%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWV444^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 10:57:46 AM UTC 2026
% Result : Theorem 0.10s 0.27s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 36
% Syntax : Number of formulae : 120 ( 87 unt; 0 typ; 34 def)
% Number of atoms : 923 ( 204 equ; 0 cnn)
% Maximal formula atoms : 6 ( 7 avg)
% Number of connectives : 1860 ( 393 ~; 292 |; 16 &;1081 @)
% ( 0 <=>; 78 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 49 ( 49 >; 0 *; 0 +; 0 <<)
% Number of symbols : 54 ( 51 usr; 11 con; 0-3 aty)
% Number of variables : 327 ( 50 ^; 273 !; 4 ?; 327 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_individuals,type,
individuals: $tType ).
thf(tp_bl_all,type,
bl_all: ( individuals > $i > $o ) > $i > $o ).
thf(tp_bl_and,type,
bl_and: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_bl_atom,type,
bl_atom: ( $i > $o ) > $i > $o ).
thf(tp_bl_false,type,
bl_false: $i > $o ).
thf(tp_bl_impl,type,
bl_impl: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_bl_or,type,
bl_or: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_bl_princ,type,
bl_princ: ( $i > $o ) > $i > $o ).
thf(tp_bl_says,type,
bl_says: individuals > ( $i > $o ) > $i > $o ).
thf(tp_bl_true,type,
bl_true: $i > $o ).
thf(tp_bl_valid,type,
bl_valid: ( $i > $o ) > $o ).
thf(tp_cs4_all,type,
cs4_all: ( individuals > $i > $o ) > $i > $o ).
thf(tp_cs4_and,type,
cs4_and: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_cs4_atom,type,
cs4_atom: ( $i > $o ) > $i > $o ).
thf(tp_cs4_box,type,
cs4_box: ( $i > $o ) > $i > $o ).
thf(tp_cs4_false,type,
cs4_false: $i > $o ).
thf(tp_cs4_impl,type,
cs4_impl: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_cs4_or,type,
cs4_or: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_cs4_true,type,
cs4_true: $i > $o ).
thf(tp_cs4_valid,type,
cs4_valid: ( $i > $o ) > $o ).
thf(tp_current_world,type,
current_world: $i ).
thf(tp_loca,type,
loca: individuals ).
thf(tp_mall,type,
mall: ( individuals > $i > $o ) > $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_mcountersatisfiable,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(tp_mdia,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mexists,type,
mexists: ( individuals > $i > $o ) > $i > $o ).
thf(tp_mfalse,type,
mfalse: $i > $o ).
thf(tp_miff,type,
miff: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mimpl,type,
mimpl: ( $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_msatisfiable,type,
msatisfiable: ( $i > $o ) > $o ).
thf(tp_mtrue,type,
mtrue: $i > $o ).
thf(tp_mvalid,type,
mvalid: ( $i > $o ) > $o ).
thf(tp_princ_inj,type,
princ_inj: individuals > $i > $o ).
thf(tp_prop_a,type,
prop_a: $i > $o ).
thf(tp_prop_b,type,
prop_b: $i > $o ).
thf(tp_prop_c,type,
prop_c: $i > $o ).
thf(tp_reli,type,
reli: $i > $i > $o ).
thf(tp_relr,type,
relr: $i > $i > $o ).
thf(tp_sK1_SY163,type,
sK1_SY163: individuals ).
thf(tp_sK2_SY238,type,
sK2_SY238: $i > $o ).
thf(tp_sK3_SY251,type,
sK3_SY251: $i ).
thf(tp_sK4_SY263,type,
sK4_SY263: $i ).
thf(tp_sK5_SY279,type,
sK5_SY279: $i ).
thf(tp_sK6_SY284,type,
sK6_SY284: $i ).
thf(tp_sK7_SY288,type,
sK7_SY288: $i ).
thf(tp_sK8_SY292,type,
sK8_SY292: $i ).
thf(tp_sK9_SY24,type,
sK9_SY24: $i > $i > $i > $i ).
thf(bl_all,definition,
( bl_all
= ( ^ [A: individuals > $i > $o] : ( cs4_all @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bl_all) ).
thf(bl_and,definition,
( bl_and
= ( ^ [A: $i > $o,B: $i > $o] : ( cs4_and @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bl_and) ).
thf(bl_atom,definition,
( bl_atom
= ( ^ [P: $i > $o] : ( cs4_atom @ P ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bl_atom) ).
thf(bl_false,definition,
bl_false = cs4_false,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bl_false) ).
thf(bl_impl,definition,
( bl_impl
= ( ^ [A: $i > $o,B: $i > $o] : ( cs4_impl @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bl_impl) ).
thf(bl_or,definition,
( bl_or
= ( ^ [A: $i > $o,B: $i > $o] : ( cs4_or @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bl_or) ).
thf(bl_princ,definition,
( bl_princ
= ( ^ [P: $i > $o] : ( cs4_atom @ P ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bl_princ) ).
thf(bl_says,definition,
( bl_says
= ( ^ [K: individuals,A: $i > $o] : ( cs4_box @ ( cs4_impl @ ( bl_princ @ ( princ_inj @ K ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bl_says) ).
thf(bl_true,definition,
bl_true = cs4_true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bl_true) ).
thf(bl_valid,definition,
bl_valid = mvalid,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bl_valid_def) ).
thf(cs4_all,definition,
( cs4_all
= ( ^ [A: individuals > $i > $o] : ( mbox @ reli @ ( mall @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cs4_all) ).
thf(cs4_and,definition,
( cs4_and
= ( ^ [A: $i > $o,B: $i > $o] : ( mand @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cs4_and) ).
thf(cs4_atom,definition,
( cs4_atom
= ( ^ [P: $i > $o] : ( mbox @ reli @ P ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cs4_atom) ).
thf(cs4_box,definition,
( cs4_box
= ( ^ [A: $i > $o] : ( mbox @ reli @ ( mbox @ relr @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cs4_box) ).
thf(cs4_false,definition,
cs4_false = mfalse,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cs4_false) ).
thf(cs4_impl,definition,
( cs4_impl
= ( ^ [A: $i > $o,B: $i > $o] : ( mbox @ reli @ ( mimpl @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cs4_impl) ).
thf(cs4_or,definition,
( cs4_or
= ( ^ [A: $i > $o,B: $i > $o] : ( mor @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cs4_or) ).
thf(cs4_true,definition,
cs4_true = mtrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cs4_true) ).
thf(cs4_valid,definition,
( cs4_valid
= ( ^ [A: $i > $o] : ( mvalid @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cs4_valid_def) ).
thf(mall,definition,
( mall
= ( ^ [P: individuals > $i > $o,W: $i] :
! [X: individuals] : ( P @ X @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mall) ).
