ( exists_in_world @ SV47 @ SV9 )
= $false )
| ( ( exists_in_world @ SV29 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[234]) ).
thf(249,plain,
! [SV61: mu,SV11: $i,SV49: mu,SV31: mu] :
( ( ( ~ ( qmltpeq @ SV31 @ SV49 @ SV11 ) )
= $true )
| ( ( qmltpeq @ ( union @ SV61 @ SV31 ) @ ( union @ SV61 @ SV49 ) @ SV11 )
= $true )
| ( ( exists_in_world @ SV61 @ SV11 )
= $false )
| ( ( exists_in_world @ SV49 @ SV11 )
= $false )
| ( ( exists_in_world @ SV31 @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[235]) ).
thf(250,plain,
! [SV62: mu,SV12: $i,SV50: mu,SV32: mu] :
( ( ( ~ ~ ( ~ ( qmltpeq @ SV32 @ SV50 @ SV12 )
| ~ ( member @ SV32 @ SV62 @ SV12 ) ) )
= $true )
| ( ( member @ SV50 @ SV62 @ SV12 )
= $true )
| ( ( exists_in_world @ SV62 @ SV12 )
= $false )
| ( ( exists_in_world @ SV50 @ SV12 )
= $false )
| ( ( exists_in_world @ SV32 @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[236]) ).
thf(251,plain,
! [SV15: $i,SV53: mu,SV35: mu] :
( ( ( ~ ( qmltpeq @ SV35 @ SV53 @ SV15 ) )
= $true )
| ( ( ! [SY83: mu] :
( ~ ( exists_in_world @ SY83 @ SV15 )
| ~ ( ~ ( ~ ( member @ SY83 @ SV35 @ SV15 )
| ( member @ SY83 @ SV53 @ SV15 ) )
| ~ ( ~ ( member @ SY83 @ SV53 @ SV15 )
| ( member @ SY83 @ SV35 @ SV15 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV53 @ SV15 )
= $false )
| ( ( exists_in_world @ SV35 @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[237]) ).
thf(252,plain,
! [SV53: mu,SV35: mu,SV15: $i] :
( ( ( ~ ! [SY84: mu] :
( ~ ( exists_in_world @ SY84 @ SV15 )
| ~ ( ~ ( ~ ( member @ SY84 @ SV35 @ SV15 )
| ( member @ SY84 @ SV53 @ SV15 ) )
| ~ ( ~ ( member @ SY84 @ SV53 @ SV15 )
| ( member @ SY84 @ SV35 @ SV15 ) ) ) ) )
= $true )
| ( ( qmltpeq @ SV35 @ SV53 @ SV15 )
= $true )
| ( ( exists_in_world @ SV53 @ SV15 )
= $false )
| ( ( exists_in_world @ SV35 @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[238]) ).
thf(253,plain,
! [SV17: $i,SV54: mu,SV36: mu] :
( ( ( ~ ( subset @ SV36 @ SV54 @ SV17 ) )
= $true )
| ( ( ! [SY85: mu] :
( ~ ( exists_in_world @ SY85 @ SV17 )
| ~ ( member @ SY85 @ SV36 @ SV17 )
| ( member @ SY85 @ SV54 @ SV17 ) ) )
= $true )
| ( ( exists_in_world @ SV54 @ SV17 )
= $false )
| ( ( exists_in_world @ SV36 @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[239]) ).
thf(254,plain,
! [SV54: mu,SV36: mu,SV17: $i] :
( ( ( ~ ! [SY86: mu] :
( ~ ( exists_in_world @ SY86 @ SV17 )
| ~ ( member @ SY86 @ SV36 @ SV17 )
| ( member @ SY86 @ SV54 @ SV17 ) ) )
= $true )
| ( ( subset @ SV36 @ SV54 @ SV17 )
= $true )
| ( ( exists_in_world @ SV54 @ SV17 )
= $false )
| ( ( exists_in_world @ SV36 @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[240]) ).
thf(255,plain,
! [SV63: mu,SV18: $i,SV55: mu,SV37: mu] :
( ( ( ~ ~ ( ~ ( qmltpeq @ SV37 @ SV55 @ SV18 )
| ~ ( qmltpeq @ SV55 @ SV63 @ SV18 ) ) )
= $true )
| ( ( qmltpeq @ SV37 @ SV63 @ SV18 )
= $true )
| ( ( exists_in_world @ SV63 @ SV18 )
= $false )
| ( ( exists_in_world @ SV55 @ SV18 )
= $false )
| ( ( exists_in_world @ SV37 @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[241]) ).
thf(256,plain,
! [SV64: mu,SV19: $i,SV56: mu,SV38: mu] :
( ( ( ~ ~ ( ~ ( qmltpeq @ SV38 @ SV56 @ SV19 )
| ~ ( member @ SV64 @ SV38 @ SV19 ) ) )
= $true )
| ( ( member @ SV64 @ SV56 @ SV19 )
= $true )
| ( ( exists_in_world @ SV64 @ SV19 )
= $false )
| ( ( exists_in_world @ SV56 @ SV19 )
= $false )
| ( ( exists_in_world @ SV38 @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[242]) ).
thf(257,plain,
! [SV65: mu,SV20: $i,SV57: mu,SV39: mu] :
( ( ( ~ ~ ( ~ ( qmltpeq @ SV39 @ SV57 @ SV20 )
| ~ ( subset @ SV65 @ SV39 @ SV20 ) ) )
= $true )
| ( ( subset @ SV65 @ SV57 @ SV20 )
= $true )
| ( ( exists_in_world @ SV65 @ SV20 )
= $false )
| ( ( exists_in_world @ SV57 @ SV20 )
= $false )
| ( ( exists_in_world @ SV39 @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[243]) ).
thf(258,plain,
! [SV4: $i,SV44: mu,SV24: mu] :
( ( ( qmltpeq @ SV24 @ SV44 @ SV4 )
= $false )
| ( ( ~ ( ~ ( subset @ SV24 @ SV44 @ SV4 )
| ~ ( subset @ SV44 @ SV24 @ SV4 ) ) )
= $true )
| ( ( exists_in_world @ SV44 @ SV4 )
= $false )
| ( ( exists_in_world @ SV24 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[244]) ).
thf(259,plain,
! [SV4: $i,SV44: mu,SV24: mu] :
( ( ( ~ ( ~ ( subset @ SV24 @ SV44 @ SV4 )
| ~ ( subset @ SV44 @ SV24 @ SV4 ) ) )
= $false )
| ( ( qmltpeq @ SV24 @ SV44 @ SV4 )
= $true )
| ( ( exists_in_world @ SV44 @ SV4 )
= $false )
| ( ( exists_in_world @ SV24 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[245]) ).
thf(260,plain,
! [SV58: mu,SV6: $i,SV45: mu,SV26: mu] :
( ( ( qmltpeq @ SV26 @ SV45 @ SV6 )
= $false )
| ( ( qmltpeq @ ( union @ SV26 @ SV58 ) @ ( union @ SV45 @ SV58 ) @ SV6 )
= $true )
| ( ( exists_in_world @ SV58 @ SV6 )
= $false )
| ( ( exists_in_world @ SV45 @ SV6 )
= $false )
| ( ( exists_in_world @ SV26 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[246]) ).
thf(261,plain,
! [SV59: mu,SV7: $i,SV46: mu,SV27: mu] :
( ( ( ~ ( ~ ( qmltpeq @ SV27 @ SV46 @ SV7 )
| ~ ( subset @ SV27 @ SV59 @ SV7 ) ) )
= $false )
| ( ( subset @ SV46 @ SV59 @ SV7 )
= $true )
| ( ( exists_in_world @ SV59 @ SV7 )
= $false )
| ( ( exists_in_world @ SV46 @ SV7 )
= $false )
| ( ( exists_in_world @ SV27 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[247]) ).
