%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : NLP264^7 : 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 : n003.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 10:32:43 AM UTC 2026
% Result : Theorem 0.07s 0.25s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 48
% Syntax : Number of formulae : 167 ( 111 unt; 0 typ; 32 def)
% Number of atoms : 837 ( 230 equ; 0 cnn)
% Maximal formula atoms : 7 ( 5 avg)
% Number of connectives : 1217 ( 242 ~; 179 |; 13 &; 769 @)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 59 ( 59 >; 0 *; 0 +; 0 <<)
% Number of symbols : 49 ( 46 usr; 9 con; 0-3 aty)
% Number of variables : 316 ( 49 ^; 258 !; 9 ?; 316 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_mu,type,
mu: $tType ).
thf(tp_class,type,
class: mu > $i > $o ).
thf(tp_dest,type,
dest: mu > $i > $o ).
thf(tp_exists_in_world,type,
exists_in_world: mu > $i > $o ).
thf(tp_first,type,
first: mu ).
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_ninetyfive,type,
ninetyfive: mu ).
thf(tp_paris,type,
paris: mu ).
thf(tp_price,type,
price: mu > $i > $o ).
thf(tp_qmltpeq,type,
qmltpeq: mu > mu > $i > $o ).
thf(tp_rel_s4,type,
rel_s4: $i > $i > $o ).
thf(tp_sK1_SY2,type,
sK1_SY2: $i ).
thf(tp_sK2_SY106,type,
sK2_SY106: $i ).
thf(tp_sK3_SY115,type,
sK3_SY115: $i > mu ).
thf(tp_second,type,
second: mu ).
thf(tp_seventy,type,
seventy: mu ).
thf(mand,definition,
( mand
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mor @ ( mnot @ Phi ) @ ( mnot @ Psi ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mand) ).
thf(mbox,definition,
( mbox
= ( ^ [R: $i > $i > $o,Phi: $i > $o,W: $i] :
! [V: $i] :
( ~ ( R @ W @ V )
| ( Phi @ V ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox) ).
thf(mbox_s4,definition,
( mbox_s4
= ( ^ [Phi: $i > $o,W: $i] :
! [V: $i] :
( ~ ( rel_s4 @ W @ V )
| ( Phi @ V ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_s4) ).
thf(mcountersatisfiable,definition,
( mcountersatisfiable
= ( ^ [Phi: $i > $o] :
? [W: $i] :
~ ( Phi @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mcountersatisfiable) ).
thf(mdia,definition,
( mdia
= ( ^ [R: $i > $i > $o,Phi: $i > $o] : ( mnot @ ( mbox @ R @ ( mnot @ Phi ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mdia) ).
thf(mdia_s4,definition,
( mdia_s4
= ( ^ [Phi: $i > $o] : ( mnot @ ( mbox_s4 @ ( mnot @ Phi ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mdia_s4) ).
thf(meq_prop,definition,
( meq_prop
= ( ^ [X: $i > $o,Y: $i > $o,W: $i] :
( ( X @ W )
= ( Y @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',meq_prop) ).
thf(mequiv,definition,
( mequiv
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mand @ ( mimplies @ Phi @ Psi ) @ ( mimplies @ Psi @ Phi ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mequiv) ).
thf(meuclidean,definition,
( meuclidean
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ S @ U ) )
=> ( R @ T @ U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',meuclidean) ).
thf(mexists_ind,definition,
( mexists_ind
= ( ^ [Phi: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X: mu] : ( mnot @ ( Phi @ X ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mexists_ind) ).
thf(mexists_prop,definition,
( mexists_prop
= ( ^ [Phi: ( $i > $o ) > $i > $o] :
( mnot
@ ( mforall_prop
@ ^ [P: $i > $o] : ( mnot @ ( Phi @ P ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mexists_prop) ).
thf(mfalse,definition,
( mfalse
= ( mnot @ mtrue ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mfalse) ).
thf(mforall_ind,definition,
( mforall_ind
= ( ^ [Phi: mu > $i > $o,W: $i] :
! [X: mu] :
( ( exists_in_world @ X @ W )
=> ( Phi @ X @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mforall_ind) ).
thf(mforall_prop,definition,
( mforall_prop
= ( ^ [Phi: ( $i > $o ) > $i > $o,W: $i] :
! [P: $i > $o] : ( Phi @ P @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mforall_prop) ).
thf(mfunctional,definition,
( mfunctional
= ( ^ [R: $i > $i > $o] :
! [S: $i] :
? [T: $i] :
( ( R @ S @ T )
& ! [U: $i] :
( ( R @ S @ U )
=> ( T = U ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mfunctional) ).
