%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYO932^9 : 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 : n001.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 11:09:22 AM UTC 2026
% Result : Theorem 0.57s 0.28s
% Output : CNFRefutation 0.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 30
% Syntax : Number of formulae : 178 ( 84 unt; 0 typ; 24 def)
% Number of atoms : 1180 ( 325 equ; 0 cnn)
% Maximal formula atoms : 10 ( 6 avg)
% Number of connectives : 2107 ( 279 ~; 394 |; 2 &;1347 @)
% ( 0 <=>; 85 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 146 ( 146 >; 0 *; 0 +; 0 <<)
% Number of symbols : 47 ( 44 usr; 10 con; 0-3 aty)
% Number of variables : 654 ( 42 ^; 608 !; 4 ?; 654 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_individuals,type,
individuals: $tType ).
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_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_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_SY374,type,
sK10_SY374: ( $i > $o ) > $i > $i ).
thf(tp_sK11_SY385,type,
sK11_SY385: $i ).
thf(tp_sK12_SY388,type,
sK12_SY388: $i > ( $i > $o ) > $i ).
thf(tp_sK13_SY389,type,
sK13_SY389: $i ).
thf(tp_sK14_SY396,type,
sK14_SY396: $i ).
thf(tp_sK1_SY0,type,
sK1_SY0: individuals > $i > $o ).
thf(tp_sK2_SY315,type,
sK2_SY315: $i ).
thf(tp_sK3_SY327,type,
sK3_SY327: $i ).
thf(tp_sK4_SX0,type,
sK4_SX0: $i ).
thf(tp_sK5_SY365,type,
sK5_SY365: ( $i > $o ) > $i > $i ).
thf(tp_sK6_SY377,type,
sK6_SY377: individuals ).
thf(tp_sK7_SY366,type,
sK7_SY366: ( $i > $o ) > $i > $i ).
thf(tp_sK8_SY367,type,
sK8_SY367: ( $i > $o ) > $i > $i ).
thf(tp_sK9_SY371,type,
sK9_SY371: ( $i > $o ) > $i > $i ).
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,
! [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(2,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(3,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(4,axiom,
! [A: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ relr @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',refl_axiom_r) ).
thf(5,axiom,
! [A: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ reli @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',refl_axiom_i) ).
thf(6,conjecture,
! [A: individuals > $i > $o] :
( cs4_valid
@ ( cs4_impl
@ ( cs4_box
@ ( cs4_all
@ ^ [I: individuals] : ( cs4_atom @ ( A @ I ) ) ) )
@ ( cs4_all
@ ^ [I: individuals] : ( cs4_box @ ( cs4_atom @ ( A @ I ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cs4_cbarcan) ).
thf(7,negated_conjecture,
( ( ! [A: individuals > $i > $o] :
( cs4_valid
@ ( cs4_impl
@ ( cs4_box
@ ( cs4_all
@ ^ [I: individuals] : ( cs4_atom @ ( A @ I ) ) ) )
@ ( cs4_all
@ ^ [I: individuals] : ( cs4_box @ ( cs4_atom @ ( A @ I ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[6]) ).
thf(8,plain,
( ( ! [SY0: individuals > $i > $o,SY122: $i,SY123: $i] :
( ( reli @ SY122 @ SY123 )
=> ( ~ ! [SY68: $i] :
( ( reli @ SY123 @ SY68 )
=> ! [SY32: $i] :
( ( relr @ SY68 @ SY32 )
=> ! [SY27: $i] :
( ( reli @ SY32 @ SY27 )
=> ! [SY17: individuals,SY18: $i] :
( ( reli @ SY27 @ SY18 )
=> ( SY0 @ SY17 @ SY18 ) ) ) ) )
| ! [SY117: $i] :
( ( reli @ SY123 @ SY117 )
=> ! [SY106: individuals,SY107: $i] :
( ( reli @ SY117 @ SY107 )
=> ! [SY99: $i] :
( ( relr @ SY107 @ SY99 )
=> ! [SY100: $i] :
( ( reli @ SY99 @ SY100 )
=> ( SY0 @ SY106 @ SY100 ) ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[7,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(9,plain,
( ( ! [SY147: $i > $o,SY186: $i] :
( ~ ! [SY187: $i] :
( ( reli @ SY186 @ SY187 )
=> ! [SY158: $i] :
( ( relr @ SY187 @ SY158 )
=> ( SY147 @ SY158 ) ) )
| ! [SY189: $i] :
( ( relr @ SY186 @ SY189 )
=> ! [SY180: $i] :
( ( reli @ SY189 @ SY180 )
=> ( SY147 @ SY180 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1,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,
( ( ! [SY197: $i > $o,SY226: $i] :
( ~ ! [SY227: $i] :
( ( relr @ SY226 @ SY227 )
=> ( SY197 @ SY227 ) )
| ! [SY228: $i] :
( ( relr @ SY226 @ SY228 )
=> ! [SY221: $i] :
( ( relr @ SY228 @ SY221 )
=> ( SY197 @ SY221 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2,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,
( ( ! [SY235: $i > $o,SY264: $i] :
( ~ ! [SY265: $i] :
( ( reli @ SY264 @ SY265 )
=> ( SY235 @ SY265 ) )
| ! [SY266: $i] :
( ( reli @ SY264 @ SY266 )
=> ! [SY259: $i] :
( ( reli @ SY266 @ SY259 )
=> ( SY235 @ SY259 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3,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,
( ( ! [SY273: $i > $o,SY289: $i] :
( ~ ! [SY290: $i] :
( ( relr @ SY289 @ SY290 )
=> ( SY273 @ SY290 ) )
| ( SY273 @ SY289 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4,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,
( ( ! [SY294: $i > $o,SY310: $i] :
( ~ ! [SY311: $i] :
( ( reli @ SY310 @ SY311 )
=> ( SY294 @ SY311 ) )
| ( SY294 @ SY310 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5,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,
( ( ! [SY315: $i,SY316: $i] :
( ( reli @ SY315 @ SY316 )
=> ( ~ ! [SY317: $i] :
( ( reli @ SY316 @ SY317 )
=> ! [SY318: $i] :
( ( relr @ SY317 @ SY318 )
=> ! [SY319: $i] :
( ( reli @ SY318 @ SY319 )
=> ! [SY320: individuals,SY321: $i] :
( ( reli @ SY319 @ SY321 )
=> ( sK1_SY0 @ SY320 @ SY321 ) ) ) ) )
| ! [SY322: $i] :
( ( reli @ SY316 @ SY322 )
=> ! [SY323: individuals,SY324: $i] :
( ( reli @ SY322 @ SY324 )
=> ! [SY325: $i] :
( ( relr @ SY324 @ SY325 )
=> ! [SY326: $i] :
( ( reli @ SY325 @ SY326 )
=> ( sK1_SY0 @ SY323 @ SY326 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[8]) ).
thf(15,plain,
( ( ! [SY327: $i] :
( ( reli @ sK2_SY315 @ SY327 )
=> ( ~ ! [SY317: $i] :
( ( reli @ SY327 @ SY317 )
=> ! [SY318: $i] :
( ( relr @ SY317 @ SY318 )
=> ! [SY319: $i] :
( ( reli @ SY318 @ SY319 )
=> ! [SY320: individuals,SY321: $i] :
( ( reli @ SY319 @ SY321 )
=> ( sK1_SY0 @ SY320 @ SY321 ) ) ) ) )
| ! [SY322: $i] :
( ( reli @ SY327 @ SY322 )
=> ! [SY323: individuals,SY324: $i] :
( ( reli @ SY322 @ SY324 )
=> ! [SY325: $i] :
( ( relr @ SY324 @ SY325 )
=> ! [SY326: $i] :
( ( reli @ SY325 @ SY326 )
=> ( sK1_SY0 @ SY323 @ SY326 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[14]) ).
