%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET914^7 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:42:32 AM UTC 2026
% Result : Theorem 4.27s 0.92s
% Output : CNFRefutation 4.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 64
% Syntax : Number of formulae : 590 ( 227 unt; 0 typ; 32 def)
% Number of atoms : 6564 (1633 equ; 0 cnn)
% Maximal formula atoms : 12 ( 11 avg)
% Number of connectives : 14699 (2213 ~;2423 |; 13 &;9903 @)
% ( 0 <=>; 147 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 59 ( 59 >; 0 *; 0 +; 0 <<)
% Number of symbols : 54 ( 51 usr; 7 con; 0-4 aty)
% Number of variables : 2016 ( 111 ^;1896 !; 9 ?;2016 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_mu,type,
mu: $tType ).
thf(tp_disjoint,type,
disjoint: mu > mu > $i > $o ).
thf(tp_empty,type,
empty: mu > $i > $o ).
thf(tp_empty_set,type,
empty_set: mu ).
thf(tp_exists_in_world,type,
exists_in_world: mu > $i > $o ).
thf(tp_in,type,
in: mu > 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_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_sK10_SY970,type,
sK10_SY970: mu > mu > mu > $i > mu ).
thf(tp_sK1_SY27,type,
sK1_SY27: $i ).
thf(tp_sK2_SY838,type,
sK2_SY838: mu ).
thf(tp_sK3_SX0,type,
sK3_SX0: mu ).
thf(tp_sK4_SY866,type,
sK4_SY866: $i > mu ).
thf(tp_sK5_SY871,type,
sK5_SY871: $i > mu ).
thf(tp_sK6_SY883,type,
sK6_SY883: $i > mu ).
thf(tp_sK7_SY949,type,
sK7_SY949: mu ).
thf(tp_sK8_SY925,type,
sK8_SY925: mu > $i > mu ).
thf(tp_sK9_SY968,type,
sK9_SY968: mu > mu > mu > $i > mu ).
thf(tp_set_intersection2,type,
set_intersection2: mu > mu > mu ).
thf(tp_unordered_pair,type,
unordered_pair: 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
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] : ( mimplies @ ( disjoint @ A @ B ) @ ( disjoint @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
thf(2,axiom,
( mvalid
@ ( mexists_ind
@ ^ [A: mu] : ( mnot @ ( empty @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(3,axiom,
( mvalid
@ ( mexists_ind
@ ^ [A: mu] : ( empty @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(4,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] : ( qmltpeq @ ( set_intersection2 @ A @ A ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
thf(5,axiom,
mvalid @ ( empty @ empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(6,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] : ( mequiv @ ( disjoint @ A @ B ) @ ( qmltpeq @ ( set_intersection2 @ A @ B ) @ empty_set ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_xboole_0) ).
thf(7,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] :
( mequiv @ ( qmltpeq @ C @ ( set_intersection2 @ A @ B ) )
@ ( mforall_ind
@ ^ [D: mu] : ( mequiv @ ( in @ D @ C ) @ ( mand @ ( in @ D @ A ) @ ( in @ D @ B ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
thf(8,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] :
( mequiv @ ( qmltpeq @ C @ ( unordered_pair @ A @ B ) )
@ ( mforall_ind
@ ^ [D: mu] : ( mequiv @ ( in @ D @ C ) @ ( mor @ ( qmltpeq @ D @ A ) @ ( qmltpeq @ D @ B ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
thf(9,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mequiv @ ( qmltpeq @ A @ empty_set )
@ ( mforall_ind
@ ^ [B: mu] : ( mnot @ ( in @ B @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(10,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] : ( qmltpeq @ ( set_intersection2 @ A @ B ) @ ( set_intersection2 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
thf(11,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] : ( qmltpeq @ ( unordered_pair @ A @ B ) @ ( unordered_pair @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(12,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] : ( mimplies @ ( in @ A @ B ) @ ( mnot @ ( in @ B @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(13,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( in @ C @ A ) ) @ ( in @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',in_substitution_2) ).
thf(14,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( in @ A @ C ) ) @ ( in @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',in_substitution_1) ).
thf(15,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( empty @ A ) ) @ ( empty @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_substitution_1) ).
thf(16,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( disjoint @ C @ A ) ) @ ( disjoint @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',disjoint_substitution_2) ).
thf(17,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( disjoint @ A @ C ) ) @ ( disjoint @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',disjoint_substitution_1) ).
thf(18,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( unordered_pair @ C @ A ) @ ( unordered_pair @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_substitution_2) ).
thf(19,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( unordered_pair @ A @ C ) @ ( unordered_pair @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_substitution_1) ).
thf(20,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( set_intersection2 @ C @ A ) @ ( set_intersection2 @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_intersection2_substitution_2) ).
thf(21,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_intersection2_substitution_1) ).
thf(22,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(23,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(24,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X: mu] : ( qmltpeq @ X @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).
thf(25,axiom,
! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( unordered_pair @ V2 @ V1 ) @ V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_unordered_pair_ax) ).
thf(26,axiom,
! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( set_intersection2 @ V2 @ V1 ) @ V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_set_intersection2_ax) ).
thf(27,axiom,
! [V: $i] : ( exists_in_world @ empty_set @ V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_empty_set_ax) ).
thf(28,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(29,axiom,
mtransitive @ rel_s4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2) ).
thf(30,axiom,
mreflexive @ rel_s4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1) ).
thf(31,axiom,
! [V: $i] :
? [X: mu] : ( exists_in_world @ X @ V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonempty_ax) ).
thf(32,conjecture,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mnot @ ( mand @ ( disjoint @ ( unordered_pair @ A @ B ) @ C ) @ ( in @ A @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_zfmisc_1) ).
thf(33,negated_conjecture,
( ( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mnot @ ( mand @ ( disjoint @ ( unordered_pair @ A @ B ) @ C ) @ ( in @ A @ C ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[32]) ).
thf(34,plain,
( ( ! [SY27: $i,SY28: mu] :
( ( exists_in_world @ SY28 @ SY27 )
=> ! [SY29: mu] :
( ( exists_in_world @ SY29 @ SY27 )
=> ! [SY30: mu] :
( ( exists_in_world @ SY30 @ SY27 )
=> ~ ~ ( ~ ( disjoint @ ( unordered_pair @ SY28 @ SY29 ) @ SY30 @ SY27 )
| ~ ( in @ SY28 @ SY30 @ SY27 ) ) ) ) ) )
= $false ),
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(35,plain,
( ( ! [SY51: $i,SY52: mu] :
( ( exists_in_world @ SY52 @ SY51 )
=> ! [SY53: mu] :
( ( exists_in_world @ SY53 @ SY51 )
=> ( ~ ( disjoint @ SY52 @ SY53 @ SY51 )
| ( disjoint @ SY53 @ SY52 @ SY51 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(36,plain,
( ( ! [SY67: $i] :
~ ! [SY68: mu] :
( ( exists_in_world @ SY68 @ SY67 )
=> ~ ~ ( empty @ SY68 @ SY67 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(37,plain,
( ( ! [SY79: $i] :
~ ! [SY80: mu] :
( ( exists_in_world @ SY80 @ SY79 )
=> ~ ( empty @ SY80 @ SY79 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(38,plain,
( ( ! [SY92: $i,SY93: mu] :
( ( exists_in_world @ SY93 @ SY92 )
=> ! [SY94: mu] :
( ( exists_in_world @ SY94 @ SY92 )
=> ( qmltpeq @ ( set_intersection2 @ SY93 @ SY93 ) @ SY93 @ SY92 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(39,plain,
( ( ! [SY98: $i] : ( empty @ empty_set @ SY98 ) )
= $true ),
inference(unfold_def,[status(thm)],[5,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(40,plain,
( ( ! [SY132: $i,SY133: mu] :
( ( exists_in_world @ SY133 @ SY132 )
=> ! [SY134: mu] :
( ( exists_in_world @ SY134 @ SY132 )
=> ~ ( ~ ( ~ ( disjoint @ SY133 @ SY134 @ SY132 )
| ( qmltpeq @ ( set_intersection2 @ SY133 @ SY134 ) @ empty_set @ SY132 ) )
| ~ ( ~ ( qmltpeq @ ( set_intersection2 @ SY133 @ SY134 ) @ empty_set @ SY132 )
| ( disjoint @ SY133 @ SY134 @ SY132 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(41,plain,
( ( ! [SY226: $i,SY227: mu] :
( ( exists_in_world @ SY227 @ SY226 )
=> ! [SY228: mu] :
( ( exists_in_world @ SY228 @ SY226 )
=> ! [SY229: mu] :
( ( exists_in_world @ SY229 @ SY226 )
=> ~ ( ~ ( ~ ( qmltpeq @ SY229 @ ( set_intersection2 @ SY227 @ SY228 ) @ SY226 )
| ! [SY230: mu] :
( ( exists_in_world @ SY230 @ SY226 )
=> ~ ( ~ ( ~ ( in @ SY230 @ SY229 @ SY226 )
| ~ ( ~ ( in @ SY230 @ SY227 @ SY226 )
| ~ ( in @ SY230 @ SY228 @ SY226 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY230 @ SY227 @ SY226 )
| ~ ( in @ SY230 @ SY228 @ SY226 ) )
| ( in @ SY230 @ SY229 @ SY226 ) ) ) ) )
| ~ ( ~ ! [SY231: mu] :
( ( exists_in_world @ SY231 @ SY226 )
=> ~ ( ~ ( ~ ( in @ SY231 @ SY229 @ SY226 )
| ~ ( ~ ( in @ SY231 @ SY227 @ SY226 )
| ~ ( in @ SY231 @ SY228 @ SY226 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY231 @ SY227 @ SY226 )
| ~ ( in @ SY231 @ SY228 @ SY226 ) )
| ( in @ SY231 @ SY229 @ SY226 ) ) ) )
| ( qmltpeq @ SY229 @ ( set_intersection2 @ SY227 @ SY228 ) @ SY226 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(42,plain,
( ( ! [SY321: $i,SY322: mu] :
( ( exists_in_world @ SY322 @ SY321 )
=> ! [SY323: mu] :
( ( exists_in_world @ SY323 @ SY321 )
=> ! [SY324: mu] :
( ( exists_in_world @ SY324 @ SY321 )
=> ~ ( ~ ( ~ ( qmltpeq @ SY324 @ ( unordered_pair @ SY322 @ SY323 ) @ SY321 )
| ! [SY325: mu] :
( ( exists_in_world @ SY325 @ SY321 )
=> ~ ( ~ ( ~ ( in @ SY325 @ SY324 @ SY321 )
| ( qmltpeq @ SY325 @ SY322 @ SY321 )
| ( qmltpeq @ SY325 @ SY323 @ SY321 ) )
| ~ ( ~ ( ( qmltpeq @ SY325 @ SY322 @ SY321 )
| ( qmltpeq @ SY325 @ SY323 @ SY321 ) )
| ( in @ SY325 @ SY324 @ SY321 ) ) ) ) )
| ~ ( ~ ! [SY326: mu] :
( ( exists_in_world @ SY326 @ SY321 )
=> ~ ( ~ ( ~ ( in @ SY326 @ SY324 @ SY321 )
| ( qmltpeq @ SY326 @ SY322 @ SY321 )
| ( qmltpeq @ SY326 @ SY323 @ SY321 ) )
| ~ ( ~ ( ( qmltpeq @ SY326 @ SY322 @ SY321 )
| ( qmltpeq @ SY326 @ SY323 @ SY321 ) )
| ( in @ SY326 @ SY324 @ SY321 ) ) ) )
| ( qmltpeq @ SY324 @ ( unordered_pair @ SY322 @ SY323 ) @ SY321 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(43,plain,
( ( ! [SY370: $i,SY371: mu] :
( ( exists_in_world @ SY371 @ SY370 )
=> ~ ( ~ ( ~ ( qmltpeq @ SY371 @ empty_set @ SY370 )
| ! [SY372: mu] :
( ( exists_in_world @ SY372 @ SY370 )
=> ~ ( in @ SY372 @ SY371 @ SY370 ) ) )
| ~ ( ~ ! [SY373: mu] :
( ( exists_in_world @ SY373 @ SY370 )
=> ~ ( in @ SY373 @ SY371 @ SY370 ) )
| ( qmltpeq @ SY371 @ empty_set @ SY370 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(44,plain,
( ( ! [SY387: $i,SY388: mu] :
( ( exists_in_world @ SY388 @ SY387 )
=> ! [SY389: mu] :
( ( exists_in_world @ SY389 @ SY387 )
=> ( qmltpeq @ ( set_intersection2 @ SY388 @ SY389 ) @ ( set_intersection2 @ SY389 @ SY388 ) @ SY387 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(45,plain,
( ( ! [SY402: $i,SY403: mu] :
( ( exists_in_world @ SY403 @ SY402 )
=> ! [SY404: mu] :
( ( exists_in_world @ SY404 @ SY402 )
=> ( qmltpeq @ ( unordered_pair @ SY403 @ SY404 ) @ ( unordered_pair @ SY404 @ SY403 ) @ SY402 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(46,plain,
( ( ! [SY425: $i,SY426: mu] :
( ( exists_in_world @ SY426 @ SY425 )
=> ! [SY427: mu] :
( ( exists_in_world @ SY427 @ SY425 )
=> ( ~ ( in @ SY426 @ SY427 @ SY425 )
| ~ ( in @ SY427 @ SY426 @ SY425 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(47,plain,
( ( ! [SY463: $i,SY464: mu] :
( ( exists_in_world @ SY464 @ SY463 )
=> ! [SY465: mu] :
( ( exists_in_world @ SY465 @ SY463 )
=> ! [SY466: mu] :
( ( exists_in_world @ SY466 @ SY463 )
=> ( ~ ~ ( ~ ( qmltpeq @ SY464 @ SY465 @ SY463 )
| ~ ( in @ SY466 @ SY464 @ SY463 ) )
| ( in @ SY466 @ SY465 @ SY463 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(48,plain,
( ( ! [SY503: $i,SY504: mu] :
( ( exists_in_world @ SY504 @ SY503 )
=> ! [SY505: mu] :
( ( exists_in_world @ SY505 @ SY503 )
=> ! [SY506: mu] :
( ( exists_in_world @ SY506 @ SY503 )
=> ( ~ ~ ( ~ ( qmltpeq @ SY504 @ SY505 @ SY503 )
| ~ ( in @ SY504 @ SY506 @ SY503 ) )
| ( in @ SY505 @ SY506 @ SY503 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(49,plain,
( ( ! [SY535: $i,SY536: mu] :
( ( exists_in_world @ SY536 @ SY535 )
=> ! [SY537: mu] :
( ( exists_in_world @ SY537 @ SY535 )
=> ( ~ ~ ( ~ ( qmltpeq @ SY536 @ SY537 @ SY535 )
| ~ ( empty @ SY536 @ SY535 ) )
| ( empty @ SY537 @ SY535 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(50,plain,
( ( ! [SY573: $i,SY574: mu] :
( ( exists_in_world @ SY574 @ SY573 )
=> ! [SY575: mu] :
( ( exists_in_world @ SY575 @ SY573 )
=> ! [SY576: mu] :
( ( exists_in_world @ SY576 @ SY573 )
=> ( ~ ~ ( ~ ( qmltpeq @ SY574 @ SY575 @ SY573 )
| ~ ( disjoint @ SY576 @ SY574 @ SY573 ) )
| ( disjoint @ SY576 @ SY575 @ SY573 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(51,plain,
( ( ! [SY613: $i,SY614: mu] :
( ( exists_in_world @ SY614 @ SY613 )
=> ! [SY615: mu] :
( ( exists_in_world @ SY615 @ SY613 )
=> ! [SY616: mu] :
( ( exists_in_world @ SY616 @ SY613 )
=> ( ~ ~ ( ~ ( qmltpeq @ SY614 @ SY615 @ SY613 )
| ~ ( disjoint @ SY614 @ SY616 @ SY613 ) )
| ( disjoint @ SY615 @ SY616 @ SY613 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(52,plain,
( ( ! [SY645: $i,SY646: mu] :
( ( exists_in_world @ SY646 @ SY645 )
=> ! [SY647: mu] :
( ( exists_in_world @ SY647 @ SY645 )
=> ! [SY648: mu] :
( ( exists_in_world @ SY648 @ SY645 )
=> ( ~ ( qmltpeq @ SY646 @ SY647 @ SY645 )
| ( qmltpeq @ ( unordered_pair @ SY648 @ SY646 ) @ ( unordered_pair @ SY648 @ SY647 ) @ SY645 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18,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,
( ( ! [SY677: $i,SY678: mu] :
( ( exists_in_world @ SY678 @ SY677 )
=> ! [SY679: mu] :
( ( exists_in_world @ SY679 @ SY677 )
=> ! [SY680: mu] :
( ( exists_in_world @ SY680 @ SY677 )
=> ( ~ ( qmltpeq @ SY678 @ SY679 @ SY677 )
| ( qmltpeq @ ( unordered_pair @ SY678 @ SY680 ) @ ( unordered_pair @ SY679 @ SY680 ) @ SY677 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19,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,
( ( ! [SY709: $i,SY710: mu] :
( ( exists_in_world @ SY710 @ SY709 )
=> ! [SY711: mu] :
( ( exists_in_world @ SY711 @ SY709 )
=> ! [SY712: mu] :
( ( exists_in_world @ SY712 @ SY709 )
=> ( ~ ( qmltpeq @ SY710 @ SY711 @ SY709 )
| ( qmltpeq @ ( set_intersection2 @ SY712 @ SY710 ) @ ( set_intersection2 @ SY712 @ SY711 ) @ SY709 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20,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,
( ( ! [SY741: $i,SY742: mu] :
( ( exists_in_world @ SY742 @ SY741 )
=> ! [SY743: mu] :
( ( exists_in_world @ SY743 @ SY741 )
=> ! [SY744: mu] :
( ( exists_in_world @ SY744 @ SY741 )
=> ( ~ ( qmltpeq @ SY742 @ SY743 @ SY741 )
| ( qmltpeq @ ( set_intersection2 @ SY742 @ SY744 ) @ ( set_intersection2 @ SY743 @ SY744 ) @ SY741 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21,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,
( ( ! [SY781: $i,SY782: mu] :
( ( exists_in_world @ SY782 @ SY781 )
=> ! [SY783: mu] :
( ( exists_in_world @ SY783 @ SY781 )
=> ! [SY784: mu] :
( ( exists_in_world @ SY784 @ SY781 )
=> ( ~ ~ ( ~ ( qmltpeq @ SY782 @ SY783 @ SY781 )
| ~ ( qmltpeq @ SY783 @ SY784 @ SY781 ) )
| ( qmltpeq @ SY782 @ SY784 @ SY781 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22,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,
( ( ! [SY805: $i,SY806: mu] :
( ( exists_in_world @ SY806 @ SY805 )
=> ! [SY807: mu] :
( ( exists_in_world @ SY807 @ SY805 )
=> ( ~ ( qmltpeq @ SY806 @ SY807 @ SY805 )
| ( qmltpeq @ SY807 @ SY806 @ SY805 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(58,plain,
( ( ! [SY814: $i,SY815: mu] :
( ( exists_in_world @ SY815 @ SY814 )
=> ( qmltpeq @ SY815 @ SY815 @ SY814 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24,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,
( ( ! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( unordered_pair @ V2 @ V1 ) @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[25,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,
( ( ! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( set_intersection2 @ V2 @ V1 ) @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[26,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,
( ( ! [V: $i] : ( exists_in_world @ empty_set @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[27,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,
( ( ! [X: mu,V: $i,W: $i] :
( ( ( exists_in_world @ X @ V )
& ( rel_s4 @ V @ W ) )
=> ( exists_in_world @ X @ W ) ) )
= $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(63,plain,
( ( ! [SY828: $i,SY829: $i,SY830: $i] :
( ( ( rel_s4 @ SY828 @ SY829 )
& ( rel_s4 @ SY829 @ SY830 ) )
=> ( rel_s4 @ SY828 @ SY830 ) ) )
= $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(64,plain,
( ( ! [SY834: $i] : ( rel_s4 @ SY834 @ SY834 ) )
= $true ),
inference(unfold_def,[status(thm)],[30,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,
( ( ! [V: $i] :
? [X: mu] : ( exists_in_world @ X @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[31,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,
( ( ! [SY838: mu] :
( ( exists_in_world @ SY838 @ sK1_SY27 )
=> ! [SY839: mu] :
( ( exists_in_world @ SY839 @ sK1_SY27 )
=> ! [SY840: mu] :
( ( exists_in_world @ SY840 @ sK1_SY27 )
=> ~ ~ ( ~ ( disjoint @ ( unordered_pair @ SY838 @ SY839 ) @ SY840 @ sK1_SY27 )
| ~ ( in @ SY838 @ SY840 @ sK1_SY27 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[34]) ).
thf(67,plain,
( ( ( exists_in_world @ sK2_SY838 @ sK1_SY27 )
=> ! [SY841: mu] :
( ( exists_in_world @ SY841 @ sK1_SY27 )
=> ! [SY842: mu] :
( ( exists_in_world @ SY842 @ sK1_SY27 )
=> ~ ~ ( ~ ( disjoint @ ( unordered_pair @ sK2_SY838 @ SY841 ) @ SY842 @ sK1_SY27 )
| ~ ( in @ sK2_SY838 @ SY842 @ sK1_SY27 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[66]) ).
thf(68,plain,
( ( exists_in_world @ sK2_SY838 @ sK1_SY27 )
= $true ),
inference(standard_cnf,[status(thm)],[67]) ).
thf(69,plain,
( ( ! [SY841: mu] :
( ( exists_in_world @ SY841 @ sK1_SY27 )
=> ! [SY842: mu] :
( ( exists_in_world @ SY842 @ sK1_SY27 )
=> ~ ~ ( ~ ( disjoint @ ( unordered_pair @ sK2_SY838 @ SY841 ) @ SY842 @ sK1_SY27 )
| ~ ( in @ sK2_SY838 @ SY842 @ sK1_SY27 ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[67]) ).
thf(70,plain,
( ( ~ ! [SY841: mu] :
( ( exists_in_world @ SY841 @ sK1_SY27 )
=> ! [SY842: mu] :
( ( exists_in_world @ SY842 @ sK1_SY27 )
=> ~ ~ ( ~ ( disjoint @ ( unordered_pair @ sK2_SY838 @ SY841 ) @ SY842 @ sK1_SY27 )
| ~ ( in @ sK2_SY838 @ SY842 @ sK1_SY27 ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[69]) ).
thf(71,plain,
( ( ! [V: $i] :
? [X: mu] : ( exists_in_world @ X @ V ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(72,plain,
( ( ! [SY834: $i] : ( rel_s4 @ SY834 @ SY834 ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(73,plain,
( ( ! [SY828: $i,SY829: $i,SY830: $i] :
( ( ( rel_s4 @ SY828 @ SY829 )
& ( rel_s4 @ SY829 @ SY830 ) )
=> ( rel_s4 @ SY828 @ SY830 ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(74,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)],[62]) ).
thf(75,plain,
( ( ! [V: $i] : ( exists_in_world @ empty_set @ V ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(76,plain,
( ( ! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( set_intersection2 @ V2 @ V1 ) @ V ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(77,plain,
( ( ! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( unordered_pair @ V2 @ V1 ) @ V ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(78,plain,
( ( ! [SY814: $i,SY815: mu] :
( ( exists_in_world @ SY815 @ SY814 )
=> ( qmltpeq @ SY815 @ SY815 @ SY814 ) ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(79,plain,
( ( ! [SY805: $i,SY806: mu] :
( ( exists_in_world @ SY806 @ SY805 )
=> ! [SY807: mu] :
( ( exists_in_world @ SY807 @ SY805 )
=> ( ~ ( qmltpeq @ SY806 @ SY807 @ SY805 )
| ( qmltpeq @ SY807 @ SY806 @ SY805 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(80,plain,
( ( ! [SY781: $i,SY782: mu] :
( ( exists_in_world @ SY782 @ SY781 )
=> ! [SY783: mu] :
( ( exists_in_world @ SY783 @ SY781 )
=> ! [SY784: mu] :
( ( exists_in_world @ SY784 @ SY781 )
=> ( ~ ~ ( ~ ( qmltpeq @ SY782 @ SY783 @ SY781 )
| ~ ( qmltpeq @ SY783 @ SY784 @ SY781 ) )
| ( qmltpeq @ SY782 @ SY784 @ SY781 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(81,plain,
( ( ! [SY741: $i,SY742: mu] :
( ( exists_in_world @ SY742 @ SY741 )
=> ! [SY743: mu] :
( ( exists_in_world @ SY743 @ SY741 )
=> ! [SY744: mu] :
( ( exists_in_world @ SY744 @ SY741 )
=> ( ~ ( qmltpeq @ SY742 @ SY743 @ SY741 )
| ( qmltpeq @ ( set_intersection2 @ SY742 @ SY744 ) @ ( set_intersection2 @ SY743 @ SY744 ) @ SY741 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(82,plain,
( ( ! [SY709: $i,SY710: mu] :
( ( exists_in_world @ SY710 @ SY709 )
=> ! [SY711: mu] :
( ( exists_in_world @ SY711 @ SY709 )
=> ! [SY712: mu] :
( ( exists_in_world @ SY712 @ SY709 )
=> ( ~ ( qmltpeq @ SY710 @ SY711 @ SY709 )
| ( qmltpeq @ ( set_intersection2 @ SY712 @ SY710 ) @ ( set_intersection2 @ SY712 @ SY711 ) @ SY709 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(83,plain,
( ( ! [SY677: $i,SY678: mu] :
( ( exists_in_world @ SY678 @ SY677 )
=> ! [SY679: mu] :
( ( exists_in_world @ SY679 @ SY677 )
=> ! [SY680: mu] :
( ( exists_in_world @ SY680 @ SY677 )
=> ( ~ ( qmltpeq @ SY678 @ SY679 @ SY677 )
| ( qmltpeq @ ( unordered_pair @ SY678 @ SY680 ) @ ( unordered_pair @ SY679 @ SY680 ) @ SY677 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(84,plain,
( ( ! [SY645: $i,SY646: mu] :
( ( exists_in_world @ SY646 @ SY645 )
=> ! [SY647: mu] :
( ( exists_in_world @ SY647 @ SY645 )
=> ! [SY648: mu] :
( ( exists_in_world @ SY648 @ SY645 )
=> ( ~ ( qmltpeq @ SY646 @ SY647 @ SY645 )
| ( qmltpeq @ ( unordered_pair @ SY648 @ SY646 ) @ ( unordered_pair @ SY648 @ SY647 ) @ SY645 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(85,plain,
( ( ! [SY613: $i,SY614: mu] :
( ( exists_in_world @ SY614 @ SY613 )
=> ! [SY615: mu] :
( ( exists_in_world @ SY615 @ SY613 )
=> ! [SY616: mu] :
( ( exists_in_world @ SY616 @ SY613 )
=> ( ~ ~ ( ~ ( qmltpeq @ SY614 @ SY615 @ SY613 )
| ~ ( disjoint @ SY614 @ SY616 @ SY613 ) )
| ( disjoint @ SY615 @ SY616 @ SY613 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(86,plain,
( ( ! [SY573: $i,SY574: mu] :
( ( exists_in_world @ SY574 @ SY573 )
=> ! [SY575: mu] :
( ( exists_in_world @ SY575 @ SY573 )
=> ! [SY576: mu] :
( ( exists_in_world @ SY576 @ SY573 )
=> ( ~ ~ ( ~ ( qmltpeq @ SY574 @ SY575 @ SY573 )
| ~ ( disjoint @ SY576 @ SY574 @ SY573 ) )
| ( disjoint @ SY576 @ SY575 @ SY573 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(87,plain,
( ( ! [SY535: $i,SY536: mu] :
( ( exists_in_world @ SY536 @ SY535 )
=> ! [SY537: mu] :
( ( exists_in_world @ SY537 @ SY535 )
=> ( ~ ~ ( ~ ( qmltpeq @ SY536 @ SY537 @ SY535 )
| ~ ( empty @ SY536 @ SY535 ) )
| ( empty @ SY537 @ SY535 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(88,plain,
( ( ! [SY503: $i,SY504: mu] :
( ( exists_in_world @ SY504 @ SY503 )
=> ! [SY505: mu] :
( ( exists_in_world @ SY505 @ SY503 )
=> ! [SY506: mu] :
( ( exists_in_world @ SY506 @ SY503 )
=> ( ~ ~ ( ~ ( qmltpeq @ SY504 @ SY505 @ SY503 )
| ~ ( in @ SY504 @ SY506 @ SY503 ) )
| ( in @ SY505 @ SY506 @ SY503 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(89,plain,
( ( ! [SY463: $i,SY464: mu] :
( ( exists_in_world @ SY464 @ SY463 )
=> ! [SY465: mu] :
( ( exists_in_world @ SY465 @ SY463 )
=> ! [SY466: mu] :
( ( exists_in_world @ SY466 @ SY463 )
=> ( ~ ~ ( ~ ( qmltpeq @ SY464 @ SY465 @ SY463 )
| ~ ( in @ SY466 @ SY464 @ SY463 ) )
| ( in @ SY466 @ SY465 @ SY463 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(90,plain,
( ( ! [SY425: $i,SY426: mu] :
( ( exists_in_world @ SY426 @ SY425 )
=> ! [SY427: mu] :
( ( exists_in_world @ SY427 @ SY425 )
=> ( ~ ( in @ SY426 @ SY427 @ SY425 )
| ~ ( in @ SY427 @ SY426 @ SY425 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(91,plain,
( ( ! [SY402: $i,SY403: mu] :
( ( exists_in_world @ SY403 @ SY402 )
=> ! [SY404: mu] :
( ( exists_in_world @ SY404 @ SY402 )
=> ( qmltpeq @ ( unordered_pair @ SY403 @ SY404 ) @ ( unordered_pair @ SY404 @ SY403 ) @ SY402 ) ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(92,plain,
( ( ! [SY387: $i,SY388: mu] :
( ( exists_in_world @ SY388 @ SY387 )
=> ! [SY389: mu] :
( ( exists_in_world @ SY389 @ SY387 )
=> ( qmltpeq @ ( set_intersection2 @ SY388 @ SY389 ) @ ( set_intersection2 @ SY389 @ SY388 ) @ SY387 ) ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(93,plain,
( ( ! [SY370: $i,SY371: mu] :
( ( exists_in_world @ SY371 @ SY370 )
=> ~ ( ~ ( ~ ( qmltpeq @ SY371 @ empty_set @ SY370 )
| ! [SY372: mu] :
( ( exists_in_world @ SY372 @ SY370 )
=> ~ ( in @ SY372 @ SY371 @ SY370 ) ) )
| ~ ( ~ ! [SY373: mu] :
( ( exists_in_world @ SY373 @ SY370 )
=> ~ ( in @ SY373 @ SY371 @ SY370 ) )
| ( qmltpeq @ SY371 @ empty_set @ SY370 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(94,plain,
( ( ! [SY321: $i,SY322: mu] :
( ( exists_in_world @ SY322 @ SY321 )
=> ! [SY323: mu] :
( ( exists_in_world @ SY323 @ SY321 )
=> ! [SY324: mu] :
( ( exists_in_world @ SY324 @ SY321 )
=> ~ ( ~ ( ~ ( qmltpeq @ SY324 @ ( unordered_pair @ SY322 @ SY323 ) @ SY321 )
| ! [SY325: mu] :
( ( exists_in_world @ SY325 @ SY321 )
=> ~ ( ~ ( ~ ( in @ SY325 @ SY324 @ SY321 )
| ( qmltpeq @ SY325 @ SY322 @ SY321 )
| ( qmltpeq @ SY325 @ SY323 @ SY321 ) )
| ~ ( ~ ( ( qmltpeq @ SY325 @ SY322 @ SY321 )
| ( qmltpeq @ SY325 @ SY323 @ SY321 ) )
| ( in @ SY325 @ SY324 @ SY321 ) ) ) ) )
| ~ ( ~ ! [SY326: mu] :
( ( exists_in_world @ SY326 @ SY321 )
=> ~ ( ~ ( ~ ( in @ SY326 @ SY324 @ SY321 )
| ( qmltpeq @ SY326 @ SY322 @ SY321 )
| ( qmltpeq @ SY326 @ SY323 @ SY321 ) )
| ~ ( ~ ( ( qmltpeq @ SY326 @ SY322 @ SY321 )
| ( qmltpeq @ SY326 @ SY323 @ SY321 ) )
| ( in @ SY326 @ SY324 @ SY321 ) ) ) )
| ( qmltpeq @ SY324 @ ( unordered_pair @ SY322 @ SY323 ) @ SY321 ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(95,plain,
( ( ! [SY226: $i,SY227: mu] :
( ( exists_in_world @ SY227 @ SY226 )
=> ! [SY228: mu] :
( ( exists_in_world @ SY228 @ SY226 )
=> ! [SY229: mu] :
( ( exists_in_world @ SY229 @ SY226 )
=> ~ ( ~ ( ~ ( qmltpeq @ SY229 @ ( set_intersection2 @ SY227 @ SY228 ) @ SY226 )
| ! [SY230: mu] :
( ( exists_in_world @ SY230 @ SY226 )
=> ~ ( ~ ( ~ ( in @ SY230 @ SY229 @ SY226 )
| ~ ( ~ ( in @ SY230 @ SY227 @ SY226 )
| ~ ( in @ SY230 @ SY228 @ SY226 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY230 @ SY227 @ SY226 )
| ~ ( in @ SY230 @ SY228 @ SY226 ) )
| ( in @ SY230 @ SY229 @ SY226 ) ) ) ) )
| ~ ( ~ ! [SY231: mu] :
( ( exists_in_world @ SY231 @ SY226 )
=> ~ ( ~ ( ~ ( in @ SY231 @ SY229 @ SY226 )
| ~ ( ~ ( in @ SY231 @ SY227 @ SY226 )
| ~ ( in @ SY231 @ SY228 @ SY226 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY231 @ SY227 @ SY226 )
| ~ ( in @ SY231 @ SY228 @ SY226 ) )
| ( in @ SY231 @ SY229 @ SY226 ) ) ) )
| ( qmltpeq @ SY229 @ ( set_intersection2 @ SY227 @ SY228 ) @ SY226 ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(96,plain,
( ( ! [SY132: $i,SY133: mu] :
( ( exists_in_world @ SY133 @ SY132 )
=> ! [SY134: mu] :
( ( exists_in_world @ SY134 @ SY132 )
=> ~ ( ~ ( ~ ( disjoint @ SY133 @ SY134 @ SY132 )
| ( qmltpeq @ ( set_intersection2 @ SY133 @ SY134 ) @ empty_set @ SY132 ) )
| ~ ( ~ ( qmltpeq @ ( set_intersection2 @ SY133 @ SY134 ) @ empty_set @ SY132 )
| ( disjoint @ SY133 @ SY134 @ SY132 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(97,plain,
( ( ! [SY98: $i] : ( empty @ empty_set @ SY98 ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(98,plain,
( ( ! [SY92: $i,SY93: mu] :
( ( exists_in_world @ SY93 @ SY92 )
=> ! [SY94: mu] :
( ( exists_in_world @ SY94 @ SY92 )
=> ( qmltpeq @ ( set_intersection2 @ SY93 @ SY93 ) @ SY93 @ SY92 ) ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(99,plain,
( ( ! [SY79: $i] :
~ ! [SY80: mu] :
( ( exists_in_world @ SY80 @ SY79 )
=> ~ ( empty @ SY80 @ SY79 ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(100,plain,
( ( ! [SY67: $i] :
~ ! [SY68: mu] :
( ( exists_in_world @ SY68 @ SY67 )
=> ~ ~ ( empty @ SY68 @ SY67 ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(101,plain,
( ( ! [SY51: $i,SY52: mu] :
( ( exists_in_world @ SY52 @ SY51 )
=> ! [SY53: mu] :
( ( exists_in_world @ SY53 @ SY51 )
=> ( ~ ( disjoint @ SY52 @ SY53 @ SY51 )
| ( disjoint @ SY53 @ SY52 @ SY51 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(102,plain,
( ( exists_in_world @ sK2_SY838 @ sK1_SY27 )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(103,plain,
( ( ~ ! [SY841: mu] :
( ( exists_in_world @ SY841 @ sK1_SY27 )
=> ! [SY842: mu] :
( ( exists_in_world @ SY842 @ sK1_SY27 )