thf(262,plain,
! [SV9: $i,SV47: mu,SV29: mu,SV60: mu] :
( ( ( ~ ( ~ ( member @ SV60 @ ( union @ SV29 @ SV47 ) @ SV9 )
| ( member @ SV60 @ SV29 @ SV9 )
| ( member @ SV60 @ SV47 @ SV9 ) ) )
= $false )
| ( ( exists_in_world @ SV60 @ SV9 )
= $false )
| ( ( exists_in_world @ SV47 @ SV9 )
= $false )
| ( ( exists_in_world @ SV29 @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[248]) ).
thf(263,plain,
! [SV47: mu,SV9: $i,SV29: mu,SV60: mu] :
( ( ( ~ ( ~ ( ( member @ SV60 @ SV29 @ SV9 )
| ( member @ SV60 @ SV47 @ SV9 ) )
| ( member @ SV60 @ ( union @ SV29 @ SV47 ) @ SV9 ) ) )
= $false )
| ( ( exists_in_world @ SV60 @ SV9 )
= $false )
| ( ( exists_in_world @ SV47 @ SV9 )
= $false )
| ( ( exists_in_world @ SV29 @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[248]) ).
thf(264,plain,
! [SV61: mu,SV11: $i,SV49: mu,SV31: mu] :
( ( ( qmltpeq @ SV31 @ SV49 @ SV11 )
= $false )
| ( ( qmltpeq @ ( union @ SV61 @ SV31 ) @ ( union @ SV61 @ SV49 ) @ SV11 )
= $true )
| ( ( exists_in_world @ SV61 @ SV11 )
= $false )
| ( ( exists_in_world @ SV49 @ SV11 )
= $false )
| ( ( exists_in_world @ SV31 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[249]) ).
thf(265,plain,
! [SV62: mu,SV12: $i,SV50: mu,SV32: mu] :
( ( ( ~ ( ~ ( qmltpeq @ SV32 @ SV50 @ SV12 )
| ~ ( member @ SV32 @ SV62 @ SV12 ) ) )
= $false )
| ( ( member @ SV50 @ SV62 @ SV12 )
= $true )
| ( ( exists_in_world @ SV62 @ SV12 )
= $false )
| ( ( exists_in_world @ SV50 @ SV12 )
= $false )
| ( ( exists_in_world @ SV32 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[250]) ).
thf(266,plain,
! [SV15: $i,SV53: mu,SV35: mu] :
( ( ( qmltpeq @ SV35 @ SV53 @ SV15 )
= $false )
| ( ( ! [SY83: mu] :
( ~ ( exists_in_world @ SY83 @ SV15 )
| ~ ( ~ ( ~ ( member @ SY83 @ SV35 @ SV15 )
| ( member @ SY83 @ SV53 @ SV15 ) )
| ~ ( ~ ( member @ SY83 @ SV53 @ SV15 )
| ( member @ SY83 @ SV35 @ SV15 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV53 @ SV15 )
= $false )
| ( ( exists_in_world @ SV35 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[251]) ).
thf(267,plain,
! [SV53: mu,SV35: mu,SV15: $i] :
( ( ( ! [SY84: mu] :
( ~ ( exists_in_world @ SY84 @ SV15 )
| ~ ( ~ ( ~ ( member @ SY84 @ SV35 @ SV15 )
| ( member @ SY84 @ SV53 @ SV15 ) )
| ~ ( ~ ( member @ SY84 @ SV53 @ SV15 )
| ( member @ SY84 @ SV35 @ SV15 ) ) ) ) )
= $false )
| ( ( qmltpeq @ SV35 @ SV53 @ SV15 )
= $true )
| ( ( exists_in_world @ SV53 @ SV15 )
= $false )
| ( ( exists_in_world @ SV35 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[252]) ).
thf(268,plain,
! [SV17: $i,SV54: mu,SV36: mu] :
( ( ( subset @ SV36 @ SV54 @ SV17 )
= $false )
| ( ( ! [SY85: mu] :
( ~ ( exists_in_world @ SY85 @ SV17 )
| ~ ( member @ SY85 @ SV36 @ SV17 )
| ( member @ SY85 @ SV54 @ SV17 ) ) )
= $true )
| ( ( exists_in_world @ SV54 @ SV17 )
= $false )
| ( ( exists_in_world @ SV36 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[253]) ).
thf(269,plain,
! [SV54: mu,SV36: mu,SV17: $i] :
( ( ( ! [SY86: mu] :
( ~ ( exists_in_world @ SY86 @ SV17 )
| ~ ( member @ SY86 @ SV36 @ SV17 )
| ( member @ SY86 @ SV54 @ SV17 ) ) )
= $false )
| ( ( subset @ SV36 @ SV54 @ SV17 )
= $true )
| ( ( exists_in_world @ SV54 @ SV17 )
= $false )
| ( ( exists_in_world @ SV36 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[254]) ).
thf(270,plain,
! [SV63: mu,SV18: $i,SV55: mu,SV37: mu] :
( ( ( ~ ( ~ ( qmltpeq @ SV37 @ SV55 @ SV18 )
| ~ ( qmltpeq @ SV55 @ SV63 @ SV18 ) ) )
= $false )
| ( ( qmltpeq @ SV37 @ SV63 @ SV18 )
= $true )
| ( ( exists_in_world @ SV63 @ SV18 )
= $false )
| ( ( exists_in_world @ SV55 @ SV18 )
= $false )
| ( ( exists_in_world @ SV37 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[255]) ).
thf(271,plain,
! [SV64: mu,SV19: $i,SV56: mu,SV38: mu] :
( ( ( ~ ( ~ ( qmltpeq @ SV38 @ SV56 @ SV19 )
| ~ ( member @ SV64 @ SV38 @ SV19 ) ) )
= $false )
| ( ( member @ SV64 @ SV56 @ SV19 )
= $true )
| ( ( exists_in_world @ SV64 @ SV19 )
= $false )
| ( ( exists_in_world @ SV56 @ SV19 )
= $false )
| ( ( exists_in_world @ SV38 @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[256]) ).
thf(272,plain,
! [SV65: mu,SV20: $i,SV57: mu,SV39: mu] :
( ( ( ~ ( ~ ( qmltpeq @ SV39 @ SV57 @ SV20 )
| ~ ( subset @ SV65 @ SV39 @ SV20 ) ) )
= $false )
| ( ( subset @ SV65 @ SV57 @ SV20 )
= $true )
| ( ( exists_in_world @ SV65 @ SV20 )
= $false )
| ( ( exists_in_world @ SV57 @ SV20 )
= $false )
| ( ( exists_in_world @ SV39 @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[257]) ).
thf(273,plain,
! [SV4: $i,SV44: mu,SV24: mu] :
( ( ( ~ ( subset @ SV24 @ SV44 @ SV4 )
| ~ ( subset @ SV44 @ SV24 @ SV4 ) )
= $false )
| ( ( qmltpeq @ SV24 @ SV44 @ SV4 )
= $false )
| ( ( exists_in_world @ SV44 @ SV4 )
= $false )
| ( ( exists_in_world @ SV24 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[258]) ).
thf(274,plain,
! [SV4: $i,SV44: mu,SV24: mu] :
( ( ( ~ ( subset @ SV24 @ SV44 @ SV4 )
| ~ ( subset @ SV44 @ SV24 @ SV4 ) )
= $true )
| ( ( qmltpeq @ SV24 @ SV44 @ SV4 )
= $true )
| ( ( exists_in_world @ SV44 @ SV4 )
= $false )
| ( ( exists_in_world @ SV24 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[259]) ).
thf(275,plain,
! [SV59: mu,SV7: $i,SV46: mu,SV27: mu] :
( ( ( ~ ( qmltpeq @ SV27 @ SV46 @ SV7 )
| ~ ( subset @ SV27 @ SV59 @ SV7 ) )
= $true )
| ( ( subset @ SV46 @ SV59 @ SV7 )
= $true )
| ( ( exists_in_world @ SV59 @ SV7 )
= $false )
| ( ( exists_in_world @ SV46 @ SV7 )
= $false )
| ( ( exists_in_world @ SV27 @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[261]) ).