thf(mand,definition,
( mand
= ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
( ( X @ U )
& ( Y @ U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mand) ).
thf(mbox,definition,
( mbox
= ( ^ [R: $i > $i > $o,P: $i > $o,X: $i] :
! [Y: $i] :
( ( R @ X @ Y )
=> ( P @ Y ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox) ).
thf(mcountersatisfiable,definition,
( mcountersatisfiable
= ( ^ [P: $i > $o] :
? [W: $i] :
~ ( P @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mcountersatisfiable) ).
thf(mdia,definition,
( mdia
= ( ^ [R: $i > $i > $o,P: $i > $o,X: $i] :
? [Y: $i] :
( ( R @ X @ Y )
& ( P @ Y ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',individuals_decl) ).
thf(mexists,definition,
( mexists
= ( ^ [P: individuals > $i > $o,W: $i] :
? [X: individuals] : ( P @ X @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mexists) ).
thf(mfalse,definition,
( mfalse
= ( ^ [X: $i] : $false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mfalse) ).
thf(miff,definition,
( miff
= ( ^ [U: $i > $o,V: $i > $o] : ( mand @ ( mimpl @ U @ V ) @ ( mimpl @ V @ U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',miff) ).
thf(mimpl,definition,
( mimpl
= ( ^ [U: $i > $o,V: $i > $o] : ( mor @ ( mnot @ U ) @ V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimpl) ).
thf(minvalid,definition,
( minvalid
= ( ^ [P: $i > $o] :
! [W: $i] :
~ ( P @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',minvalid) ).
thf(mnot,definition,
( mnot
= ( ^ [X: $i > $o,U: $i] :
~ ( X @ U ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot) ).
thf(mor,definition,
( mor
= ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
( ( X @ U )
| ( Y @ U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor) ).
thf(msatisfiable,definition,
( msatisfiable
= ( ^ [P: $i > $o] :
? [W: $i] : ( P @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',msatisfiable) ).
thf(mtrue,definition,
( mtrue
= ( ^ [X: $i] : $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mtrue) ).
thf(mvalid,definition,
( mvalid
= ( ^ [P: $i > $o] :
! [W: $i] : ( P @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mvalid) ).
thf(1,axiom,
( cs4_valid
@ ( cs4_all
@ ^ [K: individuals] : ( cs4_impl @ ( princ_inj @ K ) @ ( princ_inj @ loca ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',loca_strength) ).
thf(7,conjecture,
! [K: individuals,A: $i > $o] : ( bl_valid @ ( bl_impl @ ( bl_says @ loca @ ( bl_atom @ A ) ) @ ( bl_says @ K @ ( bl_atom @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bl_strength) ).
thf(8,negated_conjecture,
( ( ! [K: individuals,A: $i > $o] : ( bl_valid @ ( bl_impl @ ( bl_says @ loca @ ( bl_atom @ A ) ) @ ( bl_says @ K @ ( bl_atom @ A ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[7]) ).
thf(9,plain,
( ( ! [SY163: individuals,SY164: $i > $o,SY177: $i,SY178: $i] :
( ( reli @ SY177 @ SY178 )
=> ( ~ ! [SY87: $i] :
( ( reli @ SY178 @ SY87 )
=> ! [SY50: $i] :
( ( relr @ SY87 @ SY50 )
=> ! [SY51: $i] :
( ( reli @ SY50 @ SY51 )
=> ( ~ ! [SY24: $i] :
( ( reli @ SY51 @ SY24 )
=> ( princ_inj @ loca @ SY24 ) )
| ! [SY53: $i] :
( ( reli @ SY51 @ SY53 )
=> ( SY164 @ SY53 ) ) ) ) ) )
| ! [SY158: $i] :
( ( reli @ SY178 @ SY158 )
=> ! [SY147: $i] :
( ( relr @ SY158 @ SY147 )
=> ! [SY148: $i] :
( ( reli @ SY147 @ SY148 )
=> ( ~ ! [SY121: $i] :
( ( reli @ SY148 @ SY121 )
=> ( princ_inj @ SY163 @ SY121 ) )
| ! [SY150: $i] :
( ( reli @ SY148 @ SY150 )
=> ( SY164 @ SY150 ) ) ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[8,bl_all,bl_and,bl_atom,bl_false,bl_impl,bl_or,bl_princ,bl_says,bl_true,bl_valid,cs4_all,cs4_and,cs4_atom,cs4_box,cs4_false,cs4_impl,cs4_or,cs4_true,cs4_valid,mall,mand,mbox,mcountersatisfiable,mdia,mexists,mfalse,miff,mimpl,minvalid,mnot,mor,msatisfiable,mtrue,mvalid]) ).
thf(10,plain,
( ( ! [SY230: $i,SY231: $i] :
( ( reli @ SY230 @ SY231 )
=> ! [SY228: individuals,SY229: $i] :
( ( reli @ SY231 @ SY229 )
=> ( ~ ( princ_inj @ SY228 @ SY229 )
| ( princ_inj @ loca @ SY229 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1,bl_all,bl_and,bl_atom,bl_false,bl_impl,bl_or,bl_princ,bl_says,bl_true,bl_valid,cs4_all,cs4_and,cs4_atom,cs4_box,cs4_false,cs4_impl,cs4_or,cs4_true,cs4_valid,mall,mand,mbox,mcountersatisfiable,mdia,mexists,mfalse,miff,mimpl,minvalid,mnot,mor,msatisfiable,mtrue,mvalid]) ).
thf(11,plain,
( ( ! [SY238: $i > $o,SY239: $i,SY240: $i] :
( ( reli @ SY239 @ SY240 )
=> ( ~ ! [SY87: $i] :
( ( reli @ SY240 @ SY87 )
=> ! [SY50: $i] :
( ( relr @ SY87 @ SY50 )
=> ! [SY51: $i] :
( ( reli @ SY50 @ SY51 )
=> ( ~ ! [SY24: $i] :
( ( reli @ SY51 @ SY24 )
=> ( princ_inj @ loca @ SY24 ) )
| ! [SY53: $i] :
( ( reli @ SY51 @ SY53 )
=> ( SY238 @ SY53 ) ) ) ) ) )
| ! [SY246: $i] :
( ( reli @ SY240 @ SY246 )
=> ! [SY247: $i] :
( ( relr @ SY246 @ SY247 )
=> ! [SY248: $i] :
( ( reli @ SY247 @ SY248 )
=> ( ~ ! [SY249: $i] :
( ( reli @ SY248 @ SY249 )
=> ( princ_inj @ sK1_SY163 @ SY249 ) )
| ! [SY150: $i] :
( ( reli @ SY248 @ SY150 )
=> ( SY238 @ SY150 ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[9]) ).
