%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET583^7 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 10:40:24 AM UTC 2026
% Result : Theorem 0.08s 0.25s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 42
% Syntax : Number of formulae : 217 ( 107 unt; 0 typ; 32 def)
% Number of atoms : 1880 ( 451 equ; 0 cnn)
% Maximal formula atoms : 9 ( 8 avg)
% Number of connectives : 3734 ( 573 ~; 663 |; 18 &;2442 @)
% ( 0 <=>; 38 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 59 ( 59 >; 0 *; 0 +; 0 <<)
% Number of symbols : 43 ( 40 usr; 5 con; 0-3 aty)
% Number of variables : 646 ( 74 ^; 566 !; 6 ?; 646 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_mu,type,
mu: $tType ).
thf(tp_exists_in_world,type,
exists_in_world: mu > $i > $o ).
thf(tp_mand,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mbox,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mbox_s4,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf(tp_mcountersatisfiable,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(tp_mdia,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mdia_s4,type,
mdia_s4: ( $i > $o ) > $i > $o ).
thf(tp_member,type,
member: mu > mu > $i > $o ).
thf(tp_meq_prop,type,
meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mequiv,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_meuclidean,type,
meuclidean: ( $i > $i > $o ) > $o ).
thf(tp_mexists_ind,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(tp_mexists_prop,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(tp_mfalse,type,
mfalse: $i > $o ).
thf(tp_mforall_ind,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(tp_mforall_prop,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(tp_mfunctional,type,
mfunctional: ( $i > $i > $o ) > $o ).
thf(tp_mimplied,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mimplies,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_minvalid,type,
minvalid: ( $i > $o ) > $o ).
thf(tp_mnot,type,
mnot: ( $i > $o ) > $i > $o ).
thf(tp_mor,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mpartially_functional,type,
mpartially_functional: ( $i > $i > $o ) > $o ).
thf(tp_mreflexive,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(tp_msatisfiable,type,
msatisfiable: ( $i > $o ) > $o ).
thf(tp_mserial,type,
mserial: ( $i > $i > $o ) > $o ).
thf(tp_msymmetric,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(tp_mtransitive,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(tp_mtrue,type,
mtrue: $i > $o ).
thf(tp_mvalid,type,
mvalid: ( $i > $o ) > $o ).
thf(tp_mweakly_connected,type,
mweakly_connected: ( $i > $i > $o ) > $o ).
thf(tp_mweakly_dense,type,
mweakly_dense: ( $i > $i > $o ) > $o ).
thf(tp_mweakly_directed,type,
mweakly_directed: ( $i > $i > $o ) > $o ).
thf(tp_mxor,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_qmltpeq,type,
qmltpeq: mu > mu > $i > $o ).
thf(tp_rel_s4,type,
rel_s4: $i > $i > $o ).
thf(tp_sK1_SY24,type,
sK1_SY24: $i ).
thf(tp_sK2_SY312,type,
sK2_SY312: mu ).
thf(tp_sK3_SY314,type,
sK3_SY314: mu ).
thf(tp_subset,type,
subset: mu > mu > $i > $o ).
thf(mand,definition,
( mand
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mor @ ( mnot @ Phi ) @ ( mnot @ Psi ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mand) ).
thf(mbox,definition,
( mbox
= ( ^ [R: $i > $i > $o,Phi: $i > $o,W: $i] :
! [V: $i] :
( ~ ( R @ W @ V )
| ( Phi @ V ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox) ).
thf(mbox_s4,definition,
( mbox_s4
= ( ^ [Phi: $i > $o,W: $i] :
! [V: $i] :
( ~ ( rel_s4 @ W @ V )
| ( Phi @ V ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_s4) ).
thf(mcountersatisfiable,definition,
( mcountersatisfiable
= ( ^ [Phi: $i > $o] :
? [W: $i] :
~ ( Phi @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mcountersatisfiable) ).
thf(mdia,definition,
( mdia
= ( ^ [R: $i > $i > $o,Phi: $i > $o] : ( mnot @ ( mbox @ R @ ( mnot @ Phi ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mdia) ).
thf(mdia_s4,definition,
( mdia_s4
= ( ^ [Phi: $i > $o] : ( mnot @ ( mbox_s4 @ ( mnot @ Phi ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mdia_s4) ).
thf(meq_prop,definition,
( meq_prop
= ( ^ [X: $i > $o,Y: $i > $o,W: $i] :
( ( X @ W )
= ( Y @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',meq_prop) ).
thf(mequiv,definition,
( mequiv
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mand @ ( mimplies @ Phi @ Psi ) @ ( mimplies @ Psi @ Phi ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mequiv) ).
thf(meuclidean,definition,
( meuclidean
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ S @ U ) )
=> ( R @ T @ U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',meuclidean) ).
thf(mexists_ind,definition,
( mexists_ind
= ( ^ [Phi: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X: mu] : ( mnot @ ( Phi @ X ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mexists_ind) ).
thf(mexists_prop,definition,
( mexists_prop
= ( ^ [Phi: ( $i > $o ) > $i > $o] :
( mnot
@ ( mforall_prop
@ ^ [P: $i > $o] : ( mnot @ ( Phi @ P ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mexists_prop) ).
thf(mfalse,definition,
( mfalse
= ( mnot @ mtrue ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mfalse) ).
thf(mforall_ind,definition,
( mforall_ind
= ( ^ [Phi: mu > $i > $o,W: $i] :
! [X: mu] :
( ( exists_in_world @ X @ W )
=> ( Phi @ X @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mforall_ind) ).
thf(mforall_prop,definition,
( mforall_prop
= ( ^ [Phi: ( $i > $o ) > $i > $o,W: $i] :
! [P: $i > $o] : ( Phi @ P @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mforall_prop) ).
thf(mfunctional,definition,
( mfunctional
= ( ^ [R: $i > $i > $o] :
! [S: $i] :
? [T: $i] :
( ( R @ S @ T )
& ! [U: $i] :
( ( R @ S @ U )
=> ( T = U ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mfunctional) ).
thf(mimplied,definition,
( mimplied
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Psi ) @ Phi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplied) ).
thf(mimplies,definition,
( mimplies
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Phi ) @ Psi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies) ).
thf(minvalid,definition,
( minvalid
= ( ^ [Phi: $i > $o] :
! [W: $i] :
~ ( Phi @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',minvalid) ).
thf(mnot,definition,
( mnot
= ( ^ [Phi: $i > $o,W: $i] :
~ ( Phi @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot) ).
thf(mor,definition,
( mor
= ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
( ( Phi @ W )
| ( Psi @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor) ).
thf(mpartially_functional,definition,
( mpartially_functional
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ S @ U ) )
=> ( T = U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mpartially_functional) ).
thf(mreflexive,definition,
( mreflexive
= ( ^ [R: $i > $i > $o] :
! [S: $i] : ( R @ S @ S ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mreflexive) ).
thf(msatisfiable,definition,
( msatisfiable
= ( ^ [Phi: $i > $o] :
? [W: $i] : ( Phi @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',msatisfiable) ).
thf(mserial,definition,
( mserial
= ( ^ [R: $i > $i > $o] :
! [S: $i] :
? [T: $i] : ( R @ S @ T ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mserial) ).
thf(msymmetric,definition,
( msymmetric
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i] :
( ( R @ S @ T )
=> ( R @ T @ S ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',msymmetric) ).
thf(mtransitive,definition,
( mtransitive
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ T @ U ) )
=> ( R @ S @ U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mtransitive) ).
thf(mtrue,definition,
( mtrue
= ( ^ [W: $i] : $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mtrue) ).
thf(mvalid,definition,
( mvalid
= ( ^ [Phi: $i > $o] :
! [W: $i] : ( Phi @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mvalid) ).
thf(mweakly_connected,definition,
( mweakly_connected
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ S @ U ) )
=> ( ( R @ T @ U )
| ( T = U )
| ( R @ U @ T ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mweakly_connected) ).
thf(mweakly_dense,definition,
( mweakly_dense
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( R @ S @ T )
=> ? [U: $i] :
( ( R @ S @ U )
& ( R @ U @ T ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mweakly_dense) ).
thf(mweakly_directed,definition,
( mweakly_directed
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ S @ U ) )
=> ? [V: $i] :
( ( R @ T @ V )
& ( R @ U @ V ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mweakly_directed) ).
thf(mxor,definition,
( mxor
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mequiv @ Phi @ Psi ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mxor) ).
thf(1,axiom,
( mvalid
@ ( mforall_ind
@ ^ [B: mu] : ( subset @ B @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_of_subset) ).
thf(3,axiom,
( mvalid
@ ( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mequiv @ ( qmltpeq @ B @ C ) @ ( mand @ ( subset @ B @ C ) @ ( subset @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
thf(4,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( subset @ C @ A ) ) @ ( subset @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_substitution_2) ).
thf(5,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( subset @ A @ C ) ) @ ( subset @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_substitution_1) ).
thf(6,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( member @ C @ A ) ) @ ( member @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_substitution_2) ).
thf(7,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( member @ A @ C ) ) @ ( member @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_substitution_1) ).
thf(8,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X: mu] :
( mforall_ind
@ ^ [Y: mu] :
( mforall_ind
@ ^ [Z: mu] : ( mimplies @ ( mand @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ Z ) ) @ ( qmltpeq @ X @ Z ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity) ).
thf(9,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X: mu] :
( mforall_ind
@ ^ [Y: mu] : ( mimplies @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ X ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry) ).
thf(10,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X: mu] : ( qmltpeq @ X @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).
thf(15,conjecture,
( mvalid
@ ( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mimplies @ ( mand @ ( subset @ B @ C ) @ ( subset @ C @ B ) ) @ ( qmltpeq @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_extensionality) ).
thf(16,negated_conjecture,
( ( mvalid
@ ( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mimplies @ ( mand @ ( subset @ B @ C ) @ ( subset @ C @ B ) ) @ ( qmltpeq @ B @ C ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[15]) ).
