%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWV441^1 : 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/sandbox/solver/bin/eprover /export/starexec/sandbox/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 71.76s 14.53s
% Output : CNFRefutation 71.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 41
% Syntax : Number of formulae : 239 ( 108 unt; 0 typ; 34 def)
% Number of atoms : 2013 ( 502 equ; 0 cnn)
% Maximal formula atoms : 10 ( 8 avg)
% Number of connectives : 3669 ( 523 ~; 739 |; 2 &;2244 @)
% ( 0 <=>; 161 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 160 ( 160 >; 0 *; 0 +; 0 <<)
% Number of symbols : 62 ( 59 usr; 11 con; 0-3 aty)
% Number of variables : 925 ( 50 ^; 871 !; 4 ?; 925 :)
% 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_sK10_SY635,type,
sK10_SY635: ( $i > $o ) > $i > $i ).
thf(tp_sK11_SY636,type,
sK11_SY636: ( $i > $o ) > $i > $i ).
thf(tp_sK12_SY644,type,
sK12_SY644: $i ).
thf(tp_sK13_SY653,type,
sK13_SY653: $i > ( $i > $o ) > $i ).
thf(tp_sK14_SY654,type,
sK14_SY654: $i ).
thf(tp_sK15_SY665,type,
sK15_SY665: $i ).
thf(tp_sK16_SY671,type,
sK16_SY671: $i > $i > $i > $i ).
thf(tp_sK17_SY677,type,
sK17_SY677: $i > $i > $i > $i ).
thf(tp_sK1_SY269,type,
sK1_SY269: individuals ).
thf(tp_sK2_SY526,type,
sK2_SY526: $i > $o ).
thf(tp_sK3_SY544,type,
sK3_SY544: $i > $o ).
thf(tp_sK4_SY561,type,
sK4_SY561: $i ).
thf(tp_sK5_SY577,type,
sK5_SY577: $i ).
thf(tp_sK6_SX0,type,
sK6_SX0: $i ).
thf(tp_sK7_SY628,type,
sK7_SY628: ( $i > $o ) > $i > $i ).
thf(tp_sK8_SY631,type,
sK8_SY631: ( $i > $o ) > $i > $i ).
thf(tp_sK9_SY634,type,
sK9_SY634: ( $i > $o ) > $i > $i ).
thf(bl_all,definition,
( bl_all
= ( ^ [A: individuals > $i > $o] : ( cs4_all @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bl_all) ).
thf(bl_and,definition,
( bl_and
= ( ^ [A: $i > $o,B: $i > $o] : ( cs4_and @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bl_and) ).
thf(bl_atom,definition,
( bl_atom
= ( ^ [P: $i > $o] : ( cs4_atom @ P ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bl_atom) ).
thf(bl_false,definition,
bl_false = cs4_false,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bl_false) ).
thf(bl_impl,definition,
( bl_impl
= ( ^ [A: $i > $o,B: $i > $o] : ( cs4_impl @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bl_impl) ).
thf(bl_or,definition,
( bl_or
= ( ^ [A: $i > $o,B: $i > $o] : ( cs4_or @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bl_or) ).
thf(bl_princ,definition,
( bl_princ
= ( ^ [P: $i > $o] : ( cs4_atom @ P ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',bl_says) ).
thf(bl_true,definition,
bl_true = cs4_true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bl_true) ).
thf(bl_valid,definition,
bl_valid = mvalid,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bl_valid_def) ).
thf(cs4_all,definition,
( cs4_all
= ( ^ [A: individuals > $i > $o] : ( mbox @ reli @ ( mall @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cs4_all) ).
thf(cs4_and,definition,
( cs4_and
= ( ^ [A: $i > $o,B: $i > $o] : ( mand @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cs4_and) ).
thf(cs4_atom,definition,
( cs4_atom
= ( ^ [P: $i > $o] : ( mbox @ reli @ P ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cs4_atom) ).
thf(cs4_box,definition,
( cs4_box
= ( ^ [A: $i > $o] : ( mbox @ reli @ ( mbox @ relr @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cs4_box) ).
thf(cs4_false,definition,
cs4_false = mfalse,
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',cs4_impl) ).
thf(cs4_or,definition,
( cs4_or
= ( ^ [A: $i > $o,B: $i > $o] : ( mor @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cs4_or) ).
thf(cs4_true,definition,
cs4_true = mtrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cs4_true) ).
thf(cs4_valid,definition,
( cs4_valid
= ( ^ [A: $i > $o] : ( mvalid @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cs4_valid_def) ).
thf(mall,definition,
( mall
= ( ^ [P: individuals > $i > $o,W: $i] :
! [X: individuals] : ( P @ X @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mall) ).
thf(mand,definition,
( mand
= ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
( ( X @ U )
& ( Y @ U ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',mbox) ).
thf(mcountersatisfiable,definition,
( mcountersatisfiable
= ( ^ [P: $i > $o] :
? [W: $i] :
~ ( P @ W ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',individuals_decl) ).
thf(mexists,definition,
( mexists
= ( ^ [P: individuals > $i > $o,W: $i] :
? [X: individuals] : ( P @ X @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mexists) ).
thf(mfalse,definition,
( mfalse
= ( ^ [X: $i] : $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mfalse) ).
thf(miff,definition,
( miff
= ( ^ [U: $i > $o,V: $i > $o] : ( mand @ ( mimpl @ U @ V ) @ ( mimpl @ V @ U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',miff) ).
thf(mimpl,definition,
( mimpl
= ( ^ [U: $i > $o,V: $i > $o] : ( mor @ ( mnot @ U ) @ V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimpl) ).
thf(minvalid,definition,
( minvalid
= ( ^ [P: $i > $o] :
! [W: $i] :
~ ( P @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',minvalid) ).
thf(mnot,definition,
( mnot
= ( ^ [X: $i > $o,U: $i] :
~ ( X @ U ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot) ).
thf(mor,definition,
( mor
= ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
( ( X @ U )
| ( Y @ U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor) ).
thf(msatisfiable,definition,
( msatisfiable
= ( ^ [P: $i > $o] :
? [W: $i] : ( P @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',msatisfiable) ).
thf(mtrue,definition,
( mtrue
= ( ^ [X: $i] : $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mtrue) ).
thf(mvalid,definition,
( mvalid
= ( ^ [P: $i > $o] :
! [W: $i] : ( P @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mvalid) ).
thf(1,axiom,
( cs4_valid
@ ( cs4_all
@ ^ [K: individuals] : ( cs4_impl @ ( princ_inj @ K ) @ ( princ_inj @ loca ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',loca_strength) ).
thf(2,axiom,
! [A: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ reli @ ( mbox @ relr @ A ) ) @ ( mbox @ relr @ ( mbox @ reli @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_i_r_commute) ).
thf(3,axiom,
! [A: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ relr @ A ) @ ( mbox @ relr @ ( mbox @ relr @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',trans_axiom_r) ).
thf(4,axiom,
! [A: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ reli @ A ) @ ( mbox @ reli @ ( mbox @ reli @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',trans_axiom_i) ).
thf(5,axiom,
! [A: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ relr @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',refl_axiom_r) ).
thf(6,axiom,
! [A: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ reli @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',refl_axiom_i) ).
thf(7,conjecture,
! [K: individuals,A: $i > $o,B: $i > $o] : ( bl_valid @ ( bl_impl @ ( bl_says @ K @ ( bl_impl @ A @ B ) ) @ ( bl_impl @ ( bl_says @ K @ A ) @ ( bl_says @ K @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bl_k) ).
thf(8,negated_conjecture,
( ( ! [K: individuals,A: $i > $o,B: $i > $o] : ( bl_valid @ ( bl_impl @ ( bl_says @ K @ ( bl_impl @ A @ B ) ) @ ( bl_impl @ ( bl_says @ K @ A ) @ ( bl_says @ K @ B ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[7]) ).
thf(9,plain,
( ( ! [SY269: individuals,SY270: $i > $o,SY271: $i > $o,SY288: $i,SY289: $i] :
( ( reli @ SY288 @ SY289 )
=> ( ~ ! [SY100: $i] :
( ( reli @ SY289 @ SY100 )
=> ! [SY63: $i] :
( ( relr @ SY100 @ SY63 )
=> ! [SY64: $i] :
( ( reli @ SY63 @ SY64 )
=> ( ~ ! [SY25: $i] :
( ( reli @ SY64 @ SY25 )
=> ( princ_inj @ SY269 @ SY25 ) )
| ! [SY66: $i] :
( ( reli @ SY64 @ SY66 )
=> ( ~ ( SY270 @ SY66 )
| ( SY271 @ SY66 ) ) ) ) ) ) )
| ! [SY260: $i] :
( ( reli @ SY289 @ SY260 )
=> ( ~ ! [SY187: $i] :
( ( reli @ SY260 @ SY187 )
=> ! [SY155: $i] :
( ( relr @ SY187 @ SY155 )
=> ! [SY156: $i] :
( ( reli @ SY155 @ SY156 )
=> ( ~ ! [SY134: $i] :
( ( reli @ SY156 @ SY134 )
=> ( princ_inj @ SY269 @ SY134 ) )
| ( SY270 @ SY156 ) ) ) ) )
| ! [SY249: $i] :
( ( reli @ SY260 @ SY249 )
=> ! [SY240: $i] :
( ( relr @ SY249 @ SY240 )
=> ! [SY241: $i] :
( ( reli @ SY240 @ SY241 )
=> ( ~ ! [SY219: $i] :
( ( reli @ SY241 @ SY219 )
=> ( princ_inj @ SY269 @ SY219 ) )
| ( SY271 @ SY241 ) ) ) ) ) ) ) ) ) )
= $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,
( ( ! [SY350: $i,SY351: $i] :
( ( reli @ SY350 @ SY351 )
=> ! [SY348: individuals,SY349: $i] :
( ( reli @ SY351 @ SY349 )
=> ( ~ ( princ_inj @ SY348 @ SY349 )
| ( princ_inj @ loca @ SY349 ) ) ) ) )
= $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,
( ( ! [SY358: $i > $o,SY397: $i] :
( ~ ! [SY398: $i] :
( ( reli @ SY397 @ SY398 )
=> ! [SY369: $i] :
( ( relr @ SY398 @ SY369 )
=> ( SY358 @ SY369 ) ) )
| ! [SY400: $i] :
( ( relr @ SY397 @ SY400 )
=> ! [SY391: $i] :
( ( reli @ SY400 @ SY391 )
=> ( SY358 @ SY391 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2,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(12,plain,
( ( ! [SY408: $i > $o,SY437: $i] :
( ~ ! [SY438: $i] :
( ( relr @ SY437 @ SY438 )
=> ( SY408 @ SY438 ) )
| ! [SY439: $i] :
( ( relr @ SY437 @ SY439 )
=> ! [SY432: $i] :
( ( relr @ SY439 @ SY432 )
=> ( SY408 @ SY432 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3,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(13,plain,
( ( ! [SY446: $i > $o,SY475: $i] :
( ~ ! [SY476: $i] :
( ( reli @ SY475 @ SY476 )
=> ( SY446 @ SY476 ) )
| ! [SY477: $i] :
( ( reli @ SY475 @ SY477 )
=> ! [SY470: $i] :
( ( reli @ SY477 @ SY470 )
=> ( SY446 @ SY470 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4,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(14,plain,
( ( ! [SY484: $i > $o,SY500: $i] :
( ~ ! [SY501: $i] :
( ( relr @ SY500 @ SY501 )
=> ( SY484 @ SY501 ) )
| ( SY484 @ SY500 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5,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(15,plain,
( ( ! [SY505: $i > $o,SY521: $i] :
( ~ ! [SY522: $i] :
( ( reli @ SY521 @ SY522 )
=> ( SY505 @ SY522 ) )
| ( SY505 @ SY521 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6,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(16,plain,
( ( ! [SY526: $i > $o,SY527: $i > $o,SY528: $i,SY529: $i] :
( ( reli @ SY528 @ SY529 )
=> ( ~ ! [SY530: $i] :
( ( reli @ SY529 @ SY530 )
=> ! [SY531: $i] :
( ( relr @ SY530 @ SY531 )
=> ! [SY532: $i] :
( ( reli @ SY531 @ SY532 )
=> ( ~ ! [SY533: $i] :
( ( reli @ SY532 @ SY533 )
=> ( princ_inj @ sK1_SY269 @ SY533 ) )
| ! [SY66: $i] :
( ( reli @ SY532 @ SY66 )
=> ( ~ ( SY526 @ SY66 )
| ( SY527 @ SY66 ) ) ) ) ) ) )
| ! [SY535: $i] :
( ( reli @ SY529 @ SY535 )
=> ( ~ ! [SY536: $i] :
( ( reli @ SY535 @ SY536 )
=> ! [SY537: $i] :
( ( relr @ SY536 @ SY537 )
=> ! [SY538: $i] :
( ( reli @ SY537 @ SY538 )
=> ( ~ ! [SY539: $i] :
( ( reli @ SY538 @ SY539 )
=> ( princ_inj @ sK1_SY269 @ SY539 ) )
| ( SY526 @ SY538 ) ) ) ) )
| ! [SY540: $i] :
( ( reli @ SY535 @ SY540 )
=> ! [SY541: $i] :
( ( relr @ SY540 @ SY541 )
=> ! [SY542: $i] :
( ( reli @ SY541 @ SY542 )
=> ( ~ ! [SY543: $i] :
( ( reli @ SY542 @ SY543 )
=> ( princ_inj @ sK1_SY269 @ SY543 ) )
| ( SY527 @ SY542 ) ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[9]) ).
