%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET907^7 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 10:42:31 AM UTC 2026
% Result : Theorem 1.08s 0.42s
% Output : CNFRefutation 1.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 62
% Syntax : Number of formulae : 470 ( 222 unt; 0 typ; 32 def)
% Number of atoms : 3948 ( 986 equ; 0 cnn)
% Maximal formula atoms : 9 ( 8 avg)
% Number of connectives : 7892 (1242 ~;1240 |; 13 &;5262 @)
% ( 0 <=>; 135 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 59 ( 59 >; 0 *; 0 +; 0 <<)
% Number of symbols : 50 ( 47 usr; 6 con; 0-3 aty)
% Number of variables : 1445 ( 108 ^;1328 !; 9 ?;1445 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_mu,type,
mu: $tType ).
thf(tp_empty,type,
empty: mu > $i > $o ).
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_sK1_SY32,type,
sK1_SY32: $i ).
thf(tp_sK2_SY681,type,
sK2_SY681: mu ).
thf(tp_sK3_SX0,type,
sK3_SX0: mu ).
thf(tp_sK4_SY697,type,
sK4_SY697: $i > mu ).
thf(tp_sK5_SY703,type,
sK5_SY703: $i > mu ).
thf(tp_sK6_SY715,type,
sK6_SY715: $i > mu ).
thf(tp_sK7_SY757,type,
sK7_SY757: mu ).
thf(tp_set_union2,type,
set_union2: mu > mu > mu ).
thf(tp_subset,type,
subset: mu > mu > $i > $o ).
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/sandbox2/benchmark/theBenchmark.p',mand) ).
thf(mbox,definition,
( mbox
= ( ^ [R: $i > $i > $o,Phi: $i > $o,W: $i] :
! [V: $i] :
( ~ ( R @ W @ V )
| ( Phi @ V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox) ).
thf(mbox_s4,definition,
( mbox_s4
= ( ^ [Phi: $i > $o,W: $i] :
! [V: $i] :
( ~ ( rel_s4 @ W @ V )
| ( Phi @ V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_s4) ).
thf(mcountersatisfiable,definition,
( mcountersatisfiable
= ( ^ [Phi: $i > $o] :
? [W: $i] :
~ ( Phi @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mcountersatisfiable) ).
thf(mdia,definition,
( mdia
= ( ^ [R: $i > $i > $o,Phi: $i > $o] : ( mnot @ ( mbox @ R @ ( mnot @ Phi ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia) ).
thf(mdia_s4,definition,
( mdia_s4
= ( ^ [Phi: $i > $o] : ( mnot @ ( mbox_s4 @ ( mnot @ Phi ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia_s4) ).
thf(meq_prop,definition,
( meq_prop
= ( ^ [X: $i > $o,Y: $i > $o,W: $i] :
( ( X @ W )
= ( Y @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',meq_prop) ).
thf(mequiv,definition,
( mequiv
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mand @ ( mimplies @ Phi @ Psi ) @ ( mimplies @ Psi @ Phi ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mequiv) ).
thf(meuclidean,definition,
( meuclidean
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ S @ U ) )
=> ( R @ T @ U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',meuclidean) ).
thf(mexists_ind,definition,
( mexists_ind
= ( ^ [Phi: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X: mu] : ( mnot @ ( Phi @ X ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mexists_ind) ).
thf(mexists_prop,definition,
( mexists_prop
= ( ^ [Phi: ( $i > $o ) > $i > $o] :
( mnot
@ ( mforall_prop
@ ^ [P: $i > $o] : ( mnot @ ( Phi @ P ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mexists_prop) ).
thf(mfalse,definition,
( mfalse
= ( mnot @ mtrue ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mfalse) ).
thf(mforall_ind,definition,
( mforall_ind
= ( ^ [Phi: mu > $i > $o,W: $i] :
! [X: mu] :
( ( exists_in_world @ X @ W )
=> ( Phi @ X @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mforall_ind) ).
thf(mforall_prop,definition,
( mforall_prop
= ( ^ [Phi: ( $i > $o ) > $i > $o,W: $i] :
! [P: $i > $o] : ( Phi @ P @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mforall_prop) ).
thf(mfunctional,definition,
( mfunctional
= ( ^ [R: $i > $i > $o] :
! [S: $i] :
? [T: $i] :
( ( R @ S @ T )
& ! [U: $i] :
( ( R @ S @ U )
=> ( T = U ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mfunctional) ).
thf(mimplied,definition,
( mimplied
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Psi ) @ Phi ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplied) ).
thf(mimplies,definition,
( mimplies
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Phi ) @ Psi ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies) ).
thf(minvalid,definition,
( minvalid
= ( ^ [Phi: $i > $o] :
! [W: $i] :
~ ( Phi @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',minvalid) ).
thf(mnot,definition,
( mnot
= ( ^ [Phi: $i > $o,W: $i] :
~ ( Phi @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot) ).
thf(mor,definition,
( mor
= ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
( ( Phi @ W )
| ( Psi @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor) ).
thf(mpartially_functional,definition,
( mpartially_functional
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ S @ U ) )
=> ( T = U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mpartially_functional) ).
thf(mreflexive,definition,
( mreflexive
= ( ^ [R: $i > $i > $o] :
! [S: $i] : ( R @ S @ S ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mreflexive) ).
thf(msatisfiable,definition,
( msatisfiable
= ( ^ [Phi: $i > $o] :
? [W: $i] : ( Phi @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',msatisfiable) ).
thf(mserial,definition,
( mserial
= ( ^ [R: $i > $i > $o] :
! [S: $i] :
? [T: $i] : ( R @ S @ T ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mserial) ).
thf(msymmetric,definition,
( msymmetric
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i] :
( ( R @ S @ T )
=> ( R @ T @ S ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',msymmetric) ).
thf(mtransitive,definition,
( mtransitive
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ T @ U ) )
=> ( R @ S @ U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mtransitive) ).
thf(mtrue,definition,
( mtrue
= ( ^ [W: $i] : $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mtrue) ).
thf(mvalid,definition,
( mvalid
= ( ^ [Phi: $i > $o] :
! [W: $i] : ( Phi @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mvalid) ).
thf(mweakly_connected,definition,
( mweakly_connected
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ S @ U ) )
=> ( ( R @ T @ U )
| ( T = U )
| ( R @ U @ T ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mweakly_connected) ).
thf(mweakly_dense,definition,
( mweakly_dense
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( R @ S @ T )
=> ? [U: $i] :
( ( R @ S @ U )
& ( R @ U @ T ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mweakly_dense) ).
thf(mweakly_directed,definition,
( mweakly_directed
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ S @ U ) )
=> ? [V: $i] :
( ( R @ T @ V )
& ( R @ U @ V ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mweakly_directed) ).
thf(mxor,definition,
( mxor
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mequiv @ Phi @ Psi ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mxor) ).
thf(1,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mequiv @ ( subset @ ( unordered_pair @ A @ B ) @ C ) @ ( mand @ ( in @ A @ C ) @ ( in @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_zfmisc_1) ).
thf(2,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] : ( mimplies @ ( subset @ A @ B ) @ ( qmltpeq @ ( set_union2 @ A @ B ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_xboole_1) ).
thf(3,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] : ( subset @ A @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(4,axiom,
( mvalid
@ ( mexists_ind
@ ^ [A: mu] : ( mnot @ ( empty @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(5,axiom,
( mvalid
@ ( mexists_ind
@ ^ [A: mu] : ( empty @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(6,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] : ( qmltpeq @ ( set_union2 @ A @ A ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(7,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] : ( mimplies @ ( mnot @ ( empty @ A ) ) @ ( mnot @ ( empty @ ( set_union2 @ B @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_xboole_0) ).
thf(8,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] : ( mimplies @ ( mnot @ ( empty @ A ) ) @ ( mnot @ ( empty @ ( set_union2 @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_xboole_0) ).
thf(9,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] : ( qmltpeq @ ( set_union2 @ A @ B ) @ ( set_union2 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
thf(10,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] : ( qmltpeq @ ( unordered_pair @ A @ B ) @ ( unordered_pair @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(11,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] : ( mimplies @ ( in @ A @ B ) @ ( mnot @ ( in @ B @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(12,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( subset @ C @ A ) ) @ ( subset @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_substitution_2) ).
thf(13,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( subset @ A @ C ) ) @ ( subset @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_substitution_1) ).
thf(14,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/sandbox2/benchmark/theBenchmark.p',in_substitution_2) ).
thf(15,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/sandbox2/benchmark/theBenchmark.p',in_substitution_1) ).
thf(16,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( empty @ A ) ) @ ( empty @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_substitution_1) ).
thf(17,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/sandbox2/benchmark/theBenchmark.p',unordered_pair_substitution_2) ).
thf(18,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/sandbox2/benchmark/theBenchmark.p',unordered_pair_substitution_1) ).
thf(19,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( set_union2 @ C @ A ) @ ( set_union2 @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_union2_substitution_2) ).
thf(20,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( set_union2 @ A @ C ) @ ( set_union2 @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_union2_substitution_1) ).
thf(21,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X: mu] :
( mforall_ind
@ ^ [Y: mu] :
( mforall_ind
@ ^ [Z: mu] : ( mimplies @ ( mand @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ Z ) ) @ ( qmltpeq @ X @ Z ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity) ).
thf(22,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X: mu] :
( mforall_ind
@ ^ [Y: mu] : ( mimplies @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ X ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry) ).
thf(23,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X: mu] : ( qmltpeq @ X @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).
thf(24,axiom,
! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( set_union2 @ V2 @ V1 ) @ V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_set_union2_ax) ).
thf(25,axiom,
! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( unordered_pair @ V2 @ V1 ) @ V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_unordered_pair_ax) ).
thf(26,axiom,
! [X: mu,V: $i,W: $i] :
( ( ( exists_in_world @ X @ V )
& ( rel_s4 @ V @ W ) )
=> ( exists_in_world @ X @ W ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cumulative_ax) ).
thf(27,axiom,
mtransitive @ rel_s4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2) ).
thf(28,axiom,
mreflexive @ rel_s4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a1) ).
thf(29,axiom,
! [V: $i] :
? [X: mu] : ( exists_in_world @ X @ V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonempty_ax) ).
thf(30,conjecture,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mimplies @ ( mand @ ( in @ A @ B ) @ ( in @ C @ B ) ) @ ( qmltpeq @ ( set_union2 @ ( unordered_pair @ A @ C ) @ B ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_zfmisc_1) ).
thf(31,negated_conjecture,
( ( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mimplies @ ( mand @ ( in @ A @ B ) @ ( in @ C @ B ) ) @ ( qmltpeq @ ( set_union2 @ ( unordered_pair @ A @ C ) @ B ) @ B ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[30]) ).
thf(32,plain,
( ( ! [SY32: $i,SY33: mu] :
( ( exists_in_world @ SY33 @ SY32 )
=> ! [SY34: mu] :
( ( exists_in_world @ SY34 @ SY32 )
=> ! [SY35: mu] :
( ( exists_in_world @ SY35 @ SY32 )
=> ( ~ ~ ( ~ ( in @ SY33 @ SY34 @ SY32 )
| ~ ( in @ SY35 @ SY34 @ SY32 ) )
| ( qmltpeq @ ( set_union2 @ ( unordered_pair @ SY33 @ SY35 ) @ SY34 ) @ SY34 @ SY32 ) ) ) ) ) )
= $false ),
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(33,plain,
( ( ! [SY88: $i,SY89: mu] :
( ( exists_in_world @ SY89 @ SY88 )
=> ! [SY90: mu] :
( ( exists_in_world @ SY90 @ SY88 )
=> ! [SY91: mu] :
( ( exists_in_world @ SY91 @ SY88 )
=> ~ ( ~ ( ~ ( subset @ ( unordered_pair @ SY89 @ SY90 ) @ SY91 @ SY88 )
| ~ ( ~ ( in @ SY89 @ SY91 @ SY88 )
| ~ ( in @ SY90 @ SY91 @ SY88 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY89 @ SY91 @ SY88 )
| ~ ( in @ SY90 @ SY91 @ SY88 ) )
| ( subset @ ( unordered_pair @ SY89 @ SY90 ) @ SY91 @ SY88 ) ) ) ) ) ) )
= $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(34,plain,
( ( ! [SY112: $i,SY113: mu] :
( ( exists_in_world @ SY113 @ SY112 )
=> ! [SY114: mu] :
( ( exists_in_world @ SY114 @ SY112 )
=> ( ~ ( subset @ SY113 @ SY114 @ SY112 )
| ( qmltpeq @ ( set_union2 @ SY113 @ SY114 ) @ SY114 @ SY112 ) ) ) ) )
= $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(35,plain,
( ( ! [SY127: $i,SY128: mu] :
( ( exists_in_world @ SY128 @ SY127 )
=> ! [SY129: mu] :
( ( exists_in_world @ SY129 @ SY127 )
=> ( subset @ SY128 @ SY128 @ SY127 ) ) ) )
= $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(36,plain,
( ( ! [SY143: $i] :
~ ! [SY144: mu] :
( ( exists_in_world @ SY144 @ SY143 )
=> ~ ~ ( empty @ SY144 @ SY143 ) ) )
= $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(37,plain,
( ( ! [SY155: $i] :
~ ! [SY156: mu] :
( ( exists_in_world @ SY156 @ SY155 )
=> ~ ( empty @ SY156 @ SY155 ) ) )
= $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(38,plain,
( ( ! [SY168: $i,SY169: mu] :
( ( exists_in_world @ SY169 @ SY168 )
=> ! [SY170: mu] :
( ( exists_in_world @ SY170 @ SY168 )
=> ( qmltpeq @ ( set_union2 @ SY169 @ SY169 ) @ SY169 @ SY168 ) ) ) )
= $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(39,plain,
( ( ! [SY192: $i,SY193: mu] :
( ( exists_in_world @ SY193 @ SY192 )
=> ! [SY194: mu] :
( ( exists_in_world @ SY194 @ SY192 )
=> ( ~ ~ ( empty @ SY193 @ SY192 )
| ~ ( empty @ ( set_union2 @ SY194 @ SY193 ) @ SY192 ) ) ) ) )
= $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(40,plain,
( ( ! [SY216: $i,SY217: mu] :
( ( exists_in_world @ SY217 @ SY216 )
=> ! [SY218: mu] :
( ( exists_in_world @ SY218 @ SY216 )
=> ( ~ ~ ( empty @ SY217 @ SY216 )
| ~ ( empty @ ( set_union2 @ SY217 @ SY218 ) @ SY216 ) ) ) ) )
= $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(41,plain,
( ( ! [SY231: $i,SY232: mu] :
( ( exists_in_world @ SY232 @ SY231 )
=> ! [SY233: mu] :
( ( exists_in_world @ SY233 @ SY231 )
=> ( qmltpeq @ ( set_union2 @ SY232 @ SY233 ) @ ( set_union2 @ SY233 @ SY232 ) @ SY231 ) ) ) )
= $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(42,plain,
( ( ! [SY246: $i,SY247: mu] :
( ( exists_in_world @ SY247 @ SY246 )
=> ! [SY248: mu] :
( ( exists_in_world @ SY248 @ SY246 )
=> ( qmltpeq @ ( unordered_pair @ SY247 @ SY248 ) @ ( unordered_pair @ SY248 @ SY247 ) @ SY246 ) ) ) )
= $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(43,plain,
( ( ! [SY269: $i,SY270: mu] :
( ( exists_in_world @ SY270 @ SY269 )
=> ! [SY271: mu] :
( ( exists_in_world @ SY271 @ SY269 )
=> ( ~ ( in @ SY270 @ SY271 @ SY269 )
| ~ ( in @ SY271 @ SY270 @ SY269 ) ) ) ) )
= $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(44,plain,
( ( ! [SY307: $i,SY308: mu] :
( ( exists_in_world @ SY308 @ SY307 )
=> ! [SY309: mu] :
( ( exists_in_world @ SY309 @ SY307 )
=> ! [SY310: mu] :
( ( exists_in_world @ SY310 @ SY307 )
=> ( ~ ~ ( ~ ( qmltpeq @ SY308 @ SY309 @ SY307 )
| ~ ( subset @ SY310 @ SY308 @ SY307 ) )
| ( subset @ SY310 @ SY309 @ SY307 ) ) ) ) ) )
= $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(45,plain,
( ( ! [SY347: $i,SY348: mu] :
( ( exists_in_world @ SY348 @ SY347 )
=> ! [SY349: mu] :
( ( exists_in_world @ SY349 @ SY347 )
=> ! [SY350: mu] :
( ( exists_in_world @ SY350 @ SY347 )
=> ( ~ ~ ( ~ ( qmltpeq @ SY348 @ SY349 @ SY347 )
| ~ ( subset @ SY348 @ SY350 @ SY347 ) )
| ( subset @ SY349 @ SY350 @ SY347 ) ) ) ) ) )
= $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(46,plain,
( ( ! [SY387: $i,SY388: mu] :
( ( exists_in_world @ SY388 @ SY387 )
=> ! [SY389: mu] :
( ( exists_in_world @ SY389 @ SY387 )
=> ! [SY390: mu] :
( ( exists_in_world @ SY390 @ SY387 )
=> ( ~ ~ ( ~ ( qmltpeq @ SY388 @ SY389 @ SY387 )
| ~ ( in @ SY390 @ SY388 @ SY387 ) )
| ( in @ SY390 @ SY389 @ SY387 ) ) ) ) ) )
= $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(47,plain,
( ( ! [SY427: $i,SY428: mu] :
( ( exists_in_world @ SY428 @ SY427 )
=> ! [SY429: mu] :
( ( exists_in_world @ SY429 @ SY427 )
=> ! [SY430: mu] :
( ( exists_in_world @ SY430 @ SY427 )
=> ( ~ ~ ( ~ ( qmltpeq @ SY428 @ SY429 @ SY427 )
| ~ ( in @ SY428 @ SY430 @ SY427 ) )
| ( in @ SY429 @ SY430 @ SY427 ) ) ) ) ) )
= $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(48,plain,
( ( ! [SY459: $i,SY460: mu] :
( ( exists_in_world @ SY460 @ SY459 )
=> ! [SY461: mu] :
( ( exists_in_world @ SY461 @ SY459 )
=> ( ~ ~ ( ~ ( qmltpeq @ SY460 @ SY461 @ SY459 )
| ~ ( empty @ SY460 @ SY459 ) )
| ( empty @ SY461 @ SY459 ) ) ) ) )
= $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(49,plain,
( ( ! [SY489: $i,SY490: mu] :
( ( exists_in_world @ SY490 @ SY489 )
=> ! [SY491: mu] :
( ( exists_in_world @ SY491 @ SY489 )
=> ! [SY492: mu] :
( ( exists_in_world @ SY492 @ SY489 )
=> ( ~ ( qmltpeq @ SY490 @ SY491 @ SY489 )
| ( qmltpeq @ ( unordered_pair @ SY492 @ SY490 ) @ ( unordered_pair @ SY492 @ SY491 ) @ SY489 ) ) ) ) ) )
= $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(50,plain,
( ( ! [SY521: $i,SY522: mu] :
( ( exists_in_world @ SY522 @ SY521 )
=> ! [SY523: mu] :
( ( exists_in_world @ SY523 @ SY521 )
=> ! [SY524: mu] :
( ( exists_in_world @ SY524 @ SY521 )
=> ( ~ ( qmltpeq @ SY522 @ SY523 @ SY521 )
| ( qmltpeq @ ( unordered_pair @ SY522 @ SY524 ) @ ( unordered_pair @ SY523 @ SY524 ) @ SY521 ) ) ) ) ) )
= $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(51,plain,
( ( ! [SY553: $i,SY554: mu] :
( ( exists_in_world @ SY554 @ SY553 )
=> ! [SY555: mu] :
( ( exists_in_world @ SY555 @ SY553 )
=> ! [SY556: mu] :
( ( exists_in_world @ SY556 @ SY553 )
=> ( ~ ( qmltpeq @ SY554 @ SY555 @ SY553 )
| ( qmltpeq @ ( set_union2 @ SY556 @ SY554 ) @ ( set_union2 @ SY556 @ SY555 ) @ SY553 ) ) ) ) ) )
= $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(52,plain,
( ( ! [SY585: $i,SY586: mu] :
( ( exists_in_world @ SY586 @ SY585 )
=> ! [SY587: mu] :
( ( exists_in_world @ SY587 @ SY585 )
=> ! [SY588: mu] :
( ( exists_in_world @ SY588 @ SY585 )
=> ( ~ ( qmltpeq @ SY586 @ SY587 @ SY585 )
| ( qmltpeq @ ( set_union2 @ SY586 @ SY588 ) @ ( set_union2 @ SY587 @ SY588 ) @ SY585 ) ) ) ) ) )
= $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(53,plain,
( ( ! [SY625: $i,SY626: mu] :
( ( exists_in_world @ SY626 @ SY625 )
=> ! [SY627: mu] :
( ( exists_in_world @ SY627 @ SY625 )
=> ! [SY628: mu] :
( ( exists_in_world @ SY628 @ SY625 )
=> ( ~ ~ ( ~ ( qmltpeq @ SY626 @ SY627 @ SY625 )
| ~ ( qmltpeq @ SY627 @ SY628 @ SY625 ) )
| ( qmltpeq @ SY626 @ SY628 @ SY625 ) ) ) ) ) )
= $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(54,plain,
( ( ! [SY649: $i,SY650: mu] :
( ( exists_in_world @ SY650 @ SY649 )
=> ! [SY651: mu] :
( ( exists_in_world @ SY651 @ SY649 )
=> ( ~ ( qmltpeq @ SY650 @ SY651 @ SY649 )
| ( qmltpeq @ SY651 @ SY650 @ SY649 ) ) ) ) )
= $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(55,plain,
( ( ! [SY658: $i,SY659: mu] :
( ( exists_in_world @ SY659 @ SY658 )
=> ( qmltpeq @ SY659 @ SY659 @ SY658 ) ) )
= $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(56,plain,
( ( ! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( set_union2 @ V2 @ V1 ) @ V ) )
= $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(57,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(58,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)],[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(59,plain,
( ( ! [SY671: $i,SY672: $i,SY673: $i] :
( ( ( rel_s4 @ SY671 @ SY672 )
& ( rel_s4 @ SY672 @ SY673 ) )
=> ( rel_s4 @ SY671 @ SY673 ) ) )
= $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(60,plain,
( ( ! [SY677: $i] : ( rel_s4 @ SY677 @ SY677 ) )
= $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(61,plain,
( ( ! [V: $i] :
? [X: mu] : ( exists_in_world @ X @ V ) )
= $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(62,plain,
( ( ! [SY681: mu] :
( ( exists_in_world @ SY681 @ sK1_SY32 )
=> ! [SY682: mu] :
( ( exists_in_world @ SY682 @ sK1_SY32 )
=> ! [SY683: mu] :
( ( exists_in_world @ SY683 @ sK1_SY32 )
=> ( ~ ~ ( ~ ( in @ SY681 @ SY682 @ sK1_SY32 )
| ~ ( in @ SY683 @ SY682 @ sK1_SY32 ) )
| ( qmltpeq @ ( set_union2 @ ( unordered_pair @ SY681 @ SY683 ) @ SY682 ) @ SY682 @ sK1_SY32 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[32]) ).