thf(17,plain,
( ( ! [SY24: $i,SY25: mu] :
( ( exists_in_world @ SY25 @ SY24 )
=> ! [SY26: mu] :
( ( exists_in_world @ SY26 @ SY24 )
=> ( ~ ~ ( ~ ( subset @ SY25 @ SY26 @ SY24 )
| ~ ( subset @ SY26 @ SY25 @ SY24 ) )
| ( qmltpeq @ SY25 @ SY26 @ SY24 ) ) ) ) )
= $false ),
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(18,plain,
( ( ! [SY33: $i,SY34: mu] :
( ( exists_in_world @ SY34 @ SY33 )
=> ( subset @ SY34 @ SY34 @ SY33 ) ) )
= $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(19,plain,
( ( ! [SY77: $i,SY78: mu] :
( ( exists_in_world @ SY78 @ SY77 )
=> ! [SY79: mu] :
( ( exists_in_world @ SY79 @ SY77 )
=> ~ ( ~ ( ~ ( qmltpeq @ SY78 @ SY79 @ SY77 )
| ~ ( ~ ( subset @ SY78 @ SY79 @ SY77 )
| ~ ( subset @ SY79 @ SY78 @ SY77 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SY78 @ SY79 @ SY77 )
| ~ ( subset @ SY79 @ SY78 @ SY77 ) )
| ( qmltpeq @ SY78 @ SY79 @ SY77 ) ) ) ) ) )
= $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(20,plain,
( ( ! [SY115: $i,SY116: mu] :
( ( exists_in_world @ SY116 @ SY115 )
=> ! [SY117: mu] :
( ( exists_in_world @ SY117 @ SY115 )
=> ! [SY118: mu] :
( ( exists_in_world @ SY118 @ SY115 )
=> ( ~ ~ ( ~ ( qmltpeq @ SY116 @ SY117 @ SY115 )
| ~ ( subset @ SY118 @ SY116 @ SY115 ) )
| ( subset @ SY118 @ SY117 @ SY115 ) ) ) ) ) )
= $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(21,plain,
( ( ! [SY155: $i,SY156: mu] :
( ( exists_in_world @ SY156 @ SY155 )
=> ! [SY157: mu] :
( ( exists_in_world @ SY157 @ SY155 )
=> ! [SY158: mu] :
( ( exists_in_world @ SY158 @ SY155 )
=> ( ~ ~ ( ~ ( qmltpeq @ SY156 @ SY157 @ SY155 )
| ~ ( subset @ SY156 @ SY158 @ SY155 ) )
| ( subset @ SY157 @ SY158 @ 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(22,plain,
( ( ! [SY195: $i,SY196: mu] :
( ( exists_in_world @ SY196 @ SY195 )
=> ! [SY197: mu] :
( ( exists_in_world @ SY197 @ SY195 )
=> ! [SY198: mu] :
( ( exists_in_world @ SY198 @ SY195 )
=> ( ~ ~ ( ~ ( qmltpeq @ SY196 @ SY197 @ SY195 )
| ~ ( member @ SY198 @ SY196 @ SY195 ) )
| ( member @ SY198 @ SY197 @ SY195 ) ) ) ) ) )
= $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(23,plain,
( ( ! [SY235: $i,SY236: mu] :
( ( exists_in_world @ SY236 @ SY235 )
=> ! [SY237: mu] :
( ( exists_in_world @ SY237 @ SY235 )
=> ! [SY238: mu] :
( ( exists_in_world @ SY238 @ SY235 )
=> ( ~ ~ ( ~ ( qmltpeq @ SY236 @ SY237 @ SY235 )
| ~ ( member @ SY236 @ SY238 @ SY235 ) )
| ( member @ SY237 @ SY238 @ SY235 ) ) ) ) ) )
= $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(24,plain,
( ( ! [SY275: $i,SY276: mu] :
( ( exists_in_world @ SY276 @ SY275 )
=> ! [SY277: mu] :
( ( exists_in_world @ SY277 @ SY275 )
=> ! [SY278: mu] :
( ( exists_in_world @ SY278 @ SY275 )
=> ( ~ ~ ( ~ ( qmltpeq @ SY276 @ SY277 @ SY275 )
| ~ ( qmltpeq @ SY277 @ SY278 @ SY275 ) )
| ( qmltpeq @ SY276 @ SY278 @ SY275 ) ) ) ) ) )
= $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(25,plain,
( ( ! [SY299: $i,SY300: mu] :
( ( exists_in_world @ SY300 @ SY299 )
=> ! [SY301: mu] :
( ( exists_in_world @ SY301 @ SY299 )
=> ( ~ ( qmltpeq @ SY300 @ SY301 @ SY299 )
| ( qmltpeq @ SY301 @ SY300 @ SY299 ) ) ) ) )
= $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(26,plain,
( ( ! [SY308: $i,SY309: mu] :
( ( exists_in_world @ SY309 @ SY308 )
=> ( qmltpeq @ SY309 @ SY309 @ SY308 ) ) )
= $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(27,plain,
( ( ! [SY312: mu] :
( ( exists_in_world @ SY312 @ sK1_SY24 )
=> ! [SY313: mu] :
( ( exists_in_world @ SY313 @ sK1_SY24 )
=> ( ~ ~ ( ~ ( subset @ SY312 @ SY313 @ sK1_SY24 )
| ~ ( subset @ SY313 @ SY312 @ sK1_SY24 ) )
| ( qmltpeq @ SY312 @ SY313 @ sK1_SY24 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[17]) ).
thf(28,plain,
( ( ( exists_in_world @ sK2_SY312 @ sK1_SY24 )
=> ! [SY314: mu] :
( ( exists_in_world @ SY314 @ sK1_SY24 )
=> ( ~ ~ ( ~ ( subset @ sK2_SY312 @ SY314 @ sK1_SY24 )
| ~ ( subset @ SY314 @ sK2_SY312 @ sK1_SY24 ) )
| ( qmltpeq @ sK2_SY312 @ SY314 @ sK1_SY24 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[27]) ).
thf(29,plain,
( ( exists_in_world @ sK2_SY312 @ sK1_SY24 )
= $true ),
inference(standard_cnf,[status(thm)],[28]) ).
thf(30,plain,
( ( ! [SY314: mu] :
( ( exists_in_world @ SY314 @ sK1_SY24 )
=> ( ~ ~ ( ~ ( subset @ sK2_SY312 @ SY314 @ sK1_SY24 )
| ~ ( subset @ SY314 @ sK2_SY312 @ sK1_SY24 ) )
| ( qmltpeq @ sK2_SY312 @ SY314 @ sK1_SY24 ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[28]) ).
thf(31,plain,
( ( ~ ! [SY314: mu] :
( ( exists_in_world @ SY314 @ sK1_SY24 )
=> ( ~ ~ ( ~ ( subset @ sK2_SY312 @ SY314 @ sK1_SY24 )
| ~ ( subset @ SY314 @ sK2_SY312 @ sK1_SY24 ) )
| ( qmltpeq @ sK2_SY312 @ SY314 @ sK1_SY24 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[30]) ).
thf(32,plain,
( ( ( exists_in_world @ sK3_SY314 @ sK1_SY24 )
& ( subset @ sK2_SY312 @ sK3_SY314 @ sK1_SY24 )
& ( subset @ sK3_SY314 @ sK2_SY312 @ sK1_SY24 )
& ~ ( qmltpeq @ sK2_SY312 @ sK3_SY314 @ sK1_SY24 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[31]) ).
thf(33,plain,
( ( ! [SY33: $i,SY34: mu] :
( ~ ( exists_in_world @ SY34 @ SY33 )
| ( subset @ SY34 @ SY34 @ SY33 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[18]) ).
thf(34,plain,
( ( ! [SY77: $i,SY78: mu] :
( ~ ( exists_in_world @ SY78 @ SY77 )
| ( ! [SY79: mu] :
( ~ ( exists_in_world @ SY79 @ SY77 )
| ~ ( qmltpeq @ SY78 @ SY79 @ SY77 )
| ( subset @ SY78 @ SY79 @ SY77 ) )
& ! [SY79: mu] :
( ~ ( exists_in_world @ SY79 @ SY77 )
| ~ ( qmltpeq @ SY78 @ SY79 @ SY77 )
| ( subset @ SY79 @ SY78 @ SY77 ) )
& ! [SY79: mu] :
( ~ ( exists_in_world @ SY79 @ SY77 )
| ~ ( subset @ SY78 @ SY79 @ SY77 )
| ~ ( subset @ SY79 @ SY78 @ SY77 )
| ( qmltpeq @ SY78 @ SY79 @ SY77 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[19]) ).
thf(35,plain,
( ( ! [SY115: $i,SY116: mu] :
( ~ ( exists_in_world @ SY116 @ SY115 )
| ! [SY117: mu] :
( ~ ( exists_in_world @ SY117 @ SY115 )
| ! [SY118: mu] :
( ~ ( exists_in_world @ SY118 @ SY115 )
| ~ ( qmltpeq @ SY116 @ SY117 @ SY115 )
| ~ ( subset @ SY118 @ SY116 @ SY115 )
| ( subset @ SY118 @ SY117 @ SY115 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[20]) ).
thf(36,plain,
( ( ! [SY155: $i,SY156: mu] :
( ~ ( exists_in_world @ SY156 @ SY155 )
| ! [SY157: mu] :
( ~ ( exists_in_world @ SY157 @ SY155 )
| ! [SY158: mu] :
( ~ ( exists_in_world @ SY158 @ SY155 )
| ~ ( qmltpeq @ SY156 @ SY157 @ SY155 )
| ~ ( subset @ SY156 @ SY158 @ SY155 )
| ( subset @ SY157 @ SY158 @ SY155 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[21]) ).
thf(37,plain,
( ( ! [SY195: $i,SY196: mu] :
( ~ ( exists_in_world @ SY196 @ SY195 )
| ! [SY197: mu] :
( ~ ( exists_in_world @ SY197 @ SY195 )
| ! [SY198: mu] :
( ~ ( exists_in_world @ SY198 @ SY195 )
| ~ ( qmltpeq @ SY196 @ SY197 @ SY195 )
| ~ ( member @ SY198 @ SY196 @ SY195 )
| ( member @ SY198 @ SY197 @ SY195 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[22]) ).
thf(38,plain,
( ( ! [SY235: $i,SY236: mu] :
( ~ ( exists_in_world @ SY236 @ SY235 )
| ! [SY237: mu] :
( ~ ( exists_in_world @ SY237 @ SY235 )
| ! [SY238: mu] :
( ~ ( exists_in_world @ SY238 @ SY235 )
| ~ ( qmltpeq @ SY236 @ SY237 @ SY235 )
| ~ ( member @ SY236 @ SY238 @ SY235 )
| ( member @ SY237 @ SY238 @ SY235 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[23]) ).
thf(39,plain,
( ( ! [SY275: $i,SY276: mu] :
( ~ ( exists_in_world @ SY276 @ SY275 )
| ! [SY277: mu] :
( ~ ( exists_in_world @ SY277 @ SY275 )
| ! [SY278: mu] :
( ~ ( exists_in_world @ SY278 @ SY275 )
| ~ ( qmltpeq @ SY276 @ SY277 @ SY275 )
| ~ ( qmltpeq @ SY277 @ SY278 @ SY275 )
| ( qmltpeq @ SY276 @ SY278 @ SY275 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[24]) ).
thf(40,plain,
( ( ! [SY299: $i,SY300: mu] :
( ~ ( exists_in_world @ SY300 @ SY299 )
| ! [SY301: mu] :
( ~ ( exists_in_world @ SY301 @ SY299 )
| ~ ( qmltpeq @ SY300 @ SY301 @ SY299 )
| ( qmltpeq @ SY301 @ SY300 @ SY299 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[25]) ).
thf(41,plain,
( ( ! [SY308: $i,SY309: mu] :
( ~ ( exists_in_world @ SY309 @ SY308 )
| ( qmltpeq @ SY309 @ SY309 @ SY308 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[26]) ).
