%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWV443^1 : 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 : n010.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 56.64s 11.50s
% Output : CNFRefutation 56.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 41
% Syntax : Number of formulae : 216 ( 103 unt; 0 typ; 34 def)
% Number of atoms : 1576 ( 416 equ; 0 cnn)
% Maximal formula atoms : 10 ( 7 avg)
% Number of connectives : 2782 ( 379 ~; 540 |; 2 &;1747 @)
% ( 0 <=>; 114 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 155 ( 155 >; 0 *; 0 +; 0 <<)
% Number of symbols : 60 ( 57 usr; 11 con; 0-3 aty)
% Number of variables : 767 ( 50 ^; 713 !; 4 ?; 767 :)
% 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_SY480,type,
sK10_SY480: ( $i > $o ) > $i > $i ).
thf(tp_sK11_SY483,type,
sK11_SY483: ( $i > $o ) > $i > $i ).
thf(tp_sK12_SY494,type,
sK12_SY494: $i > ( $i > $o ) > $i ).
thf(tp_sK13_SY495,type,
sK13_SY495: $i ).
thf(tp_sK14_SY504,type,
sK14_SY504: $i ).
thf(tp_sK15_SY511,type,
sK15_SY511: $i > $i > $i > $i ).
thf(tp_sK1_SY163,type,
sK1_SY163: individuals ).
thf(tp_sK2_SY406,type,
sK2_SY406: $i > $o ).
thf(tp_sK3_SY419,type,
sK3_SY419: $i ).
thf(tp_sK4_SY431,type,
sK4_SY431: $i ).
thf(tp_sK5_SX0,type,
sK5_SX0: $i ).
thf(tp_sK6_SY472,type,
sK6_SY472: ( $i > $o ) > $i > $i ).
thf(tp_sK7_SY475,type,
sK7_SY475: ( $i > $o ) > $i > $i ).
thf(tp_sK8_SY479,type,
sK8_SY479: ( $i > $o ) > $i > $i ).
thf(tp_sK9_SY486,type,
sK9_SY486: $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(2,axiom,
! [A: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ reli @ ( mbox @ relr @ A ) ) @ ( mbox @ relr @ ( mbox @ reli @ A ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',trans_axiom_i) ).
thf(5,axiom,
! [A: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ relr @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',refl_axiom_r) ).
thf(6,axiom,
! [A: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ reli @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',refl_axiom_i) ).
thf(7,conjecture,
! [K: individuals,A: $i > $o] : ( bl_valid @ ( bl_impl @ ( bl_says @ K @ ( bl_atom @ A ) ) @ ( bl_says @ K @ ( bl_atom @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bl_id2) ).
thf(8,negated_conjecture,
( ( ! [K: individuals,A: $i > $o] : ( bl_valid @ ( bl_impl @ ( bl_says @ K @ ( 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 @ SY163 @ 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,SY277: $i] :
( ~ ! [SY278: $i] :
( ( reli @ SY277 @ SY278 )
=> ! [SY249: $i] :
( ( relr @ SY278 @ SY249 )
=> ( SY238 @ SY249 ) ) )
| ! [SY280: $i] :
( ( relr @ SY277 @ SY280 )
=> ! [SY271: $i] :
( ( reli @ SY280 @ SY271 )
=> ( SY238 @ SY271 ) ) ) ) )
= $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,
( ( ! [SY288: $i > $o,SY317: $i] :
( ~ ! [SY318: $i] :
( ( relr @ SY317 @ SY318 )
=> ( SY288 @ SY318 ) )
| ! [SY319: $i] :
( ( relr @ SY317 @ SY319 )
=> ! [SY312: $i] :
( ( relr @ SY319 @ SY312 )
=> ( SY288 @ SY312 ) ) ) ) )
= $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,
( ( ! [SY326: $i > $o,SY355: $i] :
( ~ ! [SY356: $i] :
( ( reli @ SY355 @ SY356 )
=> ( SY326 @ SY356 ) )
| ! [SY357: $i] :
( ( reli @ SY355 @ SY357 )
=> ! [SY350: $i] :
( ( reli @ SY357 @ SY350 )
=> ( SY326 @ SY350 ) ) ) ) )
= $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,
( ( ! [SY364: $i > $o,SY380: $i] :
( ~ ! [SY381: $i] :
( ( relr @ SY380 @ SY381 )
=> ( SY364 @ SY381 ) )
| ( SY364 @ SY380 ) ) )
= $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,
( ( ! [SY385: $i > $o,SY401: $i] :
( ~ ! [SY402: $i] :
( ( reli @ SY401 @ SY402 )
=> ( SY385 @ SY402 ) )
| ( SY385 @ SY401 ) ) )
= $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,
( ( ! [SY406: $i > $o,SY407: $i,SY408: $i] :
( ( reli @ SY407 @ SY408 )
=> ( ~ ! [SY409: $i] :
( ( reli @ SY408 @ SY409 )
=> ! [SY410: $i] :
( ( relr @ SY409 @ SY410 )
=> ! [SY411: $i] :
( ( reli @ SY410 @ SY411 )
=> ( ~ ! [SY412: $i] :
( ( reli @ SY411 @ SY412 )
=> ( princ_inj @ sK1_SY163 @ SY412 ) )
| ! [SY53: $i] :
( ( reli @ SY411 @ SY53 )
=> ( SY406 @ SY53 ) ) ) ) ) )
| ! [SY414: $i] :
( ( reli @ SY408 @ SY414 )
=> ! [SY415: $i] :
( ( relr @ SY414 @ SY415 )
=> ! [SY416: $i] :
( ( reli @ SY415 @ SY416 )
=> ( ~ ! [SY417: $i] :
( ( reli @ SY416 @ SY417 )
=> ( princ_inj @ sK1_SY163 @ SY417 ) )
| ! [SY150: $i] :
( ( reli @ SY416 @ SY150 )
=> ( SY406 @ SY150 ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[9]) ).
thf(17,plain,
( ( ! [SY419: $i,SY420: $i] :
( ( reli @ SY419 @ SY420 )
=> ( ~ ! [SY421: $i] :
( ( reli @ SY420 @ SY421 )
=> ! [SY422: $i] :
( ( relr @ SY421 @ SY422 )
=> ! [SY423: $i] :
( ( reli @ SY422 @ SY423 )
=> ( ~ ! [SY412: $i] :
( ( reli @ SY423 @ SY412 )
=> ( princ_inj @ sK1_SY163 @ SY412 ) )
| ! [SY425: $i] :
( ( reli @ SY423 @ SY425 )
=> ( sK2_SY406 @ SY425 ) ) ) ) ) )
| ! [SY426: $i] :
( ( reli @ SY420 @ SY426 )
=> ! [SY427: $i] :
( ( relr @ SY426 @ SY427 )
=> ! [SY428: $i] :
( ( reli @ SY427 @ SY428 )
=> ( ~ ! [SY417: $i] :
( ( reli @ SY428 @ SY417 )
=> ( princ_inj @ sK1_SY163 @ SY417 ) )
| ! [SY430: $i] :
( ( reli @ SY428 @ SY430 )
=> ( sK2_SY406 @ SY430 ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[16]) ).
thf(18,plain,
( ( ! [SY431: $i] :
( ( reli @ sK3_SY419 @ SY431 )
=> ( ~ ! [SY421: $i] :
( ( reli @ SY431 @ SY421 )
=> ! [SY422: $i] :
( ( relr @ SY421 @ SY422 )
=> ! [SY423: $i] :
( ( reli @ SY422 @ SY423 )
=> ( ~ ! [SY412: $i] :
( ( reli @ SY423 @ SY412 )
=> ( princ_inj @ sK1_SY163 @ SY412 ) )
| ! [SY425: $i] :
( ( reli @ SY423 @ SY425 )
=> ( sK2_SY406 @ SY425 ) ) ) ) ) )
| ! [SY426: $i] :
( ( reli @ SY431 @ SY426 )
=> ! [SY427: $i] :
( ( relr @ SY426 @ SY427 )
=> ! [SY428: $i] :
( ( reli @ SY427 @ SY428 )
=> ( ~ ! [SY417: $i] :
( ( reli @ SY428 @ SY417 )
=> ( princ_inj @ sK1_SY163 @ SY417 ) )
| ! [SY430: $i] :
( ( reli @ SY428 @ SY430 )
=> ( sK2_SY406 @ SY430 ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[17]) ).
thf(19,plain,
( ( ( reli @ sK3_SY419 @ sK4_SY431 )
=> ( ~ ! [SY442: $i] :
( ( reli @ sK4_SY431 @ SY442 )
=> ! [SY422: $i] :
( ( relr @ SY442 @ SY422 )
=> ! [SY423: $i] :
( ( reli @ SY422 @ SY423 )
=> ( ~ ! [SY412: $i] :
( ( reli @ SY423 @ SY412 )
=> ( princ_inj @ sK1_SY163 @ SY412 ) )
| ! [SY425: $i] :
( ( reli @ SY423 @ SY425 )
=> ( sK2_SY406 @ SY425 ) ) ) ) ) )
| ! [SY447: $i] :
( ( reli @ sK4_SY431 @ SY447 )
=> ! [SY427: $i] :
( ( relr @ SY447 @ SY427 )
=> ! [SY428: $i] :
( ( reli @ SY427 @ SY428 )
=> ( ~ ! [SY417: $i] :
( ( reli @ SY428 @ SY417 )
=> ( princ_inj @ sK1_SY163 @ SY417 ) )
| ! [SY430: $i] :
( ( reli @ SY428 @ SY430 )
=> ( sK2_SY406 @ SY430 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[18]) ).