thf(63,plain,
( ( ( exists_in_world @ sK2_SY681 @ sK1_SY32 )
=> ! [SY684: mu] :
( ( exists_in_world @ SY684 @ sK1_SY32 )
=> ! [SY685: mu] :
( ( exists_in_world @ SY685 @ sK1_SY32 )
=> ( ~ ~ ( ~ ( in @ sK2_SY681 @ SY684 @ sK1_SY32 )
| ~ ( in @ SY685 @ SY684 @ sK1_SY32 ) )
| ( qmltpeq @ ( set_union2 @ ( unordered_pair @ sK2_SY681 @ SY685 ) @ SY684 ) @ SY684 @ sK1_SY32 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[62]) ).
thf(64,plain,
( ( exists_in_world @ sK2_SY681 @ sK1_SY32 )
= $true ),
inference(standard_cnf,[status(thm)],[63]) ).
thf(65,plain,
( ( ! [SY684: mu] :
( ( exists_in_world @ SY684 @ sK1_SY32 )
=> ! [SY685: mu] :
( ( exists_in_world @ SY685 @ sK1_SY32 )
=> ( ~ ~ ( ~ ( in @ sK2_SY681 @ SY684 @ sK1_SY32 )
| ~ ( in @ SY685 @ SY684 @ sK1_SY32 ) )
| ( qmltpeq @ ( set_union2 @ ( unordered_pair @ sK2_SY681 @ SY685 ) @ SY684 ) @ SY684 @ sK1_SY32 ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[63]) ).
thf(66,plain,
( ( ~ ! [SY684: mu] :
( ( exists_in_world @ SY684 @ sK1_SY32 )
=> ! [SY685: mu] :
( ( exists_in_world @ SY685 @ sK1_SY32 )
=> ( ~ ~ ( ~ ( in @ sK2_SY681 @ SY684 @ sK1_SY32 )
| ~ ( in @ SY685 @ SY684 @ sK1_SY32 ) )
| ( qmltpeq @ ( set_union2 @ ( unordered_pair @ sK2_SY681 @ SY685 ) @ SY684 ) @ SY684 @ sK1_SY32 ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[65]) ).
thf(67,plain,
( ( ! [V: $i] :
? [X: mu] : ( exists_in_world @ X @ V ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(68,plain,
( ( ! [SY677: $i] : ( rel_s4 @ SY677 @ SY677 ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(69,plain,
( ( ! [SY671: $i,SY672: $i,SY673: $i] :
( ( ( rel_s4 @ SY671 @ SY672 )
& ( rel_s4 @ SY672 @ SY673 ) )
=> ( rel_s4 @ SY671 @ SY673 ) ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(70,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)],[58]) ).
thf(71,plain,
( ( ! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( unordered_pair @ V2 @ V1 ) @ V ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(72,plain,
( ( ! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( set_union2 @ V2 @ V1 ) @ V ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(73,plain,
( ( ! [SY658: $i,SY659: mu] :
( ( exists_in_world @ SY659 @ SY658 )
=> ( qmltpeq @ SY659 @ SY659 @ SY658 ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(74,plain,
( ( ! [SY649: $i,SY650: mu] :
( ( exists_in_world @ SY650 @ SY649 )
=> ! [SY651: mu] :
( ( exists_in_world @ SY651 @ SY649 )
=> ( ~ ( qmltpeq @ SY650 @ SY651 @ SY649 )
| ( qmltpeq @ SY651 @ SY650 @ SY649 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(75,plain,
( ( ! [SY625: $i,SY626: mu] :
( ( exists_in_world @ SY626 @ SY625 )
=> ! [SY627: mu] :
( ( exists_in_world @ SY627 @ SY625 )
=> ! [SY628: mu] :
( ( exists_in_world @ SY628 @ SY625 )
=> ( ~ ~ ( ~ ( qmltpeq @ SY626 @ SY627 @ SY625 )
| ~ ( qmltpeq @ SY627 @ SY628 @ SY625 ) )
| ( qmltpeq @ SY626 @ SY628 @ SY625 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(76,plain,
( ( ! [SY585: $i,SY586: mu] :
( ( exists_in_world @ SY586 @ SY585 )
=> ! [SY587: mu] :
( ( exists_in_world @ SY587 @ SY585 )
=> ! [SY588: mu] :
( ( exists_in_world @ SY588 @ SY585 )
=> ( ~ ( qmltpeq @ SY586 @ SY587 @ SY585 )
| ( qmltpeq @ ( set_union2 @ SY586 @ SY588 ) @ ( set_union2 @ SY587 @ SY588 ) @ SY585 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(77,plain,
( ( ! [SY553: $i,SY554: mu] :
( ( exists_in_world @ SY554 @ SY553 )
=> ! [SY555: mu] :
( ( exists_in_world @ SY555 @ SY553 )
=> ! [SY556: mu] :
( ( exists_in_world @ SY556 @ SY553 )
=> ( ~ ( qmltpeq @ SY554 @ SY555 @ SY553 )
| ( qmltpeq @ ( set_union2 @ SY556 @ SY554 ) @ ( set_union2 @ SY556 @ SY555 ) @ SY553 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(78,plain,
( ( ! [SY521: $i,SY522: mu] :
( ( exists_in_world @ SY522 @ SY521 )
=> ! [SY523: mu] :
( ( exists_in_world @ SY523 @ SY521 )
=> ! [SY524: mu] :
( ( exists_in_world @ SY524 @ SY521 )
=> ( ~ ( qmltpeq @ SY522 @ SY523 @ SY521 )
| ( qmltpeq @ ( unordered_pair @ SY522 @ SY524 ) @ ( unordered_pair @ SY523 @ SY524 ) @ SY521 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(79,plain,
( ( ! [SY489: $i,SY490: mu] :
( ( exists_in_world @ SY490 @ SY489 )
=> ! [SY491: mu] :
( ( exists_in_world @ SY491 @ SY489 )
=> ! [SY492: mu] :
( ( exists_in_world @ SY492 @ SY489 )
=> ( ~ ( qmltpeq @ SY490 @ SY491 @ SY489 )
| ( qmltpeq @ ( unordered_pair @ SY492 @ SY490 ) @ ( unordered_pair @ SY492 @ SY491 ) @ SY489 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(80,plain,
( ( ! [SY459: $i,SY460: mu] :
( ( exists_in_world @ SY460 @ SY459 )
=> ! [SY461: mu] :
( ( exists_in_world @ SY461 @ SY459 )
=> ( ~ ~ ( ~ ( qmltpeq @ SY460 @ SY461 @ SY459 )
| ~ ( empty @ SY460 @ SY459 ) )
| ( empty @ SY461 @ SY459 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(81,plain,
( ( ! [SY427: $i,SY428: mu] :
( ( exists_in_world @ SY428 @ SY427 )
=> ! [SY429: mu] :
( ( exists_in_world @ SY429 @ SY427 )
=> ! [SY430: mu] :
( ( exists_in_world @ SY430 @ SY427 )
=> ( ~ ~ ( ~ ( qmltpeq @ SY428 @ SY429 @ SY427 )
| ~ ( in @ SY428 @ SY430 @ SY427 ) )
| ( in @ SY429 @ SY430 @ SY427 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(82,plain,
( ( ! [SY387: $i,SY388: mu] :
( ( exists_in_world @ SY388 @ SY387 )
=> ! [SY389: mu] :
( ( exists_in_world @ SY389 @ SY387 )
=> ! [SY390: mu] :
( ( exists_in_world @ SY390 @ SY387 )
=> ( ~ ~ ( ~ ( qmltpeq @ SY388 @ SY389 @ SY387 )
| ~ ( in @ SY390 @ SY388 @ SY387 ) )
| ( in @ SY390 @ SY389 @ SY387 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(83,plain,
( ( ! [SY347: $i,SY348: mu] :
( ( exists_in_world @ SY348 @ SY347 )
=> ! [SY349: mu] :
( ( exists_in_world @ SY349 @ SY347 )
=> ! [SY350: mu] :
( ( exists_in_world @ SY350 @ SY347 )
=> ( ~ ~ ( ~ ( qmltpeq @ SY348 @ SY349 @ SY347 )
| ~ ( subset @ SY348 @ SY350 @ SY347 ) )
| ( subset @ SY349 @ SY350 @ SY347 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(84,plain,
( ( ! [SY307: $i,SY308: mu] :
( ( exists_in_world @ SY308 @ SY307 )
=> ! [SY309: mu] :
( ( exists_in_world @ SY309 @ SY307 )
=> ! [SY310: mu] :
( ( exists_in_world @ SY310 @ SY307 )
=> ( ~ ~ ( ~ ( qmltpeq @ SY308 @ SY309 @ SY307 )
| ~ ( subset @ SY310 @ SY308 @ SY307 ) )
| ( subset @ SY310 @ SY309 @ SY307 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(85,plain,
( ( ! [SY269: $i,SY270: mu] :
( ( exists_in_world @ SY270 @ SY269 )
=> ! [SY271: mu] :
( ( exists_in_world @ SY271 @ SY269 )
=> ( ~ ( in @ SY270 @ SY271 @ SY269 )
| ~ ( in @ SY271 @ SY270 @ SY269 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(86,plain,
( ( ! [SY246: $i,SY247: mu] :
( ( exists_in_world @ SY247 @ SY246 )
=> ! [SY248: mu] :
( ( exists_in_world @ SY248 @ SY246 )
=> ( qmltpeq @ ( unordered_pair @ SY247 @ SY248 ) @ ( unordered_pair @ SY248 @ SY247 ) @ SY246 ) ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(87,plain,
( ( ! [SY231: $i,SY232: mu] :
( ( exists_in_world @ SY232 @ SY231 )
=> ! [SY233: mu] :
( ( exists_in_world @ SY233 @ SY231 )
=> ( qmltpeq @ ( set_union2 @ SY232 @ SY233 ) @ ( set_union2 @ SY233 @ SY232 ) @ SY231 ) ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(88,plain,
( ( ! [SY216: $i,SY217: mu] :
( ( exists_in_world @ SY217 @ SY216 )
=> ! [SY218: mu] :
( ( exists_in_world @ SY218 @ SY216 )
=> ( ~ ~ ( empty @ SY217 @ SY216 )
| ~ ( empty @ ( set_union2 @ SY217 @ SY218 ) @ SY216 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(89,plain,
( ( ! [SY192: $i,SY193: mu] :
( ( exists_in_world @ SY193 @ SY192 )
=> ! [SY194: mu] :
( ( exists_in_world @ SY194 @ SY192 )
=> ( ~ ~ ( empty @ SY193 @ SY192 )
| ~ ( empty @ ( set_union2 @ SY194 @ SY193 ) @ SY192 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(90,plain,
( ( ! [SY168: $i,SY169: mu] :
( ( exists_in_world @ SY169 @ SY168 )
=> ! [SY170: mu] :
( ( exists_in_world @ SY170 @ SY168 )
=> ( qmltpeq @ ( set_union2 @ SY169 @ SY169 ) @ SY169 @ SY168 ) ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(91,plain,
( ( ! [SY155: $i] :
~ ! [SY156: mu] :
( ( exists_in_world @ SY156 @ SY155 )
=> ~ ( empty @ SY156 @ SY155 ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(92,plain,
( ( ! [SY143: $i] :
~ ! [SY144: mu] :
( ( exists_in_world @ SY144 @ SY143 )
=> ~ ~ ( empty @ SY144 @ SY143 ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(93,plain,
( ( ! [SY127: $i,SY128: mu] :
( ( exists_in_world @ SY128 @ SY127 )
=> ! [SY129: mu] :
( ( exists_in_world @ SY129 @ SY127 )
=> ( subset @ SY128 @ SY128 @ SY127 ) ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(94,plain,
( ( ! [SY112: $i,SY113: mu] :
( ( exists_in_world @ SY113 @ SY112 )
=> ! [SY114: mu] :
( ( exists_in_world @ SY114 @ SY112 )
=> ( ~ ( subset @ SY113 @ SY114 @ SY112 )
| ( qmltpeq @ ( set_union2 @ SY113 @ SY114 ) @ SY114 @ SY112 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(95,plain,
( ( ! [SY88: $i,SY89: mu] :
( ( exists_in_world @ SY89 @ SY88 )
=> ! [SY90: mu] :
( ( exists_in_world @ SY90 @ SY88 )
=> ! [SY91: mu] :
( ( exists_in_world @ SY91 @ SY88 )
=> ~ ( ~ ( ~ ( subset @ ( unordered_pair @ SY89 @ SY90 ) @ SY91 @ SY88 )
| ~ ( ~ ( in @ SY89 @ SY91 @ SY88 )
| ~ ( in @ SY90 @ SY91 @ SY88 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY89 @ SY91 @ SY88 )
| ~ ( in @ SY90 @ SY91 @ SY88 ) )
| ( subset @ ( unordered_pair @ SY89 @ SY90 ) @ SY91 @ SY88 ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(96,plain,
( ( exists_in_world @ sK2_SY681 @ sK1_SY32 )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(97,plain,
( ( ~ ! [SY684: mu] :
( ( exists_in_world @ SY684 @ sK1_SY32 )
=> ! [SY685: mu] :
( ( exists_in_world @ SY685 @ sK1_SY32 )
=> ( ~ ~ ( ~ ( in @ sK2_SY681 @ SY684 @ sK1_SY32 )
| ~ ( in @ SY685 @ SY684 @ sK1_SY32 ) )
| ( qmltpeq @ ( set_union2 @ ( unordered_pair @ sK2_SY681 @ SY685 ) @ SY684 ) @ SY684 @ sK1_SY32 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(98,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)],[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(99,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ~ ~ ( empty @ SX1 @ SX0 )
| ~ ( empty @ ( set_union2 @ SX1 @ SX2 ) @ 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(100,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX0 )
| ~ ~ ( ~ ( qmltpeq @ SX1 @ SX2 @ SX0 )
| ~ ( subset @ SX1 @ SX3 @ SX0 ) )
| ( subset @ SX2 @ SX3 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[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(101,plain,
( ( ! [SX0: $i] :
~ ! [SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ~ ~ ( empty @ 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(102,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX0 )
| ~ ( ~ ( ~ ( subset @ ( unordered_pair @ SX1 @ SX2 ) @ SX3 @ SX0 )
| ~ ( ~ ( in @ SX1 @ SX3 @ SX0 )
| ~ ( in @ SX2 @ SX3 @ SX0 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX1 @ SX3 @ SX0 )
| ~ ( in @ SX2 @ SX3 @ SX0 ) )
| ( subset @ ( unordered_pair @ SX1 @ SX2 ) @ SX3 @ 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(103,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ( subset @ SX1 @ SX1 @ 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(104,plain,
( ( ~ ! [SX0: mu] :
( ~ ( exists_in_world @ SX0 @ sK1_SY32 )
| ! [SX1: mu] :
( ~ ( exists_in_world @ SX1 @ sK1_SY32 )
| ~ ~ ( ~ ( in @ sK2_SY681 @ SX0 @ sK1_SY32 )
| ~ ( in @ SX1 @ SX0 @ sK1_SY32 ) )
| ( qmltpeq @ ( set_union2 @ ( unordered_pair @ sK2_SY681 @ SX1 ) @ SX0 ) @ SX0 @ sK1_SY32 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[97,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 )
| ~ ( empty @ 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(106,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ( qmltpeq @ SX1 @ SX1 @ SX0 ) ) )
= $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(107,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)],[75,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 )
| ~ ( qmltpeq @ SX1 @ SX2 @ SX0 )
| ( qmltpeq @ SX2 @ SX1 @ SX0 ) ) ) )
= $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(109,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX0 )
| ~ ~ ( ~ ( qmltpeq @ SX1 @ SX2 @ SX0 )
| ~ ( subset @ SX3 @ SX1 @ SX0 ) )
| ( subset @ SX3 @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[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(110,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ( qmltpeq @ ( set_union2 @ SX1 @ SX2 ) @ ( set_union2 @ SX2 @ SX1 ) @ 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(111,plain,
( ( ! [SX0: $i] :
~ ! [SX1: mu] :
~ ( exists_in_world @ SX1 @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[67,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: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ( qmltpeq @ ( set_union2 @ SX1 @ SX1 ) @ 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(113,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)],[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(114,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_union2 @ SX1 @ SX3 ) @ ( set_union2 @ SX2 @ SX3 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76,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 )
| ~ ( subset @ SX1 @ SX2 @ SX0 )
| ( qmltpeq @ ( set_union2 @ SX1 @ SX2 ) @ 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(116,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)],[70,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 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX0 )
| ~ ( qmltpeq @ SX1 @ SX2 @ SX0 )
| ( qmltpeq @ ( set_union2 @ SX3 @ SX1 ) @ ( set_union2 @ SX3 @ SX2 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77,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 )
| ! [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)],[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(119,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)],[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(120,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)],[69,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 @ SX1 @ SX2 @ SX0 )
| ( qmltpeq @ ( unordered_pair @ SX3 @ SX1 ) @ ( unordered_pair @ SX3 @ SX2 ) @ 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(122,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ~ ~ ( empty @ SX1 @ SX0 )
| ~ ( empty @ ( set_union2 @ SX2 @ SX1 ) @ 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(123,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)],[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(124,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)],[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(125,plain,
! [SV1: $i] :
( ( rel_s4 @ SV1 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(126,plain,
! [SV2: $i] :
( ( ! [SY686: mu,SY687: mu] : ( exists_in_world @ ( unordered_pair @ SY686 @ SY687 ) @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(127,plain,
! [SV3: $i] :
( ( ! [SY688: mu,SY689: mu] : ( exists_in_world @ ( set_union2 @ SY688 @ SY689 ) @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(128,plain,
! [SV4: $i] :
( ( ! [SY690: mu] :
( ~ ( exists_in_world @ SY690 @ SV4 )
| ! [SY691: mu] :
( ~ ( exists_in_world @ SY691 @ SV4 )
| ( qmltpeq @ ( unordered_pair @ SY690 @ SY691 ) @ ( unordered_pair @ SY691 @ SY690 ) @ SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(129,plain,
! [SV5: $i] :
( ( ! [SY692: mu] :
( ~ ( exists_in_world @ SY692 @ SV5 )
| ! [SY693: mu] :
( ~ ( exists_in_world @ SY693 @ SV5 )
| ~ ~ ( empty @ SY692 @ SV5 )
| ~ ( empty @ ( set_union2 @ SY692 @ SY693 ) @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(130,plain,
! [SV6: $i] :
( ( ! [SY694: mu] :
( ~ ( exists_in_world @ SY694 @ SV6 )
| ! [SY695: mu] :
( ~ ( exists_in_world @ SY695 @ SV6 )
| ! [SY696: mu] :
( ~ ( exists_in_world @ SY696 @ SV6 )
| ~ ~ ( ~ ( qmltpeq @ SY694 @ SY695 @ SV6 )
| ~ ( subset @ SY694 @ SY696 @ SV6 ) )
| ( subset @ SY695 @ SY696 @ SV6 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(131,plain,
! [SV7: $i] :
( ( ~ ! [SY697: mu] :
( ~ ( exists_in_world @ SY697 @ SV7 )
| ~ ~ ( empty @ SY697 @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(132,plain,
! [SV8: $i] :
( ( ! [SY698: mu] :
( ~ ( exists_in_world @ SY698 @ SV8 )
| ! [SY699: mu] :
( ~ ( exists_in_world @ SY699 @ SV8 )
| ! [SY700: mu] :
( ~ ( exists_in_world @ SY700 @ SV8 )
| ~ ( ~ ( ~ ( subset @ ( unordered_pair @ SY698 @ SY699 ) @ SY700 @ SV8 )
| ~ ( ~ ( in @ SY698 @ SY700 @ SV8 )
| ~ ( in @ SY699 @ SY700 @ SV8 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY698 @ SY700 @ SV8 )
| ~ ( in @ SY699 @ SY700 @ SV8 ) )
| ( subset @ ( unordered_pair @ SY698 @ SY699 ) @ SY700 @ SV8 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(133,plain,
! [SV9: $i] :
( ( ! [SY701: mu] :
( ~ ( exists_in_world @ SY701 @ SV9 )
| ! [SY702: mu] :
( ~ ( exists_in_world @ SY702 @ SV9 )
| ( subset @ SY701 @ SY701 @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(134,plain,
( ( ! [SX0: mu] :
( ~ ( exists_in_world @ SX0 @ sK1_SY32 )
| ! [SX1: mu] :
( ~ ( exists_in_world @ SX1 @ sK1_SY32 )
| ~ ~ ( ~ ( in @ sK2_SY681 @ SX0 @ sK1_SY32 )
| ~ ( in @ SX1 @ SX0 @ sK1_SY32 ) )
| ( qmltpeq @ ( set_union2 @ ( unordered_pair @ sK2_SY681 @ SX1 ) @ SX0 ) @ SX0 @ sK1_SY32 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[104]) ).