=> ~ ~ ( ~ ( disjoint @ ( unordered_pair @ sK2_SY838 @ SY841 ) @ SY842 @ sK1_SY27 )
| ~ ( in @ sK2_SY838 @ SY842 @ sK1_SY27 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(104,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 )
| ~ ( disjoint @ SX3 @ SX1 @ SX0 ) )
| ( disjoint @ SX3 @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[86,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(105,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 )
| ~ ( in @ SX1 @ SX3 @ SX0 ) )
| ( in @ SX2 @ SX3 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[88,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(106,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 @ ( unordered_pair @ SX1 @ SX3 ) @ ( unordered_pair @ SX2 @ SX3 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83,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(107,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ( qmltpeq @ ( set_intersection2 @ SX1 @ SX2 ) @ ( set_intersection2 @ SX2 @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92,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(108,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 @ SX3 @ ( set_intersection2 @ SX1 @ SX2 ) @ SX0 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SX0 )
| ~ ( ~ ( ~ ( in @ SX4 @ SX3 @ SX0 )
| ~ ( ~ ( in @ SX4 @ SX1 @ SX0 )
| ~ ( in @ SX4 @ SX2 @ SX0 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX4 @ SX1 @ SX0 )
| ~ ( in @ SX4 @ SX2 @ SX0 ) )
| ( in @ SX4 @ SX3 @ SX0 ) ) ) ) )
| ~ ( ~ ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SX0 )
| ~ ( ~ ( ~ ( in @ SX4 @ SX3 @ SX0 )
| ~ ( ~ ( in @ SX4 @ SX1 @ SX0 )
| ~ ( in @ SX4 @ SX2 @ SX0 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX4 @ SX1 @ SX0 )
| ~ ( in @ SX4 @ SX2 @ SX0 ) )
| ( in @ SX4 @ SX3 @ SX0 ) ) ) )
| ( qmltpeq @ SX3 @ ( set_intersection2 @ SX1 @ SX2 ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95,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(109,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ~ ( ~ ( ~ ( qmltpeq @ SX1 @ empty_set @ SX0 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( ~ ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 @ SX0 ) )
| ( qmltpeq @ SX1 @ empty_set @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93,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(110,plain,
( ( ! [SX0: $i] :
~ ! [SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ~ ( empty @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[99,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(111,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ( qmltpeq @ ( unordered_pair @ SX1 @ SX2 ) @ ( unordered_pair @ SX2 @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91,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(112,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)],[73,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(113,plain,
( ( ! [SX0: $i] :
~ ! [SX1: mu] :
~ ( exists_in_world @ SX1 @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[71,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(114,plain,
( ( ! [SX0: mu,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( exists_in_world @ SX0 @ SX1 )
| ~ ( rel_s4 @ SX1 @ SX2 ) )
| ( exists_in_world @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[74,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(115,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 @ ( unordered_pair @ SX3 @ SX1 ) @ ( unordered_pair @ SX3 @ SX2 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84,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(116,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ~ ~ ( ~ ( qmltpeq @ SX1 @ SX2 @ SX0 )
| ~ ( empty @ SX1 @ SX0 ) )
| ( empty @ SX2 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87,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(117,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ~ ( in @ SX1 @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90,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(118,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ( qmltpeq @ ( set_intersection2 @ SX1 @ SX1 ) @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[98,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(119,plain,
( ( ! [SX0: $i] :
~ ! [SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ~ ~ ( empty @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[100,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(120,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 )
| ~ ( disjoint @ SX1 @ SX3 @ SX0 ) )
| ( disjoint @ SX2 @ SX3 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[85,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(121,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 @ SX3 @ ( unordered_pair @ SX1 @ SX2 ) @ SX0 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SX0 )
| ~ ( ~ ( ~ ( in @ SX4 @ SX3 @ SX0 )
| ( qmltpeq @ SX4 @ SX1 @ SX0 )
| ( qmltpeq @ SX4 @ SX2 @ SX0 ) )
| ~ ( ~ ( ( qmltpeq @ SX4 @ SX1 @ SX0 )
| ( qmltpeq @ SX4 @ SX2 @ SX0 ) )
| ( in @ SX4 @ SX3 @ SX0 ) ) ) ) )
| ~ ( ~ ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SX0 )
| ~ ( ~ ( ~ ( in @ SX4 @ SX3 @ SX0 )
| ( qmltpeq @ SX4 @ SX1 @ SX0 )
| ( qmltpeq @ SX4 @ SX2 @ SX0 ) )
| ~ ( ~ ( ( qmltpeq @ SX4 @ SX1 @ SX0 )
| ( qmltpeq @ SX4 @ SX2 @ SX0 ) )
| ( in @ SX4 @ SX3 @ SX0 ) ) ) )
| ( qmltpeq @ SX3 @ ( unordered_pair @ SX1 @ SX2 ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[94,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(122,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 @ ( set_intersection2 @ SX1 @ SX3 ) @ ( set_intersection2 @ SX2 @ SX3 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81,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(123,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ( qmltpeq @ SX1 @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78,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(124,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ~ ( ~ ( ~ ( disjoint @ SX1 @ SX2 @ SX0 )
| ( qmltpeq @ ( set_intersection2 @ SX1 @ SX2 ) @ empty_set @ SX0 ) )
| ~ ( ~ ( qmltpeq @ ( set_intersection2 @ SX1 @ SX2 ) @ empty_set @ SX0 )
| ( disjoint @ SX1 @ SX2 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96,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(125,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ~ ( disjoint @ SX1 @ SX2 @ SX0 )
| ( disjoint @ SX2 @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[101,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(126,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)],[79,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(127,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 )
| ~ ( in @ SX3 @ SX1 @ SX0 ) )
| ( in @ SX3 @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89,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(128,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 @ ( set_intersection2 @ SX3 @ SX1 ) @ ( set_intersection2 @ SX3 @ SX2 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[82,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(129,plain,
( ( ~ ! [SX0: mu] :
( ~ ( exists_in_world @ SX0 @ sK1_SY27 )
| ! [SX1: mu] :
( ~ ( exists_in_world @ SX1 @ sK1_SY27 )
| ~ ~ ( ~ ( disjoint @ ( unordered_pair @ sK2_SY838 @ SX0 ) @ SX1 @ sK1_SY27 )
| ~ ( in @ sK2_SY838 @ SX1 @ sK1_SY27 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[103,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(130,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)],[80,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(131,plain,
! [SV1: $i] :
( ( rel_s4 @ SV1 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(132,plain,
! [SV2: $i] :
( ( exists_in_world @ empty_set @ SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(133,plain,
! [SV3: $i] :
( ( ! [SY843: mu,SY844: mu] : ( exists_in_world @ ( set_intersection2 @ SY843 @ SY844 ) @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(134,plain,
! [SV4: $i] :
( ( ! [SY845: mu,SY846: mu] : ( exists_in_world @ ( unordered_pair @ SY845 @ SY846 ) @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(135,plain,
! [SV5: $i] :
( ( empty @ empty_set @ SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(136,plain,
! [SV6: $i] :
( ( ! [SY847: mu] :
( ~ ( exists_in_world @ SY847 @ SV6 )
| ! [SY848: mu] :
( ~ ( exists_in_world @ SY848 @ SV6 )
| ! [SY849: mu] :
( ~ ( exists_in_world @ SY849 @ SV6 )
| ~ ~ ( ~ ( qmltpeq @ SY847 @ SY848 @ SV6 )
| ~ ( disjoint @ SY849 @ SY847 @ SV6 ) )
| ( disjoint @ SY849 @ SY848 @ SV6 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(137,plain,
! [SV7: $i] :
( ( ! [SY850: mu] :
( ~ ( exists_in_world @ SY850 @ SV7 )
| ! [SY851: mu] :
( ~ ( exists_in_world @ SY851 @ SV7 )
| ! [SY852: mu] :
( ~ ( exists_in_world @ SY852 @ SV7 )
| ~ ~ ( ~ ( qmltpeq @ SY850 @ SY851 @ SV7 )
| ~ ( in @ SY850 @ SY852 @ SV7 ) )
| ( in @ SY851 @ SY852 @ SV7 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(138,plain,
! [SV8: $i] :
( ( ! [SY853: mu] :
( ~ ( exists_in_world @ SY853 @ SV8 )
| ! [SY854: mu] :
( ~ ( exists_in_world @ SY854 @ SV8 )
| ! [SY855: mu] :
( ~ ( exists_in_world @ SY855 @ SV8 )
| ~ ( qmltpeq @ SY853 @ SY854 @ SV8 )
| ( qmltpeq @ ( unordered_pair @ SY853 @ SY855 ) @ ( unordered_pair @ SY854 @ SY855 ) @ SV8 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(139,plain,
! [SV9: $i] :
( ( ! [SY856: mu] :
( ~ ( exists_in_world @ SY856 @ SV9 )
| ! [SY857: mu] :
( ~ ( exists_in_world @ SY857 @ SV9 )
| ( qmltpeq @ ( set_intersection2 @ SY856 @ SY857 ) @ ( set_intersection2 @ SY857 @ SY856 ) @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(140,plain,
! [SV10: $i] :
( ( ! [SY858: mu] :
( ~ ( exists_in_world @ SY858 @ SV10 )
| ! [SY859: mu] :
( ~ ( exists_in_world @ SY859 @ SV10 )
| ! [SY860: mu] :
( ~ ( exists_in_world @ SY860 @ SV10 )
| ~ ( ~ ( ~ ( qmltpeq @ SY860 @ ( set_intersection2 @ SY858 @ SY859 ) @ SV10 )
| ! [SY861: mu] :
( ~ ( exists_in_world @ SY861 @ SV10 )
| ~ ( ~ ( ~ ( in @ SY861 @ SY860 @ SV10 )
| ~ ( ~ ( in @ SY861 @ SY858 @ SV10 )
| ~ ( in @ SY861 @ SY859 @ SV10 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY861 @ SY858 @ SV10 )
| ~ ( in @ SY861 @ SY859 @ SV10 ) )
| ( in @ SY861 @ SY860 @ SV10 ) ) ) ) )
| ~ ( ~ ! [SY862: mu] :
( ~ ( exists_in_world @ SY862 @ SV10 )
| ~ ( ~ ( ~ ( in @ SY862 @ SY860 @ SV10 )
| ~ ( ~ ( in @ SY862 @ SY858 @ SV10 )
| ~ ( in @ SY862 @ SY859 @ SV10 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY862 @ SY858 @ SV10 )
| ~ ( in @ SY862 @ SY859 @ SV10 ) )
| ( in @ SY862 @ SY860 @ SV10 ) ) ) )
| ( qmltpeq @ SY860 @ ( set_intersection2 @ SY858 @ SY859 ) @ SV10 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(141,plain,
! [SV11: $i] :
( ( ! [SY863: mu] :
( ~ ( exists_in_world @ SY863 @ SV11 )
| ~ ( ~ ( ~ ( qmltpeq @ SY863 @ empty_set @ SV11 )
| ! [SY864: mu] :
( ~ ( exists_in_world @ SY864 @ SV11 )
| ~ ( in @ SY864 @ SY863 @ SV11 ) ) )
| ~ ( ~ ! [SY865: mu] :
( ~ ( exists_in_world @ SY865 @ SV11 )
| ~ ( in @ SY865 @ SY863 @ SV11 ) )
| ( qmltpeq @ SY863 @ empty_set @ SV11 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(142,plain,
! [SV12: $i] :
( ( ~ ! [SY866: mu] :
( ~ ( exists_in_world @ SY866 @ SV12 )
| ~ ( empty @ SY866 @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(143,plain,
! [SV13: $i] :
( ( ! [SY867: mu] :
( ~ ( exists_in_world @ SY867 @ SV13 )
| ! [SY868: mu] :
( ~ ( exists_in_world @ SY868 @ SV13 )
| ( qmltpeq @ ( unordered_pair @ SY867 @ SY868 ) @ ( unordered_pair @ SY868 @ SY867 ) @ SV13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(144,plain,
! [SV14: $i] :
( ( ! [SY869: $i,SY870: $i] :
( ~ ~ ( ~ ( rel_s4 @ SV14 @ SY869 )
| ~ ( rel_s4 @ SY869 @ SY870 ) )
| ( rel_s4 @ SV14 @ SY870 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(145,plain,
! [SV15: $i] :
( ( ~ ! [SY871: mu] :
~ ( exists_in_world @ SY871 @ SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(146,plain,
! [SV16: mu] :
( ( ! [SY872: $i,SY873: $i] :
( ~ ~ ( ~ ( exists_in_world @ SV16 @ SY872 )
| ~ ( rel_s4 @ SY872 @ SY873 ) )
| ( exists_in_world @ SV16 @ SY873 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(147,plain,
! [SV17: $i] :
( ( ! [SY874: mu] :
( ~ ( exists_in_world @ SY874 @ SV17 )
| ! [SY875: mu] :
( ~ ( exists_in_world @ SY875 @ SV17 )
| ! [SY876: mu] :
( ~ ( exists_in_world @ SY876 @ SV17 )
| ~ ( qmltpeq @ SY874 @ SY875 @ SV17 )
| ( qmltpeq @ ( unordered_pair @ SY876 @ SY874 ) @ ( unordered_pair @ SY876 @ SY875 ) @ SV17 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(148,plain,
! [SV18: $i] :
( ( ! [SY877: mu] :
( ~ ( exists_in_world @ SY877 @ SV18 )
| ! [SY878: mu] :
( ~ ( exists_in_world @ SY878 @ SV18 )
| ~ ~ ( ~ ( qmltpeq @ SY877 @ SY878 @ SV18 )
| ~ ( empty @ SY877 @ SV18 ) )
| ( empty @ SY878 @ SV18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(149,plain,
! [SV19: $i] :
( ( ! [SY879: mu] :
( ~ ( exists_in_world @ SY879 @ SV19 )
| ! [SY880: mu] :
( ~ ( exists_in_world @ SY880 @ SV19 )
| ~ ( in @ SY879 @ SY880 @ SV19 )
| ~ ( in @ SY880 @ SY879 @ SV19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(150,plain,
! [SV20: $i] :
( ( ! [SY881: mu] :
( ~ ( exists_in_world @ SY881 @ SV20 )
| ! [SY882: mu] :
( ~ ( exists_in_world @ SY882 @ SV20 )
| ( qmltpeq @ ( set_intersection2 @ SY881 @ SY881 ) @ SY881 @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(151,plain,
! [SV21: $i] :
( ( ~ ! [SY883: mu] :
( ~ ( exists_in_world @ SY883 @ SV21 )
| ~ ~ ( empty @ SY883 @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(152,plain,
! [SV22: $i] :
( ( ! [SY884: mu] :
( ~ ( exists_in_world @ SY884 @ SV22 )
| ! [SY885: mu] :
( ~ ( exists_in_world @ SY885 @ SV22 )
| ! [SY886: mu] :
( ~ ( exists_in_world @ SY886 @ SV22 )
| ~ ~ ( ~ ( qmltpeq @ SY884 @ SY885 @ SV22 )
| ~ ( disjoint @ SY884 @ SY886 @ SV22 ) )
| ( disjoint @ SY885 @ SY886 @ SV22 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(153,plain,
! [SV23: $i] :
( ( ! [SY887: mu] :
( ~ ( exists_in_world @ SY887 @ SV23 )
| ! [SY888: mu] :
( ~ ( exists_in_world @ SY888 @ SV23 )
| ! [SY889: mu] :
( ~ ( exists_in_world @ SY889 @ SV23 )
| ~ ( ~ ( ~ ( qmltpeq @ SY889 @ ( unordered_pair @ SY887 @ SY888 ) @ SV23 )
| ! [SY890: mu] :
( ~ ( exists_in_world @ SY890 @ SV23 )
| ~ ( ~ ( ~ ( in @ SY890 @ SY889 @ SV23 )
| ( qmltpeq @ SY890 @ SY887 @ SV23 )
| ( qmltpeq @ SY890 @ SY888 @ SV23 ) )
| ~ ( ~ ( ( qmltpeq @ SY890 @ SY887 @ SV23 )
| ( qmltpeq @ SY890 @ SY888 @ SV23 ) )
| ( in @ SY890 @ SY889 @ SV23 ) ) ) ) )
| ~ ( ~ ! [SY891: mu] :
( ~ ( exists_in_world @ SY891 @ SV23 )
| ~ ( ~ ( ~ ( in @ SY891 @ SY889 @ SV23 )
| ( qmltpeq @ SY891 @ SY887 @ SV23 )
| ( qmltpeq @ SY891 @ SY888 @ SV23 ) )
| ~ ( ~ ( ( qmltpeq @ SY891 @ SY887 @ SV23 )
| ( qmltpeq @ SY891 @ SY888 @ SV23 ) )
| ( in @ SY891 @ SY889 @ SV23 ) ) ) )
| ( qmltpeq @ SY889 @ ( unordered_pair @ SY887 @ SY888 ) @ SV23 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(154,plain,
! [SV24: $i] :
( ( ! [SY892: mu] :
( ~ ( exists_in_world @ SY892 @ SV24 )
| ! [SY893: mu] :
( ~ ( exists_in_world @ SY893 @ SV24 )
| ! [SY894: mu] :
( ~ ( exists_in_world @ SY894 @ SV24 )
| ~ ( qmltpeq @ SY892 @ SY893 @ SV24 )
| ( qmltpeq @ ( set_intersection2 @ SY892 @ SY894 ) @ ( set_intersection2 @ SY893 @ SY894 ) @ SV24 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(155,plain,
! [SV25: $i] :
( ( ! [SY895: mu] :
( ~ ( exists_in_world @ SY895 @ SV25 )
| ( qmltpeq @ SY895 @ SY895 @ SV25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(156,plain,
! [SV26: $i] :
( ( ! [SY896: mu] :
( ~ ( exists_in_world @ SY896 @ SV26 )
| ! [SY897: mu] :
( ~ ( exists_in_world @ SY897 @ SV26 )
| ~ ( ~ ( ~ ( disjoint @ SY896 @ SY897 @ SV26 )
| ( qmltpeq @ ( set_intersection2 @ SY896 @ SY897 ) @ empty_set @ SV26 ) )
| ~ ( ~ ( qmltpeq @ ( set_intersection2 @ SY896 @ SY897 ) @ empty_set @ SV26 )
| ( disjoint @ SY896 @ SY897 @ SV26 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(157,plain,
! [SV27: $i] :
( ( ! [SY898: mu] :
( ~ ( exists_in_world @ SY898 @ SV27 )
| ! [SY899: mu] :
( ~ ( exists_in_world @ SY899 @ SV27 )
| ~ ( disjoint @ SY898 @ SY899 @ SV27 )
| ( disjoint @ SY899 @ SY898 @ SV27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(158,plain,
! [SV28: $i] :
( ( ! [SY900: mu] :
( ~ ( exists_in_world @ SY900 @ SV28 )
| ! [SY901: mu] :
( ~ ( exists_in_world @ SY901 @ SV28 )
| ~ ( qmltpeq @ SY900 @ SY901 @ SV28 )
| ( qmltpeq @ SY901 @ SY900 @ SV28 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(159,plain,
! [SV29: $i] :
( ( ! [SY902: mu] :
( ~ ( exists_in_world @ SY902 @ SV29 )
| ! [SY903: mu] :
( ~ ( exists_in_world @ SY903 @ SV29 )
| ! [SY904: mu] :
( ~ ( exists_in_world @ SY904 @ SV29 )
| ~ ~ ( ~ ( qmltpeq @ SY902 @ SY903 @ SV29 )
| ~ ( in @ SY904 @ SY902 @ SV29 ) )
| ( in @ SY904 @ SY903 @ SV29 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(160,plain,
! [SV30: $i] :
( ( ! [SY905: mu] :
( ~ ( exists_in_world @ SY905 @ SV30 )
| ! [SY906: mu] :
( ~ ( exists_in_world @ SY906 @ SV30 )
| ! [SY907: mu] :
( ~ ( exists_in_world @ SY907 @ SV30 )
| ~ ( qmltpeq @ SY905 @ SY906 @ SV30 )
| ( qmltpeq @ ( set_intersection2 @ SY907 @ SY905 ) @ ( set_intersection2 @ SY907 @ SY906 ) @ SV30 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(161,plain,
( ( ! [SX0: mu] :
( ~ ( exists_in_world @ SX0 @ sK1_SY27 )
| ! [SX1: mu] :
( ~ ( exists_in_world @ SX1 @ sK1_SY27 )
| ~ ~ ( ~ ( disjoint @ ( unordered_pair @ sK2_SY838 @ SX0 ) @ SX1 @ sK1_SY27 )
| ~ ( in @ sK2_SY838 @ SX1 @ sK1_SY27 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[129]) ).
thf(162,plain,
! [SV31: $i] :
( ( ! [SY908: mu] :
( ~ ( exists_in_world @ SY908 @ SV31 )
| ! [SY909: mu] :
( ~ ( exists_in_world @ SY909 @ SV31 )
| ! [SY910: mu] :
( ~ ( exists_in_world @ SY910 @ SV31 )
| ~ ~ ( ~ ( qmltpeq @ SY908 @ SY909 @ SV31 )
| ~ ( qmltpeq @ SY909 @ SY910 @ SV31 ) )
| ( qmltpeq @ SY908 @ SY910 @ SV31 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(163,plain,
! [SV3: $i,SV32: mu] :
( ( ! [SY911: mu] : ( exists_in_world @ ( set_intersection2 @ SV32 @ SY911 ) @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(164,plain,
! [SV4: $i,SV33: mu] :
( ( ! [SY912: mu] : ( exists_in_world @ ( unordered_pair @ SV33 @ SY912 ) @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(165,plain,
! [SV6: $i,SV34: mu] :
( ( ~ ( exists_in_world @ SV34 @ SV6 )
| ! [SY913: mu] :
( ~ ( exists_in_world @ SY913 @ SV6 )
| ! [SY914: mu] :
( ~ ( exists_in_world @ SY914 @ SV6 )
| ~ ~ ( ~ ( qmltpeq @ SV34 @ SY913 @ SV6 )
| ~ ( disjoint @ SY914 @ SV34 @ SV6 ) )
| ( disjoint @ SY914 @ SY913 @ SV6 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(166,plain,
! [SV7: $i,SV35: mu] :
( ( ~ ( exists_in_world @ SV35 @ SV7 )
| ! [SY915: mu] :
( ~ ( exists_in_world @ SY915 @ SV7 )
| ! [SY916: mu] :
( ~ ( exists_in_world @ SY916 @ SV7 )
| ~ ~ ( ~ ( qmltpeq @ SV35 @ SY915 @ SV7 )
| ~ ( in @ SV35 @ SY916 @ SV7 ) )
| ( in @ SY915 @ SY916 @ SV7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(167,plain,
! [SV8: $i,SV36: mu] :
( ( ~ ( exists_in_world @ SV36 @ SV8 )
| ! [SY917: mu] :
( ~ ( exists_in_world @ SY917 @ SV8 )
| ! [SY918: mu] :
( ~ ( exists_in_world @ SY918 @ SV8 )
| ~ ( qmltpeq @ SV36 @ SY917 @ SV8 )
| ( qmltpeq @ ( unordered_pair @ SV36 @ SY918 ) @ ( unordered_pair @ SY917 @ SY918 ) @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(168,plain,
! [SV9: $i,SV37: mu] :
( ( ~ ( exists_in_world @ SV37 @ SV9 )
| ! [SY919: mu] :
( ~ ( exists_in_world @ SY919 @ SV9 )
| ( qmltpeq @ ( set_intersection2 @ SV37 @ SY919 ) @ ( set_intersection2 @ SY919 @ SV37 ) @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(169,plain,
! [SV10: $i,SV38: mu] :
( ( ~ ( exists_in_world @ SV38 @ SV10 )
| ! [SY920: mu] :
( ~ ( exists_in_world @ SY920 @ SV10 )
| ! [SY921: mu] :
( ~ ( exists_in_world @ SY921 @ SV10 )
| ~ ( ~ ( ~ ( qmltpeq @ SY921 @ ( set_intersection2 @ SV38 @ SY920 ) @ SV10 )
| ! [SY922: mu] :
( ~ ( exists_in_world @ SY922 @ SV10 )
| ~ ( ~ ( ~ ( in @ SY922 @ SY921 @ SV10 )
| ~ ( ~ ( in @ SY922 @ SV38 @ SV10 )
| ~ ( in @ SY922 @ SY920 @ SV10 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY922 @ SV38 @ SV10 )
| ~ ( in @ SY922 @ SY920 @ SV10 ) )
| ( in @ SY922 @ SY921 @ SV10 ) ) ) ) )
| ~ ( ~ ! [SY923: mu] :
( ~ ( exists_in_world @ SY923 @ SV10 )
| ~ ( ~ ( ~ ( in @ SY923 @ SY921 @ SV10 )
| ~ ( ~ ( in @ SY923 @ SV38 @ SV10 )
| ~ ( in @ SY923 @ SY920 @ SV10 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY923 @ SV38 @ SV10 )
| ~ ( in @ SY923 @ SY920 @ SV10 ) )
| ( in @ SY923 @ SY921 @ SV10 ) ) ) )
| ( qmltpeq @ SY921 @ ( set_intersection2 @ SV38 @ SY920 ) @ SV10 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(170,plain,
! [SV11: $i,SV39: mu] :
( ( ~ ( exists_in_world @ SV39 @ SV11 )
| ~ ( ~ ( ~ ( qmltpeq @ SV39 @ empty_set @ SV11 )
| ! [SY924: mu] :
( ~ ( exists_in_world @ SY924 @ SV11 )
| ~ ( in @ SY924 @ SV39 @ SV11 ) ) )
| ~ ( ~ ! [SY925: mu] :
( ~ ( exists_in_world @ SY925 @ SV11 )
| ~ ( in @ SY925 @ SV39 @ SV11 ) )
| ( qmltpeq @ SV39 @ empty_set @ SV11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(171,plain,
! [SV12: $i] :
( ( ! [SY866: mu] :
( ~ ( exists_in_world @ SY866 @ SV12 )
| ~ ( empty @ SY866 @ SV12 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(172,plain,
! [SV13: $i,SV40: mu] :
( ( ~ ( exists_in_world @ SV40 @ SV13 )
| ! [SY926: mu] :
( ~ ( exists_in_world @ SY926 @ SV13 )
| ( qmltpeq @ ( unordered_pair @ SV40 @ SY926 ) @ ( unordered_pair @ SY926 @ SV40 ) @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(173,plain,
! [SV41: $i,SV14: $i] :
( ( ! [SY927: $i] :
( ~ ~ ( ~ ( rel_s4 @ SV14 @ SV41 )
| ~ ( rel_s4 @ SV41 @ SY927 ) )
| ( rel_s4 @ SV14 @ SY927 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(174,plain,
! [SV15: $i] :
( ( ! [SY871: mu] :
~ ( exists_in_world @ SY871 @ SV15 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[145]) ).
thf(175,plain,
! [SV42: $i,SV16: mu] :
( ( ! [SY928: $i] :
( ~ ~ ( ~ ( exists_in_world @ SV16 @ SV42 )
| ~ ( rel_s4 @ SV42 @ SY928 ) )
| ( exists_in_world @ SV16 @ SY928 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(176,plain,
! [SV17: $i,SV43: mu] :
( ( ~ ( exists_in_world @ SV43 @ SV17 )
| ! [SY929: mu] :
( ~ ( exists_in_world @ SY929 @ SV17 )
| ! [SY930: mu] :
( ~ ( exists_in_world @ SY930 @ SV17 )
| ~ ( qmltpeq @ SV43 @ SY929 @ SV17 )
| ( qmltpeq @ ( unordered_pair @ SY930 @ SV43 ) @ ( unordered_pair @ SY930 @ SY929 ) @ SV17 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(177,plain,
! [SV18: $i,SV44: mu] :
( ( ~ ( exists_in_world @ SV44 @ SV18 )
| ! [SY931: mu] :
( ~ ( exists_in_world @ SY931 @ SV18 )
| ~ ~ ( ~ ( qmltpeq @ SV44 @ SY931 @ SV18 )
| ~ ( empty @ SV44 @ SV18 ) )
| ( empty @ SY931 @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(178,plain,
! [SV19: $i,SV45: mu] :
( ( ~ ( exists_in_world @ SV45 @ SV19 )
| ! [SY932: mu] :
( ~ ( exists_in_world @ SY932 @ SV19 )
| ~ ( in @ SV45 @ SY932 @ SV19 )
| ~ ( in @ SY932 @ SV45 @ SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(179,plain,
! [SV20: $i,SV46: mu] :
( ( ~ ( exists_in_world @ SV46 @ SV20 )
| ! [SY933: mu] :
( ~ ( exists_in_world @ SY933 @ SV20 )
| ( qmltpeq @ ( set_intersection2 @ SV46 @ SV46 ) @ SV46 @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(180,plain,
! [SV21: $i] :
( ( ! [SY883: mu] :
( ~ ( exists_in_world @ SY883 @ SV21 )
| ~ ~ ( empty @ SY883 @ SV21 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(181,plain,
! [SV22: $i,SV47: mu] :
( ( ~ ( exists_in_world @ SV47 @ SV22 )
| ! [SY934: mu] :
( ~ ( exists_in_world @ SY934 @ SV22 )
| ! [SY935: mu] :
( ~ ( exists_in_world @ SY935 @ SV22 )
| ~ ~ ( ~ ( qmltpeq @ SV47 @ SY934 @ SV22 )
| ~ ( disjoint @ SV47 @ SY935 @ SV22 ) )
| ( disjoint @ SY934 @ SY935 @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(182,plain,
! [SV23: $i,SV48: mu] :
( ( ~ ( exists_in_world @ SV48 @ SV23 )
| ! [SY936: mu] :
( ~ ( exists_in_world @ SY936 @ SV23 )
| ! [SY937: mu] :
( ~ ( exists_in_world @ SY937 @ SV23 )
| ~ ( ~ ( ~ ( qmltpeq @ SY937 @ ( unordered_pair @ SV48 @ SY936 ) @ SV23 )
| ! [SY938: mu] :
( ~ ( exists_in_world @ SY938 @ SV23 )
| ~ ( ~ ( ~ ( in @ SY938 @ SY937 @ SV23 )
| ( qmltpeq @ SY938 @ SV48 @ SV23 )
| ( qmltpeq @ SY938 @ SY936 @ SV23 ) )
| ~ ( ~ ( ( qmltpeq @ SY938 @ SV48 @ SV23 )
| ( qmltpeq @ SY938 @ SY936 @ SV23 ) )
| ( in @ SY938 @ SY937 @ SV23 ) ) ) ) )
| ~ ( ~ ! [SY939: mu] :
( ~ ( exists_in_world @ SY939 @ SV23 )
| ~ ( ~ ( ~ ( in @ SY939 @ SY937 @ SV23 )
| ( qmltpeq @ SY939 @ SV48 @ SV23 )
| ( qmltpeq @ SY939 @ SY936 @ SV23 ) )
| ~ ( ~ ( ( qmltpeq @ SY939 @ SV48 @ SV23 )
| ( qmltpeq @ SY939 @ SY936 @ SV23 ) )
| ( in @ SY939 @ SY937 @ SV23 ) ) ) )
| ( qmltpeq @ SY937 @ ( unordered_pair @ SV48 @ SY936 ) @ SV23 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(183,plain,
! [SV24: $i,SV49: mu] :
( ( ~ ( exists_in_world @ SV49 @ SV24 )
| ! [SY940: mu] :
( ~ ( exists_in_world @ SY940 @ SV24 )
| ! [SY941: mu] :
( ~ ( exists_in_world @ SY941 @ SV24 )
| ~ ( qmltpeq @ SV49 @ SY940 @ SV24 )
| ( qmltpeq @ ( set_intersection2 @ SV49 @ SY941 ) @ ( set_intersection2 @ SY940 @ SY941 ) @ SV24 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(184,plain,
! [SV25: $i,SV50: mu] :
( ( ~ ( exists_in_world @ SV50 @ SV25 )
| ( qmltpeq @ SV50 @ SV50 @ SV25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(185,plain,
! [SV26: $i,SV51: mu] :
( ( ~ ( exists_in_world @ SV51 @ SV26 )
| ! [SY942: mu] :
( ~ ( exists_in_world @ SY942 @ SV26 )
| ~ ( ~ ( ~ ( disjoint @ SV51 @ SY942 @ SV26 )
| ( qmltpeq @ ( set_intersection2 @ SV51 @ SY942 ) @ empty_set @ SV26 ) )
| ~ ( ~ ( qmltpeq @ ( set_intersection2 @ SV51 @ SY942 ) @ empty_set @ SV26 )
| ( disjoint @ SV51 @ SY942 @ SV26 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(186,plain,
! [SV27: $i,SV52: mu] :
( ( ~ ( exists_in_world @ SV52 @ SV27 )
| ! [SY943: mu] :
( ~ ( exists_in_world @ SY943 @ SV27 )
| ~ ( disjoint @ SV52 @ SY943 @ SV27 )
| ( disjoint @ SY943 @ SV52 @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(187,plain,
! [SV28: $i,SV53: mu] :
( ( ~ ( exists_in_world @ SV53 @ SV28 )
| ! [SY944: mu] :
( ~ ( exists_in_world @ SY944 @ SV28 )
| ~ ( qmltpeq @ SV53 @ SY944 @ SV28 )
| ( qmltpeq @ SY944 @ SV53 @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(188,plain,
! [SV29: $i,SV54: mu] :
( ( ~ ( exists_in_world @ SV54 @ SV29 )
| ! [SY945: mu] :
( ~ ( exists_in_world @ SY945 @ SV29 )
| ! [SY946: mu] :
( ~ ( exists_in_world @ SY946 @ SV29 )
| ~ ~ ( ~ ( qmltpeq @ SV54 @ SY945 @ SV29 )
| ~ ( in @ SY946 @ SV54 @ SV29 ) )
| ( in @ SY946 @ SY945 @ SV29 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(189,plain,
! [SV30: $i,SV55: mu] :
( ( ~ ( exists_in_world @ SV55 @ SV30 )
| ! [SY947: mu] :
( ~ ( exists_in_world @ SY947 @ SV30 )
| ! [SY948: mu] :
( ~ ( exists_in_world @ SY948 @ SV30 )
| ~ ( qmltpeq @ SV55 @ SY947 @ SV30 )
| ( qmltpeq @ ( set_intersection2 @ SY948 @ SV55 ) @ ( set_intersection2 @ SY948 @ SY947 ) @ SV30 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(190,plain,
( ( ~ ( exists_in_world @ sK3_SX0 @ sK1_SY27 )
| ! [SY949: mu] :
( ~ ( exists_in_world @ SY949 @ sK1_SY27 )
| ~ ~ ( ~ ( disjoint @ ( unordered_pair @ sK2_SY838 @ sK3_SX0 ) @ SY949 @ sK1_SY27 )
| ~ ( in @ sK2_SY838 @ SY949 @ sK1_SY27 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[161]) ).
thf(191,plain,
! [SV31: $i,SV56: mu] :
( ( ~ ( exists_in_world @ SV56 @ SV31 )
| ! [SY950: mu] :
( ~ ( exists_in_world @ SY950 @ SV31 )
| ! [SY951: mu] :
( ~ ( exists_in_world @ SY951 @ SV31 )
| ~ ~ ( ~ ( qmltpeq @ SV56 @ SY950 @ SV31 )
| ~ ( qmltpeq @ SY950 @ SY951 @ SV31 ) )
| ( qmltpeq @ SV56 @ SY951 @ SV31 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(192,plain,
! [SV3: $i,SV57: mu,SV32: mu] :
( ( exists_in_world @ ( set_intersection2 @ SV32 @ SV57 ) @ SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(193,plain,
! [SV4: $i,SV58: mu,SV33: mu] :
( ( exists_in_world @ ( unordered_pair @ SV33 @ SV58 ) @ SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(194,plain,
! [SV6: $i,SV34: mu] :
( ( ( ~ ( exists_in_world @ SV34 @ SV6 ) )
= $true )
| ( ( ! [SY913: mu] :
( ~ ( exists_in_world @ SY913 @ SV6 )
| ! [SY914: mu] :
( ~ ( exists_in_world @ SY914 @ SV6 )
| ~ ~ ( ~ ( qmltpeq @ SV34 @ SY913 @ SV6 )
| ~ ( disjoint @ SY914 @ SV34 @ SV6 ) )
| ( disjoint @ SY914 @ SY913 @ SV6 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[165]) ).
thf(195,plain,
! [SV7: $i,SV35: mu] :
( ( ( ~ ( exists_in_world @ SV35 @ SV7 ) )
= $true )
| ( ( ! [SY915: mu] :
( ~ ( exists_in_world @ SY915 @ SV7 )
| ! [SY916: mu] :
( ~ ( exists_in_world @ SY916 @ SV7 )
| ~ ~ ( ~ ( qmltpeq @ SV35 @ SY915 @ SV7 )
| ~ ( in @ SV35 @ SY916 @ SV7 ) )
| ( in @ SY915 @ SY916 @ SV7 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[166]) ).
thf(196,plain,
! [SV8: $i,SV36: mu] :
( ( ( ~ ( exists_in_world @ SV36 @ SV8 ) )
= $true )
| ( ( ! [SY917: mu] :
( ~ ( exists_in_world @ SY917 @ SV8 )
| ! [SY918: mu] :
( ~ ( exists_in_world @ SY918 @ SV8 )
| ~ ( qmltpeq @ SV36 @ SY917 @ SV8 )
| ( qmltpeq @ ( unordered_pair @ SV36 @ SY918 ) @ ( unordered_pair @ SY917 @ SY918 ) @ SV8 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[167]) ).
thf(197,plain,
! [SV9: $i,SV37: mu] :
( ( ( ~ ( exists_in_world @ SV37 @ SV9 ) )
= $true )
| ( ( ! [SY919: mu] :
( ~ ( exists_in_world @ SY919 @ SV9 )
| ( qmltpeq @ ( set_intersection2 @ SV37 @ SY919 ) @ ( set_intersection2 @ SY919 @ SV37 ) @ SV9 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[168]) ).