thf(20,plain,
( ( reli @ sK3_SY419 @ sK4_SY431 )
= $true ),
inference(standard_cnf,[status(thm)],[19]) ).
thf(21,plain,
( ( ~ ! [SY442: $i] :
( ( reli @ sK4_SY431 @ SY442 )
=> ! [SY422: $i] :
( ( relr @ SY442 @ SY422 )
=> ! [SY423: $i] :
( ( reli @ SY422 @ SY423 )
=> ( ~ ! [SY412: $i] :
( ( reli @ SY423 @ SY412 )
=> ( princ_inj @ sK1_SY163 @ SY412 ) )
| ! [SY425: $i] :
( ( reli @ SY423 @ SY425 )
=> ( sK2_SY406 @ SY425 ) ) ) ) ) )
| ! [SY447: $i] :
( ( reli @ sK4_SY431 @ SY447 )
=> ! [SY427: $i] :
( ( relr @ SY447 @ SY427 )
=> ! [SY428: $i] :
( ( reli @ SY427 @ SY428 )
=> ( ~ ! [SY417: $i] :
( ( reli @ SY428 @ SY417 )
=> ( princ_inj @ sK1_SY163 @ SY417 ) )
| ! [SY430: $i] :
( ( reli @ SY428 @ SY430 )
=> ( sK2_SY406 @ SY430 ) ) ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[19]) ).
thf(22,plain,
( ( ~ ( ~ ! [SY442: $i] :
( ( reli @ sK4_SY431 @ SY442 )
=> ! [SY422: $i] :
( ( relr @ SY442 @ SY422 )
=> ! [SY423: $i] :
( ( reli @ SY422 @ SY423 )
=> ( ~ ! [SY412: $i] :
( ( reli @ SY423 @ SY412 )
=> ( princ_inj @ sK1_SY163 @ SY412 ) )
| ! [SY425: $i] :
( ( reli @ SY423 @ SY425 )
=> ( sK2_SY406 @ SY425 ) ) ) ) ) )
| ! [SY447: $i] :
( ( reli @ sK4_SY431 @ SY447 )
=> ! [SY427: $i] :
( ( relr @ SY447 @ SY427 )
=> ! [SY428: $i] :
( ( reli @ SY427 @ SY428 )
=> ( ~ ! [SY417: $i] :
( ( reli @ SY428 @ SY417 )
=> ( princ_inj @ sK1_SY163 @ SY417 ) )
| ! [SY430: $i] :
( ( reli @ SY428 @ SY430 )
=> ( sK2_SY406 @ SY430 ) ) ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[21]) ).
thf(23,plain,
( ( ! [SY385: $i > $o,SY401: $i] :
( ~ ! [SY402: $i] :
( ( reli @ SY401 @ SY402 )
=> ( SY385 @ SY402 ) )
| ( SY385 @ SY401 ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(24,plain,
( ( ! [SY364: $i > $o,SY380: $i] :
( ~ ! [SY381: $i] :
( ( relr @ SY380 @ SY381 )
=> ( SY364 @ SY381 ) )
| ( SY364 @ SY380 ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(25,plain,
( ( ! [SY326: $i > $o,SY355: $i] :
( ~ ! [SY356: $i] :
( ( reli @ SY355 @ SY356 )
=> ( SY326 @ SY356 ) )
| ! [SY357: $i] :
( ( reli @ SY355 @ SY357 )
=> ! [SY350: $i] :
( ( reli @ SY357 @ SY350 )
=> ( SY326 @ SY350 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(26,plain,
( ( ! [SY288: $i > $o,SY317: $i] :
( ~ ! [SY318: $i] :
( ( relr @ SY317 @ SY318 )
=> ( SY288 @ SY318 ) )
| ! [SY319: $i] :
( ( relr @ SY317 @ SY319 )
=> ! [SY312: $i] :
( ( relr @ SY319 @ SY312 )
=> ( SY288 @ SY312 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(27,plain,
( ( ! [SY238: $i > $o,SY277: $i] :
( ~ ! [SY278: $i] :
( ( reli @ SY277 @ SY278 )
=> ! [SY249: $i] :
( ( relr @ SY278 @ SY249 )
=> ( SY238 @ SY249 ) ) )
| ! [SY280: $i] :
( ( relr @ SY277 @ SY280 )
=> ! [SY271: $i] :
( ( reli @ SY280 @ SY271 )
=> ( SY238 @ SY271 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(28,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)],[10]) ).
thf(29,plain,
( ( reli @ sK3_SY419 @ sK4_SY431 )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(30,plain,
( ( ~ ( ~ ! [SY442: $i] :
( ( reli @ sK4_SY431 @ SY442 )
=> ! [SY422: $i] :
( ( relr @ SY442 @ SY422 )
=> ! [SY423: $i] :
( ( reli @ SY422 @ SY423 )
=> ( ~ ! [SY412: $i] :
( ( reli @ SY423 @ SY412 )
=> ( princ_inj @ sK1_SY163 @ SY412 ) )
| ! [SY425: $i] :
( ( reli @ SY423 @ SY425 )
=> ( sK2_SY406 @ SY425 ) ) ) ) ) )
| ! [SY447: $i] :
( ( reli @ sK4_SY431 @ SY447 )
=> ! [SY427: $i] :
( ( relr @ SY447 @ SY427 )
=> ! [SY428: $i] :
( ( reli @ SY427 @ SY428 )
=> ( ~ ! [SY417: $i] :
( ( reli @ SY428 @ SY417 )
=> ( princ_inj @ sK1_SY163 @ SY417 ) )
| ! [SY430: $i] :
( ( reli @ SY428 @ SY430 )
=> ( sK2_SY406 @ SY430 ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(31,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)],[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(32,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)],[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(33,plain,
( ( ! [SX0: $i > $o,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( relr @ 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(34,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( reli @ sK4_SY431 @ SX0 )
| ! [SX1: $i] :
( ~ ( relr @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( reli @ SX1 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( reli @ SX2 @ SX3 )
| ( princ_inj @ sK1_SY163 @ SX3 ) )
| ! [SX3: $i] :
( ~ ( reli @ SX2 @ SX3 )
| ( sK2_SY406 @ SX3 ) ) ) ) )
| ! [SX0: $i] :
( ~ ( reli @ sK4_SY431 @ SX0 )
| ! [SX1: $i] :
( ~ ( relr @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( reli @ SX1 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( reli @ SX2 @ SX3 )
| ( princ_inj @ sK1_SY163 @ SX3 ) )
| ! [SX3: $i] :
( ~ ( reli @ SX2 @ SX3 )
| ( sK2_SY406 @ SX3 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30,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] :
( ~ ( reli @ SX1 @ SX2 )
| ( SX0 @ SX2 ) )
| ! [SX2: $i] :
( ~ ( reli @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( reli @ SX2 @ SX3 )
| ( SX0 @ SX3 ) ) ) ) )
= $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(36,plain,
( ( ! [SX0: $i > $o,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( reli @ SX1 @ SX2 )
| ( SX0 @ SX2 ) )
| ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23,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,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)],[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(38,plain,
! [SV1: $i > $o] :
( ( ! [SY452: $i] :
( ~ ! [SY453: $i] :
( ~ ( relr @ SY452 @ SY453 )
| ( SV1 @ SY453 ) )
| ! [SY454: $i] :
( ~ ( relr @ SY452 @ SY454 )
| ! [SY455: $i] :
( ~ ( relr @ SY454 @ SY455 )
| ( SV1 @ SY455 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(39,plain,
! [SV2: $i > $o] :
( ( ! [SY456: $i] :
( ~ ! [SY457: $i] :
( ~ ( reli @ SY456 @ SY457 )
| ! [SY458: $i] :
( ~ ( relr @ SY457 @ SY458 )
| ( SV2 @ SY458 ) ) )
| ! [SY459: $i] :
( ~ ( relr @ SY456 @ SY459 )
| ! [SY460: $i] :
( ~ ( reli @ SY459 @ SY460 )
| ( SV2 @ SY460 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(40,plain,
! [SV3: $i > $o] :
( ( ! [SY461: $i] :
( ~ ! [SY462: $i] :
( ~ ( relr @ SY461 @ SY462 )
| ( SV3 @ SY462 ) )
| ( SV3 @ SY461 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(41,plain,
( ( ~ ! [SX0: $i] :
( ~ ( reli @ sK4_SY431 @ SX0 )
| ! [SX1: $i] :
( ~ ( relr @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( reli @ SX1 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( reli @ SX2 @ SX3 )
| ( princ_inj @ sK1_SY163 @ SX3 ) )
| ! [SX3: $i] :
( ~ ( reli @ SX2 @ SX3 )
| ( sK2_SY406 @ SX3 ) ) ) ) )
| ! [SX0: $i] :
( ~ ( reli @ sK4_SY431 @ SX0 )
| ! [SX1: $i] :
( ~ ( relr @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( reli @ SX1 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( reli @ SX2 @ SX3 )
| ( princ_inj @ sK1_SY163 @ SX3 ) )
| ! [SX3: $i] :
( ~ ( reli @ SX2 @ SX3 )
| ( sK2_SY406 @ SX3 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(42,plain,
! [SV4: $i > $o] :
( ( ! [SY463: $i] :
( ~ ! [SY464: $i] :
( ~ ( reli @ SY463 @ SY464 )
| ( SV4 @ SY464 ) )
| ! [SY465: $i] :
( ~ ( reli @ SY463 @ SY465 )
| ! [SY466: $i] :
( ~ ( reli @ SY465 @ SY466 )
| ( SV4 @ SY466 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(43,plain,
! [SV5: $i > $o] :
( ( ! [SY467: $i] :
( ~ ! [SY468: $i] :
( ~ ( reli @ SY467 @ SY468 )
| ( SV5 @ SY468 ) )
| ( SV5 @ SY467 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(44,plain,
! [SV6: $i] :
( ( ! [SY469: $i] :
( ~ ( reli @ SV6 @ SY469 )
| ! [SX2: individuals,SX3: $i] :
( ~ ( reli @ SY469 @ SX3 )
| ~ ( princ_inj @ SX2 @ SX3 )
| ( princ_inj @ loca @ SX3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(45,plain,
! [SV1: $i > $o,SV7: $i] :
( ( ~ ! [SY472: $i] :
( ~ ( relr @ SV7 @ SY472 )
| ( SV1 @ SY472 ) )
| ! [SY473: $i] :
( ~ ( relr @ SV7 @ SY473 )
| ! [SY455: $i] :
( ~ ( relr @ SY473 @ SY455 )
| ( SV1 @ SY455 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(46,plain,
! [SV2: $i > $o,SV8: $i] :
( ( ~ ! [SY475: $i] :
( ~ ( reli @ SV8 @ SY475 )
| ! [SY458: $i] :
( ~ ( relr @ SY475 @ SY458 )
| ( SV2 @ SY458 ) ) )
| ! [SY477: $i] :
( ~ ( relr @ SV8 @ SY477 )
| ! [SY460: $i] :
( ~ ( reli @ SY477 @ SY460 )
| ( SV2 @ SY460 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(47,plain,
! [SV3: $i > $o,SV9: $i] :
( ( ~ ! [SY479: $i] :
( ~ ( relr @ SV9 @ SY479 )
| ( SV3 @ SY479 ) )
| ( SV3 @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(48,plain,
( ( ~ ! [SX0: $i] :
( ~ ( reli @ sK4_SY431 @ SX0 )
| ! [SX1: $i] :
( ~ ( relr @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( reli @ SX1 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( reli @ SX2 @ SX3 )
| ( princ_inj @ sK1_SY163 @ SX3 ) )
| ! [SX3: $i] :
( ~ ( reli @ SX2 @ SX3 )
| ( sK2_SY406 @ SX3 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[41]) ).