thf(135,plain,
! [SV10: $i] :
( ( ~ ! [SY703: mu] :
( ~ ( exists_in_world @ SY703 @ SV10 )
| ~ ( empty @ SY703 @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(136,plain,
! [SV11: $i] :
( ( ! [SY704: mu] :
( ~ ( exists_in_world @ SY704 @ SV11 )
| ( qmltpeq @ SY704 @ SY704 @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(137,plain,
! [SV12: $i] :
( ( ! [SY705: mu] :
( ~ ( exists_in_world @ SY705 @ SV12 )
| ! [SY706: mu] :
( ~ ( exists_in_world @ SY706 @ SV12 )
| ! [SY707: mu] :
( ~ ( exists_in_world @ SY707 @ SV12 )
| ~ ~ ( ~ ( qmltpeq @ SY705 @ SY706 @ SV12 )
| ~ ( qmltpeq @ SY706 @ SY707 @ SV12 ) )
| ( qmltpeq @ SY705 @ SY707 @ SV12 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(138,plain,
! [SV13: $i] :
( ( ! [SY708: mu] :
( ~ ( exists_in_world @ SY708 @ SV13 )
| ! [SY709: mu] :
( ~ ( exists_in_world @ SY709 @ SV13 )
| ~ ( qmltpeq @ SY708 @ SY709 @ SV13 )
| ( qmltpeq @ SY709 @ SY708 @ SV13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(139,plain,
! [SV14: $i] :
( ( ! [SY710: mu] :
( ~ ( exists_in_world @ SY710 @ SV14 )
| ! [SY711: mu] :
( ~ ( exists_in_world @ SY711 @ SV14 )
| ! [SY712: mu] :
( ~ ( exists_in_world @ SY712 @ SV14 )
| ~ ~ ( ~ ( qmltpeq @ SY710 @ SY711 @ SV14 )
| ~ ( subset @ SY712 @ SY710 @ SV14 ) )
| ( subset @ SY712 @ SY711 @ SV14 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(140,plain,
! [SV15: $i] :
( ( ! [SY713: mu] :
( ~ ( exists_in_world @ SY713 @ SV15 )
| ! [SY714: mu] :
( ~ ( exists_in_world @ SY714 @ SV15 )
| ( qmltpeq @ ( set_union2 @ SY713 @ SY714 ) @ ( set_union2 @ SY714 @ SY713 ) @ SV15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(141,plain,
! [SV16: $i] :
( ( ~ ! [SY715: mu] :
~ ( exists_in_world @ SY715 @ SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(142,plain,
! [SV17: $i] :
( ( ! [SY716: mu] :
( ~ ( exists_in_world @ SY716 @ SV17 )
| ! [SY717: mu] :
( ~ ( exists_in_world @ SY717 @ SV17 )
| ( qmltpeq @ ( set_union2 @ SY716 @ SY716 ) @ SY716 @ SV17 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(143,plain,
! [SV18: $i] :
( ( ! [SY718: mu] :
( ~ ( exists_in_world @ SY718 @ SV18 )
| ! [SY719: mu] :
( ~ ( exists_in_world @ SY719 @ SV18 )
| ~ ( in @ SY718 @ SY719 @ SV18 )
| ~ ( in @ SY719 @ SY718 @ SV18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(144,plain,
! [SV19: $i] :
( ( ! [SY720: mu] :
( ~ ( exists_in_world @ SY720 @ SV19 )
| ! [SY721: mu] :
( ~ ( exists_in_world @ SY721 @ SV19 )
| ! [SY722: mu] :
( ~ ( exists_in_world @ SY722 @ SV19 )
| ~ ( qmltpeq @ SY720 @ SY721 @ SV19 )
| ( qmltpeq @ ( set_union2 @ SY720 @ SY722 ) @ ( set_union2 @ SY721 @ SY722 ) @ SV19 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(145,plain,
! [SV20: $i] :
( ( ! [SY723: mu] :
( ~ ( exists_in_world @ SY723 @ SV20 )
| ! [SY724: mu] :
( ~ ( exists_in_world @ SY724 @ SV20 )
| ~ ( subset @ SY723 @ SY724 @ SV20 )
| ( qmltpeq @ ( set_union2 @ SY723 @ SY724 ) @ SY724 @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(146,plain,
! [SV21: mu] :
( ( ! [SY725: $i,SY726: $i] :
( ~ ~ ( ~ ( exists_in_world @ SV21 @ SY725 )
| ~ ( rel_s4 @ SY725 @ SY726 ) )
| ( exists_in_world @ SV21 @ SY726 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(147,plain,
! [SV22: $i] :
( ( ! [SY727: mu] :
( ~ ( exists_in_world @ SY727 @ SV22 )
| ! [SY728: mu] :
( ~ ( exists_in_world @ SY728 @ SV22 )
| ! [SY729: mu] :
( ~ ( exists_in_world @ SY729 @ SV22 )
| ~ ( qmltpeq @ SY727 @ SY728 @ SV22 )
| ( qmltpeq @ ( set_union2 @ SY729 @ SY727 ) @ ( set_union2 @ SY729 @ SY728 ) @ SV22 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(148,plain,
! [SV23: $i] :
( ( ! [SY730: mu] :
( ~ ( exists_in_world @ SY730 @ SV23 )
| ! [SY731: mu] :
( ~ ( exists_in_world @ SY731 @ SV23 )
| ! [SY732: mu] :
( ~ ( exists_in_world @ SY732 @ SV23 )
| ~ ~ ( ~ ( qmltpeq @ SY730 @ SY731 @ SV23 )
| ~ ( in @ SY730 @ SY732 @ SV23 ) )
| ( in @ SY731 @ SY732 @ SV23 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(149,plain,
! [SV24: $i] :
( ( ! [SY733: mu] :
( ~ ( exists_in_world @ SY733 @ SV24 )
| ! [SY734: mu] :
( ~ ( exists_in_world @ SY734 @ SV24 )
| ! [SY735: mu] :
( ~ ( exists_in_world @ SY735 @ SV24 )
| ~ ( qmltpeq @ SY733 @ SY734 @ SV24 )
| ( qmltpeq @ ( unordered_pair @ SY733 @ SY735 ) @ ( unordered_pair @ SY734 @ SY735 ) @ SV24 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(150,plain,
! [SV25: $i] :
( ( ! [SY736: $i,SY737: $i] :
( ~ ~ ( ~ ( rel_s4 @ SV25 @ SY736 )
| ~ ( rel_s4 @ SY736 @ SY737 ) )
| ( rel_s4 @ SV25 @ SY737 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(151,plain,
! [SV26: $i] :
( ( ! [SY738: mu] :
( ~ ( exists_in_world @ SY738 @ SV26 )
| ! [SY739: mu] :
( ~ ( exists_in_world @ SY739 @ SV26 )
| ! [SY740: mu] :
( ~ ( exists_in_world @ SY740 @ SV26 )
| ~ ( qmltpeq @ SY738 @ SY739 @ SV26 )
| ( qmltpeq @ ( unordered_pair @ SY740 @ SY738 ) @ ( unordered_pair @ SY740 @ SY739 ) @ SV26 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(152,plain,
! [SV27: $i] :
( ( ! [SY741: mu] :
( ~ ( exists_in_world @ SY741 @ SV27 )
| ! [SY742: mu] :
( ~ ( exists_in_world @ SY742 @ SV27 )
| ~ ~ ( empty @ SY741 @ SV27 )
| ~ ( empty @ ( set_union2 @ SY742 @ SY741 ) @ SV27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(153,plain,
! [SV28: $i] :
( ( ! [SY743: mu] :
( ~ ( exists_in_world @ SY743 @ SV28 )
| ! [SY744: mu] :
( ~ ( exists_in_world @ SY744 @ SV28 )
| ! [SY745: mu] :
( ~ ( exists_in_world @ SY745 @ SV28 )
| ~ ~ ( ~ ( qmltpeq @ SY743 @ SY744 @ SV28 )
| ~ ( in @ SY745 @ SY743 @ SV28 ) )
| ( in @ SY745 @ SY744 @ SV28 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(154,plain,
! [SV29: $i] :
( ( ! [SY746: mu] :
( ~ ( exists_in_world @ SY746 @ SV29 )
| ! [SY747: mu] :
( ~ ( exists_in_world @ SY747 @ SV29 )
| ~ ~ ( ~ ( qmltpeq @ SY746 @ SY747 @ SV29 )
| ~ ( empty @ SY746 @ SV29 ) )
| ( empty @ SY747 @ SV29 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(155,plain,
! [SV2: $i,SV30: mu] :
( ( ! [SY748: mu] : ( exists_in_world @ ( unordered_pair @ SV30 @ SY748 ) @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(156,plain,
! [SV3: $i,SV31: mu] :
( ( ! [SY749: mu] : ( exists_in_world @ ( set_union2 @ SV31 @ SY749 ) @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(157,plain,
! [SV4: $i,SV32: mu] :
( ( ~ ( exists_in_world @ SV32 @ SV4 )
| ! [SY750: mu] :
( ~ ( exists_in_world @ SY750 @ SV4 )
| ( qmltpeq @ ( unordered_pair @ SV32 @ SY750 ) @ ( unordered_pair @ SY750 @ SV32 ) @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(158,plain,
! [SV5: $i,SV33: mu] :
( ( ~ ( exists_in_world @ SV33 @ SV5 )
| ! [SY751: mu] :
( ~ ( exists_in_world @ SY751 @ SV5 )
| ~ ~ ( empty @ SV33 @ SV5 )
| ~ ( empty @ ( set_union2 @ SV33 @ SY751 ) @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(159,plain,
! [SV6: $i,SV34: mu] :
( ( ~ ( exists_in_world @ SV34 @ SV6 )
| ! [SY752: mu] :
( ~ ( exists_in_world @ SY752 @ SV6 )
| ! [SY753: mu] :
( ~ ( exists_in_world @ SY753 @ SV6 )
| ~ ~ ( ~ ( qmltpeq @ SV34 @ SY752 @ SV6 )
| ~ ( subset @ SV34 @ SY753 @ SV6 ) )
| ( subset @ SY752 @ SY753 @ SV6 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(160,plain,
! [SV7: $i] :
( ( ! [SY697: mu] :
( ~ ( exists_in_world @ SY697 @ SV7 )
| ~ ~ ( empty @ SY697 @ SV7 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(161,plain,
! [SV8: $i,SV35: mu] :
( ( ~ ( exists_in_world @ SV35 @ SV8 )
| ! [SY754: mu] :
( ~ ( exists_in_world @ SY754 @ SV8 )
| ! [SY755: mu] :
( ~ ( exists_in_world @ SY755 @ SV8 )
| ~ ( ~ ( ~ ( subset @ ( unordered_pair @ SV35 @ SY754 ) @ SY755 @ SV8 )
| ~ ( ~ ( in @ SV35 @ SY755 @ SV8 )
| ~ ( in @ SY754 @ SY755 @ SV8 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV35 @ SY755 @ SV8 )
| ~ ( in @ SY754 @ SY755 @ SV8 ) )
| ( subset @ ( unordered_pair @ SV35 @ SY754 ) @ SY755 @ SV8 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(162,plain,
! [SV9: $i,SV36: mu] :
( ( ~ ( exists_in_world @ SV36 @ SV9 )
| ! [SY756: mu] :
( ~ ( exists_in_world @ SY756 @ SV9 )
| ( subset @ SV36 @ SV36 @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(163,plain,
( ( ~ ( exists_in_world @ sK3_SX0 @ sK1_SY32 )
| ! [SY757: mu] :
( ~ ( exists_in_world @ SY757 @ sK1_SY32 )
| ~ ~ ( ~ ( in @ sK2_SY681 @ sK3_SX0 @ sK1_SY32 )
| ~ ( in @ SY757 @ sK3_SX0 @ sK1_SY32 ) )
| ( qmltpeq @ ( set_union2 @ ( unordered_pair @ sK2_SY681 @ SY757 ) @ sK3_SX0 ) @ sK3_SX0 @ sK1_SY32 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[134]) ).
thf(164,plain,
! [SV10: $i] :
( ( ! [SY703: mu] :
( ~ ( exists_in_world @ SY703 @ SV10 )
| ~ ( empty @ SY703 @ SV10 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(165,plain,
! [SV11: $i,SV37: mu] :
( ( ~ ( exists_in_world @ SV37 @ SV11 )
| ( qmltpeq @ SV37 @ SV37 @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(166,plain,
! [SV12: $i,SV38: mu] :
( ( ~ ( exists_in_world @ SV38 @ SV12 )
| ! [SY758: mu] :
( ~ ( exists_in_world @ SY758 @ SV12 )
| ! [SY759: mu] :
( ~ ( exists_in_world @ SY759 @ SV12 )
| ~ ~ ( ~ ( qmltpeq @ SV38 @ SY758 @ SV12 )
| ~ ( qmltpeq @ SY758 @ SY759 @ SV12 ) )
| ( qmltpeq @ SV38 @ SY759 @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(167,plain,
! [SV13: $i,SV39: mu] :
( ( ~ ( exists_in_world @ SV39 @ SV13 )
| ! [SY760: mu] :
( ~ ( exists_in_world @ SY760 @ SV13 )
| ~ ( qmltpeq @ SV39 @ SY760 @ SV13 )
| ( qmltpeq @ SY760 @ SV39 @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(168,plain,
! [SV14: $i,SV40: mu] :
( ( ~ ( exists_in_world @ SV40 @ SV14 )
| ! [SY761: mu] :
( ~ ( exists_in_world @ SY761 @ SV14 )
| ! [SY762: mu] :
( ~ ( exists_in_world @ SY762 @ SV14 )
| ~ ~ ( ~ ( qmltpeq @ SV40 @ SY761 @ SV14 )
| ~ ( subset @ SY762 @ SV40 @ SV14 ) )
| ( subset @ SY762 @ SY761 @ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(169,plain,
! [SV15: $i,SV41: mu] :
( ( ~ ( exists_in_world @ SV41 @ SV15 )
| ! [SY763: mu] :
( ~ ( exists_in_world @ SY763 @ SV15 )
| ( qmltpeq @ ( set_union2 @ SV41 @ SY763 ) @ ( set_union2 @ SY763 @ SV41 ) @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(170,plain,
! [SV16: $i] :
( ( ! [SY715: mu] :
~ ( exists_in_world @ SY715 @ SV16 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(171,plain,
! [SV17: $i,SV42: mu] :
( ( ~ ( exists_in_world @ SV42 @ SV17 )
| ! [SY764: mu] :
( ~ ( exists_in_world @ SY764 @ SV17 )
| ( qmltpeq @ ( set_union2 @ SV42 @ SV42 ) @ SV42 @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(172,plain,
! [SV18: $i,SV43: mu] :
( ( ~ ( exists_in_world @ SV43 @ SV18 )
| ! [SY765: mu] :
( ~ ( exists_in_world @ SY765 @ SV18 )
| ~ ( in @ SV43 @ SY765 @ SV18 )
| ~ ( in @ SY765 @ SV43 @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(173,plain,
! [SV19: $i,SV44: mu] :
( ( ~ ( exists_in_world @ SV44 @ SV19 )
| ! [SY766: mu] :
( ~ ( exists_in_world @ SY766 @ SV19 )
| ! [SY767: mu] :
( ~ ( exists_in_world @ SY767 @ SV19 )
| ~ ( qmltpeq @ SV44 @ SY766 @ SV19 )
| ( qmltpeq @ ( set_union2 @ SV44 @ SY767 ) @ ( set_union2 @ SY766 @ SY767 ) @ SV19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(174,plain,
! [SV20: $i,SV45: mu] :
( ( ~ ( exists_in_world @ SV45 @ SV20 )
| ! [SY768: mu] :
( ~ ( exists_in_world @ SY768 @ SV20 )
| ~ ( subset @ SV45 @ SY768 @ SV20 )
| ( qmltpeq @ ( set_union2 @ SV45 @ SY768 ) @ SY768 @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(175,plain,
! [SV46: $i,SV21: mu] :
( ( ! [SY769: $i] :
( ~ ~ ( ~ ( exists_in_world @ SV21 @ SV46 )
| ~ ( rel_s4 @ SV46 @ SY769 ) )
| ( exists_in_world @ SV21 @ SY769 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(176,plain,
! [SV22: $i,SV47: mu] :
( ( ~ ( exists_in_world @ SV47 @ SV22 )
| ! [SY770: mu] :
( ~ ( exists_in_world @ SY770 @ SV22 )
| ! [SY771: mu] :
( ~ ( exists_in_world @ SY771 @ SV22 )
| ~ ( qmltpeq @ SV47 @ SY770 @ SV22 )
| ( qmltpeq @ ( set_union2 @ SY771 @ SV47 ) @ ( set_union2 @ SY771 @ SY770 ) @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(177,plain,
! [SV23: $i,SV48: mu] :
( ( ~ ( exists_in_world @ SV48 @ SV23 )
| ! [SY772: mu] :
( ~ ( exists_in_world @ SY772 @ SV23 )
| ! [SY773: mu] :
( ~ ( exists_in_world @ SY773 @ SV23 )
| ~ ~ ( ~ ( qmltpeq @ SV48 @ SY772 @ SV23 )
| ~ ( in @ SV48 @ SY773 @ SV23 ) )
| ( in @ SY772 @ SY773 @ SV23 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(178,plain,
! [SV24: $i,SV49: mu] :
( ( ~ ( exists_in_world @ SV49 @ SV24 )
| ! [SY774: mu] :
( ~ ( exists_in_world @ SY774 @ SV24 )
| ! [SY775: mu] :
( ~ ( exists_in_world @ SY775 @ SV24 )
| ~ ( qmltpeq @ SV49 @ SY774 @ SV24 )
| ( qmltpeq @ ( unordered_pair @ SV49 @ SY775 ) @ ( unordered_pair @ SY774 @ SY775 ) @ SV24 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(179,plain,
! [SV50: $i,SV25: $i] :
( ( ! [SY776: $i] :
( ~ ~ ( ~ ( rel_s4 @ SV25 @ SV50 )
| ~ ( rel_s4 @ SV50 @ SY776 ) )
| ( rel_s4 @ SV25 @ SY776 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(180,plain,
! [SV26: $i,SV51: mu] :
( ( ~ ( exists_in_world @ SV51 @ SV26 )
| ! [SY777: mu] :
( ~ ( exists_in_world @ SY777 @ SV26 )
| ! [SY778: mu] :
( ~ ( exists_in_world @ SY778 @ SV26 )
| ~ ( qmltpeq @ SV51 @ SY777 @ SV26 )
| ( qmltpeq @ ( unordered_pair @ SY778 @ SV51 ) @ ( unordered_pair @ SY778 @ SY777 ) @ SV26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(181,plain,
! [SV27: $i,SV52: mu] :
( ( ~ ( exists_in_world @ SV52 @ SV27 )
| ! [SY779: mu] :
( ~ ( exists_in_world @ SY779 @ SV27 )
| ~ ~ ( empty @ SV52 @ SV27 )
| ~ ( empty @ ( set_union2 @ SY779 @ SV52 ) @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(182,plain,
! [SV28: $i,SV53: mu] :
( ( ~ ( exists_in_world @ SV53 @ SV28 )
| ! [SY780: mu] :
( ~ ( exists_in_world @ SY780 @ SV28 )
| ! [SY781: mu] :
( ~ ( exists_in_world @ SY781 @ SV28 )
| ~ ~ ( ~ ( qmltpeq @ SV53 @ SY780 @ SV28 )
| ~ ( in @ SY781 @ SV53 @ SV28 ) )
| ( in @ SY781 @ SY780 @ SV28 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(183,plain,
! [SV29: $i,SV54: mu] :
( ( ~ ( exists_in_world @ SV54 @ SV29 )
| ! [SY782: mu] :
( ~ ( exists_in_world @ SY782 @ SV29 )
| ~ ~ ( ~ ( qmltpeq @ SV54 @ SY782 @ SV29 )
| ~ ( empty @ SV54 @ SV29 ) )
| ( empty @ SY782 @ SV29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(184,plain,
! [SV2: $i,SV55: mu,SV30: mu] :
( ( exists_in_world @ ( unordered_pair @ SV30 @ SV55 ) @ SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(185,plain,
! [SV3: $i,SV56: mu,SV31: mu] :
( ( exists_in_world @ ( set_union2 @ SV31 @ SV56 ) @ SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(186,plain,
! [SV4: $i,SV32: mu] :
( ( ( ~ ( exists_in_world @ SV32 @ SV4 ) )
= $true )
| ( ( ! [SY750: mu] :
( ~ ( exists_in_world @ SY750 @ SV4 )
| ( qmltpeq @ ( unordered_pair @ SV32 @ SY750 ) @ ( unordered_pair @ SY750 @ SV32 ) @ SV4 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[157]) ).
thf(187,plain,
! [SV5: $i,SV33: mu] :
( ( ( ~ ( exists_in_world @ SV33 @ SV5 ) )
= $true )
| ( ( ! [SY751: mu] :
( ~ ( exists_in_world @ SY751 @ SV5 )
| ~ ~ ( empty @ SV33 @ SV5 )
| ~ ( empty @ ( set_union2 @ SV33 @ SY751 ) @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[158]) ).
thf(188,plain,
! [SV6: $i,SV34: mu] :
( ( ( ~ ( exists_in_world @ SV34 @ SV6 ) )
= $true )
| ( ( ! [SY752: mu] :
( ~ ( exists_in_world @ SY752 @ SV6 )
| ! [SY753: mu] :
( ~ ( exists_in_world @ SY753 @ SV6 )
| ~ ~ ( ~ ( qmltpeq @ SV34 @ SY752 @ SV6 )
| ~ ( subset @ SV34 @ SY753 @ SV6 ) )
| ( subset @ SY752 @ SY753 @ SV6 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[159]) ).
thf(189,plain,
! [SV7: $i] :
( ( ~ ( exists_in_world @ ( sK4_SY697 @ SV7 ) @ SV7 )
| ~ ~ ( empty @ ( sK4_SY697 @ SV7 ) @ SV7 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[160]) ).
thf(190,plain,
! [SV8: $i,SV35: mu] :
( ( ( ~ ( exists_in_world @ SV35 @ SV8 ) )
= $true )
| ( ( ! [SY754: mu] :
( ~ ( exists_in_world @ SY754 @ SV8 )
| ! [SY755: mu] :
( ~ ( exists_in_world @ SY755 @ SV8 )
| ~ ( ~ ( ~ ( subset @ ( unordered_pair @ SV35 @ SY754 ) @ SY755 @ SV8 )
| ~ ( ~ ( in @ SV35 @ SY755 @ SV8 )
| ~ ( in @ SY754 @ SY755 @ SV8 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV35 @ SY755 @ SV8 )
| ~ ( in @ SY754 @ SY755 @ SV8 ) )
| ( subset @ ( unordered_pair @ SV35 @ SY754 ) @ SY755 @ SV8 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[161]) ).
thf(191,plain,
! [SV9: $i,SV36: mu] :
( ( ( ~ ( exists_in_world @ SV36 @ SV9 ) )
= $true )
| ( ( ! [SY756: mu] :
( ~ ( exists_in_world @ SY756 @ SV9 )
| ( subset @ SV36 @ SV36 @ SV9 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[162]) ).
thf(192,plain,
( ( ~ ( exists_in_world @ sK3_SX0 @ sK1_SY32 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[163]) ).
thf(193,plain,
( ( ! [SY757: mu] :
( ~ ( exists_in_world @ SY757 @ sK1_SY32 )
| ~ ~ ( ~ ( in @ sK2_SY681 @ sK3_SX0 @ sK1_SY32 )
| ~ ( in @ SY757 @ sK3_SX0 @ sK1_SY32 ) )
| ( qmltpeq @ ( set_union2 @ ( unordered_pair @ sK2_SY681 @ SY757 ) @ sK3_SX0 ) @ sK3_SX0 @ sK1_SY32 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[163]) ).
thf(194,plain,
! [SV10: $i] :
( ( ~ ( exists_in_world @ ( sK5_SY703 @ SV10 ) @ SV10 )
| ~ ( empty @ ( sK5_SY703 @ SV10 ) @ SV10 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[164]) ).
thf(195,plain,
! [SV11: $i,SV37: mu] :
( ( ( ~ ( exists_in_world @ SV37 @ SV11 ) )
= $true )
| ( ( qmltpeq @ SV37 @ SV37 @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[165]) ).
thf(196,plain,
! [SV12: $i,SV38: mu] :
( ( ( ~ ( exists_in_world @ SV38 @ SV12 ) )
= $true )
| ( ( ! [SY758: mu] :
( ~ ( exists_in_world @ SY758 @ SV12 )
| ! [SY759: mu] :
( ~ ( exists_in_world @ SY759 @ SV12 )
| ~ ~ ( ~ ( qmltpeq @ SV38 @ SY758 @ SV12 )
| ~ ( qmltpeq @ SY758 @ SY759 @ SV12 ) )
| ( qmltpeq @ SV38 @ SY759 @ SV12 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[166]) ).
thf(197,plain,
! [SV13: $i,SV39: mu] :
( ( ( ~ ( exists_in_world @ SV39 @ SV13 ) )
= $true )
| ( ( ! [SY760: mu] :
( ~ ( exists_in_world @ SY760 @ SV13 )
| ~ ( qmltpeq @ SV39 @ SY760 @ SV13 )
| ( qmltpeq @ SY760 @ SV39 @ SV13 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[167]) ).