thf(198,plain,
! [SV10: $i,SV38: mu] :
( ( ( ~ ( exists_in_world @ SV38 @ SV10 ) )
= $true )
| ( ( ! [SY920: mu] :
( ~ ( exists_in_world @ SY920 @ SV10 )
| ! [SY921: mu] :
( ~ ( exists_in_world @ SY921 @ SV10 )
| ~ ( ~ ( ~ ( qmltpeq @ SY921 @ ( set_intersection2 @ SV38 @ SY920 ) @ SV10 )
| ! [SY922: mu] :
( ~ ( exists_in_world @ SY922 @ SV10 )
| ~ ( ~ ( ~ ( in @ SY922 @ SY921 @ SV10 )
| ~ ( ~ ( in @ SY922 @ SV38 @ SV10 )
| ~ ( in @ SY922 @ SY920 @ SV10 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY922 @ SV38 @ SV10 )
| ~ ( in @ SY922 @ SY920 @ SV10 ) )
| ( in @ SY922 @ SY921 @ SV10 ) ) ) ) )
| ~ ( ~ ! [SY923: mu] :
( ~ ( exists_in_world @ SY923 @ SV10 )
| ~ ( ~ ( ~ ( in @ SY923 @ SY921 @ SV10 )
| ~ ( ~ ( in @ SY923 @ SV38 @ SV10 )
| ~ ( in @ SY923 @ SY920 @ SV10 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY923 @ SV38 @ SV10 )
| ~ ( in @ SY923 @ SY920 @ SV10 ) )
| ( in @ SY923 @ SY921 @ SV10 ) ) ) )
| ( qmltpeq @ SY921 @ ( set_intersection2 @ SV38 @ SY920 ) @ SV10 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[169]) ).
thf(199,plain,
! [SV11: $i,SV39: mu] :
( ( ( ~ ( exists_in_world @ SV39 @ SV11 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( qmltpeq @ SV39 @ empty_set @ SV11 )
| ! [SY924: mu] :
( ~ ( exists_in_world @ SY924 @ SV11 )
| ~ ( in @ SY924 @ SV39 @ SV11 ) ) )
| ~ ( ~ ! [SY925: mu] :
( ~ ( exists_in_world @ SY925 @ SV11 )
| ~ ( in @ SY925 @ SV39 @ SV11 ) )
| ( qmltpeq @ SV39 @ empty_set @ SV11 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[170]) ).
thf(200,plain,
! [SV12: $i] :
( ( ~ ( exists_in_world @ ( sK4_SY866 @ SV12 ) @ SV12 )
| ~ ( empty @ ( sK4_SY866 @ SV12 ) @ SV12 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[171]) ).
thf(201,plain,
! [SV13: $i,SV40: mu] :
( ( ( ~ ( exists_in_world @ SV40 @ SV13 ) )
= $true )
| ( ( ! [SY926: mu] :
( ~ ( exists_in_world @ SY926 @ SV13 )
| ( qmltpeq @ ( unordered_pair @ SV40 @ SY926 ) @ ( unordered_pair @ SY926 @ SV40 ) @ SV13 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[172]) ).
thf(202,plain,
! [SV59: $i,SV41: $i,SV14: $i] :
( ( ~ ~ ( ~ ( rel_s4 @ SV14 @ SV41 )
| ~ ( rel_s4 @ SV41 @ SV59 ) )
| ( rel_s4 @ SV14 @ SV59 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(203,plain,
! [SV15: $i] :
( ( ~ ( exists_in_world @ ( sK5_SY871 @ SV15 ) @ SV15 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[174]) ).
thf(204,plain,
! [SV60: $i,SV42: $i,SV16: mu] :
( ( ~ ~ ( ~ ( exists_in_world @ SV16 @ SV42 )
| ~ ( rel_s4 @ SV42 @ SV60 ) )
| ( exists_in_world @ SV16 @ SV60 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(205,plain,
! [SV17: $i,SV43: mu] :
( ( ( ~ ( exists_in_world @ SV43 @ SV17 ) )
= $true )
| ( ( ! [SY929: mu] :
( ~ ( exists_in_world @ SY929 @ SV17 )
| ! [SY930: mu] :
( ~ ( exists_in_world @ SY930 @ SV17 )
| ~ ( qmltpeq @ SV43 @ SY929 @ SV17 )
| ( qmltpeq @ ( unordered_pair @ SY930 @ SV43 ) @ ( unordered_pair @ SY930 @ SY929 ) @ SV17 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[176]) ).
thf(206,plain,
! [SV18: $i,SV44: mu] :
( ( ( ~ ( exists_in_world @ SV44 @ SV18 ) )
= $true )
| ( ( ! [SY931: mu] :
( ~ ( exists_in_world @ SY931 @ SV18 )
| ~ ~ ( ~ ( qmltpeq @ SV44 @ SY931 @ SV18 )
| ~ ( empty @ SV44 @ SV18 ) )
| ( empty @ SY931 @ SV18 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[177]) ).
thf(207,plain,
! [SV19: $i,SV45: mu] :
( ( ( ~ ( exists_in_world @ SV45 @ SV19 ) )
= $true )
| ( ( ! [SY932: mu] :
( ~ ( exists_in_world @ SY932 @ SV19 )
| ~ ( in @ SV45 @ SY932 @ SV19 )
| ~ ( in @ SY932 @ SV45 @ SV19 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[178]) ).
thf(208,plain,
! [SV20: $i,SV46: mu] :
( ( ( ~ ( exists_in_world @ SV46 @ SV20 ) )
= $true )
| ( ( ! [SY933: mu] :
( ~ ( exists_in_world @ SY933 @ SV20 )
| ( qmltpeq @ ( set_intersection2 @ SV46 @ SV46 ) @ SV46 @ SV20 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[179]) ).
thf(209,plain,
! [SV21: $i] :
( ( ~ ( exists_in_world @ ( sK6_SY883 @ SV21 ) @ SV21 )
| ~ ~ ( empty @ ( sK6_SY883 @ SV21 ) @ SV21 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[180]) ).
thf(210,plain,
! [SV22: $i,SV47: mu] :
( ( ( ~ ( exists_in_world @ SV47 @ SV22 ) )
= $true )
| ( ( ! [SY934: mu] :
( ~ ( exists_in_world @ SY934 @ SV22 )
| ! [SY935: mu] :
( ~ ( exists_in_world @ SY935 @ SV22 )
| ~ ~ ( ~ ( qmltpeq @ SV47 @ SY934 @ SV22 )
| ~ ( disjoint @ SV47 @ SY935 @ SV22 ) )
| ( disjoint @ SY934 @ SY935 @ SV22 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[181]) ).
thf(211,plain,
! [SV23: $i,SV48: mu] :
( ( ( ~ ( exists_in_world @ SV48 @ SV23 ) )
= $true )
| ( ( ! [SY936: mu] :
( ~ ( exists_in_world @ SY936 @ SV23 )
| ! [SY937: mu] :
( ~ ( exists_in_world @ SY937 @ SV23 )
| ~ ( ~ ( ~ ( qmltpeq @ SY937 @ ( unordered_pair @ SV48 @ SY936 ) @ SV23 )
| ! [SY938: mu] :
( ~ ( exists_in_world @ SY938 @ SV23 )
| ~ ( ~ ( ~ ( in @ SY938 @ SY937 @ SV23 )
| ( qmltpeq @ SY938 @ SV48 @ SV23 )
| ( qmltpeq @ SY938 @ SY936 @ SV23 ) )
| ~ ( ~ ( ( qmltpeq @ SY938 @ SV48 @ SV23 )
| ( qmltpeq @ SY938 @ SY936 @ SV23 ) )
| ( in @ SY938 @ SY937 @ SV23 ) ) ) ) )
| ~ ( ~ ! [SY939: mu] :
( ~ ( exists_in_world @ SY939 @ SV23 )
| ~ ( ~ ( ~ ( in @ SY939 @ SY937 @ SV23 )
| ( qmltpeq @ SY939 @ SV48 @ SV23 )
| ( qmltpeq @ SY939 @ SY936 @ SV23 ) )
| ~ ( ~ ( ( qmltpeq @ SY939 @ SV48 @ SV23 )
| ( qmltpeq @ SY939 @ SY936 @ SV23 ) )
| ( in @ SY939 @ SY937 @ SV23 ) ) ) )
| ( qmltpeq @ SY937 @ ( unordered_pair @ SV48 @ SY936 ) @ SV23 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[182]) ).
thf(212,plain,
! [SV24: $i,SV49: mu] :
( ( ( ~ ( exists_in_world @ SV49 @ SV24 ) )
= $true )
| ( ( ! [SY940: mu] :
( ~ ( exists_in_world @ SY940 @ SV24 )
| ! [SY941: mu] :
( ~ ( exists_in_world @ SY941 @ SV24 )
| ~ ( qmltpeq @ SV49 @ SY940 @ SV24 )
| ( qmltpeq @ ( set_intersection2 @ SV49 @ SY941 ) @ ( set_intersection2 @ SY940 @ SY941 ) @ SV24 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[183]) ).
thf(213,plain,
! [SV25: $i,SV50: mu] :
( ( ( ~ ( exists_in_world @ SV50 @ SV25 ) )
= $true )
| ( ( qmltpeq @ SV50 @ SV50 @ SV25 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[184]) ).
thf(214,plain,
! [SV26: $i,SV51: mu] :
( ( ( ~ ( exists_in_world @ SV51 @ SV26 ) )
= $true )
| ( ( ! [SY942: mu] :
( ~ ( exists_in_world @ SY942 @ SV26 )
| ~ ( ~ ( ~ ( disjoint @ SV51 @ SY942 @ SV26 )
| ( qmltpeq @ ( set_intersection2 @ SV51 @ SY942 ) @ empty_set @ SV26 ) )
| ~ ( ~ ( qmltpeq @ ( set_intersection2 @ SV51 @ SY942 ) @ empty_set @ SV26 )
| ( disjoint @ SV51 @ SY942 @ SV26 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[185]) ).
thf(215,plain,
! [SV27: $i,SV52: mu] :
( ( ( ~ ( exists_in_world @ SV52 @ SV27 ) )
= $true )
| ( ( ! [SY943: mu] :
( ~ ( exists_in_world @ SY943 @ SV27 )
| ~ ( disjoint @ SV52 @ SY943 @ SV27 )
| ( disjoint @ SY943 @ SV52 @ SV27 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[186]) ).
thf(216,plain,
! [SV28: $i,SV53: mu] :
( ( ( ~ ( exists_in_world @ SV53 @ SV28 ) )
= $true )
| ( ( ! [SY944: mu] :
( ~ ( exists_in_world @ SY944 @ SV28 )
| ~ ( qmltpeq @ SV53 @ SY944 @ SV28 )
| ( qmltpeq @ SY944 @ SV53 @ SV28 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[187]) ).
thf(217,plain,
! [SV29: $i,SV54: mu] :
( ( ( ~ ( exists_in_world @ SV54 @ SV29 ) )
= $true )
| ( ( ! [SY945: mu] :
( ~ ( exists_in_world @ SY945 @ SV29 )
| ! [SY946: mu] :
( ~ ( exists_in_world @ SY946 @ SV29 )
| ~ ~ ( ~ ( qmltpeq @ SV54 @ SY945 @ SV29 )
| ~ ( in @ SY946 @ SV54 @ SV29 ) )
| ( in @ SY946 @ SY945 @ SV29 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[188]) ).
thf(218,plain,
! [SV30: $i,SV55: mu] :
( ( ( ~ ( exists_in_world @ SV55 @ SV30 ) )
= $true )
| ( ( ! [SY947: mu] :
( ~ ( exists_in_world @ SY947 @ SV30 )
| ! [SY948: mu] :
( ~ ( exists_in_world @ SY948 @ SV30 )
| ~ ( qmltpeq @ SV55 @ SY947 @ SV30 )
| ( qmltpeq @ ( set_intersection2 @ SY948 @ SV55 ) @ ( set_intersection2 @ SY948 @ SY947 ) @ SV30 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[189]) ).
thf(219,plain,
( ( ~ ( exists_in_world @ sK3_SX0 @ sK1_SY27 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[190]) ).
thf(220,plain,
( ( ! [SY949: mu] :
( ~ ( exists_in_world @ SY949 @ sK1_SY27 )
| ~ ~ ( ~ ( disjoint @ ( unordered_pair @ sK2_SY838 @ sK3_SX0 ) @ SY949 @ sK1_SY27 )
| ~ ( in @ sK2_SY838 @ SY949 @ sK1_SY27 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[190]) ).
thf(221,plain,
! [SV31: $i,SV56: mu] :
( ( ( ~ ( exists_in_world @ SV56 @ SV31 ) )
= $true )
| ( ( ! [SY950: mu] :
( ~ ( exists_in_world @ SY950 @ SV31 )
| ! [SY951: mu] :
( ~ ( exists_in_world @ SY951 @ SV31 )
| ~ ~ ( ~ ( qmltpeq @ SV56 @ SY950 @ SV31 )
| ~ ( qmltpeq @ SY950 @ SY951 @ SV31 ) )
| ( qmltpeq @ SV56 @ SY951 @ SV31 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[191]) ).
thf(222,plain,
! [SV6: $i,SV34: mu] :
( ( ( exists_in_world @ SV34 @ SV6 )
= $false )
| ( ( ! [SY913: mu] :
( ~ ( exists_in_world @ SY913 @ SV6 )
| ! [SY914: mu] :
( ~ ( exists_in_world @ SY914 @ SV6 )
| ~ ~ ( ~ ( qmltpeq @ SV34 @ SY913 @ SV6 )
| ~ ( disjoint @ SY914 @ SV34 @ SV6 ) )
| ( disjoint @ SY914 @ SY913 @ SV6 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(223,plain,
! [SV7: $i,SV35: mu] :
( ( ( exists_in_world @ SV35 @ SV7 )
= $false )
| ( ( ! [SY915: mu] :
( ~ ( exists_in_world @ SY915 @ SV7 )
| ! [SY916: mu] :
( ~ ( exists_in_world @ SY916 @ SV7 )
| ~ ~ ( ~ ( qmltpeq @ SV35 @ SY915 @ SV7 )
| ~ ( in @ SV35 @ SY916 @ SV7 ) )
| ( in @ SY915 @ SY916 @ SV7 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(224,plain,
! [SV8: $i,SV36: mu] :
( ( ( exists_in_world @ SV36 @ SV8 )
= $false )
| ( ( ! [SY917: mu] :
( ~ ( exists_in_world @ SY917 @ SV8 )
| ! [SY918: mu] :
( ~ ( exists_in_world @ SY918 @ SV8 )
| ~ ( qmltpeq @ SV36 @ SY917 @ SV8 )
| ( qmltpeq @ ( unordered_pair @ SV36 @ SY918 ) @ ( unordered_pair @ SY917 @ SY918 ) @ SV8 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(225,plain,
! [SV9: $i,SV37: mu] :
( ( ( exists_in_world @ SV37 @ SV9 )
= $false )
| ( ( ! [SY919: mu] :
( ~ ( exists_in_world @ SY919 @ SV9 )
| ( qmltpeq @ ( set_intersection2 @ SV37 @ SY919 ) @ ( set_intersection2 @ SY919 @ SV37 ) @ SV9 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[197]) ).
thf(226,plain,
! [SV10: $i,SV38: mu] :
( ( ( exists_in_world @ SV38 @ SV10 )
= $false )
| ( ( ! [SY920: mu] :
( ~ ( exists_in_world @ SY920 @ SV10 )
| ! [SY921: mu] :
( ~ ( exists_in_world @ SY921 @ SV10 )
| ~ ( ~ ( ~ ( qmltpeq @ SY921 @ ( set_intersection2 @ SV38 @ SY920 ) @ SV10 )
| ! [SY922: mu] :
( ~ ( exists_in_world @ SY922 @ SV10 )
| ~ ( ~ ( ~ ( in @ SY922 @ SY921 @ SV10 )
| ~ ( ~ ( in @ SY922 @ SV38 @ SV10 )
| ~ ( in @ SY922 @ SY920 @ SV10 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY922 @ SV38 @ SV10 )
| ~ ( in @ SY922 @ SY920 @ SV10 ) )
| ( in @ SY922 @ SY921 @ SV10 ) ) ) ) )
| ~ ( ~ ! [SY923: mu] :
( ~ ( exists_in_world @ SY923 @ SV10 )
| ~ ( ~ ( ~ ( in @ SY923 @ SY921 @ SV10 )
| ~ ( ~ ( in @ SY923 @ SV38 @ SV10 )
| ~ ( in @ SY923 @ SY920 @ SV10 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY923 @ SV38 @ SV10 )
| ~ ( in @ SY923 @ SY920 @ SV10 ) )
| ( in @ SY923 @ SY921 @ SV10 ) ) ) )
| ( qmltpeq @ SY921 @ ( set_intersection2 @ SV38 @ SY920 ) @ SV10 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[198]) ).
thf(227,plain,
! [SV11: $i,SV39: mu] :
( ( ( exists_in_world @ SV39 @ SV11 )
= $false )
| ( ( ~ ( ~ ( ~ ( qmltpeq @ SV39 @ empty_set @ SV11 )
| ! [SY924: mu] :
( ~ ( exists_in_world @ SY924 @ SV11 )
| ~ ( in @ SY924 @ SV39 @ SV11 ) ) )
| ~ ( ~ ! [SY925: mu] :
( ~ ( exists_in_world @ SY925 @ SV11 )
| ~ ( in @ SY925 @ SV39 @ SV11 ) )
| ( qmltpeq @ SV39 @ empty_set @ SV11 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[199]) ).
thf(228,plain,
! [SV12: $i] :
( ( ~ ( exists_in_world @ ( sK4_SY866 @ SV12 ) @ SV12 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[200]) ).
thf(229,plain,
! [SV12: $i] :
( ( ~ ( empty @ ( sK4_SY866 @ SV12 ) @ SV12 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[200]) ).
thf(230,plain,
! [SV13: $i,SV40: mu] :
( ( ( exists_in_world @ SV40 @ SV13 )
= $false )
| ( ( ! [SY926: mu] :
( ~ ( exists_in_world @ SY926 @ SV13 )
| ( qmltpeq @ ( unordered_pair @ SV40 @ SY926 ) @ ( unordered_pair @ SY926 @ SV40 ) @ SV13 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(231,plain,
! [SV59: $i,SV41: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ( rel_s4 @ SV14 @ SV41 )
| ~ ( rel_s4 @ SV41 @ SV59 ) ) )
= $true )
| ( ( rel_s4 @ SV14 @ SV59 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[202]) ).
thf(232,plain,
! [SV15: $i] :
( ( exists_in_world @ ( sK5_SY871 @ SV15 ) @ SV15 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[203]) ).
thf(233,plain,
! [SV60: $i,SV42: $i,SV16: mu] :
( ( ( ~ ~ ( ~ ( exists_in_world @ SV16 @ SV42 )
| ~ ( rel_s4 @ SV42 @ SV60 ) ) )
= $true )
| ( ( exists_in_world @ SV16 @ SV60 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[204]) ).
thf(234,plain,
! [SV17: $i,SV43: mu] :
( ( ( exists_in_world @ SV43 @ SV17 )
= $false )
| ( ( ! [SY929: mu] :
( ~ ( exists_in_world @ SY929 @ SV17 )
| ! [SY930: mu] :
( ~ ( exists_in_world @ SY930 @ SV17 )
| ~ ( qmltpeq @ SV43 @ SY929 @ SV17 )
| ( qmltpeq @ ( unordered_pair @ SY930 @ SV43 ) @ ( unordered_pair @ SY930 @ SY929 ) @ SV17 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[205]) ).
thf(235,plain,
! [SV18: $i,SV44: mu] :
( ( ( exists_in_world @ SV44 @ SV18 )
= $false )
| ( ( ! [SY931: mu] :
( ~ ( exists_in_world @ SY931 @ SV18 )
| ~ ~ ( ~ ( qmltpeq @ SV44 @ SY931 @ SV18 )
| ~ ( empty @ SV44 @ SV18 ) )
| ( empty @ SY931 @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[206]) ).
thf(236,plain,
! [SV19: $i,SV45: mu] :
( ( ( exists_in_world @ SV45 @ SV19 )
= $false )
| ( ( ! [SY932: mu] :
( ~ ( exists_in_world @ SY932 @ SV19 )
| ~ ( in @ SV45 @ SY932 @ SV19 )
| ~ ( in @ SY932 @ SV45 @ SV19 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[207]) ).
thf(237,plain,
! [SV20: $i,SV46: mu] :
( ( ( exists_in_world @ SV46 @ SV20 )
= $false )
| ( ( ! [SY933: mu] :
( ~ ( exists_in_world @ SY933 @ SV20 )
| ( qmltpeq @ ( set_intersection2 @ SV46 @ SV46 ) @ SV46 @ SV20 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[208]) ).
thf(238,plain,
! [SV21: $i] :
( ( ~ ( exists_in_world @ ( sK6_SY883 @ SV21 ) @ SV21 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[209]) ).
thf(239,plain,
! [SV21: $i] :
( ( ~ ~ ( empty @ ( sK6_SY883 @ SV21 ) @ SV21 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[209]) ).
thf(240,plain,
! [SV22: $i,SV47: mu] :
( ( ( exists_in_world @ SV47 @ SV22 )
= $false )
| ( ( ! [SY934: mu] :
( ~ ( exists_in_world @ SY934 @ SV22 )
| ! [SY935: mu] :
( ~ ( exists_in_world @ SY935 @ SV22 )
| ~ ~ ( ~ ( qmltpeq @ SV47 @ SY934 @ SV22 )
| ~ ( disjoint @ SV47 @ SY935 @ SV22 ) )
| ( disjoint @ SY934 @ SY935 @ SV22 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[210]) ).
thf(241,plain,
! [SV23: $i,SV48: mu] :
( ( ( exists_in_world @ SV48 @ SV23 )
= $false )
| ( ( ! [SY936: mu] :
( ~ ( exists_in_world @ SY936 @ SV23 )
| ! [SY937: mu] :
( ~ ( exists_in_world @ SY937 @ SV23 )
| ~ ( ~ ( ~ ( qmltpeq @ SY937 @ ( unordered_pair @ SV48 @ SY936 ) @ SV23 )
| ! [SY938: mu] :
( ~ ( exists_in_world @ SY938 @ SV23 )
| ~ ( ~ ( ~ ( in @ SY938 @ SY937 @ SV23 )
| ( qmltpeq @ SY938 @ SV48 @ SV23 )
| ( qmltpeq @ SY938 @ SY936 @ SV23 ) )
| ~ ( ~ ( ( qmltpeq @ SY938 @ SV48 @ SV23 )
| ( qmltpeq @ SY938 @ SY936 @ SV23 ) )
| ( in @ SY938 @ SY937 @ SV23 ) ) ) ) )
| ~ ( ~ ! [SY939: mu] :
( ~ ( exists_in_world @ SY939 @ SV23 )
| ~ ( ~ ( ~ ( in @ SY939 @ SY937 @ SV23 )
| ( qmltpeq @ SY939 @ SV48 @ SV23 )
| ( qmltpeq @ SY939 @ SY936 @ SV23 ) )
| ~ ( ~ ( ( qmltpeq @ SY939 @ SV48 @ SV23 )
| ( qmltpeq @ SY939 @ SY936 @ SV23 ) )
| ( in @ SY939 @ SY937 @ SV23 ) ) ) )
| ( qmltpeq @ SY937 @ ( unordered_pair @ SV48 @ SY936 ) @ SV23 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[211]) ).
thf(242,plain,
! [SV24: $i,SV49: mu] :
( ( ( exists_in_world @ SV49 @ SV24 )
= $false )
| ( ( ! [SY940: mu] :
( ~ ( exists_in_world @ SY940 @ SV24 )
| ! [SY941: mu] :
( ~ ( exists_in_world @ SY941 @ SV24 )
| ~ ( qmltpeq @ SV49 @ SY940 @ SV24 )
| ( qmltpeq @ ( set_intersection2 @ SV49 @ SY941 ) @ ( set_intersection2 @ SY940 @ SY941 ) @ SV24 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[212]) ).
thf(243,plain,
! [SV25: $i,SV50: mu] :
( ( ( exists_in_world @ SV50 @ SV25 )
= $false )
| ( ( qmltpeq @ SV50 @ SV50 @ SV25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[213]) ).
thf(244,plain,
! [SV26: $i,SV51: mu] :
( ( ( exists_in_world @ SV51 @ SV26 )
= $false )
| ( ( ! [SY942: mu] :
( ~ ( exists_in_world @ SY942 @ SV26 )
| ~ ( ~ ( ~ ( disjoint @ SV51 @ SY942 @ SV26 )
| ( qmltpeq @ ( set_intersection2 @ SV51 @ SY942 ) @ empty_set @ SV26 ) )
| ~ ( ~ ( qmltpeq @ ( set_intersection2 @ SV51 @ SY942 ) @ empty_set @ SV26 )
| ( disjoint @ SV51 @ SY942 @ SV26 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[214]) ).
thf(245,plain,
! [SV27: $i,SV52: mu] :
( ( ( exists_in_world @ SV52 @ SV27 )
= $false )
| ( ( ! [SY943: mu] :
( ~ ( exists_in_world @ SY943 @ SV27 )
| ~ ( disjoint @ SV52 @ SY943 @ SV27 )
| ( disjoint @ SY943 @ SV52 @ SV27 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[215]) ).
thf(246,plain,
! [SV28: $i,SV53: mu] :
( ( ( exists_in_world @ SV53 @ SV28 )
= $false )
| ( ( ! [SY944: mu] :
( ~ ( exists_in_world @ SY944 @ SV28 )
| ~ ( qmltpeq @ SV53 @ SY944 @ SV28 )
| ( qmltpeq @ SY944 @ SV53 @ SV28 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[216]) ).
thf(247,plain,
! [SV29: $i,SV54: mu] :
( ( ( exists_in_world @ SV54 @ SV29 )
= $false )
| ( ( ! [SY945: mu] :
( ~ ( exists_in_world @ SY945 @ SV29 )
| ! [SY946: mu] :
( ~ ( exists_in_world @ SY946 @ SV29 )
| ~ ~ ( ~ ( qmltpeq @ SV54 @ SY945 @ SV29 )
| ~ ( in @ SY946 @ SV54 @ SV29 ) )
| ( in @ SY946 @ SY945 @ SV29 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[217]) ).
thf(248,plain,
! [SV30: $i,SV55: mu] :
( ( ( exists_in_world @ SV55 @ SV30 )
= $false )
| ( ( ! [SY947: mu] :
( ~ ( exists_in_world @ SY947 @ SV30 )
| ! [SY948: mu] :
( ~ ( exists_in_world @ SY948 @ SV30 )
| ~ ( qmltpeq @ SV55 @ SY947 @ SV30 )
| ( qmltpeq @ ( set_intersection2 @ SY948 @ SV55 ) @ ( set_intersection2 @ SY948 @ SY947 ) @ SV30 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[218]) ).
thf(249,plain,
( ( exists_in_world @ sK3_SX0 @ sK1_SY27 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[219]) ).
thf(250,plain,
( ( ~ ( exists_in_world @ sK7_SY949 @ sK1_SY27 )
| ~ ~ ( ~ ( disjoint @ ( unordered_pair @ sK2_SY838 @ sK3_SX0 ) @ sK7_SY949 @ sK1_SY27 )
| ~ ( in @ sK2_SY838 @ sK7_SY949 @ sK1_SY27 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[220]) ).
thf(251,plain,
! [SV31: $i,SV56: mu] :
( ( ( exists_in_world @ SV56 @ SV31 )
= $false )
| ( ( ! [SY950: mu] :
( ~ ( exists_in_world @ SY950 @ SV31 )
| ! [SY951: mu] :
( ~ ( exists_in_world @ SY951 @ SV31 )
| ~ ~ ( ~ ( qmltpeq @ SV56 @ SY950 @ SV31 )
| ~ ( qmltpeq @ SY950 @ SY951 @ SV31 ) )
| ( qmltpeq @ SV56 @ SY951 @ SV31 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[221]) ).
thf(252,plain,
! [SV34: mu,SV6: $i,SV61: mu] :
( ( ( ~ ( exists_in_world @ SV61 @ SV6 )
| ! [SY952: mu] :
( ~ ( exists_in_world @ SY952 @ SV6 )
| ~ ~ ( ~ ( qmltpeq @ SV34 @ SV61 @ SV6 )
| ~ ( disjoint @ SY952 @ SV34 @ SV6 ) )
| ( disjoint @ SY952 @ SV61 @ SV6 ) ) )
= $true )
| ( ( exists_in_world @ SV34 @ SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[222]) ).
thf(253,plain,
! [SV35: mu,SV7: $i,SV62: mu] :
( ( ( ~ ( exists_in_world @ SV62 @ SV7 )
| ! [SY953: mu] :
( ~ ( exists_in_world @ SY953 @ SV7 )
| ~ ~ ( ~ ( qmltpeq @ SV35 @ SV62 @ SV7 )
| ~ ( in @ SV35 @ SY953 @ SV7 ) )
| ( in @ SV62 @ SY953 @ SV7 ) ) )
= $true )
| ( ( exists_in_world @ SV35 @ SV7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[223]) ).
thf(254,plain,
! [SV36: mu,SV8: $i,SV63: mu] :
( ( ( ~ ( exists_in_world @ SV63 @ SV8 )
| ! [SY954: mu] :
( ~ ( exists_in_world @ SY954 @ SV8 )
| ~ ( qmltpeq @ SV36 @ SV63 @ SV8 )
| ( qmltpeq @ ( unordered_pair @ SV36 @ SY954 ) @ ( unordered_pair @ SV63 @ SY954 ) @ SV8 ) ) )
= $true )
| ( ( exists_in_world @ SV36 @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[224]) ).
thf(255,plain,
! [SV37: mu,SV9: $i,SV64: mu] :
( ( ( ~ ( exists_in_world @ SV64 @ SV9 )
| ( qmltpeq @ ( set_intersection2 @ SV37 @ SV64 ) @ ( set_intersection2 @ SV64 @ SV37 ) @ SV9 ) )
= $true )
| ( ( exists_in_world @ SV37 @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[225]) ).
thf(256,plain,
! [SV38: mu,SV10: $i,SV65: mu] :
( ( ( ~ ( exists_in_world @ SV65 @ SV10 )
| ! [SY955: mu] :
( ~ ( exists_in_world @ SY955 @ SV10 )
| ~ ( ~ ( ~ ( qmltpeq @ SY955 @ ( set_intersection2 @ SV38 @ SV65 ) @ SV10 )
| ! [SY956: mu] :
( ~ ( exists_in_world @ SY956 @ SV10 )
| ~ ( ~ ( ~ ( in @ SY956 @ SY955 @ SV10 )
| ~ ( ~ ( in @ SY956 @ SV38 @ SV10 )
| ~ ( in @ SY956 @ SV65 @ SV10 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY956 @ SV38 @ SV10 )
| ~ ( in @ SY956 @ SV65 @ SV10 ) )
| ( in @ SY956 @ SY955 @ SV10 ) ) ) ) )
| ~ ( ~ ! [SY957: mu] :
( ~ ( exists_in_world @ SY957 @ SV10 )
| ~ ( ~ ( ~ ( in @ SY957 @ SY955 @ SV10 )
| ~ ( ~ ( in @ SY957 @ SV38 @ SV10 )
| ~ ( in @ SY957 @ SV65 @ SV10 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY957 @ SV38 @ SV10 )
| ~ ( in @ SY957 @ SV65 @ SV10 ) )
| ( in @ SY957 @ SY955 @ SV10 ) ) ) )
| ( qmltpeq @ SY955 @ ( set_intersection2 @ SV38 @ SV65 ) @ SV10 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV38 @ SV10 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[226]) ).
thf(257,plain,
! [SV11: $i,SV39: mu] :
( ( ( ~ ( ~ ( qmltpeq @ SV39 @ empty_set @ SV11 )
| ! [SY924: mu] :
( ~ ( exists_in_world @ SY924 @ SV11 )
| ~ ( in @ SY924 @ SV39 @ SV11 ) ) )
| ~ ( ~ ! [SY925: mu] :
( ~ ( exists_in_world @ SY925 @ SV11 )
| ~ ( in @ SY925 @ SV39 @ SV11 ) )
| ( qmltpeq @ SV39 @ empty_set @ SV11 ) ) )
= $false )
| ( ( exists_in_world @ SV39 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[227]) ).
thf(258,plain,
! [SV12: $i] :
( ( exists_in_world @ ( sK4_SY866 @ SV12 ) @ SV12 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[228]) ).
thf(259,plain,
! [SV12: $i] :
( ( empty @ ( sK4_SY866 @ SV12 ) @ SV12 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[229]) ).
thf(260,plain,
! [SV40: mu,SV13: $i,SV66: mu] :
( ( ( ~ ( exists_in_world @ SV66 @ SV13 )
| ( qmltpeq @ ( unordered_pair @ SV40 @ SV66 ) @ ( unordered_pair @ SV66 @ SV40 ) @ SV13 ) )
= $true )
| ( ( exists_in_world @ SV40 @ SV13 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[230]) ).
thf(261,plain,
! [SV59: $i,SV41: $i,SV14: $i] :
( ( ( ~ ( ~ ( rel_s4 @ SV14 @ SV41 )
| ~ ( rel_s4 @ SV41 @ SV59 ) ) )
= $false )
| ( ( rel_s4 @ SV14 @ SV59 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[231]) ).
thf(262,plain,
! [SV60: $i,SV42: $i,SV16: mu] :
( ( ( ~ ( ~ ( exists_in_world @ SV16 @ SV42 )
| ~ ( rel_s4 @ SV42 @ SV60 ) ) )
= $false )
| ( ( exists_in_world @ SV16 @ SV60 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[233]) ).
thf(263,plain,
! [SV43: mu,SV17: $i,SV67: mu] :
( ( ( ~ ( exists_in_world @ SV67 @ SV17 )
| ! [SY958: mu] :
( ~ ( exists_in_world @ SY958 @ SV17 )
| ~ ( qmltpeq @ SV43 @ SV67 @ SV17 )
| ( qmltpeq @ ( unordered_pair @ SY958 @ SV43 ) @ ( unordered_pair @ SY958 @ SV67 ) @ SV17 ) ) )
= $true )
| ( ( exists_in_world @ SV43 @ SV17 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[234]) ).
thf(264,plain,
! [SV44: mu,SV18: $i,SV68: mu] :
( ( ( ~ ( exists_in_world @ SV68 @ SV18 )
| ~ ~ ( ~ ( qmltpeq @ SV44 @ SV68 @ SV18 )
| ~ ( empty @ SV44 @ SV18 ) )
| ( empty @ SV68 @ SV18 ) )
= $true )
| ( ( exists_in_world @ SV44 @ SV18 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[235]) ).
thf(265,plain,
! [SV45: mu,SV19: $i,SV69: mu] :
( ( ( ~ ( exists_in_world @ SV69 @ SV19 )
| ~ ( in @ SV45 @ SV69 @ SV19 )
| ~ ( in @ SV69 @ SV45 @ SV19 ) )
= $true )
| ( ( exists_in_world @ SV45 @ SV19 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[236]) ).
thf(266,plain,
! [SV46: mu,SV20: $i,SV70: mu] :
( ( ( ~ ( exists_in_world @ SV70 @ SV20 )
| ( qmltpeq @ ( set_intersection2 @ SV46 @ SV46 ) @ SV46 @ SV20 ) )
= $true )
| ( ( exists_in_world @ SV46 @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[237]) ).
thf(267,plain,
! [SV21: $i] :
( ( exists_in_world @ ( sK6_SY883 @ SV21 ) @ SV21 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[238]) ).
thf(268,plain,
! [SV21: $i] :
( ( ~ ( empty @ ( sK6_SY883 @ SV21 ) @ SV21 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[239]) ).
thf(269,plain,
! [SV47: mu,SV22: $i,SV71: mu] :
( ( ( ~ ( exists_in_world @ SV71 @ SV22 )
| ! [SY959: mu] :
( ~ ( exists_in_world @ SY959 @ SV22 )
| ~ ~ ( ~ ( qmltpeq @ SV47 @ SV71 @ SV22 )
| ~ ( disjoint @ SV47 @ SY959 @ SV22 ) )
| ( disjoint @ SV71 @ SY959 @ SV22 ) ) )
= $true )
| ( ( exists_in_world @ SV47 @ SV22 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[240]) ).