thf(42,plain,
( ( ! [SY308: $i,SY309: mu] :
( ~ ( exists_in_world @ SY309 @ SY308 )
| ( qmltpeq @ SY309 @ SY309 @ SY308 ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(43,plain,
( ( ! [SY299: $i,SY300: mu] :
( ~ ( exists_in_world @ SY300 @ SY299 )
| ! [SY301: mu] :
( ~ ( exists_in_world @ SY301 @ SY299 )
| ~ ( qmltpeq @ SY300 @ SY301 @ SY299 )
| ( qmltpeq @ SY301 @ SY300 @ SY299 ) ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(44,plain,
( ( ! [SY275: $i,SY276: mu] :
( ~ ( exists_in_world @ SY276 @ SY275 )
| ! [SY277: mu] :
( ~ ( exists_in_world @ SY277 @ SY275 )
| ! [SY278: mu] :
( ~ ( exists_in_world @ SY278 @ SY275 )
| ~ ( qmltpeq @ SY276 @ SY277 @ SY275 )
| ~ ( qmltpeq @ SY277 @ SY278 @ SY275 )
| ( qmltpeq @ SY276 @ SY278 @ SY275 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(45,plain,
( ( ! [SY235: $i,SY236: mu] :
( ~ ( exists_in_world @ SY236 @ SY235 )
| ! [SY237: mu] :
( ~ ( exists_in_world @ SY237 @ SY235 )
| ! [SY238: mu] :
( ~ ( exists_in_world @ SY238 @ SY235 )
| ~ ( qmltpeq @ SY236 @ SY237 @ SY235 )
| ~ ( member @ SY236 @ SY238 @ SY235 )
| ( member @ SY237 @ SY238 @ SY235 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(46,plain,
( ( ! [SY195: $i,SY196: mu] :
( ~ ( exists_in_world @ SY196 @ SY195 )
| ! [SY197: mu] :
( ~ ( exists_in_world @ SY197 @ SY195 )
| ! [SY198: mu] :
( ~ ( exists_in_world @ SY198 @ SY195 )
| ~ ( qmltpeq @ SY196 @ SY197 @ SY195 )
| ~ ( member @ SY198 @ SY196 @ SY195 )
| ( member @ SY198 @ SY197 @ SY195 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(47,plain,
( ( ! [SY155: $i,SY156: mu] :
( ~ ( exists_in_world @ SY156 @ SY155 )
| ! [SY157: mu] :
( ~ ( exists_in_world @ SY157 @ SY155 )
| ! [SY158: mu] :
( ~ ( exists_in_world @ SY158 @ SY155 )
| ~ ( qmltpeq @ SY156 @ SY157 @ SY155 )
| ~ ( subset @ SY156 @ SY158 @ SY155 )
| ( subset @ SY157 @ SY158 @ SY155 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(48,plain,
( ( ! [SY115: $i,SY116: mu] :
( ~ ( exists_in_world @ SY116 @ SY115 )
| ! [SY117: mu] :
( ~ ( exists_in_world @ SY117 @ SY115 )
| ! [SY118: mu] :
( ~ ( exists_in_world @ SY118 @ SY115 )
| ~ ( qmltpeq @ SY116 @ SY117 @ SY115 )
| ~ ( subset @ SY118 @ SY116 @ SY115 )
| ( subset @ SY118 @ SY117 @ SY115 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(49,plain,
( ( ! [SY77: $i,SY78: mu] :
( ~ ( exists_in_world @ SY78 @ SY77 )
| ( ! [SY79: mu] :
( ~ ( exists_in_world @ SY79 @ SY77 )
| ~ ( qmltpeq @ SY78 @ SY79 @ SY77 )
| ( subset @ SY78 @ SY79 @ SY77 ) )
& ! [SY79: mu] :
( ~ ( exists_in_world @ SY79 @ SY77 )
| ~ ( qmltpeq @ SY78 @ SY79 @ SY77 )
| ( subset @ SY79 @ SY78 @ SY77 ) )
& ! [SY79: mu] :
( ~ ( exists_in_world @ SY79 @ SY77 )
| ~ ( subset @ SY78 @ SY79 @ SY77 )
| ~ ( subset @ SY79 @ SY78 @ SY77 )
| ( qmltpeq @ SY78 @ SY79 @ SY77 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(50,plain,
( ( ! [SY33: $i,SY34: mu] :
( ~ ( exists_in_world @ SY34 @ SY33 )
| ( subset @ SY34 @ SY34 @ SY33 ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(51,plain,
( ( exists_in_world @ sK2_SY312 @ sK1_SY24 )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(52,plain,
( ( ( exists_in_world @ sK3_SY314 @ sK1_SY24 )
& ( subset @ sK2_SY312 @ sK3_SY314 @ sK1_SY24 )
& ( subset @ sK3_SY314 @ sK2_SY312 @ sK1_SY24 )
& ~ ( qmltpeq @ sK2_SY312 @ sK3_SY314 @ sK1_SY24 ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(53,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ~ ( ~ ~ ( ~ ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ~ ( qmltpeq @ SX1 @ SX2 @ SX0 )
| ( subset @ SX1 @ SX2 @ SX0 ) )
| ~ ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ~ ( qmltpeq @ SX1 @ SX2 @ SX0 )
| ( subset @ SX2 @ SX1 @ SX0 ) ) )
| ~ ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ~ ( subset @ SX1 @ SX2 @ SX0 )
| ~ ( subset @ SX2 @ SX1 @ SX0 )
| ( qmltpeq @ SX1 @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(54,plain,
( ( ~ ( ~ ( exists_in_world @ sK3_SY314 @ sK1_SY24 )
| ~ ~ ( ~ ~ ( ~ ( subset @ sK2_SY312 @ sK3_SY314 @ sK1_SY24 )
| ~ ( subset @ sK3_SY314 @ sK2_SY312 @ sK1_SY24 ) )
| ~ ~ ( qmltpeq @ sK2_SY312 @ sK3_SY314 @ sK1_SY24 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(55,plain,
! [SV1: $i] :
( ( ! [SY315: mu] :
( ~ ( exists_in_world @ SY315 @ SV1 )
| ( qmltpeq @ SY315 @ SY315 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(56,plain,
! [SV2: $i] :
( ( ! [SY316: mu] :
( ~ ( exists_in_world @ SY316 @ SV2 )
| ! [SY317: mu] :
( ~ ( exists_in_world @ SY317 @ SV2 )
| ~ ( qmltpeq @ SY316 @ SY317 @ SV2 )
| ( qmltpeq @ SY317 @ SY316 @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(57,plain,
! [SV3: $i] :
( ( ! [SY318: mu] :
( ~ ( exists_in_world @ SY318 @ SV3 )
| ! [SY319: mu] :
( ~ ( exists_in_world @ SY319 @ SV3 )
| ! [SY320: mu] :
( ~ ( exists_in_world @ SY320 @ SV3 )
| ~ ( qmltpeq @ SY318 @ SY319 @ SV3 )
| ~ ( qmltpeq @ SY319 @ SY320 @ SV3 )
| ( qmltpeq @ SY318 @ SY320 @ SV3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(58,plain,
! [SV4: $i] :
( ( ! [SY321: mu] :
( ~ ( exists_in_world @ SY321 @ SV4 )
| ! [SY322: mu] :
( ~ ( exists_in_world @ SY322 @ SV4 )
| ! [SY323: mu] :
( ~ ( exists_in_world @ SY323 @ SV4 )
| ~ ( qmltpeq @ SY321 @ SY322 @ SV4 )
| ~ ( member @ SY321 @ SY323 @ SV4 )
| ( member @ SY322 @ SY323 @ SV4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(59,plain,
! [SV5: $i] :
( ( ! [SY324: mu] :
( ~ ( exists_in_world @ SY324 @ SV5 )
| ! [SY325: mu] :
( ~ ( exists_in_world @ SY325 @ SV5 )
| ! [SY326: mu] :
( ~ ( exists_in_world @ SY326 @ SV5 )
| ~ ( qmltpeq @ SY324 @ SY325 @ SV5 )
| ~ ( member @ SY326 @ SY324 @ SV5 )
| ( member @ SY326 @ SY325 @ SV5 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(60,plain,
! [SV6: $i] :
( ( ! [SY327: mu] :
( ~ ( exists_in_world @ SY327 @ SV6 )
| ! [SY328: mu] :
( ~ ( exists_in_world @ SY328 @ SV6 )
| ! [SY329: mu] :
( ~ ( exists_in_world @ SY329 @ SV6 )
| ~ ( qmltpeq @ SY327 @ SY328 @ SV6 )
| ~ ( subset @ SY327 @ SY329 @ SV6 )
| ( subset @ SY328 @ SY329 @ SV6 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(61,plain,
! [SV7: $i] :
( ( ! [SY330: mu] :
( ~ ( exists_in_world @ SY330 @ SV7 )
| ! [SY331: mu] :
( ~ ( exists_in_world @ SY331 @ SV7 )
| ! [SY332: mu] :
( ~ ( exists_in_world @ SY332 @ SV7 )
| ~ ( qmltpeq @ SY330 @ SY331 @ SV7 )
| ~ ( subset @ SY332 @ SY330 @ SV7 )
| ( subset @ SY332 @ SY331 @ SV7 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(62,plain,
! [SV8: $i] :
( ( ! [SY333: mu] :
( ~ ( exists_in_world @ SY333 @ SV8 )
| ( subset @ SY333 @ SY333 @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(63,plain,
! [SV9: $i] :
( ( ! [SY334: mu] :
( ~ ( exists_in_world @ SY334 @ SV9 )
| ~ ( ~ ~ ( ~ ! [SY335: mu] :
( ~ ( exists_in_world @ SY335 @ SV9 )
| ~ ( qmltpeq @ SY334 @ SY335 @ SV9 )
| ( subset @ SY334 @ SY335 @ SV9 ) )
| ~ ! [SY336: mu] :
( ~ ( exists_in_world @ SY336 @ SV9 )
| ~ ( qmltpeq @ SY334 @ SY336 @ SV9 )
| ( subset @ SY336 @ SY334 @ SV9 ) ) )
| ~ ! [SY337: mu] :
( ~ ( exists_in_world @ SY337 @ SV9 )
| ~ ( subset @ SY334 @ SY337 @ SV9 )
| ~ ( subset @ SY337 @ SY334 @ SV9 )
| ( qmltpeq @ SY334 @ SY337 @ SV9 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(64,plain,
( ( ~ ( exists_in_world @ sK3_SY314 @ sK1_SY24 )
| ~ ~ ( ~ ~ ( ~ ( subset @ sK2_SY312 @ sK3_SY314 @ sK1_SY24 )
| ~ ( subset @ sK3_SY314 @ sK2_SY312 @ sK1_SY24 ) )
| ~ ~ ( qmltpeq @ sK2_SY312 @ sK3_SY314 @ sK1_SY24 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(65,plain,
! [SV1: $i,SV10: mu] :
( ( ~ ( exists_in_world @ SV10 @ SV1 )
| ( qmltpeq @ SV10 @ SV10 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(66,plain,
! [SV2: $i,SV11: mu] :
( ( ~ ( exists_in_world @ SV11 @ SV2 )
| ! [SY338: mu] :
( ~ ( exists_in_world @ SY338 @ SV2 )
| ~ ( qmltpeq @ SV11 @ SY338 @ SV2 )
| ( qmltpeq @ SY338 @ SV11 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(67,plain,
! [SV3: $i,SV12: mu] :
( ( ~ ( exists_in_world @ SV12 @ SV3 )
| ! [SY339: mu] :
( ~ ( exists_in_world @ SY339 @ SV3 )
| ! [SY340: mu] :
( ~ ( exists_in_world @ SY340 @ SV3 )
| ~ ( qmltpeq @ SV12 @ SY339 @ SV3 )
| ~ ( qmltpeq @ SY339 @ SY340 @ SV3 )
| ( qmltpeq @ SV12 @ SY340 @ SV3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(68,plain,
! [SV4: $i,SV13: mu] :
( ( ~ ( exists_in_world @ SV13 @ SV4 )
| ! [SY341: mu] :
( ~ ( exists_in_world @ SY341 @ SV4 )
| ! [SY342: mu] :
( ~ ( exists_in_world @ SY342 @ SV4 )
| ~ ( qmltpeq @ SV13 @ SY341 @ SV4 )
| ~ ( member @ SV13 @ SY342 @ SV4 )
| ( member @ SY341 @ SY342 @ SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(69,plain,
! [SV5: $i,SV14: mu] :
( ( ~ ( exists_in_world @ SV14 @ SV5 )
| ! [SY343: mu] :
( ~ ( exists_in_world @ SY343 @ SV5 )
| ! [SY344: mu] :
( ~ ( exists_in_world @ SY344 @ SV5 )
| ~ ( qmltpeq @ SV14 @ SY343 @ SV5 )
| ~ ( member @ SY344 @ SV14 @ SV5 )
| ( member @ SY344 @ SY343 @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(70,plain,
! [SV6: $i,SV15: mu] :
( ( ~ ( exists_in_world @ SV15 @ SV6 )
| ! [SY345: mu] :
( ~ ( exists_in_world @ SY345 @ SV6 )
| ! [SY346: mu] :
( ~ ( exists_in_world @ SY346 @ SV6 )
| ~ ( qmltpeq @ SV15 @ SY345 @ SV6 )
| ~ ( subset @ SV15 @ SY346 @ SV6 )
| ( subset @ SY345 @ SY346 @ SV6 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(71,plain,
! [SV7: $i,SV16: mu] :
( ( ~ ( exists_in_world @ SV16 @ SV7 )
| ! [SY347: mu] :
( ~ ( exists_in_world @ SY347 @ SV7 )
| ! [SY348: mu] :
( ~ ( exists_in_world @ SY348 @ SV7 )
| ~ ( qmltpeq @ SV16 @ SY347 @ SV7 )
| ~ ( subset @ SY348 @ SV16 @ SV7 )
| ( subset @ SY348 @ SY347 @ SV7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(72,plain,
! [SV8: $i,SV17: mu] :
( ( ~ ( exists_in_world @ SV17 @ SV8 )
| ( subset @ SV17 @ SV17 @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(73,plain,
! [SV9: $i,SV18: mu] :
( ( ~ ( exists_in_world @ SV18 @ SV9 )
| ~ ( ~ ~ ( ~ ! [SY349: mu] :
( ~ ( exists_in_world @ SY349 @ SV9 )
| ~ ( qmltpeq @ SV18 @ SY349 @ SV9 )
| ( subset @ SV18 @ SY349 @ SV9 ) )
| ~ ! [SY350: mu] :
( ~ ( exists_in_world @ SY350 @ SV9 )
| ~ ( qmltpeq @ SV18 @ SY350 @ SV9 )
| ( subset @ SY350 @ SV18 @ SV9 ) ) )
| ~ ! [SY351: mu] :
( ~ ( exists_in_world @ SY351 @ SV9 )
| ~ ( subset @ SV18 @ SY351 @ SV9 )
| ~ ( subset @ SY351 @ SV18 @ SV9 )
| ( qmltpeq @ SV18 @ SY351 @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(74,plain,
( ( ~ ( exists_in_world @ sK3_SY314 @ sK1_SY24 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[64]) ).