thf(198,plain,
! [SV14: $i,SV40: mu] :
( ( ( ~ ( exists_in_world @ SV40 @ SV14 ) )
= $true )
| ( ( ! [SY761: mu] :
( ~ ( exists_in_world @ SY761 @ SV14 )
| ! [SY762: mu] :
( ~ ( exists_in_world @ SY762 @ SV14 )
| ~ ~ ( ~ ( qmltpeq @ SV40 @ SY761 @ SV14 )
| ~ ( subset @ SY762 @ SV40 @ SV14 ) )
| ( subset @ SY762 @ SY761 @ SV14 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[168]) ).
thf(199,plain,
! [SV15: $i,SV41: mu] :
( ( ( ~ ( exists_in_world @ SV41 @ SV15 ) )
= $true )
| ( ( ! [SY763: mu] :
( ~ ( exists_in_world @ SY763 @ SV15 )
| ( qmltpeq @ ( set_union2 @ SV41 @ SY763 ) @ ( set_union2 @ SY763 @ SV41 ) @ SV15 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[169]) ).
thf(200,plain,
! [SV16: $i] :
( ( ~ ( exists_in_world @ ( sK6_SY715 @ SV16 ) @ SV16 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[170]) ).
thf(201,plain,
! [SV17: $i,SV42: mu] :
( ( ( ~ ( exists_in_world @ SV42 @ SV17 ) )
= $true )
| ( ( ! [SY764: mu] :
( ~ ( exists_in_world @ SY764 @ SV17 )
| ( qmltpeq @ ( set_union2 @ SV42 @ SV42 ) @ SV42 @ SV17 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[171]) ).
thf(202,plain,
! [SV18: $i,SV43: mu] :
( ( ( ~ ( exists_in_world @ SV43 @ SV18 ) )
= $true )
| ( ( ! [SY765: mu] :
( ~ ( exists_in_world @ SY765 @ SV18 )
| ~ ( in @ SV43 @ SY765 @ SV18 )
| ~ ( in @ SY765 @ SV43 @ SV18 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[172]) ).
thf(203,plain,
! [SV19: $i,SV44: mu] :
( ( ( ~ ( exists_in_world @ SV44 @ SV19 ) )
= $true )
| ( ( ! [SY766: mu] :
( ~ ( exists_in_world @ SY766 @ SV19 )
| ! [SY767: mu] :
( ~ ( exists_in_world @ SY767 @ SV19 )
| ~ ( qmltpeq @ SV44 @ SY766 @ SV19 )
| ( qmltpeq @ ( set_union2 @ SV44 @ SY767 ) @ ( set_union2 @ SY766 @ SY767 ) @ SV19 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[173]) ).
thf(204,plain,
! [SV20: $i,SV45: mu] :
( ( ( ~ ( exists_in_world @ SV45 @ SV20 ) )
= $true )
| ( ( ! [SY768: mu] :
( ~ ( exists_in_world @ SY768 @ SV20 )
| ~ ( subset @ SV45 @ SY768 @ SV20 )
| ( qmltpeq @ ( set_union2 @ SV45 @ SY768 ) @ SY768 @ SV20 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[174]) ).
thf(205,plain,
! [SV57: $i,SV46: $i,SV21: mu] :
( ( ~ ~ ( ~ ( exists_in_world @ SV21 @ SV46 )
| ~ ( rel_s4 @ SV46 @ SV57 ) )
| ( exists_in_world @ SV21 @ SV57 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(206,plain,
! [SV22: $i,SV47: mu] :
( ( ( ~ ( exists_in_world @ SV47 @ SV22 ) )
= $true )
| ( ( ! [SY770: mu] :
( ~ ( exists_in_world @ SY770 @ SV22 )
| ! [SY771: mu] :
( ~ ( exists_in_world @ SY771 @ SV22 )
| ~ ( qmltpeq @ SV47 @ SY770 @ SV22 )
| ( qmltpeq @ ( set_union2 @ SY771 @ SV47 ) @ ( set_union2 @ SY771 @ SY770 ) @ SV22 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[176]) ).
thf(207,plain,
! [SV23: $i,SV48: mu] :
( ( ( ~ ( exists_in_world @ SV48 @ SV23 ) )
= $true )
| ( ( ! [SY772: mu] :
( ~ ( exists_in_world @ SY772 @ SV23 )
| ! [SY773: mu] :
( ~ ( exists_in_world @ SY773 @ SV23 )
| ~ ~ ( ~ ( qmltpeq @ SV48 @ SY772 @ SV23 )
| ~ ( in @ SV48 @ SY773 @ SV23 ) )
| ( in @ SY772 @ SY773 @ SV23 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[177]) ).
thf(208,plain,
! [SV24: $i,SV49: mu] :
( ( ( ~ ( exists_in_world @ SV49 @ SV24 ) )
= $true )
| ( ( ! [SY774: mu] :
( ~ ( exists_in_world @ SY774 @ SV24 )
| ! [SY775: mu] :
( ~ ( exists_in_world @ SY775 @ SV24 )
| ~ ( qmltpeq @ SV49 @ SY774 @ SV24 )
| ( qmltpeq @ ( unordered_pair @ SV49 @ SY775 ) @ ( unordered_pair @ SY774 @ SY775 ) @ SV24 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[178]) ).
thf(209,plain,
! [SV58: $i,SV50: $i,SV25: $i] :
( ( ~ ~ ( ~ ( rel_s4 @ SV25 @ SV50 )
| ~ ( rel_s4 @ SV50 @ SV58 ) )
| ( rel_s4 @ SV25 @ SV58 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(210,plain,
! [SV26: $i,SV51: mu] :
( ( ( ~ ( exists_in_world @ SV51 @ SV26 ) )
= $true )
| ( ( ! [SY777: mu] :
( ~ ( exists_in_world @ SY777 @ SV26 )
| ! [SY778: mu] :
( ~ ( exists_in_world @ SY778 @ SV26 )
| ~ ( qmltpeq @ SV51 @ SY777 @ SV26 )
| ( qmltpeq @ ( unordered_pair @ SY778 @ SV51 ) @ ( unordered_pair @ SY778 @ SY777 ) @ SV26 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[180]) ).
thf(211,plain,
! [SV27: $i,SV52: mu] :
( ( ( ~ ( exists_in_world @ SV52 @ SV27 ) )
= $true )
| ( ( ! [SY779: mu] :
( ~ ( exists_in_world @ SY779 @ SV27 )
| ~ ~ ( empty @ SV52 @ SV27 )
| ~ ( empty @ ( set_union2 @ SY779 @ SV52 ) @ SV27 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[181]) ).
thf(212,plain,
! [SV28: $i,SV53: mu] :
( ( ( ~ ( exists_in_world @ SV53 @ SV28 ) )
= $true )
| ( ( ! [SY780: mu] :
( ~ ( exists_in_world @ SY780 @ SV28 )
| ! [SY781: mu] :
( ~ ( exists_in_world @ SY781 @ SV28 )
| ~ ~ ( ~ ( qmltpeq @ SV53 @ SY780 @ SV28 )
| ~ ( in @ SY781 @ SV53 @ SV28 ) )
| ( in @ SY781 @ SY780 @ SV28 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[182]) ).
thf(213,plain,
! [SV29: $i,SV54: mu] :
( ( ( ~ ( exists_in_world @ SV54 @ SV29 ) )
= $true )
| ( ( ! [SY782: mu] :
( ~ ( exists_in_world @ SY782 @ SV29 )
| ~ ~ ( ~ ( qmltpeq @ SV54 @ SY782 @ SV29 )
| ~ ( empty @ SV54 @ SV29 ) )
| ( empty @ SY782 @ SV29 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[183]) ).
thf(214,plain,
! [SV4: $i,SV32: mu] :
( ( ( exists_in_world @ SV32 @ SV4 )
= $false )
| ( ( ! [SY750: mu] :
( ~ ( exists_in_world @ SY750 @ SV4 )
| ( qmltpeq @ ( unordered_pair @ SV32 @ SY750 ) @ ( unordered_pair @ SY750 @ SV32 ) @ SV4 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[186]) ).
thf(215,plain,
! [SV5: $i,SV33: mu] :
( ( ( exists_in_world @ SV33 @ SV5 )
= $false )
| ( ( ! [SY751: mu] :
( ~ ( exists_in_world @ SY751 @ SV5 )
| ~ ~ ( empty @ SV33 @ SV5 )
| ~ ( empty @ ( set_union2 @ SV33 @ SY751 ) @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[187]) ).
thf(216,plain,
! [SV6: $i,SV34: mu] :
( ( ( exists_in_world @ SV34 @ SV6 )
= $false )
| ( ( ! [SY752: mu] :
( ~ ( exists_in_world @ SY752 @ SV6 )
| ! [SY753: mu] :
( ~ ( exists_in_world @ SY753 @ SV6 )
| ~ ~ ( ~ ( qmltpeq @ SV34 @ SY752 @ SV6 )
| ~ ( subset @ SV34 @ SY753 @ SV6 ) )
| ( subset @ SY752 @ SY753 @ SV6 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[188]) ).
thf(217,plain,
! [SV7: $i] :
( ( ~ ( exists_in_world @ ( sK4_SY697 @ SV7 ) @ SV7 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[189]) ).
thf(218,plain,
! [SV7: $i] :
( ( ~ ~ ( empty @ ( sK4_SY697 @ SV7 ) @ SV7 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[189]) ).
thf(219,plain,
! [SV8: $i,SV35: mu] :
( ( ( exists_in_world @ SV35 @ SV8 )
= $false )
| ( ( ! [SY754: mu] :
( ~ ( exists_in_world @ SY754 @ SV8 )
| ! [SY755: mu] :
( ~ ( exists_in_world @ SY755 @ SV8 )
| ~ ( ~ ( ~ ( subset @ ( unordered_pair @ SV35 @ SY754 ) @ SY755 @ SV8 )
| ~ ( ~ ( in @ SV35 @ SY755 @ SV8 )
| ~ ( in @ SY754 @ SY755 @ SV8 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV35 @ SY755 @ SV8 )
| ~ ( in @ SY754 @ SY755 @ SV8 ) )
| ( subset @ ( unordered_pair @ SV35 @ SY754 ) @ SY755 @ SV8 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[190]) ).
thf(220,plain,
! [SV9: $i,SV36: mu] :
( ( ( exists_in_world @ SV36 @ SV9 )
= $false )
| ( ( ! [SY756: mu] :
( ~ ( exists_in_world @ SY756 @ SV9 )
| ( subset @ SV36 @ SV36 @ SV9 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[191]) ).
thf(221,plain,
( ( exists_in_world @ sK3_SX0 @ sK1_SY32 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[192]) ).
thf(222,plain,
( ( ~ ( exists_in_world @ sK7_SY757 @ sK1_SY32 )
| ~ ~ ( ~ ( in @ sK2_SY681 @ sK3_SX0 @ sK1_SY32 )
| ~ ( in @ sK7_SY757 @ sK3_SX0 @ sK1_SY32 ) )
| ( qmltpeq @ ( set_union2 @ ( unordered_pair @ sK2_SY681 @ sK7_SY757 ) @ sK3_SX0 ) @ sK3_SX0 @ sK1_SY32 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[193]) ).
thf(223,plain,
! [SV10: $i] :
( ( ~ ( exists_in_world @ ( sK5_SY703 @ SV10 ) @ SV10 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[194]) ).
thf(224,plain,
! [SV10: $i] :
( ( ~ ( empty @ ( sK5_SY703 @ SV10 ) @ SV10 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[194]) ).
thf(225,plain,
! [SV11: $i,SV37: mu] :
( ( ( exists_in_world @ SV37 @ SV11 )
= $false )
| ( ( qmltpeq @ SV37 @ SV37 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(226,plain,
! [SV12: $i,SV38: mu] :
( ( ( exists_in_world @ SV38 @ SV12 )
= $false )
| ( ( ! [SY758: mu] :
( ~ ( exists_in_world @ SY758 @ SV12 )
| ! [SY759: mu] :
( ~ ( exists_in_world @ SY759 @ SV12 )
| ~ ~ ( ~ ( qmltpeq @ SV38 @ SY758 @ SV12 )
| ~ ( qmltpeq @ SY758 @ SY759 @ SV12 ) )
| ( qmltpeq @ SV38 @ SY759 @ SV12 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(227,plain,
! [SV13: $i,SV39: mu] :
( ( ( exists_in_world @ SV39 @ SV13 )
= $false )
| ( ( ! [SY760: mu] :
( ~ ( exists_in_world @ SY760 @ SV13 )
| ~ ( qmltpeq @ SV39 @ SY760 @ SV13 )
| ( qmltpeq @ SY760 @ SV39 @ SV13 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[197]) ).
thf(228,plain,
! [SV14: $i,SV40: mu] :
( ( ( exists_in_world @ SV40 @ SV14 )
= $false )
| ( ( ! [SY761: mu] :
( ~ ( exists_in_world @ SY761 @ SV14 )
| ! [SY762: mu] :
( ~ ( exists_in_world @ SY762 @ SV14 )
| ~ ~ ( ~ ( qmltpeq @ SV40 @ SY761 @ SV14 )
| ~ ( subset @ SY762 @ SV40 @ SV14 ) )
| ( subset @ SY762 @ SY761 @ SV14 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[198]) ).
thf(229,plain,
! [SV15: $i,SV41: mu] :
( ( ( exists_in_world @ SV41 @ SV15 )
= $false )
| ( ( ! [SY763: mu] :
( ~ ( exists_in_world @ SY763 @ SV15 )
| ( qmltpeq @ ( set_union2 @ SV41 @ SY763 ) @ ( set_union2 @ SY763 @ SV41 ) @ SV15 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[199]) ).
thf(230,plain,
! [SV16: $i] :
( ( exists_in_world @ ( sK6_SY715 @ SV16 ) @ SV16 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[200]) ).
thf(231,plain,
! [SV17: $i,SV42: mu] :
( ( ( exists_in_world @ SV42 @ SV17 )
= $false )
| ( ( ! [SY764: mu] :
( ~ ( exists_in_world @ SY764 @ SV17 )
| ( qmltpeq @ ( set_union2 @ SV42 @ SV42 ) @ SV42 @ SV17 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(232,plain,
! [SV18: $i,SV43: mu] :
( ( ( exists_in_world @ SV43 @ SV18 )
= $false )
| ( ( ! [SY765: mu] :
( ~ ( exists_in_world @ SY765 @ SV18 )
| ~ ( in @ SV43 @ SY765 @ SV18 )
| ~ ( in @ SY765 @ SV43 @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[202]) ).
thf(233,plain,
! [SV19: $i,SV44: mu] :
( ( ( exists_in_world @ SV44 @ SV19 )
= $false )
| ( ( ! [SY766: mu] :
( ~ ( exists_in_world @ SY766 @ SV19 )
| ! [SY767: mu] :
( ~ ( exists_in_world @ SY767 @ SV19 )
| ~ ( qmltpeq @ SV44 @ SY766 @ SV19 )
| ( qmltpeq @ ( set_union2 @ SV44 @ SY767 ) @ ( set_union2 @ SY766 @ SY767 ) @ SV19 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[203]) ).
thf(234,plain,
! [SV20: $i,SV45: mu] :
( ( ( exists_in_world @ SV45 @ SV20 )
= $false )
| ( ( ! [SY768: mu] :
( ~ ( exists_in_world @ SY768 @ SV20 )
| ~ ( subset @ SV45 @ SY768 @ SV20 )
| ( qmltpeq @ ( set_union2 @ SV45 @ SY768 ) @ SY768 @ SV20 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(235,plain,
! [SV57: $i,SV46: $i,SV21: mu] :
( ( ( ~ ~ ( ~ ( exists_in_world @ SV21 @ SV46 )
| ~ ( rel_s4 @ SV46 @ SV57 ) ) )
= $true )
| ( ( exists_in_world @ SV21 @ SV57 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[205]) ).
thf(236,plain,
! [SV22: $i,SV47: mu] :
( ( ( exists_in_world @ SV47 @ SV22 )
= $false )
| ( ( ! [SY770: mu] :
( ~ ( exists_in_world @ SY770 @ SV22 )
| ! [SY771: mu] :
( ~ ( exists_in_world @ SY771 @ SV22 )
| ~ ( qmltpeq @ SV47 @ SY770 @ SV22 )
| ( qmltpeq @ ( set_union2 @ SY771 @ SV47 ) @ ( set_union2 @ SY771 @ SY770 ) @ SV22 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[206]) ).
thf(237,plain,
! [SV23: $i,SV48: mu] :
( ( ( exists_in_world @ SV48 @ SV23 )
= $false )
| ( ( ! [SY772: mu] :
( ~ ( exists_in_world @ SY772 @ SV23 )
| ! [SY773: mu] :
( ~ ( exists_in_world @ SY773 @ SV23 )
| ~ ~ ( ~ ( qmltpeq @ SV48 @ SY772 @ SV23 )
| ~ ( in @ SV48 @ SY773 @ SV23 ) )
| ( in @ SY772 @ SY773 @ SV23 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[207]) ).
thf(238,plain,
! [SV24: $i,SV49: mu] :
( ( ( exists_in_world @ SV49 @ SV24 )
= $false )
| ( ( ! [SY774: mu] :
( ~ ( exists_in_world @ SY774 @ SV24 )
| ! [SY775: mu] :
( ~ ( exists_in_world @ SY775 @ SV24 )
| ~ ( qmltpeq @ SV49 @ SY774 @ SV24 )
| ( qmltpeq @ ( unordered_pair @ SV49 @ SY775 ) @ ( unordered_pair @ SY774 @ SY775 ) @ SV24 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[208]) ).
thf(239,plain,
! [SV58: $i,SV50: $i,SV25: $i] :
( ( ( ~ ~ ( ~ ( rel_s4 @ SV25 @ SV50 )
| ~ ( rel_s4 @ SV50 @ SV58 ) ) )
= $true )
| ( ( rel_s4 @ SV25 @ SV58 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[209]) ).
thf(240,plain,
! [SV26: $i,SV51: mu] :
( ( ( exists_in_world @ SV51 @ SV26 )
= $false )
| ( ( ! [SY777: mu] :
( ~ ( exists_in_world @ SY777 @ SV26 )
| ! [SY778: mu] :
( ~ ( exists_in_world @ SY778 @ SV26 )
| ~ ( qmltpeq @ SV51 @ SY777 @ SV26 )
| ( qmltpeq @ ( unordered_pair @ SY778 @ SV51 ) @ ( unordered_pair @ SY778 @ SY777 ) @ SV26 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[210]) ).
thf(241,plain,
! [SV27: $i,SV52: mu] :
( ( ( exists_in_world @ SV52 @ SV27 )
= $false )
| ( ( ! [SY779: mu] :
( ~ ( exists_in_world @ SY779 @ SV27 )
| ~ ~ ( empty @ SV52 @ SV27 )
| ~ ( empty @ ( set_union2 @ SY779 @ SV52 ) @ SV27 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[211]) ).
thf(242,plain,
! [SV28: $i,SV53: mu] :
( ( ( exists_in_world @ SV53 @ SV28 )
= $false )
| ( ( ! [SY780: mu] :
( ~ ( exists_in_world @ SY780 @ SV28 )
| ! [SY781: mu] :
( ~ ( exists_in_world @ SY781 @ SV28 )
| ~ ~ ( ~ ( qmltpeq @ SV53 @ SY780 @ SV28 )
| ~ ( in @ SY781 @ SV53 @ SV28 ) )
| ( in @ SY781 @ SY780 @ SV28 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[212]) ).
thf(243,plain,
! [SV29: $i,SV54: mu] :
( ( ( exists_in_world @ SV54 @ SV29 )
= $false )
| ( ( ! [SY782: mu] :
( ~ ( exists_in_world @ SY782 @ SV29 )
| ~ ~ ( ~ ( qmltpeq @ SV54 @ SY782 @ SV29 )
| ~ ( empty @ SV54 @ SV29 ) )
| ( empty @ SY782 @ SV29 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[213]) ).
thf(244,plain,
! [SV32: mu,SV4: $i,SV59: mu] :
( ( ( ~ ( exists_in_world @ SV59 @ SV4 )
| ( qmltpeq @ ( unordered_pair @ SV32 @ SV59 ) @ ( unordered_pair @ SV59 @ SV32 ) @ SV4 ) )
= $true )
| ( ( exists_in_world @ SV32 @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[214]) ).
thf(245,plain,
! [SV33: mu,SV5: $i,SV60: mu] :
( ( ( ~ ( exists_in_world @ SV60 @ SV5 )
| ~ ~ ( empty @ SV33 @ SV5 )
| ~ ( empty @ ( set_union2 @ SV33 @ SV60 ) @ SV5 ) )
= $true )
| ( ( exists_in_world @ SV33 @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[215]) ).
thf(246,plain,
! [SV34: mu,SV6: $i,SV61: mu] :
( ( ( ~ ( exists_in_world @ SV61 @ SV6 )
| ! [SY783: mu] :
( ~ ( exists_in_world @ SY783 @ SV6 )
| ~ ~ ( ~ ( qmltpeq @ SV34 @ SV61 @ SV6 )
| ~ ( subset @ SV34 @ SY783 @ SV6 ) )
| ( subset @ SV61 @ SY783 @ SV6 ) ) )
= $true )
| ( ( exists_in_world @ SV34 @ SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[216]) ).
thf(247,plain,
! [SV7: $i] :
( ( exists_in_world @ ( sK4_SY697 @ SV7 ) @ SV7 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[217]) ).
thf(248,plain,
! [SV7: $i] :
( ( ~ ( empty @ ( sK4_SY697 @ SV7 ) @ SV7 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[218]) ).
thf(249,plain,
! [SV35: mu,SV8: $i,SV62: mu] :
( ( ( ~ ( exists_in_world @ SV62 @ SV8 )
| ! [SY784: mu] :
( ~ ( exists_in_world @ SY784 @ SV8 )
| ~ ( ~ ( ~ ( subset @ ( unordered_pair @ SV35 @ SV62 ) @ SY784 @ SV8 )
| ~ ( ~ ( in @ SV35 @ SY784 @ SV8 )
| ~ ( in @ SV62 @ SY784 @ SV8 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV35 @ SY784 @ SV8 )
| ~ ( in @ SV62 @ SY784 @ SV8 ) )
| ( subset @ ( unordered_pair @ SV35 @ SV62 ) @ SY784 @ SV8 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV35 @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[219]) ).
thf(250,plain,
! [SV36: mu,SV9: $i,SV63: mu] :
( ( ( ~ ( exists_in_world @ SV63 @ SV9 )
| ( subset @ SV36 @ SV36 @ SV9 ) )
= $true )
| ( ( exists_in_world @ SV36 @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[220]) ).
thf(251,plain,
( ( ~ ( exists_in_world @ sK7_SY757 @ sK1_SY32 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[222]) ).