thf(17,plain,
( ( ! [SY544: $i > $o,SY545: $i,SY546: $i] :
( ( reli @ SY545 @ SY546 )
=> ( ~ ! [SY547: $i] :
( ( reli @ SY546 @ SY547 )
=> ! [SY548: $i] :
( ( relr @ SY547 @ SY548 )
=> ! [SY549: $i] :
( ( reli @ SY548 @ SY549 )
=> ( ~ ! [SY533: $i] :
( ( reli @ SY549 @ SY533 )
=> ( princ_inj @ sK1_SY269 @ SY533 ) )
| ! [SY551: $i] :
( ( reli @ SY549 @ SY551 )
=> ( ~ ( sK2_SY526 @ SY551 )
| ( SY544 @ SY551 ) ) ) ) ) ) )
| ! [SY552: $i] :
( ( reli @ SY546 @ SY552 )
=> ( ~ ! [SY553: $i] :
( ( reli @ SY552 @ SY553 )
=> ! [SY554: $i] :
( ( relr @ SY553 @ SY554 )
=> ! [SY555: $i] :
( ( reli @ SY554 @ SY555 )
=> ( ~ ! [SY539: $i] :
( ( reli @ SY555 @ SY539 )
=> ( princ_inj @ sK1_SY269 @ SY539 ) )
| ( sK2_SY526 @ SY555 ) ) ) ) )
| ! [SY540: $i] :
( ( reli @ SY552 @ SY540 )
=> ! [SY541: $i] :
( ( relr @ SY540 @ SY541 )
=> ! [SY542: $i] :
( ( reli @ SY541 @ SY542 )
=> ( ~ ! [SY543: $i] :
( ( reli @ SY542 @ SY543 )
=> ( princ_inj @ sK1_SY269 @ SY543 ) )
| ( SY544 @ SY542 ) ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[16]) ).
thf(18,plain,
( ( ! [SY561: $i,SY562: $i] :
( ( reli @ SY561 @ SY562 )
=> ( ~ ! [SY563: $i] :
( ( reli @ SY562 @ SY563 )
=> ! [SY564: $i] :
( ( relr @ SY563 @ SY564 )
=> ! [SY565: $i] :
( ( reli @ SY564 @ SY565 )
=> ( ~ ! [SY533: $i] :
( ( reli @ SY565 @ SY533 )
=> ( princ_inj @ sK1_SY269 @ SY533 ) )
| ! [SY567: $i] :
( ( reli @ SY565 @ SY567 )
=> ( ~ ( sK2_SY526 @ SY567 )
| ( sK3_SY544 @ SY567 ) ) ) ) ) ) )
| ! [SY568: $i] :
( ( reli @ SY562 @ SY568 )
=> ( ~ ! [SY553: $i] :
( ( reli @ SY568 @ SY553 )
=> ! [SY554: $i] :
( ( relr @ SY553 @ SY554 )
=> ! [SY555: $i] :
( ( reli @ SY554 @ SY555 )
=> ( ~ ! [SY539: $i] :
( ( reli @ SY555 @ SY539 )
=> ( princ_inj @ sK1_SY269 @ SY539 ) )
| ( sK2_SY526 @ SY555 ) ) ) ) )
| ! [SY573: $i] :
( ( reli @ SY568 @ SY573 )
=> ! [SY574: $i] :
( ( relr @ SY573 @ SY574 )
=> ! [SY575: $i] :
( ( reli @ SY574 @ SY575 )
=> ( ~ ! [SY543: $i] :
( ( reli @ SY575 @ SY543 )
=> ( princ_inj @ sK1_SY269 @ SY543 ) )
| ( sK3_SY544 @ SY575 ) ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[17]) ).
thf(19,plain,
( ( ! [SY577: $i] :
( ( reli @ sK4_SY561 @ SY577 )
=> ( ~ ! [SY563: $i] :
( ( reli @ SY577 @ SY563 )
=> ! [SY564: $i] :
( ( relr @ SY563 @ SY564 )
=> ! [SY565: $i] :
( ( reli @ SY564 @ SY565 )
=> ( ~ ! [SY533: $i] :
( ( reli @ SY565 @ SY533 )
=> ( princ_inj @ sK1_SY269 @ SY533 ) )
| ! [SY567: $i] :
( ( reli @ SY565 @ SY567 )
=> ( ~ ( sK2_SY526 @ SY567 )
| ( sK3_SY544 @ SY567 ) ) ) ) ) ) )
| ! [SY568: $i] :
( ( reli @ SY577 @ SY568 )
=> ( ~ ! [SY553: $i] :
( ( reli @ SY568 @ SY553 )
=> ! [SY554: $i] :
( ( relr @ SY553 @ SY554 )
=> ! [SY555: $i] :
( ( reli @ SY554 @ SY555 )
=> ( ~ ! [SY539: $i] :
( ( reli @ SY555 @ SY539 )
=> ( princ_inj @ sK1_SY269 @ SY539 ) )
| ( sK2_SY526 @ SY555 ) ) ) ) )
| ! [SY573: $i] :
( ( reli @ SY568 @ SY573 )
=> ! [SY574: $i] :
( ( relr @ SY573 @ SY574 )
=> ! [SY575: $i] :
( ( reli @ SY574 @ SY575 )
=> ( ~ ! [SY543: $i] :
( ( reli @ SY575 @ SY543 )
=> ( princ_inj @ sK1_SY269 @ SY543 ) )
| ( sK3_SY544 @ SY575 ) ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[18]) ).
thf(20,plain,
( ( ( reli @ sK4_SY561 @ sK5_SY577 )
=> ( ~ ! [SY592: $i] :
( ( reli @ sK5_SY577 @ SY592 )
=> ! [SY564: $i] :
( ( relr @ SY592 @ SY564 )
=> ! [SY565: $i] :
( ( reli @ SY564 @ SY565 )
=> ( ~ ! [SY533: $i] :
( ( reli @ SY565 @ SY533 )
=> ( princ_inj @ sK1_SY269 @ SY533 ) )
| ! [SY567: $i] :
( ( reli @ SY565 @ SY567 )
=> ( ~ ( sK2_SY526 @ SY567 )
| ( sK3_SY544 @ SY567 ) ) ) ) ) ) )
| ! [SY597: $i] :
( ( reli @ sK5_SY577 @ SY597 )
=> ( ~ ! [SY553: $i] :
( ( reli @ SY597 @ SY553 )
=> ! [SY554: $i] :
( ( relr @ SY553 @ SY554 )
=> ! [SY555: $i] :
( ( reli @ SY554 @ SY555 )
=> ( ~ ! [SY539: $i] :
( ( reli @ SY555 @ SY539 )
=> ( princ_inj @ sK1_SY269 @ SY539 ) )
| ( sK2_SY526 @ SY555 ) ) ) ) )
| ! [SY573: $i] :
( ( reli @ SY597 @ SY573 )
=> ! [SY574: $i] :
( ( relr @ SY573 @ SY574 )
=> ! [SY575: $i] :
( ( reli @ SY574 @ SY575 )
=> ( ~ ! [SY543: $i] :
( ( reli @ SY575 @ SY543 )
=> ( princ_inj @ sK1_SY269 @ SY543 ) )
| ( sK3_SY544 @ SY575 ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[19]) ).
thf(21,plain,
( ( reli @ sK4_SY561 @ sK5_SY577 )
= $true ),
inference(standard_cnf,[status(thm)],[20]) ).
thf(22,plain,
( ( ~ ! [SY592: $i] :
( ( reli @ sK5_SY577 @ SY592 )
=> ! [SY564: $i] :
( ( relr @ SY592 @ SY564 )
=> ! [SY565: $i] :
( ( reli @ SY564 @ SY565 )
=> ( ~ ! [SY533: $i] :
( ( reli @ SY565 @ SY533 )
=> ( princ_inj @ sK1_SY269 @ SY533 ) )
| ! [SY567: $i] :
( ( reli @ SY565 @ SY567 )
=> ( ~ ( sK2_SY526 @ SY567 )
| ( sK3_SY544 @ SY567 ) ) ) ) ) ) )
| ! [SY597: $i] :
( ( reli @ sK5_SY577 @ SY597 )
=> ( ~ ! [SY553: $i] :
( ( reli @ SY597 @ SY553 )
=> ! [SY554: $i] :
( ( relr @ SY553 @ SY554 )
=> ! [SY555: $i] :
( ( reli @ SY554 @ SY555 )
=> ( ~ ! [SY539: $i] :
( ( reli @ SY555 @ SY539 )
=> ( princ_inj @ sK1_SY269 @ SY539 ) )
| ( sK2_SY526 @ SY555 ) ) ) ) )
| ! [SY573: $i] :
( ( reli @ SY597 @ SY573 )
=> ! [SY574: $i] :
( ( relr @ SY573 @ SY574 )
=> ! [SY575: $i] :
( ( reli @ SY574 @ SY575 )
=> ( ~ ! [SY543: $i] :
( ( reli @ SY575 @ SY543 )
=> ( princ_inj @ sK1_SY269 @ SY543 ) )
| ( sK3_SY544 @ SY575 ) ) ) ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[20]) ).
thf(23,plain,
( ( ~ ( ~ ! [SY592: $i] :
( ( reli @ sK5_SY577 @ SY592 )
=> ! [SY564: $i] :
( ( relr @ SY592 @ SY564 )
=> ! [SY565: $i] :
( ( reli @ SY564 @ SY565 )
=> ( ~ ! [SY533: $i] :
( ( reli @ SY565 @ SY533 )
=> ( princ_inj @ sK1_SY269 @ SY533 ) )
| ! [SY567: $i] :
( ( reli @ SY565 @ SY567 )
=> ( ~ ( sK2_SY526 @ SY567 )
| ( sK3_SY544 @ SY567 ) ) ) ) ) ) )
| ! [SY597: $i] :
( ( reli @ sK5_SY577 @ SY597 )
=> ( ~ ! [SY553: $i] :
( ( reli @ SY597 @ SY553 )
=> ! [SY554: $i] :
( ( relr @ SY553 @ SY554 )
=> ! [SY555: $i] :
( ( reli @ SY554 @ SY555 )
=> ( ~ ! [SY539: $i] :
( ( reli @ SY555 @ SY539 )
=> ( princ_inj @ sK1_SY269 @ SY539 ) )
| ( sK2_SY526 @ SY555 ) ) ) ) )
| ! [SY573: $i] :
( ( reli @ SY597 @ SY573 )
=> ! [SY574: $i] :
( ( relr @ SY573 @ SY574 )
=> ! [SY575: $i] :
( ( reli @ SY574 @ SY575 )
=> ( ~ ! [SY543: $i] :
( ( reli @ SY575 @ SY543 )
=> ( princ_inj @ sK1_SY269 @ SY543 ) )
| ( sK3_SY544 @ SY575 ) ) ) ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[22]) ).