thf(12,plain,
( ( ! [SY251: $i,SY252: $i] :
( ( reli @ SY251 @ SY252 )
=> ( ~ ! [SY253: $i] :
( ( reli @ SY252 @ SY253 )
=> ! [SY254: $i] :
( ( relr @ SY253 @ SY254 )
=> ! [SY255: $i] :
( ( reli @ SY254 @ SY255 )
=> ( ~ ! [SY24: $i] :
( ( reli @ SY255 @ SY24 )
=> ( princ_inj @ loca @ SY24 ) )
| ! [SY257: $i] :
( ( reli @ SY255 @ SY257 )
=> ( sK2_SY238 @ SY257 ) ) ) ) ) )
| ! [SY258: $i] :
( ( reli @ SY252 @ SY258 )
=> ! [SY259: $i] :
( ( relr @ SY258 @ SY259 )
=> ! [SY260: $i] :
( ( reli @ SY259 @ SY260 )
=> ( ~ ! [SY249: $i] :
( ( reli @ SY260 @ SY249 )
=> ( princ_inj @ sK1_SY163 @ SY249 ) )
| ! [SY262: $i] :
( ( reli @ SY260 @ SY262 )
=> ( sK2_SY238 @ SY262 ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[11]) ).
thf(13,plain,
( ( ! [SY263: $i] :
( ( reli @ sK3_SY251 @ SY263 )
=> ( ~ ! [SY253: $i] :
( ( reli @ SY263 @ SY253 )
=> ! [SY254: $i] :
( ( relr @ SY253 @ SY254 )
=> ! [SY255: $i] :
( ( reli @ SY254 @ SY255 )
=> ( ~ ! [SY24: $i] :
( ( reli @ SY255 @ SY24 )
=> ( princ_inj @ loca @ SY24 ) )
| ! [SY257: $i] :
( ( reli @ SY255 @ SY257 )
=> ( sK2_SY238 @ SY257 ) ) ) ) ) )
| ! [SY258: $i] :
( ( reli @ SY263 @ SY258 )
=> ! [SY259: $i] :
( ( relr @ SY258 @ SY259 )
=> ! [SY260: $i] :
( ( reli @ SY259 @ SY260 )
=> ( ~ ! [SY249: $i] :
( ( reli @ SY260 @ SY249 )
=> ( princ_inj @ sK1_SY163 @ SY249 ) )
| ! [SY262: $i] :
( ( reli @ SY260 @ SY262 )
=> ( sK2_SY238 @ SY262 ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[12]) ).
thf(14,plain,
( ( ( reli @ sK3_SY251 @ sK4_SY263 )
=> ( ~ ! [SY274: $i] :
( ( reli @ sK4_SY263 @ SY274 )
=> ! [SY254: $i] :
( ( relr @ SY274 @ SY254 )
=> ! [SY255: $i] :
( ( reli @ SY254 @ SY255 )
=> ( ~ ! [SY24: $i] :
( ( reli @ SY255 @ SY24 )
=> ( princ_inj @ loca @ SY24 ) )
| ! [SY257: $i] :
( ( reli @ SY255 @ SY257 )
=> ( sK2_SY238 @ SY257 ) ) ) ) ) )
| ! [SY279: $i] :
( ( reli @ sK4_SY263 @ SY279 )
=> ! [SY259: $i] :
( ( relr @ SY279 @ SY259 )
=> ! [SY260: $i] :
( ( reli @ SY259 @ SY260 )
=> ( ~ ! [SY249: $i] :
( ( reli @ SY260 @ SY249 )
=> ( princ_inj @ sK1_SY163 @ SY249 ) )
| ! [SY262: $i] :
( ( reli @ SY260 @ SY262 )
=> ( sK2_SY238 @ SY262 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[13]) ).
thf(15,plain,
( ( reli @ sK3_SY251 @ sK4_SY263 )
= $true ),
inference(standard_cnf,[status(thm)],[14]) ).
thf(16,plain,
( ( ~ ! [SY274: $i] :
( ( reli @ sK4_SY263 @ SY274 )
=> ! [SY254: $i] :
( ( relr @ SY274 @ SY254 )
=> ! [SY255: $i] :
( ( reli @ SY254 @ SY255 )
=> ( ~ ! [SY24: $i] :
( ( reli @ SY255 @ SY24 )
=> ( princ_inj @ loca @ SY24 ) )
| ! [SY257: $i] :
( ( reli @ SY255 @ SY257 )
=> ( sK2_SY238 @ SY257 ) ) ) ) ) )
| ! [SY279: $i] :
( ( reli @ sK4_SY263 @ SY279 )
=> ! [SY259: $i] :
( ( relr @ SY279 @ SY259 )
=> ! [SY260: $i] :
( ( reli @ SY259 @ SY260 )
=> ( ~ ! [SY249: $i] :
( ( reli @ SY260 @ SY249 )
=> ( princ_inj @ sK1_SY163 @ SY249 ) )
| ! [SY262: $i] :
( ( reli @ SY260 @ SY262 )
=> ( sK2_SY238 @ SY262 ) ) ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[14]) ).
thf(17,plain,
( ( ~ ( ~ ! [SY274: $i] :
( ( reli @ sK4_SY263 @ SY274 )
=> ! [SY254: $i] :
( ( relr @ SY274 @ SY254 )
=> ! [SY255: $i] :
( ( reli @ SY254 @ SY255 )
=> ( ~ ! [SY24: $i] :
( ( reli @ SY255 @ SY24 )
=> ( princ_inj @ loca @ SY24 ) )
| ! [SY257: $i] :
( ( reli @ SY255 @ SY257 )
=> ( sK2_SY238 @ SY257 ) ) ) ) ) )
| ! [SY279: $i] :
( ( reli @ sK4_SY263 @ SY279 )
=> ! [SY259: $i] :
( ( relr @ SY279 @ SY259 )
=> ! [SY260: $i] :
( ( reli @ SY259 @ SY260 )
=> ( ~ ! [SY249: $i] :
( ( reli @ SY260 @ SY249 )
=> ( princ_inj @ sK1_SY163 @ SY249 ) )
| ! [SY262: $i] :
( ( reli @ SY260 @ SY262 )
=> ( sK2_SY238 @ SY262 ) ) ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[16]) ).