thf(252,plain,
( ( ~ ~ ( ~ ( in @ sK2_SY681 @ sK3_SX0 @ sK1_SY32 )
| ~ ( in @ sK7_SY757 @ sK3_SX0 @ sK1_SY32 ) )
| ( qmltpeq @ ( set_union2 @ ( unordered_pair @ sK2_SY681 @ sK7_SY757 ) @ sK3_SX0 ) @ sK3_SX0 @ sK1_SY32 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[222]) ).
thf(253,plain,
! [SV10: $i] :
( ( exists_in_world @ ( sK5_SY703 @ SV10 ) @ SV10 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[223]) ).
thf(254,plain,
! [SV10: $i] :
( ( empty @ ( sK5_SY703 @ SV10 ) @ SV10 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[224]) ).
thf(255,plain,
! [SV38: mu,SV12: $i,SV64: mu] :
( ( ( ~ ( exists_in_world @ SV64 @ SV12 )
| ! [SY785: mu] :
( ~ ( exists_in_world @ SY785 @ SV12 )
| ~ ~ ( ~ ( qmltpeq @ SV38 @ SV64 @ SV12 )
| ~ ( qmltpeq @ SV64 @ SY785 @ SV12 ) )
| ( qmltpeq @ SV38 @ SY785 @ SV12 ) ) )
= $true )
| ( ( exists_in_world @ SV38 @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[226]) ).
thf(256,plain,
! [SV39: mu,SV13: $i,SV65: mu] :
( ( ( ~ ( exists_in_world @ SV65 @ SV13 )
| ~ ( qmltpeq @ SV39 @ SV65 @ SV13 )
| ( qmltpeq @ SV65 @ SV39 @ SV13 ) )
= $true )
| ( ( exists_in_world @ SV39 @ SV13 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[227]) ).
thf(257,plain,
! [SV40: mu,SV14: $i,SV66: mu] :
( ( ( ~ ( exists_in_world @ SV66 @ SV14 )
| ! [SY786: mu] :
( ~ ( exists_in_world @ SY786 @ SV14 )
| ~ ~ ( ~ ( qmltpeq @ SV40 @ SV66 @ SV14 )
| ~ ( subset @ SY786 @ SV40 @ SV14 ) )
| ( subset @ SY786 @ SV66 @ SV14 ) ) )
= $true )
| ( ( exists_in_world @ SV40 @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[228]) ).
thf(258,plain,
! [SV41: mu,SV15: $i,SV67: mu] :
( ( ( ~ ( exists_in_world @ SV67 @ SV15 )
| ( qmltpeq @ ( set_union2 @ SV41 @ SV67 ) @ ( set_union2 @ SV67 @ SV41 ) @ SV15 ) )
= $true )
| ( ( exists_in_world @ SV41 @ SV15 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[229]) ).
thf(259,plain,
! [SV42: mu,SV17: $i,SV68: mu] :
( ( ( ~ ( exists_in_world @ SV68 @ SV17 )
| ( qmltpeq @ ( set_union2 @ SV42 @ SV42 ) @ SV42 @ SV17 ) )
= $true )
| ( ( exists_in_world @ SV42 @ SV17 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[231]) ).
thf(260,plain,
! [SV43: mu,SV18: $i,SV69: mu] :
( ( ( ~ ( exists_in_world @ SV69 @ SV18 )
| ~ ( in @ SV43 @ SV69 @ SV18 )
| ~ ( in @ SV69 @ SV43 @ SV18 ) )
= $true )
| ( ( exists_in_world @ SV43 @ SV18 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[232]) ).
thf(261,plain,
! [SV44: mu,SV19: $i,SV70: mu] :
( ( ( ~ ( exists_in_world @ SV70 @ SV19 )
| ! [SY787: mu] :
( ~ ( exists_in_world @ SY787 @ SV19 )
| ~ ( qmltpeq @ SV44 @ SV70 @ SV19 )
| ( qmltpeq @ ( set_union2 @ SV44 @ SY787 ) @ ( set_union2 @ SV70 @ SY787 ) @ SV19 ) ) )
= $true )
| ( ( exists_in_world @ SV44 @ SV19 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[233]) ).
thf(262,plain,
! [SV45: mu,SV20: $i,SV71: mu] :
( ( ( ~ ( exists_in_world @ SV71 @ SV20 )
| ~ ( subset @ SV45 @ SV71 @ SV20 )
| ( qmltpeq @ ( set_union2 @ SV45 @ SV71 ) @ SV71 @ SV20 ) )
= $true )
| ( ( exists_in_world @ SV45 @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[234]) ).
thf(263,plain,
! [SV57: $i,SV46: $i,SV21: mu] :
( ( ( ~ ( ~ ( exists_in_world @ SV21 @ SV46 )
| ~ ( rel_s4 @ SV46 @ SV57 ) ) )
= $false )
| ( ( exists_in_world @ SV21 @ SV57 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[235]) ).
thf(264,plain,
! [SV47: mu,SV22: $i,SV72: mu] :
( ( ( ~ ( exists_in_world @ SV72 @ SV22 )
| ! [SY788: mu] :
( ~ ( exists_in_world @ SY788 @ SV22 )
| ~ ( qmltpeq @ SV47 @ SV72 @ SV22 )
| ( qmltpeq @ ( set_union2 @ SY788 @ SV47 ) @ ( set_union2 @ SY788 @ SV72 ) @ SV22 ) ) )
= $true )
| ( ( exists_in_world @ SV47 @ SV22 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[236]) ).
thf(265,plain,
! [SV48: mu,SV23: $i,SV73: mu] :
( ( ( ~ ( exists_in_world @ SV73 @ SV23 )
| ! [SY789: mu] :
( ~ ( exists_in_world @ SY789 @ SV23 )
| ~ ~ ( ~ ( qmltpeq @ SV48 @ SV73 @ SV23 )
| ~ ( in @ SV48 @ SY789 @ SV23 ) )
| ( in @ SV73 @ SY789 @ SV23 ) ) )
= $true )
| ( ( exists_in_world @ SV48 @ SV23 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[237]) ).
thf(266,plain,
! [SV49: mu,SV24: $i,SV74: mu] :
( ( ( ~ ( exists_in_world @ SV74 @ SV24 )
| ! [SY790: mu] :
( ~ ( exists_in_world @ SY790 @ SV24 )
| ~ ( qmltpeq @ SV49 @ SV74 @ SV24 )
| ( qmltpeq @ ( unordered_pair @ SV49 @ SY790 ) @ ( unordered_pair @ SV74 @ SY790 ) @ SV24 ) ) )
= $true )
| ( ( exists_in_world @ SV49 @ SV24 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[238]) ).
thf(267,plain,
! [SV58: $i,SV50: $i,SV25: $i] :
( ( ( ~ ( ~ ( rel_s4 @ SV25 @ SV50 )
| ~ ( rel_s4 @ SV50 @ SV58 ) ) )
= $false )
| ( ( rel_s4 @ SV25 @ SV58 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[239]) ).
thf(268,plain,
! [SV51: mu,SV26: $i,SV75: mu] :
( ( ( ~ ( exists_in_world @ SV75 @ SV26 )
| ! [SY791: mu] :
( ~ ( exists_in_world @ SY791 @ SV26 )
| ~ ( qmltpeq @ SV51 @ SV75 @ SV26 )
| ( qmltpeq @ ( unordered_pair @ SY791 @ SV51 ) @ ( unordered_pair @ SY791 @ SV75 ) @ SV26 ) ) )
= $true )
| ( ( exists_in_world @ SV51 @ SV26 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[240]) ).
thf(269,plain,
! [SV52: mu,SV27: $i,SV76: mu] :
( ( ( ~ ( exists_in_world @ SV76 @ SV27 )
| ~ ~ ( empty @ SV52 @ SV27 )
| ~ ( empty @ ( set_union2 @ SV76 @ SV52 ) @ SV27 ) )
= $true )
| ( ( exists_in_world @ SV52 @ SV27 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[241]) ).
thf(270,plain,
! [SV53: mu,SV28: $i,SV77: mu] :
( ( ( ~ ( exists_in_world @ SV77 @ SV28 )
| ! [SY792: mu] :
( ~ ( exists_in_world @ SY792 @ SV28 )
| ~ ~ ( ~ ( qmltpeq @ SV53 @ SV77 @ SV28 )
| ~ ( in @ SY792 @ SV53 @ SV28 ) )
| ( in @ SY792 @ SV77 @ SV28 ) ) )
= $true )
| ( ( exists_in_world @ SV53 @ SV28 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[242]) ).
thf(271,plain,
! [SV54: mu,SV29: $i,SV78: mu] :
( ( ( ~ ( exists_in_world @ SV78 @ SV29 )
| ~ ~ ( ~ ( qmltpeq @ SV54 @ SV78 @ SV29 )
| ~ ( empty @ SV54 @ SV29 ) )
| ( empty @ SV78 @ SV29 ) )
= $true )
| ( ( exists_in_world @ SV54 @ SV29 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[243]) ).
thf(272,plain,
! [SV32: mu,SV4: $i,SV59: mu] :
( ( ( ~ ( exists_in_world @ SV59 @ SV4 ) )
= $true )
| ( ( qmltpeq @ ( unordered_pair @ SV32 @ SV59 ) @ ( unordered_pair @ SV59 @ SV32 ) @ SV4 )
= $true )
| ( ( exists_in_world @ SV32 @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[244]) ).
thf(273,plain,
! [SV33: mu,SV5: $i,SV60: mu] :
( ( ( ~ ( exists_in_world @ SV60 @ SV5 ) )
= $true )
| ( ( ~ ~ ( empty @ SV33 @ SV5 )
| ~ ( empty @ ( set_union2 @ SV33 @ SV60 ) @ SV5 ) )
= $true )
| ( ( exists_in_world @ SV33 @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[245]) ).
thf(274,plain,
! [SV34: mu,SV6: $i,SV61: mu] :
( ( ( ~ ( exists_in_world @ SV61 @ SV6 ) )
= $true )
| ( ( ! [SY783: mu] :
( ~ ( exists_in_world @ SY783 @ SV6 )
| ~ ~ ( ~ ( qmltpeq @ SV34 @ SV61 @ SV6 )
| ~ ( subset @ SV34 @ SY783 @ SV6 ) )
| ( subset @ SV61 @ SY783 @ SV6 ) ) )
= $true )
| ( ( exists_in_world @ SV34 @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[246]) ).
thf(275,plain,
! [SV7: $i] :
( ( empty @ ( sK4_SY697 @ SV7 ) @ SV7 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[248]) ).
thf(276,plain,
! [SV35: mu,SV8: $i,SV62: mu] :
( ( ( ~ ( exists_in_world @ SV62 @ SV8 ) )
= $true )
| ( ( ! [SY784: mu] :
( ~ ( exists_in_world @ SY784 @ SV8 )
| ~ ( ~ ( ~ ( subset @ ( unordered_pair @ SV35 @ SV62 ) @ SY784 @ SV8 )
| ~ ( ~ ( in @ SV35 @ SY784 @ SV8 )
| ~ ( in @ SV62 @ SY784 @ SV8 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV35 @ SY784 @ SV8 )
| ~ ( in @ SV62 @ SY784 @ SV8 ) )
| ( subset @ ( unordered_pair @ SV35 @ SV62 ) @ SY784 @ SV8 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV35 @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[249]) ).
thf(277,plain,
! [SV36: mu,SV9: $i,SV63: mu] :
( ( ( ~ ( exists_in_world @ SV63 @ SV9 ) )
= $true )
| ( ( subset @ SV36 @ SV36 @ SV9 )
= $true )
| ( ( exists_in_world @ SV36 @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[250]) ).
thf(278,plain,
( ( exists_in_world @ sK7_SY757 @ sK1_SY32 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[251]) ).
thf(279,plain,
( ( ~ ~ ( ~ ( in @ sK2_SY681 @ sK3_SX0 @ sK1_SY32 )
| ~ ( in @ sK7_SY757 @ sK3_SX0 @ sK1_SY32 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[252]) ).
thf(280,plain,
( ( qmltpeq @ ( set_union2 @ ( unordered_pair @ sK2_SY681 @ sK7_SY757 ) @ sK3_SX0 ) @ sK3_SX0 @ sK1_SY32 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[252]) ).
thf(281,plain,
! [SV38: mu,SV12: $i,SV64: mu] :
( ( ( ~ ( exists_in_world @ SV64 @ SV12 ) )
= $true )
| ( ( ! [SY785: mu] :
( ~ ( exists_in_world @ SY785 @ SV12 )
| ~ ~ ( ~ ( qmltpeq @ SV38 @ SV64 @ SV12 )
| ~ ( qmltpeq @ SV64 @ SY785 @ SV12 ) )
| ( qmltpeq @ SV38 @ SY785 @ SV12 ) ) )
= $true )
| ( ( exists_in_world @ SV38 @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[255]) ).
thf(282,plain,
! [SV39: mu,SV13: $i,SV65: mu] :
( ( ( ~ ( exists_in_world @ SV65 @ SV13 ) )
= $true )
| ( ( ~ ( qmltpeq @ SV39 @ SV65 @ SV13 )
| ( qmltpeq @ SV65 @ SV39 @ SV13 ) )
= $true )
| ( ( exists_in_world @ SV39 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[256]) ).
thf(283,plain,
! [SV40: mu,SV14: $i,SV66: mu] :
( ( ( ~ ( exists_in_world @ SV66 @ SV14 ) )
= $true )
| ( ( ! [SY786: mu] :
( ~ ( exists_in_world @ SY786 @ SV14 )
| ~ ~ ( ~ ( qmltpeq @ SV40 @ SV66 @ SV14 )
| ~ ( subset @ SY786 @ SV40 @ SV14 ) )
| ( subset @ SY786 @ SV66 @ SV14 ) ) )
= $true )
| ( ( exists_in_world @ SV40 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[257]) ).
thf(284,plain,
! [SV41: mu,SV15: $i,SV67: mu] :
( ( ( ~ ( exists_in_world @ SV67 @ SV15 ) )
= $true )
| ( ( qmltpeq @ ( set_union2 @ SV41 @ SV67 ) @ ( set_union2 @ SV67 @ SV41 ) @ SV15 )
= $true )
| ( ( exists_in_world @ SV41 @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[258]) ).
thf(285,plain,
! [SV42: mu,SV17: $i,SV68: mu] :
( ( ( ~ ( exists_in_world @ SV68 @ SV17 ) )
= $true )
| ( ( qmltpeq @ ( set_union2 @ SV42 @ SV42 ) @ SV42 @ SV17 )
= $true )
| ( ( exists_in_world @ SV42 @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[259]) ).
thf(286,plain,
! [SV43: mu,SV18: $i,SV69: mu] :
( ( ( ~ ( exists_in_world @ SV69 @ SV18 ) )
= $true )
| ( ( ~ ( in @ SV43 @ SV69 @ SV18 )
| ~ ( in @ SV69 @ SV43 @ SV18 ) )
= $true )
| ( ( exists_in_world @ SV43 @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[260]) ).
thf(287,plain,
! [SV44: mu,SV19: $i,SV70: mu] :
( ( ( ~ ( exists_in_world @ SV70 @ SV19 ) )
= $true )
| ( ( ! [SY787: mu] :
( ~ ( exists_in_world @ SY787 @ SV19 )
| ~ ( qmltpeq @ SV44 @ SV70 @ SV19 )
| ( qmltpeq @ ( set_union2 @ SV44 @ SY787 ) @ ( set_union2 @ SV70 @ SY787 ) @ SV19 ) ) )
= $true )
| ( ( exists_in_world @ SV44 @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[261]) ).
thf(288,plain,
! [SV45: mu,SV20: $i,SV71: mu] :
( ( ( ~ ( exists_in_world @ SV71 @ SV20 ) )
= $true )
| ( ( ~ ( subset @ SV45 @ SV71 @ SV20 )
| ( qmltpeq @ ( set_union2 @ SV45 @ SV71 ) @ SV71 @ SV20 ) )
= $true )
| ( ( exists_in_world @ SV45 @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[262]) ).
thf(289,plain,
! [SV57: $i,SV46: $i,SV21: mu] :
( ( ( ~ ( exists_in_world @ SV21 @ SV46 )
| ~ ( rel_s4 @ SV46 @ SV57 ) )
= $true )
| ( ( exists_in_world @ SV21 @ SV57 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[263]) ).
thf(290,plain,
! [SV47: mu,SV22: $i,SV72: mu] :
( ( ( ~ ( exists_in_world @ SV72 @ SV22 ) )
= $true )
| ( ( ! [SY788: mu] :
( ~ ( exists_in_world @ SY788 @ SV22 )
| ~ ( qmltpeq @ SV47 @ SV72 @ SV22 )
| ( qmltpeq @ ( set_union2 @ SY788 @ SV47 ) @ ( set_union2 @ SY788 @ SV72 ) @ SV22 ) ) )
= $true )
| ( ( exists_in_world @ SV47 @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[264]) ).
thf(291,plain,
! [SV48: mu,SV23: $i,SV73: mu] :
( ( ( ~ ( exists_in_world @ SV73 @ SV23 ) )
= $true )
| ( ( ! [SY789: mu] :
( ~ ( exists_in_world @ SY789 @ SV23 )
| ~ ~ ( ~ ( qmltpeq @ SV48 @ SV73 @ SV23 )
| ~ ( in @ SV48 @ SY789 @ SV23 ) )
| ( in @ SV73 @ SY789 @ SV23 ) ) )
= $true )
| ( ( exists_in_world @ SV48 @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[265]) ).
thf(292,plain,
! [SV49: mu,SV24: $i,SV74: mu] :
( ( ( ~ ( exists_in_world @ SV74 @ SV24 ) )
= $true )
| ( ( ! [SY790: mu] :
( ~ ( exists_in_world @ SY790 @ SV24 )
| ~ ( qmltpeq @ SV49 @ SV74 @ SV24 )
| ( qmltpeq @ ( unordered_pair @ SV49 @ SY790 ) @ ( unordered_pair @ SV74 @ SY790 ) @ SV24 ) ) )
= $true )
| ( ( exists_in_world @ SV49 @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[266]) ).
thf(293,plain,
! [SV58: $i,SV50: $i,SV25: $i] :
( ( ( ~ ( rel_s4 @ SV25 @ SV50 )
| ~ ( rel_s4 @ SV50 @ SV58 ) )
= $true )
| ( ( rel_s4 @ SV25 @ SV58 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[267]) ).
thf(294,plain,
! [SV51: mu,SV26: $i,SV75: mu] :
( ( ( ~ ( exists_in_world @ SV75 @ SV26 ) )
= $true )
| ( ( ! [SY791: mu] :
( ~ ( exists_in_world @ SY791 @ SV26 )
| ~ ( qmltpeq @ SV51 @ SV75 @ SV26 )
| ( qmltpeq @ ( unordered_pair @ SY791 @ SV51 ) @ ( unordered_pair @ SY791 @ SV75 ) @ SV26 ) ) )
= $true )
| ( ( exists_in_world @ SV51 @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[268]) ).
thf(295,plain,
! [SV52: mu,SV27: $i,SV76: mu] :
( ( ( ~ ( exists_in_world @ SV76 @ SV27 ) )
= $true )
| ( ( ~ ~ ( empty @ SV52 @ SV27 )
| ~ ( empty @ ( set_union2 @ SV76 @ SV52 ) @ SV27 ) )
= $true )
| ( ( exists_in_world @ SV52 @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[269]) ).
thf(296,plain,
! [SV53: mu,SV28: $i,SV77: mu] :
( ( ( ~ ( exists_in_world @ SV77 @ SV28 ) )
= $true )
| ( ( ! [SY792: mu] :
( ~ ( exists_in_world @ SY792 @ SV28 )
| ~ ~ ( ~ ( qmltpeq @ SV53 @ SV77 @ SV28 )
| ~ ( in @ SY792 @ SV53 @ SV28 ) )
| ( in @ SY792 @ SV77 @ SV28 ) ) )
= $true )
| ( ( exists_in_world @ SV53 @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[270]) ).
thf(297,plain,
! [SV54: mu,SV29: $i,SV78: mu] :
( ( ( ~ ( exists_in_world @ SV78 @ SV29 ) )
= $true )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV54 @ SV78 @ SV29 )
| ~ ( empty @ SV54 @ SV29 ) )
| ( empty @ SV78 @ SV29 ) )
= $true )
| ( ( exists_in_world @ SV54 @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[271]) ).
thf(298,plain,
! [SV32: mu,SV4: $i,SV59: mu] :
( ( ( exists_in_world @ SV59 @ SV4 )
= $false )
| ( ( qmltpeq @ ( unordered_pair @ SV32 @ SV59 ) @ ( unordered_pair @ SV59 @ SV32 ) @ SV4 )
= $true )
| ( ( exists_in_world @ SV32 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[272]) ).
thf(299,plain,
! [SV33: mu,SV5: $i,SV60: mu] :
( ( ( exists_in_world @ SV60 @ SV5 )
= $false )
| ( ( ~ ~ ( empty @ SV33 @ SV5 )
| ~ ( empty @ ( set_union2 @ SV33 @ SV60 ) @ SV5 ) )
= $true )
| ( ( exists_in_world @ SV33 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[273]) ).
thf(300,plain,
! [SV34: mu,SV6: $i,SV61: mu] :
( ( ( exists_in_world @ SV61 @ SV6 )
= $false )
| ( ( ! [SY783: mu] :
( ~ ( exists_in_world @ SY783 @ SV6 )
| ~ ~ ( ~ ( qmltpeq @ SV34 @ SV61 @ SV6 )
| ~ ( subset @ SV34 @ SY783 @ SV6 ) )
| ( subset @ SV61 @ SY783 @ SV6 ) ) )
= $true )
| ( ( exists_in_world @ SV34 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[274]) ).
thf(301,plain,
! [SV35: mu,SV8: $i,SV62: mu] :
( ( ( exists_in_world @ SV62 @ SV8 )
= $false )
| ( ( ! [SY784: mu] :
( ~ ( exists_in_world @ SY784 @ SV8 )
| ~ ( ~ ( ~ ( subset @ ( unordered_pair @ SV35 @ SV62 ) @ SY784 @ SV8 )
| ~ ( ~ ( in @ SV35 @ SY784 @ SV8 )
| ~ ( in @ SV62 @ SY784 @ SV8 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV35 @ SY784 @ SV8 )
| ~ ( in @ SV62 @ SY784 @ SV8 ) )
| ( subset @ ( unordered_pair @ SV35 @ SV62 ) @ SY784 @ SV8 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV35 @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[276]) ).
thf(302,plain,
! [SV36: mu,SV9: $i,SV63: mu] :
( ( ( exists_in_world @ SV63 @ SV9 )
= $false )
| ( ( subset @ SV36 @ SV36 @ SV9 )
= $true )
| ( ( exists_in_world @ SV36 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[277]) ).
thf(303,plain,
( ( ~ ( ~ ( in @ sK2_SY681 @ sK3_SX0 @ sK1_SY32 )
| ~ ( in @ sK7_SY757 @ sK3_SX0 @ sK1_SY32 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[279]) ).