thf(24,plain,
( ( ! [SY505: $i > $o,SY521: $i] :
( ~ ! [SY522: $i] :
( ( reli @ SY521 @ SY522 )
=> ( SY505 @ SY522 ) )
| ( SY505 @ SY521 ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(25,plain,
( ( ! [SY484: $i > $o,SY500: $i] :
( ~ ! [SY501: $i] :
( ( relr @ SY500 @ SY501 )
=> ( SY484 @ SY501 ) )
| ( SY484 @ SY500 ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(26,plain,
( ( ! [SY446: $i > $o,SY475: $i] :
( ~ ! [SY476: $i] :
( ( reli @ SY475 @ SY476 )
=> ( SY446 @ SY476 ) )
| ! [SY477: $i] :
( ( reli @ SY475 @ SY477 )
=> ! [SY470: $i] :
( ( reli @ SY477 @ SY470 )
=> ( SY446 @ SY470 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(27,plain,
( ( ! [SY408: $i > $o,SY437: $i] :
( ~ ! [SY438: $i] :
( ( relr @ SY437 @ SY438 )
=> ( SY408 @ SY438 ) )
| ! [SY439: $i] :
( ( relr @ SY437 @ SY439 )
=> ! [SY432: $i] :
( ( relr @ SY439 @ SY432 )
=> ( SY408 @ SY432 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(28,plain,
( ( ! [SY358: $i > $o,SY397: $i] :
( ~ ! [SY398: $i] :
( ( reli @ SY397 @ SY398 )
=> ! [SY369: $i] :
( ( relr @ SY398 @ SY369 )
=> ( SY358 @ SY369 ) ) )
| ! [SY400: $i] :
( ( relr @ SY397 @ SY400 )
=> ! [SY391: $i] :
( ( reli @ SY400 @ SY391 )
=> ( SY358 @ SY391 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(29,plain,
( ( ! [SY350: $i,SY351: $i] :
( ( reli @ SY350 @ SY351 )
=> ! [SY348: individuals,SY349: $i] :
( ( reli @ SY351 @ SY349 )
=> ( ~ ( princ_inj @ SY348 @ SY349 )
| ( princ_inj @ loca @ SY349 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(30,plain,
( ( reli @ sK4_SY561 @ sK5_SY577 )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(31,plain,
( ( ~ ( ~ ! [SY592: $i] :
( ( reli @ sK5_SY577 @ SY592 )
=> ! [SY564: $i] :
( ( relr @ SY592 @ SY564 )
=> ! [SY565: $i] :
( ( reli @ SY564 @ SY565 )
=> ( ~ ! [SY533: $i] :
( ( reli @ SY565 @ SY533 )
=> ( princ_inj @ sK1_SY269 @ SY533 ) )
| ! [SY567: $i] :
( ( reli @ SY565 @ SY567 )
=> ( ~ ( sK2_SY526 @ SY567 )
| ( sK3_SY544 @ SY567 ) ) ) ) ) ) )
| ! [SY597: $i] :
( ( reli @ sK5_SY577 @ SY597 )
=> ( ~ ! [SY553: $i] :
( ( reli @ SY597 @ SY553 )
=> ! [SY554: $i] :
( ( relr @ SY553 @ SY554 )
=> ! [SY555: $i] :
( ( reli @ SY554 @ SY555 )
=> ( ~ ! [SY539: $i] :
( ( reli @ SY555 @ SY539 )
=> ( princ_inj @ sK1_SY269 @ SY539 ) )
| ( sK2_SY526 @ SY555 ) ) ) ) )
| ! [SY573: $i] :
( ( reli @ SY597 @ SY573 )
=> ! [SY574: $i] :
( ( relr @ SY573 @ SY574 )
=> ! [SY575: $i] :
( ( reli @ SY574 @ SY575 )
=> ( ~ ! [SY543: $i] :
( ( reli @ SY575 @ SY543 )
=> ( princ_inj @ sK1_SY269 @ SY543 ) )
| ( sK3_SY544 @ SY575 ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(32,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( reli @ SX0 @ SX1 )
| ! [SX2: individuals,SX3: $i] :
( ~ ( reli @ SX1 @ SX3 )
| ~ ( princ_inj @ SX2 @ SX3 )
| ( princ_inj @ loca @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29,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(33,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( reli @ sK5_SY577 @ SX0 )
| ! [SX1: $i] :
( ~ ( relr @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( reli @ SX1 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( reli @ SX2 @ SX3 )
| ( princ_inj @ sK1_SY269 @ SX3 ) )
| ! [SX3: $i] :
( ~ ( reli @ SX2 @ SX3 )
| ~ ( sK2_SY526 @ SX3 )
| ( sK3_SY544 @ SX3 ) ) ) ) )
| ! [SX0: $i] :
( ~ ( reli @ sK5_SY577 @ SX0 )
| ~ ! [SX1: $i] :
( ~ ( reli @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( relr @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( reli @ SX2 @ SX3 )
| ~ ! [SX4: $i] :
( ~ ( reli @ SX3 @ SX4 )
| ( princ_inj @ sK1_SY269 @ SX4 ) )
| ( sK2_SY526 @ SX3 ) ) ) )
| ! [SX1: $i] :
( ~ ( reli @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( relr @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( reli @ SX2 @ SX3 )
| ~ ! [SX4: $i] :
( ~ ( reli @ SX3 @ SX4 )
| ( princ_inj @ sK1_SY269 @ SX4 ) )
| ( sK3_SY544 @ SX3 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31,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(34,plain,
( ( ! [SX0: $i > $o,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( reli @ SX1 @ SX2 )
| ( SX0 @ SX2 ) )
| ! [SX2: $i] :
( ~ ( reli @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( reli @ SX2 @ SX3 )
| ( SX0 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26,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(35,plain,
( ( ! [SX0: $i > $o,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( relr @ SX1 @ SX2 )
| ( SX0 @ SX2 ) )
| ! [SX2: $i] :
( ~ ( relr @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( relr @ SX2 @ SX3 )
| ( SX0 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27,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(36,plain,
( ( ! [SX0: $i > $o,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( reli @ SX1 @ SX2 )
| ( SX0 @ SX2 ) )
| ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24,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(37,plain,
( ( ! [SX0: $i > $o,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( relr @ SX1 @ SX2 )
| ( SX0 @ SX2 ) )
| ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25,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(38,plain,
( ( ! [SX0: $i > $o,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( reli @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( relr @ SX2 @ SX3 )
| ( SX0 @ SX3 ) ) )
| ! [SX2: $i] :
( ~ ( relr @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( reli @ SX2 @ SX3 )
| ( SX0 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28,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(39,plain,
! [SV1: $i] :
( ( ! [SY606: $i] :
( ~ ( reli @ SV1 @ SY606 )
| ! [SX2: individuals,SX3: $i] :
( ~ ( reli @ SY606 @ SX3 )
| ~ ( princ_inj @ SX2 @ SX3 )
| ( princ_inj @ loca @ SX3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(40,plain,
( ( ~ ! [SX0: $i] :
( ~ ( reli @ sK5_SY577 @ SX0 )
| ! [SX1: $i] :
( ~ ( relr @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( reli @ SX1 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( reli @ SX2 @ SX3 )
| ( princ_inj @ sK1_SY269 @ SX3 ) )
| ! [SX3: $i] :
( ~ ( reli @ SX2 @ SX3 )
| ~ ( sK2_SY526 @ SX3 )
| ( sK3_SY544 @ SX3 ) ) ) ) )
| ! [SX0: $i] :
( ~ ( reli @ sK5_SY577 @ SX0 )
| ~ ! [SX1: $i] :
( ~ ( reli @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( relr @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( reli @ SX2 @ SX3 )
| ~ ! [SX4: $i] :
( ~ ( reli @ SX3 @ SX4 )
| ( princ_inj @ sK1_SY269 @ SX4 ) )
| ( sK2_SY526 @ SX3 ) ) ) )
| ! [SX1: $i] :
( ~ ( reli @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( relr @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( reli @ SX2 @ SX3 )
| ~ ! [SX4: $i] :
( ~ ( reli @ SX3 @ SX4 )
| ( princ_inj @ sK1_SY269 @ SX4 ) )
| ( sK3_SY544 @ SX3 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(41,plain,
! [SV2: $i > $o] :
( ( ! [SY609: $i] :
( ~ ! [SY610: $i] :
( ~ ( reli @ SY609 @ SY610 )
| ( SV2 @ SY610 ) )
| ! [SY611: $i] :
( ~ ( reli @ SY609 @ SY611 )
| ! [SY612: $i] :
( ~ ( reli @ SY611 @ SY612 )
| ( SV2 @ SY612 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(42,plain,
! [SV3: $i > $o] :
( ( ! [SY613: $i] :
( ~ ! [SY614: $i] :
( ~ ( relr @ SY613 @ SY614 )
| ( SV3 @ SY614 ) )
| ! [SY615: $i] :
( ~ ( relr @ SY613 @ SY615 )
| ! [SY616: $i] :
( ~ ( relr @ SY615 @ SY616 )
| ( SV3 @ SY616 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(43,plain,
! [SV4: $i > $o] :
( ( ! [SY617: $i] :
( ~ ! [SY618: $i] :
( ~ ( reli @ SY617 @ SY618 )
| ( SV4 @ SY618 ) )
| ( SV4 @ SY617 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(44,plain,
! [SV5: $i > $o] :
( ( ! [SY619: $i] :
( ~ ! [SY620: $i] :
( ~ ( relr @ SY619 @ SY620 )
| ( SV5 @ SY620 ) )
| ( SV5 @ SY619 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(45,plain,
! [SV6: $i > $o] :
( ( ! [SY621: $i] :
( ~ ! [SY622: $i] :
( ~ ( reli @ SY621 @ SY622 )
| ! [SY623: $i] :
( ~ ( relr @ SY622 @ SY623 )
| ( SV6 @ SY623 ) ) )
| ! [SY624: $i] :
( ~ ( relr @ SY621 @ SY624 )
| ! [SY625: $i] :
( ~ ( reli @ SY624 @ SY625 )
| ( SV6 @ SY625 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(46,plain,
! [SV7: $i,SV1: $i] :
( ( ~ ( reli @ SV1 @ SV7 )
| ! [SY626: individuals,SY627: $i] :
( ~ ( reli @ SV7 @ SY627 )
| ~ ( princ_inj @ SY626 @ SY627 )
| ( princ_inj @ loca @ SY627 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(47,plain,
( ( ~ ! [SX0: $i] :
( ~ ( reli @ sK5_SY577 @ SX0 )
| ! [SX1: $i] :
( ~ ( relr @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( reli @ SX1 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( reli @ SX2 @ SX3 )
| ( princ_inj @ sK1_SY269 @ SX3 ) )
| ! [SX3: $i] :
( ~ ( reli @ SX2 @ SX3 )
| ~ ( sK2_SY526 @ SX3 )
| ( sK3_SY544 @ SX3 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[40]) ).
thf(48,plain,
( ( ! [SX0: $i] :
( ~ ( reli @ sK5_SY577 @ SX0 )
| ~ ! [SX1: $i] :
( ~ ( reli @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( relr @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( reli @ SX2 @ SX3 )
| ~ ! [SX4: $i] :
( ~ ( reli @ SX3 @ SX4 )
| ( princ_inj @ sK1_SY269 @ SX4 ) )
| ( sK2_SY526 @ SX3 ) ) ) )
| ! [SX1: $i] :
( ~ ( reli @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( relr @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( reli @ SX2 @ SX3 )
| ~ ! [SX4: $i] :
( ~ ( reli @ SX3 @ SX4 )
| ( princ_inj @ sK1_SY269 @ SX4 ) )
| ( sK3_SY544 @ SX3 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[40]) ).
thf(49,plain,
! [SV2: $i > $o,SV8: $i] :
( ( ~ ! [SY628: $i] :
( ~ ( reli @ SV8 @ SY628 )
| ( SV2 @ SY628 ) )
| ! [SY629: $i] :
( ~ ( reli @ SV8 @ SY629 )
| ! [SY612: $i] :
( ~ ( reli @ SY629 @ SY612 )
| ( SV2 @ SY612 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(50,plain,
! [SV3: $i > $o,SV9: $i] :
( ( ~ ! [SY631: $i] :
( ~ ( relr @ SV9 @ SY631 )
| ( SV3 @ SY631 ) )
| ! [SY632: $i] :
( ~ ( relr @ SV9 @ SY632 )
| ! [SY616: $i] :
( ~ ( relr @ SY632 @ SY616 )
| ( SV3 @ SY616 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(51,plain,
! [SV4: $i > $o,SV10: $i] :
( ( ~ ! [SY634: $i] :
( ~ ( reli @ SV10 @ SY634 )
| ( SV4 @ SY634 ) )
| ( SV4 @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(52,plain,
! [SV5: $i > $o,SV11: $i] :
( ( ~ ! [SY635: $i] :
( ~ ( relr @ SV11 @ SY635 )
| ( SV5 @ SY635 ) )
| ( SV5 @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(53,plain,
! [SV6: $i > $o,SV12: $i] :
( ( ~ ! [SY636: $i] :
( ~ ( reli @ SV12 @ SY636 )
| ! [SY623: $i] :
( ~ ( relr @ SY636 @ SY623 )
| ( SV6 @ SY623 ) ) )
| ! [SY638: $i] :
( ~ ( relr @ SV12 @ SY638 )
| ! [SY625: $i] :
( ~ ( reli @ SY638 @ SY625 )
| ( SV6 @ SY625 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(54,plain,
! [SV7: $i,SV1: $i] :
( ( ( ~ ( reli @ SV1 @ SV7 ) )
= $true )
| ( ( ! [SY626: individuals,SY627: $i] :
( ~ ( reli @ SV7 @ SY627 )
| ~ ( princ_inj @ SY626 @ SY627 )
| ( princ_inj @ loca @ SY627 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[46]) ).
thf(55,plain,
( ( ! [SX0: $i] :
( ~ ( reli @ sK5_SY577 @ SX0 )
| ! [SX1: $i] :
( ~ ( relr @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( reli @ SX1 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( reli @ SX2 @ SX3 )
| ( princ_inj @ sK1_SY269 @ SX3 ) )
| ! [SX3: $i] :
( ~ ( reli @ SX2 @ SX3 )
| ~ ( sK2_SY526 @ SX3 )
| ( sK3_SY544 @ SX3 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[47]) ).
thf(56,plain,
( ( ~ ( reli @ sK5_SY577 @ sK6_SX0 )
| ~ ! [SY640: $i] :
( ~ ( reli @ sK6_SX0 @ SY640 )
| ! [SX2: $i] :
( ~ ( relr @ SY640 @ SX2 )
| ! [SX3: $i] :
( ~ ( reli @ SX2 @ SX3 )
| ~ ! [SX4: $i] :
( ~ ( reli @ SX3 @ SX4 )
| ( princ_inj @ sK1_SY269 @ SX4 ) )
| ( sK2_SY526 @ SX3 ) ) ) )
| ! [SY644: $i] :
( ~ ( reli @ sK6_SX0 @ SY644 )
| ! [SX2: $i] :
( ~ ( relr @ SY644 @ SX2 )
| ! [SX3: $i] :
( ~ ( reli @ SX2 @ SX3 )
| ~ ! [SX4: $i] :
( ~ ( reli @ SX3 @ SX4 )
| ( princ_inj @ sK1_SY269 @ SX4 ) )
| ( sK3_SY544 @ SX3 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[48]) ).