thf(mimplied,definition,
( mimplied
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Psi ) @ Phi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplied) ).
thf(mimplies,definition,
( mimplies
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Phi ) @ Psi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies) ).
thf(minvalid,definition,
( minvalid
= ( ^ [Phi: $i > $o] :
! [W: $i] :
~ ( Phi @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',minvalid) ).
thf(mnot,definition,
( mnot
= ( ^ [Phi: $i > $o,W: $i] :
~ ( Phi @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot) ).
thf(mor,definition,
( mor
= ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
( ( Phi @ W )
| ( Psi @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor) ).
thf(mpartially_functional,definition,
( mpartially_functional
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ S @ U ) )
=> ( T = U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mpartially_functional) ).
thf(mreflexive,definition,
( mreflexive
= ( ^ [R: $i > $i > $o] :
! [S: $i] : ( R @ S @ S ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mreflexive) ).
thf(msatisfiable,definition,
( msatisfiable
= ( ^ [Phi: $i > $o] :
? [W: $i] : ( Phi @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',msatisfiable) ).
thf(mserial,definition,
( mserial
= ( ^ [R: $i > $i > $o] :
! [S: $i] :
? [T: $i] : ( R @ S @ T ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mserial) ).
thf(msymmetric,definition,
( msymmetric
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i] :
( ( R @ S @ T )
=> ( R @ T @ S ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',msymmetric) ).
thf(mtransitive,definition,
( mtransitive
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ T @ U ) )
=> ( R @ S @ U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mtransitive) ).
thf(mtrue,definition,
( mtrue
= ( ^ [W: $i] : $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mtrue) ).
thf(mvalid,definition,
( mvalid
= ( ^ [Phi: $i > $o] :
! [W: $i] : ( Phi @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mvalid) ).
thf(mweakly_connected,definition,
( mweakly_connected
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ S @ U ) )
=> ( ( R @ T @ U )
| ( T = U )
| ( R @ U @ T ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mweakly_connected) ).
thf(mweakly_dense,definition,
( mweakly_dense
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( R @ S @ T )
=> ? [U: $i] :
( ( R @ S @ U )
& ( R @ U @ T ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mweakly_dense) ).
thf(mweakly_directed,definition,
( mweakly_directed
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ S @ U ) )
=> ? [V: $i] :
( ( R @ T @ V )
& ( R @ U @ V ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mweakly_directed) ).
thf(mxor,definition,
( mxor
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mequiv @ Phi @ Psi ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mxor) ).
thf(1,axiom,
mvalid @ ( mbox_s4 @ ( class @ second ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',belief2) ).
thf(2,axiom,
mvalid @ ( mbox_s4 @ ( dest @ paris ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',belief1) ).
thf(3,axiom,
mvalid @ ( mbox_s4 @ ( mnot @ ( mand @ ( price @ ninetyfive ) @ ( price @ seventy ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',law4) ).
thf(4,axiom,
mvalid @ ( mbox_s4 @ ( mnot @ ( mand @ ( class @ first ) @ ( class @ second ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',law3) ).
thf(5,axiom,
mvalid @ ( mbox_s4 @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ second ) ) @ ( price @ seventy ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',law2) ).
thf(6,axiom,
mvalid @ ( mbox_s4 @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ first ) ) @ ( price @ ninetyfive ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',law1) ).
thf(7,axiom,
! [V: $i] : ( exists_in_world @ seventy @ V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_seventy_ax) ).
thf(8,axiom,
! [V: $i] : ( exists_in_world @ second @ V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_second_ax) ).
thf(9,axiom,
! [V: $i] : ( exists_in_world @ paris @ V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_paris_ax) ).
thf(10,axiom,
! [V: $i] : ( exists_in_world @ ninetyfive @ V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_ninetyfive_ax) ).
thf(11,axiom,
! [V: $i] : ( exists_in_world @ first @ V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_first_ax) ).
thf(12,axiom,
! [X: mu,V: $i,W: $i] :
( ( ( exists_in_world @ X @ V )
& ( rel_s4 @ V @ W ) )
=> ( exists_in_world @ X @ W ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cumulative_ax) ).
thf(13,axiom,
mtransitive @ rel_s4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2) ).
thf(14,axiom,
mreflexive @ rel_s4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1) ).
thf(15,axiom,
! [V: $i] :
? [X: mu] : ( exists_in_world @ X @ V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonempty_ax) ).