thf(304,plain,
! [SV38: mu,SV12: $i,SV64: mu] :
( ( ( exists_in_world @ SV64 @ SV12 )
= $false )
| ( ( ! [SY785: mu] :
( ~ ( exists_in_world @ SY785 @ SV12 )
| ~ ~ ( ~ ( qmltpeq @ SV38 @ SV64 @ SV12 )
| ~ ( qmltpeq @ SV64 @ SY785 @ SV12 ) )
| ( qmltpeq @ SV38 @ SY785 @ SV12 ) ) )
= $true )
| ( ( exists_in_world @ SV38 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[281]) ).
thf(305,plain,
! [SV39: mu,SV13: $i,SV65: mu] :
( ( ( exists_in_world @ SV65 @ SV13 )
= $false )
| ( ( ~ ( qmltpeq @ SV39 @ SV65 @ SV13 )
| ( qmltpeq @ SV65 @ SV39 @ SV13 ) )
= $true )
| ( ( exists_in_world @ SV39 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[282]) ).
thf(306,plain,
! [SV40: mu,SV14: $i,SV66: mu] :
( ( ( exists_in_world @ SV66 @ SV14 )
= $false )
| ( ( ! [SY786: mu] :
( ~ ( exists_in_world @ SY786 @ SV14 )
| ~ ~ ( ~ ( qmltpeq @ SV40 @ SV66 @ SV14 )
| ~ ( subset @ SY786 @ SV40 @ SV14 ) )
| ( subset @ SY786 @ SV66 @ SV14 ) ) )
= $true )
| ( ( exists_in_world @ SV40 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[283]) ).
thf(307,plain,
! [SV41: mu,SV15: $i,SV67: mu] :
( ( ( exists_in_world @ SV67 @ SV15 )
= $false )
| ( ( qmltpeq @ ( set_union2 @ SV41 @ SV67 ) @ ( set_union2 @ SV67 @ SV41 ) @ SV15 )
= $true )
| ( ( exists_in_world @ SV41 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[284]) ).
thf(308,plain,
! [SV42: mu,SV17: $i,SV68: mu] :
( ( ( exists_in_world @ SV68 @ SV17 )
= $false )
| ( ( qmltpeq @ ( set_union2 @ SV42 @ SV42 ) @ SV42 @ SV17 )
= $true )
| ( ( exists_in_world @ SV42 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[285]) ).
thf(309,plain,
! [SV43: mu,SV18: $i,SV69: mu] :
( ( ( exists_in_world @ SV69 @ SV18 )
= $false )
| ( ( ~ ( in @ SV43 @ SV69 @ SV18 )
| ~ ( in @ SV69 @ SV43 @ SV18 ) )
= $true )
| ( ( exists_in_world @ SV43 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[286]) ).
thf(310,plain,
! [SV44: mu,SV19: $i,SV70: mu] :
( ( ( exists_in_world @ SV70 @ SV19 )
= $false )
| ( ( ! [SY787: mu] :
( ~ ( exists_in_world @ SY787 @ SV19 )
| ~ ( qmltpeq @ SV44 @ SV70 @ SV19 )
| ( qmltpeq @ ( set_union2 @ SV44 @ SY787 ) @ ( set_union2 @ SV70 @ SY787 ) @ SV19 ) ) )
= $true )
| ( ( exists_in_world @ SV44 @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[287]) ).
thf(311,plain,
! [SV45: mu,SV20: $i,SV71: mu] :
( ( ( exists_in_world @ SV71 @ SV20 )
= $false )
| ( ( ~ ( subset @ SV45 @ SV71 @ SV20 )
| ( qmltpeq @ ( set_union2 @ SV45 @ SV71 ) @ SV71 @ SV20 ) )
= $true )
| ( ( exists_in_world @ SV45 @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[288]) ).
thf(312,plain,
! [SV57: $i,SV46: $i,SV21: mu] :
( ( ( ~ ( exists_in_world @ SV21 @ SV46 ) )
= $true )
| ( ( ~ ( rel_s4 @ SV46 @ SV57 ) )
= $true )
| ( ( exists_in_world @ SV21 @ SV57 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[289]) ).
thf(313,plain,
! [SV47: mu,SV22: $i,SV72: mu] :
( ( ( exists_in_world @ SV72 @ SV22 )
= $false )
| ( ( ! [SY788: mu] :
( ~ ( exists_in_world @ SY788 @ SV22 )
| ~ ( qmltpeq @ SV47 @ SV72 @ SV22 )
| ( qmltpeq @ ( set_union2 @ SY788 @ SV47 ) @ ( set_union2 @ SY788 @ SV72 ) @ SV22 ) ) )
= $true )
| ( ( exists_in_world @ SV47 @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[290]) ).
thf(314,plain,
! [SV48: mu,SV23: $i,SV73: mu] :
( ( ( exists_in_world @ SV73 @ SV23 )
= $false )
| ( ( ! [SY789: mu] :
( ~ ( exists_in_world @ SY789 @ SV23 )
| ~ ~ ( ~ ( qmltpeq @ SV48 @ SV73 @ SV23 )
| ~ ( in @ SV48 @ SY789 @ SV23 ) )
| ( in @ SV73 @ SY789 @ SV23 ) ) )
= $true )
| ( ( exists_in_world @ SV48 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[291]) ).
thf(315,plain,
! [SV49: mu,SV24: $i,SV74: mu] :
( ( ( exists_in_world @ SV74 @ SV24 )
= $false )
| ( ( ! [SY790: mu] :
( ~ ( exists_in_world @ SY790 @ SV24 )
| ~ ( qmltpeq @ SV49 @ SV74 @ SV24 )
| ( qmltpeq @ ( unordered_pair @ SV49 @ SY790 ) @ ( unordered_pair @ SV74 @ SY790 ) @ SV24 ) ) )
= $true )
| ( ( exists_in_world @ SV49 @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[292]) ).
thf(316,plain,
! [SV58: $i,SV50: $i,SV25: $i] :
( ( ( ~ ( rel_s4 @ SV25 @ SV50 ) )
= $true )
| ( ( ~ ( rel_s4 @ SV50 @ SV58 ) )
= $true )
| ( ( rel_s4 @ SV25 @ SV58 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[293]) ).
thf(317,plain,
! [SV51: mu,SV26: $i,SV75: mu] :
( ( ( exists_in_world @ SV75 @ SV26 )
= $false )
| ( ( ! [SY791: mu] :
( ~ ( exists_in_world @ SY791 @ SV26 )
| ~ ( qmltpeq @ SV51 @ SV75 @ SV26 )
| ( qmltpeq @ ( unordered_pair @ SY791 @ SV51 ) @ ( unordered_pair @ SY791 @ SV75 ) @ SV26 ) ) )
= $true )
| ( ( exists_in_world @ SV51 @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[294]) ).
thf(318,plain,
! [SV52: mu,SV27: $i,SV76: mu] :
( ( ( exists_in_world @ SV76 @ SV27 )
= $false )
| ( ( ~ ~ ( empty @ SV52 @ SV27 )
| ~ ( empty @ ( set_union2 @ SV76 @ SV52 ) @ SV27 ) )
= $true )
| ( ( exists_in_world @ SV52 @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[295]) ).
thf(319,plain,
! [SV53: mu,SV28: $i,SV77: mu] :
( ( ( exists_in_world @ SV77 @ SV28 )
= $false )
| ( ( ! [SY792: mu] :
( ~ ( exists_in_world @ SY792 @ SV28 )
| ~ ~ ( ~ ( qmltpeq @ SV53 @ SV77 @ SV28 )
| ~ ( in @ SY792 @ SV53 @ SV28 ) )
| ( in @ SY792 @ SV77 @ SV28 ) ) )
= $true )
| ( ( exists_in_world @ SV53 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[296]) ).
thf(320,plain,
! [SV54: mu,SV29: $i,SV78: mu] :
( ( ( exists_in_world @ SV78 @ SV29 )
= $false )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV54 @ SV78 @ SV29 )
| ~ ( empty @ SV54 @ SV29 ) )
| ( empty @ SV78 @ SV29 ) )
= $true )
| ( ( exists_in_world @ SV54 @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[297]) ).
thf(321,plain,
! [SV60: mu,SV5: $i,SV33: mu] :
( ( ( ~ ~ ( empty @ SV33 @ SV5 ) )
= $true )
| ( ( ~ ( empty @ ( set_union2 @ SV33 @ SV60 ) @ SV5 ) )
= $true )
| ( ( exists_in_world @ SV60 @ SV5 )
= $false )
| ( ( exists_in_world @ SV33 @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[299]) ).
thf(322,plain,
! [SV61: mu,SV34: mu,SV6: $i,SV79: mu] :
( ( ( ~ ( exists_in_world @ SV79 @ SV6 )
| ~ ~ ( ~ ( qmltpeq @ SV34 @ SV61 @ SV6 )
| ~ ( subset @ SV34 @ SV79 @ SV6 ) )
| ( subset @ SV61 @ SV79 @ SV6 ) )
= $true )
| ( ( exists_in_world @ SV61 @ SV6 )
= $false )
| ( ( exists_in_world @ SV34 @ SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[300]) ).
thf(323,plain,
! [SV62: mu,SV35: mu,SV8: $i,SV80: mu] :
( ( ( ~ ( exists_in_world @ SV80 @ SV8 )
| ~ ( ~ ( ~ ( subset @ ( unordered_pair @ SV35 @ SV62 ) @ SV80 @ SV8 )
| ~ ( ~ ( in @ SV35 @ SV80 @ SV8 )
| ~ ( in @ SV62 @ SV80 @ SV8 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV35 @ SV80 @ SV8 )
| ~ ( in @ SV62 @ SV80 @ SV8 ) )
| ( subset @ ( unordered_pair @ SV35 @ SV62 ) @ SV80 @ SV8 ) ) ) )
= $true )
| ( ( exists_in_world @ SV62 @ SV8 )
= $false )
| ( ( exists_in_world @ SV35 @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[301]) ).
thf(324,plain,
( ( ~ ( in @ sK2_SY681 @ sK3_SX0 @ sK1_SY32 )
| ~ ( in @ sK7_SY757 @ sK3_SX0 @ sK1_SY32 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[303]) ).
thf(325,plain,
! [SV64: mu,SV38: mu,SV12: $i,SV81: mu] :
( ( ( ~ ( exists_in_world @ SV81 @ SV12 )
| ~ ~ ( ~ ( qmltpeq @ SV38 @ SV64 @ SV12 )
| ~ ( qmltpeq @ SV64 @ SV81 @ SV12 ) )
| ( qmltpeq @ SV38 @ SV81 @ SV12 ) )
= $true )
| ( ( exists_in_world @ SV64 @ SV12 )
= $false )
| ( ( exists_in_world @ SV38 @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[304]) ).
thf(326,plain,
! [SV13: $i,SV65: mu,SV39: mu] :
( ( ( ~ ( qmltpeq @ SV39 @ SV65 @ SV13 ) )
= $true )
| ( ( qmltpeq @ SV65 @ SV39 @ SV13 )
= $true )
| ( ( exists_in_world @ SV65 @ SV13 )
= $false )
| ( ( exists_in_world @ SV39 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[305]) ).
thf(327,plain,
! [SV66: mu,SV40: mu,SV14: $i,SV82: mu] :
( ( ( ~ ( exists_in_world @ SV82 @ SV14 )
| ~ ~ ( ~ ( qmltpeq @ SV40 @ SV66 @ SV14 )
| ~ ( subset @ SV82 @ SV40 @ SV14 ) )
| ( subset @ SV82 @ SV66 @ SV14 ) )
= $true )
| ( ( exists_in_world @ SV66 @ SV14 )
= $false )
| ( ( exists_in_world @ SV40 @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[306]) ).
thf(328,plain,
! [SV18: $i,SV69: mu,SV43: mu] :
( ( ( ~ ( in @ SV43 @ SV69 @ SV18 ) )
= $true )
| ( ( ~ ( in @ SV69 @ SV43 @ SV18 ) )
= $true )
| ( ( exists_in_world @ SV69 @ SV18 )
= $false )
| ( ( exists_in_world @ SV43 @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[309]) ).
thf(329,plain,
! [SV70: mu,SV44: mu,SV19: $i,SV83: mu] :
( ( ( ~ ( exists_in_world @ SV83 @ SV19 )
| ~ ( qmltpeq @ SV44 @ SV70 @ SV19 )
| ( qmltpeq @ ( set_union2 @ SV44 @ SV83 ) @ ( set_union2 @ SV70 @ SV83 ) @ SV19 ) )
= $true )
| ( ( exists_in_world @ SV70 @ SV19 )
= $false )
| ( ( exists_in_world @ SV44 @ SV19 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[310]) ).
thf(330,plain,
! [SV20: $i,SV71: mu,SV45: mu] :
( ( ( ~ ( subset @ SV45 @ SV71 @ SV20 ) )
= $true )
| ( ( qmltpeq @ ( set_union2 @ SV45 @ SV71 ) @ SV71 @ SV20 )
= $true )
| ( ( exists_in_world @ SV71 @ SV20 )
= $false )
| ( ( exists_in_world @ SV45 @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[311]) ).
thf(331,plain,
! [SV57: $i,SV46: $i,SV21: mu] :
( ( ( exists_in_world @ SV21 @ SV46 )
= $false )
| ( ( ~ ( rel_s4 @ SV46 @ SV57 ) )
= $true )
| ( ( exists_in_world @ SV21 @ SV57 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[312]) ).
thf(332,plain,
! [SV72: mu,SV47: mu,SV22: $i,SV84: mu] :
( ( ( ~ ( exists_in_world @ SV84 @ SV22 )
| ~ ( qmltpeq @ SV47 @ SV72 @ SV22 )
| ( qmltpeq @ ( set_union2 @ SV84 @ SV47 ) @ ( set_union2 @ SV84 @ SV72 ) @ SV22 ) )
= $true )
| ( ( exists_in_world @ SV72 @ SV22 )
= $false )
| ( ( exists_in_world @ SV47 @ SV22 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[313]) ).
thf(333,plain,
! [SV73: mu,SV48: mu,SV23: $i,SV85: mu] :
( ( ( ~ ( exists_in_world @ SV85 @ SV23 )
| ~ ~ ( ~ ( qmltpeq @ SV48 @ SV73 @ SV23 )
| ~ ( in @ SV48 @ SV85 @ SV23 ) )
| ( in @ SV73 @ SV85 @ SV23 ) )
= $true )
| ( ( exists_in_world @ SV73 @ SV23 )
= $false )
| ( ( exists_in_world @ SV48 @ SV23 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[314]) ).
thf(334,plain,
! [SV74: mu,SV49: mu,SV24: $i,SV86: mu] :
( ( ( ~ ( exists_in_world @ SV86 @ SV24 )
| ~ ( qmltpeq @ SV49 @ SV74 @ SV24 )
| ( qmltpeq @ ( unordered_pair @ SV49 @ SV86 ) @ ( unordered_pair @ SV74 @ SV86 ) @ SV24 ) )
= $true )
| ( ( exists_in_world @ SV74 @ SV24 )
= $false )
| ( ( exists_in_world @ SV49 @ SV24 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[315]) ).
thf(335,plain,
! [SV58: $i,SV50: $i,SV25: $i] :
( ( ( rel_s4 @ SV25 @ SV50 )
= $false )
| ( ( ~ ( rel_s4 @ SV50 @ SV58 ) )
= $true )
| ( ( rel_s4 @ SV25 @ SV58 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[316]) ).
thf(336,plain,
! [SV75: mu,SV51: mu,SV26: $i,SV87: mu] :
( ( ( ~ ( exists_in_world @ SV87 @ SV26 )
| ~ ( qmltpeq @ SV51 @ SV75 @ SV26 )
| ( qmltpeq @ ( unordered_pair @ SV87 @ SV51 ) @ ( unordered_pair @ SV87 @ SV75 ) @ SV26 ) )
= $true )
| ( ( exists_in_world @ SV75 @ SV26 )
= $false )
| ( ( exists_in_world @ SV51 @ SV26 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[317]) ).
thf(337,plain,
! [SV76: mu,SV27: $i,SV52: mu] :
( ( ( ~ ~ ( empty @ SV52 @ SV27 ) )
= $true )
| ( ( ~ ( empty @ ( set_union2 @ SV76 @ SV52 ) @ SV27 ) )
= $true )
| ( ( exists_in_world @ SV76 @ SV27 )
= $false )
| ( ( exists_in_world @ SV52 @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[318]) ).
thf(338,plain,
! [SV77: mu,SV53: mu,SV28: $i,SV88: mu] :
( ( ( ~ ( exists_in_world @ SV88 @ SV28 )
| ~ ~ ( ~ ( qmltpeq @ SV53 @ SV77 @ SV28 )
| ~ ( in @ SV88 @ SV53 @ SV28 ) )
| ( in @ SV88 @ SV77 @ SV28 ) )
= $true )
| ( ( exists_in_world @ SV77 @ SV28 )
= $false )
| ( ( exists_in_world @ SV53 @ SV28 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[319]) ).
thf(339,plain,
! [SV29: $i,SV78: mu,SV54: mu] :
( ( ( ~ ~ ( ~ ( qmltpeq @ SV54 @ SV78 @ SV29 )
| ~ ( empty @ SV54 @ SV29 ) ) )
= $true )
| ( ( empty @ SV78 @ SV29 )
= $true )
| ( ( exists_in_world @ SV78 @ SV29 )
= $false )
| ( ( exists_in_world @ SV54 @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[320]) ).
thf(340,plain,
! [SV60: mu,SV5: $i,SV33: mu] :
( ( ( ~ ( empty @ SV33 @ SV5 ) )
= $false )
| ( ( ~ ( empty @ ( set_union2 @ SV33 @ SV60 ) @ SV5 ) )
= $true )
| ( ( exists_in_world @ SV60 @ SV5 )
= $false )
| ( ( exists_in_world @ SV33 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[321]) ).
thf(341,plain,
! [SV61: mu,SV34: mu,SV6: $i,SV79: mu] :
( ( ( ~ ( exists_in_world @ SV79 @ SV6 ) )
= $true )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV34 @ SV61 @ SV6 )
| ~ ( subset @ SV34 @ SV79 @ SV6 ) )
| ( subset @ SV61 @ SV79 @ SV6 ) )
= $true )
| ( ( exists_in_world @ SV61 @ SV6 )
= $false )
| ( ( exists_in_world @ SV34 @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[322]) ).
thf(342,plain,
! [SV62: mu,SV35: mu,SV8: $i,SV80: mu] :
( ( ( ~ ( exists_in_world @ SV80 @ SV8 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( subset @ ( unordered_pair @ SV35 @ SV62 ) @ SV80 @ SV8 )
| ~ ( ~ ( in @ SV35 @ SV80 @ SV8 )
| ~ ( in @ SV62 @ SV80 @ SV8 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV35 @ SV80 @ SV8 )
| ~ ( in @ SV62 @ SV80 @ SV8 ) )
| ( subset @ ( unordered_pair @ SV35 @ SV62 ) @ SV80 @ SV8 ) ) ) )
= $true )
| ( ( exists_in_world @ SV62 @ SV8 )
= $false )
| ( ( exists_in_world @ SV35 @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[323]) ).
thf(343,plain,
( ( ~ ( in @ sK2_SY681 @ sK3_SX0 @ sK1_SY32 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[324]) ).
thf(344,plain,
( ( ~ ( in @ sK7_SY757 @ sK3_SX0 @ sK1_SY32 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[324]) ).
thf(345,plain,
! [SV64: mu,SV38: mu,SV12: $i,SV81: mu] :
( ( ( ~ ( exists_in_world @ SV81 @ SV12 ) )
= $true )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV38 @ SV64 @ SV12 )
| ~ ( qmltpeq @ SV64 @ SV81 @ SV12 ) )
| ( qmltpeq @ SV38 @ SV81 @ SV12 ) )
= $true )
| ( ( exists_in_world @ SV64 @ SV12 )
= $false )
| ( ( exists_in_world @ SV38 @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[325]) ).
thf(346,plain,
! [SV13: $i,SV65: mu,SV39: mu] :
( ( ( qmltpeq @ SV39 @ SV65 @ SV13 )
= $false )
| ( ( qmltpeq @ SV65 @ SV39 @ SV13 )
= $true )
| ( ( exists_in_world @ SV65 @ SV13 )
= $false )
| ( ( exists_in_world @ SV39 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[326]) ).
thf(347,plain,
! [SV66: mu,SV40: mu,SV14: $i,SV82: mu] :
( ( ( ~ ( exists_in_world @ SV82 @ SV14 ) )
= $true )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV40 @ SV66 @ SV14 )
| ~ ( subset @ SV82 @ SV40 @ SV14 ) )
| ( subset @ SV82 @ SV66 @ SV14 ) )
= $true )
| ( ( exists_in_world @ SV66 @ SV14 )
= $false )
| ( ( exists_in_world @ SV40 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[327]) ).
thf(348,plain,
! [SV18: $i,SV69: mu,SV43: mu] :
( ( ( in @ SV43 @ SV69 @ SV18 )
= $false )
| ( ( ~ ( in @ SV69 @ SV43 @ SV18 ) )
= $true )
| ( ( exists_in_world @ SV69 @ SV18 )
= $false )
| ( ( exists_in_world @ SV43 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[328]) ).
thf(349,plain,
! [SV70: mu,SV44: mu,SV19: $i,SV83: mu] :
( ( ( ~ ( exists_in_world @ SV83 @ SV19 ) )
= $true )
| ( ( ~ ( qmltpeq @ SV44 @ SV70 @ SV19 )
| ( qmltpeq @ ( set_union2 @ SV44 @ SV83 ) @ ( set_union2 @ SV70 @ SV83 ) @ SV19 ) )
= $true )
| ( ( exists_in_world @ SV70 @ SV19 )
= $false )
| ( ( exists_in_world @ SV44 @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[329]) ).
thf(350,plain,
! [SV20: $i,SV71: mu,SV45: mu] :
( ( ( subset @ SV45 @ SV71 @ SV20 )
= $false )
| ( ( qmltpeq @ ( set_union2 @ SV45 @ SV71 ) @ SV71 @ SV20 )
= $true )
| ( ( exists_in_world @ SV71 @ SV20 )
= $false )
| ( ( exists_in_world @ SV45 @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[330]) ).
thf(351,plain,
! [SV21: mu,SV57: $i,SV46: $i] :
( ( ( rel_s4 @ SV46 @ SV57 )
= $false )
| ( ( exists_in_world @ SV21 @ SV46 )
= $false )
| ( ( exists_in_world @ SV21 @ SV57 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[331]) ).
thf(352,plain,
! [SV72: mu,SV47: mu,SV22: $i,SV84: mu] :
( ( ( ~ ( exists_in_world @ SV84 @ SV22 ) )
= $true )
| ( ( ~ ( qmltpeq @ SV47 @ SV72 @ SV22 )
| ( qmltpeq @ ( set_union2 @ SV84 @ SV47 ) @ ( set_union2 @ SV84 @ SV72 ) @ SV22 ) )
= $true )
| ( ( exists_in_world @ SV72 @ SV22 )
= $false )
| ( ( exists_in_world @ SV47 @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[332]) ).