thf(16,plain,
( ( ( reli @ sK2_SY315 @ sK3_SY327 )
=> ( ~ ! [SY338: $i] :
( ( reli @ sK3_SY327 @ SY338 )
=> ! [SY318: $i] :
( ( relr @ SY338 @ SY318 )
=> ! [SY319: $i] :
( ( reli @ SY318 @ SY319 )
=> ! [SY320: individuals,SY321: $i] :
( ( reli @ SY319 @ SY321 )
=> ( sK1_SY0 @ SY320 @ SY321 ) ) ) ) )
| ! [SY343: $i] :
( ( reli @ sK3_SY327 @ SY343 )
=> ! [SY323: individuals,SY324: $i] :
( ( reli @ SY343 @ SY324 )
=> ! [SY325: $i] :
( ( relr @ SY324 @ SY325 )
=> ! [SY326: $i] :
( ( reli @ SY325 @ SY326 )
=> ( sK1_SY0 @ SY323 @ SY326 ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[15]) ).
thf(17,plain,
( ( reli @ sK2_SY315 @ sK3_SY327 )
= $true ),
inference(standard_cnf,[status(thm)],[16]) ).
thf(18,plain,
( ( ~ ! [SY338: $i] :
( ( reli @ sK3_SY327 @ SY338 )
=> ! [SY318: $i] :
( ( relr @ SY338 @ SY318 )
=> ! [SY319: $i] :
( ( reli @ SY318 @ SY319 )
=> ! [SY320: individuals,SY321: $i] :
( ( reli @ SY319 @ SY321 )
=> ( sK1_SY0 @ SY320 @ SY321 ) ) ) ) )
| ! [SY343: $i] :
( ( reli @ sK3_SY327 @ SY343 )
=> ! [SY323: individuals,SY324: $i] :
( ( reli @ SY343 @ SY324 )
=> ! [SY325: $i] :
( ( relr @ SY324 @ SY325 )
=> ! [SY326: $i] :
( ( reli @ SY325 @ SY326 )
=> ( sK1_SY0 @ SY323 @ SY326 ) ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[16]) ).
thf(19,plain,
( ( ~ ( ~ ! [SY338: $i] :
( ( reli @ sK3_SY327 @ SY338 )
=> ! [SY318: $i] :
( ( relr @ SY338 @ SY318 )
=> ! [SY319: $i] :
( ( reli @ SY318 @ SY319 )
=> ! [SY320: individuals,SY321: $i] :
( ( reli @ SY319 @ SY321 )
=> ( sK1_SY0 @ SY320 @ SY321 ) ) ) ) )
| ! [SY343: $i] :
( ( reli @ sK3_SY327 @ SY343 )
=> ! [SY323: individuals,SY324: $i] :
( ( reli @ SY343 @ SY324 )
=> ! [SY325: $i] :
( ( relr @ SY324 @ SY325 )
=> ! [SY326: $i] :
( ( reli @ SY325 @ SY326 )
=> ( sK1_SY0 @ SY323 @ SY326 ) ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[18]) ).
thf(20,plain,
( ( ! [SY294: $i > $o,SY310: $i] :
( ~ ! [SY311: $i] :
( ( reli @ SY310 @ SY311 )
=> ( SY294 @ SY311 ) )
| ( SY294 @ SY310 ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(21,plain,
( ( ! [SY273: $i > $o,SY289: $i] :
( ~ ! [SY290: $i] :
( ( relr @ SY289 @ SY290 )
=> ( SY273 @ SY290 ) )
| ( SY273 @ SY289 ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(22,plain,
( ( ! [SY235: $i > $o,SY264: $i] :
( ~ ! [SY265: $i] :
( ( reli @ SY264 @ SY265 )
=> ( SY235 @ SY265 ) )
| ! [SY266: $i] :
( ( reli @ SY264 @ SY266 )
=> ! [SY259: $i] :
( ( reli @ SY266 @ SY259 )
=> ( SY235 @ SY259 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(23,plain,
( ( ! [SY197: $i > $o,SY226: $i] :
( ~ ! [SY227: $i] :
( ( relr @ SY226 @ SY227 )
=> ( SY197 @ SY227 ) )
| ! [SY228: $i] :
( ( relr @ SY226 @ SY228 )
=> ! [SY221: $i] :
( ( relr @ SY228 @ SY221 )
=> ( SY197 @ SY221 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(24,plain,
( ( ! [SY147: $i > $o,SY186: $i] :
( ~ ! [SY187: $i] :
( ( reli @ SY186 @ SY187 )
=> ! [SY158: $i] :
( ( relr @ SY187 @ SY158 )
=> ( SY147 @ SY158 ) ) )
| ! [SY189: $i] :
( ( relr @ SY186 @ SY189 )
=> ! [SY180: $i] :
( ( reli @ SY189 @ SY180 )
=> ( SY147 @ SY180 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(25,plain,
( ( reli @ sK2_SY315 @ sK3_SY327 )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(26,plain,
( ( ~ ( ~ ! [SY338: $i] :
( ( reli @ sK3_SY327 @ SY338 )
=> ! [SY318: $i] :
( ( relr @ SY338 @ SY318 )
=> ! [SY319: $i] :
( ( reli @ SY318 @ SY319 )
=> ! [SY320: individuals,SY321: $i] :
( ( reli @ SY319 @ SY321 )
=> ( sK1_SY0 @ SY320 @ SY321 ) ) ) ) )
| ! [SY343: $i] :
( ( reli @ sK3_SY327 @ SY343 )
=> ! [SY323: individuals,SY324: $i] :
( ( reli @ SY343 @ SY324 )
=> ! [SY325: $i] :
( ( relr @ SY324 @ SY325 )
=> ! [SY326: $i] :
( ( reli @ SY325 @ SY326 )
=> ( sK1_SY0 @ SY323 @ SY326 ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(27,plain,
( ( ! [SX0: $i > $o,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( reli @ SX1 @ SX2 )
| ( SX0 @ SX2 ) )
| ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20,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(28,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( reli @ sK3_SY327 @ SX0 )
| ! [SX1: $i] :
( ~ ( relr @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( reli @ SX1 @ SX2 )
| ! [SX3: individuals,SX4: $i] :
( ~ ( reli @ SX2 @ SX4 )
| ( sK1_SY0 @ SX3 @ SX4 ) ) ) ) )
| ! [SX0: $i] :
( ~ ( reli @ sK3_SY327 @ SX0 )
| ! [SX1: individuals,SX2: $i] :
( ~ ( reli @ SX0 @ SX2 )
| ! [SX3: $i] :
( ~ ( relr @ SX2 @ SX3 )
| ! [SX4: $i] :
( ~ ( reli @ SX3 @ SX4 )
| ( sK1_SY0 @ SX1 @ SX4 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26,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(29,plain,
( ( ! [SX0: $i > $o,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( relr @ SX1 @ SX2 )
| ( SX0 @ SX2 ) )
| ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21,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(30,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)],[24,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(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)],[23,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 )
| ( SX0 @ SX2 ) )
| ! [SX2: $i] :
( ~ ( reli @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( reli @ SX2 @ SX3 )
| ( SX0 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22,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,