thf(16,conjecture,
mvalid @ ( mbox_s4 @ ( price @ seventy ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(17,negated_conjecture,
( ( mvalid @ ( mbox_s4 @ ( price @ seventy ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[16]) ).
thf(18,plain,
( ( ! [SY2: $i,SY3: $i] :
( ~ ( rel_s4 @ SY2 @ SY3 )
| ( price @ seventy @ SY3 ) ) )
= $false ),
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(19,plain,
( ( ! [SY8: $i,SY9: $i] :
( ~ ( rel_s4 @ SY8 @ SY9 )
| ( class @ second @ SY9 ) ) )
= $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(20,plain,
( ( ! [SY14: $i,SY15: $i] :
( ~ ( rel_s4 @ SY14 @ SY15 )
| ( dest @ paris @ SY15 ) ) )
= $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(21,plain,
( ( ! [SY29: $i,SY30: $i] :
( ~ ( rel_s4 @ SY29 @ SY30 )
| ~ ~ ( ~ ( price @ ninetyfive @ SY30 )
| ~ ( price @ seventy @ SY30 ) ) ) )
= $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(22,plain,
( ( ! [SY44: $i,SY45: $i] :
( ~ ( rel_s4 @ SY44 @ SY45 )
| ~ ~ ( ~ ( class @ first @ SY45 )
| ~ ( class @ second @ SY45 ) ) ) )
= $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(23,plain,
( ( ! [SY64: $i,SY65: $i] :
( ~ ( rel_s4 @ SY64 @ SY65 )
| ~ ~ ( ~ ( dest @ paris @ SY65 )
| ~ ( class @ second @ SY65 ) )
| ( price @ seventy @ SY65 ) ) )
= $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(24,plain,
( ( ! [SY84: $i,SY85: $i] :
( ~ ( rel_s4 @ SY84 @ SY85 )
| ~ ~ ( ~ ( dest @ paris @ SY85 )
| ~ ( class @ first @ SY85 ) )
| ( price @ ninetyfive @ SY85 ) ) )
= $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(25,plain,
( ( ! [V: $i] : ( exists_in_world @ seventy @ V ) )
= $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(26,plain,
( ( ! [V: $i] : ( exists_in_world @ second @ V ) )
= $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(27,plain,
( ( ! [V: $i] : ( exists_in_world @ paris @ V ) )
= $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(28,plain,
( ( ! [V: $i] : ( exists_in_world @ ninetyfive @ V ) )
= $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(29,plain,
( ( ! [V: $i] : ( exists_in_world @ first @ V ) )
= $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(30,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)],[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(31,plain,
( ( ! [SY96: $i,SY97: $i,SY98: $i] :
( ( ( rel_s4 @ SY96 @ SY97 )
& ( rel_s4 @ SY97 @ SY98 ) )
=> ( rel_s4 @ SY96 @ SY98 ) ) )
= $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(32,plain,
( ( ! [SY102: $i] : ( rel_s4 @ SY102 @ SY102 ) )
= $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(33,plain,
( ( ! [V: $i] :
? [X: mu] : ( exists_in_world @ X @ V ) )
= $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(34,plain,
( ( ! [SY106: $i] :
( ~ ( rel_s4 @ sK1_SY2 @ SY106 )
| ( price @ seventy @ SY106 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[18]) ).
thf(35,plain,
( ( ~ ( rel_s4 @ sK1_SY2 @ sK2_SY106 )
| ( price @ seventy @ sK2_SY106 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[34]) ).
thf(36,plain,
( ( ~ ( ~ ( rel_s4 @ sK1_SY2 @ sK2_SY106 )
| ( price @ seventy @ sK2_SY106 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[35]) ).
thf(37,plain,
( ( ! [V: $i] :
? [X: mu] : ( exists_in_world @ X @ V ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(38,plain,
( ( ! [SY102: $i] : ( rel_s4 @ SY102 @ SY102 ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(39,plain,
( ( ! [SY96: $i,SY97: $i,SY98: $i] :
( ( ( rel_s4 @ SY96 @ SY97 )
& ( rel_s4 @ SY97 @ SY98 ) )
=> ( rel_s4 @ SY96 @ SY98 ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(40,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)],[30]) ).