thf(270,plain,
! [SV48: mu,SV23: $i,SV72: mu] :
( ( ( ~ ( exists_in_world @ SV72 @ SV23 )
| ! [SY960: mu] :
( ~ ( exists_in_world @ SY960 @ SV23 )
| ~ ( ~ ( ~ ( qmltpeq @ SY960 @ ( unordered_pair @ SV48 @ SV72 ) @ SV23 )
| ! [SY961: mu] :
( ~ ( exists_in_world @ SY961 @ SV23 )
| ~ ( ~ ( ~ ( in @ SY961 @ SY960 @ SV23 )
| ( qmltpeq @ SY961 @ SV48 @ SV23 )
| ( qmltpeq @ SY961 @ SV72 @ SV23 ) )
| ~ ( ~ ( ( qmltpeq @ SY961 @ SV48 @ SV23 )
| ( qmltpeq @ SY961 @ SV72 @ SV23 ) )
| ( in @ SY961 @ SY960 @ SV23 ) ) ) ) )
| ~ ( ~ ! [SY962: mu] :
( ~ ( exists_in_world @ SY962 @ SV23 )
| ~ ( ~ ( ~ ( in @ SY962 @ SY960 @ SV23 )
| ( qmltpeq @ SY962 @ SV48 @ SV23 )
| ( qmltpeq @ SY962 @ SV72 @ SV23 ) )
| ~ ( ~ ( ( qmltpeq @ SY962 @ SV48 @ SV23 )
| ( qmltpeq @ SY962 @ SV72 @ SV23 ) )
| ( in @ SY962 @ SY960 @ SV23 ) ) ) )
| ( qmltpeq @ SY960 @ ( unordered_pair @ SV48 @ SV72 ) @ SV23 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV48 @ SV23 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[241]) ).
thf(271,plain,
! [SV49: mu,SV24: $i,SV73: mu] :
( ( ( ~ ( exists_in_world @ SV73 @ SV24 )
| ! [SY963: mu] :
( ~ ( exists_in_world @ SY963 @ SV24 )
| ~ ( qmltpeq @ SV49 @ SV73 @ SV24 )
| ( qmltpeq @ ( set_intersection2 @ SV49 @ SY963 ) @ ( set_intersection2 @ SV73 @ SY963 ) @ SV24 ) ) )
= $true )
| ( ( exists_in_world @ SV49 @ SV24 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[242]) ).
thf(272,plain,
! [SV51: mu,SV26: $i,SV74: mu] :
( ( ( ~ ( exists_in_world @ SV74 @ SV26 )
| ~ ( ~ ( ~ ( disjoint @ SV51 @ SV74 @ SV26 )
| ( qmltpeq @ ( set_intersection2 @ SV51 @ SV74 ) @ empty_set @ SV26 ) )
| ~ ( ~ ( qmltpeq @ ( set_intersection2 @ SV51 @ SV74 ) @ empty_set @ SV26 )
| ( disjoint @ SV51 @ SV74 @ SV26 ) ) ) )
= $true )
| ( ( exists_in_world @ SV51 @ SV26 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[244]) ).
thf(273,plain,
! [SV52: mu,SV27: $i,SV75: mu] :
( ( ( ~ ( exists_in_world @ SV75 @ SV27 )
| ~ ( disjoint @ SV52 @ SV75 @ SV27 )
| ( disjoint @ SV75 @ SV52 @ SV27 ) )
= $true )
| ( ( exists_in_world @ SV52 @ SV27 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[245]) ).
thf(274,plain,
! [SV53: mu,SV28: $i,SV76: mu] :
( ( ( ~ ( exists_in_world @ SV76 @ SV28 )
| ~ ( qmltpeq @ SV53 @ SV76 @ SV28 )
| ( qmltpeq @ SV76 @ SV53 @ SV28 ) )
= $true )
| ( ( exists_in_world @ SV53 @ SV28 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[246]) ).
thf(275,plain,
! [SV54: mu,SV29: $i,SV77: mu] :
( ( ( ~ ( exists_in_world @ SV77 @ SV29 )
| ! [SY964: mu] :
( ~ ( exists_in_world @ SY964 @ SV29 )
| ~ ~ ( ~ ( qmltpeq @ SV54 @ SV77 @ SV29 )
| ~ ( in @ SY964 @ SV54 @ SV29 ) )
| ( in @ SY964 @ SV77 @ SV29 ) ) )
= $true )
| ( ( exists_in_world @ SV54 @ SV29 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[247]) ).
thf(276,plain,
! [SV55: mu,SV30: $i,SV78: mu] :
( ( ( ~ ( exists_in_world @ SV78 @ SV30 )
| ! [SY965: mu] :
( ~ ( exists_in_world @ SY965 @ SV30 )
| ~ ( qmltpeq @ SV55 @ SV78 @ SV30 )
| ( qmltpeq @ ( set_intersection2 @ SY965 @ SV55 ) @ ( set_intersection2 @ SY965 @ SV78 ) @ SV30 ) ) )
= $true )
| ( ( exists_in_world @ SV55 @ SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[248]) ).
thf(277,plain,
( ( ~ ( exists_in_world @ sK7_SY949 @ sK1_SY27 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[250]) ).
thf(278,plain,
( ( ~ ~ ( ~ ( disjoint @ ( unordered_pair @ sK2_SY838 @ sK3_SX0 ) @ sK7_SY949 @ sK1_SY27 )
| ~ ( in @ sK2_SY838 @ sK7_SY949 @ sK1_SY27 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[250]) ).
thf(279,plain,
! [SV56: mu,SV31: $i,SV79: mu] :
( ( ( ~ ( exists_in_world @ SV79 @ SV31 )
| ! [SY966: mu] :
( ~ ( exists_in_world @ SY966 @ SV31 )
| ~ ~ ( ~ ( qmltpeq @ SV56 @ SV79 @ SV31 )
| ~ ( qmltpeq @ SV79 @ SY966 @ SV31 ) )
| ( qmltpeq @ SV56 @ SY966 @ SV31 ) ) )
= $true )
| ( ( exists_in_world @ SV56 @ SV31 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[251]) ).
thf(280,plain,
! [SV34: mu,SV6: $i,SV61: mu] :
( ( ( ~ ( exists_in_world @ SV61 @ SV6 ) )
= $true )
| ( ( ! [SY952: mu] :
( ~ ( exists_in_world @ SY952 @ SV6 )
| ~ ~ ( ~ ( qmltpeq @ SV34 @ SV61 @ SV6 )
| ~ ( disjoint @ SY952 @ SV34 @ SV6 ) )
| ( disjoint @ SY952 @ SV61 @ SV6 ) ) )
= $true )
| ( ( exists_in_world @ SV34 @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[252]) ).
thf(281,plain,
! [SV35: mu,SV7: $i,SV62: mu] :
( ( ( ~ ( exists_in_world @ SV62 @ SV7 ) )
= $true )
| ( ( ! [SY953: mu] :
( ~ ( exists_in_world @ SY953 @ SV7 )
| ~ ~ ( ~ ( qmltpeq @ SV35 @ SV62 @ SV7 )
| ~ ( in @ SV35 @ SY953 @ SV7 ) )
| ( in @ SV62 @ SY953 @ SV7 ) ) )
= $true )
| ( ( exists_in_world @ SV35 @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[253]) ).
thf(282,plain,
! [SV36: mu,SV8: $i,SV63: mu] :
( ( ( ~ ( exists_in_world @ SV63 @ SV8 ) )
= $true )
| ( ( ! [SY954: mu] :
( ~ ( exists_in_world @ SY954 @ SV8 )
| ~ ( qmltpeq @ SV36 @ SV63 @ SV8 )
| ( qmltpeq @ ( unordered_pair @ SV36 @ SY954 ) @ ( unordered_pair @ SV63 @ SY954 ) @ SV8 ) ) )
= $true )
| ( ( exists_in_world @ SV36 @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[254]) ).
thf(283,plain,
! [SV37: mu,SV9: $i,SV64: mu] :
( ( ( ~ ( exists_in_world @ SV64 @ SV9 ) )
= $true )
| ( ( qmltpeq @ ( set_intersection2 @ SV37 @ SV64 ) @ ( set_intersection2 @ SV64 @ SV37 ) @ SV9 )
= $true )
| ( ( exists_in_world @ SV37 @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[255]) ).
thf(284,plain,
! [SV38: mu,SV10: $i,SV65: mu] :
( ( ( ~ ( exists_in_world @ SV65 @ SV10 ) )
= $true )
| ( ( ! [SY955: mu] :
( ~ ( exists_in_world @ SY955 @ SV10 )
| ~ ( ~ ( ~ ( qmltpeq @ SY955 @ ( set_intersection2 @ SV38 @ SV65 ) @ SV10 )
| ! [SY956: mu] :
( ~ ( exists_in_world @ SY956 @ SV10 )
| ~ ( ~ ( ~ ( in @ SY956 @ SY955 @ SV10 )
| ~ ( ~ ( in @ SY956 @ SV38 @ SV10 )
| ~ ( in @ SY956 @ SV65 @ SV10 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY956 @ SV38 @ SV10 )
| ~ ( in @ SY956 @ SV65 @ SV10 ) )
| ( in @ SY956 @ SY955 @ SV10 ) ) ) ) )
| ~ ( ~ ! [SY957: mu] :
( ~ ( exists_in_world @ SY957 @ SV10 )
| ~ ( ~ ( ~ ( in @ SY957 @ SY955 @ SV10 )
| ~ ( ~ ( in @ SY957 @ SV38 @ SV10 )
| ~ ( in @ SY957 @ SV65 @ SV10 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY957 @ SV38 @ SV10 )
| ~ ( in @ SY957 @ SV65 @ SV10 ) )
| ( in @ SY957 @ SY955 @ SV10 ) ) ) )
| ( qmltpeq @ SY955 @ ( set_intersection2 @ SV38 @ SV65 ) @ SV10 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV38 @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[256]) ).
thf(285,plain,
! [SV11: $i,SV39: mu] :
( ( ( ~ ( ~ ( qmltpeq @ SV39 @ empty_set @ SV11 )
| ! [SY924: mu] :
( ~ ( exists_in_world @ SY924 @ SV11 )
| ~ ( in @ SY924 @ SV39 @ SV11 ) ) ) )
= $false )
| ( ( exists_in_world @ SV39 @ SV11 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[257]) ).
thf(286,plain,
! [SV39: mu,SV11: $i] :
( ( ( ~ ( ~ ! [SY925: mu] :
( ~ ( exists_in_world @ SY925 @ SV11 )
| ~ ( in @ SY925 @ SV39 @ SV11 ) )
| ( qmltpeq @ SV39 @ empty_set @ SV11 ) ) )
= $false )
| ( ( exists_in_world @ SV39 @ SV11 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[257]) ).
thf(287,plain,
! [SV40: mu,SV13: $i,SV66: mu] :
( ( ( ~ ( exists_in_world @ SV66 @ SV13 ) )
= $true )
| ( ( qmltpeq @ ( unordered_pair @ SV40 @ SV66 ) @ ( unordered_pair @ SV66 @ SV40 ) @ SV13 )
= $true )
| ( ( exists_in_world @ SV40 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[260]) ).
thf(288,plain,
! [SV59: $i,SV41: $i,SV14: $i] :
( ( ( ~ ( rel_s4 @ SV14 @ SV41 )
| ~ ( rel_s4 @ SV41 @ SV59 ) )
= $true )
| ( ( rel_s4 @ SV14 @ SV59 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[261]) ).
thf(289,plain,
! [SV60: $i,SV42: $i,SV16: mu] :
( ( ( ~ ( exists_in_world @ SV16 @ SV42 )
| ~ ( rel_s4 @ SV42 @ SV60 ) )
= $true )
| ( ( exists_in_world @ SV16 @ SV60 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[262]) ).
thf(290,plain,
! [SV43: mu,SV17: $i,SV67: mu] :
( ( ( ~ ( exists_in_world @ SV67 @ SV17 ) )
= $true )
| ( ( ! [SY958: mu] :
( ~ ( exists_in_world @ SY958 @ SV17 )
| ~ ( qmltpeq @ SV43 @ SV67 @ SV17 )
| ( qmltpeq @ ( unordered_pair @ SY958 @ SV43 ) @ ( unordered_pair @ SY958 @ SV67 ) @ SV17 ) ) )
= $true )
| ( ( exists_in_world @ SV43 @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[263]) ).
thf(291,plain,
! [SV44: mu,SV18: $i,SV68: mu] :
( ( ( ~ ( exists_in_world @ SV68 @ SV18 ) )
= $true )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV44 @ SV68 @ SV18 )
| ~ ( empty @ SV44 @ SV18 ) )
| ( empty @ SV68 @ SV18 ) )
= $true )
| ( ( exists_in_world @ SV44 @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[264]) ).
thf(292,plain,
! [SV45: mu,SV19: $i,SV69: mu] :
( ( ( ~ ( exists_in_world @ SV69 @ SV19 ) )
= $true )
| ( ( ~ ( in @ SV45 @ SV69 @ SV19 )
| ~ ( in @ SV69 @ SV45 @ SV19 ) )
= $true )
| ( ( exists_in_world @ SV45 @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[265]) ).
thf(293,plain,
! [SV46: mu,SV20: $i,SV70: mu] :
( ( ( ~ ( exists_in_world @ SV70 @ SV20 ) )
= $true )
| ( ( qmltpeq @ ( set_intersection2 @ SV46 @ SV46 ) @ SV46 @ SV20 )
= $true )
| ( ( exists_in_world @ SV46 @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[266]) ).
thf(294,plain,
! [SV21: $i] :
( ( empty @ ( sK6_SY883 @ SV21 ) @ SV21 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[268]) ).
thf(295,plain,
! [SV47: mu,SV22: $i,SV71: mu] :
( ( ( ~ ( exists_in_world @ SV71 @ SV22 ) )
= $true )
| ( ( ! [SY959: mu] :
( ~ ( exists_in_world @ SY959 @ SV22 )
| ~ ~ ( ~ ( qmltpeq @ SV47 @ SV71 @ SV22 )
| ~ ( disjoint @ SV47 @ SY959 @ SV22 ) )
| ( disjoint @ SV71 @ SY959 @ SV22 ) ) )
= $true )
| ( ( exists_in_world @ SV47 @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[269]) ).
thf(296,plain,
! [SV48: mu,SV23: $i,SV72: mu] :
( ( ( ~ ( exists_in_world @ SV72 @ SV23 ) )
= $true )
| ( ( ! [SY960: mu] :
( ~ ( exists_in_world @ SY960 @ SV23 )
| ~ ( ~ ( ~ ( qmltpeq @ SY960 @ ( unordered_pair @ SV48 @ SV72 ) @ SV23 )
| ! [SY961: mu] :
( ~ ( exists_in_world @ SY961 @ SV23 )
| ~ ( ~ ( ~ ( in @ SY961 @ SY960 @ SV23 )
| ( qmltpeq @ SY961 @ SV48 @ SV23 )
| ( qmltpeq @ SY961 @ SV72 @ SV23 ) )
| ~ ( ~ ( ( qmltpeq @ SY961 @ SV48 @ SV23 )
| ( qmltpeq @ SY961 @ SV72 @ SV23 ) )
| ( in @ SY961 @ SY960 @ SV23 ) ) ) ) )
| ~ ( ~ ! [SY962: mu] :
( ~ ( exists_in_world @ SY962 @ SV23 )
| ~ ( ~ ( ~ ( in @ SY962 @ SY960 @ SV23 )
| ( qmltpeq @ SY962 @ SV48 @ SV23 )
| ( qmltpeq @ SY962 @ SV72 @ SV23 ) )
| ~ ( ~ ( ( qmltpeq @ SY962 @ SV48 @ SV23 )
| ( qmltpeq @ SY962 @ SV72 @ SV23 ) )
| ( in @ SY962 @ SY960 @ SV23 ) ) ) )
| ( qmltpeq @ SY960 @ ( unordered_pair @ SV48 @ SV72 ) @ SV23 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV48 @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[270]) ).
thf(297,plain,
! [SV49: mu,SV24: $i,SV73: mu] :
( ( ( ~ ( exists_in_world @ SV73 @ SV24 ) )
= $true )
| ( ( ! [SY963: mu] :
( ~ ( exists_in_world @ SY963 @ SV24 )
| ~ ( qmltpeq @ SV49 @ SV73 @ SV24 )
| ( qmltpeq @ ( set_intersection2 @ SV49 @ SY963 ) @ ( set_intersection2 @ SV73 @ SY963 ) @ SV24 ) ) )
= $true )
| ( ( exists_in_world @ SV49 @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[271]) ).
thf(298,plain,
! [SV51: mu,SV26: $i,SV74: mu] :
( ( ( ~ ( exists_in_world @ SV74 @ SV26 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( disjoint @ SV51 @ SV74 @ SV26 )
| ( qmltpeq @ ( set_intersection2 @ SV51 @ SV74 ) @ empty_set @ SV26 ) )
| ~ ( ~ ( qmltpeq @ ( set_intersection2 @ SV51 @ SV74 ) @ empty_set @ SV26 )
| ( disjoint @ SV51 @ SV74 @ SV26 ) ) ) )
= $true )
| ( ( exists_in_world @ SV51 @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[272]) ).
thf(299,plain,
! [SV52: mu,SV27: $i,SV75: mu] :
( ( ( ~ ( exists_in_world @ SV75 @ SV27 ) )
= $true )
| ( ( ~ ( disjoint @ SV52 @ SV75 @ SV27 )
| ( disjoint @ SV75 @ SV52 @ SV27 ) )
= $true )
| ( ( exists_in_world @ SV52 @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[273]) ).
thf(300,plain,
! [SV53: mu,SV28: $i,SV76: mu] :
( ( ( ~ ( exists_in_world @ SV76 @ SV28 ) )
= $true )
| ( ( ~ ( qmltpeq @ SV53 @ SV76 @ SV28 )
| ( qmltpeq @ SV76 @ SV53 @ SV28 ) )
= $true )
| ( ( exists_in_world @ SV53 @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[274]) ).
thf(301,plain,
! [SV54: mu,SV29: $i,SV77: mu] :
( ( ( ~ ( exists_in_world @ SV77 @ SV29 ) )
= $true )
| ( ( ! [SY964: mu] :
( ~ ( exists_in_world @ SY964 @ SV29 )
| ~ ~ ( ~ ( qmltpeq @ SV54 @ SV77 @ SV29 )
| ~ ( in @ SY964 @ SV54 @ SV29 ) )
| ( in @ SY964 @ SV77 @ SV29 ) ) )
= $true )
| ( ( exists_in_world @ SV54 @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[275]) ).
thf(302,plain,
! [SV55: mu,SV30: $i,SV78: mu] :
( ( ( ~ ( exists_in_world @ SV78 @ SV30 ) )
= $true )
| ( ( ! [SY965: mu] :
( ~ ( exists_in_world @ SY965 @ SV30 )
| ~ ( qmltpeq @ SV55 @ SV78 @ SV30 )
| ( qmltpeq @ ( set_intersection2 @ SY965 @ SV55 ) @ ( set_intersection2 @ SY965 @ SV78 ) @ SV30 ) ) )
= $true )
| ( ( exists_in_world @ SV55 @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[276]) ).
thf(303,plain,
( ( exists_in_world @ sK7_SY949 @ sK1_SY27 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[277]) ).
thf(304,plain,
( ( ~ ( ~ ( disjoint @ ( unordered_pair @ sK2_SY838 @ sK3_SX0 ) @ sK7_SY949 @ sK1_SY27 )
| ~ ( in @ sK2_SY838 @ sK7_SY949 @ sK1_SY27 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[278]) ).
thf(305,plain,
! [SV56: mu,SV31: $i,SV79: mu] :
( ( ( ~ ( exists_in_world @ SV79 @ SV31 ) )
= $true )
| ( ( ! [SY966: mu] :
( ~ ( exists_in_world @ SY966 @ SV31 )
| ~ ~ ( ~ ( qmltpeq @ SV56 @ SV79 @ SV31 )
| ~ ( qmltpeq @ SV79 @ SY966 @ SV31 ) )
| ( qmltpeq @ SV56 @ SY966 @ SV31 ) ) )
= $true )
| ( ( exists_in_world @ SV56 @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[279]) ).
thf(306,plain,
! [SV34: mu,SV6: $i,SV61: mu] :
( ( ( exists_in_world @ SV61 @ SV6 )
= $false )
| ( ( ! [SY952: mu] :
( ~ ( exists_in_world @ SY952 @ SV6 )
| ~ ~ ( ~ ( qmltpeq @ SV34 @ SV61 @ SV6 )
| ~ ( disjoint @ SY952 @ SV34 @ SV6 ) )
| ( disjoint @ SY952 @ SV61 @ SV6 ) ) )
= $true )
| ( ( exists_in_world @ SV34 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[280]) ).
thf(307,plain,
! [SV35: mu,SV7: $i,SV62: mu] :
( ( ( exists_in_world @ SV62 @ SV7 )
= $false )
| ( ( ! [SY953: mu] :
( ~ ( exists_in_world @ SY953 @ SV7 )
| ~ ~ ( ~ ( qmltpeq @ SV35 @ SV62 @ SV7 )
| ~ ( in @ SV35 @ SY953 @ SV7 ) )
| ( in @ SV62 @ SY953 @ SV7 ) ) )
= $true )
| ( ( exists_in_world @ SV35 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[281]) ).
thf(308,plain,
! [SV36: mu,SV8: $i,SV63: mu] :
( ( ( exists_in_world @ SV63 @ SV8 )
= $false )
| ( ( ! [SY954: mu] :
( ~ ( exists_in_world @ SY954 @ SV8 )
| ~ ( qmltpeq @ SV36 @ SV63 @ SV8 )
| ( qmltpeq @ ( unordered_pair @ SV36 @ SY954 ) @ ( unordered_pair @ SV63 @ SY954 ) @ SV8 ) ) )
= $true )
| ( ( exists_in_world @ SV36 @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[282]) ).
thf(309,plain,
! [SV37: mu,SV9: $i,SV64: mu] :
( ( ( exists_in_world @ SV64 @ SV9 )
= $false )
| ( ( qmltpeq @ ( set_intersection2 @ SV37 @ SV64 ) @ ( set_intersection2 @ SV64 @ SV37 ) @ SV9 )
= $true )
| ( ( exists_in_world @ SV37 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[283]) ).
thf(310,plain,
! [SV38: mu,SV10: $i,SV65: mu] :
( ( ( exists_in_world @ SV65 @ SV10 )
= $false )
| ( ( ! [SY955: mu] :
( ~ ( exists_in_world @ SY955 @ SV10 )
| ~ ( ~ ( ~ ( qmltpeq @ SY955 @ ( set_intersection2 @ SV38 @ SV65 ) @ SV10 )
| ! [SY956: mu] :
( ~ ( exists_in_world @ SY956 @ SV10 )
| ~ ( ~ ( ~ ( in @ SY956 @ SY955 @ SV10 )
| ~ ( ~ ( in @ SY956 @ SV38 @ SV10 )
| ~ ( in @ SY956 @ SV65 @ SV10 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY956 @ SV38 @ SV10 )
| ~ ( in @ SY956 @ SV65 @ SV10 ) )
| ( in @ SY956 @ SY955 @ SV10 ) ) ) ) )
| ~ ( ~ ! [SY957: mu] :
( ~ ( exists_in_world @ SY957 @ SV10 )
| ~ ( ~ ( ~ ( in @ SY957 @ SY955 @ SV10 )
| ~ ( ~ ( in @ SY957 @ SV38 @ SV10 )
| ~ ( in @ SY957 @ SV65 @ SV10 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY957 @ SV38 @ SV10 )
| ~ ( in @ SY957 @ SV65 @ SV10 ) )
| ( in @ SY957 @ SY955 @ SV10 ) ) ) )
| ( qmltpeq @ SY955 @ ( set_intersection2 @ SV38 @ SV65 ) @ SV10 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV38 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[284]) ).
thf(311,plain,
! [SV11: $i,SV39: mu] :
( ( ( ~ ( qmltpeq @ SV39 @ empty_set @ SV11 )
| ! [SY924: mu] :
( ~ ( exists_in_world @ SY924 @ SV11 )
| ~ ( in @ SY924 @ SV39 @ SV11 ) ) )
= $true )
| ( ( exists_in_world @ SV39 @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[285]) ).
thf(312,plain,
! [SV39: mu,SV11: $i] :
( ( ( ~ ! [SY925: mu] :
( ~ ( exists_in_world @ SY925 @ SV11 )
| ~ ( in @ SY925 @ SV39 @ SV11 ) )
| ( qmltpeq @ SV39 @ empty_set @ SV11 ) )
= $true )
| ( ( exists_in_world @ SV39 @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[286]) ).
thf(313,plain,
! [SV40: mu,SV13: $i,SV66: mu] :
( ( ( exists_in_world @ SV66 @ SV13 )
= $false )
| ( ( qmltpeq @ ( unordered_pair @ SV40 @ SV66 ) @ ( unordered_pair @ SV66 @ SV40 ) @ SV13 )
= $true )
| ( ( exists_in_world @ SV40 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[287]) ).
thf(314,plain,
! [SV59: $i,SV41: $i,SV14: $i] :
( ( ( ~ ( rel_s4 @ SV14 @ SV41 ) )
= $true )
| ( ( ~ ( rel_s4 @ SV41 @ SV59 ) )
= $true )
| ( ( rel_s4 @ SV14 @ SV59 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[288]) ).
thf(315,plain,
! [SV60: $i,SV42: $i,SV16: mu] :
( ( ( ~ ( exists_in_world @ SV16 @ SV42 ) )
= $true )
| ( ( ~ ( rel_s4 @ SV42 @ SV60 ) )
= $true )
| ( ( exists_in_world @ SV16 @ SV60 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[289]) ).
thf(316,plain,
! [SV43: mu,SV17: $i,SV67: mu] :
( ( ( exists_in_world @ SV67 @ SV17 )
= $false )
| ( ( ! [SY958: mu] :
( ~ ( exists_in_world @ SY958 @ SV17 )
| ~ ( qmltpeq @ SV43 @ SV67 @ SV17 )
| ( qmltpeq @ ( unordered_pair @ SY958 @ SV43 ) @ ( unordered_pair @ SY958 @ SV67 ) @ SV17 ) ) )
= $true )
| ( ( exists_in_world @ SV43 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[290]) ).
thf(317,plain,
! [SV44: mu,SV18: $i,SV68: mu] :
( ( ( exists_in_world @ SV68 @ SV18 )
= $false )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV44 @ SV68 @ SV18 )
| ~ ( empty @ SV44 @ SV18 ) )
| ( empty @ SV68 @ SV18 ) )
= $true )
| ( ( exists_in_world @ SV44 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[291]) ).
thf(318,plain,
! [SV45: mu,SV19: $i,SV69: mu] :
( ( ( exists_in_world @ SV69 @ SV19 )
= $false )
| ( ( ~ ( in @ SV45 @ SV69 @ SV19 )
| ~ ( in @ SV69 @ SV45 @ SV19 ) )
= $true )
| ( ( exists_in_world @ SV45 @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[292]) ).
thf(319,plain,
! [SV46: mu,SV20: $i,SV70: mu] :
( ( ( exists_in_world @ SV70 @ SV20 )
= $false )
| ( ( qmltpeq @ ( set_intersection2 @ SV46 @ SV46 ) @ SV46 @ SV20 )
= $true )
| ( ( exists_in_world @ SV46 @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[293]) ).
thf(320,plain,
! [SV47: mu,SV22: $i,SV71: mu] :
( ( ( exists_in_world @ SV71 @ SV22 )
= $false )
| ( ( ! [SY959: mu] :
( ~ ( exists_in_world @ SY959 @ SV22 )
| ~ ~ ( ~ ( qmltpeq @ SV47 @ SV71 @ SV22 )
| ~ ( disjoint @ SV47 @ SY959 @ SV22 ) )
| ( disjoint @ SV71 @ SY959 @ SV22 ) ) )
= $true )
| ( ( exists_in_world @ SV47 @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[295]) ).
thf(321,plain,
! [SV48: mu,SV23: $i,SV72: mu] :
( ( ( exists_in_world @ SV72 @ SV23 )
= $false )
| ( ( ! [SY960: mu] :
( ~ ( exists_in_world @ SY960 @ SV23 )
| ~ ( ~ ( ~ ( qmltpeq @ SY960 @ ( unordered_pair @ SV48 @ SV72 ) @ SV23 )
| ! [SY961: mu] :
( ~ ( exists_in_world @ SY961 @ SV23 )
| ~ ( ~ ( ~ ( in @ SY961 @ SY960 @ SV23 )
| ( qmltpeq @ SY961 @ SV48 @ SV23 )
| ( qmltpeq @ SY961 @ SV72 @ SV23 ) )
| ~ ( ~ ( ( qmltpeq @ SY961 @ SV48 @ SV23 )
| ( qmltpeq @ SY961 @ SV72 @ SV23 ) )
| ( in @ SY961 @ SY960 @ SV23 ) ) ) ) )
| ~ ( ~ ! [SY962: mu] :
( ~ ( exists_in_world @ SY962 @ SV23 )
| ~ ( ~ ( ~ ( in @ SY962 @ SY960 @ SV23 )
| ( qmltpeq @ SY962 @ SV48 @ SV23 )
| ( qmltpeq @ SY962 @ SV72 @ SV23 ) )
| ~ ( ~ ( ( qmltpeq @ SY962 @ SV48 @ SV23 )
| ( qmltpeq @ SY962 @ SV72 @ SV23 ) )
| ( in @ SY962 @ SY960 @ SV23 ) ) ) )
| ( qmltpeq @ SY960 @ ( unordered_pair @ SV48 @ SV72 ) @ SV23 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV48 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[296]) ).
thf(322,plain,
! [SV49: mu,SV24: $i,SV73: mu] :
( ( ( exists_in_world @ SV73 @ SV24 )
= $false )
| ( ( ! [SY963: mu] :
( ~ ( exists_in_world @ SY963 @ SV24 )
| ~ ( qmltpeq @ SV49 @ SV73 @ SV24 )
| ( qmltpeq @ ( set_intersection2 @ SV49 @ SY963 ) @ ( set_intersection2 @ SV73 @ SY963 ) @ SV24 ) ) )
= $true )
| ( ( exists_in_world @ SV49 @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[297]) ).
thf(323,plain,
! [SV51: mu,SV26: $i,SV74: mu] :
( ( ( exists_in_world @ SV74 @ SV26 )
= $false )
| ( ( ~ ( ~ ( ~ ( disjoint @ SV51 @ SV74 @ SV26 )
| ( qmltpeq @ ( set_intersection2 @ SV51 @ SV74 ) @ empty_set @ SV26 ) )
| ~ ( ~ ( qmltpeq @ ( set_intersection2 @ SV51 @ SV74 ) @ empty_set @ SV26 )
| ( disjoint @ SV51 @ SV74 @ SV26 ) ) ) )
= $true )
| ( ( exists_in_world @ SV51 @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[298]) ).
thf(324,plain,
! [SV52: mu,SV27: $i,SV75: mu] :
( ( ( exists_in_world @ SV75 @ SV27 )
= $false )
| ( ( ~ ( disjoint @ SV52 @ SV75 @ SV27 )
| ( disjoint @ SV75 @ SV52 @ SV27 ) )
= $true )
| ( ( exists_in_world @ SV52 @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[299]) ).
thf(325,plain,
! [SV53: mu,SV28: $i,SV76: mu] :
( ( ( exists_in_world @ SV76 @ SV28 )
= $false )
| ( ( ~ ( qmltpeq @ SV53 @ SV76 @ SV28 )
| ( qmltpeq @ SV76 @ SV53 @ SV28 ) )
= $true )
| ( ( exists_in_world @ SV53 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[300]) ).
thf(326,plain,
! [SV54: mu,SV29: $i,SV77: mu] :
( ( ( exists_in_world @ SV77 @ SV29 )
= $false )
| ( ( ! [SY964: mu] :
( ~ ( exists_in_world @ SY964 @ SV29 )
| ~ ~ ( ~ ( qmltpeq @ SV54 @ SV77 @ SV29 )
| ~ ( in @ SY964 @ SV54 @ SV29 ) )
| ( in @ SY964 @ SV77 @ SV29 ) ) )
= $true )
| ( ( exists_in_world @ SV54 @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[301]) ).
thf(327,plain,
! [SV55: mu,SV30: $i,SV78: mu] :
( ( ( exists_in_world @ SV78 @ SV30 )
= $false )
| ( ( ! [SY965: mu] :
( ~ ( exists_in_world @ SY965 @ SV30 )
| ~ ( qmltpeq @ SV55 @ SV78 @ SV30 )
| ( qmltpeq @ ( set_intersection2 @ SY965 @ SV55 ) @ ( set_intersection2 @ SY965 @ SV78 ) @ SV30 ) ) )
= $true )
| ( ( exists_in_world @ SV55 @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[302]) ).
thf(328,plain,
( ( ~ ( disjoint @ ( unordered_pair @ sK2_SY838 @ sK3_SX0 ) @ sK7_SY949 @ sK1_SY27 )
| ~ ( in @ sK2_SY838 @ sK7_SY949 @ sK1_SY27 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[304]) ).
thf(329,plain,
! [SV56: mu,SV31: $i,SV79: mu] :
( ( ( exists_in_world @ SV79 @ SV31 )
= $false )
| ( ( ! [SY966: mu] :
( ~ ( exists_in_world @ SY966 @ SV31 )
| ~ ~ ( ~ ( qmltpeq @ SV56 @ SV79 @ SV31 )
| ~ ( qmltpeq @ SV79 @ SY966 @ SV31 ) )
| ( qmltpeq @ SV56 @ SY966 @ SV31 ) ) )
= $true )
| ( ( exists_in_world @ SV56 @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[305]) ).
thf(330,plain,
! [SV61: mu,SV34: mu,SV6: $i,SV80: mu] :
( ( ( ~ ( exists_in_world @ SV80 @ SV6 )
| ~ ~ ( ~ ( qmltpeq @ SV34 @ SV61 @ SV6 )
| ~ ( disjoint @ SV80 @ SV34 @ SV6 ) )
| ( disjoint @ SV80 @ SV61 @ SV6 ) )
= $true )
| ( ( exists_in_world @ SV61 @ SV6 )
= $false )
| ( ( exists_in_world @ SV34 @ SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[306]) ).
thf(331,plain,
! [SV62: mu,SV35: mu,SV7: $i,SV81: mu] :
( ( ( ~ ( exists_in_world @ SV81 @ SV7 )
| ~ ~ ( ~ ( qmltpeq @ SV35 @ SV62 @ SV7 )
| ~ ( in @ SV35 @ SV81 @ SV7 ) )
| ( in @ SV62 @ SV81 @ SV7 ) )
= $true )
| ( ( exists_in_world @ SV62 @ SV7 )
= $false )
| ( ( exists_in_world @ SV35 @ SV7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[307]) ).
thf(332,plain,
! [SV63: mu,SV36: mu,SV8: $i,SV82: mu] :
( ( ( ~ ( exists_in_world @ SV82 @ SV8 )
| ~ ( qmltpeq @ SV36 @ SV63 @ SV8 )
| ( qmltpeq @ ( unordered_pair @ SV36 @ SV82 ) @ ( unordered_pair @ SV63 @ SV82 ) @ SV8 ) )
= $true )
| ( ( exists_in_world @ SV63 @ SV8 )
= $false )
| ( ( exists_in_world @ SV36 @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[308]) ).
thf(333,plain,
! [SV65: mu,SV38: mu,SV10: $i,SV83: mu] :
( ( ( ~ ( exists_in_world @ SV83 @ SV10 )
| ~ ( ~ ( ~ ( qmltpeq @ SV83 @ ( set_intersection2 @ SV38 @ SV65 ) @ SV10 )
| ! [SY967: mu] :
( ~ ( exists_in_world @ SY967 @ SV10 )
| ~ ( ~ ( ~ ( in @ SY967 @ SV83 @ SV10 )
| ~ ( ~ ( in @ SY967 @ SV38 @ SV10 )
| ~ ( in @ SY967 @ SV65 @ SV10 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY967 @ SV38 @ SV10 )
| ~ ( in @ SY967 @ SV65 @ SV10 ) )
| ( in @ SY967 @ SV83 @ SV10 ) ) ) ) )
| ~ ( ~ ! [SY968: mu] :
( ~ ( exists_in_world @ SY968 @ SV10 )
| ~ ( ~ ( ~ ( in @ SY968 @ SV83 @ SV10 )
| ~ ( ~ ( in @ SY968 @ SV38 @ SV10 )
| ~ ( in @ SY968 @ SV65 @ SV10 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY968 @ SV38 @ SV10 )
| ~ ( in @ SY968 @ SV65 @ SV10 ) )
| ( in @ SY968 @ SV83 @ SV10 ) ) ) )
| ( qmltpeq @ SV83 @ ( set_intersection2 @ SV38 @ SV65 ) @ SV10 ) ) ) )
= $true )
| ( ( exists_in_world @ SV65 @ SV10 )
= $false )
| ( ( exists_in_world @ SV38 @ SV10 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[310]) ).
thf(334,plain,
! [SV11: $i,SV39: mu] :
( ( ( ~ ( qmltpeq @ SV39 @ empty_set @ SV11 ) )
= $true )
| ( ( ! [SY924: mu] :
( ~ ( exists_in_world @ SY924 @ SV11 )
| ~ ( in @ SY924 @ SV39 @ SV11 ) ) )
= $true )
| ( ( exists_in_world @ SV39 @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[311]) ).