thf(18,plain,
( ( ! [SY274: $i] :
( ~ ( reli @ sK4_SY263 @ SY274 )
| ! [SY254: $i] :
( ~ ( relr @ SY274 @ SY254 )
| ! [SY255: $i] :
( ~ ( reli @ SY254 @ SY255 )
| ( ( reli @ SY255 @ ( sK9_SY24 @ SY255 @ SY254 @ SY274 ) )
& ~ ( princ_inj @ loca @ ( sK9_SY24 @ SY255 @ SY254 @ SY274 ) ) )
| ! [SY257: $i] :
( ~ ( reli @ SY255 @ SY257 )
| ( sK2_SY238 @ SY257 ) ) ) ) )
& ( reli @ sK4_SY263 @ sK5_SY279 )
& ( relr @ sK5_SY279 @ sK6_SY284 )
& ( reli @ sK6_SY284 @ sK7_SY288 )
& ! [SY291: $i] :
( ~ ( reli @ sK7_SY288 @ SY291 )
| ( princ_inj @ sK1_SY163 @ SY291 ) )
& ( reli @ sK7_SY288 @ sK8_SY292 )
& ~ ( sK2_SY238 @ sK8_SY292 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[17]) ).
thf(19,plain,
( ( ! [SY230: $i,SY231: $i] :
( ~ ( reli @ SY230 @ SY231 )
| ! [SY228: individuals,SY229: $i] :
( ~ ( reli @ SY231 @ SY229 )
| ~ ( princ_inj @ SY228 @ SY229 )
| ( princ_inj @ loca @ SY229 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[10]) ).
thf(20,plain,
( ( ! [SY230: $i,SY231: $i] :
( ~ ( reli @ SY230 @ SY231 )
| ! [SY228: individuals,SY229: $i] :
( ~ ( reli @ SY231 @ SY229 )
| ~ ( princ_inj @ SY228 @ SY229 )
| ( princ_inj @ loca @ SY229 ) ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(21,plain,
( ( reli @ sK3_SY251 @ sK4_SY263 )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(22,plain,
( ( ! [SY274: $i] :
( ~ ( reli @ sK4_SY263 @ SY274 )
| ! [SY254: $i] :
( ~ ( relr @ SY274 @ SY254 )
| ! [SY255: $i] :
( ~ ( reli @ SY254 @ SY255 )
| ( ( reli @ SY255 @ ( sK9_SY24 @ SY255 @ SY254 @ SY274 ) )
& ~ ( princ_inj @ loca @ ( sK9_SY24 @ SY255 @ SY254 @ SY274 ) ) )
| ! [SY257: $i] :
( ~ ( reli @ SY255 @ SY257 )
| ( sK2_SY238 @ SY257 ) ) ) ) )
& ( reli @ sK4_SY263 @ sK5_SY279 )
& ( relr @ sK5_SY279 @ sK6_SY284 )
& ( reli @ sK6_SY284 @ sK7_SY288 )
& ! [SY291: $i] :
( ~ ( reli @ sK7_SY288 @ SY291 )
| ( princ_inj @ sK1_SY163 @ SY291 ) )
& ( reli @ sK7_SY288 @ sK8_SY292 )
& ~ ( sK2_SY238 @ sK8_SY292 ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(23,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( reli @ sK4_SY263 @ SX0 )
| ! [SX1: $i] :
( ~ ( relr @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( reli @ SX1 @ SX2 )
| ~ ( ~ ( reli @ SX2 @ ( sK9_SY24 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( princ_inj @ loca @ ( sK9_SY24 @ SX2 @ SX1 @ SX0 ) ) )
| ! [SX3: $i] :
( ~ ( reli @ SX2 @ SX3 )
| ( sK2_SY238 @ SX3 ) ) ) ) )
| ~ ~ ( ~ ( reli @ sK4_SY263 @ sK5_SY279 )
| ~ ~ ( ~ ( relr @ sK5_SY279 @ sK6_SY284 )
| ~ ~ ( ~ ( reli @ sK6_SY284 @ sK7_SY288 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( reli @ sK7_SY288 @ SX0 )
| ( princ_inj @ sK1_SY163 @ SX0 ) )
| ~ ~ ( ~ ( reli @ sK7_SY288 @ sK8_SY292 )
| ~ ~ ( sK2_SY238 @ sK8_SY292 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22,bl_all,bl_and,bl_atom,bl_false,bl_impl,bl_or,bl_princ,bl_says,bl_true,bl_valid,cs4_all,cs4_and,cs4_atom,cs4_box,cs4_false,cs4_impl,cs4_or,cs4_true,cs4_valid,mall,mand,mbox,mcountersatisfiable,mdia,mexists,mfalse,miff,mimpl,minvalid,mnot,mor,msatisfiable,mtrue,mvalid]) ).
thf(24,plain,
! [SV1: $i] :
( ( ! [SY293: $i] :
( ~ ( reli @ SV1 @ SY293 )
| ! [SY228: individuals,SY229: $i] :
( ~ ( reli @ SY293 @ SY229 )
| ~ ( princ_inj @ SY228 @ SY229 )
| ( princ_inj @ loca @ SY229 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(25,plain,
( ( ~ ! [SX0: $i] :
( ~ ( reli @ sK4_SY263 @ SX0 )
| ! [SX1: $i] :
( ~ ( relr @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( reli @ SX1 @ SX2 )
| ~ ( ~ ( reli @ SX2 @ ( sK9_SY24 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( princ_inj @ loca @ ( sK9_SY24 @ SX2 @ SX1 @ SX0 ) ) )
| ! [SX3: $i] :
( ~ ( reli @ SX2 @ SX3 )
| ( sK2_SY238 @ SX3 ) ) ) ) )
| ~ ~ ( ~ ( reli @ sK4_SY263 @ sK5_SY279 )
| ~ ~ ( ~ ( relr @ sK5_SY279 @ sK6_SY284 )
| ~ ~ ( ~ ( reli @ sK6_SY284 @ sK7_SY288 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( reli @ sK7_SY288 @ SX0 )
| ( princ_inj @ sK1_SY163 @ SX0 ) )
| ~ ~ ( ~ ( reli @ sK7_SY288 @ sK8_SY292 )
| ~ ~ ( sK2_SY238 @ sK8_SY292 ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(26,plain,
! [SV2: $i,SV1: $i] :
( ( ~ ( reli @ SV1 @ SV2 )
| ! [SY296: individuals,SY297: $i] :
( ~ ( reli @ SV2 @ SY297 )
| ~ ( princ_inj @ SY296 @ SY297 )
| ( princ_inj @ loca @ SY297 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(27,plain,
( ( ~ ! [SX0: $i] :
( ~ ( reli @ sK4_SY263 @ SX0 )
| ! [SX1: $i] :
( ~ ( relr @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( reli @ SX1 @ SX2 )
| ~ ( ~ ( reli @ SX2 @ ( sK9_SY24 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( princ_inj @ loca @ ( sK9_SY24 @ SX2 @ SX1 @ SX0 ) ) )
| ! [SX3: $i] :
( ~ ( reli @ SX2 @ SX3 )
| ( sK2_SY238 @ SX3 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[25]) ).