! [SV1: $i > $o] :
( ( ! [SY348: $i] :
( ~ ! [SY349: $i] :
( ~ ( reli @ SY348 @ SY349 )
| ( SV1 @ SY349 ) )
| ( SV1 @ SY348 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(34,plain,
( ( ~ ! [SX0: $i] :
( ~ ( reli @ sK3_SY327 @ SX0 )
| ! [SX1: $i] :
( ~ ( relr @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( reli @ SX1 @ SX2 )
| ! [SX3: individuals,SX4: $i] :
( ~ ( reli @ SX2 @ SX4 )
| ( sK1_SY0 @ SX3 @ SX4 ) ) ) ) )
| ! [SX0: $i] :
( ~ ( reli @ sK3_SY327 @ SX0 )
| ! [SX1: individuals,SX2: $i] :
( ~ ( reli @ SX0 @ SX2 )
| ! [SX3: $i] :
( ~ ( relr @ SX2 @ SX3 )
| ! [SX4: $i] :
( ~ ( reli @ SX3 @ SX4 )
| ( sK1_SY0 @ SX1 @ SX4 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(35,plain,
! [SV2: $i > $o] :
( ( ! [SY350: $i] :
( ~ ! [SY351: $i] :
( ~ ( relr @ SY350 @ SY351 )
| ( SV2 @ SY351 ) )
| ( SV2 @ SY350 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(36,plain,
! [SV3: $i > $o] :
( ( ! [SY352: $i] :
( ~ ! [SY353: $i] :
( ~ ( reli @ SY352 @ SY353 )
| ! [SY354: $i] :
( ~ ( relr @ SY353 @ SY354 )
| ( SV3 @ SY354 ) ) )
| ! [SY355: $i] :
( ~ ( relr @ SY352 @ SY355 )
| ! [SY356: $i] :
( ~ ( reli @ SY355 @ SY356 )
| ( SV3 @ SY356 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(37,plain,
! [SV4: $i > $o] :
( ( ! [SY357: $i] :
( ~ ! [SY358: $i] :
( ~ ( relr @ SY357 @ SY358 )
| ( SV4 @ SY358 ) )
| ! [SY359: $i] :
( ~ ( relr @ SY357 @ SY359 )
| ! [SY360: $i] :
( ~ ( relr @ SY359 @ SY360 )
| ( SV4 @ SY360 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(38,plain,
! [SV5: $i > $o] :
( ( ! [SY361: $i] :
( ~ ! [SY362: $i] :
( ~ ( reli @ SY361 @ SY362 )
| ( SV5 @ SY362 ) )
| ! [SY363: $i] :
( ~ ( reli @ SY361 @ SY363 )
| ! [SY364: $i] :
( ~ ( reli @ SY363 @ SY364 )
| ( SV5 @ SY364 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(39,plain,
! [SV1: $i > $o,SV6: $i] :
( ( ~ ! [SY365: $i] :
( ~ ( reli @ SV6 @ SY365 )
| ( SV1 @ SY365 ) )
| ( SV1 @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(40,plain,
( ( ~ ! [SX0: $i] :
( ~ ( reli @ sK3_SY327 @ SX0 )
| ! [SX1: $i] :
( ~ ( relr @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( reli @ SX1 @ SX2 )
| ! [SX3: individuals,SX4: $i] :
( ~ ( reli @ SX2 @ SX4 )
| ( sK1_SY0 @ SX3 @ SX4 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[34]) ).
thf(41,plain,
( ( ! [SX0: $i] :
( ~ ( reli @ sK3_SY327 @ SX0 )
| ! [SX1: individuals,SX2: $i] :
( ~ ( reli @ SX0 @ SX2 )
| ! [SX3: $i] :
( ~ ( relr @ SX2 @ SX3 )
| ! [SX4: $i] :
( ~ ( reli @ SX3 @ SX4 )
| ( sK1_SY0 @ SX1 @ SX4 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[34]) ).
thf(42,plain,
! [SV2: $i > $o,SV7: $i] :
( ( ~ ! [SY366: $i] :
( ~ ( relr @ SV7 @ SY366 )
| ( SV2 @ SY366 ) )
| ( SV2 @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(43,plain,
! [SV3: $i > $o,SV8: $i] :
( ( ~ ! [SY367: $i] :
( ~ ( reli @ SV8 @ SY367 )
| ! [SY354: $i] :
( ~ ( relr @ SY367 @ SY354 )
| ( SV3 @ SY354 ) ) )
| ! [SY369: $i] :
( ~ ( relr @ SV8 @ SY369 )
| ! [SY356: $i] :
( ~ ( reli @ SY369 @ SY356 )
| ( SV3 @ SY356 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(44,plain,
! [SV4: $i > $o,SV9: $i] :
( ( ~ ! [SY371: $i] :
( ~ ( relr @ SV9 @ SY371 )
| ( SV4 @ SY371 ) )
| ! [SY372: $i] :
( ~ ( relr @ SV9 @ SY372 )
| ! [SY360: $i] :
( ~ ( relr @ SY372 @ SY360 )
| ( SV4 @ SY360 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(45,plain,
! [SV5: $i > $o,SV10: $i] :
( ( ~ ! [SY374: $i] :
( ~ ( reli @ SV10 @ SY374 )
| ( SV5 @ SY374 ) )
| ! [SY375: $i] :
( ~ ( reli @ SV10 @ SY375 )
| ! [SY364: $i] :
( ~ ( reli @ SY375 @ SY364 )
| ( SV5 @ SY364 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(46,plain,
! [SV1: $i > $o,SV6: $i] :
( ( ( ~ ! [SY365: $i] :
( ~ ( reli @ SV6 @ SY365 )
| ( SV1 @ SY365 ) ) )
= $true )
| ( ( SV1 @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[39]) ).
thf(47,plain,
( ( ! [SX0: $i] :
( ~ ( reli @ sK3_SY327 @ SX0 )
| ! [SX1: $i] :
( ~ ( relr @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( reli @ SX1 @ SX2 )
| ! [SX3: individuals,SX4: $i] :
( ~ ( reli @ SX2 @ SX4 )
| ( sK1_SY0 @ SX3 @ SX4 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[40]) ).
thf(48,plain,
( ( ~ ( reli @ sK3_SY327 @ sK4_SX0 )
| ! [SY377: individuals,SY378: $i] :
( ~ ( reli @ sK4_SX0 @ SY378 )
| ! [SX3: $i] :
( ~ ( relr @ SY378 @ SX3 )
| ! [SX4: $i] :
( ~ ( reli @ SX3 @ SX4 )
| ( sK1_SY0 @ SY377 @ SX4 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[41]) ).
thf(49,plain,
! [SV2: $i > $o,SV7: $i] :
( ( ( ~ ! [SY366: $i] :
( ~ ( relr @ SV7 @ SY366 )
| ( SV2 @ SY366 ) ) )
= $true )
| ( ( SV2 @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[42]) ).
thf(50,plain,
! [SV3: $i > $o,SV8: $i] :
( ( ( ~ ! [SY367: $i] :
( ~ ( reli @ SV8 @ SY367 )
| ! [SY354: $i] :
( ~ ( relr @ SY367 @ SY354 )
| ( SV3 @ SY354 ) ) ) )
= $true )
| ( ( ! [SY369: $i] :
( ~ ( relr @ SV8 @ SY369 )
| ! [SY356: $i] :
( ~ ( reli @ SY369 @ SY356 )
| ( SV3 @ SY356 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[43]) ).
thf(51,plain,
! [SV4: $i > $o,SV9: $i] :
( ( ( ~ ! [SY371: $i] :
( ~ ( relr @ SV9 @ SY371 )
| ( SV4 @ SY371 ) ) )
= $true )
| ( ( ! [SY372: $i] :
( ~ ( relr @ SV9 @ SY372 )
| ! [SY360: $i] :
( ~ ( relr @ SY372 @ SY360 )
| ( SV4 @ SY360 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[44]) ).