thf(49,plain,
( ( ! [SX0: $i] :
( ~ ( reli @ sK4_SY431 @ SX0 )
| ! [SX1: $i] :
( ~ ( relr @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( reli @ SX1 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( reli @ SX2 @ SX3 )
| ( princ_inj @ sK1_SY163 @ SX3 ) )
| ! [SX3: $i] :
( ~ ( reli @ SX2 @ SX3 )
| ( sK2_SY406 @ SX3 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[41]) ).
thf(50,plain,
! [SV4: $i > $o,SV10: $i] :
( ( ~ ! [SY480: $i] :
( ~ ( reli @ SV10 @ SY480 )
| ( SV4 @ SY480 ) )
| ! [SY481: $i] :
( ~ ( reli @ SV10 @ SY481 )
| ! [SY466: $i] :
( ~ ( reli @ SY481 @ SY466 )
| ( SV4 @ SY466 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(51,plain,
! [SV5: $i > $o,SV11: $i] :
( ( ~ ! [SY483: $i] :
( ~ ( reli @ SV11 @ SY483 )
| ( SV5 @ SY483 ) )
| ( SV5 @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(52,plain,
! [SV12: $i,SV6: $i] :
( ( ~ ( reli @ SV6 @ SV12 )
| ! [SY484: individuals,SY485: $i] :
( ~ ( reli @ SV12 @ SY485 )
| ~ ( princ_inj @ SY484 @ SY485 )
| ( princ_inj @ loca @ SY485 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(53,plain,
! [SV1: $i > $o,SV7: $i] :
( ( ( ~ ! [SY472: $i] :
( ~ ( relr @ SV7 @ SY472 )
| ( SV1 @ SY472 ) ) )
= $true )
| ( ( ! [SY473: $i] :
( ~ ( relr @ SV7 @ SY473 )
| ! [SY455: $i] :
( ~ ( relr @ SY473 @ SY455 )
| ( SV1 @ SY455 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[45]) ).
thf(54,plain,
! [SV2: $i > $o,SV8: $i] :
( ( ( ~ ! [SY475: $i] :
( ~ ( reli @ SV8 @ SY475 )
| ! [SY458: $i] :
( ~ ( relr @ SY475 @ SY458 )
| ( SV2 @ SY458 ) ) ) )
= $true )
| ( ( ! [SY477: $i] :
( ~ ( relr @ SV8 @ SY477 )
| ! [SY460: $i] :
( ~ ( reli @ SY477 @ SY460 )
| ( SV2 @ SY460 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[46]) ).
thf(55,plain,
! [SV3: $i > $o,SV9: $i] :
( ( ( ~ ! [SY479: $i] :
( ~ ( relr @ SV9 @ SY479 )
| ( SV3 @ SY479 ) ) )
= $true )
| ( ( SV3 @ SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[47]) ).
thf(56,plain,
( ( ! [SX0: $i] :
( ~ ( reli @ sK4_SY431 @ SX0 )
| ! [SX1: $i] :
( ~ ( relr @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( reli @ SX1 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( reli @ SX2 @ SX3 )
| ( princ_inj @ sK1_SY163 @ SX3 ) )
| ! [SX3: $i] :
( ~ ( reli @ SX2 @ SX3 )
| ( sK2_SY406 @ SX3 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[48]) ).
thf(57,plain,
( ( ~ ( reli @ sK4_SY431 @ sK5_SX0 )
| ! [SY486: $i] :
( ~ ( relr @ sK5_SX0 @ SY486 )
| ! [SX2: $i] :
( ~ ( reli @ SY486 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( reli @ SX2 @ SX3 )
| ( princ_inj @ sK1_SY163 @ SX3 ) )
| ! [SX3: $i] :
( ~ ( reli @ SX2 @ SX3 )
| ( sK2_SY406 @ SX3 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[49]) ).
thf(58,plain,
! [SV4: $i > $o,SV10: $i] :
( ( ( ~ ! [SY480: $i] :
( ~ ( reli @ SV10 @ SY480 )
| ( SV4 @ SY480 ) ) )
= $true )
| ( ( ! [SY481: $i] :
( ~ ( reli @ SV10 @ SY481 )
| ! [SY466: $i] :
( ~ ( reli @ SY481 @ SY466 )
| ( SV4 @ SY466 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[50]) ).
thf(59,plain,
! [SV5: $i > $o,SV11: $i] :
( ( ( ~ ! [SY483: $i] :
( ~ ( reli @ SV11 @ SY483 )
| ( SV5 @ SY483 ) ) )
= $true )
| ( ( SV5 @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[51]) ).
thf(60,plain,
! [SV12: $i,SV6: $i] :
( ( ( ~ ( reli @ SV6 @ SV12 ) )
= $true )
| ( ( ! [SY484: individuals,SY485: $i] :
( ~ ( reli @ SV12 @ SY485 )
| ~ ( princ_inj @ SY484 @ SY485 )
| ( princ_inj @ loca @ SY485 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[52]) ).
thf(61,plain,
! [SV1: $i > $o,SV7: $i] :
( ( ( ! [SY472: $i] :
( ~ ( relr @ SV7 @ SY472 )
| ( SV1 @ SY472 ) ) )
= $false )
| ( ( ! [SY473: $i] :
( ~ ( relr @ SV7 @ SY473 )
| ! [SY455: $i] :
( ~ ( relr @ SY473 @ SY455 )
| ( SV1 @ SY455 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(62,plain,
! [SV2: $i > $o,SV8: $i] :
( ( ( ! [SY475: $i] :
( ~ ( reli @ SV8 @ SY475 )
| ! [SY458: $i] :
( ~ ( relr @ SY475 @ SY458 )
| ( SV2 @ SY458 ) ) ) )
= $false )
| ( ( ! [SY477: $i] :
( ~ ( relr @ SV8 @ SY477 )
| ! [SY460: $i] :
( ~ ( reli @ SY477 @ SY460 )
| ( SV2 @ SY460 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(63,plain,
! [SV3: $i > $o,SV9: $i] :
( ( ( ! [SY479: $i] :
( ~ ( relr @ SV9 @ SY479 )
| ( SV3 @ SY479 ) ) )
= $false )
| ( ( SV3 @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(64,plain,
! [SV13: $i] :
( ( ~ ( reli @ sK4_SY431 @ SV13 )
| ! [SY490: $i] :
( ~ ( relr @ SV13 @ SY490 )
| ! [SX2: $i] :
( ~ ( reli @ SY490 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( reli @ SX2 @ SX3 )
| ( princ_inj @ sK1_SY163 @ SX3 ) )
| ! [SX3: $i] :
( ~ ( reli @ SX2 @ SX3 )
| ( sK2_SY406 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(65,plain,
( ( ~ ( reli @ sK4_SY431 @ sK5_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[57]) ).