thf(75,plain,
( ( ~ ~ ( ~ ~ ( ~ ( subset @ sK2_SY312 @ sK3_SY314 @ sK1_SY24 )
| ~ ( subset @ sK3_SY314 @ sK2_SY312 @ sK1_SY24 ) )
| ~ ~ ( qmltpeq @ sK2_SY312 @ sK3_SY314 @ sK1_SY24 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[64]) ).
thf(76,plain,
! [SV1: $i,SV10: mu] :
( ( ( ~ ( exists_in_world @ SV10 @ SV1 ) )
= $true )
| ( ( qmltpeq @ SV10 @ SV10 @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[65]) ).
thf(77,plain,
! [SV2: $i,SV11: mu] :
( ( ( ~ ( exists_in_world @ SV11 @ SV2 ) )
= $true )
| ( ( ! [SY338: mu] :
( ~ ( exists_in_world @ SY338 @ SV2 )
| ~ ( qmltpeq @ SV11 @ SY338 @ SV2 )
| ( qmltpeq @ SY338 @ SV11 @ SV2 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[66]) ).
thf(78,plain,
! [SV3: $i,SV12: mu] :
( ( ( ~ ( exists_in_world @ SV12 @ SV3 ) )
= $true )
| ( ( ! [SY339: mu] :
( ~ ( exists_in_world @ SY339 @ SV3 )
| ! [SY340: mu] :
( ~ ( exists_in_world @ SY340 @ SV3 )
| ~ ( qmltpeq @ SV12 @ SY339 @ SV3 )
| ~ ( qmltpeq @ SY339 @ SY340 @ SV3 )
| ( qmltpeq @ SV12 @ SY340 @ SV3 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[67]) ).
thf(79,plain,
! [SV4: $i,SV13: mu] :
( ( ( ~ ( exists_in_world @ SV13 @ SV4 ) )
= $true )
| ( ( ! [SY341: mu] :
( ~ ( exists_in_world @ SY341 @ SV4 )
| ! [SY342: mu] :
( ~ ( exists_in_world @ SY342 @ SV4 )
| ~ ( qmltpeq @ SV13 @ SY341 @ SV4 )
| ~ ( member @ SV13 @ SY342 @ SV4 )
| ( member @ SY341 @ SY342 @ SV4 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[68]) ).
thf(80,plain,
! [SV5: $i,SV14: mu] :
( ( ( ~ ( exists_in_world @ SV14 @ SV5 ) )
= $true )
| ( ( ! [SY343: mu] :
( ~ ( exists_in_world @ SY343 @ SV5 )
| ! [SY344: mu] :
( ~ ( exists_in_world @ SY344 @ SV5 )
| ~ ( qmltpeq @ SV14 @ SY343 @ SV5 )
| ~ ( member @ SY344 @ SV14 @ SV5 )
| ( member @ SY344 @ SY343 @ SV5 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[69]) ).
thf(81,plain,
! [SV6: $i,SV15: mu] :
( ( ( ~ ( exists_in_world @ SV15 @ SV6 ) )
= $true )
| ( ( ! [SY345: mu] :
( ~ ( exists_in_world @ SY345 @ SV6 )
| ! [SY346: mu] :
( ~ ( exists_in_world @ SY346 @ SV6 )
| ~ ( qmltpeq @ SV15 @ SY345 @ SV6 )
| ~ ( subset @ SV15 @ SY346 @ SV6 )
| ( subset @ SY345 @ SY346 @ SV6 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[70]) ).
thf(82,plain,
! [SV7: $i,SV16: mu] :
( ( ( ~ ( exists_in_world @ SV16 @ SV7 ) )
= $true )
| ( ( ! [SY347: mu] :
( ~ ( exists_in_world @ SY347 @ SV7 )
| ! [SY348: mu] :
( ~ ( exists_in_world @ SY348 @ SV7 )
| ~ ( qmltpeq @ SV16 @ SY347 @ SV7 )
| ~ ( subset @ SY348 @ SV16 @ SV7 )
| ( subset @ SY348 @ SY347 @ SV7 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[71]) ).
thf(83,plain,
! [SV8: $i,SV17: mu] :
( ( ( ~ ( exists_in_world @ SV17 @ SV8 ) )
= $true )
| ( ( subset @ SV17 @ SV17 @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[72]) ).
thf(84,plain,
! [SV9: $i,SV18: mu] :
( ( ( ~ ( exists_in_world @ SV18 @ SV9 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY349: mu] :
( ~ ( exists_in_world @ SY349 @ SV9 )
| ~ ( qmltpeq @ SV18 @ SY349 @ SV9 )
| ( subset @ SV18 @ SY349 @ SV9 ) )
| ~ ! [SY350: mu] :
( ~ ( exists_in_world @ SY350 @ SV9 )
| ~ ( qmltpeq @ SV18 @ SY350 @ SV9 )
| ( subset @ SY350 @ SV18 @ SV9 ) ) )
| ~ ! [SY351: mu] :
( ~ ( exists_in_world @ SY351 @ SV9 )
| ~ ( subset @ SV18 @ SY351 @ SV9 )
| ~ ( subset @ SY351 @ SV18 @ SV9 )
| ( qmltpeq @ SV18 @ SY351 @ SV9 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[73]) ).
thf(85,plain,
( ( exists_in_world @ sK3_SY314 @ sK1_SY24 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[74]) ).
thf(86,plain,
( ( ~ ( ~ ~ ( ~ ( subset @ sK2_SY312 @ sK3_SY314 @ sK1_SY24 )
| ~ ( subset @ sK3_SY314 @ sK2_SY312 @ sK1_SY24 ) )
| ~ ~ ( qmltpeq @ sK2_SY312 @ sK3_SY314 @ sK1_SY24 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[75]) ).
thf(87,plain,
! [SV1: $i,SV10: mu] :
( ( ( exists_in_world @ SV10 @ SV1 )
= $false )
| ( ( qmltpeq @ SV10 @ SV10 @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(88,plain,
! [SV2: $i,SV11: mu] :
( ( ( exists_in_world @ SV11 @ SV2 )
= $false )
| ( ( ! [SY338: mu] :
( ~ ( exists_in_world @ SY338 @ SV2 )
| ~ ( qmltpeq @ SV11 @ SY338 @ SV2 )
| ( qmltpeq @ SY338 @ SV11 @ SV2 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(89,plain,
! [SV3: $i,SV12: mu] :
( ( ( exists_in_world @ SV12 @ SV3 )
= $false )
| ( ( ! [SY339: mu] :
( ~ ( exists_in_world @ SY339 @ SV3 )
| ! [SY340: mu] :
( ~ ( exists_in_world @ SY340 @ SV3 )
| ~ ( qmltpeq @ SV12 @ SY339 @ SV3 )
| ~ ( qmltpeq @ SY339 @ SY340 @ SV3 )
| ( qmltpeq @ SV12 @ SY340 @ SV3 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(90,plain,
! [SV4: $i,SV13: mu] :
( ( ( exists_in_world @ SV13 @ SV4 )
= $false )
| ( ( ! [SY341: mu] :
( ~ ( exists_in_world @ SY341 @ SV4 )
| ! [SY342: mu] :
( ~ ( exists_in_world @ SY342 @ SV4 )
| ~ ( qmltpeq @ SV13 @ SY341 @ SV4 )
| ~ ( member @ SV13 @ SY342 @ SV4 )
| ( member @ SY341 @ SY342 @ SV4 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(91,plain,
! [SV5: $i,SV14: mu] :
( ( ( exists_in_world @ SV14 @ SV5 )
= $false )
| ( ( ! [SY343: mu] :
( ~ ( exists_in_world @ SY343 @ SV5 )
| ! [SY344: mu] :
( ~ ( exists_in_world @ SY344 @ SV5 )
| ~ ( qmltpeq @ SV14 @ SY343 @ SV5 )
| ~ ( member @ SY344 @ SV14 @ SV5 )
| ( member @ SY344 @ SY343 @ SV5 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(92,plain,
! [SV6: $i,SV15: mu] :
( ( ( exists_in_world @ SV15 @ SV6 )
= $false )
| ( ( ! [SY345: mu] :
( ~ ( exists_in_world @ SY345 @ SV6 )
| ! [SY346: mu] :
( ~ ( exists_in_world @ SY346 @ SV6 )
| ~ ( qmltpeq @ SV15 @ SY345 @ SV6 )
| ~ ( subset @ SV15 @ SY346 @ SV6 )
| ( subset @ SY345 @ SY346 @ SV6 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(93,plain,
! [SV7: $i,SV16: mu] :
( ( ( exists_in_world @ SV16 @ SV7 )
= $false )
| ( ( ! [SY347: mu] :
( ~ ( exists_in_world @ SY347 @ SV7 )
| ! [SY348: mu] :
( ~ ( exists_in_world @ SY348 @ SV7 )
| ~ ( qmltpeq @ SV16 @ SY347 @ SV7 )
| ~ ( subset @ SY348 @ SV16 @ SV7 )
| ( subset @ SY348 @ SY347 @ SV7 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(94,plain,
! [SV8: $i,SV17: mu] :
( ( ( exists_in_world @ SV17 @ SV8 )
= $false )
| ( ( subset @ SV17 @ SV17 @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[83]) ).