thf(52,plain,
! [SV5: $i > $o,SV10: $i] :
( ( ( ~ ! [SY374: $i] :
( ~ ( reli @ SV10 @ SY374 )
| ( SV5 @ SY374 ) ) )
= $true )
| ( ( ! [SY375: $i] :
( ~ ( reli @ SV10 @ SY375 )
| ! [SY364: $i] :
( ~ ( reli @ SY375 @ SY364 )
| ( SV5 @ SY364 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[45]) ).
thf(53,plain,
! [SV1: $i > $o,SV6: $i] :
( ( ( ! [SY365: $i] :
( ~ ( reli @ SV6 @ SY365 )
| ( SV1 @ SY365 ) ) )
= $false )
| ( ( SV1 @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(54,plain,
! [SV11: $i] :
( ( ~ ( reli @ sK3_SY327 @ SV11 )
| ! [SY381: $i] :
( ~ ( relr @ SV11 @ SY381 )
| ! [SX2: $i] :
( ~ ( reli @ SY381 @ SX2 )
| ! [SX3: individuals,SX4: $i] :
( ~ ( reli @ SX2 @ SX4 )
| ( sK1_SY0 @ SX3 @ SX4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(55,plain,
( ( ~ ( reli @ sK3_SY327 @ sK4_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[48]) ).
thf(56,plain,
( ( ! [SY377: individuals,SY378: $i] :
( ~ ( reli @ sK4_SX0 @ SY378 )
| ! [SX3: $i] :
( ~ ( relr @ SY378 @ SX3 )
| ! [SX4: $i] :
( ~ ( reli @ SX3 @ SX4 )
| ( sK1_SY0 @ SY377 @ SX4 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[48]) ).
thf(57,plain,
! [SV2: $i > $o,SV7: $i] :
( ( ( ! [SY366: $i] :
( ~ ( relr @ SV7 @ SY366 )
| ( SV2 @ SY366 ) ) )
= $false )
| ( ( SV2 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(58,plain,
! [SV3: $i > $o,SV8: $i] :
( ( ( ! [SY367: $i] :
( ~ ( reli @ SV8 @ SY367 )
| ! [SY354: $i] :
( ~ ( relr @ SY367 @ SY354 )
| ( SV3 @ SY354 ) ) ) )
= $false )
| ( ( ! [SY369: $i] :
( ~ ( relr @ SV8 @ SY369 )
| ! [SY356: $i] :
( ~ ( reli @ SY369 @ SY356 )
| ( SV3 @ SY356 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(59,plain,
! [SV4: $i > $o,SV9: $i] :
( ( ( ! [SY371: $i] :
( ~ ( relr @ SV9 @ SY371 )
| ( SV4 @ SY371 ) ) )
= $false )
| ( ( ! [SY372: $i] :
( ~ ( relr @ SV9 @ SY372 )
| ! [SY360: $i] :
( ~ ( relr @ SY372 @ SY360 )
| ( SV4 @ SY360 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(60,plain,
! [SV5: $i > $o,SV10: $i] :
( ( ( ! [SY374: $i] :
( ~ ( reli @ SV10 @ SY374 )
| ( SV5 @ SY374 ) ) )
= $false )
| ( ( ! [SY375: $i] :
( ~ ( reli @ SV10 @ SY375 )
| ! [SY364: $i] :
( ~ ( reli @ SY375 @ SY364 )
| ( SV5 @ SY364 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(61,plain,
! [SV1: $i > $o,SV6: $i] :
( ( ( ~ ( reli @ SV6 @ ( sK5_SY365 @ SV1 @ SV6 ) )
| ( SV1 @ ( sK5_SY365 @ SV1 @ SV6 ) ) )
= $false )
| ( ( SV1 @ SV6 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[53]) ).
thf(62,plain,
! [SV11: $i] :
( ( ( ~ ( reli @ sK3_SY327 @ SV11 ) )
= $true )
| ( ( ! [SY381: $i] :
( ~ ( relr @ SV11 @ SY381 )
| ! [SX2: $i] :
( ~ ( reli @ SY381 @ SX2 )
| ! [SX3: individuals,SX4: $i] :
( ~ ( reli @ SX2 @ SX4 )
| ( sK1_SY0 @ SX3 @ SX4 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[54]) ).
thf(63,plain,
( ( reli @ sK3_SY327 @ sK4_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[55]) ).
thf(64,plain,
( ( ! [SY385: $i] :
( ~ ( reli @ sK4_SX0 @ SY385 )
| ! [SY386: $i] :
( ~ ( relr @ SY385 @ SY386 )
| ! [SY387: $i] :
( ~ ( reli @ SY386 @ SY387 )
| ( sK1_SY0 @ sK6_SY377 @ SY387 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[56]) ).
thf(65,plain,
! [SV2: $i > $o,SV7: $i] :
( ( ( ~ ( relr @ SV7 @ ( sK7_SY366 @ SV2 @ SV7 ) )
| ( SV2 @ ( sK7_SY366 @ SV2 @ SV7 ) ) )
= $false )
| ( ( SV2 @ SV7 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[57]) ).
thf(66,plain,
! [SV3: $i > $o,SV8: $i] :
( ( ( ~ ( reli @ SV8 @ ( sK8_SY367 @ SV3 @ SV8 ) )
| ! [SY388: $i] :
( ~ ( relr @ ( sK8_SY367 @ SV3 @ SV8 ) @ SY388 )
| ( SV3 @ SY388 ) ) )
= $false )
| ( ( ! [SY369: $i] :
( ~ ( relr @ SV8 @ SY369 )
| ! [SY356: $i] :
( ~ ( reli @ SY369 @ SY356 )
| ( SV3 @ SY356 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[58]) ).
thf(67,plain,
! [SV4: $i > $o,SV9: $i] :
( ( ( ~ ( relr @ SV9 @ ( sK9_SY371 @ SV4 @ SV9 ) )
| ( SV4 @ ( sK9_SY371 @ SV4 @ SV9 ) ) )
= $false )
| ( ( ! [SY372: $i] :
( ~ ( relr @ SV9 @ SY372 )
| ! [SY360: $i] :
( ~ ( relr @ SY372 @ SY360 )
| ( SV4 @ SY360 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[59]) ).
thf(68,plain,
! [SV5: $i > $o,SV10: $i] :
( ( ( ~ ( reli @ SV10 @ ( sK10_SY374 @ SV5 @ SV10 ) )
| ( SV5 @ ( sK10_SY374 @ SV5 @ SV10 ) ) )
= $false )
| ( ( ! [SY375: $i] :
( ~ ( reli @ SV10 @ SY375 )
| ! [SY364: $i] :
( ~ ( reli @ SY375 @ SY364 )
| ( SV5 @ SY364 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[60]) ).
thf(69,plain,
! [SV1: $i > $o,SV6: $i] :
( ( ( ~ ( reli @ SV6 @ ( sK5_SY365 @ SV1 @ SV6 ) ) )
= $false )
| ( ( SV1 @ SV6 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[61]) ).
thf(70,plain,
! [SV6: $i,SV1: $i > $o] :
( ( ( SV1 @ ( sK5_SY365 @ SV1 @ SV6 ) )
= $false )
| ( ( SV1 @ SV6 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[61]) ).