thf(335,plain,
! [SV39: mu,SV11: $i] :
( ( ( ~ ! [SY925: mu] :
( ~ ( exists_in_world @ SY925 @ SV11 )
| ~ ( in @ SY925 @ SV39 @ SV11 ) ) )
= $true )
| ( ( qmltpeq @ SV39 @ empty_set @ SV11 )
= $true )
| ( ( exists_in_world @ SV39 @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[312]) ).
thf(336,plain,
! [SV59: $i,SV41: $i,SV14: $i] :
( ( ( rel_s4 @ SV14 @ SV41 )
= $false )
| ( ( ~ ( rel_s4 @ SV41 @ SV59 ) )
= $true )
| ( ( rel_s4 @ SV14 @ SV59 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[314]) ).
thf(337,plain,
! [SV60: $i,SV42: $i,SV16: mu] :
( ( ( exists_in_world @ SV16 @ SV42 )
= $false )
| ( ( ~ ( rel_s4 @ SV42 @ SV60 ) )
= $true )
| ( ( exists_in_world @ SV16 @ SV60 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[315]) ).
thf(338,plain,
! [SV67: mu,SV43: mu,SV17: $i,SV84: mu] :
( ( ( ~ ( exists_in_world @ SV84 @ SV17 )
| ~ ( qmltpeq @ SV43 @ SV67 @ SV17 )
| ( qmltpeq @ ( unordered_pair @ SV84 @ SV43 ) @ ( unordered_pair @ SV84 @ SV67 ) @ SV17 ) )
= $true )
| ( ( exists_in_world @ SV67 @ SV17 )
= $false )
| ( ( exists_in_world @ SV43 @ SV17 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[316]) ).
thf(339,plain,
! [SV18: $i,SV68: mu,SV44: mu] :
( ( ( ~ ~ ( ~ ( qmltpeq @ SV44 @ SV68 @ SV18 )
| ~ ( empty @ SV44 @ SV18 ) ) )
= $true )
| ( ( empty @ SV68 @ SV18 )
= $true )
| ( ( exists_in_world @ SV68 @ SV18 )
= $false )
| ( ( exists_in_world @ SV44 @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[317]) ).
thf(340,plain,
! [SV19: $i,SV69: mu,SV45: mu] :
( ( ( ~ ( in @ SV45 @ SV69 @ SV19 ) )
= $true )
| ( ( ~ ( in @ SV69 @ SV45 @ SV19 ) )
= $true )
| ( ( exists_in_world @ SV69 @ SV19 )
= $false )
| ( ( exists_in_world @ SV45 @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[318]) ).
thf(341,plain,
! [SV71: mu,SV47: mu,SV22: $i,SV85: mu] :
( ( ( ~ ( exists_in_world @ SV85 @ SV22 )
| ~ ~ ( ~ ( qmltpeq @ SV47 @ SV71 @ SV22 )
| ~ ( disjoint @ SV47 @ SV85 @ SV22 ) )
| ( disjoint @ SV71 @ SV85 @ SV22 ) )
= $true )
| ( ( exists_in_world @ SV71 @ SV22 )
= $false )
| ( ( exists_in_world @ SV47 @ SV22 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[320]) ).
thf(342,plain,
! [SV72: mu,SV48: mu,SV23: $i,SV86: mu] :
( ( ( ~ ( exists_in_world @ SV86 @ SV23 )
| ~ ( ~ ( ~ ( qmltpeq @ SV86 @ ( unordered_pair @ SV48 @ SV72 ) @ SV23 )
| ! [SY969: mu] :
( ~ ( exists_in_world @ SY969 @ SV23 )
| ~ ( ~ ( ~ ( in @ SY969 @ SV86 @ SV23 )
| ( qmltpeq @ SY969 @ SV48 @ SV23 )
| ( qmltpeq @ SY969 @ SV72 @ SV23 ) )
| ~ ( ~ ( ( qmltpeq @ SY969 @ SV48 @ SV23 )
| ( qmltpeq @ SY969 @ SV72 @ SV23 ) )
| ( in @ SY969 @ SV86 @ SV23 ) ) ) ) )
| ~ ( ~ ! [SY970: mu] :
( ~ ( exists_in_world @ SY970 @ SV23 )
| ~ ( ~ ( ~ ( in @ SY970 @ SV86 @ SV23 )
| ( qmltpeq @ SY970 @ SV48 @ SV23 )
| ( qmltpeq @ SY970 @ SV72 @ SV23 ) )
| ~ ( ~ ( ( qmltpeq @ SY970 @ SV48 @ SV23 )
| ( qmltpeq @ SY970 @ SV72 @ SV23 ) )
| ( in @ SY970 @ SV86 @ SV23 ) ) ) )
| ( qmltpeq @ SV86 @ ( unordered_pair @ SV48 @ SV72 ) @ SV23 ) ) ) )
= $true )
| ( ( exists_in_world @ SV72 @ SV23 )
= $false )
| ( ( exists_in_world @ SV48 @ SV23 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[321]) ).
thf(343,plain,
! [SV73: mu,SV49: mu,SV24: $i,SV87: mu] :
( ( ( ~ ( exists_in_world @ SV87 @ SV24 )
| ~ ( qmltpeq @ SV49 @ SV73 @ SV24 )
| ( qmltpeq @ ( set_intersection2 @ SV49 @ SV87 ) @ ( set_intersection2 @ SV73 @ SV87 ) @ SV24 ) )
= $true )
| ( ( exists_in_world @ SV73 @ SV24 )
= $false )
| ( ( exists_in_world @ SV49 @ SV24 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[322]) ).
thf(344,plain,
! [SV26: $i,SV74: mu,SV51: mu] :
( ( ( ~ ( ~ ( disjoint @ SV51 @ SV74 @ SV26 )
| ( qmltpeq @ ( set_intersection2 @ SV51 @ SV74 ) @ empty_set @ SV26 ) )
| ~ ( ~ ( qmltpeq @ ( set_intersection2 @ SV51 @ SV74 ) @ empty_set @ SV26 )
| ( disjoint @ SV51 @ SV74 @ SV26 ) ) )
= $false )
| ( ( exists_in_world @ SV74 @ SV26 )
= $false )
| ( ( exists_in_world @ SV51 @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[323]) ).
thf(345,plain,
! [SV27: $i,SV75: mu,SV52: mu] :
( ( ( ~ ( disjoint @ SV52 @ SV75 @ SV27 ) )
= $true )
| ( ( disjoint @ SV75 @ SV52 @ SV27 )
= $true )
| ( ( exists_in_world @ SV75 @ SV27 )
= $false )
| ( ( exists_in_world @ SV52 @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[324]) ).
thf(346,plain,
! [SV28: $i,SV76: mu,SV53: mu] :
( ( ( ~ ( qmltpeq @ SV53 @ SV76 @ SV28 ) )
= $true )
| ( ( qmltpeq @ SV76 @ SV53 @ SV28 )
= $true )
| ( ( exists_in_world @ SV76 @ SV28 )
= $false )
| ( ( exists_in_world @ SV53 @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[325]) ).
thf(347,plain,
! [SV77: mu,SV54: mu,SV29: $i,SV88: mu] :
( ( ( ~ ( exists_in_world @ SV88 @ SV29 )
| ~ ~ ( ~ ( qmltpeq @ SV54 @ SV77 @ SV29 )
| ~ ( in @ SV88 @ SV54 @ SV29 ) )
| ( in @ SV88 @ SV77 @ SV29 ) )
= $true )
| ( ( exists_in_world @ SV77 @ SV29 )
= $false )
| ( ( exists_in_world @ SV54 @ SV29 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[326]) ).
thf(348,plain,
! [SV78: mu,SV55: mu,SV30: $i,SV89: mu] :
( ( ( ~ ( exists_in_world @ SV89 @ SV30 )
| ~ ( qmltpeq @ SV55 @ SV78 @ SV30 )
| ( qmltpeq @ ( set_intersection2 @ SV89 @ SV55 ) @ ( set_intersection2 @ SV89 @ SV78 ) @ SV30 ) )
= $true )
| ( ( exists_in_world @ SV78 @ SV30 )
= $false )
| ( ( exists_in_world @ SV55 @ SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[327]) ).
thf(349,plain,
( ( ~ ( disjoint @ ( unordered_pair @ sK2_SY838 @ sK3_SX0 ) @ sK7_SY949 @ sK1_SY27 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[328]) ).
thf(350,plain,
( ( ~ ( in @ sK2_SY838 @ sK7_SY949 @ sK1_SY27 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[328]) ).
thf(351,plain,
! [SV79: mu,SV56: mu,SV31: $i,SV90: mu] :
( ( ( ~ ( exists_in_world @ SV90 @ SV31 )
| ~ ~ ( ~ ( qmltpeq @ SV56 @ SV79 @ SV31 )
| ~ ( qmltpeq @ SV79 @ SV90 @ SV31 ) )
| ( qmltpeq @ SV56 @ SV90 @ SV31 ) )
= $true )
| ( ( exists_in_world @ SV79 @ SV31 )
= $false )
| ( ( exists_in_world @ SV56 @ SV31 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[329]) ).
thf(352,plain,
! [SV61: mu,SV34: mu,SV6: $i,SV80: mu] :
( ( ( ~ ( exists_in_world @ SV80 @ SV6 ) )
= $true )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV34 @ SV61 @ SV6 )
| ~ ( disjoint @ SV80 @ SV34 @ SV6 ) )
| ( disjoint @ SV80 @ SV61 @ SV6 ) )
= $true )
| ( ( exists_in_world @ SV61 @ SV6 )
= $false )
| ( ( exists_in_world @ SV34 @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[330]) ).
thf(353,plain,
! [SV62: mu,SV35: mu,SV7: $i,SV81: mu] :
( ( ( ~ ( exists_in_world @ SV81 @ SV7 ) )
= $true )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV35 @ SV62 @ SV7 )
| ~ ( in @ SV35 @ SV81 @ SV7 ) )
| ( in @ SV62 @ SV81 @ SV7 ) )
= $true )
| ( ( exists_in_world @ SV62 @ SV7 )
= $false )
| ( ( exists_in_world @ SV35 @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[331]) ).
thf(354,plain,
! [SV63: mu,SV36: mu,SV8: $i,SV82: mu] :
( ( ( ~ ( exists_in_world @ SV82 @ SV8 ) )
= $true )
| ( ( ~ ( qmltpeq @ SV36 @ SV63 @ SV8 )
| ( qmltpeq @ ( unordered_pair @ SV36 @ SV82 ) @ ( unordered_pair @ SV63 @ SV82 ) @ SV8 ) )
= $true )
| ( ( exists_in_world @ SV63 @ SV8 )
= $false )
| ( ( exists_in_world @ SV36 @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[332]) ).
thf(355,plain,
! [SV65: mu,SV38: mu,SV10: $i,SV83: mu] :
( ( ( ~ ( exists_in_world @ SV83 @ SV10 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( qmltpeq @ SV83 @ ( set_intersection2 @ SV38 @ SV65 ) @ SV10 )
| ! [SY967: mu] :
( ~ ( exists_in_world @ SY967 @ SV10 )
| ~ ( ~ ( ~ ( in @ SY967 @ SV83 @ SV10 )
| ~ ( ~ ( in @ SY967 @ SV38 @ SV10 )
| ~ ( in @ SY967 @ SV65 @ SV10 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY967 @ SV38 @ SV10 )
| ~ ( in @ SY967 @ SV65 @ SV10 ) )
| ( in @ SY967 @ SV83 @ SV10 ) ) ) ) )
| ~ ( ~ ! [SY968: mu] :
( ~ ( exists_in_world @ SY968 @ SV10 )
| ~ ( ~ ( ~ ( in @ SY968 @ SV83 @ SV10 )
| ~ ( ~ ( in @ SY968 @ SV38 @ SV10 )
| ~ ( in @ SY968 @ SV65 @ SV10 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY968 @ SV38 @ SV10 )
| ~ ( in @ SY968 @ SV65 @ SV10 ) )
| ( in @ SY968 @ SV83 @ SV10 ) ) ) )
| ( qmltpeq @ SV83 @ ( set_intersection2 @ SV38 @ SV65 ) @ SV10 ) ) ) )
= $true )
| ( ( exists_in_world @ SV65 @ SV10 )
= $false )
| ( ( exists_in_world @ SV38 @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[333]) ).
thf(356,plain,
! [SV11: $i,SV39: mu] :
( ( ( qmltpeq @ SV39 @ empty_set @ SV11 )
= $false )
| ( ( ! [SY924: mu] :
( ~ ( exists_in_world @ SY924 @ SV11 )
| ~ ( in @ SY924 @ SV39 @ SV11 ) ) )
= $true )
| ( ( exists_in_world @ SV39 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[334]) ).
thf(357,plain,
! [SV39: mu,SV11: $i] :
( ( ( ! [SY925: mu] :
( ~ ( exists_in_world @ SY925 @ SV11 )
| ~ ( in @ SY925 @ SV39 @ SV11 ) ) )
= $false )
| ( ( qmltpeq @ SV39 @ empty_set @ SV11 )
= $true )
| ( ( exists_in_world @ SV39 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[335]) ).
thf(358,plain,
! [SV14: $i,SV59: $i,SV41: $i] :
( ( ( rel_s4 @ SV41 @ SV59 )
= $false )
| ( ( rel_s4 @ SV14 @ SV41 )
= $false )
| ( ( rel_s4 @ SV14 @ SV59 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[336]) ).
thf(359,plain,
! [SV16: mu,SV60: $i,SV42: $i] :
( ( ( rel_s4 @ SV42 @ SV60 )
= $false )
| ( ( exists_in_world @ SV16 @ SV42 )
= $false )
| ( ( exists_in_world @ SV16 @ SV60 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[337]) ).
thf(360,plain,
! [SV67: mu,SV43: mu,SV17: $i,SV84: mu] :
( ( ( ~ ( exists_in_world @ SV84 @ SV17 ) )
= $true )
| ( ( ~ ( qmltpeq @ SV43 @ SV67 @ SV17 )
| ( qmltpeq @ ( unordered_pair @ SV84 @ SV43 ) @ ( unordered_pair @ SV84 @ SV67 ) @ SV17 ) )
= $true )
| ( ( exists_in_world @ SV67 @ SV17 )
= $false )
| ( ( exists_in_world @ SV43 @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[338]) ).
thf(361,plain,
! [SV18: $i,SV68: mu,SV44: mu] :
( ( ( ~ ( ~ ( qmltpeq @ SV44 @ SV68 @ SV18 )
| ~ ( empty @ SV44 @ SV18 ) ) )
= $false )
| ( ( empty @ SV68 @ SV18 )
= $true )
| ( ( exists_in_world @ SV68 @ SV18 )
= $false )
| ( ( exists_in_world @ SV44 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[339]) ).
thf(362,plain,
! [SV19: $i,SV69: mu,SV45: mu] :
( ( ( in @ SV45 @ SV69 @ SV19 )
= $false )
| ( ( ~ ( in @ SV69 @ SV45 @ SV19 ) )
= $true )
| ( ( exists_in_world @ SV69 @ SV19 )
= $false )
| ( ( exists_in_world @ SV45 @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[340]) ).
thf(363,plain,
! [SV71: mu,SV47: mu,SV22: $i,SV85: mu] :
( ( ( ~ ( exists_in_world @ SV85 @ SV22 ) )
= $true )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV47 @ SV71 @ SV22 )
| ~ ( disjoint @ SV47 @ SV85 @ SV22 ) )
| ( disjoint @ SV71 @ SV85 @ SV22 ) )
= $true )
| ( ( exists_in_world @ SV71 @ SV22 )
= $false )
| ( ( exists_in_world @ SV47 @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[341]) ).
thf(364,plain,
! [SV72: mu,SV48: mu,SV23: $i,SV86: mu] :
( ( ( ~ ( exists_in_world @ SV86 @ SV23 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( qmltpeq @ SV86 @ ( unordered_pair @ SV48 @ SV72 ) @ SV23 )
| ! [SY969: mu] :
( ~ ( exists_in_world @ SY969 @ SV23 )
| ~ ( ~ ( ~ ( in @ SY969 @ SV86 @ SV23 )
| ( qmltpeq @ SY969 @ SV48 @ SV23 )
| ( qmltpeq @ SY969 @ SV72 @ SV23 ) )
| ~ ( ~ ( ( qmltpeq @ SY969 @ SV48 @ SV23 )
| ( qmltpeq @ SY969 @ SV72 @ SV23 ) )
| ( in @ SY969 @ SV86 @ SV23 ) ) ) ) )
| ~ ( ~ ! [SY970: mu] :
( ~ ( exists_in_world @ SY970 @ SV23 )
| ~ ( ~ ( ~ ( in @ SY970 @ SV86 @ SV23 )
| ( qmltpeq @ SY970 @ SV48 @ SV23 )
| ( qmltpeq @ SY970 @ SV72 @ SV23 ) )
| ~ ( ~ ( ( qmltpeq @ SY970 @ SV48 @ SV23 )
| ( qmltpeq @ SY970 @ SV72 @ SV23 ) )
| ( in @ SY970 @ SV86 @ SV23 ) ) ) )
| ( qmltpeq @ SV86 @ ( unordered_pair @ SV48 @ SV72 ) @ SV23 ) ) ) )
= $true )
| ( ( exists_in_world @ SV72 @ SV23 )
= $false )
| ( ( exists_in_world @ SV48 @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[342]) ).
thf(365,plain,
! [SV73: mu,SV49: mu,SV24: $i,SV87: mu] :
( ( ( ~ ( exists_in_world @ SV87 @ SV24 ) )
= $true )
| ( ( ~ ( qmltpeq @ SV49 @ SV73 @ SV24 )
| ( qmltpeq @ ( set_intersection2 @ SV49 @ SV87 ) @ ( set_intersection2 @ SV73 @ SV87 ) @ SV24 ) )
= $true )
| ( ( exists_in_world @ SV73 @ SV24 )
= $false )
| ( ( exists_in_world @ SV49 @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[343]) ).
thf(366,plain,
! [SV26: $i,SV74: mu,SV51: mu] :
( ( ( ~ ( ~ ( disjoint @ SV51 @ SV74 @ SV26 )
| ( qmltpeq @ ( set_intersection2 @ SV51 @ SV74 ) @ empty_set @ SV26 ) ) )
= $false )
| ( ( exists_in_world @ SV74 @ SV26 )
= $false )
| ( ( exists_in_world @ SV51 @ SV26 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[344]) ).
thf(367,plain,
! [SV26: $i,SV74: mu,SV51: mu] :
( ( ( ~ ( ~ ( qmltpeq @ ( set_intersection2 @ SV51 @ SV74 ) @ empty_set @ SV26 )
| ( disjoint @ SV51 @ SV74 @ SV26 ) ) )
= $false )
| ( ( exists_in_world @ SV74 @ SV26 )
= $false )
| ( ( exists_in_world @ SV51 @ SV26 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[344]) ).
thf(368,plain,
! [SV27: $i,SV75: mu,SV52: mu] :
( ( ( disjoint @ SV52 @ SV75 @ SV27 )
= $false )
| ( ( disjoint @ SV75 @ SV52 @ SV27 )
= $true )
| ( ( exists_in_world @ SV75 @ SV27 )
= $false )
| ( ( exists_in_world @ SV52 @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[345]) ).
thf(369,plain,
! [SV28: $i,SV76: mu,SV53: mu] :
( ( ( qmltpeq @ SV53 @ SV76 @ SV28 )
= $false )
| ( ( qmltpeq @ SV76 @ SV53 @ SV28 )
= $true )
| ( ( exists_in_world @ SV76 @ SV28 )
= $false )
| ( ( exists_in_world @ SV53 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[346]) ).
thf(370,plain,
! [SV77: mu,SV54: mu,SV29: $i,SV88: mu] :
( ( ( ~ ( exists_in_world @ SV88 @ SV29 ) )
= $true )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV54 @ SV77 @ SV29 )
| ~ ( in @ SV88 @ SV54 @ SV29 ) )
| ( in @ SV88 @ SV77 @ SV29 ) )
= $true )
| ( ( exists_in_world @ SV77 @ SV29 )
= $false )
| ( ( exists_in_world @ SV54 @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[347]) ).
thf(371,plain,
! [SV78: mu,SV55: mu,SV30: $i,SV89: mu] :
( ( ( ~ ( exists_in_world @ SV89 @ SV30 ) )
= $true )
| ( ( ~ ( qmltpeq @ SV55 @ SV78 @ SV30 )
| ( qmltpeq @ ( set_intersection2 @ SV89 @ SV55 ) @ ( set_intersection2 @ SV89 @ SV78 ) @ SV30 ) )
= $true )
| ( ( exists_in_world @ SV78 @ SV30 )
= $false )
| ( ( exists_in_world @ SV55 @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[348]) ).
thf(372,plain,
( ( disjoint @ ( unordered_pair @ sK2_SY838 @ sK3_SX0 ) @ sK7_SY949 @ sK1_SY27 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[349]) ).
thf(373,plain,
( ( in @ sK2_SY838 @ sK7_SY949 @ sK1_SY27 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[350]) ).
thf(374,plain,
! [SV79: mu,SV56: mu,SV31: $i,SV90: mu] :
( ( ( ~ ( exists_in_world @ SV90 @ SV31 ) )
= $true )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV56 @ SV79 @ SV31 )
| ~ ( qmltpeq @ SV79 @ SV90 @ SV31 ) )
| ( qmltpeq @ SV56 @ SV90 @ SV31 ) )
= $true )
| ( ( exists_in_world @ SV79 @ SV31 )
= $false )
| ( ( exists_in_world @ SV56 @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[351]) ).
thf(375,plain,
! [SV61: mu,SV34: mu,SV6: $i,SV80: mu] :
( ( ( exists_in_world @ SV80 @ SV6 )
= $false )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV34 @ SV61 @ SV6 )
| ~ ( disjoint @ SV80 @ SV34 @ SV6 ) )
| ( disjoint @ SV80 @ SV61 @ SV6 ) )
= $true )
| ( ( exists_in_world @ SV61 @ SV6 )
= $false )
| ( ( exists_in_world @ SV34 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[352]) ).
thf(376,plain,
! [SV62: mu,SV35: mu,SV7: $i,SV81: mu] :
( ( ( exists_in_world @ SV81 @ SV7 )
= $false )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV35 @ SV62 @ SV7 )
| ~ ( in @ SV35 @ SV81 @ SV7 ) )
| ( in @ SV62 @ SV81 @ SV7 ) )
= $true )
| ( ( exists_in_world @ SV62 @ SV7 )
= $false )
| ( ( exists_in_world @ SV35 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[353]) ).
thf(377,plain,
! [SV63: mu,SV36: mu,SV8: $i,SV82: mu] :
( ( ( exists_in_world @ SV82 @ SV8 )
= $false )
| ( ( ~ ( qmltpeq @ SV36 @ SV63 @ SV8 )
| ( qmltpeq @ ( unordered_pair @ SV36 @ SV82 ) @ ( unordered_pair @ SV63 @ SV82 ) @ SV8 ) )
= $true )
| ( ( exists_in_world @ SV63 @ SV8 )
= $false )
| ( ( exists_in_world @ SV36 @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[354]) ).
thf(378,plain,
! [SV65: mu,SV38: mu,SV10: $i,SV83: mu] :
( ( ( exists_in_world @ SV83 @ SV10 )
= $false )
| ( ( ~ ( ~ ( ~ ( qmltpeq @ SV83 @ ( set_intersection2 @ SV38 @ SV65 ) @ SV10 )
| ! [SY967: mu] :
( ~ ( exists_in_world @ SY967 @ SV10 )
| ~ ( ~ ( ~ ( in @ SY967 @ SV83 @ SV10 )
| ~ ( ~ ( in @ SY967 @ SV38 @ SV10 )
| ~ ( in @ SY967 @ SV65 @ SV10 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY967 @ SV38 @ SV10 )
| ~ ( in @ SY967 @ SV65 @ SV10 ) )
| ( in @ SY967 @ SV83 @ SV10 ) ) ) ) )
| ~ ( ~ ! [SY968: mu] :
( ~ ( exists_in_world @ SY968 @ SV10 )
| ~ ( ~ ( ~ ( in @ SY968 @ SV83 @ SV10 )
| ~ ( ~ ( in @ SY968 @ SV38 @ SV10 )
| ~ ( in @ SY968 @ SV65 @ SV10 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY968 @ SV38 @ SV10 )
| ~ ( in @ SY968 @ SV65 @ SV10 ) )
| ( in @ SY968 @ SV83 @ SV10 ) ) ) )
| ( qmltpeq @ SV83 @ ( set_intersection2 @ SV38 @ SV65 ) @ SV10 ) ) ) )
= $true )
| ( ( exists_in_world @ SV65 @ SV10 )
= $false )
| ( ( exists_in_world @ SV38 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[355]) ).
thf(379,plain,
! [SV39: mu,SV11: $i,SV91: mu] :
( ( ( ~ ( exists_in_world @ SV91 @ SV11 )
| ~ ( in @ SV91 @ SV39 @ SV11 ) )
= $true )
| ( ( qmltpeq @ SV39 @ empty_set @ SV11 )
= $false )
| ( ( exists_in_world @ SV39 @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[356]) ).
thf(380,plain,
! [SV11: $i,SV39: mu] :
( ( ( ~ ( exists_in_world @ ( sK8_SY925 @ SV39 @ SV11 ) @ SV11 )
| ~ ( in @ ( sK8_SY925 @ SV39 @ SV11 ) @ SV39 @ SV11 ) )
= $false )
| ( ( qmltpeq @ SV39 @ empty_set @ SV11 )
= $true )
| ( ( exists_in_world @ SV39 @ SV11 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[357]) ).
thf(381,plain,
! [SV67: mu,SV43: mu,SV17: $i,SV84: mu] :
( ( ( exists_in_world @ SV84 @ SV17 )
= $false )
| ( ( ~ ( qmltpeq @ SV43 @ SV67 @ SV17 )
| ( qmltpeq @ ( unordered_pair @ SV84 @ SV43 ) @ ( unordered_pair @ SV84 @ SV67 ) @ SV17 ) )
= $true )
| ( ( exists_in_world @ SV67 @ SV17 )
= $false )
| ( ( exists_in_world @ SV43 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[360]) ).
thf(382,plain,
! [SV18: $i,SV68: mu,SV44: mu] :
( ( ( ~ ( qmltpeq @ SV44 @ SV68 @ SV18 )
| ~ ( empty @ SV44 @ SV18 ) )
= $true )
| ( ( empty @ SV68 @ SV18 )
= $true )
| ( ( exists_in_world @ SV68 @ SV18 )
= $false )
| ( ( exists_in_world @ SV44 @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[361]) ).
thf(383,plain,
! [SV19: $i,SV45: mu,SV69: mu] :
( ( ( in @ SV69 @ SV45 @ SV19 )
= $false )
| ( ( in @ SV45 @ SV69 @ SV19 )
= $false )
| ( ( exists_in_world @ SV69 @ SV19 )
= $false )
| ( ( exists_in_world @ SV45 @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[362]) ).
thf(384,plain,
! [SV71: mu,SV47: mu,SV22: $i,SV85: mu] :
( ( ( exists_in_world @ SV85 @ SV22 )
= $false )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV47 @ SV71 @ SV22 )
| ~ ( disjoint @ SV47 @ SV85 @ SV22 ) )
| ( disjoint @ SV71 @ SV85 @ SV22 ) )
= $true )
| ( ( exists_in_world @ SV71 @ SV22 )
= $false )
| ( ( exists_in_world @ SV47 @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[363]) ).
thf(385,plain,
! [SV72: mu,SV48: mu,SV23: $i,SV86: mu] :
( ( ( exists_in_world @ SV86 @ SV23 )
= $false )
| ( ( ~ ( ~ ( ~ ( qmltpeq @ SV86 @ ( unordered_pair @ SV48 @ SV72 ) @ SV23 )
| ! [SY969: mu] :
( ~ ( exists_in_world @ SY969 @ SV23 )
| ~ ( ~ ( ~ ( in @ SY969 @ SV86 @ SV23 )
| ( qmltpeq @ SY969 @ SV48 @ SV23 )
| ( qmltpeq @ SY969 @ SV72 @ SV23 ) )
| ~ ( ~ ( ( qmltpeq @ SY969 @ SV48 @ SV23 )
| ( qmltpeq @ SY969 @ SV72 @ SV23 ) )
| ( in @ SY969 @ SV86 @ SV23 ) ) ) ) )
| ~ ( ~ ! [SY970: mu] :
( ~ ( exists_in_world @ SY970 @ SV23 )
| ~ ( ~ ( ~ ( in @ SY970 @ SV86 @ SV23 )
| ( qmltpeq @ SY970 @ SV48 @ SV23 )
| ( qmltpeq @ SY970 @ SV72 @ SV23 ) )
| ~ ( ~ ( ( qmltpeq @ SY970 @ SV48 @ SV23 )
| ( qmltpeq @ SY970 @ SV72 @ SV23 ) )
| ( in @ SY970 @ SV86 @ SV23 ) ) ) )
| ( qmltpeq @ SV86 @ ( unordered_pair @ SV48 @ SV72 ) @ SV23 ) ) ) )
= $true )
| ( ( exists_in_world @ SV72 @ SV23 )
= $false )
| ( ( exists_in_world @ SV48 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[364]) ).
thf(386,plain,
! [SV73: mu,SV49: mu,SV24: $i,SV87: mu] :
( ( ( exists_in_world @ SV87 @ SV24 )
= $false )
| ( ( ~ ( qmltpeq @ SV49 @ SV73 @ SV24 )
| ( qmltpeq @ ( set_intersection2 @ SV49 @ SV87 ) @ ( set_intersection2 @ SV73 @ SV87 ) @ SV24 ) )
= $true )
| ( ( exists_in_world @ SV73 @ SV24 )
= $false )
| ( ( exists_in_world @ SV49 @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[365]) ).
thf(387,plain,
! [SV26: $i,SV74: mu,SV51: mu] :
( ( ( ~ ( disjoint @ SV51 @ SV74 @ SV26 )
| ( qmltpeq @ ( set_intersection2 @ SV51 @ SV74 ) @ empty_set @ SV26 ) )
= $true )
| ( ( exists_in_world @ SV74 @ SV26 )
= $false )
| ( ( exists_in_world @ SV51 @ SV26 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[366]) ).
thf(388,plain,
! [SV26: $i,SV74: mu,SV51: mu] :
( ( ( ~ ( qmltpeq @ ( set_intersection2 @ SV51 @ SV74 ) @ empty_set @ SV26 )
| ( disjoint @ SV51 @ SV74 @ SV26 ) )
= $true )
| ( ( exists_in_world @ SV74 @ SV26 )
= $false )
| ( ( exists_in_world @ SV51 @ SV26 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[367]) ).
thf(389,plain,
! [SV77: mu,SV54: mu,SV29: $i,SV88: mu] :
( ( ( exists_in_world @ SV88 @ SV29 )
= $false )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV54 @ SV77 @ SV29 )
| ~ ( in @ SV88 @ SV54 @ SV29 ) )
| ( in @ SV88 @ SV77 @ SV29 ) )
= $true )
| ( ( exists_in_world @ SV77 @ SV29 )
= $false )
| ( ( exists_in_world @ SV54 @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[370]) ).
thf(390,plain,
! [SV78: mu,SV55: mu,SV30: $i,SV89: mu] :
( ( ( exists_in_world @ SV89 @ SV30 )
= $false )
| ( ( ~ ( qmltpeq @ SV55 @ SV78 @ SV30 )
| ( qmltpeq @ ( set_intersection2 @ SV89 @ SV55 ) @ ( set_intersection2 @ SV89 @ SV78 ) @ SV30 ) )
= $true )
| ( ( exists_in_world @ SV78 @ SV30 )
= $false )
| ( ( exists_in_world @ SV55 @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[371]) ).
thf(391,plain,
! [SV79: mu,SV56: mu,SV31: $i,SV90: mu] :
( ( ( exists_in_world @ SV90 @ SV31 )
= $false )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV56 @ SV79 @ SV31 )
| ~ ( qmltpeq @ SV79 @ SV90 @ SV31 ) )
| ( qmltpeq @ SV56 @ SV90 @ SV31 ) )
= $true )
| ( ( exists_in_world @ SV79 @ SV31 )
= $false )
| ( ( exists_in_world @ SV56 @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[374]) ).
thf(392,plain,
! [SV80: mu,SV6: $i,SV61: mu,SV34: mu] :
( ( ( ~ ~ ( ~ ( qmltpeq @ SV34 @ SV61 @ SV6 )
| ~ ( disjoint @ SV80 @ SV34 @ SV6 ) ) )
= $true )
| ( ( disjoint @ SV80 @ SV61 @ SV6 )
= $true )
| ( ( exists_in_world @ SV80 @ SV6 )
= $false )
| ( ( exists_in_world @ SV61 @ SV6 )
= $false )
| ( ( exists_in_world @ SV34 @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[375]) ).
thf(393,plain,
! [SV81: mu,SV7: $i,SV62: mu,SV35: mu] :
( ( ( ~ ~ ( ~ ( qmltpeq @ SV35 @ SV62 @ SV7 )
| ~ ( in @ SV35 @ SV81 @ SV7 ) ) )
= $true )
| ( ( in @ SV62 @ SV81 @ SV7 )
= $true )
| ( ( exists_in_world @ SV81 @ SV7 )
= $false )
| ( ( exists_in_world @ SV62 @ SV7 )
= $false )
| ( ( exists_in_world @ SV35 @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[376]) ).
thf(394,plain,
! [SV82: mu,SV8: $i,SV63: mu,SV36: mu] :
( ( ( ~ ( qmltpeq @ SV36 @ SV63 @ SV8 ) )
= $true )
| ( ( qmltpeq @ ( unordered_pair @ SV36 @ SV82 ) @ ( unordered_pair @ SV63 @ SV82 ) @ SV8 )
= $true )
| ( ( exists_in_world @ SV82 @ SV8 )
= $false )
| ( ( exists_in_world @ SV63 @ SV8 )
= $false )
| ( ( exists_in_world @ SV36 @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[377]) ).
thf(395,plain,
! [SV10: $i,SV65: mu,SV38: mu,SV83: mu] :
( ( ( ~ ( ~ ( qmltpeq @ SV83 @ ( set_intersection2 @ SV38 @ SV65 ) @ SV10 )
| ! [SY967: mu] :
( ~ ( exists_in_world @ SY967 @ SV10 )
| ~ ( ~ ( ~ ( in @ SY967 @ SV83 @ SV10 )
| ~ ( ~ ( in @ SY967 @ SV38 @ SV10 )
| ~ ( in @ SY967 @ SV65 @ SV10 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY967 @ SV38 @ SV10 )
| ~ ( in @ SY967 @ SV65 @ SV10 ) )
| ( in @ SY967 @ SV83 @ SV10 ) ) ) ) )
| ~ ( ~ ! [SY968: mu] :
( ~ ( exists_in_world @ SY968 @ SV10 )
| ~ ( ~ ( ~ ( in @ SY968 @ SV83 @ SV10 )
| ~ ( ~ ( in @ SY968 @ SV38 @ SV10 )
| ~ ( in @ SY968 @ SV65 @ SV10 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY968 @ SV38 @ SV10 )
| ~ ( in @ SY968 @ SV65 @ SV10 ) )
| ( in @ SY968 @ SV83 @ SV10 ) ) ) )
| ( qmltpeq @ SV83 @ ( set_intersection2 @ SV38 @ SV65 ) @ SV10 ) ) )
= $false )
| ( ( exists_in_world @ SV83 @ SV10 )
= $false )
| ( ( exists_in_world @ SV65 @ SV10 )
= $false )
| ( ( exists_in_world @ SV38 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[378]) ).
thf(396,plain,
! [SV39: mu,SV11: $i,SV91: mu] :
( ( ( ~ ( exists_in_world @ SV91 @ SV11 ) )
= $true )
| ( ( ~ ( in @ SV91 @ SV39 @ SV11 ) )
= $true )
| ( ( qmltpeq @ SV39 @ empty_set @ SV11 )
= $false )
| ( ( exists_in_world @ SV39 @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[379]) ).
thf(397,plain,
! [SV11: $i,SV39: mu] :
( ( ( ~ ( exists_in_world @ ( sK8_SY925 @ SV39 @ SV11 ) @ SV11 ) )
= $false )
| ( ( qmltpeq @ SV39 @ empty_set @ SV11 )
= $true )
| ( ( exists_in_world @ SV39 @ SV11 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[380]) ).
thf(398,plain,
! [SV11: $i,SV39: mu] :
( ( ( ~ ( in @ ( sK8_SY925 @ SV39 @ SV11 ) @ SV39 @ SV11 ) )
= $false )
| ( ( qmltpeq @ SV39 @ empty_set @ SV11 )
= $true )
| ( ( exists_in_world @ SV39 @ SV11 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[380]) ).
thf(399,plain,
! [SV84: mu,SV17: $i,SV67: mu,SV43: mu] :
( ( ( ~ ( qmltpeq @ SV43 @ SV67 @ SV17 ) )
= $true )
| ( ( qmltpeq @ ( unordered_pair @ SV84 @ SV43 ) @ ( unordered_pair @ SV84 @ SV67 ) @ SV17 )
= $true )
| ( ( exists_in_world @ SV84 @ SV17 )
= $false )
| ( ( exists_in_world @ SV67 @ SV17 )
= $false )
| ( ( exists_in_world @ SV43 @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[381]) ).