thf(66,plain,
( ( ! [SY486: $i] :
( ~ ( relr @ sK5_SX0 @ SY486 )
| ! [SX2: $i] :
( ~ ( reli @ SY486 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( reli @ SX2 @ SX3 )
| ( princ_inj @ sK1_SY163 @ SX3 ) )
| ! [SX3: $i] :
( ~ ( reli @ SX2 @ SX3 )
| ( sK2_SY406 @ SX3 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[57]) ).
thf(67,plain,
! [SV4: $i > $o,SV10: $i] :
( ( ( ! [SY480: $i] :
( ~ ( reli @ SV10 @ SY480 )
| ( SV4 @ SY480 ) ) )
= $false )
| ( ( ! [SY481: $i] :
( ~ ( reli @ SV10 @ SY481 )
| ! [SY466: $i] :
( ~ ( reli @ SY481 @ SY466 )
| ( SV4 @ SY466 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(68,plain,
! [SV5: $i > $o,SV11: $i] :
( ( ( ! [SY483: $i] :
( ~ ( reli @ SV11 @ SY483 )
| ( SV5 @ SY483 ) ) )
= $false )
| ( ( SV5 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(69,plain,
! [SV12: $i,SV6: $i] :
( ( ( reli @ SV6 @ SV12 )
= $false )
| ( ( ! [SY484: individuals,SY485: $i] :
( ~ ( reli @ SV12 @ SY485 )
| ~ ( princ_inj @ SY484 @ SY485 )
| ( princ_inj @ loca @ SY485 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(70,plain,
! [SV1: $i > $o,SV7: $i] :
( ( ( ~ ( relr @ SV7 @ ( sK6_SY472 @ SV1 @ SV7 ) )
| ( SV1 @ ( sK6_SY472 @ SV1 @ SV7 ) ) )
= $false )
| ( ( ! [SY473: $i] :
( ~ ( relr @ SV7 @ SY473 )
| ! [SY455: $i] :
( ~ ( relr @ SY473 @ SY455 )
| ( SV1 @ SY455 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[61]) ).
thf(71,plain,
! [SV2: $i > $o,SV8: $i] :
( ( ( ~ ( reli @ SV8 @ ( sK7_SY475 @ SV2 @ SV8 ) )
| ! [SY494: $i] :
( ~ ( relr @ ( sK7_SY475 @ SV2 @ SV8 ) @ SY494 )
| ( SV2 @ SY494 ) ) )
= $false )
| ( ( ! [SY477: $i] :
( ~ ( relr @ SV8 @ SY477 )
| ! [SY460: $i] :
( ~ ( reli @ SY477 @ SY460 )
| ( SV2 @ SY460 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[62]) ).
thf(72,plain,
! [SV3: $i > $o,SV9: $i] :
( ( ( ~ ( relr @ SV9 @ ( sK8_SY479 @ SV3 @ SV9 ) )
| ( SV3 @ ( sK8_SY479 @ SV3 @ SV9 ) ) )
= $false )
| ( ( SV3 @ SV9 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[63]) ).
thf(73,plain,
! [SV13: $i] :
( ( ( ~ ( reli @ sK4_SY431 @ SV13 ) )
= $true )
| ( ( ! [SY490: $i] :
( ~ ( relr @ SV13 @ SY490 )
| ! [SX2: $i] :
( ~ ( reli @ SY490 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( reli @ SX2 @ SX3 )
| ( princ_inj @ sK1_SY163 @ SX3 ) )
| ! [SX3: $i] :
( ~ ( reli @ SX2 @ SX3 )
| ( sK2_SY406 @ SX3 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[64]) ).
thf(74,plain,
( ( reli @ sK4_SY431 @ sK5_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[65]) ).
thf(75,plain,
( ( ~ ( relr @ sK5_SX0 @ sK9_SY486 )
| ! [SY495: $i] :
( ~ ( reli @ sK9_SY486 @ SY495 )
| ~ ! [SX3: $i] :
( ~ ( reli @ SY495 @ SX3 )
| ( princ_inj @ sK1_SY163 @ SX3 ) )
| ! [SX3: $i] :
( ~ ( reli @ SY495 @ SX3 )
| ( sK2_SY406 @ SX3 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[66]) ).
thf(76,plain,
! [SV4: $i > $o,SV10: $i] :
( ( ( ~ ( reli @ SV10 @ ( sK10_SY480 @ SV4 @ SV10 ) )
| ( SV4 @ ( sK10_SY480 @ SV4 @ SV10 ) ) )
= $false )
| ( ( ! [SY481: $i] :
( ~ ( reli @ SV10 @ SY481 )
| ! [SY466: $i] :
( ~ ( reli @ SY481 @ SY466 )
| ( SV4 @ SY466 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[67]) ).
thf(77,plain,
! [SV5: $i > $o,SV11: $i] :
( ( ( ~ ( reli @ SV11 @ ( sK11_SY483 @ SV5 @ SV11 ) )
| ( SV5 @ ( sK11_SY483 @ SV5 @ SV11 ) ) )
= $false )
| ( ( SV5 @ SV11 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[68]) ).
thf(78,plain,
! [SV6: $i,SV14: individuals,SV12: $i] :
( ( ( ! [SY498: $i] :
( ~ ( reli @ SV12 @ SY498 )
| ~ ( princ_inj @ SV14 @ SY498 )
| ( princ_inj @ loca @ SY498 ) ) )
= $true )
| ( ( reli @ SV6 @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(79,plain,
! [SV1: $i > $o,SV7: $i] :
( ( ( ~ ( relr @ SV7 @ ( sK6_SY472 @ SV1 @ SV7 ) ) )
= $false )
| ( ( ! [SY473: $i] :
( ~ ( relr @ SV7 @ SY473 )
| ! [SY455: $i] :
( ~ ( relr @ SY473 @ SY455 )
| ( SV1 @ SY455 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[70]) ).
thf(80,plain,
! [SV7: $i,SV1: $i > $o] :
( ( ( SV1 @ ( sK6_SY472 @ SV1 @ SV7 ) )
= $false )
| ( ( ! [SY473: $i] :
( ~ ( relr @ SV7 @ SY473 )
| ! [SY455: $i] :
( ~ ( relr @ SY473 @ SY455 )
| ( SV1 @ SY455 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[70]) ).
thf(81,plain,
! [SV2: $i > $o,SV8: $i] :
( ( ( ~ ( reli @ SV8 @ ( sK7_SY475 @ SV2 @ SV8 ) ) )
= $false )
| ( ( ! [SY477: $i] :
( ~ ( relr @ SV8 @ SY477 )
| ! [SY460: $i] :
( ~ ( reli @ SY477 @ SY460 )
| ( SV2 @ SY460 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[71]) ).
thf(82,plain,
! [SV8: $i,SV2: $i > $o] :
( ( ( ! [SY494: $i] :
( ~ ( relr @ ( sK7_SY475 @ SV2 @ SV8 ) @ SY494 )
| ( SV2 @ SY494 ) ) )
= $false )
| ( ( ! [SY477: $i] :
( ~ ( relr @ SV8 @ SY477 )
| ! [SY460: $i] :
( ~ ( reli @ SY477 @ SY460 )
| ( SV2 @ SY460 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[71]) ).
thf(83,plain,
! [SV3: $i > $o,SV9: $i] :
( ( ( ~ ( relr @ SV9 @ ( sK8_SY479 @ SV3 @ SV9 ) ) )
= $false )
| ( ( SV3 @ SV9 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[72]) ).
thf(84,plain,
! [SV9: $i,SV3: $i > $o] :
( ( ( SV3 @ ( sK8_SY479 @ SV3 @ SV9 ) )
= $false )
| ( ( SV3 @ SV9 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[72]) ).
thf(85,plain,
! [SV13: $i] :
( ( ( reli @ sK4_SY431 @ SV13 )
= $false )
| ( ( ! [SY490: $i] :
( ~ ( relr @ SV13 @ SY490 )
| ! [SX2: $i] :
( ~ ( reli @ SY490 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( reli @ SX2 @ SX3 )
| ( princ_inj @ sK1_SY163 @ SX3 ) )
| ! [SX3: $i] :
( ~ ( reli @ SX2 @ SX3 )
| ( sK2_SY406 @ SX3 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(86,plain,
( ( ~ ( relr @ sK5_SX0 @ sK9_SY486 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[75]) ).
thf(87,plain,
( ( ! [SY495: $i] :
( ~ ( reli @ sK9_SY486 @ SY495 )
| ~ ! [SX3: $i] :
( ~ ( reli @ SY495 @ SX3 )
| ( princ_inj @ sK1_SY163 @ SX3 ) )
| ! [SX3: $i] :
( ~ ( reli @ SY495 @ SX3 )
| ( sK2_SY406 @ SX3 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[75]) ).
thf(88,plain,
! [SV4: $i > $o,SV10: $i] :
( ( ( ~ ( reli @ SV10 @ ( sK10_SY480 @ SV4 @ SV10 ) ) )
= $false )
| ( ( ! [SY481: $i] :
( ~ ( reli @ SV10 @ SY481 )
| ! [SY466: $i] :
( ~ ( reli @ SY481 @ SY466 )
| ( SV4 @ SY466 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[76]) ).
thf(89,plain,
! [SV10: $i,SV4: $i > $o] :
( ( ( SV4 @ ( sK10_SY480 @ SV4 @ SV10 ) )
= $false )
| ( ( ! [SY481: $i] :
( ~ ( reli @ SV10 @ SY481 )
| ! [SY466: $i] :
( ~ ( reli @ SY481 @ SY466 )
| ( SV4 @ SY466 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[76]) ).