thf(57,plain,
! [SV2: $i > $o,SV8: $i] :
( ( ( ~ ! [SY628: $i] :
( ~ ( reli @ SV8 @ SY628 )
| ( SV2 @ SY628 ) ) )
= $true )
| ( ( ! [SY629: $i] :
( ~ ( reli @ SV8 @ SY629 )
| ! [SY612: $i] :
( ~ ( reli @ SY629 @ SY612 )
| ( SV2 @ SY612 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[49]) ).
thf(58,plain,
! [SV3: $i > $o,SV9: $i] :
( ( ( ~ ! [SY631: $i] :
( ~ ( relr @ SV9 @ SY631 )
| ( SV3 @ SY631 ) ) )
= $true )
| ( ( ! [SY632: $i] :
( ~ ( relr @ SV9 @ SY632 )
| ! [SY616: $i] :
( ~ ( relr @ SY632 @ SY616 )
| ( SV3 @ SY616 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[50]) ).
thf(59,plain,
! [SV4: $i > $o,SV10: $i] :
( ( ( ~ ! [SY634: $i] :
( ~ ( reli @ SV10 @ SY634 )
| ( SV4 @ SY634 ) ) )
= $true )
| ( ( SV4 @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[51]) ).
thf(60,plain,
! [SV5: $i > $o,SV11: $i] :
( ( ( ~ ! [SY635: $i] :
( ~ ( relr @ SV11 @ SY635 )
| ( SV5 @ SY635 ) ) )
= $true )
| ( ( SV5 @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[52]) ).
thf(61,plain,
! [SV6: $i > $o,SV12: $i] :
( ( ( ~ ! [SY636: $i] :
( ~ ( reli @ SV12 @ SY636 )
| ! [SY623: $i] :
( ~ ( relr @ SY636 @ SY623 )
| ( SV6 @ SY623 ) ) ) )
= $true )
| ( ( ! [SY638: $i] :
( ~ ( relr @ SV12 @ SY638 )
| ! [SY625: $i] :
( ~ ( reli @ SY638 @ SY625 )
| ( SV6 @ SY625 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[53]) ).
thf(62,plain,
! [SV7: $i,SV1: $i] :
( ( ( reli @ SV1 @ SV7 )
= $false )
| ( ( ! [SY626: individuals,SY627: $i] :
( ~ ( reli @ SV7 @ SY627 )
| ~ ( princ_inj @ SY626 @ SY627 )
| ( princ_inj @ loca @ SY627 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(63,plain,
! [SV13: $i] :
( ( ~ ( reli @ sK5_SY577 @ SV13 )
| ! [SY648: $i] :
( ~ ( relr @ SV13 @ SY648 )
| ! [SX2: $i] :
( ~ ( reli @ SY648 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( reli @ SX2 @ SX3 )
| ( princ_inj @ sK1_SY269 @ SX3 ) )
| ! [SX3: $i] :
( ~ ( reli @ SX2 @ SX3 )
| ~ ( sK2_SY526 @ SX3 )
| ( sK3_SY544 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(64,plain,
( ( ~ ( reli @ sK5_SY577 @ sK6_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[56]) ).
thf(65,plain,
( ( ~ ! [SY640: $i] :
( ~ ( reli @ sK6_SX0 @ SY640 )
| ! [SX2: $i] :
( ~ ( relr @ SY640 @ SX2 )
| ! [SX3: $i] :
( ~ ( reli @ SX2 @ SX3 )
| ~ ! [SX4: $i] :
( ~ ( reli @ SX3 @ SX4 )
| ( princ_inj @ sK1_SY269 @ SX4 ) )
| ( sK2_SY526 @ SX3 ) ) ) )
| ! [SY644: $i] :
( ~ ( reli @ sK6_SX0 @ SY644 )
| ! [SX2: $i] :
( ~ ( relr @ SY644 @ SX2 )
| ! [SX3: $i] :
( ~ ( reli @ SX2 @ SX3 )
| ~ ! [SX4: $i] :
( ~ ( reli @ SX3 @ SX4 )
| ( princ_inj @ sK1_SY269 @ SX4 ) )
| ( sK3_SY544 @ SX3 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[56]) ).
thf(66,plain,
! [SV2: $i > $o,SV8: $i] :
( ( ( ! [SY628: $i] :
( ~ ( reli @ SV8 @ SY628 )
| ( SV2 @ SY628 ) ) )
= $false )
| ( ( ! [SY629: $i] :
( ~ ( reli @ SV8 @ SY629 )
| ! [SY612: $i] :
( ~ ( reli @ SY629 @ SY612 )
| ( SV2 @ SY612 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(67,plain,
! [SV3: $i > $o,SV9: $i] :
( ( ( ! [SY631: $i] :
( ~ ( relr @ SV9 @ SY631 )
| ( SV3 @ SY631 ) ) )
= $false )
| ( ( ! [SY632: $i] :
( ~ ( relr @ SV9 @ SY632 )
| ! [SY616: $i] :
( ~ ( relr @ SY632 @ SY616 )
| ( SV3 @ SY616 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(68,plain,
! [SV4: $i > $o,SV10: $i] :
( ( ( ! [SY634: $i] :
( ~ ( reli @ SV10 @ SY634 )
| ( SV4 @ SY634 ) ) )
= $false )
| ( ( SV4 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(69,plain,
! [SV5: $i > $o,SV11: $i] :
( ( ( ! [SY635: $i] :
( ~ ( relr @ SV11 @ SY635 )
| ( SV5 @ SY635 ) ) )
= $false )
| ( ( SV5 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(70,plain,
! [SV6: $i > $o,SV12: $i] :
( ( ( ! [SY636: $i] :
( ~ ( reli @ SV12 @ SY636 )
| ! [SY623: $i] :
( ~ ( relr @ SY636 @ SY623 )
| ( SV6 @ SY623 ) ) ) )
= $false )
| ( ( ! [SY638: $i] :
( ~ ( relr @ SV12 @ SY638 )
| ! [SY625: $i] :
( ~ ( reli @ SY638 @ SY625 )
| ( SV6 @ SY625 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(71,plain,
! [SV1: $i,SV14: individuals,SV7: $i] :
( ( ( ! [SY652: $i] :
( ~ ( reli @ SV7 @ SY652 )
| ~ ( princ_inj @ SV14 @ SY652 )
| ( princ_inj @ loca @ SY652 ) ) )
= $true )
| ( ( reli @ SV1 @ SV7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(72,plain,
! [SV13: $i] :
( ( ( ~ ( reli @ sK5_SY577 @ SV13 ) )
= $true )
| ( ( ! [SY648: $i] :
( ~ ( relr @ SV13 @ SY648 )
| ! [SX2: $i] :
( ~ ( reli @ SY648 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( reli @ SX2 @ SX3 )
| ( princ_inj @ sK1_SY269 @ SX3 ) )
| ! [SX3: $i] :
( ~ ( reli @ SX2 @ SX3 )
| ~ ( sK2_SY526 @ SX3 )
| ( sK3_SY544 @ SX3 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[63]) ).
thf(73,plain,
( ( reli @ sK5_SY577 @ sK6_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[64]) ).
thf(74,plain,
( ( ~ ! [SY640: $i] :
( ~ ( reli @ sK6_SX0 @ SY640 )
| ! [SX2: $i] :
( ~ ( relr @ SY640 @ SX2 )
| ! [SX3: $i] :
( ~ ( reli @ SX2 @ SX3 )
| ~ ! [SX4: $i] :
( ~ ( reli @ SX3 @ SX4 )
| ( princ_inj @ sK1_SY269 @ SX4 ) )
| ( sK2_SY526 @ SX3 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[65]) ).
thf(75,plain,
( ( ! [SY644: $i] :
( ~ ( reli @ sK6_SX0 @ SY644 )
| ! [SX2: $i] :
( ~ ( relr @ SY644 @ SX2 )
| ! [SX3: $i] :
( ~ ( reli @ SX2 @ SX3 )
| ~ ! [SX4: $i] :
( ~ ( reli @ SX3 @ SX4 )
| ( princ_inj @ sK1_SY269 @ SX4 ) )
| ( sK3_SY544 @ SX3 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[65]) ).
thf(76,plain,
! [SV2: $i > $o,SV8: $i] :
( ( ( ~ ( reli @ SV8 @ ( sK7_SY628 @ SV2 @ SV8 ) )
| ( SV2 @ ( sK7_SY628 @ SV2 @ SV8 ) ) )
= $false )
| ( ( ! [SY629: $i] :
( ~ ( reli @ SV8 @ SY629 )
| ! [SY612: $i] :
( ~ ( reli @ SY629 @ SY612 )
| ( SV2 @ SY612 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[66]) ).
thf(77,plain,
! [SV3: $i > $o,SV9: $i] :
( ( ( ~ ( relr @ SV9 @ ( sK8_SY631 @ SV3 @ SV9 ) )
| ( SV3 @ ( sK8_SY631 @ SV3 @ SV9 ) ) )
= $false )
| ( ( ! [SY632: $i] :
( ~ ( relr @ SV9 @ SY632 )
| ! [SY616: $i] :
( ~ ( relr @ SY632 @ SY616 )
| ( SV3 @ SY616 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[67]) ).
thf(78,plain,
! [SV4: $i > $o,SV10: $i] :
( ( ( ~ ( reli @ SV10 @ ( sK9_SY634 @ SV4 @ SV10 ) )
| ( SV4 @ ( sK9_SY634 @ SV4 @ SV10 ) ) )
= $false )
| ( ( SV4 @ SV10 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[68]) ).
thf(79,plain,
! [SV5: $i > $o,SV11: $i] :
( ( ( ~ ( relr @ SV11 @ ( sK10_SY635 @ SV5 @ SV11 ) )
| ( SV5 @ ( sK10_SY635 @ SV5 @ SV11 ) ) )
= $false )
| ( ( SV5 @ SV11 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[69]) ).
thf(80,plain,
! [SV6: $i > $o,SV12: $i] :
( ( ( ~ ( reli @ SV12 @ ( sK11_SY636 @ SV6 @ SV12 ) )
| ! [SY653: $i] :
( ~ ( relr @ ( sK11_SY636 @ SV6 @ SV12 ) @ SY653 )
| ( SV6 @ SY653 ) ) )
= $false )
| ( ( ! [SY638: $i] :
( ~ ( relr @ SV12 @ SY638 )
| ! [SY625: $i] :
( ~ ( reli @ SY638 @ SY625 )
| ( SV6 @ SY625 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[70]) ).
thf(81,plain,
! [SV1: $i,SV14: individuals,SV15: $i,SV7: $i] :
( ( ( ~ ( reli @ SV7 @ SV15 )
| ~ ( princ_inj @ SV14 @ SV15 )
| ( princ_inj @ loca @ SV15 ) )
= $true )
| ( ( reli @ SV1 @ SV7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(82,plain,
! [SV13: $i] :
( ( ( reli @ sK5_SY577 @ SV13 )
= $false )
| ( ( ! [SY648: $i] :
( ~ ( relr @ SV13 @ SY648 )
| ! [SX2: $i] :
( ~ ( reli @ SY648 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( reli @ SX2 @ SX3 )
| ( princ_inj @ sK1_SY269 @ SX3 ) )
| ! [SX3: $i] :
( ~ ( reli @ SX2 @ SX3 )
| ~ ( sK2_SY526 @ SX3 )
| ( sK3_SY544 @ SX3 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(83,plain,
( ( ! [SY640: $i] :
( ~ ( reli @ sK6_SX0 @ SY640 )
| ! [SX2: $i] :
( ~ ( relr @ SY640 @ SX2 )
| ! [SX3: $i] :
( ~ ( reli @ SX2 @ SX3 )
| ~ ! [SX4: $i] :
( ~ ( reli @ SX3 @ SX4 )
| ( princ_inj @ sK1_SY269 @ SX4 ) )
| ( sK2_SY526 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[74]) ).
thf(84,plain,
( ( ~ ( reli @ sK6_SX0 @ sK12_SY644 )
| ! [SY654: $i] :
( ~ ( relr @ sK12_SY644 @ SY654 )
| ! [SX3: $i] :
( ~ ( reli @ SY654 @ SX3 )
| ~ ! [SX4: $i] :
( ~ ( reli @ SX3 @ SX4 )
| ( princ_inj @ sK1_SY269 @ SX4 ) )
| ( sK3_SY544 @ SX3 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[75]) ).