thf(28,plain,
( ( ~ ~ ( ~ ( reli @ sK4_SY263 @ sK5_SY279 )
| ~ ~ ( ~ ( relr @ sK5_SY279 @ sK6_SY284 )
| ~ ~ ( ~ ( reli @ sK6_SY284 @ sK7_SY288 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( reli @ sK7_SY288 @ SX0 )
| ( princ_inj @ sK1_SY163 @ SX0 ) )
| ~ ~ ( ~ ( reli @ sK7_SY288 @ sK8_SY292 )
| ~ ~ ( sK2_SY238 @ sK8_SY292 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[25]) ).
thf(29,plain,
! [SV2: $i,SV1: $i] :
( ( ( ~ ( reli @ SV1 @ SV2 ) )
= $true )
| ( ( ! [SY296: individuals,SY297: $i] :
( ~ ( reli @ SV2 @ SY297 )
| ~ ( princ_inj @ SY296 @ SY297 )
| ( princ_inj @ loca @ SY297 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[26]) ).
thf(30,plain,
( ( ! [SX0: $i] :
( ~ ( reli @ sK4_SY263 @ SX0 )
| ! [SX1: $i] :
( ~ ( relr @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( reli @ SX1 @ SX2 )
| ~ ( ~ ( reli @ SX2 @ ( sK9_SY24 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( princ_inj @ loca @ ( sK9_SY24 @ SX2 @ SX1 @ SX0 ) ) )
| ! [SX3: $i] :
( ~ ( reli @ SX2 @ SX3 )
| ( sK2_SY238 @ SX3 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[27]) ).
thf(31,plain,
( ( ~ ( ~ ( reli @ sK4_SY263 @ sK5_SY279 )
| ~ ~ ( ~ ( relr @ sK5_SY279 @ sK6_SY284 )
| ~ ~ ( ~ ( reli @ sK6_SY284 @ sK7_SY288 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( reli @ sK7_SY288 @ SX0 )
| ( princ_inj @ sK1_SY163 @ SX0 ) )
| ~ ~ ( ~ ( reli @ sK7_SY288 @ sK8_SY292 )
| ~ ~ ( sK2_SY238 @ sK8_SY292 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[28]) ).
thf(32,plain,
! [SV2: $i,SV1: $i] :
( ( ( reli @ SV1 @ SV2 )
= $false )
| ( ( ! [SY296: individuals,SY297: $i] :
( ~ ( reli @ SV2 @ SY297 )
| ~ ( princ_inj @ SY296 @ SY297 )
| ( princ_inj @ loca @ SY297 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[29]) ).
thf(33,plain,
! [SV3: $i] :
( ( ~ ( reli @ sK4_SY263 @ SV3 )
| ! [SY298: $i] :
( ~ ( relr @ SV3 @ SY298 )
| ! [SY299: $i] :
( ~ ( reli @ SY298 @ SY299 )
| ~ ( ~ ( reli @ SY299 @ ( sK9_SY24 @ SY299 @ SY298 @ SV3 ) )
| ~ ~ ( princ_inj @ loca @ ( sK9_SY24 @ SY299 @ SY298 @ SV3 ) ) )
| ! [SX3: $i] :
( ~ ( reli @ SY299 @ SX3 )
| ( sK2_SY238 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(34,plain,
( ( ~ ( reli @ sK4_SY263 @ sK5_SY279 )
| ~ ~ ( ~ ( relr @ sK5_SY279 @ sK6_SY284 )
| ~ ~ ( ~ ( reli @ sK6_SY284 @ sK7_SY288 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( reli @ sK7_SY288 @ SX0 )
| ( princ_inj @ sK1_SY163 @ SX0 ) )
| ~ ~ ( ~ ( reli @ sK7_SY288 @ sK8_SY292 )
| ~ ~ ( sK2_SY238 @ sK8_SY292 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(35,plain,
! [SV1: $i,SV4: individuals,SV2: $i] :
( ( ( ! [SY301: $i] :
( ~ ( reli @ SV2 @ SY301 )
| ~ ( princ_inj @ SV4 @ SY301 )
| ( princ_inj @ loca @ SY301 ) ) )
= $true )
| ( ( reli @ SV1 @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(36,plain,
! [SV3: $i] :
( ( ( ~ ( reli @ sK4_SY263 @ SV3 ) )
= $true )
| ( ( ! [SY298: $i] :
( ~ ( relr @ SV3 @ SY298 )
| ! [SY299: $i] :
( ~ ( reli @ SY298 @ SY299 )
| ~ ( ~ ( reli @ SY299 @ ( sK9_SY24 @ SY299 @ SY298 @ SV3 ) )
| ~ ~ ( princ_inj @ loca @ ( sK9_SY24 @ SY299 @ SY298 @ SV3 ) ) )
| ! [SX3: $i] :
( ~ ( reli @ SY299 @ SX3 )
| ( sK2_SY238 @ SX3 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[33]) ).
thf(37,plain,
( ( ~ ( reli @ sK4_SY263 @ sK5_SY279 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[34]) ).
thf(38,plain,
( ( ~ ~ ( ~ ( relr @ sK5_SY279 @ sK6_SY284 )
| ~ ~ ( ~ ( reli @ sK6_SY284 @ sK7_SY288 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( reli @ sK7_SY288 @ SX0 )
| ( princ_inj @ sK1_SY163 @ SX0 ) )
| ~ ~ ( ~ ( reli @ sK7_SY288 @ sK8_SY292 )
| ~ ~ ( sK2_SY238 @ sK8_SY292 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[34]) ).
thf(39,plain,
! [SV1: $i,SV4: individuals,SV5: $i,SV2: $i] :
( ( ( ~ ( reli @ SV2 @ SV5 )
| ~ ( princ_inj @ SV4 @ SV5 )
| ( princ_inj @ loca @ SV5 ) )
= $true )
| ( ( reli @ SV1 @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(40,plain,
! [SV3: $i] :
( ( ( reli @ sK4_SY263 @ SV3 )
= $false )
| ( ( ! [SY298: $i] :
( ~ ( relr @ SV3 @ SY298 )
| ! [SY299: $i] :
( ~ ( reli @ SY298 @ SY299 )
| ~ ( ~ ( reli @ SY299 @ ( sK9_SY24 @ SY299 @ SY298 @ SV3 ) )
| ~ ~ ( princ_inj @ loca @ ( sK9_SY24 @ SY299 @ SY298 @ SV3 ) ) )
| ! [SX3: $i] :
( ~ ( reli @ SY299 @ SX3 )
| ( sK2_SY238 @ SX3 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(41,plain,
( ( reli @ sK4_SY263 @ sK5_SY279 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[37]) ).