thf(71,plain,
! [SV11: $i] :
( ( ( reli @ sK3_SY327 @ SV11 )
= $false )
| ( ( ! [SY381: $i] :
( ~ ( relr @ SV11 @ SY381 )
| ! [SX2: $i] :
( ~ ( reli @ SY381 @ SX2 )
| ! [SX3: individuals,SX4: $i] :
( ~ ( reli @ SX2 @ SX4 )
| ( sK1_SY0 @ SX3 @ SX4 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(72,plain,
( ( ~ ( reli @ sK4_SX0 @ sK11_SY385 )
| ! [SY389: $i] :
( ~ ( relr @ sK11_SY385 @ SY389 )
| ! [SY387: $i] :
( ~ ( reli @ SY389 @ SY387 )
| ( sK1_SY0 @ sK6_SY377 @ SY387 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[64]) ).
thf(73,plain,
! [SV2: $i > $o,SV7: $i] :
( ( ( ~ ( relr @ SV7 @ ( sK7_SY366 @ SV2 @ SV7 ) ) )
= $false )
| ( ( SV2 @ SV7 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[65]) ).
thf(74,plain,
! [SV7: $i,SV2: $i > $o] :
( ( ( SV2 @ ( sK7_SY366 @ SV2 @ SV7 ) )
= $false )
| ( ( SV2 @ SV7 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[65]) ).
thf(75,plain,
! [SV3: $i > $o,SV8: $i] :
( ( ( ~ ( reli @ SV8 @ ( sK8_SY367 @ SV3 @ SV8 ) ) )
= $false )
| ( ( ! [SY369: $i] :
( ~ ( relr @ SV8 @ SY369 )
| ! [SY356: $i] :
( ~ ( reli @ SY369 @ SY356 )
| ( SV3 @ SY356 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[66]) ).
thf(76,plain,
! [SV8: $i,SV3: $i > $o] :
( ( ( ! [SY388: $i] :
( ~ ( relr @ ( sK8_SY367 @ SV3 @ SV8 ) @ SY388 )
| ( SV3 @ SY388 ) ) )
= $false )
| ( ( ! [SY369: $i] :
( ~ ( relr @ SV8 @ SY369 )
| ! [SY356: $i] :
( ~ ( reli @ SY369 @ SY356 )
| ( SV3 @ SY356 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[66]) ).
thf(77,plain,
! [SV4: $i > $o,SV9: $i] :
( ( ( ~ ( relr @ SV9 @ ( sK9_SY371 @ SV4 @ SV9 ) ) )
= $false )
| ( ( ! [SY372: $i] :
( ~ ( relr @ SV9 @ SY372 )
| ! [SY360: $i] :
( ~ ( relr @ SY372 @ SY360 )
| ( SV4 @ SY360 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[67]) ).
thf(78,plain,
! [SV9: $i,SV4: $i > $o] :
( ( ( SV4 @ ( sK9_SY371 @ SV4 @ SV9 ) )
= $false )
| ( ( ! [SY372: $i] :
( ~ ( relr @ SV9 @ SY372 )
| ! [SY360: $i] :
( ~ ( relr @ SY372 @ SY360 )
| ( SV4 @ SY360 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[67]) ).
thf(79,plain,
! [SV5: $i > $o,SV10: $i] :
( ( ( ~ ( reli @ SV10 @ ( sK10_SY374 @ SV5 @ SV10 ) ) )
= $false )
| ( ( ! [SY375: $i] :
( ~ ( reli @ SV10 @ SY375 )
| ! [SY364: $i] :
( ~ ( reli @ SY375 @ SY364 )
| ( SV5 @ SY364 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[68]) ).
thf(80,plain,
! [SV10: $i,SV5: $i > $o] :
( ( ( SV5 @ ( sK10_SY374 @ SV5 @ SV10 ) )
= $false )
| ( ( ! [SY375: $i] :
( ~ ( reli @ SV10 @ SY375 )
| ! [SY364: $i] :
( ~ ( reli @ SY375 @ SY364 )
| ( SV5 @ SY364 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[68]) ).
thf(81,plain,
! [SV1: $i > $o,SV6: $i] :
( ( ( reli @ SV6 @ ( sK5_SY365 @ SV1 @ SV6 ) )
= $true )
| ( ( SV1 @ SV6 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[69]) ).
thf(82,plain,
! [SV12: $i,SV11: $i] :
( ( ( ~ ( relr @ SV11 @ SV12 )
| ! [SY391: $i] :
( ~ ( reli @ SV12 @ SY391 )
| ! [SX3: individuals,SX4: $i] :
( ~ ( reli @ SY391 @ SX4 )
| ( sK1_SY0 @ SX3 @ SX4 ) ) ) )
= $true )
| ( ( reli @ sK3_SY327 @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(83,plain,
( ( ~ ( reli @ sK4_SX0 @ sK11_SY385 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[72]) ).
thf(84,plain,
( ( ! [SY389: $i] :
( ~ ( relr @ sK11_SY385 @ SY389 )
| ! [SY387: $i] :
( ~ ( reli @ SY389 @ SY387 )
| ( sK1_SY0 @ sK6_SY377 @ SY387 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[72]) ).
thf(85,plain,
! [SV2: $i > $o,SV7: $i] :
( ( ( relr @ SV7 @ ( sK7_SY366 @ SV2 @ SV7 ) )
= $true )
| ( ( SV2 @ SV7 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[73]) ).
thf(86,plain,
! [SV3: $i > $o,SV8: $i] :
( ( ( reli @ SV8 @ ( sK8_SY367 @ SV3 @ SV8 ) )
= $true )
| ( ( ! [SY369: $i] :
( ~ ( relr @ SV8 @ SY369 )
| ! [SY356: $i] :
( ~ ( reli @ SY369 @ SY356 )
| ( SV3 @ SY356 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[75]) ).
thf(87,plain,
! [SV8: $i,SV3: $i > $o] :
( ( ( ~ ( relr @ ( sK8_SY367 @ SV3 @ SV8 ) @ ( sK12_SY388 @ SV8 @ SV3 ) )
| ( SV3 @ ( sK12_SY388 @ SV8 @ SV3 ) ) )
= $false )
| ( ( ! [SY369: $i] :
( ~ ( relr @ SV8 @ SY369 )
| ! [SY356: $i] :
( ~ ( reli @ SY369 @ SY356 )
| ( SV3 @ SY356 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[76]) ).
thf(88,plain,
! [SV4: $i > $o,SV9: $i] :
( ( ( relr @ SV9 @ ( sK9_SY371 @ SV4 @ SV9 ) )
= $true )
| ( ( ! [SY372: $i] :
( ~ ( relr @ SV9 @ SY372 )
| ! [SY360: $i] :
( ~ ( relr @ SY372 @ SY360 )
| ( SV4 @ SY360 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[77]) ).
thf(89,plain,
! [SV4: $i > $o,SV13: $i,SV9: $i] :
( ( ( ~ ( relr @ SV9 @ SV13 )
| ! [SY394: $i] :
( ~ ( relr @ SV13 @ SY394 )
| ( SV4 @ SY394 ) ) )
= $true )
| ( ( SV4 @ ( sK9_SY371 @ SV4 @ SV9 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(90,plain,
! [SV5: $i > $o,SV10: $i] :
( ( ( reli @ SV10 @ ( sK10_SY374 @ SV5 @ SV10 ) )
= $true )
| ( ( ! [SY375: $i] :
( ~ ( reli @ SV10 @ SY375 )
| ! [SY364: $i] :
( ~ ( reli @ SY375 @ SY364 )
| ( SV5 @ SY364 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[79]) ).