thf(41,plain,
( ( ! [V: $i] : ( exists_in_world @ first @ V ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(42,plain,
( ( ! [V: $i] : ( exists_in_world @ ninetyfive @ V ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(43,plain,
( ( ! [V: $i] : ( exists_in_world @ paris @ V ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(44,plain,
( ( ! [V: $i] : ( exists_in_world @ second @ V ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(45,plain,
( ( ! [V: $i] : ( exists_in_world @ seventy @ V ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(46,plain,
( ( ! [SY84: $i,SY85: $i] :
( ~ ( rel_s4 @ SY84 @ SY85 )
| ~ ~ ( ~ ( dest @ paris @ SY85 )
| ~ ( class @ first @ SY85 ) )
| ( price @ ninetyfive @ SY85 ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(47,plain,
( ( ! [SY64: $i,SY65: $i] :
( ~ ( rel_s4 @ SY64 @ SY65 )
| ~ ~ ( ~ ( dest @ paris @ SY65 )
| ~ ( class @ second @ SY65 ) )
| ( price @ seventy @ SY65 ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(48,plain,
( ( ! [SY44: $i,SY45: $i] :
( ~ ( rel_s4 @ SY44 @ SY45 )
| ~ ~ ( ~ ( class @ first @ SY45 )
| ~ ( class @ second @ SY45 ) ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(49,plain,
( ( ! [SY29: $i,SY30: $i] :
( ~ ( rel_s4 @ SY29 @ SY30 )
| ~ ~ ( ~ ( price @ ninetyfive @ SY30 )
| ~ ( price @ seventy @ SY30 ) ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(50,plain,
( ( ! [SY14: $i,SY15: $i] :
( ~ ( rel_s4 @ SY14 @ SY15 )
| ( dest @ paris @ SY15 ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(51,plain,
( ( ! [SY8: $i,SY9: $i] :
( ~ ( rel_s4 @ SY8 @ SY9 )
| ( class @ second @ SY9 ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(52,plain,
( ( ~ ( ~ ( rel_s4 @ sK1_SY2 @ sK2_SY106 )
| ( price @ seventy @ sK2_SY106 ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(53,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)],[39,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(54,plain,
( ( ! [SX0: $i] :
~ ! [SX1: mu] :
~ ( exists_in_world @ SX1 @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[37,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(55,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)],[40,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(56,plain,
! [SV1: $i] :
( ( rel_s4 @ SV1 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(57,plain,
! [SV2: $i] :
( ( exists_in_world @ first @ SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(58,plain,
! [SV3: $i] :
( ( exists_in_world @ ninetyfive @ SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(59,plain,
! [SV4: $i] :
( ( exists_in_world @ paris @ SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(60,plain,
! [SV5: $i] :
( ( exists_in_world @ second @ SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(61,plain,
! [SV6: $i] :
( ( exists_in_world @ seventy @ SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(62,plain,
! [SV7: $i] :
( ( ! [SY107: $i] :
( ~ ( rel_s4 @ SV7 @ SY107 )
| ~ ~ ( ~ ( dest @ paris @ SY107 )
| ~ ( class @ first @ SY107 ) )
| ( price @ ninetyfive @ SY107 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(63,plain,
! [SV8: $i] :
( ( ! [SY108: $i] :
( ~ ( rel_s4 @ SV8 @ SY108 )
| ~ ~ ( ~ ( dest @ paris @ SY108 )
| ~ ( class @ second @ SY108 ) )
| ( price @ seventy @ SY108 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(64,plain,
! [SV9: $i] :
( ( ! [SY109: $i] :
( ~ ( rel_s4 @ SV9 @ SY109 )
| ~ ~ ( ~ ( class @ first @ SY109 )
| ~ ( class @ second @ SY109 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(65,plain,
! [SV10: $i] :
( ( ! [SY110: $i] :
( ~ ( rel_s4 @ SV10 @ SY110 )
| ~ ~ ( ~ ( price @ ninetyfive @ SY110 )
| ~ ( price @ seventy @ SY110 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(66,plain,
! [SV11: $i] :
( ( ! [SY111: $i] :
( ~ ( rel_s4 @ SV11 @ SY111 )
| ( dest @ paris @ SY111 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(67,plain,
! [SV12: $i] :
( ( ! [SY112: $i] :
( ~ ( rel_s4 @ SV12 @ SY112 )