thf(95,plain,
! [SV9: $i,SV18: mu] :
( ( ( exists_in_world @ SV18 @ SV9 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ! [SY349: mu] :
( ~ ( exists_in_world @ SY349 @ SV9 )
| ~ ( qmltpeq @ SV18 @ SY349 @ SV9 )
| ( subset @ SV18 @ SY349 @ SV9 ) )
| ~ ! [SY350: mu] :
( ~ ( exists_in_world @ SY350 @ SV9 )
| ~ ( qmltpeq @ SV18 @ SY350 @ SV9 )
| ( subset @ SY350 @ SV18 @ SV9 ) ) )
| ~ ! [SY351: mu] :
( ~ ( exists_in_world @ SY351 @ SV9 )
| ~ ( subset @ SV18 @ SY351 @ SV9 )
| ~ ( subset @ SY351 @ SV18 @ SV9 )
| ( qmltpeq @ SV18 @ SY351 @ SV9 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[84]) ).
thf(96,plain,
( ( ~ ~ ( ~ ( subset @ sK2_SY312 @ sK3_SY314 @ sK1_SY24 )
| ~ ( subset @ sK3_SY314 @ sK2_SY312 @ sK1_SY24 ) )
| ~ ~ ( qmltpeq @ sK2_SY312 @ sK3_SY314 @ sK1_SY24 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(97,plain,
! [SV11: mu,SV2: $i,SV19: mu] :
( ( ( ~ ( exists_in_world @ SV19 @ SV2 )
| ~ ( qmltpeq @ SV11 @ SV19 @ SV2 )
| ( qmltpeq @ SV19 @ SV11 @ SV2 ) )
= $true )
| ( ( exists_in_world @ SV11 @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(98,plain,
! [SV12: mu,SV3: $i,SV20: mu] :
( ( ( ~ ( exists_in_world @ SV20 @ SV3 )
| ! [SY352: mu] :
( ~ ( exists_in_world @ SY352 @ SV3 )
| ~ ( qmltpeq @ SV12 @ SV20 @ SV3 )
| ~ ( qmltpeq @ SV20 @ SY352 @ SV3 )
| ( qmltpeq @ SV12 @ SY352 @ SV3 ) ) )
= $true )
| ( ( exists_in_world @ SV12 @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(99,plain,
! [SV13: mu,SV4: $i,SV21: mu] :
( ( ( ~ ( exists_in_world @ SV21 @ SV4 )
| ! [SY353: mu] :
( ~ ( exists_in_world @ SY353 @ SV4 )
| ~ ( qmltpeq @ SV13 @ SV21 @ SV4 )
| ~ ( member @ SV13 @ SY353 @ SV4 )
| ( member @ SV21 @ SY353 @ SV4 ) ) )
= $true )
| ( ( exists_in_world @ SV13 @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(100,plain,
! [SV14: mu,SV5: $i,SV22: mu] :
( ( ( ~ ( exists_in_world @ SV22 @ SV5 )
| ! [SY354: mu] :
( ~ ( exists_in_world @ SY354 @ SV5 )
| ~ ( qmltpeq @ SV14 @ SV22 @ SV5 )
| ~ ( member @ SY354 @ SV14 @ SV5 )
| ( member @ SY354 @ SV22 @ SV5 ) ) )
= $true )
| ( ( exists_in_world @ SV14 @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(101,plain,
! [SV15: mu,SV6: $i,SV23: mu] :
( ( ( ~ ( exists_in_world @ SV23 @ SV6 )
| ! [SY355: mu] :
( ~ ( exists_in_world @ SY355 @ SV6 )
| ~ ( qmltpeq @ SV15 @ SV23 @ SV6 )
| ~ ( subset @ SV15 @ SY355 @ SV6 )
| ( subset @ SV23 @ SY355 @ SV6 ) ) )
= $true )
| ( ( exists_in_world @ SV15 @ SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(102,plain,
! [SV16: mu,SV7: $i,SV24: mu] :
( ( ( ~ ( exists_in_world @ SV24 @ SV7 )
| ! [SY356: mu] :
( ~ ( exists_in_world @ SY356 @ SV7 )
| ~ ( qmltpeq @ SV16 @ SV24 @ SV7 )
| ~ ( subset @ SY356 @ SV16 @ SV7 )
| ( subset @ SY356 @ SV24 @ SV7 ) ) )
= $true )
| ( ( exists_in_world @ SV16 @ SV7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(103,plain,
! [SV18: mu,SV9: $i] :
( ( ( ~ ~ ( ~ ! [SY349: mu] :
( ~ ( exists_in_world @ SY349 @ SV9 )
| ~ ( qmltpeq @ SV18 @ SY349 @ SV9 )
| ( subset @ SV18 @ SY349 @ SV9 ) )
| ~ ! [SY350: mu] :
( ~ ( exists_in_world @ SY350 @ SV9 )
| ~ ( qmltpeq @ SV18 @ SY350 @ SV9 )
| ( subset @ SY350 @ SV18 @ SV9 ) ) )
| ~ ! [SY351: mu] :
( ~ ( exists_in_world @ SY351 @ SV9 )
| ~ ( subset @ SV18 @ SY351 @ SV9 )
| ~ ( subset @ SY351 @ SV18 @ SV9 )
| ( qmltpeq @ SV18 @ SY351 @ SV9 ) ) )
= $false )
| ( ( exists_in_world @ SV18 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(104,plain,
( ( ~ ~ ( ~ ( subset @ sK2_SY312 @ sK3_SY314 @ sK1_SY24 )
| ~ ( subset @ sK3_SY314 @ sK2_SY312 @ sK1_SY24 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[96]) ).
thf(105,plain,
( ( ~ ~ ( qmltpeq @ sK2_SY312 @ sK3_SY314 @ sK1_SY24 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[96]) ).
thf(106,plain,
! [SV11: mu,SV2: $i,SV19: mu] :
( ( ( ~ ( exists_in_world @ SV19 @ SV2 ) )
= $true )
| ( ( ~ ( qmltpeq @ SV11 @ SV19 @ SV2 )
| ( qmltpeq @ SV19 @ SV11 @ SV2 ) )
= $true )
| ( ( exists_in_world @ SV11 @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[97]) ).
thf(107,plain,
! [SV12: mu,SV3: $i,SV20: mu] :
( ( ( ~ ( exists_in_world @ SV20 @ SV3 ) )
= $true )
| ( ( ! [SY352: mu] :
( ~ ( exists_in_world @ SY352 @ SV3 )
| ~ ( qmltpeq @ SV12 @ SV20 @ SV3 )
| ~ ( qmltpeq @ SV20 @ SY352 @ SV3 )
| ( qmltpeq @ SV12 @ SY352 @ SV3 ) ) )
= $true )
| ( ( exists_in_world @ SV12 @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[98]) ).
thf(108,plain,
! [SV13: mu,SV4: $i,SV21: mu] :
( ( ( ~ ( exists_in_world @ SV21 @ SV4 ) )
= $true )
| ( ( ! [SY353: mu] :
( ~ ( exists_in_world @ SY353 @ SV4 )
| ~ ( qmltpeq @ SV13 @ SV21 @ SV4 )
| ~ ( member @ SV13 @ SY353 @ SV4 )
| ( member @ SV21 @ SY353 @ SV4 ) ) )
= $true )
| ( ( exists_in_world @ SV13 @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[99]) ).
thf(109,plain,
! [SV14: mu,SV5: $i,SV22: mu] :
( ( ( ~ ( exists_in_world @ SV22 @ SV5 ) )
= $true )
| ( ( ! [SY354: mu] :
( ~ ( exists_in_world @ SY354 @ SV5 )
| ~ ( qmltpeq @ SV14 @ SV22 @ SV5 )
| ~ ( member @ SY354 @ SV14 @ SV5 )
| ( member @ SY354 @ SV22 @ SV5 ) ) )
= $true )
| ( ( exists_in_world @ SV14 @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[100]) ).
thf(110,plain,
! [SV15: mu,SV6: $i,SV23: mu] :
( ( ( ~ ( exists_in_world @ SV23 @ SV6 ) )
= $true )
| ( ( ! [SY355: mu] :
( ~ ( exists_in_world @ SY355 @ SV6 )
| ~ ( qmltpeq @ SV15 @ SV23 @ SV6 )
| ~ ( subset @ SV15 @ SY355 @ SV6 )
| ( subset @ SV23 @ SY355 @ SV6 ) ) )
= $true )
| ( ( exists_in_world @ SV15 @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[101]) ).
thf(111,plain,
! [SV16: mu,SV7: $i,SV24: mu] :
( ( ( ~ ( exists_in_world @ SV24 @ SV7 ) )
= $true )
| ( ( ! [SY356: mu] :
( ~ ( exists_in_world @ SY356 @ SV7 )
| ~ ( qmltpeq @ SV16 @ SV24 @ SV7 )
| ~ ( subset @ SY356 @ SV16 @ SV7 )
| ( subset @ SY356 @ SV24 @ SV7 ) ) )
= $true )
| ( ( exists_in_world @ SV16 @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[102]) ).
thf(112,plain,
! [SV18: mu,SV9: $i] :
( ( ( ~ ~ ( ~ ! [SY349: mu] :
( ~ ( exists_in_world @ SY349 @ SV9 )
| ~ ( qmltpeq @ SV18 @ SY349 @ SV9 )
| ( subset @ SV18 @ SY349 @ SV9 ) )
| ~ ! [SY350: mu] :
( ~ ( exists_in_world @ SY350 @ SV9 )
| ~ ( qmltpeq @ SV18 @ SY350 @ SV9 )
| ( subset @ SY350 @ SV18 @ SV9 ) ) ) )
= $false )
| ( ( exists_in_world @ SV18 @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[103]) ).
thf(113,plain,
! [SV18: mu,SV9: $i] :
( ( ( ~ ! [SY351: mu] :
( ~ ( exists_in_world @ SY351 @ SV9 )
| ~ ( subset @ SV18 @ SY351 @ SV9 )
| ~ ( subset @ SY351 @ SV18 @ SV9 )
| ( qmltpeq @ SV18 @ SY351 @ SV9 ) ) )
= $false )
| ( ( exists_in_world @ SV18 @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[103]) ).
thf(114,plain,
( ( ~ ( ~ ( subset @ sK2_SY312 @ sK3_SY314 @ sK1_SY24 )
| ~ ( subset @ sK3_SY314 @ sK2_SY312 @ sK1_SY24 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[104]) ).
thf(115,plain,
( ( ~ ( qmltpeq @ sK2_SY312 @ sK3_SY314 @ sK1_SY24 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[105]) ).