thf(353,plain,
! [SV73: mu,SV48: mu,SV23: $i,SV85: mu] :
( ( ( ~ ( exists_in_world @ SV85 @ SV23 ) )
= $true )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV48 @ SV73 @ SV23 )
| ~ ( in @ SV48 @ SV85 @ SV23 ) )
| ( in @ SV73 @ SV85 @ SV23 ) )
= $true )
| ( ( exists_in_world @ SV73 @ SV23 )
= $false )
| ( ( exists_in_world @ SV48 @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[333]) ).
thf(354,plain,
! [SV74: mu,SV49: mu,SV24: $i,SV86: mu] :
( ( ( ~ ( exists_in_world @ SV86 @ SV24 ) )
= $true )
| ( ( ~ ( qmltpeq @ SV49 @ SV74 @ SV24 )
| ( qmltpeq @ ( unordered_pair @ SV49 @ SV86 ) @ ( unordered_pair @ SV74 @ SV86 ) @ SV24 ) )
= $true )
| ( ( exists_in_world @ SV74 @ SV24 )
= $false )
| ( ( exists_in_world @ SV49 @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[334]) ).
thf(355,plain,
! [SV25: $i,SV58: $i,SV50: $i] :
( ( ( rel_s4 @ SV50 @ SV58 )
= $false )
| ( ( rel_s4 @ SV25 @ SV50 )
= $false )
| ( ( rel_s4 @ SV25 @ SV58 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[335]) ).
thf(356,plain,
! [SV75: mu,SV51: mu,SV26: $i,SV87: mu] :
( ( ( ~ ( exists_in_world @ SV87 @ SV26 ) )
= $true )
| ( ( ~ ( qmltpeq @ SV51 @ SV75 @ SV26 )
| ( qmltpeq @ ( unordered_pair @ SV87 @ SV51 ) @ ( unordered_pair @ SV87 @ SV75 ) @ SV26 ) )
= $true )
| ( ( exists_in_world @ SV75 @ SV26 )
= $false )
| ( ( exists_in_world @ SV51 @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[336]) ).
thf(357,plain,
! [SV76: mu,SV27: $i,SV52: mu] :
( ( ( ~ ( empty @ SV52 @ SV27 ) )
= $false )
| ( ( ~ ( empty @ ( set_union2 @ SV76 @ SV52 ) @ SV27 ) )
= $true )
| ( ( exists_in_world @ SV76 @ SV27 )
= $false )
| ( ( exists_in_world @ SV52 @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[337]) ).
thf(358,plain,
! [SV77: mu,SV53: mu,SV28: $i,SV88: mu] :
( ( ( ~ ( exists_in_world @ SV88 @ SV28 ) )
= $true )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV53 @ SV77 @ SV28 )
| ~ ( in @ SV88 @ SV53 @ SV28 ) )
| ( in @ SV88 @ SV77 @ SV28 ) )
= $true )
| ( ( exists_in_world @ SV77 @ SV28 )
= $false )
| ( ( exists_in_world @ SV53 @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[338]) ).
thf(359,plain,
! [SV29: $i,SV78: mu,SV54: mu] :
( ( ( ~ ( ~ ( qmltpeq @ SV54 @ SV78 @ SV29 )
| ~ ( empty @ SV54 @ SV29 ) ) )
= $false )
| ( ( empty @ SV78 @ SV29 )
= $true )
| ( ( exists_in_world @ SV78 @ SV29 )
= $false )
| ( ( exists_in_world @ SV54 @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[339]) ).
thf(360,plain,
! [SV60: mu,SV5: $i,SV33: mu] :
( ( ( empty @ SV33 @ SV5 )
= $true )
| ( ( ~ ( empty @ ( set_union2 @ SV33 @ SV60 ) @ SV5 ) )
= $true )
| ( ( exists_in_world @ SV60 @ SV5 )
= $false )
| ( ( exists_in_world @ SV33 @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[340]) ).
thf(361,plain,
! [SV61: mu,SV34: mu,SV6: $i,SV79: mu] :
( ( ( exists_in_world @ SV79 @ SV6 )
= $false )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV34 @ SV61 @ SV6 )
| ~ ( subset @ SV34 @ SV79 @ SV6 ) )
| ( subset @ SV61 @ SV79 @ SV6 ) )
= $true )
| ( ( exists_in_world @ SV61 @ SV6 )
= $false )
| ( ( exists_in_world @ SV34 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[341]) ).
thf(362,plain,
! [SV62: mu,SV35: mu,SV8: $i,SV80: mu] :
( ( ( exists_in_world @ SV80 @ SV8 )
= $false )
| ( ( ~ ( ~ ( ~ ( subset @ ( unordered_pair @ SV35 @ SV62 ) @ SV80 @ SV8 )
| ~ ( ~ ( in @ SV35 @ SV80 @ SV8 )
| ~ ( in @ SV62 @ SV80 @ SV8 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV35 @ SV80 @ SV8 )
| ~ ( in @ SV62 @ SV80 @ SV8 ) )
| ( subset @ ( unordered_pair @ SV35 @ SV62 ) @ SV80 @ SV8 ) ) ) )
= $true )
| ( ( exists_in_world @ SV62 @ SV8 )
= $false )
| ( ( exists_in_world @ SV35 @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[342]) ).
thf(363,plain,
( ( in @ sK2_SY681 @ sK3_SX0 @ sK1_SY32 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[343]) ).
thf(364,plain,
( ( in @ sK7_SY757 @ sK3_SX0 @ sK1_SY32 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[344]) ).
thf(365,plain,
! [SV64: mu,SV38: mu,SV12: $i,SV81: mu] :
( ( ( exists_in_world @ SV81 @ SV12 )
= $false )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV38 @ SV64 @ SV12 )
| ~ ( qmltpeq @ SV64 @ SV81 @ SV12 ) )
| ( qmltpeq @ SV38 @ SV81 @ SV12 ) )
= $true )
| ( ( exists_in_world @ SV64 @ SV12 )
= $false )
| ( ( exists_in_world @ SV38 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[345]) ).
thf(366,plain,
! [SV66: mu,SV40: mu,SV14: $i,SV82: mu] :
( ( ( exists_in_world @ SV82 @ SV14 )
= $false )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV40 @ SV66 @ SV14 )
| ~ ( subset @ SV82 @ SV40 @ SV14 ) )
| ( subset @ SV82 @ SV66 @ SV14 ) )
= $true )
| ( ( exists_in_world @ SV66 @ SV14 )
= $false )
| ( ( exists_in_world @ SV40 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[347]) ).
thf(367,plain,
! [SV18: $i,SV43: mu,SV69: mu] :
( ( ( in @ SV69 @ SV43 @ SV18 )
= $false )
| ( ( in @ SV43 @ SV69 @ SV18 )
= $false )
| ( ( exists_in_world @ SV69 @ SV18 )
= $false )
| ( ( exists_in_world @ SV43 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[348]) ).
thf(368,plain,
! [SV70: mu,SV44: mu,SV19: $i,SV83: mu] :
( ( ( exists_in_world @ SV83 @ SV19 )
= $false )
| ( ( ~ ( qmltpeq @ SV44 @ SV70 @ SV19 )
| ( qmltpeq @ ( set_union2 @ SV44 @ SV83 ) @ ( set_union2 @ SV70 @ SV83 ) @ SV19 ) )
= $true )
| ( ( exists_in_world @ SV70 @ SV19 )
= $false )
| ( ( exists_in_world @ SV44 @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[349]) ).
thf(369,plain,
! [SV72: mu,SV47: mu,SV22: $i,SV84: mu] :
( ( ( exists_in_world @ SV84 @ SV22 )
= $false )
| ( ( ~ ( qmltpeq @ SV47 @ SV72 @ SV22 )
| ( qmltpeq @ ( set_union2 @ SV84 @ SV47 ) @ ( set_union2 @ SV84 @ SV72 ) @ SV22 ) )
= $true )
| ( ( exists_in_world @ SV72 @ SV22 )
= $false )
| ( ( exists_in_world @ SV47 @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[352]) ).
thf(370,plain,
! [SV73: mu,SV48: mu,SV23: $i,SV85: mu] :
( ( ( exists_in_world @ SV85 @ SV23 )
= $false )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV48 @ SV73 @ SV23 )
| ~ ( in @ SV48 @ SV85 @ SV23 ) )
| ( in @ SV73 @ SV85 @ SV23 ) )
= $true )
| ( ( exists_in_world @ SV73 @ SV23 )
= $false )
| ( ( exists_in_world @ SV48 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[353]) ).
thf(371,plain,
! [SV74: mu,SV49: mu,SV24: $i,SV86: mu] :
( ( ( exists_in_world @ SV86 @ SV24 )
= $false )
| ( ( ~ ( qmltpeq @ SV49 @ SV74 @ SV24 )
| ( qmltpeq @ ( unordered_pair @ SV49 @ SV86 ) @ ( unordered_pair @ SV74 @ SV86 ) @ SV24 ) )
= $true )
| ( ( exists_in_world @ SV74 @ SV24 )
= $false )
| ( ( exists_in_world @ SV49 @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[354]) ).
thf(372,plain,
! [SV75: mu,SV51: mu,SV26: $i,SV87: mu] :
( ( ( exists_in_world @ SV87 @ SV26 )
= $false )
| ( ( ~ ( qmltpeq @ SV51 @ SV75 @ SV26 )
| ( qmltpeq @ ( unordered_pair @ SV87 @ SV51 ) @ ( unordered_pair @ SV87 @ SV75 ) @ SV26 ) )
= $true )
| ( ( exists_in_world @ SV75 @ SV26 )
= $false )
| ( ( exists_in_world @ SV51 @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[356]) ).
thf(373,plain,
! [SV76: mu,SV27: $i,SV52: mu] :
( ( ( empty @ SV52 @ SV27 )
= $true )
| ( ( ~ ( empty @ ( set_union2 @ SV76 @ SV52 ) @ SV27 ) )
= $true )
| ( ( exists_in_world @ SV76 @ SV27 )
= $false )
| ( ( exists_in_world @ SV52 @ SV27 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[357]) ).
thf(374,plain,
! [SV77: mu,SV53: mu,SV28: $i,SV88: mu] :
( ( ( exists_in_world @ SV88 @ SV28 )
= $false )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV53 @ SV77 @ SV28 )
| ~ ( in @ SV88 @ SV53 @ SV28 ) )
| ( in @ SV88 @ SV77 @ SV28 ) )
= $true )
| ( ( exists_in_world @ SV77 @ SV28 )
= $false )
| ( ( exists_in_world @ SV53 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[358]) ).
thf(375,plain,
! [SV29: $i,SV78: mu,SV54: mu] :
( ( ( ~ ( qmltpeq @ SV54 @ SV78 @ SV29 )
| ~ ( empty @ SV54 @ SV29 ) )
= $true )
| ( ( empty @ SV78 @ SV29 )
= $true )
| ( ( exists_in_world @ SV78 @ SV29 )
= $false )
| ( ( exists_in_world @ SV54 @ SV29 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[359]) ).
thf(376,plain,
! [SV5: $i,SV60: mu,SV33: mu] :
( ( ( empty @ ( set_union2 @ SV33 @ SV60 ) @ SV5 )
= $false )
| ( ( empty @ SV33 @ SV5 )
= $true )
| ( ( exists_in_world @ SV60 @ SV5 )
= $false )
| ( ( exists_in_world @ SV33 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[360]) ).
thf(377,plain,
! [SV79: mu,SV6: $i,SV61: mu,SV34: mu] :
( ( ( ~ ~ ( ~ ( qmltpeq @ SV34 @ SV61 @ SV6 )
| ~ ( subset @ SV34 @ SV79 @ SV6 ) ) )
= $true )
| ( ( subset @ SV61 @ SV79 @ SV6 )
= $true )
| ( ( exists_in_world @ SV79 @ SV6 )
= $false )
| ( ( exists_in_world @ SV61 @ SV6 )
= $false )
| ( ( exists_in_world @ SV34 @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[361]) ).
thf(378,plain,
! [SV8: $i,SV80: mu,SV62: mu,SV35: mu] :
( ( ( ~ ( ~ ( subset @ ( unordered_pair @ SV35 @ SV62 ) @ SV80 @ SV8 )
| ~ ( ~ ( in @ SV35 @ SV80 @ SV8 )
| ~ ( in @ SV62 @ SV80 @ SV8 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV35 @ SV80 @ SV8 )
| ~ ( in @ SV62 @ SV80 @ SV8 ) )
| ( subset @ ( unordered_pair @ SV35 @ SV62 ) @ SV80 @ SV8 ) ) )
= $false )
| ( ( exists_in_world @ SV80 @ SV8 )
= $false )
| ( ( exists_in_world @ SV62 @ SV8 )
= $false )
| ( ( exists_in_world @ SV35 @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[362]) ).
thf(379,plain,
! [SV81: mu,SV12: $i,SV64: mu,SV38: mu] :
( ( ( ~ ~ ( ~ ( qmltpeq @ SV38 @ SV64 @ SV12 )
| ~ ( qmltpeq @ SV64 @ SV81 @ SV12 ) ) )
= $true )
| ( ( qmltpeq @ SV38 @ SV81 @ SV12 )
= $true )
| ( ( exists_in_world @ SV81 @ SV12 )
= $false )
| ( ( exists_in_world @ SV64 @ SV12 )
= $false )
| ( ( exists_in_world @ SV38 @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[365]) ).
thf(380,plain,
! [SV82: mu,SV14: $i,SV66: mu,SV40: mu] :
( ( ( ~ ~ ( ~ ( qmltpeq @ SV40 @ SV66 @ SV14 )
| ~ ( subset @ SV82 @ SV40 @ SV14 ) ) )
= $true )
| ( ( subset @ SV82 @ SV66 @ SV14 )
= $true )
| ( ( exists_in_world @ SV82 @ SV14 )
= $false )
| ( ( exists_in_world @ SV66 @ SV14 )
= $false )
| ( ( exists_in_world @ SV40 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[366]) ).
thf(381,plain,
! [SV83: mu,SV19: $i,SV70: mu,SV44: mu] :
( ( ( ~ ( qmltpeq @ SV44 @ SV70 @ SV19 ) )
= $true )
| ( ( qmltpeq @ ( set_union2 @ SV44 @ SV83 ) @ ( set_union2 @ SV70 @ SV83 ) @ SV19 )
= $true )
| ( ( exists_in_world @ SV83 @ SV19 )
= $false )
| ( ( exists_in_world @ SV70 @ SV19 )
= $false )
| ( ( exists_in_world @ SV44 @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[368]) ).
thf(382,plain,
! [SV84: mu,SV22: $i,SV72: mu,SV47: mu] :
( ( ( ~ ( qmltpeq @ SV47 @ SV72 @ SV22 ) )
= $true )
| ( ( qmltpeq @ ( set_union2 @ SV84 @ SV47 ) @ ( set_union2 @ SV84 @ SV72 ) @ SV22 )
= $true )
| ( ( exists_in_world @ SV84 @ SV22 )
= $false )
| ( ( exists_in_world @ SV72 @ SV22 )
= $false )
| ( ( exists_in_world @ SV47 @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[369]) ).
thf(383,plain,
! [SV85: mu,SV23: $i,SV73: mu,SV48: mu] :
( ( ( ~ ~ ( ~ ( qmltpeq @ SV48 @ SV73 @ SV23 )
| ~ ( in @ SV48 @ SV85 @ SV23 ) ) )
= $true )
| ( ( in @ SV73 @ SV85 @ SV23 )
= $true )
| ( ( exists_in_world @ SV85 @ SV23 )
= $false )
| ( ( exists_in_world @ SV73 @ SV23 )
= $false )
| ( ( exists_in_world @ SV48 @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[370]) ).
thf(384,plain,
! [SV86: mu,SV24: $i,SV74: mu,SV49: mu] :
( ( ( ~ ( qmltpeq @ SV49 @ SV74 @ SV24 ) )
= $true )
| ( ( qmltpeq @ ( unordered_pair @ SV49 @ SV86 ) @ ( unordered_pair @ SV74 @ SV86 ) @ SV24 )
= $true )
| ( ( exists_in_world @ SV86 @ SV24 )
= $false )
| ( ( exists_in_world @ SV74 @ SV24 )
= $false )
| ( ( exists_in_world @ SV49 @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[371]) ).
thf(385,plain,
! [SV87: mu,SV26: $i,SV75: mu,SV51: mu] :
( ( ( ~ ( qmltpeq @ SV51 @ SV75 @ SV26 ) )
= $true )
| ( ( qmltpeq @ ( unordered_pair @ SV87 @ SV51 ) @ ( unordered_pair @ SV87 @ SV75 ) @ SV26 )
= $true )
| ( ( exists_in_world @ SV87 @ SV26 )
= $false )
| ( ( exists_in_world @ SV75 @ SV26 )
= $false )
| ( ( exists_in_world @ SV51 @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[372]) ).
thf(386,plain,
! [SV27: $i,SV52: mu,SV76: mu] :
( ( ( empty @ ( set_union2 @ SV76 @ SV52 ) @ SV27 )
= $false )
| ( ( empty @ SV52 @ SV27 )
= $true )
| ( ( exists_in_world @ SV76 @ SV27 )
= $false )
| ( ( exists_in_world @ SV52 @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[373]) ).
thf(387,plain,
! [SV88: mu,SV28: $i,SV77: mu,SV53: mu] :
( ( ( ~ ~ ( ~ ( qmltpeq @ SV53 @ SV77 @ SV28 )
| ~ ( in @ SV88 @ SV53 @ SV28 ) ) )
= $true )
| ( ( in @ SV88 @ SV77 @ SV28 )
= $true )
| ( ( exists_in_world @ SV88 @ SV28 )
= $false )
| ( ( exists_in_world @ SV77 @ SV28 )
= $false )
| ( ( exists_in_world @ SV53 @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[374]) ).
thf(388,plain,
! [SV29: $i,SV78: mu,SV54: mu] :
( ( ( ~ ( qmltpeq @ SV54 @ SV78 @ SV29 ) )
= $true )
| ( ( ~ ( empty @ SV54 @ SV29 ) )
= $true )
| ( ( empty @ SV78 @ SV29 )
= $true )
| ( ( exists_in_world @ SV78 @ SV29 )
= $false )
| ( ( exists_in_world @ SV54 @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[375]) ).
thf(389,plain,
! [SV79: mu,SV6: $i,SV61: mu,SV34: mu] :
( ( ( ~ ( ~ ( qmltpeq @ SV34 @ SV61 @ SV6 )
| ~ ( subset @ SV34 @ SV79 @ SV6 ) ) )
= $false )
| ( ( subset @ SV61 @ SV79 @ SV6 )
= $true )
| ( ( exists_in_world @ SV79 @ SV6 )
= $false )
| ( ( exists_in_world @ SV61 @ SV6 )
= $false )
| ( ( exists_in_world @ SV34 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[377]) ).
thf(390,plain,
! [SV8: $i,SV80: mu,SV62: mu,SV35: mu] :
( ( ( ~ ( ~ ( subset @ ( unordered_pair @ SV35 @ SV62 ) @ SV80 @ SV8 )
| ~ ( ~ ( in @ SV35 @ SV80 @ SV8 )
| ~ ( in @ SV62 @ SV80 @ SV8 ) ) ) )
= $false )
| ( ( exists_in_world @ SV80 @ SV8 )
= $false )
| ( ( exists_in_world @ SV62 @ SV8 )
= $false )
| ( ( exists_in_world @ SV35 @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[378]) ).
thf(391,plain,
! [SV62: mu,SV8: $i,SV80: mu,SV35: mu] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV35 @ SV80 @ SV8 )
| ~ ( in @ SV62 @ SV80 @ SV8 ) )
| ( subset @ ( unordered_pair @ SV35 @ SV62 ) @ SV80 @ SV8 ) ) )
= $false )
| ( ( exists_in_world @ SV80 @ SV8 )
= $false )
| ( ( exists_in_world @ SV62 @ SV8 )
= $false )
| ( ( exists_in_world @ SV35 @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[378]) ).
thf(392,plain,
! [SV81: mu,SV12: $i,SV64: mu,SV38: mu] :
( ( ( ~ ( ~ ( qmltpeq @ SV38 @ SV64 @ SV12 )
| ~ ( qmltpeq @ SV64 @ SV81 @ SV12 ) ) )
= $false )
| ( ( qmltpeq @ SV38 @ SV81 @ SV12 )
= $true )
| ( ( exists_in_world @ SV81 @ SV12 )
= $false )
| ( ( exists_in_world @ SV64 @ SV12 )
= $false )
| ( ( exists_in_world @ SV38 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[379]) ).
thf(393,plain,
! [SV82: mu,SV14: $i,SV66: mu,SV40: mu] :
( ( ( ~ ( ~ ( qmltpeq @ SV40 @ SV66 @ SV14 )
| ~ ( subset @ SV82 @ SV40 @ SV14 ) ) )
= $false )
| ( ( subset @ SV82 @ SV66 @ SV14 )
= $true )
| ( ( exists_in_world @ SV82 @ SV14 )
= $false )
| ( ( exists_in_world @ SV66 @ SV14 )
= $false )
| ( ( exists_in_world @ SV40 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[380]) ).
thf(394,plain,
! [SV83: mu,SV19: $i,SV70: mu,SV44: mu] :
( ( ( qmltpeq @ SV44 @ SV70 @ SV19 )
= $false )
| ( ( qmltpeq @ ( set_union2 @ SV44 @ SV83 ) @ ( set_union2 @ SV70 @ SV83 ) @ SV19 )
= $true )
| ( ( exists_in_world @ SV83 @ SV19 )
= $false )
| ( ( exists_in_world @ SV70 @ SV19 )
= $false )
| ( ( exists_in_world @ SV44 @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[381]) ).
thf(395,plain,
! [SV84: mu,SV22: $i,SV72: mu,SV47: mu] :
( ( ( qmltpeq @ SV47 @ SV72 @ SV22 )
= $false )
| ( ( qmltpeq @ ( set_union2 @ SV84 @ SV47 ) @ ( set_union2 @ SV84 @ SV72 ) @ SV22 )
= $true )
| ( ( exists_in_world @ SV84 @ SV22 )
= $false )
| ( ( exists_in_world @ SV72 @ SV22 )
= $false )
| ( ( exists_in_world @ SV47 @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[382]) ).
thf(396,plain,
! [SV85: mu,SV23: $i,SV73: mu,SV48: mu] :
( ( ( ~ ( ~ ( qmltpeq @ SV48 @ SV73 @ SV23 )
| ~ ( in @ SV48 @ SV85 @ SV23 ) ) )
= $false )
| ( ( in @ SV73 @ SV85 @ SV23 )
= $true )
| ( ( exists_in_world @ SV85 @ SV23 )
= $false )
| ( ( exists_in_world @ SV73 @ SV23 )
= $false )
| ( ( exists_in_world @ SV48 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[383]) ).
thf(397,plain,
! [SV86: mu,SV24: $i,SV74: mu,SV49: mu] :
( ( ( qmltpeq @ SV49 @ SV74 @ SV24 )
= $false )
| ( ( qmltpeq @ ( unordered_pair @ SV49 @ SV86 ) @ ( unordered_pair @ SV74 @ SV86 ) @ SV24 )
= $true )
| ( ( exists_in_world @ SV86 @ SV24 )
= $false )
| ( ( exists_in_world @ SV74 @ SV24 )
= $false )
| ( ( exists_in_world @ SV49 @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[384]) ).