| ( class @ second @ SY112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(68,plain,
( ( ~ ( rel_s4 @ sK1_SY2 @ sK2_SY106 )
| ( price @ seventy @ sK2_SY106 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(69,plain,
! [SV13: $i] :
( ( ! [SY113: $i,SY114: $i] :
( ~ ~ ( ~ ( rel_s4 @ SV13 @ SY113 )
| ~ ( rel_s4 @ SY113 @ SY114 ) )
| ( rel_s4 @ SV13 @ SY114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(70,plain,
! [SV14: $i] :
( ( ~ ! [SY115: mu] :
~ ( exists_in_world @ SY115 @ SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(71,plain,
! [SV15: mu] :
( ( ! [SY116: $i,SY117: $i] :
( ~ ~ ( ~ ( exists_in_world @ SV15 @ SY116 )
| ~ ( rel_s4 @ SY116 @ SY117 ) )
| ( exists_in_world @ SV15 @ SY117 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(72,plain,
! [SV16: $i,SV7: $i] :
( ( ~ ( rel_s4 @ SV7 @ SV16 )
| ~ ~ ( ~ ( dest @ paris @ SV16 )
| ~ ( class @ first @ SV16 ) )
| ( price @ ninetyfive @ SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(73,plain,
! [SV17: $i,SV8: $i] :
( ( ~ ( rel_s4 @ SV8 @ SV17 )
| ~ ~ ( ~ ( dest @ paris @ SV17 )
| ~ ( class @ second @ SV17 ) )
| ( price @ seventy @ SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(74,plain,
! [SV18: $i,SV9: $i] :
( ( ~ ( rel_s4 @ SV9 @ SV18 )
| ~ ~ ( ~ ( class @ first @ SV18 )
| ~ ( class @ second @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(75,plain,
! [SV19: $i,SV10: $i] :
( ( ~ ( rel_s4 @ SV10 @ SV19 )
| ~ ~ ( ~ ( price @ ninetyfive @ SV19 )
| ~ ( price @ seventy @ SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(76,plain,
! [SV20: $i,SV11: $i] :
( ( ~ ( rel_s4 @ SV11 @ SV20 )
| ( dest @ paris @ SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(77,plain,
! [SV21: $i,SV12: $i] :
( ( ~ ( rel_s4 @ SV12 @ SV21 )
| ( class @ second @ SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(78,plain,
( ( ~ ( rel_s4 @ sK1_SY2 @ sK2_SY106 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[68]) ).
thf(79,plain,
( ( price @ seventy @ sK2_SY106 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[68]) ).
thf(80,plain,
! [SV22: $i,SV13: $i] :
( ( ! [SY118: $i] :
( ~ ~ ( ~ ( rel_s4 @ SV13 @ SV22 )
| ~ ( rel_s4 @ SV22 @ SY118 ) )
| ( rel_s4 @ SV13 @ SY118 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(81,plain,
! [SV14: $i] :
( ( ! [SY115: mu] :
~ ( exists_in_world @ SY115 @ SV14 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(82,plain,
! [SV23: $i,SV15: mu] :
( ( ! [SY119: $i] :
( ~ ~ ( ~ ( exists_in_world @ SV15 @ SV23 )
| ~ ( rel_s4 @ SV23 @ SY119 ) )
| ( exists_in_world @ SV15 @ SY119 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(83,plain,
! [SV16: $i,SV7: $i] :
( ( ( ~ ( rel_s4 @ SV7 @ SV16 ) )
= $true )
| ( ( ~ ~ ( ~ ( dest @ paris @ SV16 )
| ~ ( class @ first @ SV16 ) )
| ( price @ ninetyfive @ SV16 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[72]) ).
thf(84,plain,
! [SV17: $i,SV8: $i] :
( ( ( ~ ( rel_s4 @ SV8 @ SV17 ) )
= $true )
| ( ( ~ ~ ( ~ ( dest @ paris @ SV17 )
| ~ ( class @ second @ SV17 ) )
| ( price @ seventy @ SV17 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[73]) ).
thf(85,plain,
! [SV18: $i,SV9: $i] :
( ( ( ~ ( rel_s4 @ SV9 @ SV18 ) )
= $true )
| ( ( ~ ~ ( ~ ( class @ first @ SV18 )
| ~ ( class @ second @ SV18 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[74]) ).
thf(86,plain,
! [SV19: $i,SV10: $i] :
( ( ( ~ ( rel_s4 @ SV10 @ SV19 ) )
= $true )
| ( ( ~ ~ ( ~ ( price @ ninetyfive @ SV19 )
| ~ ( price @ seventy @ SV19 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[75]) ).
thf(87,plain,
! [SV20: $i,SV11: $i] :
( ( ( ~ ( rel_s4 @ SV11 @ SV20 ) )
= $true )
| ( ( dest @ paris @ SV20 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[76]) ).
thf(88,plain,
! [SV21: $i,SV12: $i] :
( ( ( ~ ( rel_s4 @ SV12 @ SV21 ) )
= $true )
| ( ( class @ second @ SV21 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[77]) ).
thf(89,plain,
( ( rel_s4 @ sK1_SY2 @ sK2_SY106 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[78]) ).