thf(91,plain,
! [SV5: $i > $o,SV14: $i,SV10: $i] :
( ( ( ~ ( reli @ SV10 @ SV14 )
| ! [SY395: $i] :
( ~ ( reli @ SV14 @ SY395 )
| ( SV5 @ SY395 ) ) )
= $true )
| ( ( SV5 @ ( sK10_SY374 @ SV5 @ SV10 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(92,plain,
! [SV12: $i,SV11: $i] :
( ( ( ~ ( relr @ SV11 @ SV12 ) )
= $true )
| ( ( ! [SY391: $i] :
( ~ ( reli @ SV12 @ SY391 )
| ! [SX3: individuals,SX4: $i] :
( ~ ( reli @ SY391 @ SX4 )
| ( sK1_SY0 @ SX3 @ SX4 ) ) ) )
= $true )
| ( ( reli @ sK3_SY327 @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[82]) ).
thf(93,plain,
( ( reli @ sK4_SX0 @ sK11_SY385 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[83]) ).
thf(94,plain,
( ( ~ ( relr @ sK11_SY385 @ sK13_SY389 )
| ! [SY396: $i] :
( ~ ( reli @ sK13_SY389 @ SY396 )
| ( sK1_SY0 @ sK6_SY377 @ SY396 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[84]) ).
thf(95,plain,
! [SV3: $i > $o,SV15: $i,SV8: $i] :
( ( ( ~ ( relr @ SV8 @ SV15 )
| ! [SY397: $i] :
( ~ ( reli @ SV15 @ SY397 )
| ( SV3 @ SY397 ) ) )
= $true )
| ( ( reli @ SV8 @ ( sK8_SY367 @ SV3 @ SV8 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(96,plain,
! [SV8: $i,SV3: $i > $o] :
( ( ( ~ ( relr @ ( sK8_SY367 @ SV3 @ SV8 ) @ ( sK12_SY388 @ SV8 @ SV3 ) ) )
= $false )
| ( ( ! [SY369: $i] :
( ~ ( relr @ SV8 @ SY369 )
| ! [SY356: $i] :
( ~ ( reli @ SY369 @ SY356 )
| ( SV3 @ SY356 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[87]) ).
thf(97,plain,
! [SV8: $i,SV3: $i > $o] :
( ( ( SV3 @ ( sK12_SY388 @ SV8 @ SV3 ) )
= $false )
| ( ( ! [SY369: $i] :
( ~ ( relr @ SV8 @ SY369 )
| ! [SY356: $i] :
( ~ ( reli @ SY369 @ SY356 )
| ( SV3 @ SY356 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[87]) ).
thf(98,plain,
! [SV4: $i > $o,SV16: $i,SV9: $i] :
( ( ( ~ ( relr @ SV9 @ SV16 )
| ! [SY398: $i] :
( ~ ( relr @ SV16 @ SY398 )
| ( SV4 @ SY398 ) ) )
= $true )
| ( ( relr @ SV9 @ ( sK9_SY371 @ SV4 @ SV9 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(99,plain,
! [SV4: $i > $o,SV13: $i,SV9: $i] :
( ( ( ~ ( relr @ SV9 @ SV13 ) )
= $true )
| ( ( ! [SY394: $i] :
( ~ ( relr @ SV13 @ SY394 )
| ( SV4 @ SY394 ) ) )
= $true )
| ( ( SV4 @ ( sK9_SY371 @ SV4 @ SV9 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[89]) ).
thf(100,plain,
! [SV5: $i > $o,SV17: $i,SV10: $i] :
( ( ( ~ ( reli @ SV10 @ SV17 )
| ! [SY399: $i] :
( ~ ( reli @ SV17 @ SY399 )
| ( SV5 @ SY399 ) ) )
= $true )
| ( ( reli @ SV10 @ ( sK10_SY374 @ SV5 @ SV10 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(101,plain,
! [SV5: $i > $o,SV14: $i,SV10: $i] :
( ( ( ~ ( reli @ SV10 @ SV14 ) )
= $true )
| ( ( ! [SY395: $i] :
( ~ ( reli @ SV14 @ SY395 )
| ( SV5 @ SY395 ) ) )
= $true )
| ( ( SV5 @ ( sK10_SY374 @ SV5 @ SV10 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[91]) ).
thf(102,plain,
! [SV12: $i,SV11: $i] :
( ( ( relr @ SV11 @ SV12 )
= $false )
| ( ( ! [SY391: $i] :
( ~ ( reli @ SV12 @ SY391 )
| ! [SX3: individuals,SX4: $i] :
( ~ ( reli @ SY391 @ SX4 )
| ( sK1_SY0 @ SX3 @ SX4 ) ) ) )
= $true )
| ( ( reli @ sK3_SY327 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(103,plain,
( ( ~ ( relr @ sK11_SY385 @ sK13_SY389 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[94]) ).
thf(104,plain,
( ( ! [SY396: $i] :
( ~ ( reli @ sK13_SY389 @ SY396 )
| ( sK1_SY0 @ sK6_SY377 @ SY396 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[94]) ).
thf(105,plain,
! [SV3: $i > $o,SV15: $i,SV8: $i] :
( ( ( ~ ( relr @ SV8 @ SV15 ) )
= $true )
| ( ( ! [SY397: $i] :
( ~ ( reli @ SV15 @ SY397 )
| ( SV3 @ SY397 ) ) )
= $true )
| ( ( reli @ SV8 @ ( sK8_SY367 @ SV3 @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[95]) ).
thf(106,plain,
! [SV8: $i,SV3: $i > $o] :
( ( ( relr @ ( sK8_SY367 @ SV3 @ SV8 ) @ ( sK12_SY388 @ SV8 @ SV3 ) )
= $true )
| ( ( ! [SY369: $i] :
( ~ ( relr @ SV8 @ SY369 )
| ! [SY356: $i] :
( ~ ( reli @ SY369 @ SY356 )
| ( SV3 @ SY356 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[96]) ).
thf(107,plain,
! [SV3: $i > $o,SV18: $i,SV8: $i] :
( ( ( ~ ( relr @ SV8 @ SV18 )
| ! [SY400: $i] :
( ~ ( reli @ SV18 @ SY400 )
| ( SV3 @ SY400 ) ) )
= $true )
| ( ( SV3 @ ( sK12_SY388 @ SV8 @ SV3 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(108,plain,
! [SV4: $i > $o,SV16: $i,SV9: $i] :
( ( ( ~ ( relr @ SV9 @ SV16 ) )
= $true )
| ( ( ! [SY398: $i] :
( ~ ( relr @ SV16 @ SY398 )
| ( SV4 @ SY398 ) ) )
= $true )
| ( ( relr @ SV9 @ ( sK9_SY371 @ SV4 @ SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[98]) ).
thf(109,plain,
! [SV4: $i > $o,SV13: $i,SV9: $i] :
( ( ( relr @ SV9 @ SV13 )
= $false )
| ( ( ! [SY394: $i] :
( ~ ( relr @ SV13 @ SY394 )
| ( SV4 @ SY394 ) ) )
= $true )
| ( ( SV4 @ ( sK9_SY371 @ SV4 @ SV9 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(110,plain,
! [SV5: $i > $o,SV17: $i,SV10: $i] :
( ( ( ~ ( reli @ SV10 @ SV17 ) )
= $true )
| ( ( ! [SY399: $i] :
( ~ ( reli @ SV17 @ SY399 )
| ( SV5 @ SY399 ) ) )
= $true )
| ( ( reli @ SV10 @ ( sK10_SY374 @ SV5 @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[100]) ).
thf(111,plain,
! [SV5: $i > $o,SV14: $i,SV10: $i] :
( ( ( reli @ SV10 @ SV14 )
= $false )
| ( ( ! [SY395: $i] :
( ~ ( reli @ SV14 @ SY395 )
| ( SV5 @ SY395 ) ) )
= $true )
| ( ( SV5 @ ( sK10_SY374 @ SV5 @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(112,plain,
! [SV11: $i,SV19: $i,SV12: $i] :
( ( ( ~ ( reli @ SV12 @ SV19 )
| ! [SY401: individuals,SY402: $i] :
( ~ ( reli @ SV19 @ SY402 )
| ( sK1_SY0 @ SY401 @ SY402 ) ) )
= $true )
| ( ( relr @ SV11 @ SV12 )
= $false )
| ( ( reli @ sK3_SY327 @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(113,plain,
( ( relr @ sK11_SY385 @ sK13_SY389 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[103]) ).