thf(400,plain,
! [SV18: $i,SV68: mu,SV44: mu] :
( ( ( ~ ( qmltpeq @ SV44 @ SV68 @ SV18 ) )
= $true )
| ( ( ~ ( empty @ SV44 @ SV18 ) )
= $true )
| ( ( empty @ SV68 @ SV18 )
= $true )
| ( ( exists_in_world @ SV68 @ SV18 )
= $false )
| ( ( exists_in_world @ SV44 @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[382]) ).
thf(401,plain,
! [SV85: mu,SV22: $i,SV71: mu,SV47: mu] :
( ( ( ~ ~ ( ~ ( qmltpeq @ SV47 @ SV71 @ SV22 )
| ~ ( disjoint @ SV47 @ SV85 @ SV22 ) ) )
= $true )
| ( ( disjoint @ SV71 @ SV85 @ SV22 )
= $true )
| ( ( exists_in_world @ SV85 @ SV22 )
= $false )
| ( ( exists_in_world @ SV71 @ SV22 )
= $false )
| ( ( exists_in_world @ SV47 @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[384]) ).
thf(402,plain,
! [SV23: $i,SV72: mu,SV48: mu,SV86: mu] :
( ( ( ~ ( ~ ( qmltpeq @ SV86 @ ( unordered_pair @ SV48 @ SV72 ) @ SV23 )
| ! [SY969: mu] :
( ~ ( exists_in_world @ SY969 @ SV23 )
| ~ ( ~ ( ~ ( in @ SY969 @ SV86 @ SV23 )
| ( qmltpeq @ SY969 @ SV48 @ SV23 )
| ( qmltpeq @ SY969 @ SV72 @ SV23 ) )
| ~ ( ~ ( ( qmltpeq @ SY969 @ SV48 @ SV23 )
| ( qmltpeq @ SY969 @ SV72 @ SV23 ) )
| ( in @ SY969 @ SV86 @ SV23 ) ) ) ) )
| ~ ( ~ ! [SY970: mu] :
( ~ ( exists_in_world @ SY970 @ SV23 )
| ~ ( ~ ( ~ ( in @ SY970 @ SV86 @ SV23 )
| ( qmltpeq @ SY970 @ SV48 @ SV23 )
| ( qmltpeq @ SY970 @ SV72 @ SV23 ) )
| ~ ( ~ ( ( qmltpeq @ SY970 @ SV48 @ SV23 )
| ( qmltpeq @ SY970 @ SV72 @ SV23 ) )
| ( in @ SY970 @ SV86 @ SV23 ) ) ) )
| ( qmltpeq @ SV86 @ ( unordered_pair @ SV48 @ SV72 ) @ SV23 ) ) )
= $false )
| ( ( exists_in_world @ SV86 @ SV23 )
= $false )
| ( ( exists_in_world @ SV72 @ SV23 )
= $false )
| ( ( exists_in_world @ SV48 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[385]) ).
thf(403,plain,
! [SV87: mu,SV24: $i,SV73: mu,SV49: mu] :
( ( ( ~ ( qmltpeq @ SV49 @ SV73 @ SV24 ) )
= $true )
| ( ( qmltpeq @ ( set_intersection2 @ SV49 @ SV87 ) @ ( set_intersection2 @ SV73 @ SV87 ) @ SV24 )
= $true )
| ( ( exists_in_world @ SV87 @ SV24 )
= $false )
| ( ( exists_in_world @ SV73 @ SV24 )
= $false )
| ( ( exists_in_world @ SV49 @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[386]) ).
thf(404,plain,
! [SV26: $i,SV74: mu,SV51: mu] :
( ( ( ~ ( disjoint @ SV51 @ SV74 @ SV26 ) )
= $true )
| ( ( qmltpeq @ ( set_intersection2 @ SV51 @ SV74 ) @ empty_set @ SV26 )
= $true )
| ( ( exists_in_world @ SV74 @ SV26 )
= $false )
| ( ( exists_in_world @ SV51 @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[387]) ).
thf(405,plain,
! [SV26: $i,SV74: mu,SV51: mu] :
( ( ( ~ ( qmltpeq @ ( set_intersection2 @ SV51 @ SV74 ) @ empty_set @ SV26 ) )
= $true )
| ( ( disjoint @ SV51 @ SV74 @ SV26 )
= $true )
| ( ( exists_in_world @ SV74 @ SV26 )
= $false )
| ( ( exists_in_world @ SV51 @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[388]) ).
thf(406,plain,
! [SV88: mu,SV29: $i,SV77: mu,SV54: mu] :
( ( ( ~ ~ ( ~ ( qmltpeq @ SV54 @ SV77 @ SV29 )
| ~ ( in @ SV88 @ SV54 @ SV29 ) ) )
= $true )
| ( ( in @ SV88 @ SV77 @ SV29 )
= $true )
| ( ( exists_in_world @ SV88 @ SV29 )
= $false )
| ( ( exists_in_world @ SV77 @ SV29 )
= $false )
| ( ( exists_in_world @ SV54 @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[389]) ).
thf(407,plain,
! [SV89: mu,SV30: $i,SV78: mu,SV55: mu] :
( ( ( ~ ( qmltpeq @ SV55 @ SV78 @ SV30 ) )
= $true )
| ( ( qmltpeq @ ( set_intersection2 @ SV89 @ SV55 ) @ ( set_intersection2 @ SV89 @ SV78 ) @ SV30 )
= $true )
| ( ( exists_in_world @ SV89 @ SV30 )
= $false )
| ( ( exists_in_world @ SV78 @ SV30 )
= $false )
| ( ( exists_in_world @ SV55 @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[390]) ).
thf(408,plain,
! [SV90: mu,SV31: $i,SV79: mu,SV56: mu] :
( ( ( ~ ~ ( ~ ( qmltpeq @ SV56 @ SV79 @ SV31 )
| ~ ( qmltpeq @ SV79 @ SV90 @ SV31 ) ) )
= $true )
| ( ( qmltpeq @ SV56 @ SV90 @ SV31 )
= $true )
| ( ( exists_in_world @ SV90 @ SV31 )
= $false )
| ( ( exists_in_world @ SV79 @ SV31 )
= $false )
| ( ( exists_in_world @ SV56 @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[391]) ).
thf(409,plain,
! [SV80: mu,SV6: $i,SV61: mu,SV34: mu] :
( ( ( ~ ( ~ ( qmltpeq @ SV34 @ SV61 @ SV6 )
| ~ ( disjoint @ SV80 @ SV34 @ SV6 ) ) )
= $false )
| ( ( disjoint @ SV80 @ SV61 @ SV6 )
= $true )
| ( ( exists_in_world @ SV80 @ SV6 )
= $false )
| ( ( exists_in_world @ SV61 @ SV6 )
= $false )
| ( ( exists_in_world @ SV34 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[392]) ).
thf(410,plain,
! [SV81: mu,SV7: $i,SV62: mu,SV35: mu] :
( ( ( ~ ( ~ ( qmltpeq @ SV35 @ SV62 @ SV7 )
| ~ ( in @ SV35 @ SV81 @ SV7 ) ) )
= $false )
| ( ( in @ SV62 @ SV81 @ SV7 )
= $true )
| ( ( exists_in_world @ SV81 @ SV7 )
= $false )
| ( ( exists_in_world @ SV62 @ SV7 )
= $false )
| ( ( exists_in_world @ SV35 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[393]) ).
thf(411,plain,
! [SV82: mu,SV8: $i,SV63: mu,SV36: mu] :
( ( ( qmltpeq @ SV36 @ SV63 @ SV8 )
= $false )
| ( ( qmltpeq @ ( unordered_pair @ SV36 @ SV82 ) @ ( unordered_pair @ SV63 @ SV82 ) @ SV8 )
= $true )
| ( ( exists_in_world @ SV82 @ SV8 )
= $false )
| ( ( exists_in_world @ SV63 @ SV8 )
= $false )
| ( ( exists_in_world @ SV36 @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[394]) ).
thf(412,plain,
! [SV10: $i,SV65: mu,SV38: mu,SV83: mu] :
( ( ( ~ ( ~ ( qmltpeq @ SV83 @ ( set_intersection2 @ SV38 @ SV65 ) @ SV10 )
| ! [SY967: mu] :
( ~ ( exists_in_world @ SY967 @ SV10 )
| ~ ( ~ ( ~ ( in @ SY967 @ SV83 @ SV10 )
| ~ ( ~ ( in @ SY967 @ SV38 @ SV10 )
| ~ ( in @ SY967 @ SV65 @ SV10 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY967 @ SV38 @ SV10 )
| ~ ( in @ SY967 @ SV65 @ SV10 ) )
| ( in @ SY967 @ SV83 @ SV10 ) ) ) ) ) )
= $false )
| ( ( exists_in_world @ SV83 @ SV10 )
= $false )
| ( ( exists_in_world @ SV65 @ SV10 )
= $false )
| ( ( exists_in_world @ SV38 @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[395]) ).
thf(413,plain,
! [SV65: mu,SV38: mu,SV83: mu,SV10: $i] :
( ( ( ~ ( ~ ! [SY968: mu] :
( ~ ( exists_in_world @ SY968 @ SV10 )
| ~ ( ~ ( ~ ( in @ SY968 @ SV83 @ SV10 )
| ~ ( ~ ( in @ SY968 @ SV38 @ SV10 )
| ~ ( in @ SY968 @ SV65 @ SV10 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY968 @ SV38 @ SV10 )
| ~ ( in @ SY968 @ SV65 @ SV10 ) )
| ( in @ SY968 @ SV83 @ SV10 ) ) ) )
| ( qmltpeq @ SV83 @ ( set_intersection2 @ SV38 @ SV65 ) @ SV10 ) ) )
= $false )
| ( ( exists_in_world @ SV83 @ SV10 )
= $false )
| ( ( exists_in_world @ SV65 @ SV10 )
= $false )
| ( ( exists_in_world @ SV38 @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[395]) ).
thf(414,plain,
! [SV39: mu,SV11: $i,SV91: mu] :
( ( ( exists_in_world @ SV91 @ SV11 )
= $false )
| ( ( ~ ( in @ SV91 @ SV39 @ SV11 ) )
= $true )
| ( ( qmltpeq @ SV39 @ empty_set @ SV11 )
= $false )
| ( ( exists_in_world @ SV39 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[396]) ).
thf(415,plain,
! [SV11: $i,SV39: mu] :
( ( ( exists_in_world @ ( sK8_SY925 @ SV39 @ SV11 ) @ SV11 )
= $true )
| ( ( qmltpeq @ SV39 @ empty_set @ SV11 )
= $true )
| ( ( exists_in_world @ SV39 @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[397]) ).
thf(416,plain,
! [SV11: $i,SV39: mu] :
( ( ( in @ ( sK8_SY925 @ SV39 @ SV11 ) @ SV39 @ SV11 )
= $true )
| ( ( qmltpeq @ SV39 @ empty_set @ SV11 )
= $true )
| ( ( exists_in_world @ SV39 @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[398]) ).
thf(417,plain,
! [SV84: mu,SV17: $i,SV67: mu,SV43: mu] :
( ( ( qmltpeq @ SV43 @ SV67 @ SV17 )
= $false )
| ( ( qmltpeq @ ( unordered_pair @ SV84 @ SV43 ) @ ( unordered_pair @ SV84 @ SV67 ) @ SV17 )
= $true )
| ( ( exists_in_world @ SV84 @ SV17 )
= $false )
| ( ( exists_in_world @ SV67 @ SV17 )
= $false )
| ( ( exists_in_world @ SV43 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[399]) ).
thf(418,plain,
! [SV18: $i,SV68: mu,SV44: mu] :
( ( ( qmltpeq @ SV44 @ SV68 @ SV18 )
= $false )
| ( ( ~ ( empty @ SV44 @ SV18 ) )
= $true )
| ( ( empty @ SV68 @ SV18 )
= $true )
| ( ( exists_in_world @ SV68 @ SV18 )
= $false )
| ( ( exists_in_world @ SV44 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[400]) ).
thf(419,plain,
! [SV85: mu,SV22: $i,SV71: mu,SV47: mu] :
( ( ( ~ ( ~ ( qmltpeq @ SV47 @ SV71 @ SV22 )
| ~ ( disjoint @ SV47 @ SV85 @ SV22 ) ) )
= $false )
| ( ( disjoint @ SV71 @ SV85 @ SV22 )
= $true )
| ( ( exists_in_world @ SV85 @ SV22 )
= $false )
| ( ( exists_in_world @ SV71 @ SV22 )
= $false )
| ( ( exists_in_world @ SV47 @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[401]) ).
thf(420,plain,
! [SV23: $i,SV72: mu,SV48: mu,SV86: mu] :
( ( ( ~ ( ~ ( qmltpeq @ SV86 @ ( unordered_pair @ SV48 @ SV72 ) @ SV23 )
| ! [SY969: mu] :
( ~ ( exists_in_world @ SY969 @ SV23 )
| ~ ( ~ ( ~ ( in @ SY969 @ SV86 @ SV23 )
| ( qmltpeq @ SY969 @ SV48 @ SV23 )
| ( qmltpeq @ SY969 @ SV72 @ SV23 ) )
| ~ ( ~ ( ( qmltpeq @ SY969 @ SV48 @ SV23 )
| ( qmltpeq @ SY969 @ SV72 @ SV23 ) )
| ( in @ SY969 @ SV86 @ SV23 ) ) ) ) ) )
= $false )
| ( ( exists_in_world @ SV86 @ SV23 )
= $false )
| ( ( exists_in_world @ SV72 @ SV23 )
= $false )
| ( ( exists_in_world @ SV48 @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[402]) ).
thf(421,plain,
! [SV72: mu,SV48: mu,SV86: mu,SV23: $i] :
( ( ( ~ ( ~ ! [SY970: mu] :
( ~ ( exists_in_world @ SY970 @ SV23 )
| ~ ( ~ ( ~ ( in @ SY970 @ SV86 @ SV23 )
| ( qmltpeq @ SY970 @ SV48 @ SV23 )
| ( qmltpeq @ SY970 @ SV72 @ SV23 ) )
| ~ ( ~ ( ( qmltpeq @ SY970 @ SV48 @ SV23 )
| ( qmltpeq @ SY970 @ SV72 @ SV23 ) )
| ( in @ SY970 @ SV86 @ SV23 ) ) ) )
| ( qmltpeq @ SV86 @ ( unordered_pair @ SV48 @ SV72 ) @ SV23 ) ) )
= $false )
| ( ( exists_in_world @ SV86 @ SV23 )
= $false )
| ( ( exists_in_world @ SV72 @ SV23 )
= $false )
| ( ( exists_in_world @ SV48 @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[402]) ).
thf(422,plain,
! [SV87: mu,SV24: $i,SV73: mu,SV49: mu] :
( ( ( qmltpeq @ SV49 @ SV73 @ SV24 )
= $false )
| ( ( qmltpeq @ ( set_intersection2 @ SV49 @ SV87 ) @ ( set_intersection2 @ SV73 @ SV87 ) @ SV24 )
= $true )
| ( ( exists_in_world @ SV87 @ SV24 )
= $false )
| ( ( exists_in_world @ SV73 @ SV24 )
= $false )
| ( ( exists_in_world @ SV49 @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[403]) ).
thf(423,plain,
! [SV26: $i,SV74: mu,SV51: mu] :
( ( ( disjoint @ SV51 @ SV74 @ SV26 )
= $false )
| ( ( qmltpeq @ ( set_intersection2 @ SV51 @ SV74 ) @ empty_set @ SV26 )
= $true )
| ( ( exists_in_world @ SV74 @ SV26 )
= $false )
| ( ( exists_in_world @ SV51 @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[404]) ).
thf(424,plain,
! [SV26: $i,SV74: mu,SV51: mu] :
( ( ( qmltpeq @ ( set_intersection2 @ SV51 @ SV74 ) @ empty_set @ SV26 )
= $false )
| ( ( disjoint @ SV51 @ SV74 @ SV26 )
= $true )
| ( ( exists_in_world @ SV74 @ SV26 )
= $false )
| ( ( exists_in_world @ SV51 @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[405]) ).
thf(425,plain,
! [SV88: mu,SV29: $i,SV77: mu,SV54: mu] :
( ( ( ~ ( ~ ( qmltpeq @ SV54 @ SV77 @ SV29 )
| ~ ( in @ SV88 @ SV54 @ SV29 ) ) )
= $false )
| ( ( in @ SV88 @ SV77 @ SV29 )
= $true )
| ( ( exists_in_world @ SV88 @ SV29 )
= $false )
| ( ( exists_in_world @ SV77 @ SV29 )
= $false )
| ( ( exists_in_world @ SV54 @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[406]) ).
thf(426,plain,
! [SV89: mu,SV30: $i,SV78: mu,SV55: mu] :
( ( ( qmltpeq @ SV55 @ SV78 @ SV30 )
= $false )
| ( ( qmltpeq @ ( set_intersection2 @ SV89 @ SV55 ) @ ( set_intersection2 @ SV89 @ SV78 ) @ SV30 )
= $true )
| ( ( exists_in_world @ SV89 @ SV30 )
= $false )
| ( ( exists_in_world @ SV78 @ SV30 )
= $false )
| ( ( exists_in_world @ SV55 @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[407]) ).
thf(427,plain,
! [SV90: mu,SV31: $i,SV79: mu,SV56: mu] :
( ( ( ~ ( ~ ( qmltpeq @ SV56 @ SV79 @ SV31 )
| ~ ( qmltpeq @ SV79 @ SV90 @ SV31 ) ) )
= $false )
| ( ( qmltpeq @ SV56 @ SV90 @ SV31 )
= $true )
| ( ( exists_in_world @ SV90 @ SV31 )
= $false )
| ( ( exists_in_world @ SV79 @ SV31 )
= $false )
| ( ( exists_in_world @ SV56 @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[408]) ).
thf(428,plain,
! [SV80: mu,SV6: $i,SV61: mu,SV34: mu] :
( ( ( ~ ( qmltpeq @ SV34 @ SV61 @ SV6 )
| ~ ( disjoint @ SV80 @ SV34 @ SV6 ) )
= $true )
| ( ( disjoint @ SV80 @ SV61 @ SV6 )
= $true )
| ( ( exists_in_world @ SV80 @ SV6 )
= $false )
| ( ( exists_in_world @ SV61 @ SV6 )
= $false )
| ( ( exists_in_world @ SV34 @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[409]) ).
thf(429,plain,
! [SV81: mu,SV7: $i,SV62: mu,SV35: mu] :
( ( ( ~ ( qmltpeq @ SV35 @ SV62 @ SV7 )
| ~ ( in @ SV35 @ SV81 @ SV7 ) )
= $true )
| ( ( in @ SV62 @ SV81 @ SV7 )
= $true )
| ( ( exists_in_world @ SV81 @ SV7 )
= $false )
| ( ( exists_in_world @ SV62 @ SV7 )
= $false )
| ( ( exists_in_world @ SV35 @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[410]) ).
thf(430,plain,
! [SV10: $i,SV65: mu,SV38: mu,SV83: mu] :
( ( ( ~ ( qmltpeq @ SV83 @ ( set_intersection2 @ SV38 @ SV65 ) @ SV10 )
| ! [SY967: mu] :
( ~ ( exists_in_world @ SY967 @ SV10 )
| ~ ( ~ ( ~ ( in @ SY967 @ SV83 @ SV10 )
| ~ ( ~ ( in @ SY967 @ SV38 @ SV10 )
| ~ ( in @ SY967 @ SV65 @ SV10 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY967 @ SV38 @ SV10 )
| ~ ( in @ SY967 @ SV65 @ SV10 ) )
| ( in @ SY967 @ SV83 @ SV10 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV83 @ SV10 )
= $false )
| ( ( exists_in_world @ SV65 @ SV10 )
= $false )
| ( ( exists_in_world @ SV38 @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[412]) ).
thf(431,plain,
! [SV65: mu,SV38: mu,SV83: mu,SV10: $i] :
( ( ( ~ ! [SY968: mu] :
( ~ ( exists_in_world @ SY968 @ SV10 )
| ~ ( ~ ( ~ ( in @ SY968 @ SV83 @ SV10 )
| ~ ( ~ ( in @ SY968 @ SV38 @ SV10 )
| ~ ( in @ SY968 @ SV65 @ SV10 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY968 @ SV38 @ SV10 )
| ~ ( in @ SY968 @ SV65 @ SV10 ) )
| ( in @ SY968 @ SV83 @ SV10 ) ) ) )
| ( qmltpeq @ SV83 @ ( set_intersection2 @ SV38 @ SV65 ) @ SV10 ) )
= $true )
| ( ( exists_in_world @ SV83 @ SV10 )
= $false )
| ( ( exists_in_world @ SV65 @ SV10 )
= $false )
| ( ( exists_in_world @ SV38 @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[413]) ).
thf(432,plain,
! [SV11: $i,SV39: mu,SV91: mu] :
( ( ( in @ SV91 @ SV39 @ SV11 )
= $false )
| ( ( exists_in_world @ SV91 @ SV11 )
= $false )
| ( ( qmltpeq @ SV39 @ empty_set @ SV11 )
= $false )
| ( ( exists_in_world @ SV39 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[414]) ).
thf(433,plain,
! [SV68: mu,SV18: $i,SV44: mu] :
( ( ( empty @ SV44 @ SV18 )
= $false )
| ( ( qmltpeq @ SV44 @ SV68 @ SV18 )
= $false )
| ( ( empty @ SV68 @ SV18 )
= $true )
| ( ( exists_in_world @ SV68 @ SV18 )
= $false )
| ( ( exists_in_world @ SV44 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[418]) ).
thf(434,plain,
! [SV85: mu,SV22: $i,SV71: mu,SV47: mu] :
( ( ( ~ ( qmltpeq @ SV47 @ SV71 @ SV22 )
| ~ ( disjoint @ SV47 @ SV85 @ SV22 ) )
= $true )
| ( ( disjoint @ SV71 @ SV85 @ SV22 )
= $true )
| ( ( exists_in_world @ SV85 @ SV22 )
= $false )
| ( ( exists_in_world @ SV71 @ SV22 )
= $false )
| ( ( exists_in_world @ SV47 @ SV22 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[419]) ).
thf(435,plain,
! [SV23: $i,SV72: mu,SV48: mu,SV86: mu] :
( ( ( ~ ( qmltpeq @ SV86 @ ( unordered_pair @ SV48 @ SV72 ) @ SV23 )
| ! [SY969: mu] :
( ~ ( exists_in_world @ SY969 @ SV23 )
| ~ ( ~ ( ~ ( in @ SY969 @ SV86 @ SV23 )
| ( qmltpeq @ SY969 @ SV48 @ SV23 )
| ( qmltpeq @ SY969 @ SV72 @ SV23 ) )
| ~ ( ~ ( ( qmltpeq @ SY969 @ SV48 @ SV23 )
| ( qmltpeq @ SY969 @ SV72 @ SV23 ) )
| ( in @ SY969 @ SV86 @ SV23 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV86 @ SV23 )
= $false )
| ( ( exists_in_world @ SV72 @ SV23 )
= $false )
| ( ( exists_in_world @ SV48 @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[420]) ).
thf(436,plain,
! [SV72: mu,SV48: mu,SV86: mu,SV23: $i] :
( ( ( ~ ! [SY970: mu] :
( ~ ( exists_in_world @ SY970 @ SV23 )
| ~ ( ~ ( ~ ( in @ SY970 @ SV86 @ SV23 )
| ( qmltpeq @ SY970 @ SV48 @ SV23 )
| ( qmltpeq @ SY970 @ SV72 @ SV23 ) )
| ~ ( ~ ( ( qmltpeq @ SY970 @ SV48 @ SV23 )
| ( qmltpeq @ SY970 @ SV72 @ SV23 ) )
| ( in @ SY970 @ SV86 @ SV23 ) ) ) )
| ( qmltpeq @ SV86 @ ( unordered_pair @ SV48 @ SV72 ) @ SV23 ) )
= $true )
| ( ( exists_in_world @ SV86 @ SV23 )
= $false )
| ( ( exists_in_world @ SV72 @ SV23 )
= $false )
| ( ( exists_in_world @ SV48 @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[421]) ).
thf(437,plain,
! [SV88: mu,SV29: $i,SV77: mu,SV54: mu] :
( ( ( ~ ( qmltpeq @ SV54 @ SV77 @ SV29 )
| ~ ( in @ SV88 @ SV54 @ SV29 ) )
= $true )
| ( ( in @ SV88 @ SV77 @ SV29 )
= $true )
| ( ( exists_in_world @ SV88 @ SV29 )
= $false )
| ( ( exists_in_world @ SV77 @ SV29 )
= $false )
| ( ( exists_in_world @ SV54 @ SV29 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[425]) ).
thf(438,plain,
! [SV90: mu,SV31: $i,SV79: mu,SV56: mu] :
( ( ( ~ ( qmltpeq @ SV56 @ SV79 @ SV31 )
| ~ ( qmltpeq @ SV79 @ SV90 @ SV31 ) )
= $true )
| ( ( qmltpeq @ SV56 @ SV90 @ SV31 )
= $true )
| ( ( exists_in_world @ SV90 @ SV31 )
= $false )
| ( ( exists_in_world @ SV79 @ SV31 )
= $false )
| ( ( exists_in_world @ SV56 @ SV31 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[427]) ).
thf(439,plain,
! [SV80: mu,SV6: $i,SV61: mu,SV34: mu] :
( ( ( ~ ( qmltpeq @ SV34 @ SV61 @ SV6 ) )
= $true )
| ( ( ~ ( disjoint @ SV80 @ SV34 @ SV6 ) )
= $true )
| ( ( disjoint @ SV80 @ SV61 @ SV6 )
= $true )
| ( ( exists_in_world @ SV80 @ SV6 )
= $false )
| ( ( exists_in_world @ SV61 @ SV6 )
= $false )
| ( ( exists_in_world @ SV34 @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[428]) ).
thf(440,plain,
! [SV81: mu,SV7: $i,SV62: mu,SV35: mu] :
( ( ( ~ ( qmltpeq @ SV35 @ SV62 @ SV7 ) )
= $true )
| ( ( ~ ( in @ SV35 @ SV81 @ SV7 ) )
= $true )
| ( ( in @ SV62 @ SV81 @ SV7 )
= $true )
| ( ( exists_in_world @ SV81 @ SV7 )
= $false )
| ( ( exists_in_world @ SV62 @ SV7 )
= $false )
| ( ( exists_in_world @ SV35 @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[429]) ).
thf(441,plain,
! [SV10: $i,SV65: mu,SV38: mu,SV83: mu] :
( ( ( ~ ( qmltpeq @ SV83 @ ( set_intersection2 @ SV38 @ SV65 ) @ SV10 ) )
= $true )
| ( ( ! [SY967: mu] :
( ~ ( exists_in_world @ SY967 @ SV10 )
| ~ ( ~ ( ~ ( in @ SY967 @ SV83 @ SV10 )
| ~ ( ~ ( in @ SY967 @ SV38 @ SV10 )
| ~ ( in @ SY967 @ SV65 @ SV10 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY967 @ SV38 @ SV10 )
| ~ ( in @ SY967 @ SV65 @ SV10 ) )
| ( in @ SY967 @ SV83 @ SV10 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV83 @ SV10 )
= $false )
| ( ( exists_in_world @ SV65 @ SV10 )
= $false )
| ( ( exists_in_world @ SV38 @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[430]) ).
thf(442,plain,
! [SV65: mu,SV38: mu,SV83: mu,SV10: $i] :
( ( ( ~ ! [SY968: mu] :
( ~ ( exists_in_world @ SY968 @ SV10 )
| ~ ( ~ ( ~ ( in @ SY968 @ SV83 @ SV10 )
| ~ ( ~ ( in @ SY968 @ SV38 @ SV10 )
| ~ ( in @ SY968 @ SV65 @ SV10 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY968 @ SV38 @ SV10 )
| ~ ( in @ SY968 @ SV65 @ SV10 ) )
| ( in @ SY968 @ SV83 @ SV10 ) ) ) ) )
= $true )
| ( ( qmltpeq @ SV83 @ ( set_intersection2 @ SV38 @ SV65 ) @ SV10 )
= $true )
| ( ( exists_in_world @ SV83 @ SV10 )
= $false )
| ( ( exists_in_world @ SV65 @ SV10 )
= $false )
| ( ( exists_in_world @ SV38 @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[431]) ).
thf(443,plain,
! [SV85: mu,SV22: $i,SV71: mu,SV47: mu] :
( ( ( ~ ( qmltpeq @ SV47 @ SV71 @ SV22 ) )
= $true )
| ( ( ~ ( disjoint @ SV47 @ SV85 @ SV22 ) )
= $true )
| ( ( disjoint @ SV71 @ SV85 @ SV22 )
= $true )
| ( ( exists_in_world @ SV85 @ SV22 )
= $false )
| ( ( exists_in_world @ SV71 @ SV22 )
= $false )
| ( ( exists_in_world @ SV47 @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[434]) ).
thf(444,plain,
! [SV23: $i,SV72: mu,SV48: mu,SV86: mu] :
( ( ( ~ ( qmltpeq @ SV86 @ ( unordered_pair @ SV48 @ SV72 ) @ SV23 ) )
= $true )
| ( ( ! [SY969: mu] :
( ~ ( exists_in_world @ SY969 @ SV23 )
| ~ ( ~ ( ~ ( in @ SY969 @ SV86 @ SV23 )
| ( qmltpeq @ SY969 @ SV48 @ SV23 )
| ( qmltpeq @ SY969 @ SV72 @ SV23 ) )
| ~ ( ~ ( ( qmltpeq @ SY969 @ SV48 @ SV23 )
| ( qmltpeq @ SY969 @ SV72 @ SV23 ) )
| ( in @ SY969 @ SV86 @ SV23 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV86 @ SV23 )
= $false )
| ( ( exists_in_world @ SV72 @ SV23 )
= $false )
| ( ( exists_in_world @ SV48 @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[435]) ).
thf(445,plain,
! [SV72: mu,SV48: mu,SV86: mu,SV23: $i] :
( ( ( ~ ! [SY970: mu] :
( ~ ( exists_in_world @ SY970 @ SV23 )
| ~ ( ~ ( ~ ( in @ SY970 @ SV86 @ SV23 )
| ( qmltpeq @ SY970 @ SV48 @ SV23 )
| ( qmltpeq @ SY970 @ SV72 @ SV23 ) )
| ~ ( ~ ( ( qmltpeq @ SY970 @ SV48 @ SV23 )
| ( qmltpeq @ SY970 @ SV72 @ SV23 ) )
| ( in @ SY970 @ SV86 @ SV23 ) ) ) ) )
= $true )
| ( ( qmltpeq @ SV86 @ ( unordered_pair @ SV48 @ SV72 ) @ SV23 )
= $true )
| ( ( exists_in_world @ SV86 @ SV23 )
= $false )
| ( ( exists_in_world @ SV72 @ SV23 )
= $false )
| ( ( exists_in_world @ SV48 @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[436]) ).
thf(446,plain,
! [SV88: mu,SV29: $i,SV77: mu,SV54: mu] :
( ( ( ~ ( qmltpeq @ SV54 @ SV77 @ SV29 ) )
= $true )
| ( ( ~ ( in @ SV88 @ SV54 @ SV29 ) )
= $true )
| ( ( in @ SV88 @ SV77 @ SV29 )
= $true )
| ( ( exists_in_world @ SV88 @ SV29 )
= $false )
| ( ( exists_in_world @ SV77 @ SV29 )
= $false )
| ( ( exists_in_world @ SV54 @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[437]) ).
thf(447,plain,
! [SV90: mu,SV31: $i,SV79: mu,SV56: mu] :
( ( ( ~ ( qmltpeq @ SV56 @ SV79 @ SV31 ) )
= $true )
| ( ( ~ ( qmltpeq @ SV79 @ SV90 @ SV31 ) )
= $true )
| ( ( qmltpeq @ SV56 @ SV90 @ SV31 )
= $true )
| ( ( exists_in_world @ SV90 @ SV31 )
= $false )
| ( ( exists_in_world @ SV79 @ SV31 )
= $false )
| ( ( exists_in_world @ SV56 @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[438]) ).
thf(448,plain,
! [SV80: mu,SV6: $i,SV61: mu,SV34: mu] :
( ( ( qmltpeq @ SV34 @ SV61 @ SV6 )
= $false )
| ( ( ~ ( disjoint @ SV80 @ SV34 @ SV6 ) )
= $true )
| ( ( disjoint @ SV80 @ SV61 @ SV6 )
= $true )
| ( ( exists_in_world @ SV80 @ SV6 )
= $false )
| ( ( exists_in_world @ SV61 @ SV6 )
= $false )
| ( ( exists_in_world @ SV34 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[439]) ).
thf(449,plain,
! [SV81: mu,SV7: $i,SV62: mu,SV35: mu] :
( ( ( qmltpeq @ SV35 @ SV62 @ SV7 )
= $false )
| ( ( ~ ( in @ SV35 @ SV81 @ SV7 ) )
= $true )
| ( ( in @ SV62 @ SV81 @ SV7 )
= $true )
| ( ( exists_in_world @ SV81 @ SV7 )
= $false )
| ( ( exists_in_world @ SV62 @ SV7 )
= $false )
| ( ( exists_in_world @ SV35 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[440]) ).
thf(450,plain,
! [SV10: $i,SV65: mu,SV38: mu,SV83: mu] :
( ( ( qmltpeq @ SV83 @ ( set_intersection2 @ SV38 @ SV65 ) @ SV10 )
= $false )
| ( ( ! [SY967: mu] :
( ~ ( exists_in_world @ SY967 @ SV10 )
| ~ ( ~ ( ~ ( in @ SY967 @ SV83 @ SV10 )
| ~ ( ~ ( in @ SY967 @ SV38 @ SV10 )
| ~ ( in @ SY967 @ SV65 @ SV10 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY967 @ SV38 @ SV10 )
| ~ ( in @ SY967 @ SV65 @ SV10 ) )
| ( in @ SY967 @ SV83 @ SV10 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV83 @ SV10 )
= $false )
| ( ( exists_in_world @ SV65 @ SV10 )
= $false )
| ( ( exists_in_world @ SV38 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[441]) ).
thf(451,plain,
! [SV65: mu,SV38: mu,SV83: mu,SV10: $i] :
( ( ( ! [SY968: mu] :
( ~ ( exists_in_world @ SY968 @ SV10 )
| ~ ( ~ ( ~ ( in @ SY968 @ SV83 @ SV10 )
| ~ ( ~ ( in @ SY968 @ SV38 @ SV10 )
| ~ ( in @ SY968 @ SV65 @ SV10 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY968 @ SV38 @ SV10 )
| ~ ( in @ SY968 @ SV65 @ SV10 ) )
| ( in @ SY968 @ SV83 @ SV10 ) ) ) ) )
= $false )
| ( ( qmltpeq @ SV83 @ ( set_intersection2 @ SV38 @ SV65 ) @ SV10 )
= $true )
| ( ( exists_in_world @ SV83 @ SV10 )
= $false )
| ( ( exists_in_world @ SV65 @ SV10 )
= $false )
| ( ( exists_in_world @ SV38 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[442]) ).
thf(452,plain,
! [SV85: mu,SV22: $i,SV71: mu,SV47: mu] :
( ( ( qmltpeq @ SV47 @ SV71 @ SV22 )
= $false )
| ( ( ~ ( disjoint @ SV47 @ SV85 @ SV22 ) )
= $true )
| ( ( disjoint @ SV71 @ SV85 @ SV22 )
= $true )
| ( ( exists_in_world @ SV85 @ SV22 )
= $false )
| ( ( exists_in_world @ SV71 @ SV22 )
= $false )
| ( ( exists_in_world @ SV47 @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[443]) ).
thf(453,plain,
! [SV23: $i,SV72: mu,SV48: mu,SV86: mu] :
( ( ( qmltpeq @ SV86 @ ( unordered_pair @ SV48 @ SV72 ) @ SV23 )
= $false )
| ( ( ! [SY969: mu] :
( ~ ( exists_in_world @ SY969 @ SV23 )
| ~ ( ~ ( ~ ( in @ SY969 @ SV86 @ SV23 )
| ( qmltpeq @ SY969 @ SV48 @ SV23 )
| ( qmltpeq @ SY969 @ SV72 @ SV23 ) )
| ~ ( ~ ( ( qmltpeq @ SY969 @ SV48 @ SV23 )
| ( qmltpeq @ SY969 @ SV72 @ SV23 ) )
| ( in @ SY969 @ SV86 @ SV23 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV86 @ SV23 )
= $false )
| ( ( exists_in_world @ SV72 @ SV23 )
= $false )
| ( ( exists_in_world @ SV48 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[444]) ).