thf(116,plain,
! [SV11: mu,SV2: $i,SV19: mu] :
( ( ( exists_in_world @ SV19 @ SV2 )
= $false )
| ( ( ~ ( qmltpeq @ SV11 @ SV19 @ SV2 )
| ( qmltpeq @ SV19 @ SV11 @ SV2 ) )
= $true )
| ( ( exists_in_world @ SV11 @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(117,plain,
! [SV12: mu,SV3: $i,SV20: mu] :
( ( ( exists_in_world @ SV20 @ SV3 )
= $false )
| ( ( ! [SY352: mu] :
( ~ ( exists_in_world @ SY352 @ SV3 )
| ~ ( qmltpeq @ SV12 @ SV20 @ SV3 )
| ~ ( qmltpeq @ SV20 @ SY352 @ SV3 )
| ( qmltpeq @ SV12 @ SY352 @ SV3 ) ) )
= $true )
| ( ( exists_in_world @ SV12 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(118,plain,
! [SV13: mu,SV4: $i,SV21: mu] :
( ( ( exists_in_world @ SV21 @ SV4 )
= $false )
| ( ( ! [SY353: mu] :
( ~ ( exists_in_world @ SY353 @ SV4 )
| ~ ( qmltpeq @ SV13 @ SV21 @ SV4 )
| ~ ( member @ SV13 @ SY353 @ SV4 )
| ( member @ SV21 @ SY353 @ SV4 ) ) )
= $true )
| ( ( exists_in_world @ SV13 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(119,plain,
! [SV14: mu,SV5: $i,SV22: mu] :
( ( ( exists_in_world @ SV22 @ SV5 )
= $false )
| ( ( ! [SY354: mu] :
( ~ ( exists_in_world @ SY354 @ SV5 )
| ~ ( qmltpeq @ SV14 @ SV22 @ SV5 )
| ~ ( member @ SY354 @ SV14 @ SV5 )
| ( member @ SY354 @ SV22 @ SV5 ) ) )
= $true )
| ( ( exists_in_world @ SV14 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(120,plain,
! [SV15: mu,SV6: $i,SV23: mu] :
( ( ( exists_in_world @ SV23 @ SV6 )
= $false )
| ( ( ! [SY355: mu] :
( ~ ( exists_in_world @ SY355 @ SV6 )
| ~ ( qmltpeq @ SV15 @ SV23 @ SV6 )
| ~ ( subset @ SV15 @ SY355 @ SV6 )
| ( subset @ SV23 @ SY355 @ SV6 ) ) )
= $true )
| ( ( exists_in_world @ SV15 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(121,plain,
! [SV16: mu,SV7: $i,SV24: mu] :
( ( ( exists_in_world @ SV24 @ SV7 )
= $false )
| ( ( ! [SY356: mu] :
( ~ ( exists_in_world @ SY356 @ SV7 )
| ~ ( qmltpeq @ SV16 @ SV24 @ SV7 )
| ~ ( subset @ SY356 @ SV16 @ SV7 )
| ( subset @ SY356 @ SV24 @ SV7 ) ) )
= $true )
| ( ( exists_in_world @ SV16 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(122,plain,
! [SV18: mu,SV9: $i] :
( ( ( ~ ( ~ ! [SY349: mu] :
( ~ ( exists_in_world @ SY349 @ SV9 )
| ~ ( qmltpeq @ SV18 @ SY349 @ SV9 )
| ( subset @ SV18 @ SY349 @ SV9 ) )
| ~ ! [SY350: mu] :
( ~ ( exists_in_world @ SY350 @ SV9 )
| ~ ( qmltpeq @ SV18 @ SY350 @ SV9 )
| ( subset @ SY350 @ SV18 @ SV9 ) ) ) )
= $true )
| ( ( exists_in_world @ SV18 @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[112]) ).
thf(123,plain,
! [SV18: mu,SV9: $i] :
( ( ( ! [SY351: mu] :
( ~ ( exists_in_world @ SY351 @ SV9 )
| ~ ( subset @ SV18 @ SY351 @ SV9 )
| ~ ( subset @ SY351 @ SV18 @ SV9 )
| ( qmltpeq @ SV18 @ SY351 @ SV9 ) ) )
= $true )
| ( ( exists_in_world @ SV18 @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[113]) ).
thf(124,plain,
( ( ~ ( subset @ sK2_SY312 @ sK3_SY314 @ sK1_SY24 )
| ~ ( subset @ sK3_SY314 @ sK2_SY312 @ sK1_SY24 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[114]) ).
thf(125,plain,
( ( qmltpeq @ sK2_SY312 @ sK3_SY314 @ sK1_SY24 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(126,plain,
! [SV2: $i,SV19: mu,SV11: mu] :
( ( ( ~ ( qmltpeq @ SV11 @ SV19 @ SV2 ) )
= $true )
| ( ( qmltpeq @ SV19 @ SV11 @ SV2 )
= $true )
| ( ( exists_in_world @ SV19 @ SV2 )
= $false )
| ( ( exists_in_world @ SV11 @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[116]) ).
thf(127,plain,
! [SV20: mu,SV12: mu,SV3: $i,SV25: mu] :
( ( ( ~ ( exists_in_world @ SV25 @ SV3 )
| ~ ( qmltpeq @ SV12 @ SV20 @ SV3 )
| ~ ( qmltpeq @ SV20 @ SV25 @ SV3 )
| ( qmltpeq @ SV12 @ SV25 @ SV3 ) )
= $true )
| ( ( exists_in_world @ SV20 @ SV3 )
= $false )
| ( ( exists_in_world @ SV12 @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(128,plain,
! [SV21: mu,SV13: mu,SV4: $i,SV26: mu] :
( ( ( ~ ( exists_in_world @ SV26 @ SV4 )
| ~ ( qmltpeq @ SV13 @ SV21 @ SV4 )
| ~ ( member @ SV13 @ SV26 @ SV4 )
| ( member @ SV21 @ SV26 @ SV4 ) )
= $true )
| ( ( exists_in_world @ SV21 @ SV4 )
= $false )
| ( ( exists_in_world @ SV13 @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(129,plain,
! [SV22: mu,SV14: mu,SV5: $i,SV27: mu] :
( ( ( ~ ( exists_in_world @ SV27 @ SV5 )
| ~ ( qmltpeq @ SV14 @ SV22 @ SV5 )
| ~ ( member @ SV27 @ SV14 @ SV5 )
| ( member @ SV27 @ SV22 @ SV5 ) )
= $true )
| ( ( exists_in_world @ SV22 @ SV5 )
= $false )
| ( ( exists_in_world @ SV14 @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(130,plain,
! [SV23: mu,SV15: mu,SV6: $i,SV28: mu] :
( ( ( ~ ( exists_in_world @ SV28 @ SV6 )
| ~ ( qmltpeq @ SV15 @ SV23 @ SV6 )
| ~ ( subset @ SV15 @ SV28 @ SV6 )
| ( subset @ SV23 @ SV28 @ SV6 ) )
= $true )
| ( ( exists_in_world @ SV23 @ SV6 )
= $false )
| ( ( exists_in_world @ SV15 @ SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(131,plain,
! [SV24: mu,SV16: mu,SV7: $i,SV29: mu] :
( ( ( ~ ( exists_in_world @ SV29 @ SV7 )
| ~ ( qmltpeq @ SV16 @ SV24 @ SV7 )
| ~ ( subset @ SV29 @ SV16 @ SV7 )
| ( subset @ SV29 @ SV24 @ SV7 ) )
= $true )
| ( ( exists_in_world @ SV24 @ SV7 )
= $false )
| ( ( exists_in_world @ SV16 @ SV7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(132,plain,
! [SV18: mu,SV9: $i] :
( ( ( ~ ! [SY349: mu] :
( ~ ( exists_in_world @ SY349 @ SV9 )
| ~ ( qmltpeq @ SV18 @ SY349 @ SV9 )
| ( subset @ SV18 @ SY349 @ SV9 ) )
| ~ ! [SY350: mu] :
( ~ ( exists_in_world @ SY350 @ SV9 )
| ~ ( qmltpeq @ SV18 @ SY350 @ SV9 )
| ( subset @ SY350 @ SV18 @ SV9 ) ) )
= $false )
| ( ( exists_in_world @ SV18 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(133,plain,
! [SV18: mu,SV9: $i,SV30: mu] :
( ( ( ~ ( exists_in_world @ SV30 @ SV9 )
| ~ ( subset @ SV18 @ SV30 @ SV9 )
| ~ ( subset @ SV30 @ SV18 @ SV9 )
| ( qmltpeq @ SV18 @ SV30 @ SV9 ) )
= $true )
| ( ( exists_in_world @ SV18 @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(134,plain,
( ( ~ ( subset @ sK2_SY312 @ sK3_SY314 @ sK1_SY24 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[124]) ).
thf(135,plain,
( ( ~ ( subset @ sK3_SY314 @ sK2_SY312 @ sK1_SY24 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[124]) ).
thf(136,plain,
! [SV2: $i,SV19: mu,SV11: mu] :
( ( ( qmltpeq @ SV11 @ SV19 @ SV2 )
= $false )
| ( ( qmltpeq @ SV19 @ SV11 @ SV2 )
= $true )
| ( ( exists_in_world @ SV19 @ SV2 )
= $false )
| ( ( exists_in_world @ SV11 @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[126]) ).
thf(137,plain,
! [SV20: mu,SV12: mu,SV3: $i,SV25: mu] :
( ( ( ~ ( exists_in_world @ SV25 @ SV3 ) )
= $true )
| ( ( ~ ( qmltpeq @ SV12 @ SV20 @ SV3 )
| ~ ( qmltpeq @ SV20 @ SV25 @ SV3 )
| ( qmltpeq @ SV12 @ SV25 @ SV3 ) )
= $true )
| ( ( exists_in_world @ SV20 @ SV3 )
= $false )
| ( ( exists_in_world @ SV12 @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[127]) ).
thf(138,plain,
! [SV21: mu,SV13: mu,SV4: $i,SV26: mu] :
( ( ( ~ ( exists_in_world @ SV26 @ SV4 ) )
= $true )
| ( ( ~ ( qmltpeq @ SV13 @ SV21 @ SV4 )
| ~ ( member @ SV13 @ SV26 @ SV4 )
| ( member @ SV21 @ SV26 @ SV4 ) )
= $true )
| ( ( exists_in_world @ SV21 @ SV4 )
= $false )
| ( ( exists_in_world @ SV13 @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[128]) ).
thf(139,plain,
! [SV22: mu,SV14: mu,SV5: $i,SV27: mu] :
( ( ( ~ ( exists_in_world @ SV27 @ SV5 ) )
= $true )
| ( ( ~ ( qmltpeq @ SV14 @ SV22 @ SV5 )
| ~ ( member @ SV27 @ SV14 @ SV5 )
| ( member @ SV27 @ SV22 @ SV5 ) )
= $true )
| ( ( exists_in_world @ SV22 @ SV5 )
= $false )
| ( ( exists_in_world @ SV14 @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[129]) ).
thf(140,plain,
! [SV23: mu,SV15: mu,SV6: $i,SV28: mu] :
( ( ( ~ ( exists_in_world @ SV28 @ SV6 ) )
= $true )
| ( ( ~ ( qmltpeq @ SV15 @ SV23 @ SV6 )
| ~ ( subset @ SV15 @ SV28 @ SV6 )
| ( subset @ SV23 @ SV28 @ SV6 ) )
= $true )
| ( ( exists_in_world @ SV23 @ SV6 )
= $false )
| ( ( exists_in_world @ SV15 @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[130]) ).
thf(141,plain,
! [SV24: mu,SV16: mu,SV7: $i,SV29: mu] :
( ( ( ~ ( exists_in_world @ SV29 @ SV7 ) )
= $true )
| ( ( ~ ( qmltpeq @ SV16 @ SV24 @ SV7 )
| ~ ( subset @ SV29 @ SV16 @ SV7 )
| ( subset @ SV29 @ SV24 @ SV7 ) )
= $true )
| ( ( exists_in_world @ SV24 @ SV7 )
= $false )
| ( ( exists_in_world @ SV16 @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[131]) ).
thf(142,plain,
! [SV18: mu,SV9: $i] :
( ( ( ~ ! [SY349: mu] :
( ~ ( exists_in_world @ SY349 @ SV9 )
| ~ ( qmltpeq @ SV18 @ SY349 @ SV9 )
| ( subset @ SV18 @ SY349 @ SV9 ) ) )
= $false )
| ( ( exists_in_world @ SV18 @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[132]) ).
thf(143,plain,
! [SV18: mu,SV9: $i] :
( ( ( ~ ! [SY350: mu] :
( ~ ( exists_in_world @ SY350 @ SV9 )
| ~ ( qmltpeq @ SV18 @ SY350 @ SV9 )
| ( subset @ SY350 @ SV18 @ SV9 ) ) )
= $false )
| ( ( exists_in_world @ SV18 @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[132]) ).