thf(276,plain,
! [SV9: $i,SV47: mu,SV29: mu,SV60: mu] :
( ( ( ~ ( member @ SV60 @ ( union @ SV29 @ SV47 ) @ SV9 )
| ( member @ SV60 @ SV29 @ SV9 )
| ( member @ SV60 @ SV47 @ SV9 ) )
= $true )
| ( ( exists_in_world @ SV60 @ SV9 )
= $false )
| ( ( exists_in_world @ SV47 @ SV9 )
= $false )
| ( ( exists_in_world @ SV29 @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[262]) ).
thf(277,plain,
! [SV47: mu,SV9: $i,SV29: mu,SV60: mu] :
( ( ( ~ ( ( member @ SV60 @ SV29 @ SV9 )
| ( member @ SV60 @ SV47 @ SV9 ) )
| ( member @ SV60 @ ( union @ SV29 @ SV47 ) @ SV9 ) )
= $true )
| ( ( exists_in_world @ SV60 @ SV9 )
= $false )
| ( ( exists_in_world @ SV47 @ SV9 )
= $false )
| ( ( exists_in_world @ SV29 @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[263]) ).
thf(278,plain,
! [SV62: mu,SV12: $i,SV50: mu,SV32: mu] :
( ( ( ~ ( qmltpeq @ SV32 @ SV50 @ SV12 )
| ~ ( member @ SV32 @ SV62 @ SV12 ) )
= $true )
| ( ( member @ SV50 @ SV62 @ SV12 )
= $true )
| ( ( exists_in_world @ SV62 @ SV12 )
= $false )
| ( ( exists_in_world @ SV50 @ SV12 )
= $false )
| ( ( exists_in_world @ SV32 @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[265]) ).
thf(279,plain,
! [SV53: mu,SV35: mu,SV15: $i,SV66: mu] :
( ( ( ~ ( exists_in_world @ SV66 @ SV15 )
| ~ ( ~ ( ~ ( member @ SV66 @ SV35 @ SV15 )
| ( member @ SV66 @ SV53 @ SV15 ) )
| ~ ( ~ ( member @ SV66 @ SV53 @ SV15 )
| ( member @ SV66 @ SV35 @ SV15 ) ) ) )
= $true )
| ( ( qmltpeq @ SV35 @ SV53 @ SV15 )
= $false )
| ( ( exists_in_world @ SV53 @ SV15 )
= $false )
| ( ( exists_in_world @ SV35 @ SV15 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[266]) ).
thf(280,plain,
! [SV15: $i,SV35: mu,SV53: mu] :
( ( ( ~ ( exists_in_world @ ( sK4_SY84 @ SV53 @ SV35 @ SV15 ) @ SV15 )
| ~ ( ~ ( ~ ( member @ ( sK4_SY84 @ SV53 @ SV35 @ SV15 ) @ SV35 @ SV15 )
| ( member @ ( sK4_SY84 @ SV53 @ SV35 @ SV15 ) @ SV53 @ SV15 ) )
| ~ ( ~ ( member @ ( sK4_SY84 @ SV53 @ SV35 @ SV15 ) @ SV53 @ SV15 )
| ( member @ ( sK4_SY84 @ SV53 @ SV35 @ SV15 ) @ SV35 @ SV15 ) ) ) )
= $false )
| ( ( qmltpeq @ SV35 @ SV53 @ SV15 )
= $true )
| ( ( exists_in_world @ SV53 @ SV15 )
= $false )
| ( ( exists_in_world @ SV35 @ SV15 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[267]) ).
thf(281,plain,
! [SV54: mu,SV36: mu,SV17: $i,SV67: mu] :
( ( ( ~ ( exists_in_world @ SV67 @ SV17 )
| ~ ( member @ SV67 @ SV36 @ SV17 )
| ( member @ SV67 @ SV54 @ SV17 ) )
= $true )
| ( ( subset @ SV36 @ SV54 @ SV17 )
= $false )
| ( ( exists_in_world @ SV54 @ SV17 )
= $false )
| ( ( exists_in_world @ SV36 @ SV17 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[268]) ).
thf(282,plain,
! [SV17: $i,SV36: mu,SV54: mu] :
( ( ( ~ ( exists_in_world @ ( sK5_SY86 @ SV54 @ SV36 @ SV17 ) @ SV17 )
| ~ ( member @ ( sK5_SY86 @ SV54 @ SV36 @ SV17 ) @ SV36 @ SV17 )
| ( member @ ( sK5_SY86 @ SV54 @ SV36 @ SV17 ) @ SV54 @ SV17 ) )
= $false )
| ( ( subset @ SV36 @ SV54 @ SV17 )
= $true )
| ( ( exists_in_world @ SV54 @ SV17 )
= $false )
| ( ( exists_in_world @ SV36 @ SV17 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[269]) ).
thf(283,plain,
! [SV63: mu,SV18: $i,SV55: mu,SV37: mu] :
( ( ( ~ ( qmltpeq @ SV37 @ SV55 @ SV18 )
| ~ ( qmltpeq @ SV55 @ SV63 @ SV18 ) )
= $true )
| ( ( qmltpeq @ SV37 @ SV63 @ SV18 )
= $true )
| ( ( exists_in_world @ SV63 @ SV18 )
= $false )
| ( ( exists_in_world @ SV55 @ SV18 )
= $false )
| ( ( exists_in_world @ SV37 @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[270]) ).
thf(284,plain,
! [SV64: mu,SV19: $i,SV56: mu,SV38: mu] :
( ( ( ~ ( qmltpeq @ SV38 @ SV56 @ SV19 )
| ~ ( member @ SV64 @ SV38 @ SV19 ) )
= $true )
| ( ( member @ SV64 @ SV56 @ SV19 )
= $true )
| ( ( exists_in_world @ SV64 @ SV19 )
= $false )
| ( ( exists_in_world @ SV56 @ SV19 )
= $false )
| ( ( exists_in_world @ SV38 @ SV19 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[271]) ).
thf(285,plain,
! [SV65: mu,SV20: $i,SV57: mu,SV39: mu] :
( ( ( ~ ( qmltpeq @ SV39 @ SV57 @ SV20 )
| ~ ( subset @ SV65 @ SV39 @ SV20 ) )
= $true )
| ( ( subset @ SV65 @ SV57 @ SV20 )
= $true )
| ( ( exists_in_world @ SV65 @ SV20 )
= $false )
| ( ( exists_in_world @ SV57 @ SV20 )
= $false )
| ( ( exists_in_world @ SV39 @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[272]) ).
thf(286,plain,
! [SV4: $i,SV44: mu,SV24: mu] :
( ( ( ~ ( subset @ SV24 @ SV44 @ SV4 ) )
= $false )
| ( ( qmltpeq @ SV24 @ SV44 @ SV4 )
= $false )
| ( ( exists_in_world @ SV44 @ SV4 )
= $false )
| ( ( exists_in_world @ SV24 @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[273]) ).
thf(287,plain,
! [SV4: $i,SV24: mu,SV44: mu] :
( ( ( ~ ( subset @ SV44 @ SV24 @ SV4 ) )
= $false )
| ( ( qmltpeq @ SV24 @ SV44 @ SV4 )
= $false )
| ( ( exists_in_world @ SV44 @ SV4 )
= $false )
| ( ( exists_in_world @ SV24 @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[273]) ).
thf(288,plain,
! [SV4: $i,SV44: mu,SV24: mu] :
( ( ( ~ ( subset @ SV24 @ SV44 @ SV4 ) )
= $true )
| ( ( ~ ( subset @ SV44 @ SV24 @ SV4 ) )
= $true )
| ( ( qmltpeq @ SV24 @ SV44 @ SV4 )
= $true )
| ( ( exists_in_world @ SV44 @ SV4 )
= $false )
| ( ( exists_in_world @ SV24 @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[274]) ).