thf(454,plain,
! [SV72: mu,SV48: mu,SV86: mu,SV23: $i] :
( ( ( ! [SY970: mu] :
( ~ ( exists_in_world @ SY970 @ SV23 )
| ~ ( ~ ( ~ ( in @ SY970 @ SV86 @ SV23 )
| ( qmltpeq @ SY970 @ SV48 @ SV23 )
| ( qmltpeq @ SY970 @ SV72 @ SV23 ) )
| ~ ( ~ ( ( qmltpeq @ SY970 @ SV48 @ SV23 )
| ( qmltpeq @ SY970 @ SV72 @ SV23 ) )
| ( in @ SY970 @ SV86 @ SV23 ) ) ) ) )
= $false )
| ( ( qmltpeq @ SV86 @ ( unordered_pair @ SV48 @ SV72 ) @ SV23 )
= $true )
| ( ( exists_in_world @ SV86 @ SV23 )
= $false )
| ( ( exists_in_world @ SV72 @ SV23 )
= $false )
| ( ( exists_in_world @ SV48 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[445]) ).
thf(455,plain,
! [SV88: mu,SV29: $i,SV77: mu,SV54: mu] :
( ( ( qmltpeq @ SV54 @ SV77 @ SV29 )
= $false )
| ( ( ~ ( in @ SV88 @ SV54 @ SV29 ) )
= $true )
| ( ( in @ SV88 @ SV77 @ SV29 )
= $true )
| ( ( exists_in_world @ SV88 @ SV29 )
= $false )
| ( ( exists_in_world @ SV77 @ SV29 )
= $false )
| ( ( exists_in_world @ SV54 @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[446]) ).
thf(456,plain,
! [SV90: mu,SV31: $i,SV79: mu,SV56: mu] :
( ( ( qmltpeq @ SV56 @ SV79 @ SV31 )
= $false )
| ( ( ~ ( qmltpeq @ SV79 @ SV90 @ SV31 ) )
= $true )
| ( ( qmltpeq @ SV56 @ SV90 @ SV31 )
= $true )
| ( ( exists_in_world @ SV90 @ SV31 )
= $false )
| ( ( exists_in_world @ SV79 @ SV31 )
= $false )
| ( ( exists_in_world @ SV56 @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[447]) ).
thf(457,plain,
! [SV61: mu,SV6: $i,SV34: mu,SV80: mu] :
( ( ( disjoint @ SV80 @ SV34 @ SV6 )
= $false )
| ( ( qmltpeq @ SV34 @ SV61 @ SV6 )
= $false )
| ( ( disjoint @ SV80 @ SV61 @ SV6 )
= $true )
| ( ( exists_in_world @ SV80 @ SV6 )
= $false )
| ( ( exists_in_world @ SV61 @ SV6 )
= $false )
| ( ( exists_in_world @ SV34 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[448]) ).
thf(458,plain,
! [SV62: mu,SV7: $i,SV81: mu,SV35: mu] :
( ( ( in @ SV35 @ SV81 @ SV7 )
= $false )
| ( ( qmltpeq @ SV35 @ SV62 @ SV7 )
= $false )
| ( ( in @ SV62 @ SV81 @ SV7 )
= $true )
| ( ( exists_in_world @ SV81 @ SV7 )
= $false )
| ( ( exists_in_world @ SV62 @ SV7 )
= $false )
| ( ( exists_in_world @ SV35 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[449]) ).
thf(459,plain,
! [SV65: mu,SV38: mu,SV83: mu,SV10: $i,SV92: mu] :
( ( ( ~ ( exists_in_world @ SV92 @ SV10 )
| ~ ( ~ ( ~ ( in @ SV92 @ SV83 @ SV10 )
| ~ ( ~ ( in @ SV92 @ SV38 @ SV10 )
| ~ ( in @ SV92 @ SV65 @ SV10 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV92 @ SV38 @ SV10 )
| ~ ( in @ SV92 @ SV65 @ SV10 ) )
| ( in @ SV92 @ SV83 @ SV10 ) ) ) )
= $true )
| ( ( qmltpeq @ SV83 @ ( set_intersection2 @ SV38 @ SV65 ) @ SV10 )
= $false )
| ( ( exists_in_world @ SV83 @ SV10 )
= $false )
| ( ( exists_in_world @ SV65 @ SV10 )
= $false )
| ( ( exists_in_world @ SV38 @ SV10 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[450]) ).
thf(460,plain,
! [SV10: $i,SV83: mu,SV38: mu,SV65: mu] :
( ( ( ~ ( exists_in_world @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV10 )
| ~ ( ~ ( ~ ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV83 @ SV10 )
| ~ ( ~ ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV38 @ SV10 )
| ~ ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV65 @ SV10 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV38 @ SV10 )
| ~ ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV65 @ SV10 ) )
| ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV83 @ SV10 ) ) ) )
= $false )
| ( ( qmltpeq @ SV83 @ ( set_intersection2 @ SV38 @ SV65 ) @ SV10 )
= $true )
| ( ( exists_in_world @ SV83 @ SV10 )
= $false )
| ( ( exists_in_world @ SV65 @ SV10 )
= $false )
| ( ( exists_in_world @ SV38 @ SV10 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[451]) ).
thf(461,plain,
! [SV71: mu,SV22: $i,SV85: mu,SV47: mu] :
( ( ( disjoint @ SV47 @ SV85 @ SV22 )
= $false )
| ( ( qmltpeq @ SV47 @ SV71 @ SV22 )
= $false )
| ( ( disjoint @ SV71 @ SV85 @ SV22 )
= $true )
| ( ( exists_in_world @ SV85 @ SV22 )
= $false )
| ( ( exists_in_world @ SV71 @ SV22 )
= $false )
| ( ( exists_in_world @ SV47 @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[452]) ).
thf(462,plain,
! [SV72: mu,SV48: mu,SV86: mu,SV23: $i,SV93: mu] :
( ( ( ~ ( exists_in_world @ SV93 @ SV23 )
| ~ ( ~ ( ~ ( in @ SV93 @ SV86 @ SV23 )
| ( qmltpeq @ SV93 @ SV48 @ SV23 )
| ( qmltpeq @ SV93 @ SV72 @ SV23 ) )
| ~ ( ~ ( ( qmltpeq @ SV93 @ SV48 @ SV23 )
| ( qmltpeq @ SV93 @ SV72 @ SV23 ) )
| ( in @ SV93 @ SV86 @ SV23 ) ) ) )
= $true )
| ( ( qmltpeq @ SV86 @ ( unordered_pair @ SV48 @ SV72 ) @ SV23 )
= $false )
| ( ( exists_in_world @ SV86 @ SV23 )
= $false )
| ( ( exists_in_world @ SV72 @ SV23 )
= $false )
| ( ( exists_in_world @ SV48 @ SV23 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[453]) ).
thf(463,plain,
! [SV23: $i,SV86: mu,SV48: mu,SV72: mu] :
( ( ( ~ ( exists_in_world @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV23 )
| ~ ( ~ ( ~ ( in @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV86 @ SV23 )
| ( qmltpeq @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV48 @ SV23 )
| ( qmltpeq @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV72 @ SV23 ) )
| ~ ( ~ ( ( qmltpeq @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV48 @ SV23 )
| ( qmltpeq @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV72 @ SV23 ) )
| ( in @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV86 @ SV23 ) ) ) )
= $false )
| ( ( qmltpeq @ SV86 @ ( unordered_pair @ SV48 @ SV72 ) @ SV23 )
= $true )
| ( ( exists_in_world @ SV86 @ SV23 )
= $false )
| ( ( exists_in_world @ SV72 @ SV23 )
= $false )
| ( ( exists_in_world @ SV48 @ SV23 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[454]) ).
thf(464,plain,
! [SV77: mu,SV29: $i,SV54: mu,SV88: mu] :
( ( ( in @ SV88 @ SV54 @ SV29 )
= $false )
| ( ( qmltpeq @ SV54 @ SV77 @ SV29 )
= $false )
| ( ( in @ SV88 @ SV77 @ SV29 )
= $true )
| ( ( exists_in_world @ SV88 @ SV29 )
= $false )
| ( ( exists_in_world @ SV77 @ SV29 )
= $false )
| ( ( exists_in_world @ SV54 @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[455]) ).
thf(465,plain,
! [SV56: mu,SV31: $i,SV90: mu,SV79: mu] :
( ( ( qmltpeq @ SV79 @ SV90 @ SV31 )
= $false )
| ( ( qmltpeq @ SV56 @ SV79 @ SV31 )
= $false )
| ( ( qmltpeq @ SV56 @ SV90 @ SV31 )
= $true )
| ( ( exists_in_world @ SV90 @ SV31 )
= $false )
| ( ( exists_in_world @ SV79 @ SV31 )
= $false )
| ( ( exists_in_world @ SV56 @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[456]) ).
thf(466,plain,
! [SV65: mu,SV38: mu,SV83: mu,SV10: $i,SV92: mu] :
( ( ( ~ ( exists_in_world @ SV92 @ SV10 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ SV92 @ SV83 @ SV10 )
| ~ ( ~ ( in @ SV92 @ SV38 @ SV10 )
| ~ ( in @ SV92 @ SV65 @ SV10 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV92 @ SV38 @ SV10 )
| ~ ( in @ SV92 @ SV65 @ SV10 ) )
| ( in @ SV92 @ SV83 @ SV10 ) ) ) )
= $true )
| ( ( qmltpeq @ SV83 @ ( set_intersection2 @ SV38 @ SV65 ) @ SV10 )
= $false )
| ( ( exists_in_world @ SV83 @ SV10 )
= $false )
| ( ( exists_in_world @ SV65 @ SV10 )
= $false )
| ( ( exists_in_world @ SV38 @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[459]) ).
thf(467,plain,
! [SV10: $i,SV83: mu,SV38: mu,SV65: mu] :
( ( ( ~ ( exists_in_world @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV10 ) )
= $false )
| ( ( qmltpeq @ SV83 @ ( set_intersection2 @ SV38 @ SV65 ) @ SV10 )
= $true )
| ( ( exists_in_world @ SV83 @ SV10 )
= $false )
| ( ( exists_in_world @ SV65 @ SV10 )
= $false )
| ( ( exists_in_world @ SV38 @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[460]) ).
thf(468,plain,
! [SV10: $i,SV83: mu,SV38: mu,SV65: mu] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV83 @ SV10 )
| ~ ( ~ ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV38 @ SV10 )
| ~ ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV65 @ SV10 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV38 @ SV10 )
| ~ ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV65 @ SV10 ) )
| ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV83 @ SV10 ) ) ) )
= $false )
| ( ( qmltpeq @ SV83 @ ( set_intersection2 @ SV38 @ SV65 ) @ SV10 )
= $true )
| ( ( exists_in_world @ SV83 @ SV10 )
= $false )
| ( ( exists_in_world @ SV65 @ SV10 )
= $false )
| ( ( exists_in_world @ SV38 @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[460]) ).
thf(469,plain,
! [SV72: mu,SV48: mu,SV86: mu,SV23: $i,SV93: mu] :
( ( ( ~ ( exists_in_world @ SV93 @ SV23 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ SV93 @ SV86 @ SV23 )
| ( qmltpeq @ SV93 @ SV48 @ SV23 )
| ( qmltpeq @ SV93 @ SV72 @ SV23 ) )
| ~ ( ~ ( ( qmltpeq @ SV93 @ SV48 @ SV23 )
| ( qmltpeq @ SV93 @ SV72 @ SV23 ) )
| ( in @ SV93 @ SV86 @ SV23 ) ) ) )
= $true )
| ( ( qmltpeq @ SV86 @ ( unordered_pair @ SV48 @ SV72 ) @ SV23 )
= $false )
| ( ( exists_in_world @ SV86 @ SV23 )
= $false )
| ( ( exists_in_world @ SV72 @ SV23 )
= $false )
| ( ( exists_in_world @ SV48 @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[462]) ).
thf(470,plain,
! [SV23: $i,SV86: mu,SV48: mu,SV72: mu] :
( ( ( ~ ( exists_in_world @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV23 ) )
= $false )
| ( ( qmltpeq @ SV86 @ ( unordered_pair @ SV48 @ SV72 ) @ SV23 )
= $true )
| ( ( exists_in_world @ SV86 @ SV23 )
= $false )
| ( ( exists_in_world @ SV72 @ SV23 )
= $false )
| ( ( exists_in_world @ SV48 @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[463]) ).
thf(471,plain,
! [SV23: $i,SV86: mu,SV48: mu,SV72: mu] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV86 @ SV23 )
| ( qmltpeq @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV48 @ SV23 )
| ( qmltpeq @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV72 @ SV23 ) )
| ~ ( ~ ( ( qmltpeq @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV48 @ SV23 )
| ( qmltpeq @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV72 @ SV23 ) )
| ( in @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV86 @ SV23 ) ) ) )
= $false )
| ( ( qmltpeq @ SV86 @ ( unordered_pair @ SV48 @ SV72 ) @ SV23 )
= $true )
| ( ( exists_in_world @ SV86 @ SV23 )
= $false )
| ( ( exists_in_world @ SV72 @ SV23 )
= $false )
| ( ( exists_in_world @ SV48 @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[463]) ).
thf(472,plain,
! [SV65: mu,SV38: mu,SV83: mu,SV10: $i,SV92: mu] :
( ( ( exists_in_world @ SV92 @ SV10 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ SV92 @ SV83 @ SV10 )
| ~ ( ~ ( in @ SV92 @ SV38 @ SV10 )
| ~ ( in @ SV92 @ SV65 @ SV10 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV92 @ SV38 @ SV10 )
| ~ ( in @ SV92 @ SV65 @ SV10 ) )
| ( in @ SV92 @ SV83 @ SV10 ) ) ) )
= $true )
| ( ( qmltpeq @ SV83 @ ( set_intersection2 @ SV38 @ SV65 ) @ SV10 )
= $false )
| ( ( exists_in_world @ SV83 @ SV10 )
= $false )
| ( ( exists_in_world @ SV65 @ SV10 )
= $false )
| ( ( exists_in_world @ SV38 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[466]) ).
thf(473,plain,
! [SV10: $i,SV83: mu,SV38: mu,SV65: mu] :
( ( ( exists_in_world @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV10 )
= $true )
| ( ( qmltpeq @ SV83 @ ( set_intersection2 @ SV38 @ SV65 ) @ SV10 )
= $true )
| ( ( exists_in_world @ SV83 @ SV10 )
= $false )
| ( ( exists_in_world @ SV65 @ SV10 )
= $false )
| ( ( exists_in_world @ SV38 @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[467]) ).
thf(474,plain,
! [SV10: $i,SV83: mu,SV38: mu,SV65: mu] :
( ( ( ~ ( ~ ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV83 @ SV10 )
| ~ ( ~ ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV38 @ SV10 )
| ~ ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV65 @ SV10 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV38 @ SV10 )
| ~ ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV65 @ SV10 ) )
| ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV83 @ SV10 ) ) )
= $true )
| ( ( qmltpeq @ SV83 @ ( set_intersection2 @ SV38 @ SV65 ) @ SV10 )
= $true )
| ( ( exists_in_world @ SV83 @ SV10 )
= $false )
| ( ( exists_in_world @ SV65 @ SV10 )
= $false )
| ( ( exists_in_world @ SV38 @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[468]) ).
thf(475,plain,
! [SV72: mu,SV48: mu,SV86: mu,SV23: $i,SV93: mu] :
( ( ( exists_in_world @ SV93 @ SV23 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ SV93 @ SV86 @ SV23 )
| ( qmltpeq @ SV93 @ SV48 @ SV23 )
| ( qmltpeq @ SV93 @ SV72 @ SV23 ) )
| ~ ( ~ ( ( qmltpeq @ SV93 @ SV48 @ SV23 )
| ( qmltpeq @ SV93 @ SV72 @ SV23 ) )
| ( in @ SV93 @ SV86 @ SV23 ) ) ) )
= $true )
| ( ( qmltpeq @ SV86 @ ( unordered_pair @ SV48 @ SV72 ) @ SV23 )
= $false )
| ( ( exists_in_world @ SV86 @ SV23 )
= $false )
| ( ( exists_in_world @ SV72 @ SV23 )
= $false )
| ( ( exists_in_world @ SV48 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[469]) ).
thf(476,plain,
! [SV23: $i,SV86: mu,SV48: mu,SV72: mu] :
( ( ( exists_in_world @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV23 )
= $true )
| ( ( qmltpeq @ SV86 @ ( unordered_pair @ SV48 @ SV72 ) @ SV23 )
= $true )
| ( ( exists_in_world @ SV86 @ SV23 )
= $false )
| ( ( exists_in_world @ SV72 @ SV23 )
= $false )
| ( ( exists_in_world @ SV48 @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[470]) ).
thf(477,plain,
! [SV23: $i,SV86: mu,SV48: mu,SV72: mu] :
( ( ( ~ ( ~ ( in @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV86 @ SV23 )
| ( qmltpeq @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV48 @ SV23 )
| ( qmltpeq @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV72 @ SV23 ) )
| ~ ( ~ ( ( qmltpeq @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV48 @ SV23 )
| ( qmltpeq @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV72 @ SV23 ) )
| ( in @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV86 @ SV23 ) ) )
= $true )
| ( ( qmltpeq @ SV86 @ ( unordered_pair @ SV48 @ SV72 ) @ SV23 )
= $true )
| ( ( exists_in_world @ SV86 @ SV23 )
= $false )
| ( ( exists_in_world @ SV72 @ SV23 )
= $false )
| ( ( exists_in_world @ SV48 @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[471]) ).
thf(478,plain,
! [SV65: mu,SV38: mu,SV10: $i,SV83: mu,SV92: mu] :
( ( ( ~ ( ~ ( in @ SV92 @ SV83 @ SV10 )
| ~ ( ~ ( in @ SV92 @ SV38 @ SV10 )
| ~ ( in @ SV92 @ SV65 @ SV10 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV92 @ SV38 @ SV10 )
| ~ ( in @ SV92 @ SV65 @ SV10 ) )
| ( in @ SV92 @ SV83 @ SV10 ) ) )
= $false )
| ( ( exists_in_world @ SV92 @ SV10 )
= $false )
| ( ( qmltpeq @ SV83 @ ( set_intersection2 @ SV38 @ SV65 ) @ SV10 )
= $false )
| ( ( exists_in_world @ SV83 @ SV10 )
= $false )
| ( ( exists_in_world @ SV65 @ SV10 )
= $false )
| ( ( exists_in_world @ SV38 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[472]) ).
thf(479,plain,
! [SV10: $i,SV83: mu,SV38: mu,SV65: mu] :
( ( ( ~ ( ~ ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV83 @ SV10 )
| ~ ( ~ ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV38 @ SV10 )
| ~ ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV65 @ SV10 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV38 @ SV10 )
| ~ ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV65 @ SV10 ) )
| ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV83 @ SV10 ) ) )
= $true )
| ( ( qmltpeq @ SV83 @ ( set_intersection2 @ SV38 @ SV65 ) @ SV10 )
= $true )
| ( ( exists_in_world @ SV83 @ SV10 )
= $false )
| ( ( exists_in_world @ SV65 @ SV10 )
= $false )
| ( ( exists_in_world @ SV38 @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[474]) ).
thf(480,plain,
! [SV72: mu,SV48: mu,SV23: $i,SV86: mu,SV93: mu] :
( ( ( ~ ( ~ ( in @ SV93 @ SV86 @ SV23 )
| ( qmltpeq @ SV93 @ SV48 @ SV23 )
| ( qmltpeq @ SV93 @ SV72 @ SV23 ) )
| ~ ( ~ ( ( qmltpeq @ SV93 @ SV48 @ SV23 )
| ( qmltpeq @ SV93 @ SV72 @ SV23 ) )
| ( in @ SV93 @ SV86 @ SV23 ) ) )
= $false )
| ( ( exists_in_world @ SV93 @ SV23 )
= $false )
| ( ( qmltpeq @ SV86 @ ( unordered_pair @ SV48 @ SV72 ) @ SV23 )
= $false )
| ( ( exists_in_world @ SV86 @ SV23 )
= $false )
| ( ( exists_in_world @ SV72 @ SV23 )
= $false )
| ( ( exists_in_world @ SV48 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[475]) ).
thf(481,plain,
! [SV23: $i,SV86: mu,SV48: mu,SV72: mu] :
( ( ( ~ ( ~ ( in @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV86 @ SV23 )
| ( qmltpeq @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV48 @ SV23 )
| ( qmltpeq @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV72 @ SV23 ) ) )
= $true )
| ( ( ~ ( ~ ( ( qmltpeq @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV48 @ SV23 )
| ( qmltpeq @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV72 @ SV23 ) )
| ( in @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV86 @ SV23 ) ) )
= $true )
| ( ( qmltpeq @ SV86 @ ( unordered_pair @ SV48 @ SV72 ) @ SV23 )
= $true )
| ( ( exists_in_world @ SV86 @ SV23 )
= $false )
| ( ( exists_in_world @ SV72 @ SV23 )
= $false )
| ( ( exists_in_world @ SV48 @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[477]) ).
thf(482,plain,
! [SV65: mu,SV38: mu,SV10: $i,SV83: mu,SV92: mu] :
( ( ( ~ ( ~ ( in @ SV92 @ SV83 @ SV10 )
| ~ ( ~ ( in @ SV92 @ SV38 @ SV10 )
| ~ ( in @ SV92 @ SV65 @ SV10 ) ) ) )
= $false )
| ( ( exists_in_world @ SV92 @ SV10 )
= $false )
| ( ( qmltpeq @ SV83 @ ( set_intersection2 @ SV38 @ SV65 ) @ SV10 )
= $false )
| ( ( exists_in_world @ SV83 @ SV10 )
= $false )
| ( ( exists_in_world @ SV65 @ SV10 )
= $false )
| ( ( exists_in_world @ SV38 @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[478]) ).
thf(483,plain,
! [SV83: mu,SV65: mu,SV10: $i,SV38: mu,SV92: mu] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV92 @ SV38 @ SV10 )
| ~ ( in @ SV92 @ SV65 @ SV10 ) )
| ( in @ SV92 @ SV83 @ SV10 ) ) )
= $false )
| ( ( exists_in_world @ SV92 @ SV10 )
= $false )
| ( ( qmltpeq @ SV83 @ ( set_intersection2 @ SV38 @ SV65 ) @ SV10 )
= $false )
| ( ( exists_in_world @ SV83 @ SV10 )
= $false )
| ( ( exists_in_world @ SV65 @ SV10 )
= $false )
| ( ( exists_in_world @ SV38 @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[478]) ).
thf(484,plain,
! [SV10: $i,SV83: mu,SV38: mu,SV65: mu] :
( ( ( ~ ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV83 @ SV10 )
| ~ ( ~ ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV38 @ SV10 )
| ~ ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV65 @ SV10 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV38 @ SV10 )
| ~ ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV65 @ SV10 ) )
| ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV83 @ SV10 ) ) )
= $true )
| ( ( qmltpeq @ SV83 @ ( set_intersection2 @ SV38 @ SV65 ) @ SV10 )
= $true )
| ( ( exists_in_world @ SV83 @ SV10 )
= $false )
| ( ( exists_in_world @ SV65 @ SV10 )
= $false )
| ( ( exists_in_world @ SV38 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[479]) ).
thf(485,plain,
! [SV72: mu,SV48: mu,SV23: $i,SV86: mu,SV93: mu] :
( ( ( ~ ( ~ ( in @ SV93 @ SV86 @ SV23 )
| ( qmltpeq @ SV93 @ SV48 @ SV23 )
| ( qmltpeq @ SV93 @ SV72 @ SV23 ) ) )
= $false )
| ( ( exists_in_world @ SV93 @ SV23 )
= $false )
| ( ( qmltpeq @ SV86 @ ( unordered_pair @ SV48 @ SV72 ) @ SV23 )
= $false )
| ( ( exists_in_world @ SV86 @ SV23 )
= $false )
| ( ( exists_in_world @ SV72 @ SV23 )
= $false )
| ( ( exists_in_world @ SV48 @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[480]) ).
thf(486,plain,
! [SV86: mu,SV72: mu,SV23: $i,SV48: mu,SV93: mu] :
( ( ( ~ ( ~ ( ( qmltpeq @ SV93 @ SV48 @ SV23 )
| ( qmltpeq @ SV93 @ SV72 @ SV23 ) )
| ( in @ SV93 @ SV86 @ SV23 ) ) )
= $false )
| ( ( exists_in_world @ SV93 @ SV23 )
= $false )
| ( ( qmltpeq @ SV86 @ ( unordered_pair @ SV48 @ SV72 ) @ SV23 )
= $false )
| ( ( exists_in_world @ SV86 @ SV23 )
= $false )
| ( ( exists_in_world @ SV72 @ SV23 )
= $false )
| ( ( exists_in_world @ SV48 @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[480]) ).
thf(487,plain,
! [SV23: $i,SV86: mu,SV48: mu,SV72: mu] :
( ( ( ~ ( in @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV86 @ SV23 )
| ( qmltpeq @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV48 @ SV23 )
| ( qmltpeq @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV72 @ SV23 ) )
= $false )
| ( ( ~ ( ~ ( ( qmltpeq @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV48 @ SV23 )
| ( qmltpeq @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV72 @ SV23 ) )
| ( in @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV86 @ SV23 ) ) )
= $true )
| ( ( qmltpeq @ SV86 @ ( unordered_pair @ SV48 @ SV72 ) @ SV23 )
= $true )
| ( ( exists_in_world @ SV86 @ SV23 )
= $false )
| ( ( exists_in_world @ SV72 @ SV23 )
= $false )
| ( ( exists_in_world @ SV48 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[481]) ).
thf(488,plain,
! [SV65: mu,SV38: mu,SV10: $i,SV83: mu,SV92: mu] :
( ( ( ~ ( in @ SV92 @ SV83 @ SV10 )
| ~ ( ~ ( in @ SV92 @ SV38 @ SV10 )
| ~ ( in @ SV92 @ SV65 @ SV10 ) ) )
= $true )
| ( ( exists_in_world @ SV92 @ SV10 )
= $false )
| ( ( qmltpeq @ SV83 @ ( set_intersection2 @ SV38 @ SV65 ) @ SV10 )
= $false )
| ( ( exists_in_world @ SV83 @ SV10 )
= $false )
| ( ( exists_in_world @ SV65 @ SV10 )
= $false )
| ( ( exists_in_world @ SV38 @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[482]) ).
thf(489,plain,
! [SV83: mu,SV65: mu,SV10: $i,SV38: mu,SV92: mu] :
( ( ( ~ ~ ( ~ ( in @ SV92 @ SV38 @ SV10 )
| ~ ( in @ SV92 @ SV65 @ SV10 ) )
| ( in @ SV92 @ SV83 @ SV10 ) )
= $true )
| ( ( exists_in_world @ SV92 @ SV10 )
= $false )
| ( ( qmltpeq @ SV83 @ ( set_intersection2 @ SV38 @ SV65 ) @ SV10 )
= $false )
| ( ( exists_in_world @ SV83 @ SV10 )
= $false )
| ( ( exists_in_world @ SV65 @ SV10 )
= $false )
| ( ( exists_in_world @ SV38 @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[483]) ).
thf(490,plain,
! [SV10: $i,SV83: mu,SV38: mu,SV65: mu] :
( ( ( ~ ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV83 @ SV10 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV38 @ SV10 )
| ~ ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV65 @ SV10 ) )
| ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV83 @ SV10 ) ) )
= $true )
| ( ( qmltpeq @ SV83 @ ( set_intersection2 @ SV38 @ SV65 ) @ SV10 )
= $true )
| ( ( exists_in_world @ SV83 @ SV10 )
= $false )
| ( ( exists_in_world @ SV65 @ SV10 )
= $false )
| ( ( exists_in_world @ SV38 @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[484]) ).
thf(491,plain,
! [SV10: $i,SV83: mu,SV38: mu,SV65: mu] :
( ( ( ~ ( ~ ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV38 @ SV10 )
| ~ ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV65 @ SV10 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV38 @ SV10 )
| ~ ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV65 @ SV10 ) )
| ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV83 @ SV10 ) ) )
= $true )
| ( ( qmltpeq @ SV83 @ ( set_intersection2 @ SV38 @ SV65 ) @ SV10 )
= $true )
| ( ( exists_in_world @ SV83 @ SV10 )
= $false )
| ( ( exists_in_world @ SV65 @ SV10 )
= $false )
| ( ( exists_in_world @ SV38 @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[484]) ).
thf(492,plain,
! [SV72: mu,SV48: mu,SV23: $i,SV86: mu,SV93: mu] :
( ( ( ~ ( in @ SV93 @ SV86 @ SV23 )
| ( qmltpeq @ SV93 @ SV48 @ SV23 )
| ( qmltpeq @ SV93 @ SV72 @ SV23 ) )
= $true )
| ( ( exists_in_world @ SV93 @ SV23 )
= $false )
| ( ( qmltpeq @ SV86 @ ( unordered_pair @ SV48 @ SV72 ) @ SV23 )
= $false )
| ( ( exists_in_world @ SV86 @ SV23 )
= $false )
| ( ( exists_in_world @ SV72 @ SV23 )
= $false )
| ( ( exists_in_world @ SV48 @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[485]) ).
thf(493,plain,
! [SV86: mu,SV72: mu,SV23: $i,SV48: mu,SV93: mu] :
( ( ( ~ ( ( qmltpeq @ SV93 @ SV48 @ SV23 )
| ( qmltpeq @ SV93 @ SV72 @ SV23 ) )
| ( in @ SV93 @ SV86 @ SV23 ) )
= $true )
| ( ( exists_in_world @ SV93 @ SV23 )
= $false )
| ( ( qmltpeq @ SV86 @ ( unordered_pair @ SV48 @ SV72 ) @ SV23 )
= $false )
| ( ( exists_in_world @ SV86 @ SV23 )
= $false )
| ( ( exists_in_world @ SV72 @ SV23 )
= $false )
| ( ( exists_in_world @ SV48 @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[486]) ).
thf(494,plain,
! [SV23: $i,SV86: mu,SV48: mu,SV72: mu] :
( ( ( ~ ( in @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV86 @ SV23 ) )
= $false )
| ( ( ~ ( ~ ( ( qmltpeq @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV48 @ SV23 )
| ( qmltpeq @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV72 @ SV23 ) )
| ( in @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV86 @ SV23 ) ) )
= $true )
| ( ( qmltpeq @ SV86 @ ( unordered_pair @ SV48 @ SV72 ) @ SV23 )
= $true )
| ( ( exists_in_world @ SV86 @ SV23 )
= $false )
| ( ( exists_in_world @ SV72 @ SV23 )
= $false )
| ( ( exists_in_world @ SV48 @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[487]) ).
thf(495,plain,
! [SV23: $i,SV86: mu,SV48: mu,SV72: mu] :
( ( ( ( qmltpeq @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV48 @ SV23 )
| ( qmltpeq @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV72 @ SV23 ) )
= $false )
| ( ( ~ ( ~ ( ( qmltpeq @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV48 @ SV23 )
| ( qmltpeq @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV72 @ SV23 ) )
| ( in @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV86 @ SV23 ) ) )
= $true )
| ( ( qmltpeq @ SV86 @ ( unordered_pair @ SV48 @ SV72 ) @ SV23 )
= $true )
| ( ( exists_in_world @ SV86 @ SV23 )
= $false )
| ( ( exists_in_world @ SV72 @ SV23 )
= $false )
| ( ( exists_in_world @ SV48 @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[487]) ).
thf(496,plain,
! [SV65: mu,SV38: mu,SV10: $i,SV83: mu,SV92: mu] :
( ( ( ~ ( in @ SV92 @ SV83 @ SV10 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV92 @ SV38 @ SV10 )
| ~ ( in @ SV92 @ SV65 @ SV10 ) ) )
= $true )
| ( ( exists_in_world @ SV92 @ SV10 )
= $false )
| ( ( qmltpeq @ SV83 @ ( set_intersection2 @ SV38 @ SV65 ) @ SV10 )
= $false )
| ( ( exists_in_world @ SV83 @ SV10 )
= $false )
| ( ( exists_in_world @ SV65 @ SV10 )
= $false )
| ( ( exists_in_world @ SV38 @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[488]) ).
thf(497,plain,
! [SV83: mu,SV65: mu,SV10: $i,SV38: mu,SV92: mu] :
( ( ( ~ ~ ( ~ ( in @ SV92 @ SV38 @ SV10 )
| ~ ( in @ SV92 @ SV65 @ SV10 ) ) )
= $true )
| ( ( in @ SV92 @ SV83 @ SV10 )
= $true )
| ( ( exists_in_world @ SV92 @ SV10 )
= $false )
| ( ( qmltpeq @ SV83 @ ( set_intersection2 @ SV38 @ SV65 ) @ SV10 )
= $false )
| ( ( exists_in_world @ SV83 @ SV10 )
= $false )
| ( ( exists_in_world @ SV65 @ SV10 )
= $false )
| ( ( exists_in_world @ SV38 @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[489]) ).
thf(498,plain,
! [SV10: $i,SV83: mu,SV38: mu,SV65: mu] :
( ( ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV83 @ SV10 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV38 @ SV10 )
| ~ ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV65 @ SV10 ) )
| ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV83 @ SV10 ) ) )
= $true )
| ( ( qmltpeq @ SV83 @ ( set_intersection2 @ SV38 @ SV65 ) @ SV10 )
= $true )
| ( ( exists_in_world @ SV83 @ SV10 )
= $false )
| ( ( exists_in_world @ SV65 @ SV10 )
= $false )
| ( ( exists_in_world @ SV38 @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[490]) ).
thf(499,plain,
! [SV10: $i,SV83: mu,SV38: mu,SV65: mu] :
( ( ( ~ ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV38 @ SV10 )
| ~ ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV65 @ SV10 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV38 @ SV10 )
| ~ ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV65 @ SV10 ) )
| ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV83 @ SV10 ) ) )
= $true )
| ( ( qmltpeq @ SV83 @ ( set_intersection2 @ SV38 @ SV65 ) @ SV10 )
= $true )
| ( ( exists_in_world @ SV83 @ SV10 )
= $false )
| ( ( exists_in_world @ SV65 @ SV10 )
= $false )
| ( ( exists_in_world @ SV38 @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[491]) ).
thf(500,plain,
! [SV72: mu,SV48: mu,SV23: $i,SV86: mu,SV93: mu] :
( ( ( ~ ( in @ SV93 @ SV86 @ SV23 ) )
= $true )
| ( ( ( qmltpeq @ SV93 @ SV48 @ SV23 )
| ( qmltpeq @ SV93 @ SV72 @ SV23 ) )
= $true )
| ( ( exists_in_world @ SV93 @ SV23 )
= $false )
| ( ( qmltpeq @ SV86 @ ( unordered_pair @ SV48 @ SV72 ) @ SV23 )
= $false )
| ( ( exists_in_world @ SV86 @ SV23 )
= $false )
| ( ( exists_in_world @ SV72 @ SV23 )
= $false )
| ( ( exists_in_world @ SV48 @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[492]) ).
thf(501,plain,
! [SV86: mu,SV72: mu,SV23: $i,SV48: mu,SV93: mu] :
( ( ( ~ ( ( qmltpeq @ SV93 @ SV48 @ SV23 )
| ( qmltpeq @ SV93 @ SV72 @ SV23 ) ) )
= $true )
| ( ( in @ SV93 @ SV86 @ SV23 )
= $true )
| ( ( exists_in_world @ SV93 @ SV23 )
= $false )
| ( ( qmltpeq @ SV86 @ ( unordered_pair @ SV48 @ SV72 ) @ SV23 )
= $false )
| ( ( exists_in_world @ SV86 @ SV23 )
= $false )
| ( ( exists_in_world @ SV72 @ SV23 )
= $false )
| ( ( exists_in_world @ SV48 @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[493]) ).
thf(502,plain,
! [SV23: $i,SV86: mu,SV48: mu,SV72: mu] :
( ( ( in @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV86 @ SV23 )
= $true )
| ( ( ~ ( ~ ( ( qmltpeq @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV48 @ SV23 )
| ( qmltpeq @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV72 @ SV23 ) )
| ( in @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV86 @ SV23 ) ) )
= $true )
| ( ( qmltpeq @ SV86 @ ( unordered_pair @ SV48 @ SV72 ) @ SV23 )
= $true )
| ( ( exists_in_world @ SV86 @ SV23 )
= $false )
| ( ( exists_in_world @ SV72 @ SV23 )
= $false )
| ( ( exists_in_world @ SV48 @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[494]) ).
thf(503,plain,
! [SV23: $i,SV86: mu,SV48: mu,SV72: mu] :
( ( ( qmltpeq @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV48 @ SV23 )
= $false )
| ( ( ~ ( ~ ( ( qmltpeq @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV48 @ SV23 )
| ( qmltpeq @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV72 @ SV23 ) )
| ( in @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV86 @ SV23 ) ) )
= $true )
| ( ( qmltpeq @ SV86 @ ( unordered_pair @ SV48 @ SV72 ) @ SV23 )
= $true )
| ( ( exists_in_world @ SV86 @ SV23 )
= $false )
| ( ( exists_in_world @ SV72 @ SV23 )
= $false )
| ( ( exists_in_world @ SV48 @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[495]) ).