thf(90,plain,
! [SV5: $i > $o,SV11: $i] :
( ( ( ~ ( reli @ SV11 @ ( sK11_SY483 @ SV5 @ SV11 ) ) )
= $false )
| ( ( SV5 @ SV11 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[77]) ).
thf(91,plain,
! [SV11: $i,SV5: $i > $o] :
( ( ( SV5 @ ( sK11_SY483 @ SV5 @ SV11 ) )
= $false )
| ( ( SV5 @ SV11 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[77]) ).
thf(92,plain,
! [SV6: $i,SV14: individuals,SV15: $i,SV12: $i] :
( ( ( ~ ( reli @ SV12 @ SV15 )
| ~ ( princ_inj @ SV14 @ SV15 )
| ( princ_inj @ loca @ SV15 ) )
= $true )
| ( ( reli @ SV6 @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(93,plain,
! [SV1: $i > $o,SV7: $i] :
( ( ( relr @ SV7 @ ( sK6_SY472 @ SV1 @ SV7 ) )
= $true )
| ( ( ! [SY473: $i] :
( ~ ( relr @ SV7 @ SY473 )
| ! [SY455: $i] :
( ~ ( relr @ SY473 @ SY455 )
| ( SV1 @ SY455 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[79]) ).
thf(94,plain,
! [SV1: $i > $o,SV16: $i,SV7: $i] :
( ( ( ~ ( relr @ SV7 @ SV16 )
| ! [SY499: $i] :
( ~ ( relr @ SV16 @ SY499 )
| ( SV1 @ SY499 ) ) )
= $true )
| ( ( SV1 @ ( sK6_SY472 @ SV1 @ SV7 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(95,plain,
! [SV2: $i > $o,SV8: $i] :
( ( ( reli @ SV8 @ ( sK7_SY475 @ SV2 @ SV8 ) )
= $true )
| ( ( ! [SY477: $i] :
( ~ ( relr @ SV8 @ SY477 )
| ! [SY460: $i] :
( ~ ( reli @ SY477 @ SY460 )
| ( SV2 @ SY460 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[81]) ).
thf(96,plain,
! [SV8: $i,SV2: $i > $o] :
( ( ( ~ ( relr @ ( sK7_SY475 @ SV2 @ SV8 ) @ ( sK12_SY494 @ SV8 @ SV2 ) )
| ( SV2 @ ( sK12_SY494 @ SV8 @ SV2 ) ) )
= $false )
| ( ( ! [SY477: $i] :
( ~ ( relr @ SV8 @ SY477 )
| ! [SY460: $i] :
( ~ ( reli @ SY477 @ SY460 )
| ( SV2 @ SY460 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[82]) ).
thf(97,plain,
! [SV3: $i > $o,SV9: $i] :
( ( ( relr @ SV9 @ ( sK8_SY479 @ SV3 @ SV9 ) )
= $true )
| ( ( SV3 @ SV9 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[83]) ).
thf(98,plain,
! [SV17: $i,SV13: $i] :
( ( ( ~ ( relr @ SV13 @ SV17 )
| ! [SY500: $i] :
( ~ ( reli @ SV17 @ SY500 )
| ~ ! [SX3: $i] :
( ~ ( reli @ SY500 @ SX3 )
| ( princ_inj @ sK1_SY163 @ SX3 ) )
| ! [SX3: $i] :
( ~ ( reli @ SY500 @ SX3 )
| ( sK2_SY406 @ SX3 ) ) ) )
= $true )
| ( ( reli @ sK4_SY431 @ SV13 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(99,plain,
( ( relr @ sK5_SX0 @ sK9_SY486 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[86]) ).
thf(100,plain,
( ( ~ ( reli @ sK9_SY486 @ sK13_SY495 )
| ~ ! [SY503: $i] :
( ~ ( reli @ sK13_SY495 @ SY503 )
| ( princ_inj @ sK1_SY163 @ SY503 ) )
| ! [SY504: $i] :
( ~ ( reli @ sK13_SY495 @ SY504 )
| ( sK2_SY406 @ SY504 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[87]) ).
thf(101,plain,
! [SV4: $i > $o,SV10: $i] :
( ( ( reli @ SV10 @ ( sK10_SY480 @ SV4 @ SV10 ) )
= $true )
| ( ( ! [SY481: $i] :
( ~ ( reli @ SV10 @ SY481 )
| ! [SY466: $i] :
( ~ ( reli @ SY481 @ SY466 )
| ( SV4 @ SY466 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[88]) ).
thf(102,plain,
! [SV4: $i > $o,SV18: $i,SV10: $i] :
( ( ( ~ ( reli @ SV10 @ SV18 )
| ! [SY505: $i] :
( ~ ( reli @ SV18 @ SY505 )
| ( SV4 @ SY505 ) ) )
= $true )
| ( ( SV4 @ ( sK10_SY480 @ SV4 @ SV10 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(103,plain,
! [SV5: $i > $o,SV11: $i] :
( ( ( reli @ SV11 @ ( sK11_SY483 @ SV5 @ SV11 ) )
= $true )
| ( ( SV5 @ SV11 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[90]) ).
thf(104,plain,
! [SV6: $i,SV14: individuals,SV15: $i,SV12: $i] :
( ( ( ~ ( reli @ SV12 @ SV15 ) )
= $true )
| ( ( ~ ( princ_inj @ SV14 @ SV15 )
| ( princ_inj @ loca @ SV15 ) )
= $true )
| ( ( reli @ SV6 @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[92]) ).
thf(105,plain,
! [SV1: $i > $o,SV19: $i,SV7: $i] :
( ( ( ~ ( relr @ SV7 @ SV19 )
| ! [SY506: $i] :
( ~ ( relr @ SV19 @ SY506 )
| ( SV1 @ SY506 ) ) )
= $true )
| ( ( relr @ SV7 @ ( sK6_SY472 @ SV1 @ SV7 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(106,plain,
! [SV1: $i > $o,SV16: $i,SV7: $i] :
( ( ( ~ ( relr @ SV7 @ SV16 ) )
= $true )
| ( ( ! [SY499: $i] :
( ~ ( relr @ SV16 @ SY499 )
| ( SV1 @ SY499 ) ) )
= $true )
| ( ( SV1 @ ( sK6_SY472 @ SV1 @ SV7 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(107,plain,
! [SV2: $i > $o,SV20: $i,SV8: $i] :
( ( ( ~ ( relr @ SV8 @ SV20 )
| ! [SY507: $i] :
( ~ ( reli @ SV20 @ SY507 )
| ( SV2 @ SY507 ) ) )
= $true )
| ( ( reli @ SV8 @ ( sK7_SY475 @ SV2 @ SV8 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(108,plain,
! [SV8: $i,SV2: $i > $o] :
( ( ( ~ ( relr @ ( sK7_SY475 @ SV2 @ SV8 ) @ ( sK12_SY494 @ SV8 @ SV2 ) ) )
= $false )
| ( ( ! [SY477: $i] :
( ~ ( relr @ SV8 @ SY477 )
| ! [SY460: $i] :
( ~ ( reli @ SY477 @ SY460 )
| ( SV2 @ SY460 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[96]) ).
thf(109,plain,
! [SV8: $i,SV2: $i > $o] :
( ( ( SV2 @ ( sK12_SY494 @ SV8 @ SV2 ) )
= $false )
| ( ( ! [SY477: $i] :
( ~ ( relr @ SV8 @ SY477 )
| ! [SY460: $i] :
( ~ ( reli @ SY477 @ SY460 )
| ( SV2 @ SY460 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[96]) ).
thf(110,plain,
! [SV17: $i,SV13: $i] :
( ( ( ~ ( relr @ SV13 @ SV17 ) )
= $true )
| ( ( ! [SY500: $i] :
( ~ ( reli @ SV17 @ SY500 )
| ~ ! [SX3: $i] :
( ~ ( reli @ SY500 @ SX3 )
| ( princ_inj @ sK1_SY163 @ SX3 ) )
| ! [SX3: $i] :
( ~ ( reli @ SY500 @ SX3 )
| ( sK2_SY406 @ SX3 ) ) ) )
= $true )
| ( ( reli @ sK4_SY431 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[98]) ).
thf(111,plain,
( ( ~ ( reli @ sK9_SY486 @ sK13_SY495 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[100]) ).
thf(112,plain,
( ( ~ ! [SY503: $i] :
( ~ ( reli @ sK13_SY495 @ SY503 )
| ( princ_inj @ sK1_SY163 @ SY503 ) )
| ! [SY504: $i] :
( ~ ( reli @ sK13_SY495 @ SY504 )
| ( sK2_SY406 @ SY504 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[100]) ).
thf(113,plain,
! [SV4: $i > $o,SV21: $i,SV10: $i] :
( ( ( ~ ( reli @ SV10 @ SV21 )
| ! [SY508: $i] :
( ~ ( reli @ SV21 @ SY508 )
| ( SV4 @ SY508 ) ) )
= $true )
| ( ( reli @ SV10 @ ( sK10_SY480 @ SV4 @ SV10 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(114,plain,
! [SV4: $i > $o,SV18: $i,SV10: $i] :
( ( ( ~ ( reli @ SV10 @ SV18 ) )
= $true )
| ( ( ! [SY505: $i] :
( ~ ( reli @ SV18 @ SY505 )
| ( SV4 @ SY505 ) ) )
= $true )
| ( ( SV4 @ ( sK10_SY480 @ SV4 @ SV10 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[102]) ).