thf(289,plain,
! [SV59: mu,SV7: $i,SV46: mu,SV27: mu] :
( ( ( ~ ( qmltpeq @ SV27 @ SV46 @ SV7 ) )
= $true )
| ( ( ~ ( subset @ SV27 @ SV59 @ SV7 ) )
= $true )
| ( ( subset @ SV46 @ SV59 @ SV7 )
= $true )
| ( ( exists_in_world @ SV59 @ SV7 )
= $false )
| ( ( exists_in_world @ SV46 @ SV7 )
= $false )
| ( ( exists_in_world @ SV27 @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[275]) ).
thf(290,plain,
! [SV9: $i,SV47: mu,SV29: mu,SV60: mu] :
( ( ( ~ ( member @ SV60 @ ( union @ SV29 @ SV47 ) @ SV9 ) )
= $true )
| ( ( ( member @ SV60 @ SV29 @ SV9 )
| ( member @ SV60 @ SV47 @ SV9 ) )
= $true )
| ( ( exists_in_world @ SV60 @ SV9 )
= $false )
| ( ( exists_in_world @ SV47 @ SV9 )
= $false )
| ( ( exists_in_world @ SV29 @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[276]) ).
thf(291,plain,
! [SV47: mu,SV9: $i,SV29: mu,SV60: mu] :
( ( ( ~ ( ( member @ SV60 @ SV29 @ SV9 )
| ( member @ SV60 @ SV47 @ SV9 ) ) )
= $true )
| ( ( member @ SV60 @ ( union @ SV29 @ SV47 ) @ SV9 )
= $true )
| ( ( exists_in_world @ SV60 @ SV9 )
= $false )
| ( ( exists_in_world @ SV47 @ SV9 )
= $false )
| ( ( exists_in_world @ SV29 @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[277]) ).
thf(292,plain,
! [SV62: mu,SV12: $i,SV50: mu,SV32: mu] :
( ( ( ~ ( qmltpeq @ SV32 @ SV50 @ SV12 ) )
= $true )
| ( ( ~ ( member @ SV32 @ SV62 @ SV12 ) )
= $true )
| ( ( member @ SV50 @ SV62 @ SV12 )
= $true )
| ( ( exists_in_world @ SV62 @ SV12 )
= $false )
| ( ( exists_in_world @ SV50 @ SV12 )
= $false )
| ( ( exists_in_world @ SV32 @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[278]) ).
thf(293,plain,
! [SV53: mu,SV35: mu,SV15: $i,SV66: mu] :
( ( ( ~ ( exists_in_world @ SV66 @ SV15 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( member @ SV66 @ SV35 @ SV15 )
| ( member @ SV66 @ SV53 @ SV15 ) )
| ~ ( ~ ( member @ SV66 @ SV53 @ SV15 )
| ( member @ SV66 @ SV35 @ SV15 ) ) ) )
= $true )
| ( ( qmltpeq @ SV35 @ SV53 @ SV15 )
= $false )
| ( ( exists_in_world @ SV53 @ SV15 )
= $false )
| ( ( exists_in_world @ SV35 @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[279]) ).
thf(294,plain,
! [SV15: $i,SV35: mu,SV53: mu] :
( ( ( ~ ( exists_in_world @ ( sK4_SY84 @ SV53 @ SV35 @ SV15 ) @ SV15 ) )
= $false )
| ( ( qmltpeq @ SV35 @ SV53 @ SV15 )
= $true )
| ( ( exists_in_world @ SV53 @ SV15 )
= $false )
| ( ( exists_in_world @ SV35 @ SV15 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[280]) ).
thf(295,plain,
! [SV15: $i,SV35: mu,SV53: mu] :
( ( ( ~ ( ~ ( ~ ( member @ ( sK4_SY84 @ SV53 @ SV35 @ SV15 ) @ SV35 @ SV15 )
| ( member @ ( sK4_SY84 @ SV53 @ SV35 @ SV15 ) @ SV53 @ SV15 ) )
| ~ ( ~ ( member @ ( sK4_SY84 @ SV53 @ SV35 @ SV15 ) @ SV53 @ SV15 )
| ( member @ ( sK4_SY84 @ SV53 @ SV35 @ SV15 ) @ SV35 @ SV15 ) ) ) )
= $false )
| ( ( qmltpeq @ SV35 @ SV53 @ SV15 )
= $true )
| ( ( exists_in_world @ SV53 @ SV15 )
= $false )
| ( ( exists_in_world @ SV35 @ SV15 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[280]) ).
thf(296,plain,
! [SV54: mu,SV36: mu,SV17: $i,SV67: mu] :
( ( ( ~ ( exists_in_world @ SV67 @ SV17 ) )
= $true )
| ( ( ~ ( member @ SV67 @ SV36 @ SV17 )
| ( member @ SV67 @ SV54 @ SV17 ) )
= $true )
| ( ( subset @ SV36 @ SV54 @ SV17 )
= $false )
| ( ( exists_in_world @ SV54 @ SV17 )
= $false )
| ( ( exists_in_world @ SV36 @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[281]) ).
thf(297,plain,
! [SV17: $i,SV36: mu,SV54: mu] :
( ( ( ~ ( exists_in_world @ ( sK5_SY86 @ SV54 @ SV36 @ SV17 ) @ SV17 ) )
= $false )
| ( ( subset @ SV36 @ SV54 @ SV17 )
= $true )
| ( ( exists_in_world @ SV54 @ SV17 )
= $false )
| ( ( exists_in_world @ SV36 @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[282]) ).
thf(298,plain,
! [SV17: $i,SV36: mu,SV54: mu] :
( ( ( ~ ( member @ ( sK5_SY86 @ SV54 @ SV36 @ SV17 ) @ SV36 @ SV17 )
| ( member @ ( sK5_SY86 @ SV54 @ SV36 @ SV17 ) @ SV54 @ SV17 ) )
= $false )
| ( ( subset @ SV36 @ SV54 @ SV17 )
= $true )
| ( ( exists_in_world @ SV54 @ SV17 )
= $false )
| ( ( exists_in_world @ SV36 @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[282]) ).
thf(299,plain,
! [SV63: mu,SV18: $i,SV55: mu,SV37: mu] :
( ( ( ~ ( qmltpeq @ SV37 @ SV55 @ SV18 ) )
= $true )
| ( ( ~ ( qmltpeq @ SV55 @ SV63 @ SV18 ) )
= $true )
| ( ( qmltpeq @ SV37 @ SV63 @ SV18 )
= $true )
| ( ( exists_in_world @ SV63 @ SV18 )
= $false )
| ( ( exists_in_world @ SV55 @ SV18 )
= $false )
| ( ( exists_in_world @ SV37 @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[283]) ).
thf(300,plain,
! [SV64: mu,SV19: $i,SV56: mu,SV38: mu] :
( ( ( ~ ( qmltpeq @ SV38 @ SV56 @ SV19 ) )
= $true )
| ( ( ~ ( member @ SV64 @ SV38 @ SV19 ) )
= $true )
| ( ( member @ SV64 @ SV56 @ SV19 )
= $true )
| ( ( exists_in_world @ SV64 @ SV19 )
= $false )
| ( ( exists_in_world @ SV56 @ SV19 )
= $false )
| ( ( exists_in_world @ SV38 @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[284]) ).
thf(301,plain,
! [SV65: mu,SV20: $i,SV57: mu,SV39: mu] :
( ( ( ~ ( qmltpeq @ SV39 @ SV57 @ SV20 ) )
= $true )
| ( ( ~ ( subset @ SV65 @ SV39 @ SV20 ) )
= $true )
| ( ( subset @ SV65 @ SV57 @ SV20 )
= $true )
| ( ( exists_in_world @ SV65 @ SV20 )
= $false )
| ( ( exists_in_world @ SV57 @ SV20 )
= $false )
| ( ( exists_in_world @ SV39 @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[285]) ).