thf(42,plain,
( ( ~ ( ~ ( relr @ sK5_SY279 @ sK6_SY284 )
| ~ ~ ( ~ ( reli @ sK6_SY284 @ sK7_SY288 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( reli @ sK7_SY288 @ SX0 )
| ( princ_inj @ sK1_SY163 @ SX0 ) )
| ~ ~ ( ~ ( reli @ sK7_SY288 @ sK8_SY292 )
| ~ ~ ( sK2_SY238 @ sK8_SY292 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[38]) ).
thf(43,plain,
! [SV1: $i,SV4: individuals,SV5: $i,SV2: $i] :
( ( ( ~ ( reli @ SV2 @ SV5 ) )
= $true )
| ( ( ~ ( princ_inj @ SV4 @ SV5 )
| ( princ_inj @ loca @ SV5 ) )
= $true )
| ( ( reli @ SV1 @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[39]) ).
thf(44,plain,
! [SV6: $i,SV3: $i] :
( ( ( ~ ( relr @ SV3 @ SV6 )
| ! [SY302: $i] :
( ~ ( reli @ SV6 @ SY302 )
| ~ ( ~ ( reli @ SY302 @ ( sK9_SY24 @ SY302 @ SV6 @ SV3 ) )
| ~ ~ ( princ_inj @ loca @ ( sK9_SY24 @ SY302 @ SV6 @ SV3 ) ) )
| ! [SX3: $i] :
( ~ ( reli @ SY302 @ SX3 )
| ( sK2_SY238 @ SX3 ) ) ) )
= $true )
| ( ( reli @ sK4_SY263 @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(45,plain,
( ( ~ ( relr @ sK5_SY279 @ sK6_SY284 )
| ~ ~ ( ~ ( reli @ sK6_SY284 @ sK7_SY288 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( reli @ sK7_SY288 @ SX0 )
| ( princ_inj @ sK1_SY163 @ SX0 ) )
| ~ ~ ( ~ ( reli @ sK7_SY288 @ sK8_SY292 )
| ~ ~ ( sK2_SY238 @ sK8_SY292 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(46,plain,
! [SV1: $i,SV4: individuals,SV5: $i,SV2: $i] :
( ( ( reli @ SV2 @ SV5 )
= $false )
| ( ( ~ ( princ_inj @ SV4 @ SV5 )
| ( princ_inj @ loca @ SV5 ) )
= $true )
| ( ( reli @ SV1 @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(47,plain,
! [SV6: $i,SV3: $i] :
( ( ( ~ ( relr @ SV3 @ SV6 ) )
= $true )
| ( ( ! [SY302: $i] :
( ~ ( reli @ SV6 @ SY302 )
| ~ ( ~ ( reli @ SY302 @ ( sK9_SY24 @ SY302 @ SV6 @ SV3 ) )
| ~ ~ ( princ_inj @ loca @ ( sK9_SY24 @ SY302 @ SV6 @ SV3 ) ) )
| ! [SX3: $i] :
( ~ ( reli @ SY302 @ SX3 )
| ( sK2_SY238 @ SX3 ) ) ) )
= $true )
| ( ( reli @ sK4_SY263 @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[44]) ).
thf(48,plain,
( ( ~ ( relr @ sK5_SY279 @ sK6_SY284 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[45]) ).
thf(49,plain,
( ( ~ ~ ( ~ ( reli @ sK6_SY284 @ sK7_SY288 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( reli @ sK7_SY288 @ SX0 )
| ( princ_inj @ sK1_SY163 @ SX0 ) )
| ~ ~ ( ~ ( reli @ sK7_SY288 @ sK8_SY292 )
| ~ ~ ( sK2_SY238 @ sK8_SY292 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[45]) ).
thf(50,plain,
! [SV1: $i,SV2: $i,SV5: $i,SV4: individuals] :
( ( ( ~ ( princ_inj @ SV4 @ SV5 ) )
= $true )
| ( ( princ_inj @ loca @ SV5 )
= $true )
| ( ( reli @ SV2 @ SV5 )
= $false )
| ( ( reli @ SV1 @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[46]) ).
thf(51,plain,
! [SV6: $i,SV3: $i] :
( ( ( relr @ SV3 @ SV6 )
= $false )
| ( ( ! [SY302: $i] :
( ~ ( reli @ SV6 @ SY302 )
| ~ ( ~ ( reli @ SY302 @ ( sK9_SY24 @ SY302 @ SV6 @ SV3 ) )
| ~ ~ ( princ_inj @ loca @ ( sK9_SY24 @ SY302 @ SV6 @ SV3 ) ) )
| ! [SX3: $i] :
( ~ ( reli @ SY302 @ SX3 )
| ( sK2_SY238 @ SX3 ) ) ) )
= $true )
| ( ( reli @ sK4_SY263 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(52,plain,
( ( relr @ sK5_SY279 @ sK6_SY284 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[48]) ).
thf(53,plain,
( ( ~ ( ~ ( reli @ sK6_SY284 @ sK7_SY288 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( reli @ sK7_SY288 @ SX0 )
| ( princ_inj @ sK1_SY163 @ SX0 ) )
| ~ ~ ( ~ ( reli @ sK7_SY288 @ sK8_SY292 )
| ~ ~ ( sK2_SY238 @ sK8_SY292 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[49]) ).
thf(54,plain,
! [SV1: $i,SV2: $i,SV5: $i,SV4: individuals] :
( ( ( princ_inj @ SV4 @ SV5 )
= $false )
| ( ( princ_inj @ loca @ SV5 )
= $true )
| ( ( reli @ SV2 @ SV5 )
= $false )
| ( ( reli @ SV1 @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(55,plain,
! [SV3: $i,SV7: $i,SV6: $i] :
( ( ( ~ ( reli @ SV6 @ SV7 )
| ~ ( ~ ( reli @ SV7 @ ( sK9_SY24 @ SV7 @ SV6 @ SV3 ) )
| ~ ~ ( princ_inj @ loca @ ( sK9_SY24 @ SV7 @ SV6 @ SV3 ) ) )
| ! [SY304: $i] :
( ~ ( reli @ SV7 @ SY304 )
| ( sK2_SY238 @ SY304 ) ) )
= $true )
| ( ( relr @ SV3 @ SV6 )
= $false )
| ( ( reli @ sK4_SY263 @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(56,plain,
( ( ~ ( reli @ sK6_SY284 @ sK7_SY288 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( reli @ sK7_SY288 @ SX0 )
| ( princ_inj @ sK1_SY163 @ SX0 ) )
| ~ ~ ( ~ ( reli @ sK7_SY288 @ sK8_SY292 )
| ~ ~ ( sK2_SY238 @ sK8_SY292 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(57,plain,
! [SV3: $i,SV7: $i,SV6: $i] :
( ( ( ~ ( reli @ SV6 @ SV7 ) )
= $true )
| ( ( ~ ( ~ ( reli @ SV7 @ ( sK9_SY24 @ SV7 @ SV6 @ SV3 ) )
| ~ ~ ( princ_inj @ loca @ ( sK9_SY24 @ SV7 @ SV6 @ SV3 ) ) )
| ! [SY304: $i] :
( ~ ( reli @ SV7 @ SY304 )
| ( sK2_SY238 @ SY304 ) ) )
= $true )
| ( ( relr @ SV3 @ SV6 )
= $false )
| ( ( reli @ sK4_SY263 @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[55]) ).