thf(90,plain,
! [SV24: $i,SV22: $i,SV13: $i] :
( ( ~ ~ ( ~ ( rel_s4 @ SV13 @ SV22 )
| ~ ( rel_s4 @ SV22 @ SV24 ) )
| ( rel_s4 @ SV13 @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(91,plain,
! [SV14: $i] :
( ( ~ ( exists_in_world @ ( sK3_SY115 @ SV14 ) @ SV14 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[81]) ).
thf(92,plain,
! [SV25: $i,SV23: $i,SV15: mu] :
( ( ~ ~ ( ~ ( exists_in_world @ SV15 @ SV23 )
| ~ ( rel_s4 @ SV23 @ SV25 ) )
| ( exists_in_world @ SV15 @ SV25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(93,plain,
! [SV16: $i,SV7: $i] :
( ( ( rel_s4 @ SV7 @ SV16 )
= $false )
| ( ( ~ ~ ( ~ ( dest @ paris @ SV16 )
| ~ ( class @ first @ SV16 ) )
| ( price @ ninetyfive @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[83]) ).
thf(94,plain,
! [SV17: $i,SV8: $i] :
( ( ( rel_s4 @ SV8 @ SV17 )
= $false )
| ( ( ~ ~ ( ~ ( dest @ paris @ SV17 )
| ~ ( class @ second @ SV17 ) )
| ( price @ seventy @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[84]) ).
thf(95,plain,
! [SV18: $i,SV9: $i] :
( ( ( rel_s4 @ SV9 @ SV18 )
= $false )
| ( ( ~ ~ ( ~ ( class @ first @ SV18 )
| ~ ( class @ second @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[85]) ).
thf(96,plain,
! [SV19: $i,SV10: $i] :
( ( ( rel_s4 @ SV10 @ SV19 )
= $false )
| ( ( ~ ~ ( ~ ( price @ ninetyfive @ SV19 )
| ~ ( price @ seventy @ SV19 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(97,plain,
! [SV20: $i,SV11: $i] :
( ( ( rel_s4 @ SV11 @ SV20 )
= $false )
| ( ( dest @ paris @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[87]) ).
thf(98,plain,
! [SV21: $i,SV12: $i] :
( ( ( rel_s4 @ SV12 @ SV21 )
= $false )
| ( ( class @ second @ SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(99,plain,
! [SV24: $i,SV22: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ( rel_s4 @ SV13 @ SV22 )
| ~ ( rel_s4 @ SV22 @ SV24 ) ) )
= $true )
| ( ( rel_s4 @ SV13 @ SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[90]) ).
thf(100,plain,
! [SV14: $i] :
( ( exists_in_world @ ( sK3_SY115 @ SV14 ) @ SV14 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[91]) ).
thf(101,plain,
! [SV25: $i,SV23: $i,SV15: mu] :
( ( ( ~ ~ ( ~ ( exists_in_world @ SV15 @ SV23 )
| ~ ( rel_s4 @ SV23 @ SV25 ) ) )
= $true )
| ( ( exists_in_world @ SV15 @ SV25 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[92]) ).
thf(102,plain,
! [SV7: $i,SV16: $i] :
( ( ( ~ ~ ( ~ ( dest @ paris @ SV16 )
| ~ ( class @ first @ SV16 ) ) )
= $true )
| ( ( price @ ninetyfive @ SV16 )
= $true )
| ( ( rel_s4 @ SV7 @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[93]) ).
thf(103,plain,
! [SV8: $i,SV17: $i] :
( ( ( ~ ~ ( ~ ( dest @ paris @ SV17 )
| ~ ( class @ second @ SV17 ) ) )
= $true )
| ( ( price @ seventy @ SV17 )
= $true )
| ( ( rel_s4 @ SV8 @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(104,plain,
! [SV9: $i,SV18: $i] :
( ( ( ~ ( ~ ( class @ first @ SV18 )
| ~ ( class @ second @ SV18 ) ) )
= $false )
| ( ( rel_s4 @ SV9 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(105,plain,
! [SV10: $i,SV19: $i] :
( ( ( ~ ( ~ ( price @ ninetyfive @ SV19 )
| ~ ( price @ seventy @ SV19 ) ) )
= $false )
| ( ( rel_s4 @ SV10 @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(106,plain,
! [SV24: $i,SV22: $i,SV13: $i] :
( ( ( ~ ( ~ ( rel_s4 @ SV13 @ SV22 )
| ~ ( rel_s4 @ SV22 @ SV24 ) ) )
= $false )
| ( ( rel_s4 @ SV13 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(107,plain,
! [SV25: $i,SV23: $i,SV15: mu] :
( ( ( ~ ( ~ ( exists_in_world @ SV15 @ SV23 )
| ~ ( rel_s4 @ SV23 @ SV25 ) ) )
= $false )
| ( ( exists_in_world @ SV15 @ SV25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(108,plain,
! [SV7: $i,SV16: $i] :
( ( ( ~ ( ~ ( dest @ paris @ SV16 )
| ~ ( class @ first @ SV16 ) ) )
= $false )
| ( ( price @ ninetyfive @ SV16 )
= $true )
| ( ( rel_s4 @ SV7 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(109,plain,
! [SV8: $i,SV17: $i] :
( ( ( ~ ( ~ ( dest @ paris @ SV17 )
| ~ ( class @ second @ SV17 ) ) )
= $false )
| ( ( price @ seventy @ SV17 )
= $true )
| ( ( rel_s4 @ SV8 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(110,plain,
! [SV9: $i,SV18: $i] :
( ( ( ~ ( class @ first @ SV18 )
| ~ ( class @ second @ SV18 ) )
= $true )
| ( ( rel_s4 @ SV9 @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[104]) ).