thf(302,plain,
! [SV4: $i,SV44: mu,SV24: mu] :
( ( ( subset @ SV24 @ SV44 @ SV4 )
= $true )
| ( ( qmltpeq @ SV24 @ SV44 @ SV4 )
= $false )
| ( ( exists_in_world @ SV44 @ SV4 )
= $false )
| ( ( exists_in_world @ SV24 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[286]) ).
thf(303,plain,
! [SV4: $i,SV24: mu,SV44: mu] :
( ( ( subset @ SV44 @ SV24 @ SV4 )
= $true )
| ( ( qmltpeq @ SV24 @ SV44 @ SV4 )
= $false )
| ( ( exists_in_world @ SV44 @ SV4 )
= $false )
| ( ( exists_in_world @ SV24 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[287]) ).
thf(304,plain,
! [SV4: $i,SV44: mu,SV24: mu] :
( ( ( subset @ SV24 @ SV44 @ SV4 )
= $false )
| ( ( ~ ( subset @ SV44 @ SV24 @ SV4 ) )
= $true )
| ( ( qmltpeq @ SV24 @ SV44 @ SV4 )
= $true )
| ( ( exists_in_world @ SV44 @ SV4 )
= $false )
| ( ( exists_in_world @ SV24 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[288]) ).
thf(305,plain,
! [SV59: mu,SV7: $i,SV46: mu,SV27: mu] :
( ( ( qmltpeq @ SV27 @ SV46 @ SV7 )
= $false )
| ( ( ~ ( subset @ SV27 @ SV59 @ SV7 ) )
= $true )
| ( ( subset @ SV46 @ SV59 @ SV7 )
= $true )
| ( ( exists_in_world @ SV59 @ SV7 )
= $false )
| ( ( exists_in_world @ SV46 @ SV7 )
= $false )
| ( ( exists_in_world @ SV27 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[289]) ).
thf(306,plain,
! [SV9: $i,SV47: mu,SV29: mu,SV60: mu] :
( ( ( member @ SV60 @ ( union @ SV29 @ SV47 ) @ SV9 )
= $false )
| ( ( ( member @ SV60 @ SV29 @ SV9 )
| ( member @ SV60 @ SV47 @ SV9 ) )
= $true )
| ( ( exists_in_world @ SV60 @ SV9 )
= $false )
| ( ( exists_in_world @ SV47 @ SV9 )
= $false )
| ( ( exists_in_world @ SV29 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[290]) ).
thf(307,plain,
! [SV47: mu,SV9: $i,SV29: mu,SV60: mu] :
( ( ( ( member @ SV60 @ SV29 @ SV9 )
| ( member @ SV60 @ SV47 @ SV9 ) )
= $false )
| ( ( member @ SV60 @ ( union @ SV29 @ SV47 ) @ SV9 )
= $true )
| ( ( exists_in_world @ SV60 @ SV9 )
= $false )
| ( ( exists_in_world @ SV47 @ SV9 )
= $false )
| ( ( exists_in_world @ SV29 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[291]) ).
thf(308,plain,
! [SV62: mu,SV12: $i,SV50: mu,SV32: mu] :
( ( ( qmltpeq @ SV32 @ SV50 @ SV12 )
= $false )
| ( ( ~ ( member @ SV32 @ SV62 @ SV12 ) )
= $true )
| ( ( member @ SV50 @ SV62 @ SV12 )
= $true )
| ( ( exists_in_world @ SV62 @ SV12 )
= $false )
| ( ( exists_in_world @ SV50 @ SV12 )
= $false )
| ( ( exists_in_world @ SV32 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[292]) ).
thf(309,plain,
! [SV53: mu,SV35: mu,SV15: $i,SV66: mu] :
( ( ( exists_in_world @ SV66 @ SV15 )
= $false )
| ( ( ~ ( ~ ( ~ ( member @ SV66 @ SV35 @ SV15 )
| ( member @ SV66 @ SV53 @ SV15 ) )
| ~ ( ~ ( member @ SV66 @ SV53 @ SV15 )
| ( member @ SV66 @ SV35 @ SV15 ) ) ) )
= $true )
| ( ( qmltpeq @ SV35 @ SV53 @ SV15 )
= $false )
| ( ( exists_in_world @ SV53 @ SV15 )
= $false )
| ( ( exists_in_world @ SV35 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[293]) ).
thf(310,plain,
! [SV15: $i,SV35: mu,SV53: mu] :
( ( ( exists_in_world @ ( sK4_SY84 @ SV53 @ SV35 @ SV15 ) @ SV15 )
= $true )
| ( ( qmltpeq @ SV35 @ SV53 @ SV15 )
= $true )
| ( ( exists_in_world @ SV53 @ SV15 )
= $false )
| ( ( exists_in_world @ SV35 @ SV15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[294]) ).
thf(311,plain,
! [SV15: $i,SV35: mu,SV53: mu] :
( ( ( ~ ( ~ ( member @ ( sK4_SY84 @ SV53 @ SV35 @ SV15 ) @ SV35 @ SV15 )
| ( member @ ( sK4_SY84 @ SV53 @ SV35 @ SV15 ) @ SV53 @ SV15 ) )
| ~ ( ~ ( member @ ( sK4_SY84 @ SV53 @ SV35 @ SV15 ) @ SV53 @ SV15 )
| ( member @ ( sK4_SY84 @ SV53 @ SV35 @ SV15 ) @ SV35 @ SV15 ) ) )
= $true )
| ( ( qmltpeq @ SV35 @ SV53 @ SV15 )
= $true )
| ( ( exists_in_world @ SV53 @ SV15 )
= $false )
| ( ( exists_in_world @ SV35 @ SV15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[295]) ).
thf(312,plain,
! [SV54: mu,SV36: mu,SV17: $i,SV67: mu] :
( ( ( exists_in_world @ SV67 @ SV17 )
= $false )
| ( ( ~ ( member @ SV67 @ SV36 @ SV17 )
| ( member @ SV67 @ SV54 @ SV17 ) )
= $true )
| ( ( subset @ SV36 @ SV54 @ SV17 )
= $false )
| ( ( exists_in_world @ SV54 @ SV17 )
= $false )
| ( ( exists_in_world @ SV36 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[296]) ).
thf(313,plain,
! [SV17: $i,SV36: mu,SV54: mu] :
( ( ( exists_in_world @ ( sK5_SY86 @ SV54 @ SV36 @ SV17 ) @ SV17 )
= $true )
| ( ( subset @ SV36 @ SV54 @ SV17 )
= $true )
| ( ( exists_in_world @ SV54 @ SV17 )
= $false )
| ( ( exists_in_world @ SV36 @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[297]) ).
thf(314,plain,
! [SV17: $i,SV36: mu,SV54: mu] :
( ( ( ~ ( member @ ( sK5_SY86 @ SV54 @ SV36 @ SV17 ) @ SV36 @ SV17 ) )
= $false )
| ( ( subset @ SV36 @ SV54 @ SV17 )
= $true )
| ( ( exists_in_world @ SV54 @ SV17 )
= $false )
| ( ( exists_in_world @ SV36 @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[298]) ).
thf(315,plain,
! [SV17: $i,SV36: mu,SV54: mu] :
( ( ( member @ ( sK5_SY86 @ SV54 @ SV36 @ SV17 ) @ SV54 @ SV17 )
= $false )
| ( ( subset @ SV36 @ SV54 @ SV17 )
= $true )
| ( ( exists_in_world @ SV54 @ SV17 )
= $false )
| ( ( exists_in_world @ SV36 @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[298]) ).
thf(316,plain,
! [SV63: mu,SV18: $i,SV55: mu,SV37: mu] :
( ( ( qmltpeq @ SV37 @ SV55 @ SV18 )
= $false )
| ( ( ~ ( qmltpeq @ SV55 @ SV63 @ SV18 ) )
= $true )
| ( ( qmltpeq @ SV37 @ SV63 @ SV18 )
= $true )
| ( ( exists_in_world @ SV63 @ SV18 )
= $false )
| ( ( exists_in_world @ SV55 @ SV18 )
= $false )
| ( ( exists_in_world @ SV37 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[299]) ).