thf(398,plain,
! [SV87: mu,SV26: $i,SV75: mu,SV51: mu] :
( ( ( qmltpeq @ SV51 @ SV75 @ SV26 )
= $false )
| ( ( qmltpeq @ ( unordered_pair @ SV87 @ SV51 ) @ ( unordered_pair @ SV87 @ SV75 ) @ SV26 )
= $true )
| ( ( exists_in_world @ SV87 @ SV26 )
= $false )
| ( ( exists_in_world @ SV75 @ SV26 )
= $false )
| ( ( exists_in_world @ SV51 @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[385]) ).
thf(399,plain,
! [SV88: mu,SV28: $i,SV77: mu,SV53: mu] :
( ( ( ~ ( ~ ( qmltpeq @ SV53 @ SV77 @ SV28 )
| ~ ( in @ SV88 @ SV53 @ SV28 ) ) )
= $false )
| ( ( in @ SV88 @ SV77 @ SV28 )
= $true )
| ( ( exists_in_world @ SV88 @ SV28 )
= $false )
| ( ( exists_in_world @ SV77 @ SV28 )
= $false )
| ( ( exists_in_world @ SV53 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[387]) ).
thf(400,plain,
! [SV29: $i,SV78: mu,SV54: mu] :
( ( ( qmltpeq @ SV54 @ SV78 @ SV29 )
= $false )
| ( ( ~ ( empty @ SV54 @ SV29 ) )
= $true )
| ( ( empty @ SV78 @ SV29 )
= $true )
| ( ( exists_in_world @ SV78 @ SV29 )
= $false )
| ( ( exists_in_world @ SV54 @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[388]) ).
thf(401,plain,
! [SV79: mu,SV6: $i,SV61: mu,SV34: mu] :
( ( ( ~ ( qmltpeq @ SV34 @ SV61 @ SV6 )
| ~ ( subset @ SV34 @ SV79 @ SV6 ) )
= $true )
| ( ( subset @ SV61 @ SV79 @ SV6 )
= $true )
| ( ( exists_in_world @ SV79 @ SV6 )
= $false )
| ( ( exists_in_world @ SV61 @ SV6 )
= $false )
| ( ( exists_in_world @ SV34 @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[389]) ).
thf(402,plain,
! [SV8: $i,SV80: mu,SV62: mu,SV35: mu] :
( ( ( ~ ( subset @ ( unordered_pair @ SV35 @ SV62 ) @ SV80 @ SV8 )
| ~ ( ~ ( in @ SV35 @ SV80 @ SV8 )
| ~ ( in @ SV62 @ SV80 @ SV8 ) ) )
= $true )
| ( ( exists_in_world @ SV80 @ SV8 )
= $false )
| ( ( exists_in_world @ SV62 @ SV8 )
= $false )
| ( ( exists_in_world @ SV35 @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[390]) ).
thf(403,plain,
! [SV62: mu,SV8: $i,SV80: mu,SV35: mu] :
( ( ( ~ ~ ( ~ ( in @ SV35 @ SV80 @ SV8 )
| ~ ( in @ SV62 @ SV80 @ SV8 ) )
| ( subset @ ( unordered_pair @ SV35 @ SV62 ) @ SV80 @ SV8 ) )
= $true )
| ( ( exists_in_world @ SV80 @ SV8 )
= $false )
| ( ( exists_in_world @ SV62 @ SV8 )
= $false )
| ( ( exists_in_world @ SV35 @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[391]) ).
thf(404,plain,
! [SV81: mu,SV12: $i,SV64: mu,SV38: mu] :
( ( ( ~ ( qmltpeq @ SV38 @ SV64 @ SV12 )
| ~ ( qmltpeq @ SV64 @ SV81 @ SV12 ) )
= $true )
| ( ( qmltpeq @ SV38 @ SV81 @ SV12 )
= $true )
| ( ( exists_in_world @ SV81 @ SV12 )
= $false )
| ( ( exists_in_world @ SV64 @ SV12 )
= $false )
| ( ( exists_in_world @ SV38 @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[392]) ).
thf(405,plain,
! [SV82: mu,SV14: $i,SV66: mu,SV40: mu] :
( ( ( ~ ( qmltpeq @ SV40 @ SV66 @ SV14 )
| ~ ( subset @ SV82 @ SV40 @ SV14 ) )
= $true )
| ( ( subset @ SV82 @ SV66 @ SV14 )
= $true )
| ( ( exists_in_world @ SV82 @ SV14 )
= $false )
| ( ( exists_in_world @ SV66 @ SV14 )
= $false )
| ( ( exists_in_world @ SV40 @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[393]) ).
thf(406,plain,
! [SV85: mu,SV23: $i,SV73: mu,SV48: mu] :
( ( ( ~ ( qmltpeq @ SV48 @ SV73 @ SV23 )
| ~ ( in @ SV48 @ SV85 @ SV23 ) )
= $true )
| ( ( in @ SV73 @ SV85 @ SV23 )
= $true )
| ( ( exists_in_world @ SV85 @ SV23 )
= $false )
| ( ( exists_in_world @ SV73 @ SV23 )
= $false )
| ( ( exists_in_world @ SV48 @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[396]) ).
thf(407,plain,
! [SV88: mu,SV28: $i,SV77: mu,SV53: mu] :
( ( ( ~ ( qmltpeq @ SV53 @ SV77 @ SV28 )
| ~ ( in @ SV88 @ SV53 @ SV28 ) )
= $true )
| ( ( in @ SV88 @ SV77 @ SV28 )
= $true )
| ( ( exists_in_world @ SV88 @ SV28 )
= $false )
| ( ( exists_in_world @ SV77 @ SV28 )
= $false )
| ( ( exists_in_world @ SV53 @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[399]) ).
thf(408,plain,
! [SV78: mu,SV29: $i,SV54: mu] :
( ( ( empty @ SV54 @ SV29 )
= $false )
| ( ( qmltpeq @ SV54 @ SV78 @ SV29 )
= $false )
| ( ( empty @ SV78 @ SV29 )
= $true )
| ( ( exists_in_world @ SV78 @ SV29 )
= $false )
| ( ( exists_in_world @ SV54 @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[400]) ).
thf(409,plain,
! [SV79: mu,SV6: $i,SV61: mu,SV34: mu] :
( ( ( ~ ( qmltpeq @ SV34 @ SV61 @ SV6 ) )
= $true )
| ( ( ~ ( subset @ SV34 @ SV79 @ SV6 ) )
= $true )
| ( ( subset @ SV61 @ SV79 @ SV6 )
= $true )
| ( ( exists_in_world @ SV79 @ SV6 )
= $false )
| ( ( exists_in_world @ SV61 @ SV6 )
= $false )
| ( ( exists_in_world @ SV34 @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[401]) ).
thf(410,plain,
! [SV8: $i,SV80: mu,SV62: mu,SV35: mu] :
( ( ( ~ ( subset @ ( unordered_pair @ SV35 @ SV62 ) @ SV80 @ SV8 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV35 @ SV80 @ SV8 )
| ~ ( in @ SV62 @ SV80 @ SV8 ) ) )
= $true )
| ( ( exists_in_world @ SV80 @ SV8 )
= $false )
| ( ( exists_in_world @ SV62 @ SV8 )
= $false )
| ( ( exists_in_world @ SV35 @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[402]) ).
thf(411,plain,
! [SV62: mu,SV8: $i,SV80: mu,SV35: mu] :
( ( ( ~ ~ ( ~ ( in @ SV35 @ SV80 @ SV8 )
| ~ ( in @ SV62 @ SV80 @ SV8 ) ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV35 @ SV62 ) @ SV80 @ SV8 )
= $true )
| ( ( exists_in_world @ SV80 @ SV8 )
= $false )
| ( ( exists_in_world @ SV62 @ SV8 )
= $false )
| ( ( exists_in_world @ SV35 @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[403]) ).
thf(412,plain,
! [SV81: mu,SV12: $i,SV64: mu,SV38: mu] :
( ( ( ~ ( qmltpeq @ SV38 @ SV64 @ SV12 ) )
= $true )
| ( ( ~ ( qmltpeq @ SV64 @ SV81 @ SV12 ) )
= $true )
| ( ( qmltpeq @ SV38 @ SV81 @ SV12 )
= $true )
| ( ( exists_in_world @ SV81 @ SV12 )
= $false )
| ( ( exists_in_world @ SV64 @ SV12 )
= $false )
| ( ( exists_in_world @ SV38 @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[404]) ).
thf(413,plain,
! [SV82: mu,SV14: $i,SV66: mu,SV40: mu] :
( ( ( ~ ( qmltpeq @ SV40 @ SV66 @ SV14 ) )
= $true )
| ( ( ~ ( subset @ SV82 @ SV40 @ SV14 ) )
= $true )
| ( ( subset @ SV82 @ SV66 @ SV14 )
= $true )
| ( ( exists_in_world @ SV82 @ SV14 )
= $false )
| ( ( exists_in_world @ SV66 @ SV14 )
= $false )
| ( ( exists_in_world @ SV40 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[405]) ).
thf(414,plain,
! [SV85: mu,SV23: $i,SV73: mu,SV48: mu] :
( ( ( ~ ( qmltpeq @ SV48 @ SV73 @ SV23 ) )
= $true )
| ( ( ~ ( in @ SV48 @ SV85 @ SV23 ) )
= $true )
| ( ( in @ SV73 @ SV85 @ SV23 )
= $true )
| ( ( exists_in_world @ SV85 @ SV23 )
= $false )
| ( ( exists_in_world @ SV73 @ SV23 )
= $false )
| ( ( exists_in_world @ SV48 @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[406]) ).
thf(415,plain,
! [SV88: mu,SV28: $i,SV77: mu,SV53: mu] :
( ( ( ~ ( qmltpeq @ SV53 @ SV77 @ SV28 ) )
= $true )
| ( ( ~ ( in @ SV88 @ SV53 @ SV28 ) )
= $true )
| ( ( in @ SV88 @ SV77 @ SV28 )
= $true )
| ( ( exists_in_world @ SV88 @ SV28 )
= $false )
| ( ( exists_in_world @ SV77 @ SV28 )
= $false )
| ( ( exists_in_world @ SV53 @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[407]) ).
thf(416,plain,
! [SV79: mu,SV6: $i,SV61: mu,SV34: mu] :
( ( ( qmltpeq @ SV34 @ SV61 @ SV6 )
= $false )
| ( ( ~ ( subset @ SV34 @ SV79 @ SV6 ) )
= $true )
| ( ( subset @ SV61 @ SV79 @ SV6 )
= $true )
| ( ( exists_in_world @ SV79 @ SV6 )
= $false )
| ( ( exists_in_world @ SV61 @ SV6 )
= $false )
| ( ( exists_in_world @ SV34 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[409]) ).
thf(417,plain,
! [SV8: $i,SV80: mu,SV62: mu,SV35: mu] :
( ( ( subset @ ( unordered_pair @ SV35 @ SV62 ) @ SV80 @ SV8 )
= $false )
| ( ( ~ ( ~ ( in @ SV35 @ SV80 @ SV8 )
| ~ ( in @ SV62 @ SV80 @ SV8 ) ) )
= $true )
| ( ( exists_in_world @ SV80 @ SV8 )
= $false )
| ( ( exists_in_world @ SV62 @ SV8 )
= $false )
| ( ( exists_in_world @ SV35 @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[410]) ).
thf(418,plain,
! [SV62: mu,SV8: $i,SV80: mu,SV35: mu] :
( ( ( ~ ( ~ ( in @ SV35 @ SV80 @ SV8 )
| ~ ( in @ SV62 @ SV80 @ SV8 ) ) )
= $false )
| ( ( subset @ ( unordered_pair @ SV35 @ SV62 ) @ SV80 @ SV8 )
= $true )
| ( ( exists_in_world @ SV80 @ SV8 )
= $false )
| ( ( exists_in_world @ SV62 @ SV8 )
= $false )
| ( ( exists_in_world @ SV35 @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[411]) ).
thf(419,plain,
! [SV81: mu,SV12: $i,SV64: mu,SV38: mu] :
( ( ( qmltpeq @ SV38 @ SV64 @ SV12 )
= $false )
| ( ( ~ ( qmltpeq @ SV64 @ SV81 @ SV12 ) )
= $true )
| ( ( qmltpeq @ SV38 @ SV81 @ SV12 )
= $true )
| ( ( exists_in_world @ SV81 @ SV12 )
= $false )
| ( ( exists_in_world @ SV64 @ SV12 )
= $false )
| ( ( exists_in_world @ SV38 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[412]) ).
thf(420,plain,
! [SV82: mu,SV14: $i,SV66: mu,SV40: mu] :
( ( ( qmltpeq @ SV40 @ SV66 @ SV14 )
= $false )
| ( ( ~ ( subset @ SV82 @ SV40 @ SV14 ) )
= $true )
| ( ( subset @ SV82 @ SV66 @ SV14 )
= $true )
| ( ( exists_in_world @ SV82 @ SV14 )
= $false )
| ( ( exists_in_world @ SV66 @ SV14 )
= $false )
| ( ( exists_in_world @ SV40 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[413]) ).
thf(421,plain,
! [SV85: mu,SV23: $i,SV73: mu,SV48: mu] :
( ( ( qmltpeq @ SV48 @ SV73 @ SV23 )
= $false )
| ( ( ~ ( in @ SV48 @ SV85 @ SV23 ) )
= $true )
| ( ( in @ SV73 @ SV85 @ SV23 )
= $true )
| ( ( exists_in_world @ SV85 @ SV23 )
= $false )
| ( ( exists_in_world @ SV73 @ SV23 )
= $false )
| ( ( exists_in_world @ SV48 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[414]) ).
thf(422,plain,
! [SV88: mu,SV28: $i,SV77: mu,SV53: mu] :
( ( ( qmltpeq @ SV53 @ SV77 @ SV28 )
= $false )
| ( ( ~ ( in @ SV88 @ SV53 @ SV28 ) )
= $true )
| ( ( in @ SV88 @ SV77 @ SV28 )
= $true )
| ( ( exists_in_world @ SV88 @ SV28 )
= $false )
| ( ( exists_in_world @ SV77 @ SV28 )
= $false )
| ( ( exists_in_world @ SV53 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[415]) ).
thf(423,plain,
! [SV61: mu,SV6: $i,SV79: mu,SV34: mu] :
( ( ( subset @ SV34 @ SV79 @ SV6 )
= $false )
| ( ( qmltpeq @ SV34 @ SV61 @ SV6 )
= $false )
| ( ( subset @ SV61 @ SV79 @ SV6 )
= $true )
| ( ( exists_in_world @ SV79 @ SV6 )
= $false )
| ( ( exists_in_world @ SV61 @ SV6 )
= $false )
| ( ( exists_in_world @ SV34 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[416]) ).
thf(424,plain,
! [SV62: mu,SV8: $i,SV80: mu,SV35: mu] :
( ( ( ~ ( in @ SV35 @ SV80 @ SV8 )
| ~ ( in @ SV62 @ SV80 @ SV8 ) )
= $false )
| ( ( subset @ ( unordered_pair @ SV35 @ SV62 ) @ SV80 @ SV8 )
= $false )
| ( ( exists_in_world @ SV80 @ SV8 )
= $false )
| ( ( exists_in_world @ SV62 @ SV8 )
= $false )
| ( ( exists_in_world @ SV35 @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[417]) ).
thf(425,plain,
! [SV62: mu,SV8: $i,SV80: mu,SV35: mu] :
( ( ( ~ ( in @ SV35 @ SV80 @ SV8 )
| ~ ( in @ SV62 @ SV80 @ SV8 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV35 @ SV62 ) @ SV80 @ SV8 )
= $true )
| ( ( exists_in_world @ SV80 @ SV8 )
= $false )
| ( ( exists_in_world @ SV62 @ SV8 )
= $false )
| ( ( exists_in_world @ SV35 @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[418]) ).
thf(426,plain,
! [SV38: mu,SV12: $i,SV81: mu,SV64: mu] :
( ( ( qmltpeq @ SV64 @ SV81 @ SV12 )
= $false )
| ( ( qmltpeq @ SV38 @ SV64 @ SV12 )
= $false )
| ( ( qmltpeq @ SV38 @ SV81 @ SV12 )
= $true )
| ( ( exists_in_world @ SV81 @ SV12 )
= $false )
| ( ( exists_in_world @ SV64 @ SV12 )
= $false )
| ( ( exists_in_world @ SV38 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[419]) ).
thf(427,plain,
! [SV66: mu,SV14: $i,SV40: mu,SV82: mu] :
( ( ( subset @ SV82 @ SV40 @ SV14 )
= $false )
| ( ( qmltpeq @ SV40 @ SV66 @ SV14 )
= $false )
| ( ( subset @ SV82 @ SV66 @ SV14 )
= $true )
| ( ( exists_in_world @ SV82 @ SV14 )
= $false )
| ( ( exists_in_world @ SV66 @ SV14 )
= $false )
| ( ( exists_in_world @ SV40 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[420]) ).
thf(428,plain,
! [SV73: mu,SV23: $i,SV85: mu,SV48: mu] :
( ( ( in @ SV48 @ SV85 @ SV23 )
= $false )
| ( ( qmltpeq @ SV48 @ SV73 @ SV23 )
= $false )
| ( ( in @ SV73 @ SV85 @ SV23 )
= $true )
| ( ( exists_in_world @ SV85 @ SV23 )
= $false )
| ( ( exists_in_world @ SV73 @ SV23 )
= $false )
| ( ( exists_in_world @ SV48 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[421]) ).
thf(429,plain,
! [SV77: mu,SV28: $i,SV53: mu,SV88: mu] :
( ( ( in @ SV88 @ SV53 @ SV28 )
= $false )
| ( ( qmltpeq @ SV53 @ SV77 @ SV28 )
= $false )
| ( ( in @ SV88 @ SV77 @ SV28 )
= $true )
| ( ( exists_in_world @ SV88 @ SV28 )
= $false )
| ( ( exists_in_world @ SV77 @ SV28 )
= $false )
| ( ( exists_in_world @ SV53 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[422]) ).
thf(430,plain,
! [SV62: mu,SV8: $i,SV80: mu,SV35: mu] :
( ( ( ~ ( in @ SV35 @ SV80 @ SV8 ) )
= $false )
| ( ( subset @ ( unordered_pair @ SV35 @ SV62 ) @ SV80 @ SV8 )
= $false )
| ( ( exists_in_world @ SV80 @ SV8 )
= $false )
| ( ( exists_in_world @ SV62 @ SV8 )
= $false )
| ( ( exists_in_world @ SV35 @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[424]) ).
thf(431,plain,
! [SV35: mu,SV8: $i,SV80: mu,SV62: mu] :
( ( ( ~ ( in @ SV62 @ SV80 @ SV8 ) )
= $false )
| ( ( subset @ ( unordered_pair @ SV35 @ SV62 ) @ SV80 @ SV8 )
= $false )
| ( ( exists_in_world @ SV80 @ SV8 )
= $false )
| ( ( exists_in_world @ SV62 @ SV8 )
= $false )
| ( ( exists_in_world @ SV35 @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[424]) ).
thf(432,plain,
! [SV62: mu,SV8: $i,SV80: mu,SV35: mu] :
( ( ( ~ ( in @ SV35 @ SV80 @ SV8 ) )
= $true )
| ( ( ~ ( in @ SV62 @ SV80 @ SV8 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV35 @ SV62 ) @ SV80 @ SV8 )
= $true )
| ( ( exists_in_world @ SV80 @ SV8 )
= $false )
| ( ( exists_in_world @ SV62 @ SV8 )
= $false )
| ( ( exists_in_world @ SV35 @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[425]) ).
thf(433,plain,
! [SV62: mu,SV8: $i,SV80: mu,SV35: mu] :
( ( ( in @ SV35 @ SV80 @ SV8 )
= $true )
| ( ( subset @ ( unordered_pair @ SV35 @ SV62 ) @ SV80 @ SV8 )
= $false )
| ( ( exists_in_world @ SV80 @ SV8 )
= $false )
| ( ( exists_in_world @ SV62 @ SV8 )
= $false )
| ( ( exists_in_world @ SV35 @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[430]) ).
thf(434,plain,
! [SV35: mu,SV8: $i,SV80: mu,SV62: mu] :
( ( ( in @ SV62 @ SV80 @ SV8 )
= $true )
| ( ( subset @ ( unordered_pair @ SV35 @ SV62 ) @ SV80 @ SV8 )
= $false )
| ( ( exists_in_world @ SV80 @ SV8 )
= $false )
| ( ( exists_in_world @ SV62 @ SV8 )
= $false )
| ( ( exists_in_world @ SV35 @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[431]) ).
thf(435,plain,
! [SV62: mu,SV8: $i,SV80: mu,SV35: mu] :
( ( ( in @ SV35 @ SV80 @ SV8 )
= $false )
| ( ( ~ ( in @ SV62 @ SV80 @ SV8 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV35 @ SV62 ) @ SV80 @ SV8 )
= $true )
| ( ( exists_in_world @ SV80 @ SV8 )
= $false )
| ( ( exists_in_world @ SV62 @ SV8 )
= $false )
| ( ( exists_in_world @ SV35 @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[432]) ).
thf(436,plain,
! [SV35: mu,SV8: $i,SV80: mu,SV62: mu] :
( ( ( in @ SV62 @ SV80 @ SV8 )
= $false )
| ( ( in @ SV35 @ SV80 @ SV8 )
= $false )
| ( ( subset @ ( unordered_pair @ SV35 @ SV62 ) @ SV80 @ SV8 )
= $true )
| ( ( exists_in_world @ SV80 @ SV8 )
= $false )
| ( ( exists_in_world @ SV62 @ SV8 )
= $false )
| ( ( exists_in_world @ SV35 @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[435]) ).
thf(437,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[96,436,434,433,429,428,427,426,423,408,398,397,395,394,386,376,367,364,363,355,351,350,346,308,307,302,298,280,278,275,254,253,247,230,225,221,185,184,125]) ).
thf(438,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[437]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET907^7 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.18 % Computer : n002.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Oct 6 14:58:27 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.08/0.42
% 1.08/0.42 No.of.Axioms: 29
% 1.08/0.42
% 1.08/0.42 Length.of.Defs: 5540
% 1.08/0.42
% 1.08/0.42 Contains.Choice.Funs: false
% 1.08/0.42 ...........................
% 1.08/0.42
% 1.08/0.42 ********************************
% 1.08/0.42 * All subproblems solved! *
% 1.08/0.42 ********************************
% 1.08/0.42 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:30,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:437,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.08/0.42
% 1.08/0.42 %**** Beginning of derivation protocol ****
% 1.08/0.42 % SZS output start CNFRefutation
% See solution above
% 1.08/0.42
% 1.08/0.42 %**** End of derivation protocol ****
% 1.08/0.42 %**** no. of clauses in derivation: 438 ****
% 1.08/0.42 %**** clause counter: 437 ****
% 1.08/0.42
% 1.08/0.42 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:30,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:437,loop_count:0,foatp_calls:1,translation:fof_full)
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