thf(114,plain,
( ( ~ ( reli @ sK13_SY389 @ sK14_SY396 )
| ( sK1_SY0 @ sK6_SY377 @ sK14_SY396 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[104]) ).
thf(115,plain,
! [SV3: $i > $o,SV15: $i,SV8: $i] :
( ( ( relr @ SV8 @ SV15 )
= $false )
| ( ( ! [SY397: $i] :
( ~ ( reli @ SV15 @ SY397 )
| ( SV3 @ SY397 ) ) )
= $true )
| ( ( reli @ SV8 @ ( sK8_SY367 @ SV3 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(116,plain,
! [SV3: $i > $o,SV20: $i,SV8: $i] :
( ( ( ~ ( relr @ SV8 @ SV20 )
| ! [SY403: $i] :
( ~ ( reli @ SV20 @ SY403 )
| ( SV3 @ SY403 ) ) )
= $true )
| ( ( relr @ ( sK8_SY367 @ SV3 @ SV8 ) @ ( sK12_SY388 @ SV8 @ SV3 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(117,plain,
! [SV3: $i > $o,SV18: $i,SV8: $i] :
( ( ( ~ ( relr @ SV8 @ SV18 ) )
= $true )
| ( ( ! [SY400: $i] :
( ~ ( reli @ SV18 @ SY400 )
| ( SV3 @ SY400 ) ) )
= $true )
| ( ( SV3 @ ( sK12_SY388 @ SV8 @ SV3 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[107]) ).
thf(118,plain,
! [SV4: $i > $o,SV16: $i,SV9: $i] :
( ( ( relr @ SV9 @ SV16 )
= $false )
| ( ( ! [SY398: $i] :
( ~ ( relr @ SV16 @ SY398 )
| ( SV4 @ SY398 ) ) )
= $true )
| ( ( relr @ SV9 @ ( sK9_SY371 @ SV4 @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(119,plain,
! [SV9: $i,SV4: $i > $o,SV21: $i,SV13: $i] :
( ( ( ~ ( relr @ SV13 @ SV21 )
| ( SV4 @ SV21 ) )
= $true )
| ( ( relr @ SV9 @ SV13 )
= $false )
| ( ( SV4 @ ( sK9_SY371 @ SV4 @ SV9 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(120,plain,
! [SV5: $i > $o,SV17: $i,SV10: $i] :
( ( ( reli @ SV10 @ SV17 )
= $false )
| ( ( ! [SY399: $i] :
( ~ ( reli @ SV17 @ SY399 )
| ( SV5 @ SY399 ) ) )
= $true )
| ( ( reli @ SV10 @ ( sK10_SY374 @ SV5 @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(121,plain,
! [SV10: $i,SV5: $i > $o,SV22: $i,SV14: $i] :
( ( ( ~ ( reli @ SV14 @ SV22 )
| ( SV5 @ SV22 ) )
= $true )
| ( ( reli @ SV10 @ SV14 )
= $false )
| ( ( SV5 @ ( sK10_SY374 @ SV5 @ SV10 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(122,plain,
! [SV11: $i,SV19: $i,SV12: $i] :
( ( ( ~ ( reli @ SV12 @ SV19 ) )
= $true )
| ( ( ! [SY401: individuals,SY402: $i] :
( ~ ( reli @ SV19 @ SY402 )
| ( sK1_SY0 @ SY401 @ SY402 ) ) )
= $true )
| ( ( relr @ SV11 @ SV12 )
= $false )
| ( ( reli @ sK3_SY327 @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[112]) ).
thf(123,plain,
( ( ~ ( reli @ sK13_SY389 @ sK14_SY396 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[114]) ).
thf(124,plain,
( ( sK1_SY0 @ sK6_SY377 @ sK14_SY396 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[114]) ).
thf(125,plain,
! [SV8: $i,SV3: $i > $o,SV23: $i,SV15: $i] :
( ( ( ~ ( reli @ SV15 @ SV23 )
| ( SV3 @ SV23 ) )
= $true )
| ( ( relr @ SV8 @ SV15 )
= $false )
| ( ( reli @ SV8 @ ( sK8_SY367 @ SV3 @ SV8 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(126,plain,
! [SV3: $i > $o,SV20: $i,SV8: $i] :
( ( ( ~ ( relr @ SV8 @ SV20 ) )
= $true )
| ( ( ! [SY403: $i] :
( ~ ( reli @ SV20 @ SY403 )
| ( SV3 @ SY403 ) ) )
= $true )
| ( ( relr @ ( sK8_SY367 @ SV3 @ SV8 ) @ ( sK12_SY388 @ SV8 @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[116]) ).
thf(127,plain,
! [SV3: $i > $o,SV18: $i,SV8: $i] :
( ( ( relr @ SV8 @ SV18 )
= $false )
| ( ( ! [SY400: $i] :
( ~ ( reli @ SV18 @ SY400 )
| ( SV3 @ SY400 ) ) )
= $true )
| ( ( SV3 @ ( sK12_SY388 @ SV8 @ SV3 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(128,plain,
! [SV9: $i,SV4: $i > $o,SV24: $i,SV16: $i] :
( ( ( ~ ( relr @ SV16 @ SV24 )
| ( SV4 @ SV24 ) )
= $true )
| ( ( relr @ SV9 @ SV16 )
= $false )
| ( ( relr @ SV9 @ ( sK9_SY371 @ SV4 @ SV9 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(129,plain,
! [SV9: $i,SV4: $i > $o,SV21: $i,SV13: $i] :
( ( ( ~ ( relr @ SV13 @ SV21 ) )
= $true )
| ( ( SV4 @ SV21 )
= $true )
| ( ( relr @ SV9 @ SV13 )
= $false )
| ( ( SV4 @ ( sK9_SY371 @ SV4 @ SV9 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[119]) ).
thf(130,plain,
! [SV10: $i,SV5: $i > $o,SV25: $i,SV17: $i] :
( ( ( ~ ( reli @ SV17 @ SV25 )
| ( SV5 @ SV25 ) )
= $true )
| ( ( reli @ SV10 @ SV17 )
= $false )
| ( ( reli @ SV10 @ ( sK10_SY374 @ SV5 @ SV10 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(131,plain,
! [SV10: $i,SV5: $i > $o,SV22: $i,SV14: $i] :
( ( ( ~ ( reli @ SV14 @ SV22 ) )
= $true )
| ( ( SV5 @ SV22 )
= $true )
| ( ( reli @ SV10 @ SV14 )
= $false )
| ( ( SV5 @ ( sK10_SY374 @ SV5 @ SV10 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[121]) ).
thf(132,plain,
! [SV11: $i,SV19: $i,SV12: $i] :
( ( ( reli @ SV12 @ SV19 )
= $false )
| ( ( ! [SY401: individuals,SY402: $i] :
( ~ ( reli @ SV19 @ SY402 )
| ( sK1_SY0 @ SY401 @ SY402 ) ) )
= $true )
| ( ( relr @ SV11 @ SV12 )
= $false )
| ( ( reli @ sK3_SY327 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(133,plain,
( ( reli @ sK13_SY389 @ sK14_SY396 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[123]) ).