thf(317,plain,
! [SV64: mu,SV19: $i,SV56: mu,SV38: mu] :
( ( ( qmltpeq @ SV38 @ SV56 @ SV19 )
= $false )
| ( ( ~ ( member @ SV64 @ SV38 @ SV19 ) )
= $true )
| ( ( member @ SV64 @ SV56 @ SV19 )
= $true )
| ( ( exists_in_world @ SV64 @ SV19 )
= $false )
| ( ( exists_in_world @ SV56 @ SV19 )
= $false )
| ( ( exists_in_world @ SV38 @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[300]) ).
thf(318,plain,
! [SV65: mu,SV20: $i,SV57: mu,SV39: mu] :
( ( ( qmltpeq @ SV39 @ SV57 @ SV20 )
= $false )
| ( ( ~ ( subset @ SV65 @ SV39 @ SV20 ) )
= $true )
| ( ( subset @ SV65 @ SV57 @ SV20 )
= $true )
| ( ( exists_in_world @ SV65 @ SV20 )
= $false )
| ( ( exists_in_world @ SV57 @ SV20 )
= $false )
| ( ( exists_in_world @ SV39 @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[301]) ).
thf(319,plain,
! [SV4: $i,SV24: mu,SV44: mu] :
( ( ( subset @ SV44 @ SV24 @ SV4 )
= $false )
| ( ( subset @ SV24 @ SV44 @ SV4 )
= $false )
| ( ( qmltpeq @ SV24 @ SV44 @ SV4 )
= $true )
| ( ( exists_in_world @ SV44 @ SV4 )
= $false )
| ( ( exists_in_world @ SV24 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[304]) ).
thf(320,plain,
! [SV46: mu,SV7: $i,SV59: mu,SV27: mu] :
( ( ( subset @ SV27 @ SV59 @ SV7 )
= $false )
| ( ( qmltpeq @ SV27 @ SV46 @ SV7 )
= $false )
| ( ( subset @ SV46 @ SV59 @ SV7 )
= $true )
| ( ( exists_in_world @ SV59 @ SV7 )
= $false )
| ( ( exists_in_world @ SV46 @ SV7 )
= $false )
| ( ( exists_in_world @ SV27 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[305]) ).
thf(321,plain,
! [SV47: mu,SV9: $i,SV29: mu,SV60: mu] :
( ( ( member @ SV60 @ SV29 @ SV9 )
= $true )
| ( ( member @ SV60 @ SV47 @ SV9 )
= $true )
| ( ( member @ SV60 @ ( union @ SV29 @ SV47 ) @ SV9 )
= $false )
| ( ( exists_in_world @ SV60 @ SV9 )
= $false )
| ( ( exists_in_world @ SV47 @ SV9 )
= $false )
| ( ( exists_in_world @ SV29 @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[306]) ).
thf(322,plain,
! [SV47: mu,SV9: $i,SV29: mu,SV60: mu] :
( ( ( member @ SV60 @ SV29 @ SV9 )
= $false )
| ( ( member @ SV60 @ ( union @ SV29 @ SV47 ) @ SV9 )
= $true )
| ( ( exists_in_world @ SV60 @ SV9 )
= $false )
| ( ( exists_in_world @ SV47 @ SV9 )
= $false )
| ( ( exists_in_world @ SV29 @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[307]) ).
thf(323,plain,
! [SV29: mu,SV9: $i,SV47: mu,SV60: mu] :
( ( ( member @ SV60 @ SV47 @ SV9 )
= $false )
| ( ( member @ SV60 @ ( union @ SV29 @ SV47 ) @ SV9 )
= $true )
| ( ( exists_in_world @ SV60 @ SV9 )
= $false )
| ( ( exists_in_world @ SV47 @ SV9 )
= $false )
| ( ( exists_in_world @ SV29 @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[307]) ).
thf(324,plain,
! [SV50: mu,SV12: $i,SV62: mu,SV32: mu] :
( ( ( member @ SV32 @ SV62 @ SV12 )
= $false )
| ( ( qmltpeq @ SV32 @ SV50 @ SV12 )
= $false )
| ( ( member @ SV50 @ SV62 @ SV12 )
= $true )
| ( ( exists_in_world @ SV62 @ SV12 )
= $false )
| ( ( exists_in_world @ SV50 @ SV12 )
= $false )
| ( ( exists_in_world @ SV32 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[308]) ).
thf(325,plain,
! [SV53: mu,SV15: $i,SV35: mu,SV66: mu] :
( ( ( ~ ( ~ ( member @ SV66 @ SV35 @ SV15 )
| ( member @ SV66 @ SV53 @ SV15 ) )
| ~ ( ~ ( member @ SV66 @ SV53 @ SV15 )
| ( member @ SV66 @ SV35 @ SV15 ) ) )
= $false )
| ( ( exists_in_world @ SV66 @ SV15 )
= $false )
| ( ( qmltpeq @ SV35 @ SV53 @ SV15 )
= $false )
| ( ( exists_in_world @ SV53 @ SV15 )
= $false )
| ( ( exists_in_world @ SV35 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[309]) ).
thf(326,plain,
! [SV15: $i,SV35: mu,SV53: mu] :
( ( ( ~ ( ~ ( member @ ( sK4_SY84 @ SV53 @ SV35 @ SV15 ) @ SV35 @ SV15 )
| ( member @ ( sK4_SY84 @ SV53 @ SV35 @ SV15 ) @ SV53 @ SV15 ) ) )
= $true )
| ( ( ~ ( ~ ( member @ ( sK4_SY84 @ SV53 @ SV35 @ SV15 ) @ SV53 @ SV15 )
| ( member @ ( sK4_SY84 @ SV53 @ SV35 @ SV15 ) @ SV35 @ SV15 ) ) )
= $true )
| ( ( qmltpeq @ SV35 @ SV53 @ SV15 )
= $true )
| ( ( exists_in_world @ SV53 @ SV15 )
= $false )
| ( ( exists_in_world @ SV35 @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[311]) ).
thf(327,plain,
! [SV54: mu,SV17: $i,SV36: mu,SV67: mu] :
( ( ( ~ ( member @ SV67 @ SV36 @ SV17 ) )
= $true )
| ( ( member @ SV67 @ SV54 @ SV17 )
= $true )
| ( ( exists_in_world @ SV67 @ SV17 )
= $false )
| ( ( subset @ SV36 @ SV54 @ SV17 )
= $false )
| ( ( exists_in_world @ SV54 @ SV17 )
= $false )
| ( ( exists_in_world @ SV36 @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[312]) ).
thf(328,plain,
! [SV17: $i,SV36: mu,SV54: mu] :
( ( ( member @ ( sK5_SY86 @ SV54 @ SV36 @ SV17 ) @ SV36 @ SV17 )
= $true )
| ( ( subset @ SV36 @ SV54 @ SV17 )
= $true )
| ( ( exists_in_world @ SV54 @ SV17 )
= $false )
| ( ( exists_in_world @ SV36 @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[314]) ).
thf(329,plain,
! [SV37: mu,SV18: $i,SV63: mu,SV55: mu] :
( ( ( qmltpeq @ SV55 @ SV63 @ SV18 )
= $false )
| ( ( qmltpeq @ SV37 @ SV55 @ SV18 )
= $false )
| ( ( qmltpeq @ SV37 @ SV63 @ SV18 )
= $true )
| ( ( exists_in_world @ SV63 @ SV18 )
= $false )
| ( ( exists_in_world @ SV55 @ SV18 )
= $false )
| ( ( exists_in_world @ SV37 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[316]) ).