thf(58,plain,
( ( ~ ( reli @ sK6_SY284 @ sK7_SY288 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[56]) ).
thf(59,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( reli @ sK7_SY288 @ SX0 )
| ( princ_inj @ sK1_SY163 @ SX0 ) )
| ~ ~ ( ~ ( reli @ sK7_SY288 @ sK8_SY292 )
| ~ ~ ( sK2_SY238 @ sK8_SY292 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[56]) ).
thf(60,plain,
! [SV3: $i,SV7: $i,SV6: $i] :
( ( ( reli @ SV6 @ SV7 )
= $false )
| ( ( ~ ( ~ ( reli @ SV7 @ ( sK9_SY24 @ SV7 @ SV6 @ SV3 ) )
| ~ ~ ( princ_inj @ loca @ ( sK9_SY24 @ SV7 @ SV6 @ SV3 ) ) )
| ! [SY304: $i] :
( ~ ( reli @ SV7 @ SY304 )
| ( sK2_SY238 @ SY304 ) ) )
= $true )
| ( ( relr @ SV3 @ SV6 )
= $false )
| ( ( reli @ sK4_SY263 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(61,plain,
( ( reli @ sK6_SY284 @ sK7_SY288 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[58]) ).
thf(62,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( reli @ sK7_SY288 @ SX0 )
| ( princ_inj @ sK1_SY163 @ SX0 ) )
| ~ ~ ( ~ ( reli @ sK7_SY288 @ sK8_SY292 )
| ~ ~ ( sK2_SY238 @ sK8_SY292 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[59]) ).
thf(63,plain,
! [SV3: $i,SV6: $i,SV7: $i] :
( ( ( ~ ( ~ ( reli @ SV7 @ ( sK9_SY24 @ SV7 @ SV6 @ SV3 ) )
| ~ ~ ( princ_inj @ loca @ ( sK9_SY24 @ SV7 @ SV6 @ SV3 ) ) ) )
= $true )
| ( ( ! [SY304: $i] :
( ~ ( reli @ SV7 @ SY304 )
| ( sK2_SY238 @ SY304 ) ) )
= $true )
| ( ( reli @ SV6 @ SV7 )
= $false )
| ( ( relr @ SV3 @ SV6 )
= $false )
| ( ( reli @ sK4_SY263 @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[60]) ).
thf(64,plain,
( ( ~ ! [SX0: $i] :
( ~ ( reli @ sK7_SY288 @ SX0 )
| ( princ_inj @ sK1_SY163 @ SX0 ) )
| ~ ~ ( ~ ( reli @ sK7_SY288 @ sK8_SY292 )
| ~ ~ ( sK2_SY238 @ sK8_SY292 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(65,plain,
! [SV3: $i,SV6: $i,SV7: $i] :
( ( ( ~ ( reli @ SV7 @ ( sK9_SY24 @ SV7 @ SV6 @ SV3 ) )
| ~ ~ ( princ_inj @ loca @ ( sK9_SY24 @ SV7 @ SV6 @ SV3 ) ) )
= $false )
| ( ( ! [SY304: $i] :
( ~ ( reli @ SV7 @ SY304 )
| ( sK2_SY238 @ SY304 ) ) )
= $true )
| ( ( reli @ SV6 @ SV7 )
= $false )
| ( ( relr @ SV3 @ SV6 )
= $false )
| ( ( reli @ sK4_SY263 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(66,plain,
( ( ~ ! [SX0: $i] :
( ~ ( reli @ sK7_SY288 @ SX0 )
| ( princ_inj @ sK1_SY163 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[64]) ).
thf(67,plain,
( ( ~ ~ ( ~ ( reli @ sK7_SY288 @ sK8_SY292 )
| ~ ~ ( sK2_SY238 @ sK8_SY292 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[64]) ).
thf(68,plain,
! [SV3: $i,SV6: $i,SV7: $i] :
( ( ( ~ ( reli @ SV7 @ ( sK9_SY24 @ SV7 @ SV6 @ SV3 ) ) )
= $false )
| ( ( ! [SY304: $i] :
( ~ ( reli @ SV7 @ SY304 )
| ( sK2_SY238 @ SY304 ) ) )
= $true )
| ( ( reli @ SV6 @ SV7 )
= $false )
| ( ( relr @ SV3 @ SV6 )
= $false )
| ( ( reli @ sK4_SY263 @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[65]) ).
thf(69,plain,
! [SV3: $i,SV6: $i,SV7: $i] :
( ( ( ~ ~ ( princ_inj @ loca @ ( sK9_SY24 @ SV7 @ SV6 @ SV3 ) ) )
= $false )
| ( ( ! [SY304: $i] :
( ~ ( reli @ SV7 @ SY304 )
| ( sK2_SY238 @ SY304 ) ) )
= $true )
| ( ( reli @ SV6 @ SV7 )
= $false )
| ( ( relr @ SV3 @ SV6 )
= $false )
| ( ( reli @ sK4_SY263 @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[65]) ).
thf(70,plain,
( ( ! [SX0: $i] :
( ~ ( reli @ sK7_SY288 @ SX0 )
| ( princ_inj @ sK1_SY163 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[66]) ).
thf(71,plain,
( ( ~ ( ~ ( reli @ sK7_SY288 @ sK8_SY292 )
| ~ ~ ( sK2_SY238 @ sK8_SY292 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[67]) ).
thf(72,plain,
! [SV3: $i,SV6: $i,SV7: $i] :
( ( ( reli @ SV7 @ ( sK9_SY24 @ SV7 @ SV6 @ SV3 ) )
= $true )
| ( ( ! [SY304: $i] :
( ~ ( reli @ SV7 @ SY304 )
| ( sK2_SY238 @ SY304 ) ) )
= $true )
| ( ( reli @ SV6 @ SV7 )
= $false )
| ( ( relr @ SV3 @ SV6 )
= $false )
| ( ( reli @ sK4_SY263 @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[68]) ).