thf(115,plain,
! [SV6: $i,SV14: individuals,SV15: $i,SV12: $i] :
( ( ( reli @ SV12 @ SV15 )
= $false )
| ( ( ~ ( princ_inj @ SV14 @ SV15 )
| ( princ_inj @ loca @ SV15 ) )
= $true )
| ( ( reli @ SV6 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[104]) ).
thf(116,plain,
! [SV1: $i > $o,SV19: $i,SV7: $i] :
( ( ( ~ ( relr @ SV7 @ SV19 ) )
= $true )
| ( ( ! [SY506: $i] :
( ~ ( relr @ SV19 @ SY506 )
| ( SV1 @ SY506 ) ) )
= $true )
| ( ( relr @ SV7 @ ( sK6_SY472 @ SV1 @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[105]) ).
thf(117,plain,
! [SV1: $i > $o,SV16: $i,SV7: $i] :
( ( ( relr @ SV7 @ SV16 )
= $false )
| ( ( ! [SY499: $i] :
( ~ ( relr @ SV16 @ SY499 )
| ( SV1 @ SY499 ) ) )
= $true )
| ( ( SV1 @ ( sK6_SY472 @ SV1 @ SV7 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(118,plain,
! [SV2: $i > $o,SV20: $i,SV8: $i] :
( ( ( ~ ( relr @ SV8 @ SV20 ) )
= $true )
| ( ( ! [SY507: $i] :
( ~ ( reli @ SV20 @ SY507 )
| ( SV2 @ SY507 ) ) )
= $true )
| ( ( reli @ SV8 @ ( sK7_SY475 @ SV2 @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[107]) ).
thf(119,plain,
! [SV8: $i,SV2: $i > $o] :
( ( ( relr @ ( sK7_SY475 @ SV2 @ SV8 ) @ ( sK12_SY494 @ SV8 @ SV2 ) )
= $true )
| ( ( ! [SY477: $i] :
( ~ ( relr @ SV8 @ SY477 )
| ! [SY460: $i] :
( ~ ( reli @ SY477 @ SY460 )
| ( SV2 @ SY460 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[108]) ).
thf(120,plain,
! [SV2: $i > $o,SV22: $i,SV8: $i] :
( ( ( ~ ( relr @ SV8 @ SV22 )
| ! [SY509: $i] :
( ~ ( reli @ SV22 @ SY509 )
| ( SV2 @ SY509 ) ) )
= $true )
| ( ( SV2 @ ( sK12_SY494 @ SV8 @ SV2 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(121,plain,
! [SV17: $i,SV13: $i] :
( ( ( relr @ SV13 @ SV17 )
= $false )
| ( ( ! [SY500: $i] :
( ~ ( reli @ SV17 @ SY500 )
| ~ ! [SX3: $i] :
( ~ ( reli @ SY500 @ SX3 )
| ( princ_inj @ sK1_SY163 @ SX3 ) )
| ! [SX3: $i] :
( ~ ( reli @ SY500 @ SX3 )
| ( sK2_SY406 @ SX3 ) ) ) )
= $true )
| ( ( reli @ sK4_SY431 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(122,plain,
( ( reli @ sK9_SY486 @ sK13_SY495 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[111]) ).
thf(123,plain,
( ( ~ ! [SY503: $i] :
( ~ ( reli @ sK13_SY495 @ SY503 )
| ( princ_inj @ sK1_SY163 @ SY503 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[112]) ).
thf(124,plain,
( ( ! [SY504: $i] :
( ~ ( reli @ sK13_SY495 @ SY504 )
| ( sK2_SY406 @ SY504 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[112]) ).
thf(125,plain,
! [SV4: $i > $o,SV21: $i,SV10: $i] :
( ( ( ~ ( reli @ SV10 @ SV21 ) )
= $true )
| ( ( ! [SY508: $i] :
( ~ ( reli @ SV21 @ SY508 )
| ( SV4 @ SY508 ) ) )
= $true )
| ( ( reli @ SV10 @ ( sK10_SY480 @ SV4 @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[113]) ).
thf(126,plain,
! [SV4: $i > $o,SV18: $i,SV10: $i] :
( ( ( reli @ SV10 @ SV18 )
= $false )
| ( ( ! [SY505: $i] :
( ~ ( reli @ SV18 @ SY505 )
| ( SV4 @ SY505 ) ) )
= $true )
| ( ( SV4 @ ( sK10_SY480 @ SV4 @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[114]) ).
thf(127,plain,
! [SV6: $i,SV12: $i,SV15: $i,SV14: individuals] :
( ( ( ~ ( princ_inj @ SV14 @ SV15 ) )
= $true )
| ( ( princ_inj @ loca @ SV15 )
= $true )
| ( ( reli @ SV12 @ SV15 )
= $false )
| ( ( reli @ SV6 @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[115]) ).
thf(128,plain,
! [SV1: $i > $o,SV19: $i,SV7: $i] :
( ( ( relr @ SV7 @ SV19 )
= $false )
| ( ( ! [SY506: $i] :
( ~ ( relr @ SV19 @ SY506 )
| ( SV1 @ SY506 ) ) )
= $true )
| ( ( relr @ SV7 @ ( sK6_SY472 @ SV1 @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(129,plain,
! [SV7: $i,SV1: $i > $o,SV23: $i,SV16: $i] :
( ( ( ~ ( relr @ SV16 @ SV23 )
| ( SV1 @ SV23 ) )
= $true )
| ( ( relr @ SV7 @ SV16 )
= $false )
| ( ( SV1 @ ( sK6_SY472 @ SV1 @ SV7 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(130,plain,
! [SV2: $i > $o,SV20: $i,SV8: $i] :
( ( ( relr @ SV8 @ SV20 )
= $false )
| ( ( ! [SY507: $i] :
( ~ ( reli @ SV20 @ SY507 )
| ( SV2 @ SY507 ) ) )
= $true )
| ( ( reli @ SV8 @ ( sK7_SY475 @ SV2 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(131,plain,
! [SV2: $i > $o,SV24: $i,SV8: $i] :
( ( ( ~ ( relr @ SV8 @ SV24 )
| ! [SY510: $i] :
( ~ ( reli @ SV24 @ SY510 )
| ( SV2 @ SY510 ) ) )
= $true )
| ( ( relr @ ( sK7_SY475 @ SV2 @ SV8 ) @ ( sK12_SY494 @ SV8 @ SV2 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(132,plain,
! [SV2: $i > $o,SV22: $i,SV8: $i] :
( ( ( ~ ( relr @ SV8 @ SV22 ) )
= $true )
| ( ( ! [SY509: $i] :
( ~ ( reli @ SV22 @ SY509 )
| ( SV2 @ SY509 ) ) )
= $true )
| ( ( SV2 @ ( sK12_SY494 @ SV8 @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[120]) ).
thf(133,plain,
! [SV13: $i,SV25: $i,SV17: $i] :
( ( ( ~ ( reli @ SV17 @ SV25 )
| ~ ! [SY511: $i] :
( ~ ( reli @ SV25 @ SY511 )
| ( princ_inj @ sK1_SY163 @ SY511 ) )
| ! [SY512: $i] :
( ~ ( reli @ SV25 @ SY512 )
| ( sK2_SY406 @ SY512 ) ) )
= $true )
| ( ( relr @ SV13 @ SV17 )
= $false )
| ( ( reli @ sK4_SY431 @ SV13 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(134,plain,
( ( ! [SY503: $i] :
( ~ ( reli @ sK13_SY495 @ SY503 )
| ( princ_inj @ sK1_SY163 @ SY503 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[123]) ).
thf(135,plain,
( ( ~ ( reli @ sK13_SY495 @ sK14_SY504 )
| ( sK2_SY406 @ sK14_SY504 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[124]) ).
thf(136,plain,
! [SV4: $i > $o,SV21: $i,SV10: $i] :
( ( ( reli @ SV10 @ SV21 )
= $false )
| ( ( ! [SY508: $i] :
( ~ ( reli @ SV21 @ SY508 )
| ( SV4 @ SY508 ) ) )
= $true )
| ( ( reli @ SV10 @ ( sK10_SY480 @ SV4 @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(137,plain,
! [SV10: $i,SV4: $i > $o,SV26: $i,SV18: $i] :
( ( ( ~ ( reli @ SV18 @ SV26 )
| ( SV4 @ SV26 ) )
= $true )
| ( ( reli @ SV10 @ SV18 )
= $false )
| ( ( SV4 @ ( sK10_SY480 @ SV4 @ SV10 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(138,plain,
! [SV6: $i,SV12: $i,SV15: $i,SV14: individuals] :
( ( ( princ_inj @ SV14 @ SV15 )
= $false )
| ( ( princ_inj @ loca @ SV15 )
= $true )
| ( ( reli @ SV12 @ SV15 )
= $false )
| ( ( reli @ SV6 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[127]) ).
thf(139,plain,
! [SV7: $i,SV1: $i > $o,SV27: $i,SV19: $i] :
( ( ( ~ ( relr @ SV19 @ SV27 )
| ( SV1 @ SV27 ) )
= $true )
| ( ( relr @ SV7 @ SV19 )
= $false )
| ( ( relr @ SV7 @ ( sK6_SY472 @ SV1 @ SV7 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(140,plain,
! [SV7: $i,SV1: $i > $o,SV23: $i,SV16: $i] :
( ( ( ~ ( relr @ SV16 @ SV23 ) )
= $true )
| ( ( SV1 @ SV23 )
= $true )
| ( ( relr @ SV7 @ SV16 )
= $false )
| ( ( SV1 @ ( sK6_SY472 @ SV1 @ SV7 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[129]) ).