thf(111,plain,
! [SV10: $i,SV19: $i] :
( ( ( ~ ( price @ ninetyfive @ SV19 )
| ~ ( price @ seventy @ SV19 ) )
= $true )
| ( ( rel_s4 @ SV10 @ SV19 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[105]) ).
thf(112,plain,
! [SV24: $i,SV22: $i,SV13: $i] :
( ( ( ~ ( rel_s4 @ SV13 @ SV22 )
| ~ ( rel_s4 @ SV22 @ SV24 ) )
= $true )
| ( ( rel_s4 @ SV13 @ SV24 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[106]) ).
thf(113,plain,
! [SV25: $i,SV23: $i,SV15: mu] :
( ( ( ~ ( exists_in_world @ SV15 @ SV23 )
| ~ ( rel_s4 @ SV23 @ SV25 ) )
= $true )
| ( ( exists_in_world @ SV15 @ SV25 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[107]) ).
thf(114,plain,
! [SV7: $i,SV16: $i] :
( ( ( ~ ( dest @ paris @ SV16 )
| ~ ( class @ first @ SV16 ) )
= $true )
| ( ( price @ ninetyfive @ SV16 )
= $true )
| ( ( rel_s4 @ SV7 @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[108]) ).
thf(115,plain,
! [SV8: $i,SV17: $i] :
( ( ( ~ ( dest @ paris @ SV17 )
| ~ ( class @ second @ SV17 ) )
= $true )
| ( ( price @ seventy @ SV17 )
= $true )
| ( ( rel_s4 @ SV8 @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[109]) ).
thf(116,plain,
! [SV9: $i,SV18: $i] :
( ( ( ~ ( class @ first @ SV18 ) )
= $true )
| ( ( ~ ( class @ second @ SV18 ) )
= $true )
| ( ( rel_s4 @ SV9 @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[110]) ).
thf(117,plain,
! [SV10: $i,SV19: $i] :
( ( ( ~ ( price @ ninetyfive @ SV19 ) )
= $true )
| ( ( ~ ( price @ seventy @ SV19 ) )
= $true )
| ( ( rel_s4 @ SV10 @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[111]) ).
thf(118,plain,
! [SV24: $i,SV22: $i,SV13: $i] :
( ( ( ~ ( rel_s4 @ SV13 @ SV22 ) )
= $true )
| ( ( ~ ( rel_s4 @ SV22 @ SV24 ) )
= $true )
| ( ( rel_s4 @ SV13 @ SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[112]) ).
thf(119,plain,
! [SV25: $i,SV23: $i,SV15: mu] :
( ( ( ~ ( exists_in_world @ SV15 @ SV23 ) )
= $true )
| ( ( ~ ( rel_s4 @ SV23 @ SV25 ) )
= $true )
| ( ( exists_in_world @ SV15 @ SV25 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[113]) ).
thf(120,plain,
! [SV7: $i,SV16: $i] :
( ( ( ~ ( dest @ paris @ SV16 ) )
= $true )
| ( ( ~ ( class @ first @ SV16 ) )
= $true )
| ( ( price @ ninetyfive @ SV16 )
= $true )
| ( ( rel_s4 @ SV7 @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[114]) ).
thf(121,plain,
! [SV8: $i,SV17: $i] :
( ( ( ~ ( dest @ paris @ SV17 ) )
= $true )
| ( ( ~ ( class @ second @ SV17 ) )
= $true )
| ( ( price @ seventy @ SV17 )
= $true )
| ( ( rel_s4 @ SV8 @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[115]) ).