thf(330,plain,
! [SV56: mu,SV19: $i,SV38: mu,SV64: mu] :
( ( ( member @ SV64 @ SV38 @ SV19 )
= $false )
| ( ( qmltpeq @ SV38 @ SV56 @ SV19 )
= $false )
| ( ( member @ SV64 @ SV56 @ SV19 )
= $true )
| ( ( exists_in_world @ SV64 @ SV19 )
= $false )
| ( ( exists_in_world @ SV56 @ SV19 )
= $false )
| ( ( exists_in_world @ SV38 @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[317]) ).
thf(331,plain,
! [SV57: mu,SV20: $i,SV39: mu,SV65: mu] :
( ( ( subset @ SV65 @ SV39 @ SV20 )
= $false )
| ( ( qmltpeq @ SV39 @ SV57 @ SV20 )
= $false )
| ( ( subset @ SV65 @ SV57 @ SV20 )
= $true )
| ( ( exists_in_world @ SV65 @ SV20 )
= $false )
| ( ( exists_in_world @ SV57 @ SV20 )
= $false )
| ( ( exists_in_world @ SV39 @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[318]) ).
thf(332,plain,
! [SV53: mu,SV15: $i,SV35: mu,SV66: mu] :
( ( ( ~ ( ~ ( member @ SV66 @ SV35 @ SV15 )
| ( member @ SV66 @ SV53 @ SV15 ) ) )
= $false )
| ( ( exists_in_world @ SV66 @ SV15 )
= $false )
| ( ( qmltpeq @ SV35 @ SV53 @ SV15 )
= $false )
| ( ( exists_in_world @ SV53 @ SV15 )
= $false )
| ( ( exists_in_world @ SV35 @ SV15 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[325]) ).
thf(333,plain,
! [SV35: mu,SV15: $i,SV53: mu,SV66: mu] :
( ( ( ~ ( ~ ( member @ SV66 @ SV53 @ SV15 )
| ( member @ SV66 @ SV35 @ SV15 ) ) )
= $false )
| ( ( exists_in_world @ SV66 @ SV15 )
= $false )
| ( ( qmltpeq @ SV35 @ SV53 @ SV15 )
= $false )
| ( ( exists_in_world @ SV53 @ SV15 )
= $false )
| ( ( exists_in_world @ SV35 @ SV15 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[325]) ).
thf(334,plain,
! [SV15: $i,SV35: mu,SV53: mu] :
( ( ( ~ ( member @ ( sK4_SY84 @ SV53 @ SV35 @ SV15 ) @ SV35 @ SV15 )
| ( member @ ( sK4_SY84 @ SV53 @ SV35 @ SV15 ) @ SV53 @ SV15 ) )
= $false )
| ( ( ~ ( ~ ( member @ ( sK4_SY84 @ SV53 @ SV35 @ SV15 ) @ SV53 @ SV15 )
| ( member @ ( sK4_SY84 @ SV53 @ SV35 @ SV15 ) @ SV35 @ SV15 ) ) )
= $true )
| ( ( qmltpeq @ SV35 @ SV53 @ SV15 )
= $true )
| ( ( exists_in_world @ SV53 @ SV15 )
= $false )
| ( ( exists_in_world @ SV35 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[326]) ).
thf(335,plain,
! [SV54: mu,SV17: $i,SV36: mu,SV67: mu] :
( ( ( member @ SV67 @ SV36 @ SV17 )
= $false )
| ( ( member @ SV67 @ SV54 @ SV17 )
= $true )
| ( ( exists_in_world @ SV67 @ SV17 )
= $false )
| ( ( subset @ SV36 @ SV54 @ SV17 )
= $false )
| ( ( exists_in_world @ SV54 @ SV17 )
= $false )
| ( ( exists_in_world @ SV36 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[327]) ).
thf(336,plain,
! [SV53: mu,SV15: $i,SV35: mu,SV66: mu] :
( ( ( ~ ( member @ SV66 @ SV35 @ SV15 )
| ( member @ SV66 @ SV53 @ SV15 ) )
= $true )
| ( ( exists_in_world @ SV66 @ SV15 )
= $false )
| ( ( qmltpeq @ SV35 @ SV53 @ SV15 )
= $false )
| ( ( exists_in_world @ SV53 @ SV15 )
= $false )
| ( ( exists_in_world @ SV35 @ SV15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[332]) ).
thf(337,plain,
! [SV35: mu,SV15: $i,SV53: mu,SV66: mu] :
( ( ( ~ ( member @ SV66 @ SV53 @ SV15 )
| ( member @ SV66 @ SV35 @ SV15 ) )
= $true )
| ( ( exists_in_world @ SV66 @ SV15 )
= $false )
| ( ( qmltpeq @ SV35 @ SV53 @ SV15 )
= $false )
| ( ( exists_in_world @ SV53 @ SV15 )
= $false )
| ( ( exists_in_world @ SV35 @ SV15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[333]) ).
thf(338,plain,
! [SV15: $i,SV35: mu,SV53: mu] :
( ( ( ~ ( member @ ( sK4_SY84 @ SV53 @ SV35 @ SV15 ) @ SV35 @ SV15 ) )
= $false )
| ( ( ~ ( ~ ( member @ ( sK4_SY84 @ SV53 @ SV35 @ SV15 ) @ SV53 @ SV15 )
| ( member @ ( sK4_SY84 @ SV53 @ SV35 @ SV15 ) @ SV35 @ SV15 ) ) )
= $true )
| ( ( qmltpeq @ SV35 @ SV53 @ SV15 )
= $true )
| ( ( exists_in_world @ SV53 @ SV15 )
= $false )
| ( ( exists_in_world @ SV35 @ SV15 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[334]) ).
thf(339,plain,
! [SV15: $i,SV35: mu,SV53: mu] :
( ( ( member @ ( sK4_SY84 @ SV53 @ SV35 @ SV15 ) @ SV53 @ SV15 )
= $false )
| ( ( ~ ( ~ ( member @ ( sK4_SY84 @ SV53 @ SV35 @ SV15 ) @ SV53 @ SV15 )
| ( member @ ( sK4_SY84 @ SV53 @ SV35 @ SV15 ) @ SV35 @ SV15 ) ) )
= $true )
| ( ( qmltpeq @ SV35 @ SV53 @ SV15 )
= $true )
| ( ( exists_in_world @ SV53 @ SV15 )
= $false )
| ( ( exists_in_world @ SV35 @ SV15 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[334]) ).
thf(340,plain,
! [SV53: mu,SV15: $i,SV35: mu,SV66: mu] :
( ( ( ~ ( member @ SV66 @ SV35 @ SV15 ) )
= $true )
| ( ( member @ SV66 @ SV53 @ SV15 )
= $true )
| ( ( exists_in_world @ SV66 @ SV15 )
= $false )
| ( ( qmltpeq @ SV35 @ SV53 @ SV15 )
= $false )
| ( ( exists_in_world @ SV53 @ SV15 )
= $false )
| ( ( exists_in_world @ SV35 @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[336]) ).
thf(341,plain,
! [SV35: mu,SV15: $i,SV53: mu,SV66: mu] :
( ( ( ~ ( member @ SV66 @ SV53 @ SV15 ) )
= $true )
| ( ( member @ SV66 @ SV35 @ SV15 )
= $true )
| ( ( exists_in_world @ SV66 @ SV15 )
= $false )
| ( ( qmltpeq @ SV35 @ SV53 @ SV15 )
= $false )
| ( ( exists_in_world @ SV53 @ SV15 )
= $false )
| ( ( exists_in_world @ SV35 @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[337]) ).
thf(342,plain,
! [SV15: $i,SV35: mu,SV53: mu] :
( ( ( member @ ( sK4_SY84 @ SV53 @ SV35 @ SV15 ) @ SV35 @ SV15 )
= $true )
| ( ( ~ ( ~ ( member @ ( sK4_SY84 @ SV53 @ SV35 @ SV15 ) @ SV53 @ SV15 )
| ( member @ ( sK4_SY84 @ SV53 @ SV35 @ SV15 ) @ SV35 @ SV15 ) ) )
= $true )
| ( ( qmltpeq @ SV35 @ SV53 @ SV15 )
= $true )
| ( ( exists_in_world @ SV53 @ SV15 )
= $false )
| ( ( exists_in_world @ SV35 @ SV15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[338]) ).