thf(141,plain,
! [SV8: $i,SV2: $i > $o,SV28: $i,SV20: $i] :
( ( ( ~ ( reli @ SV20 @ SV28 )
| ( SV2 @ SV28 ) )
= $true )
| ( ( relr @ SV8 @ SV20 )
= $false )
| ( ( reli @ SV8 @ ( sK7_SY475 @ SV2 @ SV8 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(142,plain,
! [SV2: $i > $o,SV24: $i,SV8: $i] :
( ( ( ~ ( relr @ SV8 @ SV24 ) )
= $true )
| ( ( ! [SY510: $i] :
( ~ ( reli @ SV24 @ SY510 )
| ( SV2 @ SY510 ) ) )
= $true )
| ( ( relr @ ( sK7_SY475 @ SV2 @ SV8 ) @ ( sK12_SY494 @ SV8 @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[131]) ).
thf(143,plain,
! [SV2: $i > $o,SV22: $i,SV8: $i] :
( ( ( relr @ SV8 @ SV22 )
= $false )
| ( ( ! [SY509: $i] :
( ~ ( reli @ SV22 @ SY509 )
| ( SV2 @ SY509 ) ) )
= $true )
| ( ( SV2 @ ( sK12_SY494 @ SV8 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(144,plain,
! [SV13: $i,SV25: $i,SV17: $i] :
( ( ( ~ ( reli @ SV17 @ SV25 ) )
= $true )
| ( ( ~ ! [SY511: $i] :
( ~ ( reli @ SV25 @ SY511 )
| ( princ_inj @ sK1_SY163 @ SY511 ) )
| ! [SY512: $i] :
( ~ ( reli @ SV25 @ SY512 )
| ( sK2_SY406 @ SY512 ) ) )
= $true )
| ( ( relr @ SV13 @ SV17 )
= $false )
| ( ( reli @ sK4_SY431 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[133]) ).
thf(145,plain,
! [SV29: $i] :
( ( ~ ( reli @ sK13_SY495 @ SV29 )
| ( princ_inj @ sK1_SY163 @ SV29 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(146,plain,
( ( ~ ( reli @ sK13_SY495 @ sK14_SY504 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[135]) ).
thf(147,plain,
( ( sK2_SY406 @ sK14_SY504 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[135]) ).
thf(148,plain,
! [SV10: $i,SV4: $i > $o,SV30: $i,SV21: $i] :
( ( ( ~ ( reli @ SV21 @ SV30 )
| ( SV4 @ SV30 ) )
= $true )
| ( ( reli @ SV10 @ SV21 )
= $false )
| ( ( reli @ SV10 @ ( sK10_SY480 @ SV4 @ SV10 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(149,plain,
! [SV10: $i,SV4: $i > $o,SV26: $i,SV18: $i] :
( ( ( ~ ( reli @ SV18 @ SV26 ) )
= $true )
| ( ( SV4 @ SV26 )
= $true )
| ( ( reli @ SV10 @ SV18 )
= $false )
| ( ( SV4 @ ( sK10_SY480 @ SV4 @ SV10 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[137]) ).
thf(150,plain,
! [SV7: $i,SV1: $i > $o,SV27: $i,SV19: $i] :
( ( ( ~ ( relr @ SV19 @ SV27 ) )
= $true )
| ( ( SV1 @ SV27 )
= $true )
| ( ( relr @ SV7 @ SV19 )
= $false )
| ( ( relr @ SV7 @ ( sK6_SY472 @ SV1 @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[139]) ).
thf(151,plain,
! [SV7: $i,SV1: $i > $o,SV23: $i,SV16: $i] :
( ( ( relr @ SV16 @ SV23 )
= $false )
| ( ( SV1 @ SV23 )
= $true )
| ( ( relr @ SV7 @ SV16 )
= $false )
| ( ( SV1 @ ( sK6_SY472 @ SV1 @ SV7 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(152,plain,
! [SV8: $i,SV2: $i > $o,SV28: $i,SV20: $i] :
( ( ( ~ ( reli @ SV20 @ SV28 ) )
= $true )
| ( ( SV2 @ SV28 )
= $true )
| ( ( relr @ SV8 @ SV20 )
= $false )
| ( ( reli @ SV8 @ ( sK7_SY475 @ SV2 @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[141]) ).
thf(153,plain,
! [SV2: $i > $o,SV24: $i,SV8: $i] :
( ( ( relr @ SV8 @ SV24 )
= $false )
| ( ( ! [SY510: $i] :
( ~ ( reli @ SV24 @ SY510 )
| ( SV2 @ SY510 ) ) )
= $true )
| ( ( relr @ ( sK7_SY475 @ SV2 @ SV8 ) @ ( sK12_SY494 @ SV8 @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(154,plain,
! [SV8: $i,SV2: $i > $o,SV31: $i,SV22: $i] :
( ( ( ~ ( reli @ SV22 @ SV31 )
| ( SV2 @ SV31 ) )
= $true )
| ( ( relr @ SV8 @ SV22 )
= $false )
| ( ( SV2 @ ( sK12_SY494 @ SV8 @ SV2 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(155,plain,
! [SV13: $i,SV25: $i,SV17: $i] :
( ( ( reli @ SV17 @ SV25 )
= $false )
| ( ( ~ ! [SY511: $i] :
( ~ ( reli @ SV25 @ SY511 )
| ( princ_inj @ sK1_SY163 @ SY511 ) )
| ! [SY512: $i] :
( ~ ( reli @ SV25 @ SY512 )
| ( sK2_SY406 @ SY512 ) ) )
= $true )
| ( ( relr @ SV13 @ SV17 )
= $false )
| ( ( reli @ sK4_SY431 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(156,plain,
! [SV29: $i] :
( ( ( ~ ( reli @ sK13_SY495 @ SV29 ) )
= $true )
| ( ( princ_inj @ sK1_SY163 @ SV29 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[145]) ).
thf(157,plain,
( ( reli @ sK13_SY495 @ sK14_SY504 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[146]) ).
thf(158,plain,
! [SV10: $i,SV4: $i > $o,SV30: $i,SV21: $i] :
( ( ( ~ ( reli @ SV21 @ SV30 ) )
= $true )
| ( ( SV4 @ SV30 )
= $true )
| ( ( reli @ SV10 @ SV21 )
= $false )
| ( ( reli @ SV10 @ ( sK10_SY480 @ SV4 @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[148]) ).
thf(159,plain,
! [SV10: $i,SV4: $i > $o,SV26: $i,SV18: $i] :
( ( ( reli @ SV18 @ SV26 )
= $false )
| ( ( SV4 @ SV26 )
= $true )
| ( ( reli @ SV10 @ SV18 )
= $false )
| ( ( SV4 @ ( sK10_SY480 @ SV4 @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(160,plain,
! [SV7: $i,SV1: $i > $o,SV27: $i,SV19: $i] :
( ( ( relr @ SV19 @ SV27 )
= $false )
| ( ( SV1 @ SV27 )
= $true )
| ( ( relr @ SV7 @ SV19 )
= $false )
| ( ( relr @ SV7 @ ( sK6_SY472 @ SV1 @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[150]) ).
thf(161,plain,
! [SV8: $i,SV2: $i > $o,SV28: $i,SV20: $i] :
( ( ( reli @ SV20 @ SV28 )
= $false )
| ( ( SV2 @ SV28 )
= $true )
| ( ( relr @ SV8 @ SV20 )
= $false )
| ( ( reli @ SV8 @ ( sK7_SY475 @ SV2 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(162,plain,
! [SV8: $i,SV2: $i > $o,SV32: $i,SV24: $i] :
( ( ( ~ ( reli @ SV24 @ SV32 )
| ( SV2 @ SV32 ) )
= $true )
| ( ( relr @ SV8 @ SV24 )
= $false )
| ( ( relr @ ( sK7_SY475 @ SV2 @ SV8 ) @ ( sK12_SY494 @ SV8 @ SV2 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(163,plain,
! [SV8: $i,SV2: $i > $o,SV31: $i,SV22: $i] :
( ( ( ~ ( reli @ SV22 @ SV31 ) )
= $true )
| ( ( SV2 @ SV31 )
= $true )
| ( ( relr @ SV8 @ SV22 )
= $false )
| ( ( SV2 @ ( sK12_SY494 @ SV8 @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[154]) ).
thf(164,plain,
! [SV13: $i,SV17: $i,SV25: $i] :
( ( ( ~ ! [SY511: $i] :
( ~ ( reli @ SV25 @ SY511 )
| ( princ_inj @ sK1_SY163 @ SY511 ) ) )
= $true )
| ( ( ! [SY512: $i] :
( ~ ( reli @ SV25 @ SY512 )
| ( sK2_SY406 @ SY512 ) ) )
= $true )
| ( ( reli @ SV17 @ SV25 )
= $false )
| ( ( relr @ SV13 @ SV17 )
= $false )
| ( ( reli @ sK4_SY431 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[155]) ).