thf(504,plain,
! [SV23: $i,SV86: mu,SV48: mu,SV72: mu] :
( ( ( qmltpeq @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV72 @ SV23 )
= $false )
| ( ( ~ ( ~ ( ( qmltpeq @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV48 @ SV23 )
| ( qmltpeq @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV72 @ SV23 ) )
| ( in @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV86 @ SV23 ) ) )
= $true )
| ( ( qmltpeq @ SV86 @ ( unordered_pair @ SV48 @ SV72 ) @ SV23 )
= $true )
| ( ( exists_in_world @ SV86 @ SV23 )
= $false )
| ( ( exists_in_world @ SV72 @ SV23 )
= $false )
| ( ( exists_in_world @ SV48 @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[495]) ).
thf(505,plain,
! [SV65: mu,SV38: mu,SV10: $i,SV83: mu,SV92: mu] :
( ( ( in @ SV92 @ SV83 @ SV10 )
= $false )
| ( ( ~ ( ~ ( in @ SV92 @ SV38 @ SV10 )
| ~ ( in @ SV92 @ SV65 @ SV10 ) ) )
= $true )
| ( ( exists_in_world @ SV92 @ SV10 )
= $false )
| ( ( qmltpeq @ SV83 @ ( set_intersection2 @ SV38 @ SV65 ) @ SV10 )
= $false )
| ( ( exists_in_world @ SV83 @ SV10 )
= $false )
| ( ( exists_in_world @ SV65 @ SV10 )
= $false )
| ( ( exists_in_world @ SV38 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[496]) ).
thf(506,plain,
! [SV83: mu,SV65: mu,SV10: $i,SV38: mu,SV92: mu] :
( ( ( ~ ( ~ ( in @ SV92 @ SV38 @ SV10 )
| ~ ( in @ SV92 @ SV65 @ SV10 ) ) )
= $false )
| ( ( in @ SV92 @ SV83 @ SV10 )
= $true )
| ( ( exists_in_world @ SV92 @ SV10 )
= $false )
| ( ( qmltpeq @ SV83 @ ( set_intersection2 @ SV38 @ SV65 ) @ SV10 )
= $false )
| ( ( exists_in_world @ SV83 @ SV10 )
= $false )
| ( ( exists_in_world @ SV65 @ SV10 )
= $false )
| ( ( exists_in_world @ SV38 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[497]) ).
thf(507,plain,
! [SV10: $i,SV83: mu,SV38: mu,SV65: mu] :
( ( ( ~ ~ ( ~ ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV38 @ SV10 )
| ~ ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV65 @ SV10 ) )
| ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV83 @ SV10 ) )
= $false )
| ( ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV83 @ SV10 )
= $true )
| ( ( qmltpeq @ SV83 @ ( set_intersection2 @ SV38 @ SV65 ) @ SV10 )
= $true )
| ( ( exists_in_world @ SV83 @ SV10 )
= $false )
| ( ( exists_in_world @ SV65 @ SV10 )
= $false )
| ( ( exists_in_world @ SV38 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[498]) ).
thf(508,plain,
! [SV10: $i,SV83: mu,SV38: mu,SV65: mu] :
( ( ( ~ ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV38 @ SV10 ) )
= $true )
| ( ( ~ ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV65 @ SV10 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV38 @ SV10 )
| ~ ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV65 @ SV10 ) )
| ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV83 @ SV10 ) ) )
= $true )
| ( ( qmltpeq @ SV83 @ ( set_intersection2 @ SV38 @ SV65 ) @ SV10 )
= $true )
| ( ( exists_in_world @ SV83 @ SV10 )
= $false )
| ( ( exists_in_world @ SV65 @ SV10 )
= $false )
| ( ( exists_in_world @ SV38 @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[499]) ).
thf(509,plain,
! [SV72: mu,SV48: mu,SV23: $i,SV86: mu,SV93: mu] :
( ( ( in @ SV93 @ SV86 @ SV23 )
= $false )
| ( ( ( qmltpeq @ SV93 @ SV48 @ SV23 )
| ( qmltpeq @ SV93 @ SV72 @ SV23 ) )
= $true )
| ( ( exists_in_world @ SV93 @ SV23 )
= $false )
| ( ( qmltpeq @ SV86 @ ( unordered_pair @ SV48 @ SV72 ) @ SV23 )
= $false )
| ( ( exists_in_world @ SV86 @ SV23 )
= $false )
| ( ( exists_in_world @ SV72 @ SV23 )
= $false )
| ( ( exists_in_world @ SV48 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[500]) ).
thf(510,plain,
! [SV86: mu,SV72: mu,SV23: $i,SV48: mu,SV93: mu] :
( ( ( ( qmltpeq @ SV93 @ SV48 @ SV23 )
| ( qmltpeq @ SV93 @ SV72 @ SV23 ) )
= $false )
| ( ( in @ SV93 @ SV86 @ SV23 )
= $true )
| ( ( exists_in_world @ SV93 @ SV23 )
= $false )
| ( ( qmltpeq @ SV86 @ ( unordered_pair @ SV48 @ SV72 ) @ SV23 )
= $false )
| ( ( exists_in_world @ SV86 @ SV23 )
= $false )
| ( ( exists_in_world @ SV72 @ SV23 )
= $false )
| ( ( exists_in_world @ SV48 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[501]) ).
thf(511,plain,
! [SV23: $i,SV86: mu,SV48: mu,SV72: mu] :
( ( ( ~ ( ( qmltpeq @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV48 @ SV23 )
| ( qmltpeq @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV72 @ SV23 ) )
| ( in @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV86 @ SV23 ) )
= $false )
| ( ( in @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV86 @ SV23 )
= $true )
| ( ( qmltpeq @ SV86 @ ( unordered_pair @ SV48 @ SV72 ) @ SV23 )
= $true )
| ( ( exists_in_world @ SV86 @ SV23 )
= $false )
| ( ( exists_in_world @ SV72 @ SV23 )
= $false )
| ( ( exists_in_world @ SV48 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[502]) ).
thf(512,plain,
! [SV23: $i,SV86: mu,SV48: mu,SV72: mu] :
( ( ( ~ ( ( qmltpeq @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV48 @ SV23 )
| ( qmltpeq @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV72 @ SV23 ) )
| ( in @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV86 @ SV23 ) )
= $false )
| ( ( qmltpeq @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV48 @ SV23 )
= $false )
| ( ( qmltpeq @ SV86 @ ( unordered_pair @ SV48 @ SV72 ) @ SV23 )
= $true )
| ( ( exists_in_world @ SV86 @ SV23 )
= $false )
| ( ( exists_in_world @ SV72 @ SV23 )
= $false )
| ( ( exists_in_world @ SV48 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[503]) ).
thf(513,plain,
! [SV23: $i,SV86: mu,SV48: mu,SV72: mu] :
( ( ( ~ ( ( qmltpeq @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV48 @ SV23 )
| ( qmltpeq @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV72 @ SV23 ) )
| ( in @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV86 @ SV23 ) )
= $false )
| ( ( qmltpeq @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV72 @ SV23 )
= $false )
| ( ( qmltpeq @ SV86 @ ( unordered_pair @ SV48 @ SV72 ) @ SV23 )
= $true )
| ( ( exists_in_world @ SV86 @ SV23 )
= $false )
| ( ( exists_in_world @ SV72 @ SV23 )
= $false )
| ( ( exists_in_world @ SV48 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[504]) ).
thf(514,plain,
! [SV83: mu,SV65: mu,SV10: $i,SV38: mu,SV92: mu] :
( ( ( ~ ( in @ SV92 @ SV38 @ SV10 )
| ~ ( in @ SV92 @ SV65 @ SV10 ) )
= $false )
| ( ( in @ SV92 @ SV83 @ SV10 )
= $false )
| ( ( exists_in_world @ SV92 @ SV10 )
= $false )
| ( ( qmltpeq @ SV83 @ ( set_intersection2 @ SV38 @ SV65 ) @ SV10 )
= $false )
| ( ( exists_in_world @ SV83 @ SV10 )
= $false )
| ( ( exists_in_world @ SV65 @ SV10 )
= $false )
| ( ( exists_in_world @ SV38 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[505]) ).
thf(515,plain,
! [SV83: mu,SV65: mu,SV10: $i,SV38: mu,SV92: mu] :
( ( ( ~ ( in @ SV92 @ SV38 @ SV10 )
| ~ ( in @ SV92 @ SV65 @ SV10 ) )
= $true )
| ( ( in @ SV92 @ SV83 @ SV10 )
= $true )
| ( ( exists_in_world @ SV92 @ SV10 )
= $false )
| ( ( qmltpeq @ SV83 @ ( set_intersection2 @ SV38 @ SV65 ) @ SV10 )
= $false )
| ( ( exists_in_world @ SV83 @ SV10 )
= $false )
| ( ( exists_in_world @ SV65 @ SV10 )
= $false )
| ( ( exists_in_world @ SV38 @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[506]) ).
thf(516,plain,
! [SV10: $i,SV83: mu,SV38: mu,SV65: mu] :
( ( ( ~ ~ ( ~ ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV38 @ SV10 )
| ~ ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV65 @ SV10 ) ) )
= $false )
| ( ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV83 @ SV10 )
= $true )
| ( ( qmltpeq @ SV83 @ ( set_intersection2 @ SV38 @ SV65 ) @ SV10 )
= $true )
| ( ( exists_in_world @ SV83 @ SV10 )
= $false )
| ( ( exists_in_world @ SV65 @ SV10 )
= $false )
| ( ( exists_in_world @ SV38 @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[507]) ).
thf(517,plain,
! [SV10: $i,SV83: mu,SV38: mu,SV65: mu] :
( ( ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV83 @ SV10 )
= $false )
| ( ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV83 @ SV10 )
= $true )
| ( ( qmltpeq @ SV83 @ ( set_intersection2 @ SV38 @ SV65 ) @ SV10 )
= $true )
| ( ( exists_in_world @ SV83 @ SV10 )
= $false )
| ( ( exists_in_world @ SV65 @ SV10 )
= $false )
| ( ( exists_in_world @ SV38 @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[507]) ).
thf(518,plain,
! [SV10: $i,SV83: mu,SV38: mu,SV65: mu] :
( ( ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV38 @ SV10 )
= $false )
| ( ( ~ ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV65 @ SV10 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV38 @ SV10 )
| ~ ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV65 @ SV10 ) )
| ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV83 @ SV10 ) ) )
= $true )
| ( ( qmltpeq @ SV83 @ ( set_intersection2 @ SV38 @ SV65 ) @ SV10 )
= $true )
| ( ( exists_in_world @ SV83 @ SV10 )
= $false )
| ( ( exists_in_world @ SV65 @ SV10 )
= $false )
| ( ( exists_in_world @ SV38 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[508]) ).
thf(519,plain,
! [SV86: mu,SV72: mu,SV23: $i,SV48: mu,SV93: mu] :
( ( ( qmltpeq @ SV93 @ SV48 @ SV23 )
= $true )
| ( ( qmltpeq @ SV93 @ SV72 @ SV23 )
= $true )
| ( ( in @ SV93 @ SV86 @ SV23 )
= $false )
| ( ( exists_in_world @ SV93 @ SV23 )
= $false )
| ( ( qmltpeq @ SV86 @ ( unordered_pair @ SV48 @ SV72 ) @ SV23 )
= $false )
| ( ( exists_in_world @ SV86 @ SV23 )
= $false )
| ( ( exists_in_world @ SV72 @ SV23 )
= $false )
| ( ( exists_in_world @ SV48 @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[509]) ).
thf(520,plain,
! [SV72: mu,SV86: mu,SV23: $i,SV48: mu,SV93: mu] :
( ( ( qmltpeq @ SV93 @ SV48 @ SV23 )
= $false )
| ( ( in @ SV93 @ SV86 @ SV23 )
= $true )
| ( ( exists_in_world @ SV93 @ SV23 )
= $false )
| ( ( qmltpeq @ SV86 @ ( unordered_pair @ SV48 @ SV72 ) @ SV23 )
= $false )
| ( ( exists_in_world @ SV86 @ SV23 )
= $false )
| ( ( exists_in_world @ SV72 @ SV23 )
= $false )
| ( ( exists_in_world @ SV48 @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[510]) ).
thf(521,plain,
! [SV48: mu,SV86: mu,SV23: $i,SV72: mu,SV93: mu] :
( ( ( qmltpeq @ SV93 @ SV72 @ SV23 )
= $false )
| ( ( in @ SV93 @ SV86 @ SV23 )
= $true )
| ( ( exists_in_world @ SV93 @ SV23 )
= $false )
| ( ( qmltpeq @ SV86 @ ( unordered_pair @ SV48 @ SV72 ) @ SV23 )
= $false )
| ( ( exists_in_world @ SV86 @ SV23 )
= $false )
| ( ( exists_in_world @ SV72 @ SV23 )
= $false )
| ( ( exists_in_world @ SV48 @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[510]) ).
thf(522,plain,
! [SV23: $i,SV86: mu,SV48: mu,SV72: mu] :
( ( ( ~ ( ( qmltpeq @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV48 @ SV23 )
| ( qmltpeq @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV72 @ SV23 ) ) )
= $false )
| ( ( in @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV86 @ SV23 )
= $true )
| ( ( qmltpeq @ SV86 @ ( unordered_pair @ SV48 @ SV72 ) @ SV23 )
= $true )
| ( ( exists_in_world @ SV86 @ SV23 )
= $false )
| ( ( exists_in_world @ SV72 @ SV23 )
= $false )
| ( ( exists_in_world @ SV48 @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[511]) ).
thf(523,plain,
! [SV23: $i,SV86: mu,SV48: mu,SV72: mu] :
( ( ( in @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV86 @ SV23 )
= $false )
| ( ( in @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV86 @ SV23 )
= $true )
| ( ( qmltpeq @ SV86 @ ( unordered_pair @ SV48 @ SV72 ) @ SV23 )
= $true )
| ( ( exists_in_world @ SV86 @ SV23 )
= $false )
| ( ( exists_in_world @ SV72 @ SV23 )
= $false )
| ( ( exists_in_world @ SV48 @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[511]) ).
thf(524,plain,
! [SV23: $i,SV86: mu,SV48: mu,SV72: mu] :
( ( ( ~ ( ( qmltpeq @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV48 @ SV23 )
| ( qmltpeq @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV72 @ SV23 ) ) )
= $false )
| ( ( qmltpeq @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV48 @ SV23 )
= $false )
| ( ( qmltpeq @ SV86 @ ( unordered_pair @ SV48 @ SV72 ) @ SV23 )
= $true )
| ( ( exists_in_world @ SV86 @ SV23 )
= $false )
| ( ( exists_in_world @ SV72 @ SV23 )
= $false )
| ( ( exists_in_world @ SV48 @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[512]) ).
thf(525,plain,
! [SV23: $i,SV86: mu,SV48: mu,SV72: mu] :
( ( ( in @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV86 @ SV23 )
= $false )
| ( ( qmltpeq @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV48 @ SV23 )
= $false )
| ( ( qmltpeq @ SV86 @ ( unordered_pair @ SV48 @ SV72 ) @ SV23 )
= $true )
| ( ( exists_in_world @ SV86 @ SV23 )
= $false )
| ( ( exists_in_world @ SV72 @ SV23 )
= $false )
| ( ( exists_in_world @ SV48 @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[512]) ).
thf(526,plain,
! [SV23: $i,SV86: mu,SV48: mu,SV72: mu] :
( ( ( ~ ( ( qmltpeq @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV48 @ SV23 )
| ( qmltpeq @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV72 @ SV23 ) ) )
= $false )
| ( ( qmltpeq @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV72 @ SV23 )
= $false )
| ( ( qmltpeq @ SV86 @ ( unordered_pair @ SV48 @ SV72 ) @ SV23 )
= $true )
| ( ( exists_in_world @ SV86 @ SV23 )
= $false )
| ( ( exists_in_world @ SV72 @ SV23 )
= $false )
| ( ( exists_in_world @ SV48 @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[513]) ).
thf(527,plain,
! [SV23: $i,SV86: mu,SV48: mu,SV72: mu] :
( ( ( in @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV86 @ SV23 )
= $false )
| ( ( qmltpeq @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV72 @ SV23 )
= $false )
| ( ( qmltpeq @ SV86 @ ( unordered_pair @ SV48 @ SV72 ) @ SV23 )
= $true )
| ( ( exists_in_world @ SV86 @ SV23 )
= $false )
| ( ( exists_in_world @ SV72 @ SV23 )
= $false )
| ( ( exists_in_world @ SV48 @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[513]) ).
thf(528,plain,
! [SV65: mu,SV83: mu,SV10: $i,SV38: mu,SV92: mu] :
( ( ( ~ ( in @ SV92 @ SV38 @ SV10 ) )
= $false )
| ( ( in @ SV92 @ SV83 @ SV10 )
= $false )
| ( ( exists_in_world @ SV92 @ SV10 )
= $false )
| ( ( qmltpeq @ SV83 @ ( set_intersection2 @ SV38 @ SV65 ) @ SV10 )
= $false )
| ( ( exists_in_world @ SV83 @ SV10 )
= $false )
| ( ( exists_in_world @ SV65 @ SV10 )
= $false )
| ( ( exists_in_world @ SV38 @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[514]) ).
thf(529,plain,
! [SV38: mu,SV83: mu,SV10: $i,SV65: mu,SV92: mu] :
( ( ( ~ ( in @ SV92 @ SV65 @ SV10 ) )
= $false )
| ( ( in @ SV92 @ SV83 @ SV10 )
= $false )
| ( ( exists_in_world @ SV92 @ SV10 )
= $false )
| ( ( qmltpeq @ SV83 @ ( set_intersection2 @ SV38 @ SV65 ) @ SV10 )
= $false )
| ( ( exists_in_world @ SV83 @ SV10 )
= $false )
| ( ( exists_in_world @ SV65 @ SV10 )
= $false )
| ( ( exists_in_world @ SV38 @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[514]) ).
thf(530,plain,
! [SV83: mu,SV65: mu,SV10: $i,SV38: mu,SV92: mu] :
( ( ( ~ ( in @ SV92 @ SV38 @ SV10 ) )
= $true )
| ( ( ~ ( in @ SV92 @ SV65 @ SV10 ) )
= $true )
| ( ( in @ SV92 @ SV83 @ SV10 )
= $true )
| ( ( exists_in_world @ SV92 @ SV10 )
= $false )
| ( ( qmltpeq @ SV83 @ ( set_intersection2 @ SV38 @ SV65 ) @ SV10 )
= $false )
| ( ( exists_in_world @ SV83 @ SV10 )
= $false )
| ( ( exists_in_world @ SV65 @ SV10 )
= $false )
| ( ( exists_in_world @ SV38 @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[515]) ).
thf(531,plain,
! [SV10: $i,SV83: mu,SV38: mu,SV65: mu] :
( ( ( ~ ( ~ ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV38 @ SV10 )
| ~ ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV65 @ SV10 ) ) )
= $true )
| ( ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV83 @ SV10 )
= $true )
| ( ( qmltpeq @ SV83 @ ( set_intersection2 @ SV38 @ SV65 ) @ SV10 )
= $true )
| ( ( exists_in_world @ SV83 @ SV10 )
= $false )
| ( ( exists_in_world @ SV65 @ SV10 )
= $false )
| ( ( exists_in_world @ SV38 @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[516]) ).
thf(532,plain,
! [SV10: $i,SV83: mu,SV38: mu,SV65: mu] :
( ( ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV65 @ SV10 )
= $false )
| ( ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV38 @ SV10 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV38 @ SV10 )
| ~ ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV65 @ SV10 ) )
| ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV83 @ SV10 ) ) )
= $true )
| ( ( qmltpeq @ SV83 @ ( set_intersection2 @ SV38 @ SV65 ) @ SV10 )
= $true )
| ( ( exists_in_world @ SV83 @ SV10 )
= $false )
| ( ( exists_in_world @ SV65 @ SV10 )
= $false )
| ( ( exists_in_world @ SV38 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[518]) ).
thf(533,plain,
! [SV23: $i,SV86: mu,SV48: mu,SV72: mu] :
( ( ( ( qmltpeq @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV48 @ SV23 )
| ( qmltpeq @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV72 @ SV23 ) )
= $true )
| ( ( in @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV86 @ SV23 )
= $true )
| ( ( qmltpeq @ SV86 @ ( unordered_pair @ SV48 @ SV72 ) @ SV23 )
= $true )
| ( ( exists_in_world @ SV86 @ SV23 )
= $false )
| ( ( exists_in_world @ SV72 @ SV23 )
= $false )
| ( ( exists_in_world @ SV48 @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[522]) ).
thf(534,plain,
! [SV23: $i,SV86: mu,SV48: mu,SV72: mu] :
( ( ( ( qmltpeq @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV48 @ SV23 )
| ( qmltpeq @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV72 @ SV23 ) )
= $true )
| ( ( qmltpeq @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV48 @ SV23 )
= $false )
| ( ( qmltpeq @ SV86 @ ( unordered_pair @ SV48 @ SV72 ) @ SV23 )
= $true )
| ( ( exists_in_world @ SV86 @ SV23 )
= $false )
| ( ( exists_in_world @ SV72 @ SV23 )
= $false )
| ( ( exists_in_world @ SV48 @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[524]) ).
thf(535,plain,
! [SV23: $i,SV86: mu,SV48: mu,SV72: mu] :
( ( ( ( qmltpeq @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV48 @ SV23 )
| ( qmltpeq @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV72 @ SV23 ) )
= $true )
| ( ( qmltpeq @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV72 @ SV23 )
= $false )
| ( ( qmltpeq @ SV86 @ ( unordered_pair @ SV48 @ SV72 ) @ SV23 )
= $true )
| ( ( exists_in_world @ SV86 @ SV23 )
= $false )
| ( ( exists_in_world @ SV72 @ SV23 )
= $false )
| ( ( exists_in_world @ SV48 @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[526]) ).
thf(536,plain,
! [SV65: mu,SV83: mu,SV10: $i,SV38: mu,SV92: mu] :
( ( ( in @ SV92 @ SV38 @ SV10 )
= $true )
| ( ( in @ SV92 @ SV83 @ SV10 )
= $false )
| ( ( exists_in_world @ SV92 @ SV10 )
= $false )
| ( ( qmltpeq @ SV83 @ ( set_intersection2 @ SV38 @ SV65 ) @ SV10 )
= $false )
| ( ( exists_in_world @ SV83 @ SV10 )
= $false )
| ( ( exists_in_world @ SV65 @ SV10 )
= $false )
| ( ( exists_in_world @ SV38 @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[528]) ).
thf(537,plain,
! [SV38: mu,SV83: mu,SV10: $i,SV65: mu,SV92: mu] :
( ( ( in @ SV92 @ SV65 @ SV10 )
= $true )
| ( ( in @ SV92 @ SV83 @ SV10 )
= $false )
| ( ( exists_in_world @ SV92 @ SV10 )
= $false )
| ( ( qmltpeq @ SV83 @ ( set_intersection2 @ SV38 @ SV65 ) @ SV10 )
= $false )
| ( ( exists_in_world @ SV83 @ SV10 )
= $false )
| ( ( exists_in_world @ SV65 @ SV10 )
= $false )
| ( ( exists_in_world @ SV38 @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[529]) ).
thf(538,plain,
! [SV83: mu,SV65: mu,SV10: $i,SV38: mu,SV92: mu] :
( ( ( in @ SV92 @ SV38 @ SV10 )
= $false )
| ( ( ~ ( in @ SV92 @ SV65 @ SV10 ) )
= $true )
| ( ( in @ SV92 @ SV83 @ SV10 )
= $true )
| ( ( exists_in_world @ SV92 @ SV10 )
= $false )
| ( ( qmltpeq @ SV83 @ ( set_intersection2 @ SV38 @ SV65 ) @ SV10 )
= $false )
| ( ( exists_in_world @ SV83 @ SV10 )
= $false )
| ( ( exists_in_world @ SV65 @ SV10 )
= $false )
| ( ( exists_in_world @ SV38 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[530]) ).
thf(539,plain,
! [SV10: $i,SV83: mu,SV38: mu,SV65: mu] :
( ( ( ~ ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV38 @ SV10 )
| ~ ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV65 @ SV10 ) )
= $false )
| ( ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV83 @ SV10 )
= $true )
| ( ( qmltpeq @ SV83 @ ( set_intersection2 @ SV38 @ SV65 ) @ SV10 )
= $true )
| ( ( exists_in_world @ SV83 @ SV10 )
= $false )
| ( ( exists_in_world @ SV65 @ SV10 )
= $false )
| ( ( exists_in_world @ SV38 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[531]) ).
thf(540,plain,
! [SV10: $i,SV83: mu,SV38: mu,SV65: mu] :
( ( ( ~ ~ ( ~ ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV38 @ SV10 )
| ~ ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV65 @ SV10 ) )
| ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV83 @ SV10 ) )
= $false )
| ( ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV38 @ SV10 )
= $false )
| ( ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV65 @ SV10 )
= $false )
| ( ( qmltpeq @ SV83 @ ( set_intersection2 @ SV38 @ SV65 ) @ SV10 )
= $true )
| ( ( exists_in_world @ SV83 @ SV10 )
= $false )
| ( ( exists_in_world @ SV65 @ SV10 )
= $false )
| ( ( exists_in_world @ SV38 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[532]) ).
thf(541,plain,
! [SV23: $i,SV86: mu,SV48: mu,SV72: mu] :
( ( ( qmltpeq @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV48 @ SV23 )
= $true )
| ( ( qmltpeq @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV72 @ SV23 )
= $true )
| ( ( in @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV86 @ SV23 )
= $true )
| ( ( qmltpeq @ SV86 @ ( unordered_pair @ SV48 @ SV72 ) @ SV23 )
= $true )
| ( ( exists_in_world @ SV86 @ SV23 )
= $false )
| ( ( exists_in_world @ SV72 @ SV23 )
= $false )
| ( ( exists_in_world @ SV48 @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[533]) ).
thf(542,plain,
! [SV23: $i,SV86: mu,SV48: mu,SV72: mu] :
( ( ( qmltpeq @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV48 @ SV23 )
= $true )
| ( ( qmltpeq @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV72 @ SV23 )
= $true )
| ( ( qmltpeq @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV48 @ SV23 )
= $false )
| ( ( qmltpeq @ SV86 @ ( unordered_pair @ SV48 @ SV72 ) @ SV23 )
= $true )
| ( ( exists_in_world @ SV86 @ SV23 )
= $false )
| ( ( exists_in_world @ SV72 @ SV23 )
= $false )
| ( ( exists_in_world @ SV48 @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[534]) ).
thf(543,plain,
! [SV23: $i,SV86: mu,SV48: mu,SV72: mu] :
( ( ( qmltpeq @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV48 @ SV23 )
= $true )
| ( ( qmltpeq @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV72 @ SV23 )
= $true )
| ( ( qmltpeq @ ( sK10_SY970 @ SV72 @ SV48 @ SV86 @ SV23 ) @ SV72 @ SV23 )
= $false )
| ( ( qmltpeq @ SV86 @ ( unordered_pair @ SV48 @ SV72 ) @ SV23 )
= $true )
| ( ( exists_in_world @ SV86 @ SV23 )
= $false )
| ( ( exists_in_world @ SV72 @ SV23 )
= $false )
| ( ( exists_in_world @ SV48 @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[535]) ).
thf(544,plain,
! [SV83: mu,SV38: mu,SV10: $i,SV65: mu,SV92: mu] :
( ( ( in @ SV92 @ SV65 @ SV10 )
= $false )
| ( ( in @ SV92 @ SV38 @ SV10 )
= $false )
| ( ( in @ SV92 @ SV83 @ SV10 )
= $true )
| ( ( exists_in_world @ SV92 @ SV10 )
= $false )
| ( ( qmltpeq @ SV83 @ ( set_intersection2 @ SV38 @ SV65 ) @ SV10 )
= $false )
| ( ( exists_in_world @ SV83 @ SV10 )
= $false )
| ( ( exists_in_world @ SV65 @ SV10 )
= $false )
| ( ( exists_in_world @ SV38 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[538]) ).
thf(545,plain,
! [SV10: $i,SV83: mu,SV38: mu,SV65: mu] :
( ( ( ~ ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV38 @ SV10 ) )
= $false )
| ( ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV83 @ SV10 )
= $true )
| ( ( qmltpeq @ SV83 @ ( set_intersection2 @ SV38 @ SV65 ) @ SV10 )
= $true )
| ( ( exists_in_world @ SV83 @ SV10 )
= $false )
| ( ( exists_in_world @ SV65 @ SV10 )
= $false )
| ( ( exists_in_world @ SV38 @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[539]) ).
thf(546,plain,
! [SV10: $i,SV83: mu,SV38: mu,SV65: mu] :
( ( ( ~ ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV65 @ SV10 ) )
= $false )
| ( ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV83 @ SV10 )
= $true )
| ( ( qmltpeq @ SV83 @ ( set_intersection2 @ SV38 @ SV65 ) @ SV10 )
= $true )
| ( ( exists_in_world @ SV83 @ SV10 )
= $false )
| ( ( exists_in_world @ SV65 @ SV10 )
= $false )
| ( ( exists_in_world @ SV38 @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[539]) ).
thf(547,plain,
! [SV10: $i,SV83: mu,SV38: mu,SV65: mu] :
( ( ( ~ ~ ( ~ ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV38 @ SV10 )
| ~ ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV65 @ SV10 ) ) )
= $false )
| ( ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV38 @ SV10 )
= $false )
| ( ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV65 @ SV10 )
= $false )
| ( ( qmltpeq @ SV83 @ ( set_intersection2 @ SV38 @ SV65 ) @ SV10 )
= $true )
| ( ( exists_in_world @ SV83 @ SV10 )
= $false )
| ( ( exists_in_world @ SV65 @ SV10 )
= $false )
| ( ( exists_in_world @ SV38 @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[540]) ).
thf(548,plain,
! [SV10: $i,SV83: mu,SV38: mu,SV65: mu] :
( ( ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV83 @ SV10 )
= $false )
| ( ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV38 @ SV10 )
= $false )
| ( ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV65 @ SV10 )
= $false )
| ( ( qmltpeq @ SV83 @ ( set_intersection2 @ SV38 @ SV65 ) @ SV10 )
= $true )
| ( ( exists_in_world @ SV83 @ SV10 )
= $false )
| ( ( exists_in_world @ SV65 @ SV10 )
= $false )
| ( ( exists_in_world @ SV38 @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[540]) ).
thf(549,plain,
! [SV10: $i,SV83: mu,SV38: mu,SV65: mu] :
( ( ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV38 @ SV10 )
= $true )
| ( ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV83 @ SV10 )
= $true )
| ( ( qmltpeq @ SV83 @ ( set_intersection2 @ SV38 @ SV65 ) @ SV10 )
= $true )
| ( ( exists_in_world @ SV83 @ SV10 )
= $false )
| ( ( exists_in_world @ SV65 @ SV10 )
= $false )
| ( ( exists_in_world @ SV38 @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[545]) ).
thf(550,plain,
! [SV10: $i,SV83: mu,SV38: mu,SV65: mu] :
( ( ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV65 @ SV10 )
= $true )
| ( ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV83 @ SV10 )
= $true )
| ( ( qmltpeq @ SV83 @ ( set_intersection2 @ SV38 @ SV65 ) @ SV10 )
= $true )
| ( ( exists_in_world @ SV83 @ SV10 )
= $false )
| ( ( exists_in_world @ SV65 @ SV10 )
= $false )
| ( ( exists_in_world @ SV38 @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[546]) ).
thf(551,plain,
! [SV10: $i,SV83: mu,SV38: mu,SV65: mu] :
( ( ( ~ ( ~ ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV38 @ SV10 )
| ~ ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV65 @ SV10 ) ) )
= $true )
| ( ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV38 @ SV10 )
= $false )
| ( ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV65 @ SV10 )
= $false )
| ( ( qmltpeq @ SV83 @ ( set_intersection2 @ SV38 @ SV65 ) @ SV10 )
= $true )
| ( ( exists_in_world @ SV83 @ SV10 )
= $false )
| ( ( exists_in_world @ SV65 @ SV10 )
= $false )
| ( ( exists_in_world @ SV38 @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[547]) ).
thf(552,plain,
! [SV10: $i,SV83: mu,SV38: mu,SV65: mu] :
( ( ( ~ ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV38 @ SV10 )
| ~ ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV65 @ SV10 ) )
= $false )
| ( ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV38 @ SV10 )
= $false )
| ( ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV65 @ SV10 )
= $false )
| ( ( qmltpeq @ SV83 @ ( set_intersection2 @ SV38 @ SV65 ) @ SV10 )
= $true )
| ( ( exists_in_world @ SV83 @ SV10 )
= $false )
| ( ( exists_in_world @ SV65 @ SV10 )
= $false )
| ( ( exists_in_world @ SV38 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[551]) ).
thf(553,plain,
! [SV10: $i,SV83: mu,SV38: mu,SV65: mu] :
( ( ( ~ ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV38 @ SV10 ) )
= $false )
| ( ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV38 @ SV10 )
= $false )
| ( ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV65 @ SV10 )
= $false )
| ( ( qmltpeq @ SV83 @ ( set_intersection2 @ SV38 @ SV65 ) @ SV10 )
= $true )
| ( ( exists_in_world @ SV83 @ SV10 )
= $false )
| ( ( exists_in_world @ SV65 @ SV10 )
= $false )
| ( ( exists_in_world @ SV38 @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[552]) ).
thf(554,plain,
! [SV10: $i,SV83: mu,SV38: mu,SV65: mu] :
( ( ( ~ ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV65 @ SV10 ) )
= $false )
| ( ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV38 @ SV10 )
= $false )
| ( ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV65 @ SV10 )
= $false )
| ( ( qmltpeq @ SV83 @ ( set_intersection2 @ SV38 @ SV65 ) @ SV10 )
= $true )
| ( ( exists_in_world @ SV83 @ SV10 )
= $false )
| ( ( exists_in_world @ SV65 @ SV10 )
= $false )
| ( ( exists_in_world @ SV38 @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[552]) ).
thf(555,plain,
! [SV10: $i,SV83: mu,SV38: mu,SV65: mu] :
( ( ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV38 @ SV10 )
= $true )
| ( ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV38 @ SV10 )
= $false )
| ( ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV65 @ SV10 )
= $false )
| ( ( qmltpeq @ SV83 @ ( set_intersection2 @ SV38 @ SV65 ) @ SV10 )
= $true )
| ( ( exists_in_world @ SV83 @ SV10 )
= $false )
| ( ( exists_in_world @ SV65 @ SV10 )
= $false )
| ( ( exists_in_world @ SV38 @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[553]) ).
thf(556,plain,
! [SV10: $i,SV83: mu,SV38: mu,SV65: mu] :
( ( ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV65 @ SV10 )
= $true )
| ( ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV38 @ SV10 )
= $false )
| ( ( in @ ( sK9_SY968 @ SV65 @ SV38 @ SV83 @ SV10 ) @ SV65 @ SV10 )
= $false )
| ( ( qmltpeq @ SV83 @ ( set_intersection2 @ SV38 @ SV65 ) @ SV10 )
= $true )
| ( ( exists_in_world @ SV83 @ SV10 )
= $false )
| ( ( exists_in_world @ SV65 @ SV10 )
= $false )
| ( ( exists_in_world @ SV38 @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[554]) ).
thf(557,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[102,556,555,550,549,548,544,543,542,541,537,536,527,525,523,521,520,519,517,476,473,465,464,461,458,457,433,432,426,424,423,422,417,416,415,411,383,373,372,369,368,359,358,319,313,309,303,294,267,259,258,249,243,232,193,192,135,132,131]) ).
thf(558,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[557]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET914^7 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.18 % Computer : n006.cluster.edu
% 0.06/0.18 % Model : x86_64 x86_64
% 0.06/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.18 % Memory : 8046.5625MB
% 0.06/0.18 % OS : Linux 6.8.0-71-generic
% 0.06/0.18 % CPULimit : 300
% 0.06/0.18 % WCLimit : 300
% 0.06/0.18 % DateTime : Tue Oct 6 14:55:37 UTC 2026
% 0.06/0.19 % CPUTime :
% 0.06/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.27/0.92
% 4.27/0.92 No.of.Axioms: 31
% 4.27/0.92
% 4.27/0.92 Length.of.Defs: 5508
% 4.27/0.92
% 4.27/0.92 Contains.Choice.Funs: false
% 4.27/0.92 .......................................
% 4.27/0.92
% 4.27/0.92 ********************************
% 4.27/0.92 * All subproblems solved! *
% 4.27/0.92 ********************************
% 4.27/0.92 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:32,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:557,loop_count:0,foatp_calls:1,translation:fof_full)
% 4.27/0.92
% 4.27/0.92 %**** Beginning of derivation protocol ****
% 4.27/0.92 % SZS output start CNFRefutation
% See solution above
% 4.27/0.92
% 4.27/0.92 %**** End of derivation protocol ****
% 4.27/0.92 %**** no. of clauses in derivation: 558 ****
% 4.27/0.92 %**** clause counter: 557 ****
% 4.27/0.92
% 4.27/0.92 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:32,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:557,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------