thf(144,plain,
! [SV18: mu,SV9: $i,SV30: mu] :
( ( ( ~ ( exists_in_world @ SV30 @ SV9 ) )
= $true )
| ( ( ~ ( subset @ SV18 @ SV30 @ SV9 )
| ~ ( subset @ SV30 @ SV18 @ SV9 )
| ( qmltpeq @ SV18 @ SV30 @ SV9 ) )
= $true )
| ( ( exists_in_world @ SV18 @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[133]) ).
thf(145,plain,
( ( subset @ sK2_SY312 @ sK3_SY314 @ sK1_SY24 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[134]) ).
thf(146,plain,
( ( subset @ sK3_SY314 @ sK2_SY312 @ sK1_SY24 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[135]) ).
thf(147,plain,
! [SV20: mu,SV12: mu,SV3: $i,SV25: mu] :
( ( ( exists_in_world @ SV25 @ SV3 )
= $false )
| ( ( ~ ( qmltpeq @ SV12 @ SV20 @ SV3 )
| ~ ( qmltpeq @ SV20 @ SV25 @ SV3 )
| ( qmltpeq @ SV12 @ SV25 @ SV3 ) )
= $true )
| ( ( exists_in_world @ SV20 @ SV3 )
= $false )
| ( ( exists_in_world @ SV12 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(148,plain,
! [SV21: mu,SV13: mu,SV4: $i,SV26: mu] :
( ( ( exists_in_world @ SV26 @ SV4 )
= $false )
| ( ( ~ ( qmltpeq @ SV13 @ SV21 @ SV4 )
| ~ ( member @ SV13 @ SV26 @ SV4 )
| ( member @ SV21 @ SV26 @ SV4 ) )
= $true )
| ( ( exists_in_world @ SV21 @ SV4 )
= $false )
| ( ( exists_in_world @ SV13 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(149,plain,
! [SV22: mu,SV14: mu,SV5: $i,SV27: mu] :
( ( ( exists_in_world @ SV27 @ SV5 )
= $false )
| ( ( ~ ( qmltpeq @ SV14 @ SV22 @ SV5 )
| ~ ( member @ SV27 @ SV14 @ SV5 )
| ( member @ SV27 @ SV22 @ SV5 ) )
= $true )
| ( ( exists_in_world @ SV22 @ SV5 )
= $false )
| ( ( exists_in_world @ SV14 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(150,plain,
! [SV23: mu,SV15: mu,SV6: $i,SV28: mu] :
( ( ( exists_in_world @ SV28 @ SV6 )
= $false )
| ( ( ~ ( qmltpeq @ SV15 @ SV23 @ SV6 )
| ~ ( subset @ SV15 @ SV28 @ SV6 )
| ( subset @ SV23 @ SV28 @ SV6 ) )
= $true )
| ( ( exists_in_world @ SV23 @ SV6 )
= $false )
| ( ( exists_in_world @ SV15 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(151,plain,
! [SV24: mu,SV16: mu,SV7: $i,SV29: mu] :
( ( ( exists_in_world @ SV29 @ SV7 )
= $false )
| ( ( ~ ( qmltpeq @ SV16 @ SV24 @ SV7 )
| ~ ( subset @ SV29 @ SV16 @ SV7 )
| ( subset @ SV29 @ SV24 @ SV7 ) )
= $true )
| ( ( exists_in_world @ SV24 @ SV7 )
= $false )
| ( ( exists_in_world @ SV16 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(152,plain,
! [SV18: mu,SV9: $i] :
( ( ( ! [SY349: mu] :
( ~ ( exists_in_world @ SY349 @ SV9 )
| ~ ( qmltpeq @ SV18 @ SY349 @ SV9 )
| ( subset @ SV18 @ SY349 @ SV9 ) ) )
= $true )
| ( ( exists_in_world @ SV18 @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[142]) ).
thf(153,plain,
! [SV18: mu,SV9: $i] :
( ( ( ! [SY350: mu] :
( ~ ( exists_in_world @ SY350 @ SV9 )
| ~ ( qmltpeq @ SV18 @ SY350 @ SV9 )
| ( subset @ SY350 @ SV18 @ SV9 ) ) )
= $true )
| ( ( exists_in_world @ SV18 @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[143]) ).
thf(154,plain,
! [SV18: mu,SV9: $i,SV30: mu] :
( ( ( exists_in_world @ SV30 @ SV9 )
= $false )
| ( ( ~ ( subset @ SV18 @ SV30 @ SV9 )
| ~ ( subset @ SV30 @ SV18 @ SV9 )
| ( qmltpeq @ SV18 @ SV30 @ SV9 ) )
= $true )
| ( ( exists_in_world @ SV18 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(155,plain,
! [SV25: mu,SV3: $i,SV20: mu,SV12: mu] :
( ( ( ~ ( qmltpeq @ SV12 @ SV20 @ SV3 )
| ~ ( qmltpeq @ SV20 @ SV25 @ SV3 ) )
= $true )
| ( ( qmltpeq @ SV12 @ SV25 @ SV3 )
= $true )
| ( ( exists_in_world @ SV25 @ SV3 )
= $false )
| ( ( exists_in_world @ SV20 @ SV3 )
= $false )
| ( ( exists_in_world @ SV12 @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[147]) ).
thf(156,plain,
! [SV26: mu,SV4: $i,SV21: mu,SV13: mu] :
( ( ( ~ ( qmltpeq @ SV13 @ SV21 @ SV4 )
| ~ ( member @ SV13 @ SV26 @ SV4 ) )
= $true )
| ( ( member @ SV21 @ SV26 @ SV4 )
= $true )
| ( ( exists_in_world @ SV26 @ SV4 )
= $false )
| ( ( exists_in_world @ SV21 @ SV4 )
= $false )
| ( ( exists_in_world @ SV13 @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[148]) ).
thf(157,plain,
! [SV27: mu,SV5: $i,SV22: mu,SV14: mu] :
( ( ( ~ ( qmltpeq @ SV14 @ SV22 @ SV5 )
| ~ ( member @ SV27 @ SV14 @ SV5 ) )
= $true )
| ( ( member @ SV27 @ SV22 @ SV5 )
= $true )
| ( ( exists_in_world @ SV27 @ SV5 )
= $false )
| ( ( exists_in_world @ SV22 @ SV5 )
= $false )
| ( ( exists_in_world @ SV14 @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[149]) ).
thf(158,plain,
! [SV28: mu,SV6: $i,SV23: mu,SV15: mu] :
( ( ( ~ ( qmltpeq @ SV15 @ SV23 @ SV6 )
| ~ ( subset @ SV15 @ SV28 @ SV6 ) )
= $true )
| ( ( subset @ SV23 @ SV28 @ SV6 )
= $true )
| ( ( exists_in_world @ SV28 @ SV6 )
= $false )
| ( ( exists_in_world @ SV23 @ SV6 )
= $false )
| ( ( exists_in_world @ SV15 @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[150]) ).
thf(159,plain,
! [SV29: mu,SV7: $i,SV24: mu,SV16: mu] :
( ( ( ~ ( qmltpeq @ SV16 @ SV24 @ SV7 )
| ~ ( subset @ SV29 @ SV16 @ SV7 ) )
= $true )
| ( ( subset @ SV29 @ SV24 @ SV7 )
= $true )
| ( ( exists_in_world @ SV29 @ SV7 )
= $false )
| ( ( exists_in_world @ SV24 @ SV7 )
= $false )
| ( ( exists_in_world @ SV16 @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[151]) ).
thf(160,plain,
! [SV18: mu,SV9: $i,SV31: mu] :
( ( ( ~ ( exists_in_world @ SV31 @ SV9 )
| ~ ( qmltpeq @ SV18 @ SV31 @ SV9 )
| ( subset @ SV18 @ SV31 @ SV9 ) )
= $true )
| ( ( exists_in_world @ SV18 @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(161,plain,
! [SV18: mu,SV9: $i,SV32: mu] :
( ( ( ~ ( exists_in_world @ SV32 @ SV9 )
| ~ ( qmltpeq @ SV18 @ SV32 @ SV9 )
| ( subset @ SV32 @ SV18 @ SV9 ) )
= $true )
| ( ( exists_in_world @ SV18 @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(162,plain,
! [SV9: $i,SV30: mu,SV18: mu] :
( ( ( ~ ( subset @ SV18 @ SV30 @ SV9 )
| ~ ( subset @ SV30 @ SV18 @ SV9 ) )
= $true )
| ( ( qmltpeq @ SV18 @ SV30 @ SV9 )
= $true )
| ( ( exists_in_world @ SV30 @ SV9 )
= $false )
| ( ( exists_in_world @ SV18 @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[154]) ).
thf(163,plain,
! [SV25: mu,SV3: $i,SV20: mu,SV12: mu] :
( ( ( ~ ( qmltpeq @ SV12 @ SV20 @ SV3 ) )
= $true )
| ( ( ~ ( qmltpeq @ SV20 @ SV25 @ SV3 ) )
= $true )
| ( ( qmltpeq @ SV12 @ SV25 @ SV3 )
= $true )
| ( ( exists_in_world @ SV25 @ SV3 )
= $false )
| ( ( exists_in_world @ SV20 @ SV3 )
= $false )
| ( ( exists_in_world @ SV12 @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[155]) ).
thf(164,plain,
! [SV26: mu,SV4: $i,SV21: mu,SV13: mu] :
( ( ( ~ ( qmltpeq @ SV13 @ SV21 @ SV4 ) )
= $true )
| ( ( ~ ( member @ SV13 @ SV26 @ SV4 ) )
= $true )
| ( ( member @ SV21 @ SV26 @ SV4 )
= $true )
| ( ( exists_in_world @ SV26 @ SV4 )
= $false )
| ( ( exists_in_world @ SV21 @ SV4 )
= $false )
| ( ( exists_in_world @ SV13 @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[156]) ).
thf(165,plain,
! [SV27: mu,SV5: $i,SV22: mu,SV14: mu] :
( ( ( ~ ( qmltpeq @ SV14 @ SV22 @ SV5 ) )
= $true )
| ( ( ~ ( member @ SV27 @ SV14 @ SV5 ) )
= $true )
| ( ( member @ SV27 @ SV22 @ SV5 )
= $true )
| ( ( exists_in_world @ SV27 @ SV5 )
= $false )
| ( ( exists_in_world @ SV22 @ SV5 )
= $false )
| ( ( exists_in_world @ SV14 @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[157]) ).
thf(166,plain,
! [SV28: mu,SV6: $i,SV23: mu,SV15: mu] :
( ( ( ~ ( qmltpeq @ SV15 @ SV23 @ SV6 ) )
= $true )
| ( ( ~ ( subset @ SV15 @ SV28 @ SV6 ) )
= $true )
| ( ( subset @ SV23 @ SV28 @ SV6 )
= $true )
| ( ( exists_in_world @ SV28 @ SV6 )
= $false )
| ( ( exists_in_world @ SV23 @ SV6 )
= $false )
| ( ( exists_in_world @ SV15 @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[158]) ).
thf(167,plain,
! [SV29: mu,SV7: $i,SV24: mu,SV16: mu] :
( ( ( ~ ( qmltpeq @ SV16 @ SV24 @ SV7 ) )
= $true )
| ( ( ~ ( subset @ SV29 @ SV16 @ SV7 ) )
= $true )
| ( ( subset @ SV29 @ SV24 @ SV7 )
= $true )
| ( ( exists_in_world @ SV29 @ SV7 )
= $false )
| ( ( exists_in_world @ SV24 @ SV7 )
= $false )
| ( ( exists_in_world @ SV16 @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[159]) ).