thf(85,plain,
! [SV2: $i > $o,SV8: $i] :
( ( ( ~ ( reli @ SV8 @ ( sK7_SY628 @ SV2 @ SV8 ) ) )
= $false )
| ( ( ! [SY629: $i] :
( ~ ( reli @ SV8 @ SY629 )
| ! [SY612: $i] :
( ~ ( reli @ SY629 @ SY612 )
| ( SV2 @ SY612 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[76]) ).
thf(86,plain,
! [SV8: $i,SV2: $i > $o] :
( ( ( SV2 @ ( sK7_SY628 @ SV2 @ SV8 ) )
= $false )
| ( ( ! [SY629: $i] :
( ~ ( reli @ SV8 @ SY629 )
| ! [SY612: $i] :
( ~ ( reli @ SY629 @ SY612 )
| ( SV2 @ SY612 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[76]) ).
thf(87,plain,
! [SV3: $i > $o,SV9: $i] :
( ( ( ~ ( relr @ SV9 @ ( sK8_SY631 @ SV3 @ SV9 ) ) )
= $false )
| ( ( ! [SY632: $i] :
( ~ ( relr @ SV9 @ SY632 )
| ! [SY616: $i] :
( ~ ( relr @ SY632 @ SY616 )
| ( SV3 @ SY616 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[77]) ).
thf(88,plain,
! [SV9: $i,SV3: $i > $o] :
( ( ( SV3 @ ( sK8_SY631 @ SV3 @ SV9 ) )
= $false )
| ( ( ! [SY632: $i] :
( ~ ( relr @ SV9 @ SY632 )
| ! [SY616: $i] :
( ~ ( relr @ SY632 @ SY616 )
| ( SV3 @ SY616 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[77]) ).
thf(89,plain,
! [SV4: $i > $o,SV10: $i] :
( ( ( ~ ( reli @ SV10 @ ( sK9_SY634 @ SV4 @ SV10 ) ) )
= $false )
| ( ( SV4 @ SV10 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[78]) ).
thf(90,plain,
! [SV10: $i,SV4: $i > $o] :
( ( ( SV4 @ ( sK9_SY634 @ SV4 @ SV10 ) )
= $false )
| ( ( SV4 @ SV10 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[78]) ).
thf(91,plain,
! [SV5: $i > $o,SV11: $i] :
( ( ( ~ ( relr @ SV11 @ ( sK10_SY635 @ SV5 @ SV11 ) ) )
= $false )
| ( ( SV5 @ SV11 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[79]) ).
thf(92,plain,
! [SV11: $i,SV5: $i > $o] :
( ( ( SV5 @ ( sK10_SY635 @ SV5 @ SV11 ) )
= $false )
| ( ( SV5 @ SV11 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[79]) ).
thf(93,plain,
! [SV6: $i > $o,SV12: $i] :
( ( ( ~ ( reli @ SV12 @ ( sK11_SY636 @ SV6 @ SV12 ) ) )
= $false )
| ( ( ! [SY638: $i] :
( ~ ( relr @ SV12 @ SY638 )
| ! [SY625: $i] :
( ~ ( reli @ SY638 @ SY625 )
| ( SV6 @ SY625 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[80]) ).
thf(94,plain,
! [SV12: $i,SV6: $i > $o] :
( ( ( ! [SY653: $i] :
( ~ ( relr @ ( sK11_SY636 @ SV6 @ SV12 ) @ SY653 )
| ( SV6 @ SY653 ) ) )
= $false )
| ( ( ! [SY638: $i] :
( ~ ( relr @ SV12 @ SY638 )
| ! [SY625: $i] :
( ~ ( reli @ SY638 @ SY625 )
| ( SV6 @ SY625 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[80]) ).
thf(95,plain,
! [SV1: $i,SV14: individuals,SV15: $i,SV7: $i] :
( ( ( ~ ( reli @ SV7 @ SV15 ) )
= $true )
| ( ( ~ ( princ_inj @ SV14 @ SV15 )
| ( princ_inj @ loca @ SV15 ) )
= $true )
| ( ( reli @ SV1 @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[81]) ).
thf(96,plain,
! [SV16: $i,SV13: $i] :
( ( ( ~ ( relr @ SV13 @ SV16 )
| ! [SY657: $i] :
( ~ ( reli @ SV16 @ SY657 )
| ~ ! [SX3: $i] :
( ~ ( reli @ SY657 @ SX3 )
| ( princ_inj @ sK1_SY269 @ SX3 ) )
| ! [SX3: $i] :
( ~ ( reli @ SY657 @ SX3 )
| ~ ( sK2_SY526 @ SX3 )
| ( sK3_SY544 @ SX3 ) ) ) )
= $true )
| ( ( reli @ sK5_SY577 @ SV13 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(97,plain,
! [SV17: $i] :
( ( ~ ( reli @ sK6_SX0 @ SV17 )
| ! [SY660: $i] :
( ~ ( relr @ SV17 @ SY660 )
| ! [SX3: $i] :
( ~ ( reli @ SY660 @ SX3 )
| ~ ! [SX4: $i] :
( ~ ( reli @ SX3 @ SX4 )
| ( princ_inj @ sK1_SY269 @ SX4 ) )
| ( sK2_SY526 @ SX3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(98,plain,
( ( ~ ( reli @ sK6_SX0 @ sK12_SY644 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[84]) ).
thf(99,plain,
( ( ! [SY654: $i] :
( ~ ( relr @ sK12_SY644 @ SY654 )
| ! [SX3: $i] :
( ~ ( reli @ SY654 @ SX3 )
| ~ ! [SX4: $i] :
( ~ ( reli @ SX3 @ SX4 )
| ( princ_inj @ sK1_SY269 @ SX4 ) )
| ( sK3_SY544 @ SX3 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[84]) ).
thf(100,plain,
! [SV2: $i > $o,SV8: $i] :
( ( ( reli @ SV8 @ ( sK7_SY628 @ SV2 @ SV8 ) )
= $true )
| ( ( ! [SY629: $i] :
( ~ ( reli @ SV8 @ SY629 )
| ! [SY612: $i] :
( ~ ( reli @ SY629 @ SY612 )
| ( SV2 @ SY612 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[85]) ).
thf(101,plain,
! [SV2: $i > $o,SV18: $i,SV8: $i] :
( ( ( ~ ( reli @ SV8 @ SV18 )
| ! [SY663: $i] :
( ~ ( reli @ SV18 @ SY663 )
| ( SV2 @ SY663 ) ) )
= $true )
| ( ( SV2 @ ( sK7_SY628 @ SV2 @ SV8 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(102,plain,
! [SV3: $i > $o,SV9: $i] :
( ( ( relr @ SV9 @ ( sK8_SY631 @ SV3 @ SV9 ) )
= $true )
| ( ( ! [SY632: $i] :
( ~ ( relr @ SV9 @ SY632 )
| ! [SY616: $i] :
( ~ ( relr @ SY632 @ SY616 )
| ( SV3 @ SY616 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[87]) ).
thf(103,plain,
! [SV3: $i > $o,SV19: $i,SV9: $i] :
( ( ( ~ ( relr @ SV9 @ SV19 )
| ! [SY664: $i] :
( ~ ( relr @ SV19 @ SY664 )
| ( SV3 @ SY664 ) ) )
= $true )
| ( ( SV3 @ ( sK8_SY631 @ SV3 @ SV9 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(104,plain,
! [SV4: $i > $o,SV10: $i] :
( ( ( reli @ SV10 @ ( sK9_SY634 @ SV4 @ SV10 ) )
= $true )
| ( ( SV4 @ SV10 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[89]) ).
thf(105,plain,
! [SV5: $i > $o,SV11: $i] :
( ( ( relr @ SV11 @ ( sK10_SY635 @ SV5 @ SV11 ) )
= $true )
| ( ( SV5 @ SV11 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[91]) ).
thf(106,plain,
! [SV6: $i > $o,SV12: $i] :
( ( ( reli @ SV12 @ ( sK11_SY636 @ SV6 @ SV12 ) )
= $true )
| ( ( ! [SY638: $i] :
( ~ ( relr @ SV12 @ SY638 )
| ! [SY625: $i] :
( ~ ( reli @ SY638 @ SY625 )
| ( SV6 @ SY625 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[93]) ).
thf(107,plain,
! [SV12: $i,SV6: $i > $o] :
( ( ( ~ ( relr @ ( sK11_SY636 @ SV6 @ SV12 ) @ ( sK13_SY653 @ SV12 @ SV6 ) )
| ( SV6 @ ( sK13_SY653 @ SV12 @ SV6 ) ) )
= $false )
| ( ( ! [SY638: $i] :
( ~ ( relr @ SV12 @ SY638 )
| ! [SY625: $i] :
( ~ ( reli @ SY638 @ SY625 )
| ( SV6 @ SY625 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[94]) ).
thf(108,plain,
! [SV1: $i,SV14: individuals,SV15: $i,SV7: $i] :
( ( ( reli @ SV7 @ SV15 )
= $false )
| ( ( ~ ( princ_inj @ SV14 @ SV15 )
| ( princ_inj @ loca @ SV15 ) )
= $true )
| ( ( reli @ SV1 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(109,plain,
! [SV16: $i,SV13: $i] :
( ( ( ~ ( relr @ SV13 @ SV16 ) )
= $true )
| ( ( ! [SY657: $i] :
( ~ ( reli @ SV16 @ SY657 )
| ~ ! [SX3: $i] :
( ~ ( reli @ SY657 @ SX3 )
| ( princ_inj @ sK1_SY269 @ SX3 ) )
| ! [SX3: $i] :
( ~ ( reli @ SY657 @ SX3 )
| ~ ( sK2_SY526 @ SX3 )
| ( sK3_SY544 @ SX3 ) ) ) )
= $true )
| ( ( reli @ sK5_SY577 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[96]) ).
thf(110,plain,
! [SV17: $i] :
( ( ( ~ ( reli @ sK6_SX0 @ SV17 ) )
= $true )
| ( ( ! [SY660: $i] :
( ~ ( relr @ SV17 @ SY660 )
| ! [SX3: $i] :
( ~ ( reli @ SY660 @ SX3 )
| ~ ! [SX4: $i] :
( ~ ( reli @ SX3 @ SX4 )
| ( princ_inj @ sK1_SY269 @ SX4 ) )
| ( sK2_SY526 @ SX3 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[97]) ).
thf(111,plain,
( ( reli @ sK6_SX0 @ sK12_SY644 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[98]) ).
thf(112,plain,
( ( ~ ( relr @ sK12_SY644 @ sK14_SY654 )
| ! [SY665: $i] :
( ~ ( reli @ sK14_SY654 @ SY665 )
| ~ ! [SX4: $i] :
( ~ ( reli @ SY665 @ SX4 )
| ( princ_inj @ sK1_SY269 @ SX4 ) )
| ( sK3_SY544 @ SY665 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[99]) ).
thf(113,plain,
! [SV2: $i > $o,SV20: $i,SV8: $i] :
( ( ( ~ ( reli @ SV8 @ SV20 )
| ! [SY667: $i] :
( ~ ( reli @ SV20 @ SY667 )
| ( SV2 @ SY667 ) ) )
= $true )
| ( ( reli @ SV8 @ ( sK7_SY628 @ SV2 @ SV8 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(114,plain,
! [SV2: $i > $o,SV18: $i,SV8: $i] :
( ( ( ~ ( reli @ SV8 @ SV18 ) )
= $true )
| ( ( ! [SY663: $i] :
( ~ ( reli @ SV18 @ SY663 )
| ( SV2 @ SY663 ) ) )
= $true )
| ( ( SV2 @ ( sK7_SY628 @ SV2 @ SV8 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[101]) ).
thf(115,plain,
! [SV3: $i > $o,SV21: $i,SV9: $i] :
( ( ( ~ ( relr @ SV9 @ SV21 )
| ! [SY668: $i] :
( ~ ( relr @ SV21 @ SY668 )
| ( SV3 @ SY668 ) ) )
= $true )
| ( ( relr @ SV9 @ ( sK8_SY631 @ SV3 @ SV9 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(116,plain,
! [SV3: $i > $o,SV19: $i,SV9: $i] :
( ( ( ~ ( relr @ SV9 @ SV19 ) )
= $true )
| ( ( ! [SY664: $i] :
( ~ ( relr @ SV19 @ SY664 )
| ( SV3 @ SY664 ) ) )
= $true )
| ( ( SV3 @ ( sK8_SY631 @ SV3 @ SV9 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[103]) ).
thf(117,plain,
! [SV6: $i > $o,SV22: $i,SV12: $i] :
( ( ( ~ ( relr @ SV12 @ SV22 )
| ! [SY669: $i] :
( ~ ( reli @ SV22 @ SY669 )
| ( SV6 @ SY669 ) ) )
= $true )
| ( ( reli @ SV12 @ ( sK11_SY636 @ SV6 @ SV12 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(118,plain,
! [SV12: $i,SV6: $i > $o] :
( ( ( ~ ( relr @ ( sK11_SY636 @ SV6 @ SV12 ) @ ( sK13_SY653 @ SV12 @ SV6 ) ) )
= $false )
| ( ( ! [SY638: $i] :
( ~ ( relr @ SV12 @ SY638 )
| ! [SY625: $i] :
( ~ ( reli @ SY638 @ SY625 )
| ( SV6 @ SY625 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[107]) ).