thf(165,plain,
! [SV29: $i] :
( ( ( reli @ sK13_SY495 @ SV29 )
= $false )
| ( ( princ_inj @ sK1_SY163 @ SV29 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(166,plain,
! [SV10: $i,SV4: $i > $o,SV30: $i,SV21: $i] :
( ( ( reli @ SV21 @ SV30 )
= $false )
| ( ( SV4 @ SV30 )
= $true )
| ( ( reli @ SV10 @ SV21 )
= $false )
| ( ( reli @ SV10 @ ( sK10_SY480 @ SV4 @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[158]) ).
thf(167,plain,
! [SV8: $i,SV2: $i > $o,SV32: $i,SV24: $i] :
( ( ( ~ ( reli @ SV24 @ SV32 ) )
= $true )
| ( ( SV2 @ SV32 )
= $true )
| ( ( relr @ SV8 @ SV24 )
= $false )
| ( ( relr @ ( sK7_SY475 @ SV2 @ SV8 ) @ ( sK12_SY494 @ SV8 @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[162]) ).
thf(168,plain,
! [SV8: $i,SV2: $i > $o,SV31: $i,SV22: $i] :
( ( ( reli @ SV22 @ SV31 )
= $false )
| ( ( SV2 @ SV31 )
= $true )
| ( ( relr @ SV8 @ SV22 )
= $false )
| ( ( SV2 @ ( sK12_SY494 @ SV8 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[163]) ).
thf(169,plain,
! [SV13: $i,SV17: $i,SV25: $i] :
( ( ( ! [SY511: $i] :
( ~ ( reli @ SV25 @ SY511 )
| ( princ_inj @ sK1_SY163 @ SY511 ) ) )
= $false )
| ( ( ! [SY512: $i] :
( ~ ( reli @ SV25 @ SY512 )
| ( sK2_SY406 @ SY512 ) ) )
= $true )
| ( ( reli @ SV17 @ SV25 )
= $false )
| ( ( relr @ SV13 @ SV17 )
= $false )
| ( ( reli @ sK4_SY431 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(170,plain,
! [SV8: $i,SV2: $i > $o,SV32: $i,SV24: $i] :
( ( ( reli @ SV24 @ SV32 )
= $false )
| ( ( SV2 @ SV32 )
= $true )
| ( ( relr @ SV8 @ SV24 )
= $false )
| ( ( relr @ ( sK7_SY475 @ SV2 @ SV8 ) @ ( sK12_SY494 @ SV8 @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(171,plain,
! [SV17: $i,SV13: $i,SV25: $i] :
( ( ( ~ ( reli @ SV25 @ ( sK15_SY511 @ SV13 @ SV17 @ SV25 ) )
| ( princ_inj @ sK1_SY163 @ ( sK15_SY511 @ SV13 @ SV17 @ SV25 ) ) )
= $false )
| ( ( ! [SY512: $i] :
( ~ ( reli @ SV25 @ SY512 )
| ( sK2_SY406 @ SY512 ) ) )
= $true )
| ( ( reli @ SV17 @ SV25 )
= $false )
| ( ( relr @ SV13 @ SV17 )
= $false )
| ( ( reli @ sK4_SY431 @ SV13 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[169]) ).
thf(172,plain,
! [SV17: $i,SV13: $i,SV25: $i] :
( ( ( ~ ( reli @ SV25 @ ( sK15_SY511 @ SV13 @ SV17 @ SV25 ) ) )
= $false )
| ( ( ! [SY512: $i] :
( ~ ( reli @ SV25 @ SY512 )
| ( sK2_SY406 @ SY512 ) ) )
= $true )
| ( ( reli @ SV17 @ SV25 )
= $false )
| ( ( relr @ SV13 @ SV17 )
= $false )
| ( ( reli @ sK4_SY431 @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[171]) ).
thf(173,plain,
! [SV25: $i,SV17: $i,SV13: $i] :
( ( ( princ_inj @ sK1_SY163 @ ( sK15_SY511 @ SV13 @ SV17 @ SV25 ) )
= $false )
| ( ( ! [SY512: $i] :
( ~ ( reli @ SV25 @ SY512 )
| ( sK2_SY406 @ SY512 ) ) )
= $true )
| ( ( reli @ SV17 @ SV25 )
= $false )
| ( ( relr @ SV13 @ SV17 )
= $false )
| ( ( reli @ sK4_SY431 @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[171]) ).
thf(174,plain,
! [SV17: $i,SV13: $i,SV25: $i] :
( ( ( reli @ SV25 @ ( sK15_SY511 @ SV13 @ SV17 @ SV25 ) )
= $true )
| ( ( ! [SY512: $i] :
( ~ ( reli @ SV25 @ SY512 )
| ( sK2_SY406 @ SY512 ) ) )
= $true )
| ( ( reli @ SV17 @ SV25 )
= $false )
| ( ( relr @ SV13 @ SV17 )
= $false )
| ( ( reli @ sK4_SY431 @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[172]) ).
thf(175,plain,
! [SV17: $i,SV13: $i,SV33: $i,SV25: $i] :
( ( ( ~ ( reli @ SV25 @ SV33 )
| ( sK2_SY406 @ SV33 ) )
= $true )
| ( ( princ_inj @ sK1_SY163 @ ( sK15_SY511 @ SV13 @ SV17 @ SV25 ) )
= $false )
| ( ( reli @ SV17 @ SV25 )
= $false )
| ( ( relr @ SV13 @ SV17 )
= $false )
| ( ( reli @ sK4_SY431 @ SV13 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(176,plain,
! [SV17: $i,SV13: $i,SV34: $i,SV25: $i] :
( ( ( ~ ( reli @ SV25 @ SV34 )
| ( sK2_SY406 @ SV34 ) )
= $true )
| ( ( reli @ SV25 @ ( sK15_SY511 @ SV13 @ SV17 @ SV25 ) )
= $true )
| ( ( reli @ SV17 @ SV25 )
= $false )
| ( ( relr @ SV13 @ SV17 )
= $false )
| ( ( reli @ sK4_SY431 @ SV13 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(177,plain,
! [SV17: $i,SV13: $i,SV33: $i,SV25: $i] :
( ( ( ~ ( reli @ SV25 @ SV33 ) )
= $true )
| ( ( sK2_SY406 @ SV33 )
= $true )
| ( ( princ_inj @ sK1_SY163 @ ( sK15_SY511 @ SV13 @ SV17 @ SV25 ) )
= $false )
| ( ( reli @ SV17 @ SV25 )
= $false )
| ( ( relr @ SV13 @ SV17 )
= $false )
| ( ( reli @ sK4_SY431 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[175]) ).
thf(178,plain,
! [SV17: $i,SV13: $i,SV34: $i,SV25: $i] :
( ( ( ~ ( reli @ SV25 @ SV34 ) )
= $true )
| ( ( sK2_SY406 @ SV34 )
= $true )
| ( ( reli @ SV25 @ ( sK15_SY511 @ SV13 @ SV17 @ SV25 ) )
= $true )
| ( ( reli @ SV17 @ SV25 )
= $false )
| ( ( relr @ SV13 @ SV17 )
= $false )
| ( ( reli @ sK4_SY431 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[176]) ).
thf(179,plain,
! [SV17: $i,SV13: $i,SV33: $i,SV25: $i] :
( ( ( reli @ SV25 @ SV33 )
= $false )
| ( ( sK2_SY406 @ SV33 )
= $true )
| ( ( princ_inj @ sK1_SY163 @ ( sK15_SY511 @ SV13 @ SV17 @ SV25 ) )
= $false )
| ( ( reli @ SV17 @ SV25 )
= $false )
| ( ( relr @ SV13 @ SV17 )
= $false )
| ( ( reli @ sK4_SY431 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(180,plain,
! [SV17: $i,SV13: $i,SV34: $i,SV25: $i] :
( ( ( reli @ SV25 @ SV34 )
= $false )
| ( ( sK2_SY406 @ SV34 )
= $true )
| ( ( reli @ SV25 @ ( sK15_SY511 @ SV13 @ SV17 @ SV25 ) )
= $true )
| ( ( reli @ SV17 @ SV25 )
= $false )
| ( ( relr @ SV13 @ SV17 )
= $false )
| ( ( reli @ sK4_SY431 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(181,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[29,180,179,170,168,166,165,161,160,159,157,151,147,138,122,103,99,97,91,84,74]) ).
thf(182,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[181]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV443^1 : 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
% 0.09/0.17 % Computer : n010.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Oct 6 16:30:25 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 56.64/11.50
% 56.64/11.50 No.of.Axioms: 6
% 56.64/11.50
% 56.64/11.50 Length.of.Defs: 4892
% 56.64/11.50
% 56.64/11.50 Contains.Choice.Funs: false
% 56.64/11.50 ..........
% 56.64/11.50
% 56.64/11.50 ********************************
% 56.64/11.50 * All subproblems solved! *
% 56.64/11.50 ********************************
% 56.64/11.50 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:7,ps:0,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:181,loop_count:0,foatp_calls:1,translation:fof_full)
% 56.64/11.50
% 56.64/11.50 %**** Beginning of derivation protocol ****
% 56.64/11.50 % SZS output start CNFRefutation
% See solution above
% 56.64/11.50
% 56.64/11.50 %**** End of derivation protocol ****
% 56.64/11.50 %**** no. of clauses in derivation: 182 ****
% 56.64/11.50 %**** clause counter: 181 ****
% 56.64/11.50
% 56.64/11.50 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:7,ps:0,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:181,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------