thf(122,plain,
! [SV9: $i,SV18: $i] :
( ( ( class @ first @ SV18 )
= $false )
| ( ( ~ ( class @ second @ SV18 ) )
= $true )
| ( ( rel_s4 @ SV9 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(123,plain,
! [SV10: $i,SV19: $i] :
( ( ( price @ ninetyfive @ SV19 )
= $false )
| ( ( ~ ( price @ seventy @ SV19 ) )
= $true )
| ( ( rel_s4 @ SV10 @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(124,plain,
! [SV24: $i,SV22: $i,SV13: $i] :
( ( ( rel_s4 @ SV13 @ SV22 )
= $false )
| ( ( ~ ( rel_s4 @ SV22 @ SV24 ) )
= $true )
| ( ( rel_s4 @ SV13 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(125,plain,
! [SV25: $i,SV23: $i,SV15: mu] :
( ( ( exists_in_world @ SV15 @ SV23 )
= $false )
| ( ( ~ ( rel_s4 @ SV23 @ SV25 ) )
= $true )
| ( ( exists_in_world @ SV15 @ SV25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(126,plain,
! [SV7: $i,SV16: $i] :
( ( ( dest @ paris @ SV16 )
= $false )
| ( ( ~ ( class @ first @ SV16 ) )
= $true )
| ( ( price @ ninetyfive @ SV16 )
= $true )
| ( ( rel_s4 @ SV7 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(127,plain,
! [SV8: $i,SV17: $i] :
( ( ( dest @ paris @ SV17 )
= $false )
| ( ( ~ ( class @ second @ SV17 ) )
= $true )
| ( ( price @ seventy @ SV17 )
= $true )
| ( ( rel_s4 @ SV8 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[121]) ).
thf(128,plain,
! [SV9: $i,SV18: $i] :
( ( ( class @ second @ SV18 )
= $false )
| ( ( class @ first @ SV18 )
= $false )
| ( ( rel_s4 @ SV9 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(129,plain,
! [SV10: $i,SV19: $i] :
( ( ( price @ seventy @ SV19 )
= $false )
| ( ( price @ ninetyfive @ SV19 )
= $false )
| ( ( rel_s4 @ SV10 @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(130,plain,
! [SV13: $i,SV24: $i,SV22: $i] :
( ( ( rel_s4 @ SV22 @ SV24 )
= $false )
| ( ( rel_s4 @ SV13 @ SV22 )
= $false )
| ( ( rel_s4 @ SV13 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(131,plain,
! [SV15: mu,SV25: $i,SV23: $i] :
( ( ( rel_s4 @ SV23 @ SV25 )
= $false )
| ( ( exists_in_world @ SV15 @ SV23 )
= $false )
| ( ( exists_in_world @ SV15 @ SV25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(132,plain,
! [SV7: $i,SV16: $i] :
( ( ( class @ first @ SV16 )
= $false )
| ( ( dest @ paris @ SV16 )
= $false )
| ( ( price @ ninetyfive @ SV16 )
= $true )
| ( ( rel_s4 @ SV7 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[126]) ).
thf(133,plain,
! [SV8: $i,SV17: $i] :
( ( ( class @ second @ SV17 )
= $false )
| ( ( dest @ paris @ SV17 )
= $false )
| ( ( price @ seventy @ SV17 )
= $true )
| ( ( rel_s4 @ SV8 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[127]) ).
thf(134,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[56,133,132,131,130,129,128,100,98,97,89,79,61,60,59,58,57]) ).
thf(135,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[134]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NLP264^7 : 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
% 0.07/0.18 % Computer : n003.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 13:00:54 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.25
% 0.07/0.25 No.of.Axioms: 15
% 0.07/0.25
% 0.07/0.25 Length.of.Defs: 5508
% 0.07/0.25
% 0.07/0.25 Contains.Choice.Funs: false
% 0.07/0.25 ....
% 0.07/0.25
% 0.07/0.25 ********************************
% 0.07/0.25 * All subproblems solved! *
% 0.07/0.25 ********************************
% 0.07/0.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:15,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:134,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.07/0.25
% 0.07/0.25 %**** Beginning of derivation protocol ****
% 0.07/0.25 % SZS output start CNFRefutation
% See solution above
% 0.07/0.25
% 0.07/0.25 %**** End of derivation protocol ****
% 0.07/0.25 %**** no. of clauses in derivation: 135 ****
% 0.07/0.25 %**** clause counter: 134 ****
% 0.07/0.25
% 0.07/0.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:15,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:134,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------