thf(119,plain,
! [SV12: $i,SV6: $i > $o] :
( ( ( SV6 @ ( sK13_SY653 @ SV12 @ SV6 ) )
= $false )
| ( ( ! [SY638: $i] :
( ~ ( relr @ SV12 @ SY638 )
| ! [SY625: $i] :
( ~ ( reli @ SY638 @ SY625 )
| ( SV6 @ SY625 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[107]) ).
thf(120,plain,
! [SV1: $i,SV7: $i,SV15: $i,SV14: individuals] :
( ( ( ~ ( princ_inj @ SV14 @ SV15 ) )
= $true )
| ( ( princ_inj @ loca @ SV15 )
= $true )
| ( ( reli @ SV7 @ SV15 )
= $false )
| ( ( reli @ SV1 @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[108]) ).
thf(121,plain,
! [SV16: $i,SV13: $i] :
( ( ( relr @ SV13 @ SV16 )
= $false )
| ( ( ! [SY657: $i] :
( ~ ( reli @ SV16 @ SY657 )
| ~ ! [SX3: $i] :
( ~ ( reli @ SY657 @ SX3 )
| ( princ_inj @ sK1_SY269 @ SX3 ) )
| ! [SX3: $i] :
( ~ ( reli @ SY657 @ SX3 )
| ~ ( sK2_SY526 @ SX3 )
| ( sK3_SY544 @ SX3 ) ) ) )
= $true )
| ( ( reli @ sK5_SY577 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(122,plain,
! [SV17: $i] :
( ( ( reli @ sK6_SX0 @ SV17 )
= $false )
| ( ( ! [SY660: $i] :
( ~ ( relr @ SV17 @ SY660 )
| ! [SX3: $i] :
( ~ ( reli @ SY660 @ SX3 )
| ~ ! [SX4: $i] :
( ~ ( reli @ SX3 @ SX4 )
| ( princ_inj @ sK1_SY269 @ SX4 ) )
| ( sK2_SY526 @ SX3 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(123,plain,
( ( ~ ( relr @ sK12_SY644 @ sK14_SY654 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[112]) ).
thf(124,plain,
( ( ! [SY665: $i] :
( ~ ( reli @ sK14_SY654 @ SY665 )
| ~ ! [SX4: $i] :
( ~ ( reli @ SY665 @ SX4 )
| ( princ_inj @ sK1_SY269 @ SX4 ) )
| ( sK3_SY544 @ SY665 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[112]) ).
thf(125,plain,
! [SV2: $i > $o,SV20: $i,SV8: $i] :
( ( ( ~ ( reli @ SV8 @ SV20 ) )
= $true )
| ( ( ! [SY667: $i] :
( ~ ( reli @ SV20 @ SY667 )
| ( SV2 @ SY667 ) ) )
= $true )
| ( ( reli @ SV8 @ ( sK7_SY628 @ SV2 @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[113]) ).
thf(126,plain,
! [SV2: $i > $o,SV18: $i,SV8: $i] :
( ( ( reli @ SV8 @ SV18 )
= $false )
| ( ( ! [SY663: $i] :
( ~ ( reli @ SV18 @ SY663 )
| ( SV2 @ SY663 ) ) )
= $true )
| ( ( SV2 @ ( sK7_SY628 @ SV2 @ SV8 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[114]) ).
thf(127,plain,
! [SV3: $i > $o,SV21: $i,SV9: $i] :
( ( ( ~ ( relr @ SV9 @ SV21 ) )
= $true )
| ( ( ! [SY668: $i] :
( ~ ( relr @ SV21 @ SY668 )
| ( SV3 @ SY668 ) ) )
= $true )
| ( ( relr @ SV9 @ ( sK8_SY631 @ SV3 @ SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[115]) ).
thf(128,plain,
! [SV3: $i > $o,SV19: $i,SV9: $i] :
( ( ( relr @ SV9 @ SV19 )
= $false )
| ( ( ! [SY664: $i] :
( ~ ( relr @ SV19 @ SY664 )
| ( SV3 @ SY664 ) ) )
= $true )
| ( ( SV3 @ ( sK8_SY631 @ SV3 @ SV9 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(129,plain,
! [SV6: $i > $o,SV22: $i,SV12: $i] :
( ( ( ~ ( relr @ SV12 @ SV22 ) )
= $true )
| ( ( ! [SY669: $i] :
( ~ ( reli @ SV22 @ SY669 )
| ( SV6 @ SY669 ) ) )
= $true )
| ( ( reli @ SV12 @ ( sK11_SY636 @ SV6 @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[117]) ).
thf(130,plain,
! [SV12: $i,SV6: $i > $o] :
( ( ( relr @ ( sK11_SY636 @ SV6 @ SV12 ) @ ( sK13_SY653 @ SV12 @ SV6 ) )
= $true )
| ( ( ! [SY638: $i] :
( ~ ( relr @ SV12 @ SY638 )
| ! [SY625: $i] :
( ~ ( reli @ SY638 @ SY625 )
| ( SV6 @ SY625 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[118]) ).
thf(131,plain,
! [SV6: $i > $o,SV23: $i,SV12: $i] :
( ( ( ~ ( relr @ SV12 @ SV23 )
| ! [SY670: $i] :
( ~ ( reli @ SV23 @ SY670 )
| ( SV6 @ SY670 ) ) )
= $true )
| ( ( SV6 @ ( sK13_SY653 @ SV12 @ SV6 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(132,plain,
! [SV1: $i,SV7: $i,SV15: $i,SV14: individuals] :
( ( ( princ_inj @ SV14 @ SV15 )
= $false )
| ( ( princ_inj @ loca @ SV15 )
= $true )
| ( ( reli @ SV7 @ SV15 )
= $false )
| ( ( reli @ SV1 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(133,plain,
! [SV13: $i,SV24: $i,SV16: $i] :
( ( ( ~ ( reli @ SV16 @ SV24 )
| ~ ! [SY671: $i] :
( ~ ( reli @ SV24 @ SY671 )
| ( princ_inj @ sK1_SY269 @ SY671 ) )
| ! [SY672: $i] :
( ~ ( reli @ SV24 @ SY672 )
| ~ ( sK2_SY526 @ SY672 )
| ( sK3_SY544 @ SY672 ) ) )
= $true )
| ( ( relr @ SV13 @ SV16 )
= $false )
| ( ( reli @ sK5_SY577 @ SV13 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(134,plain,
! [SV25: $i,SV17: $i] :
( ( ( ~ ( relr @ SV17 @ SV25 )
| ! [SY673: $i] :
( ~ ( reli @ SV25 @ SY673 )
| ~ ! [SX4: $i] :
( ~ ( reli @ SY673 @ SX4 )
| ( princ_inj @ sK1_SY269 @ SX4 ) )
| ( sK2_SY526 @ SY673 ) ) )
= $true )
| ( ( reli @ sK6_SX0 @ SV17 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(135,plain,
( ( relr @ sK12_SY644 @ sK14_SY654 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[123]) ).
thf(136,plain,
( ( ~ ( reli @ sK14_SY654 @ sK15_SY665 )
| ~ ! [SY675: $i] :
( ~ ( reli @ sK15_SY665 @ SY675 )
| ( princ_inj @ sK1_SY269 @ SY675 ) )
| ( sK3_SY544 @ sK15_SY665 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[124]) ).
thf(137,plain,
! [SV2: $i > $o,SV20: $i,SV8: $i] :
( ( ( reli @ SV8 @ SV20 )
= $false )
| ( ( ! [SY667: $i] :
( ~ ( reli @ SV20 @ SY667 )
| ( SV2 @ SY667 ) ) )
= $true )
| ( ( reli @ SV8 @ ( sK7_SY628 @ SV2 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(138,plain,
! [SV8: $i,SV2: $i > $o,SV26: $i,SV18: $i] :
( ( ( ~ ( reli @ SV18 @ SV26 )
| ( SV2 @ SV26 ) )
= $true )
| ( ( reli @ SV8 @ SV18 )
= $false )
| ( ( SV2 @ ( sK7_SY628 @ SV2 @ SV8 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(139,plain,
! [SV3: $i > $o,SV21: $i,SV9: $i] :
( ( ( relr @ SV9 @ SV21 )
= $false )
| ( ( ! [SY668: $i] :
( ~ ( relr @ SV21 @ SY668 )
| ( SV3 @ SY668 ) ) )
= $true )
| ( ( relr @ SV9 @ ( sK8_SY631 @ SV3 @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[127]) ).
thf(140,plain,
! [SV9: $i,SV3: $i > $o,SV27: $i,SV19: $i] :
( ( ( ~ ( relr @ SV19 @ SV27 )
| ( SV3 @ SV27 ) )
= $true )
| ( ( relr @ SV9 @ SV19 )
= $false )
| ( ( SV3 @ ( sK8_SY631 @ SV3 @ SV9 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(141,plain,
! [SV6: $i > $o,SV22: $i,SV12: $i] :
( ( ( relr @ SV12 @ SV22 )
= $false )
| ( ( ! [SY669: $i] :
( ~ ( reli @ SV22 @ SY669 )
| ( SV6 @ SY669 ) ) )
= $true )
| ( ( reli @ SV12 @ ( sK11_SY636 @ SV6 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[129]) ).
thf(142,plain,
! [SV6: $i > $o,SV28: $i,SV12: $i] :
( ( ( ~ ( relr @ SV12 @ SV28 )
| ! [SY676: $i] :
( ~ ( reli @ SV28 @ SY676 )
| ( SV6 @ SY676 ) ) )
= $true )
| ( ( relr @ ( sK11_SY636 @ SV6 @ SV12 ) @ ( sK13_SY653 @ SV12 @ SV6 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(143,plain,
! [SV6: $i > $o,SV23: $i,SV12: $i] :
( ( ( ~ ( relr @ SV12 @ SV23 ) )
= $true )
| ( ( ! [SY670: $i] :
( ~ ( reli @ SV23 @ SY670 )
| ( SV6 @ SY670 ) ) )
= $true )
| ( ( SV6 @ ( sK13_SY653 @ SV12 @ SV6 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[131]) ).
thf(144,plain,
! [SV13: $i,SV24: $i,SV16: $i] :
( ( ( ~ ( reli @ SV16 @ SV24 ) )
= $true )
| ( ( ~ ! [SY671: $i] :
( ~ ( reli @ SV24 @ SY671 )
| ( princ_inj @ sK1_SY269 @ SY671 ) )
| ! [SY672: $i] :
( ~ ( reli @ SV24 @ SY672 )
| ~ ( sK2_SY526 @ SY672 )
| ( sK3_SY544 @ SY672 ) ) )
= $true )
| ( ( relr @ SV13 @ SV16 )
= $false )
| ( ( reli @ sK5_SY577 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[133]) ).
thf(145,plain,
! [SV25: $i,SV17: $i] :
( ( ( ~ ( relr @ SV17 @ SV25 ) )
= $true )
| ( ( ! [SY673: $i] :
( ~ ( reli @ SV25 @ SY673 )
| ~ ! [SX4: $i] :
( ~ ( reli @ SY673 @ SX4 )
| ( princ_inj @ sK1_SY269 @ SX4 ) )
| ( sK2_SY526 @ SY673 ) ) )
= $true )
| ( ( reli @ sK6_SX0 @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[134]) ).
thf(146,plain,
( ( ~ ( reli @ sK14_SY654 @ sK15_SY665 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[136]) ).
thf(147,plain,
( ( ~ ! [SY675: $i] :
( ~ ( reli @ sK15_SY665 @ SY675 )
| ( princ_inj @ sK1_SY269 @ SY675 ) )
| ( sK3_SY544 @ sK15_SY665 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[136]) ).
thf(148,plain,
! [SV8: $i,SV2: $i > $o,SV29: $i,SV20: $i] :
( ( ( ~ ( reli @ SV20 @ SV29 )
| ( SV2 @ SV29 ) )
= $true )
| ( ( reli @ SV8 @ SV20 )
= $false )
| ( ( reli @ SV8 @ ( sK7_SY628 @ SV2 @ SV8 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(149,plain,
! [SV8: $i,SV2: $i > $o,SV26: $i,SV18: $i] :
( ( ( ~ ( reli @ SV18 @ SV26 ) )
= $true )
| ( ( SV2 @ SV26 )
= $true )
| ( ( reli @ SV8 @ SV18 )
= $false )
| ( ( SV2 @ ( sK7_SY628 @ SV2 @ SV8 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[138]) ).
thf(150,plain,
! [SV9: $i,SV3: $i > $o,SV30: $i,SV21: $i] :
( ( ( ~ ( relr @ SV21 @ SV30 )
| ( SV3 @ SV30 ) )
= $true )
| ( ( relr @ SV9 @ SV21 )
= $false )
| ( ( relr @ SV9 @ ( sK8_SY631 @ SV3 @ SV9 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(151,plain,
! [SV9: $i,SV3: $i > $o,SV27: $i,SV19: $i] :
( ( ( ~ ( relr @ SV19 @ SV27 ) )
= $true )
| ( ( SV3 @ SV27 )
= $true )
| ( ( relr @ SV9 @ SV19 )
= $false )
| ( ( SV3 @ ( sK8_SY631 @ SV3 @ SV9 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[140]) ).