thf(168,plain,
! [SV18: mu,SV9: $i,SV31: mu] :
( ( ( ~ ( exists_in_world @ SV31 @ SV9 ) )
= $true )
| ( ( ~ ( qmltpeq @ SV18 @ SV31 @ SV9 )
| ( subset @ SV18 @ SV31 @ SV9 ) )
= $true )
| ( ( exists_in_world @ SV18 @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[160]) ).
thf(169,plain,
! [SV18: mu,SV9: $i,SV32: mu] :
( ( ( ~ ( exists_in_world @ SV32 @ SV9 ) )
= $true )
| ( ( ~ ( qmltpeq @ SV18 @ SV32 @ SV9 )
| ( subset @ SV32 @ SV18 @ SV9 ) )
= $true )
| ( ( exists_in_world @ SV18 @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[161]) ).
thf(170,plain,
! [SV9: $i,SV30: mu,SV18: mu] :
( ( ( ~ ( subset @ SV18 @ SV30 @ SV9 ) )
= $true )
| ( ( ~ ( subset @ SV30 @ SV18 @ SV9 ) )
= $true )
| ( ( qmltpeq @ SV18 @ SV30 @ SV9 )
= $true )
| ( ( exists_in_world @ SV30 @ SV9 )
= $false )
| ( ( exists_in_world @ SV18 @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[162]) ).
thf(171,plain,
! [SV25: mu,SV3: $i,SV20: mu,SV12: mu] :
( ( ( qmltpeq @ SV12 @ SV20 @ SV3 )
= $false )
| ( ( ~ ( qmltpeq @ SV20 @ SV25 @ SV3 ) )
= $true )
| ( ( qmltpeq @ SV12 @ SV25 @ SV3 )
= $true )
| ( ( exists_in_world @ SV25 @ SV3 )
= $false )
| ( ( exists_in_world @ SV20 @ SV3 )
= $false )
| ( ( exists_in_world @ SV12 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[163]) ).
thf(172,plain,
! [SV26: mu,SV4: $i,SV21: mu,SV13: mu] :
( ( ( qmltpeq @ SV13 @ SV21 @ SV4 )
= $false )
| ( ( ~ ( member @ SV13 @ SV26 @ SV4 ) )
= $true )
| ( ( member @ SV21 @ SV26 @ SV4 )
= $true )
| ( ( exists_in_world @ SV26 @ SV4 )
= $false )
| ( ( exists_in_world @ SV21 @ SV4 )
= $false )
| ( ( exists_in_world @ SV13 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(173,plain,
! [SV27: mu,SV5: $i,SV22: mu,SV14: mu] :
( ( ( qmltpeq @ SV14 @ SV22 @ SV5 )
= $false )
| ( ( ~ ( member @ SV27 @ SV14 @ SV5 ) )
= $true )
| ( ( member @ SV27 @ SV22 @ SV5 )
= $true )
| ( ( exists_in_world @ SV27 @ SV5 )
= $false )
| ( ( exists_in_world @ SV22 @ SV5 )
= $false )
| ( ( exists_in_world @ SV14 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[165]) ).
thf(174,plain,
! [SV28: mu,SV6: $i,SV23: mu,SV15: mu] :
( ( ( qmltpeq @ SV15 @ SV23 @ SV6 )
= $false )
| ( ( ~ ( subset @ SV15 @ SV28 @ SV6 ) )
= $true )
| ( ( subset @ SV23 @ SV28 @ SV6 )
= $true )
| ( ( exists_in_world @ SV28 @ SV6 )
= $false )
| ( ( exists_in_world @ SV23 @ SV6 )
= $false )
| ( ( exists_in_world @ SV15 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(175,plain,
! [SV29: mu,SV7: $i,SV24: mu,SV16: mu] :
( ( ( qmltpeq @ SV16 @ SV24 @ SV7 )
= $false )
| ( ( ~ ( subset @ SV29 @ SV16 @ SV7 ) )
= $true )
| ( ( subset @ SV29 @ SV24 @ SV7 )
= $true )
| ( ( exists_in_world @ SV29 @ SV7 )
= $false )
| ( ( exists_in_world @ SV24 @ SV7 )
= $false )
| ( ( exists_in_world @ SV16 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(176,plain,
! [SV18: mu,SV9: $i,SV31: mu] :
( ( ( exists_in_world @ SV31 @ SV9 )
= $false )
| ( ( ~ ( qmltpeq @ SV18 @ SV31 @ SV9 )
| ( subset @ SV18 @ SV31 @ SV9 ) )
= $true )
| ( ( exists_in_world @ SV18 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[168]) ).
thf(177,plain,
! [SV18: mu,SV9: $i,SV32: mu] :
( ( ( exists_in_world @ SV32 @ SV9 )
= $false )
| ( ( ~ ( qmltpeq @ SV18 @ SV32 @ SV9 )
| ( subset @ SV32 @ SV18 @ SV9 ) )
= $true )
| ( ( exists_in_world @ SV18 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(178,plain,
! [SV9: $i,SV30: mu,SV18: mu] :
( ( ( subset @ SV18 @ SV30 @ SV9 )
= $false )
| ( ( ~ ( subset @ SV30 @ SV18 @ SV9 ) )
= $true )
| ( ( qmltpeq @ SV18 @ SV30 @ SV9 )
= $true )
| ( ( exists_in_world @ SV30 @ SV9 )
= $false )
| ( ( exists_in_world @ SV18 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(179,plain,
! [SV12: mu,SV3: $i,SV25: mu,SV20: mu] :
( ( ( qmltpeq @ SV20 @ SV25 @ SV3 )
= $false )
| ( ( qmltpeq @ SV12 @ SV20 @ SV3 )
= $false )
| ( ( qmltpeq @ SV12 @ SV25 @ SV3 )
= $true )
| ( ( exists_in_world @ SV25 @ SV3 )
= $false )
| ( ( exists_in_world @ SV20 @ SV3 )
= $false )
| ( ( exists_in_world @ SV12 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(180,plain,
! [SV21: mu,SV4: $i,SV26: mu,SV13: mu] :
( ( ( member @ SV13 @ SV26 @ SV4 )
= $false )
| ( ( qmltpeq @ SV13 @ SV21 @ SV4 )
= $false )
| ( ( member @ SV21 @ SV26 @ SV4 )
= $true )
| ( ( exists_in_world @ SV26 @ SV4 )
= $false )
| ( ( exists_in_world @ SV21 @ SV4 )
= $false )
| ( ( exists_in_world @ SV13 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(181,plain,
! [SV22: mu,SV5: $i,SV14: mu,SV27: mu] :
( ( ( member @ SV27 @ SV14 @ SV5 )
= $false )
| ( ( qmltpeq @ SV14 @ SV22 @ SV5 )
= $false )
| ( ( member @ SV27 @ SV22 @ SV5 )
= $true )
| ( ( exists_in_world @ SV27 @ SV5 )
= $false )
| ( ( exists_in_world @ SV22 @ SV5 )
= $false )
| ( ( exists_in_world @ SV14 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[173]) ).
thf(182,plain,
! [SV23: mu,SV6: $i,SV28: mu,SV15: mu] :
( ( ( subset @ SV15 @ SV28 @ SV6 )
= $false )
| ( ( qmltpeq @ SV15 @ SV23 @ SV6 )
= $false )
| ( ( subset @ SV23 @ SV28 @ SV6 )
= $true )
| ( ( exists_in_world @ SV28 @ SV6 )
= $false )
| ( ( exists_in_world @ SV23 @ SV6 )
= $false )
| ( ( exists_in_world @ SV15 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[174]) ).
thf(183,plain,
! [SV24: mu,SV7: $i,SV16: mu,SV29: mu] :
( ( ( subset @ SV29 @ SV16 @ SV7 )
= $false )
| ( ( qmltpeq @ SV16 @ SV24 @ SV7 )
= $false )
| ( ( subset @ SV29 @ SV24 @ SV7 )
= $true )
| ( ( exists_in_world @ SV29 @ SV7 )
= $false )
| ( ( exists_in_world @ SV24 @ SV7 )
= $false )
| ( ( exists_in_world @ SV16 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[175]) ).
thf(184,plain,
! [SV9: $i,SV31: mu,SV18: mu] :
( ( ( ~ ( qmltpeq @ SV18 @ SV31 @ SV9 ) )
= $true )
| ( ( subset @ SV18 @ SV31 @ SV9 )
= $true )
| ( ( exists_in_world @ SV31 @ SV9 )
= $false )
| ( ( exists_in_world @ SV18 @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[176]) ).
thf(185,plain,
! [SV9: $i,SV32: mu,SV18: mu] :
( ( ( ~ ( qmltpeq @ SV18 @ SV32 @ SV9 ) )
= $true )
| ( ( subset @ SV32 @ SV18 @ SV9 )
= $true )
| ( ( exists_in_world @ SV32 @ SV9 )
= $false )
| ( ( exists_in_world @ SV18 @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[177]) ).
thf(186,plain,
! [SV9: $i,SV18: mu,SV30: mu] :
( ( ( subset @ SV30 @ SV18 @ SV9 )
= $false )
| ( ( subset @ SV18 @ SV30 @ SV9 )
= $false )
| ( ( qmltpeq @ SV18 @ SV30 @ SV9 )
= $true )
| ( ( exists_in_world @ SV30 @ SV9 )
= $false )
| ( ( exists_in_world @ SV18 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(187,plain,
! [SV9: $i,SV31: mu,SV18: mu] :
( ( ( qmltpeq @ SV18 @ SV31 @ SV9 )
= $false )
| ( ( subset @ SV18 @ SV31 @ SV9 )
= $true )
| ( ( exists_in_world @ SV31 @ SV9 )
= $false )
| ( ( exists_in_world @ SV18 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[184]) ).
thf(188,plain,
! [SV9: $i,SV32: mu,SV18: mu] :
( ( ( qmltpeq @ SV18 @ SV32 @ SV9 )
= $false )
| ( ( subset @ SV32 @ SV18 @ SV9 )
= $true )
| ( ( exists_in_world @ SV32 @ SV9 )
= $false )
| ( ( exists_in_world @ SV18 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[185]) ).
thf(189,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[51,188,187,186,183,182,181,180,179,146,145,136,125,94,87,85]) ).
thf(190,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[189]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET583^7 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.16 % Computer : n016.cluster.edu
% 0.08/0.16 % Model : x86_64 x86_64
% 0.08/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.16 % Memory : 8046.5625MB
% 0.08/0.16 % OS : Linux 6.8.0-71-generic
% 0.08/0.16 % CPULimit : 300
% 0.08/0.16 % WCLimit : 300
% 0.08/0.16 % DateTime : Tue Oct 6 14:51:29 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.25
% 0.08/0.25 No.of.Axioms: 14
% 0.08/0.25
% 0.08/0.25 Length.of.Defs: 5508
% 0.08/0.25
% 0.08/0.25 Contains.Choice.Funs: false
% 0.08/0.25 ............
% 0.08/0.25
% 0.08/0.25 ********************************
% 0.08/0.25 * All subproblems solved! *
% 0.08/0.25 ********************************
% 0.08/0.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:10,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:189,loop_count:0,foatp_calls:1,translation:fof_experiment)
% 0.08/0.25
% 0.08/0.25 %**** Beginning of derivation protocol ****
% 0.08/0.25 % SZS output start CNFRefutation
% See solution above
% 0.08/0.25
% 0.08/0.25 %**** End of derivation protocol ****
% 0.08/0.25 %**** no. of clauses in derivation: 185 ****
% 0.08/0.25 %**** clause counter: 189 ****
% 0.08/0.25
% 0.08/0.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:10,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:189,loop_count:0,foatp_calls:1,translation:fof_experiment)
%------------------------------------------------------------------------------