thf(73,plain,
! [SV3: $i,SV6: $i,SV7: $i] :
( ( ( ~ ( princ_inj @ loca @ ( sK9_SY24 @ SV7 @ SV6 @ SV3 ) ) )
= $true )
| ( ( ! [SY304: $i] :
( ~ ( reli @ SV7 @ SY304 )
| ( sK2_SY238 @ SY304 ) ) )
= $true )
| ( ( reli @ SV6 @ SV7 )
= $false )
| ( ( relr @ SV3 @ SV6 )
= $false )
| ( ( reli @ sK4_SY263 @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[69]) ).
thf(74,plain,
! [SV8: $i] :
( ( ~ ( reli @ sK7_SY288 @ SV8 )
| ( princ_inj @ sK1_SY163 @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(75,plain,
( ( ~ ( reli @ sK7_SY288 @ sK8_SY292 )
| ~ ~ ( sK2_SY238 @ sK8_SY292 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(76,plain,
! [SV3: $i,SV6: $i,SV9: $i,SV7: $i] :
( ( ( ~ ( reli @ SV7 @ SV9 )
| ( sK2_SY238 @ SV9 ) )
= $true )
| ( ( reli @ SV7 @ ( sK9_SY24 @ SV7 @ SV6 @ SV3 ) )
= $true )
| ( ( reli @ SV6 @ SV7 )
= $false )
| ( ( relr @ SV3 @ SV6 )
= $false )
| ( ( reli @ sK4_SY263 @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(77,plain,
! [SV3: $i,SV6: $i,SV7: $i] :
( ( ( princ_inj @ loca @ ( sK9_SY24 @ SV7 @ SV6 @ SV3 ) )
= $false )
| ( ( ! [SY304: $i] :
( ~ ( reli @ SV7 @ SY304 )
| ( sK2_SY238 @ SY304 ) ) )
= $true )
| ( ( reli @ SV6 @ SV7 )
= $false )
| ( ( relr @ SV3 @ SV6 )
= $false )
| ( ( reli @ sK4_SY263 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(78,plain,
! [SV8: $i] :
( ( ( ~ ( reli @ sK7_SY288 @ SV8 ) )
= $true )
| ( ( princ_inj @ sK1_SY163 @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[74]) ).
thf(79,plain,
( ( ~ ( reli @ sK7_SY288 @ sK8_SY292 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[75]) ).
thf(80,plain,
( ( ~ ~ ( sK2_SY238 @ sK8_SY292 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[75]) ).
thf(81,plain,
! [SV3: $i,SV6: $i,SV9: $i,SV7: $i] :
( ( ( ~ ( reli @ SV7 @ SV9 ) )
= $true )
| ( ( sK2_SY238 @ SV9 )
= $true )
| ( ( reli @ SV7 @ ( sK9_SY24 @ SV7 @ SV6 @ SV3 ) )
= $true )
| ( ( reli @ SV6 @ SV7 )
= $false )
| ( ( relr @ SV3 @ SV6 )
= $false )
| ( ( reli @ sK4_SY263 @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[76]) ).
thf(82,plain,
! [SV3: $i,SV6: $i,SV10: $i,SV7: $i] :
( ( ( ~ ( reli @ SV7 @ SV10 )
| ( sK2_SY238 @ SV10 ) )
= $true )
| ( ( princ_inj @ loca @ ( sK9_SY24 @ SV7 @ SV6 @ SV3 ) )
= $false )
| ( ( reli @ SV6 @ SV7 )
= $false )
| ( ( relr @ SV3 @ SV6 )
= $false )
| ( ( reli @ sK4_SY263 @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(83,plain,
! [SV8: $i] :
( ( ( reli @ sK7_SY288 @ SV8 )
= $false )
| ( ( princ_inj @ sK1_SY163 @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(84,plain,
( ( reli @ sK7_SY288 @ sK8_SY292 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[79]) ).
thf(85,plain,
( ( ~ ( sK2_SY238 @ sK8_SY292 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[80]) ).
thf(86,plain,
! [SV3: $i,SV6: $i,SV9: $i,SV7: $i] :
( ( ( reli @ SV7 @ SV9 )
= $false )
| ( ( sK2_SY238 @ SV9 )
= $true )
| ( ( reli @ SV7 @ ( sK9_SY24 @ SV7 @ SV6 @ SV3 ) )
= $true )
| ( ( reli @ SV6 @ SV7 )
= $false )
| ( ( relr @ SV3 @ SV6 )
= $false )
| ( ( reli @ sK4_SY263 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(87,plain,
! [SV3: $i,SV6: $i,SV10: $i,SV7: $i] :
( ( ( ~ ( reli @ SV7 @ SV10 ) )
= $true )
| ( ( sK2_SY238 @ SV10 )
= $true )
| ( ( princ_inj @ loca @ ( sK9_SY24 @ SV7 @ SV6 @ SV3 ) )
= $false )
| ( ( reli @ SV6 @ SV7 )
= $false )
| ( ( relr @ SV3 @ SV6 )
= $false )
| ( ( reli @ sK4_SY263 @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[82]) ).
thf(88,plain,
( ( sK2_SY238 @ sK8_SY292 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[85]) ).
thf(89,plain,
! [SV3: $i,SV6: $i,SV10: $i,SV7: $i] :
( ( ( reli @ SV7 @ SV10 )
= $false )
| ( ( sK2_SY238 @ SV10 )
= $true )
| ( ( princ_inj @ loca @ ( sK9_SY24 @ SV7 @ SV6 @ SV3 ) )
= $false )
| ( ( reli @ SV6 @ SV7 )
= $false )
| ( ( relr @ SV3 @ SV6 )
= $false )
| ( ( reli @ sK4_SY263 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[87]) ).
thf(90,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[21,89,88,86,84,83,61,54,52,41]) ).
thf(91,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[90]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV444^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.19 % Computer : n011.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Oct 6 16:30:06 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.27
% 0.10/0.27 No.of.Axioms: 6
% 0.10/0.27
% 0.10/0.27 Length.of.Defs: 4892
% 0.10/0.27
% 0.10/0.27 Contains.Choice.Funs: false
% 0.10/0.27 ......
% 0.10/0.27
% 0.10/0.27 ********************************
% 0.10/0.27 * All subproblems solved! *
% 0.10/0.27 ********************************
% 0.10/0.27 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:2,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:90,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.10/0.27
% 0.10/0.27 %**** Beginning of derivation protocol ****
% 0.10/0.27 % SZS output start CNFRefutation
% See solution above
% 0.10/0.27
% 0.10/0.27 %**** End of derivation protocol ****
% 0.10/0.27 %**** no. of clauses in derivation: 86 ****
% 0.10/0.27 %**** clause counter: 90 ****
% 0.10/0.27
% 0.10/0.27 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:2,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:90,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------