thf(152,plain,
! [SV12: $i,SV6: $i > $o,SV31: $i,SV22: $i] :
( ( ( ~ ( reli @ SV22 @ SV31 )
| ( SV6 @ SV31 ) )
= $true )
| ( ( relr @ SV12 @ SV22 )
= $false )
| ( ( reli @ SV12 @ ( sK11_SY636 @ SV6 @ SV12 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(153,plain,
! [SV6: $i > $o,SV28: $i,SV12: $i] :
( ( ( ~ ( relr @ SV12 @ SV28 ) )
= $true )
| ( ( ! [SY676: $i] :
( ~ ( reli @ SV28 @ SY676 )
| ( SV6 @ SY676 ) ) )
= $true )
| ( ( relr @ ( sK11_SY636 @ SV6 @ SV12 ) @ ( sK13_SY653 @ SV12 @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[142]) ).
thf(154,plain,
! [SV6: $i > $o,SV23: $i,SV12: $i] :
( ( ( relr @ SV12 @ SV23 )
= $false )
| ( ( ! [SY670: $i] :
( ~ ( reli @ SV23 @ SY670 )
| ( SV6 @ SY670 ) ) )
= $true )
| ( ( SV6 @ ( sK13_SY653 @ SV12 @ SV6 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[143]) ).
thf(155,plain,
! [SV13: $i,SV24: $i,SV16: $i] :
( ( ( reli @ SV16 @ SV24 )
= $false )
| ( ( ~ ! [SY671: $i] :
( ~ ( reli @ SV24 @ SY671 )
| ( princ_inj @ sK1_SY269 @ SY671 ) )
| ! [SY672: $i] :
( ~ ( reli @ SV24 @ SY672 )
| ~ ( sK2_SY526 @ SY672 )
| ( sK3_SY544 @ SY672 ) ) )
= $true )
| ( ( relr @ SV13 @ SV16 )
= $false )
| ( ( reli @ sK5_SY577 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(156,plain,
! [SV25: $i,SV17: $i] :
( ( ( relr @ SV17 @ SV25 )
= $false )
| ( ( ! [SY673: $i] :
( ~ ( reli @ SV25 @ SY673 )
| ~ ! [SX4: $i] :
( ~ ( reli @ SY673 @ SX4 )
| ( princ_inj @ sK1_SY269 @ SX4 ) )
| ( sK2_SY526 @ SY673 ) ) )
= $true )
| ( ( reli @ sK6_SX0 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[145]) ).
thf(157,plain,
( ( reli @ sK14_SY654 @ sK15_SY665 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[146]) ).
thf(158,plain,
( ( ~ ! [SY675: $i] :
( ~ ( reli @ sK15_SY665 @ SY675 )
| ( princ_inj @ sK1_SY269 @ SY675 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[147]) ).
thf(159,plain,
( ( sK3_SY544 @ sK15_SY665 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[147]) ).
thf(160,plain,
! [SV8: $i,SV2: $i > $o,SV29: $i,SV20: $i] :
( ( ( ~ ( reli @ SV20 @ SV29 ) )
= $true )
| ( ( SV2 @ SV29 )
= $true )
| ( ( reli @ SV8 @ SV20 )
= $false )
| ( ( reli @ SV8 @ ( sK7_SY628 @ SV2 @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[148]) ).
thf(161,plain,
! [SV8: $i,SV2: $i > $o,SV26: $i,SV18: $i] :
( ( ( reli @ SV18 @ SV26 )
= $false )
| ( ( SV2 @ SV26 )
= $true )
| ( ( reli @ SV8 @ SV18 )
= $false )
| ( ( SV2 @ ( sK7_SY628 @ SV2 @ SV8 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(162,plain,
! [SV9: $i,SV3: $i > $o,SV30: $i,SV21: $i] :
( ( ( ~ ( relr @ SV21 @ SV30 ) )
= $true )
| ( ( SV3 @ SV30 )
= $true )
| ( ( relr @ SV9 @ SV21 )
= $false )
| ( ( relr @ SV9 @ ( sK8_SY631 @ SV3 @ SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[150]) ).
thf(163,plain,
! [SV9: $i,SV3: $i > $o,SV27: $i,SV19: $i] :
( ( ( relr @ SV19 @ SV27 )
= $false )
| ( ( SV3 @ SV27 )
= $true )
| ( ( relr @ SV9 @ SV19 )
= $false )
| ( ( SV3 @ ( sK8_SY631 @ SV3 @ SV9 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(164,plain,
! [SV12: $i,SV6: $i > $o,SV31: $i,SV22: $i] :
( ( ( ~ ( reli @ SV22 @ SV31 ) )
= $true )
| ( ( SV6 @ SV31 )
= $true )
| ( ( relr @ SV12 @ SV22 )
= $false )
| ( ( reli @ SV12 @ ( sK11_SY636 @ SV6 @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[152]) ).
thf(165,plain,
! [SV6: $i > $o,SV28: $i,SV12: $i] :
( ( ( relr @ SV12 @ SV28 )
= $false )
| ( ( ! [SY676: $i] :
( ~ ( reli @ SV28 @ SY676 )
| ( SV6 @ SY676 ) ) )
= $true )
| ( ( relr @ ( sK11_SY636 @ SV6 @ SV12 ) @ ( sK13_SY653 @ SV12 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(166,plain,
! [SV12: $i,SV6: $i > $o,SV32: $i,SV23: $i] :
( ( ( ~ ( reli @ SV23 @ SV32 )
| ( SV6 @ SV32 ) )
= $true )
| ( ( relr @ SV12 @ SV23 )
= $false )
| ( ( SV6 @ ( sK13_SY653 @ SV12 @ SV6 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(167,plain,
! [SV13: $i,SV16: $i,SV24: $i] :
( ( ( ~ ! [SY671: $i] :
( ~ ( reli @ SV24 @ SY671 )
| ( princ_inj @ sK1_SY269 @ SY671 ) ) )
= $true )
| ( ( ! [SY672: $i] :
( ~ ( reli @ SV24 @ SY672 )
| ~ ( sK2_SY526 @ SY672 )
| ( sK3_SY544 @ SY672 ) ) )
= $true )
| ( ( reli @ SV16 @ SV24 )
= $false )
| ( ( relr @ SV13 @ SV16 )
= $false )
| ( ( reli @ sK5_SY577 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[155]) ).
thf(168,plain,
! [SV17: $i,SV33: $i,SV25: $i] :
( ( ( ~ ( reli @ SV25 @ SV33 )
| ~ ! [SY677: $i] :
( ~ ( reli @ SV33 @ SY677 )
| ( princ_inj @ sK1_SY269 @ SY677 ) )
| ( sK2_SY526 @ SV33 ) )
= $true )
| ( ( relr @ SV17 @ SV25 )
= $false )
| ( ( reli @ sK6_SX0 @ SV17 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(169,plain,
( ( ! [SY675: $i] :
( ~ ( reli @ sK15_SY665 @ SY675 )
| ( princ_inj @ sK1_SY269 @ SY675 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[158]) ).
thf(170,plain,
! [SV8: $i,SV2: $i > $o,SV29: $i,SV20: $i] :
( ( ( reli @ SV20 @ SV29 )
= $false )
| ( ( SV2 @ SV29 )
= $true )
| ( ( reli @ SV8 @ SV20 )
= $false )
| ( ( reli @ SV8 @ ( sK7_SY628 @ SV2 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(171,plain,
! [SV9: $i,SV3: $i > $o,SV30: $i,SV21: $i] :
( ( ( relr @ SV21 @ SV30 )
= $false )
| ( ( SV3 @ SV30 )
= $true )
| ( ( relr @ SV9 @ SV21 )
= $false )
| ( ( relr @ SV9 @ ( sK8_SY631 @ SV3 @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(172,plain,
! [SV12: $i,SV6: $i > $o,SV31: $i,SV22: $i] :
( ( ( reli @ SV22 @ SV31 )
= $false )
| ( ( SV6 @ SV31 )
= $true )
| ( ( relr @ SV12 @ SV22 )
= $false )
| ( ( reli @ SV12 @ ( sK11_SY636 @ SV6 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(173,plain,
! [SV12: $i,SV6: $i > $o,SV34: $i,SV28: $i] :
( ( ( ~ ( reli @ SV28 @ SV34 )
| ( SV6 @ SV34 ) )
= $true )
| ( ( relr @ SV12 @ SV28 )
= $false )
| ( ( relr @ ( sK11_SY636 @ SV6 @ SV12 ) @ ( sK13_SY653 @ SV12 @ SV6 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(174,plain,
! [SV12: $i,SV6: $i > $o,SV32: $i,SV23: $i] :
( ( ( ~ ( reli @ SV23 @ SV32 ) )
= $true )
| ( ( SV6 @ SV32 )
= $true )
| ( ( relr @ SV12 @ SV23 )
= $false )
| ( ( SV6 @ ( sK13_SY653 @ SV12 @ SV6 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[166]) ).
thf(175,plain,
! [SV13: $i,SV16: $i,SV24: $i] :
( ( ( ! [SY671: $i] :
( ~ ( reli @ SV24 @ SY671 )
| ( princ_inj @ sK1_SY269 @ SY671 ) ) )
= $false )
| ( ( ! [SY672: $i] :
( ~ ( reli @ SV24 @ SY672 )
| ~ ( sK2_SY526 @ SY672 )
| ( sK3_SY544 @ SY672 ) ) )
= $true )
| ( ( reli @ SV16 @ SV24 )
= $false )
| ( ( relr @ SV13 @ SV16 )
= $false )
| ( ( reli @ sK5_SY577 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(176,plain,
! [SV17: $i,SV33: $i,SV25: $i] :
( ( ( ~ ( reli @ SV25 @ SV33 ) )
= $true )
| ( ( ~ ! [SY677: $i] :
( ~ ( reli @ SV33 @ SY677 )
| ( princ_inj @ sK1_SY269 @ SY677 ) )
| ( sK2_SY526 @ SV33 ) )
= $true )
| ( ( relr @ SV17 @ SV25 )
= $false )
| ( ( reli @ sK6_SX0 @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[168]) ).
thf(177,plain,
! [SV35: $i] :
( ( ~ ( reli @ sK15_SY665 @ SV35 )
| ( princ_inj @ sK1_SY269 @ SV35 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[169]) ).
thf(178,plain,
! [SV12: $i,SV6: $i > $o,SV34: $i,SV28: $i] :
( ( ( ~ ( reli @ SV28 @ SV34 ) )
= $true )
| ( ( SV6 @ SV34 )
= $true )
| ( ( relr @ SV12 @ SV28 )
= $false )
| ( ( relr @ ( sK11_SY636 @ SV6 @ SV12 ) @ ( sK13_SY653 @ SV12 @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[173]) ).
thf(179,plain,
! [SV12: $i,SV6: $i > $o,SV32: $i,SV23: $i] :
( ( ( reli @ SV23 @ SV32 )
= $false )
| ( ( SV6 @ SV32 )
= $true )
| ( ( relr @ SV12 @ SV23 )
= $false )
| ( ( SV6 @ ( sK13_SY653 @ SV12 @ SV6 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[174]) ).
thf(180,plain,
! [SV16: $i,SV13: $i,SV24: $i] :
( ( ( ~ ( reli @ SV24 @ ( sK16_SY671 @ SV13 @ SV16 @ SV24 ) )
| ( princ_inj @ sK1_SY269 @ ( sK16_SY671 @ SV13 @ SV16 @ SV24 ) ) )
= $false )
| ( ( ! [SY672: $i] :
( ~ ( reli @ SV24 @ SY672 )
| ~ ( sK2_SY526 @ SY672 )
| ( sK3_SY544 @ SY672 ) ) )
= $true )
| ( ( reli @ SV16 @ SV24 )
= $false )
| ( ( relr @ SV13 @ SV16 )
= $false )
| ( ( reli @ sK5_SY577 @ SV13 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[175]) ).
thf(181,plain,
! [SV17: $i,SV33: $i,SV25: $i] :
( ( ( reli @ SV25 @ SV33 )
= $false )
| ( ( ~ ! [SY677: $i] :
( ~ ( reli @ SV33 @ SY677 )
| ( princ_inj @ sK1_SY269 @ SY677 ) )
| ( sK2_SY526 @ SV33 ) )
= $true )
| ( ( relr @ SV17 @ SV25 )
= $false )
| ( ( reli @ sK6_SX0 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[176]) ).
thf(182,plain,
! [SV35: $i] :
( ( ( ~ ( reli @ sK15_SY665 @ SV35 ) )
= $true )
| ( ( princ_inj @ sK1_SY269 @ SV35 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[177]) ).