thf(343,plain,
! [SV15: $i,SV35: mu,SV53: mu] :
( ( ( ~ ( member @ ( sK4_SY84 @ SV53 @ SV35 @ SV15 ) @ SV53 @ SV15 )
| ( member @ ( sK4_SY84 @ SV53 @ SV35 @ SV15 ) @ SV35 @ SV15 ) )
= $false )
| ( ( member @ ( sK4_SY84 @ SV53 @ SV35 @ SV15 ) @ SV53 @ SV15 )
= $false )
| ( ( qmltpeq @ SV35 @ SV53 @ SV15 )
= $true )
| ( ( exists_in_world @ SV53 @ SV15 )
= $false )
| ( ( exists_in_world @ SV35 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[339]) ).
thf(344,plain,
! [SV53: mu,SV15: $i,SV35: mu,SV66: mu] :
( ( ( member @ SV66 @ SV35 @ SV15 )
= $false )
| ( ( member @ SV66 @ SV53 @ SV15 )
= $true )
| ( ( exists_in_world @ SV66 @ SV15 )
= $false )
| ( ( qmltpeq @ SV35 @ SV53 @ SV15 )
= $false )
| ( ( exists_in_world @ SV53 @ SV15 )
= $false )
| ( ( exists_in_world @ SV35 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[340]) ).
thf(345,plain,
! [SV35: mu,SV15: $i,SV53: mu,SV66: mu] :
( ( ( member @ SV66 @ SV53 @ SV15 )
= $false )
| ( ( member @ SV66 @ SV35 @ SV15 )
= $true )
| ( ( exists_in_world @ SV66 @ SV15 )
= $false )
| ( ( qmltpeq @ SV35 @ SV53 @ SV15 )
= $false )
| ( ( exists_in_world @ SV53 @ SV15 )
= $false )
| ( ( exists_in_world @ SV35 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[341]) ).
thf(346,plain,
! [SV15: $i,SV35: mu,SV53: mu] :
( ( ( ~ ( member @ ( sK4_SY84 @ SV53 @ SV35 @ SV15 ) @ SV53 @ SV15 )
| ( member @ ( sK4_SY84 @ SV53 @ SV35 @ SV15 ) @ SV35 @ SV15 ) )
= $false )
| ( ( member @ ( sK4_SY84 @ SV53 @ SV35 @ SV15 ) @ SV35 @ SV15 )
= $true )
| ( ( qmltpeq @ SV35 @ SV53 @ SV15 )
= $true )
| ( ( exists_in_world @ SV53 @ SV15 )
= $false )
| ( ( exists_in_world @ SV35 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[342]) ).
thf(347,plain,
! [SV15: $i,SV35: mu,SV53: mu] :
( ( ( ~ ( member @ ( sK4_SY84 @ SV53 @ SV35 @ SV15 ) @ SV53 @ SV15 ) )
= $false )
| ( ( member @ ( sK4_SY84 @ SV53 @ SV35 @ SV15 ) @ SV53 @ SV15 )
= $false )
| ( ( qmltpeq @ SV35 @ SV53 @ SV15 )
= $true )
| ( ( exists_in_world @ SV53 @ SV15 )
= $false )
| ( ( exists_in_world @ SV35 @ SV15 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[343]) ).
thf(348,plain,
! [SV15: $i,SV35: mu,SV53: mu] :
( ( ( member @ ( sK4_SY84 @ SV53 @ SV35 @ SV15 ) @ SV35 @ SV15 )
= $false )
| ( ( member @ ( sK4_SY84 @ SV53 @ SV35 @ SV15 ) @ SV53 @ SV15 )
= $false )
| ( ( qmltpeq @ SV35 @ SV53 @ SV15 )
= $true )
| ( ( exists_in_world @ SV53 @ SV15 )
= $false )
| ( ( exists_in_world @ SV35 @ SV15 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[343]) ).
thf(349,plain,
! [SV15: $i,SV35: mu,SV53: mu] :
( ( ( ~ ( member @ ( sK4_SY84 @ SV53 @ SV35 @ SV15 ) @ SV53 @ SV15 ) )
= $false )
| ( ( member @ ( sK4_SY84 @ SV53 @ SV35 @ SV15 ) @ SV35 @ SV15 )
= $true )
| ( ( qmltpeq @ SV35 @ SV53 @ SV15 )
= $true )
| ( ( exists_in_world @ SV53 @ SV15 )
= $false )
| ( ( exists_in_world @ SV35 @ SV15 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[346]) ).
thf(350,plain,
! [SV15: $i,SV35: mu,SV53: mu] :
( ( ( member @ ( sK4_SY84 @ SV53 @ SV35 @ SV15 ) @ SV35 @ SV15 )
= $false )
| ( ( member @ ( sK4_SY84 @ SV53 @ SV35 @ SV15 ) @ SV35 @ SV15 )
= $true )
| ( ( qmltpeq @ SV35 @ SV53 @ SV15 )
= $true )
| ( ( exists_in_world @ SV53 @ SV15 )
= $false )
| ( ( exists_in_world @ SV35 @ SV15 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[346]) ).
thf(351,plain,
! [SV15: $i,SV35: mu,SV53: mu] :
( ( ( member @ ( sK4_SY84 @ SV53 @ SV35 @ SV15 ) @ SV53 @ SV15 )
= $true )
| ( ( member @ ( sK4_SY84 @ SV53 @ SV35 @ SV15 ) @ SV53 @ SV15 )
= $false )
| ( ( qmltpeq @ SV35 @ SV53 @ SV15 )
= $true )
| ( ( exists_in_world @ SV53 @ SV15 )
= $false )
| ( ( exists_in_world @ SV35 @ SV15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[347]) ).
thf(352,plain,
! [SV15: $i,SV35: mu,SV53: mu] :
( ( ( member @ ( sK4_SY84 @ SV53 @ SV35 @ SV15 ) @ SV53 @ SV15 )
= $true )
| ( ( member @ ( sK4_SY84 @ SV53 @ SV35 @ SV15 ) @ SV35 @ SV15 )
= $true )
| ( ( qmltpeq @ SV35 @ SV53 @ SV15 )
= $true )
| ( ( exists_in_world @ SV53 @ SV15 )
= $false )
| ( ( exists_in_world @ SV35 @ SV15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[349]) ).
thf(353,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[68,352,351,350,348,345,344,335,331,330,329,328,324,323,322,321,320,319,315,313,310,303,302,264,260,222,219,215,193,183,163,149,145,135,111,83]) ).
thf(354,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[353]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET002^7 : TPTP v8.1.0. Released v5.5.0.
% 0.07/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jul 10 15:49:33 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.37
% 0.13/0.37 No.of.Axioms: 21
% 0.13/0.37
% 0.13/0.37 Length.of.Defs: 5508
% 0.13/0.37
% 0.13/0.37 Contains.Choice.Funs: false
% 0.20/0.39 (rf:0,axioms:21,ps:3,u:6,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:23,loop_count:0,foatp_calls:0,translation:fof_full).....................
% 0.39/0.60
% 0.39/0.60 ********************************
% 0.39/0.60 * All subproblems solved! *
% 0.39/0.60 ********************************
% 0.39/0.60 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:21,ps:3,u:6,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:353,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.47/0.65
% 0.47/0.65 %**** Beginning of derivation protocol ****
% 0.47/0.65 % SZS output start CNFRefutation
% See solution above
% 0.47/0.65
% 0.47/0.65 %**** End of derivation protocol ****
% 0.47/0.65 %**** no. of clauses in derivation: 354 ****
% 0.47/0.65 %**** clause counter: 353 ****
% 0.47/0.65
% 0.47/0.65 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:21,ps:3,u:6,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:353,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------