thf(183,plain,
! [SV12: $i,SV6: $i > $o,SV34: $i,SV28: $i] :
( ( ( reli @ SV28 @ SV34 )
= $false )
| ( ( SV6 @ SV34 )
= $true )
| ( ( relr @ SV12 @ SV28 )
= $false )
| ( ( relr @ ( sK11_SY636 @ SV6 @ SV12 ) @ ( sK13_SY653 @ SV12 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(184,plain,
! [SV16: $i,SV13: $i,SV24: $i] :
( ( ( ~ ( reli @ SV24 @ ( sK16_SY671 @ SV13 @ SV16 @ SV24 ) ) )
= $false )
| ( ( ! [SY672: $i] :
( ~ ( reli @ SV24 @ SY672 )
| ~ ( sK2_SY526 @ SY672 )
| ( sK3_SY544 @ SY672 ) ) )
= $true )
| ( ( reli @ SV16 @ SV24 )
= $false )
| ( ( relr @ SV13 @ SV16 )
= $false )
| ( ( reli @ sK5_SY577 @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[180]) ).
thf(185,plain,
! [SV24: $i,SV16: $i,SV13: $i] :
( ( ( princ_inj @ sK1_SY269 @ ( sK16_SY671 @ SV13 @ SV16 @ SV24 ) )
= $false )
| ( ( ! [SY672: $i] :
( ~ ( reli @ SV24 @ SY672 )
| ~ ( sK2_SY526 @ SY672 )
| ( sK3_SY544 @ SY672 ) ) )
= $true )
| ( ( reli @ SV16 @ SV24 )
= $false )
| ( ( relr @ SV13 @ SV16 )
= $false )
| ( ( reli @ sK5_SY577 @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[180]) ).
thf(186,plain,
! [SV17: $i,SV25: $i,SV33: $i] :
( ( ( ~ ! [SY677: $i] :
( ~ ( reli @ SV33 @ SY677 )
| ( princ_inj @ sK1_SY269 @ SY677 ) ) )
= $true )
| ( ( sK2_SY526 @ SV33 )
= $true )
| ( ( reli @ SV25 @ SV33 )
= $false )
| ( ( relr @ SV17 @ SV25 )
= $false )
| ( ( reli @ sK6_SX0 @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[181]) ).
thf(187,plain,
! [SV35: $i] :
( ( ( reli @ sK15_SY665 @ SV35 )
= $false )
| ( ( princ_inj @ sK1_SY269 @ SV35 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[182]) ).
thf(188,plain,
! [SV16: $i,SV13: $i,SV24: $i] :
( ( ( reli @ SV24 @ ( sK16_SY671 @ SV13 @ SV16 @ SV24 ) )
= $true )
| ( ( ! [SY672: $i] :
( ~ ( reli @ SV24 @ SY672 )
| ~ ( sK2_SY526 @ SY672 )
| ( sK3_SY544 @ SY672 ) ) )
= $true )
| ( ( reli @ SV16 @ SV24 )
= $false )
| ( ( relr @ SV13 @ SV16 )
= $false )
| ( ( reli @ sK5_SY577 @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[184]) ).
thf(189,plain,
! [SV16: $i,SV13: $i,SV36: $i,SV24: $i] :
( ( ( ~ ( reli @ SV24 @ SV36 )
| ~ ( sK2_SY526 @ SV36 )
| ( sK3_SY544 @ SV36 ) )
= $true )
| ( ( princ_inj @ sK1_SY269 @ ( sK16_SY671 @ SV13 @ SV16 @ SV24 ) )
= $false )
| ( ( reli @ SV16 @ SV24 )
= $false )
| ( ( relr @ SV13 @ SV16 )
= $false )
| ( ( reli @ sK5_SY577 @ SV13 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[185]) ).
thf(190,plain,
! [SV17: $i,SV25: $i,SV33: $i] :
( ( ( ! [SY677: $i] :
( ~ ( reli @ SV33 @ SY677 )
| ( princ_inj @ sK1_SY269 @ SY677 ) ) )
= $false )
| ( ( sK2_SY526 @ SV33 )
= $true )
| ( ( reli @ SV25 @ SV33 )
= $false )
| ( ( relr @ SV17 @ SV25 )
= $false )
| ( ( reli @ sK6_SX0 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[186]) ).
thf(191,plain,
! [SV16: $i,SV13: $i,SV37: $i,SV24: $i] :
( ( ( ~ ( reli @ SV24 @ SV37 )
| ~ ( sK2_SY526 @ SV37 )
| ( sK3_SY544 @ SV37 ) )
= $true )
| ( ( reli @ SV24 @ ( sK16_SY671 @ SV13 @ SV16 @ SV24 ) )
= $true )
| ( ( reli @ SV16 @ SV24 )
= $false )
| ( ( relr @ SV13 @ SV16 )
= $false )
| ( ( reli @ sK5_SY577 @ SV13 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(192,plain,
! [SV16: $i,SV13: $i,SV36: $i,SV24: $i] :
( ( ( ~ ( reli @ SV24 @ SV36 ) )
= $true )
| ( ( ~ ( sK2_SY526 @ SV36 )
| ( sK3_SY544 @ SV36 ) )
= $true )
| ( ( princ_inj @ sK1_SY269 @ ( sK16_SY671 @ SV13 @ SV16 @ SV24 ) )
= $false )
| ( ( reli @ SV16 @ SV24 )
= $false )
| ( ( relr @ SV13 @ SV16 )
= $false )
| ( ( reli @ sK5_SY577 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[189]) ).
thf(193,plain,
! [SV25: $i,SV17: $i,SV33: $i] :
( ( ( ~ ( reli @ SV33 @ ( sK17_SY677 @ SV17 @ SV25 @ SV33 ) )
| ( princ_inj @ sK1_SY269 @ ( sK17_SY677 @ SV17 @ SV25 @ SV33 ) ) )
= $false )
| ( ( sK2_SY526 @ SV33 )
= $true )
| ( ( reli @ SV25 @ SV33 )
= $false )
| ( ( relr @ SV17 @ SV25 )
= $false )
| ( ( reli @ sK6_SX0 @ SV17 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[190]) ).
thf(194,plain,
! [SV16: $i,SV13: $i,SV37: $i,SV24: $i] :
( ( ( ~ ( reli @ SV24 @ SV37 ) )
= $true )
| ( ( ~ ( sK2_SY526 @ SV37 )
| ( sK3_SY544 @ SV37 ) )
= $true )
| ( ( reli @ SV24 @ ( sK16_SY671 @ SV13 @ SV16 @ SV24 ) )
= $true )
| ( ( reli @ SV16 @ SV24 )
= $false )
| ( ( relr @ SV13 @ SV16 )
= $false )
| ( ( reli @ sK5_SY577 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[191]) ).
thf(195,plain,
! [SV16: $i,SV13: $i,SV36: $i,SV24: $i] :
( ( ( reli @ SV24 @ SV36 )
= $false )
| ( ( ~ ( sK2_SY526 @ SV36 )
| ( sK3_SY544 @ SV36 ) )
= $true )
| ( ( princ_inj @ sK1_SY269 @ ( sK16_SY671 @ SV13 @ SV16 @ SV24 ) )
= $false )
| ( ( reli @ SV16 @ SV24 )
= $false )
| ( ( relr @ SV13 @ SV16 )
= $false )
| ( ( reli @ sK5_SY577 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(196,plain,
! [SV25: $i,SV17: $i,SV33: $i] :
( ( ( ~ ( reli @ SV33 @ ( sK17_SY677 @ SV17 @ SV25 @ SV33 ) ) )
= $false )
| ( ( sK2_SY526 @ SV33 )
= $true )
| ( ( reli @ SV25 @ SV33 )
= $false )
| ( ( relr @ SV17 @ SV25 )
= $false )
| ( ( reli @ sK6_SX0 @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[193]) ).
thf(197,plain,
! [SV33: $i,SV25: $i,SV17: $i] :
( ( ( princ_inj @ sK1_SY269 @ ( sK17_SY677 @ SV17 @ SV25 @ SV33 ) )
= $false )
| ( ( sK2_SY526 @ SV33 )
= $true )
| ( ( reli @ SV25 @ SV33 )
= $false )
| ( ( relr @ SV17 @ SV25 )
= $false )
| ( ( reli @ sK6_SX0 @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[193]) ).
thf(198,plain,
! [SV16: $i,SV13: $i,SV37: $i,SV24: $i] :
( ( ( reli @ SV24 @ SV37 )
= $false )
| ( ( ~ ( sK2_SY526 @ SV37 )
| ( sK3_SY544 @ SV37 ) )
= $true )
| ( ( reli @ SV24 @ ( sK16_SY671 @ SV13 @ SV16 @ SV24 ) )
= $true )
| ( ( reli @ SV16 @ SV24 )
= $false )
| ( ( relr @ SV13 @ SV16 )
= $false )
| ( ( reli @ sK5_SY577 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(199,plain,
! [SV16: $i,SV13: $i,SV24: $i,SV36: $i] :
( ( ( ~ ( sK2_SY526 @ SV36 ) )
= $true )
| ( ( sK3_SY544 @ SV36 )
= $true )
| ( ( reli @ SV24 @ SV36 )
= $false )
| ( ( princ_inj @ sK1_SY269 @ ( sK16_SY671 @ SV13 @ SV16 @ SV24 ) )
= $false )
| ( ( reli @ SV16 @ SV24 )
= $false )
| ( ( relr @ SV13 @ SV16 )
= $false )
| ( ( reli @ sK5_SY577 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[195]) ).
thf(200,plain,
! [SV25: $i,SV17: $i,SV33: $i] :
( ( ( reli @ SV33 @ ( sK17_SY677 @ SV17 @ SV25 @ SV33 ) )
= $true )
| ( ( sK2_SY526 @ SV33 )
= $true )
| ( ( reli @ SV25 @ SV33 )
= $false )
| ( ( relr @ SV17 @ SV25 )
= $false )
| ( ( reli @ sK6_SX0 @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[196]) ).
thf(201,plain,
! [SV16: $i,SV13: $i,SV24: $i,SV37: $i] :
( ( ( ~ ( sK2_SY526 @ SV37 ) )
= $true )
| ( ( sK3_SY544 @ SV37 )
= $true )
| ( ( reli @ SV24 @ SV37 )
= $false )
| ( ( reli @ SV24 @ ( sK16_SY671 @ SV13 @ SV16 @ SV24 ) )
= $true )
| ( ( reli @ SV16 @ SV24 )
= $false )
| ( ( relr @ SV13 @ SV16 )
= $false )
| ( ( reli @ sK5_SY577 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[198]) ).
thf(202,plain,
! [SV16: $i,SV13: $i,SV24: $i,SV36: $i] :
( ( ( sK2_SY526 @ SV36 )
= $false )
| ( ( sK3_SY544 @ SV36 )
= $true )
| ( ( reli @ SV24 @ SV36 )
= $false )
| ( ( princ_inj @ sK1_SY269 @ ( sK16_SY671 @ SV13 @ SV16 @ SV24 ) )
= $false )
| ( ( reli @ SV16 @ SV24 )
= $false )
| ( ( relr @ SV13 @ SV16 )
= $false )
| ( ( reli @ sK5_SY577 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[199]) ).
thf(203,plain,
! [SV16: $i,SV13: $i,SV24: $i,SV37: $i] :
( ( ( sK2_SY526 @ SV37 )
= $false )
| ( ( sK3_SY544 @ SV37 )
= $true )
| ( ( reli @ SV24 @ SV37 )
= $false )
| ( ( reli @ SV24 @ ( sK16_SY671 @ SV13 @ SV16 @ SV24 ) )
= $true )
| ( ( reli @ SV16 @ SV24 )
= $false )
| ( ( relr @ SV13 @ SV16 )
= $false )
| ( ( reli @ sK5_SY577 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(204,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[30,203,202,200,197,187,183,179,172,171,170,163,161,159,157,135,132,111,105,104,92,90,73]) ).
thf(205,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[204]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV441^1 : 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.16 % Computer : n011.cluster.edu
% 0.10/0.16 % Model : x86_64 x86_64
% 0.10/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.16 % Memory : 8046.5625MB
% 0.10/0.16 % OS : Linux 6.8.0-71-generic
% 0.10/0.16 % CPULimit : 300
% 0.10/0.16 % WCLimit : 300
% 0.10/0.16 % DateTime : Tue Oct 6 16:30:06 UTC 2026
% 0.10/0.16 % CPUTime :
% 0.10/0.16 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 71.76/14.53
% 71.76/14.53 No.of.Axioms: 6
% 71.76/14.53
% 71.76/14.53 Length.of.Defs: 4858
% 71.76/14.53
% 71.76/14.53 Contains.Choice.Funs: false
% 71.76/14.53 ..............
% 71.76/14.53
% 71.76/14.53 ********************************
% 71.76/14.53 * All subproblems solved! *
% 71.76/14.53 ********************************
% 71.76/14.53 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:7,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:204,loop_count:0,foatp_calls:1,translation:fof_full)
% 71.76/14.53
% 71.76/14.53 %**** Beginning of derivation protocol ****
% 71.76/14.53 % SZS output start CNFRefutation
% See solution above
% 71.76/14.53
% 71.76/14.53 %**** End of derivation protocol ****
% 71.76/14.53 %**** no. of clauses in derivation: 205 ****
% 71.76/14.53 %**** clause counter: 204 ****
% 71.76/14.53
% 71.76/14.53 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:7,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:204,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------