thf(134,plain,
! [SV8: $i,SV3: $i > $o,SV23: $i,SV15: $i] :
( ( ( ~ ( reli @ SV15 @ SV23 ) )
= $true )
| ( ( SV3 @ SV23 )
= $true )
| ( ( relr @ SV8 @ SV15 )
= $false )
| ( ( reli @ SV8 @ ( sK8_SY367 @ SV3 @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[125]) ).
thf(135,plain,
! [SV3: $i > $o,SV20: $i,SV8: $i] :
( ( ( relr @ SV8 @ SV20 )
= $false )
| ( ( ! [SY403: $i] :
( ~ ( reli @ SV20 @ SY403 )
| ( SV3 @ SY403 ) ) )
= $true )
| ( ( relr @ ( sK8_SY367 @ SV3 @ SV8 ) @ ( sK12_SY388 @ SV8 @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[126]) ).
thf(136,plain,
! [SV8: $i,SV3: $i > $o,SV26: $i,SV18: $i] :
( ( ( ~ ( reli @ SV18 @ SV26 )
| ( SV3 @ SV26 ) )
= $true )
| ( ( relr @ SV8 @ SV18 )
= $false )
| ( ( SV3 @ ( sK12_SY388 @ SV8 @ SV3 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(137,plain,
! [SV9: $i,SV4: $i > $o,SV24: $i,SV16: $i] :
( ( ( ~ ( relr @ SV16 @ SV24 ) )
= $true )
| ( ( SV4 @ SV24 )
= $true )
| ( ( relr @ SV9 @ SV16 )
= $false )
| ( ( relr @ SV9 @ ( sK9_SY371 @ SV4 @ SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[128]) ).
thf(138,plain,
! [SV9: $i,SV4: $i > $o,SV21: $i,SV13: $i] :
( ( ( relr @ SV13 @ SV21 )
= $false )
| ( ( SV4 @ SV21 )
= $true )
| ( ( relr @ SV9 @ SV13 )
= $false )
| ( ( SV4 @ ( sK9_SY371 @ SV4 @ SV9 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[129]) ).
thf(139,plain,
! [SV10: $i,SV5: $i > $o,SV25: $i,SV17: $i] :
( ( ( ~ ( reli @ SV17 @ SV25 ) )
= $true )
| ( ( SV5 @ SV25 )
= $true )
| ( ( reli @ SV10 @ SV17 )
= $false )
| ( ( reli @ SV10 @ ( sK10_SY374 @ SV5 @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[130]) ).
thf(140,plain,
! [SV10: $i,SV5: $i > $o,SV22: $i,SV14: $i] :
( ( ( reli @ SV14 @ SV22 )
= $false )
| ( ( SV5 @ SV22 )
= $true )
| ( ( reli @ SV10 @ SV14 )
= $false )
| ( ( SV5 @ ( sK10_SY374 @ SV5 @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(141,plain,
! [SV11: $i,SV12: $i,SV27: individuals,SV19: $i] :
( ( ( ! [SY404: $i] :
( ~ ( reli @ SV19 @ SY404 )
| ( sK1_SY0 @ SV27 @ SY404 ) ) )
= $true )
| ( ( reli @ SV12 @ SV19 )
= $false )
| ( ( relr @ SV11 @ SV12 )
= $false )
| ( ( reli @ sK3_SY327 @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(142,plain,
! [SV8: $i,SV3: $i > $o,SV23: $i,SV15: $i] :
( ( ( reli @ SV15 @ SV23 )
= $false )
| ( ( SV3 @ SV23 )
= $true )
| ( ( relr @ SV8 @ SV15 )
= $false )
| ( ( reli @ SV8 @ ( sK8_SY367 @ SV3 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(143,plain,
! [SV8: $i,SV3: $i > $o,SV28: $i,SV20: $i] :
( ( ( ~ ( reli @ SV20 @ SV28 )
| ( SV3 @ SV28 ) )
= $true )
| ( ( relr @ SV8 @ SV20 )
= $false )
| ( ( relr @ ( sK8_SY367 @ SV3 @ SV8 ) @ ( sK12_SY388 @ SV8 @ SV3 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(144,plain,
! [SV8: $i,SV3: $i > $o,SV26: $i,SV18: $i] :
( ( ( ~ ( reli @ SV18 @ SV26 ) )
= $true )
| ( ( SV3 @ SV26 )
= $true )
| ( ( relr @ SV8 @ SV18 )
= $false )
| ( ( SV3 @ ( sK12_SY388 @ SV8 @ SV3 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[136]) ).
thf(145,plain,
! [SV9: $i,SV4: $i > $o,SV24: $i,SV16: $i] :
( ( ( relr @ SV16 @ SV24 )
= $false )
| ( ( SV4 @ SV24 )
= $true )
| ( ( relr @ SV9 @ SV16 )
= $false )
| ( ( relr @ SV9 @ ( sK9_SY371 @ SV4 @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(146,plain,
! [SV10: $i,SV5: $i > $o,SV25: $i,SV17: $i] :
( ( ( reli @ SV17 @ SV25 )
= $false )
| ( ( SV5 @ SV25 )
= $true )
| ( ( reli @ SV10 @ SV17 )
= $false )
| ( ( reli @ SV10 @ ( sK10_SY374 @ SV5 @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(147,plain,
! [SV11: $i,SV12: $i,SV27: individuals,SV29: $i,SV19: $i] :
( ( ( ~ ( reli @ SV19 @ SV29 )
| ( sK1_SY0 @ SV27 @ SV29 ) )
= $true )
| ( ( reli @ SV12 @ SV19 )
= $false )
| ( ( relr @ SV11 @ SV12 )
= $false )
| ( ( reli @ sK3_SY327 @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(148,plain,
! [SV8: $i,SV3: $i > $o,SV28: $i,SV20: $i] :
( ( ( ~ ( reli @ SV20 @ SV28 ) )
= $true )
| ( ( SV3 @ SV28 )
= $true )
| ( ( relr @ SV8 @ SV20 )
= $false )
| ( ( relr @ ( sK8_SY367 @ SV3 @ SV8 ) @ ( sK12_SY388 @ SV8 @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[143]) ).
thf(149,plain,
! [SV8: $i,SV3: $i > $o,SV26: $i,SV18: $i] :
( ( ( reli @ SV18 @ SV26 )
= $false )
| ( ( SV3 @ SV26 )
= $true )
| ( ( relr @ SV8 @ SV18 )
= $false )
| ( ( SV3 @ ( sK12_SY388 @ SV8 @ SV3 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(150,plain,
! [SV11: $i,SV12: $i,SV27: individuals,SV29: $i,SV19: $i] :
( ( ( ~ ( reli @ SV19 @ SV29 ) )
= $true )
| ( ( sK1_SY0 @ SV27 @ SV29 )
= $true )
| ( ( reli @ SV12 @ SV19 )
= $false )
| ( ( relr @ SV11 @ SV12 )
= $false )
| ( ( reli @ sK3_SY327 @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[147]) ).
thf(151,plain,
! [SV8: $i,SV3: $i > $o,SV28: $i,SV20: $i] :
( ( ( reli @ SV20 @ SV28 )
= $false )
| ( ( SV3 @ SV28 )
= $true )
| ( ( relr @ SV8 @ SV20 )
= $false )
| ( ( relr @ ( sK8_SY367 @ SV3 @ SV8 ) @ ( sK12_SY388 @ SV8 @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(152,plain,
! [SV11: $i,SV12: $i,SV27: individuals,SV29: $i,SV19: $i] :
( ( ( reli @ SV19 @ SV29 )
= $false )
| ( ( sK1_SY0 @ SV27 @ SV29 )
= $true )
| ( ( reli @ SV12 @ SV19 )
= $false )
| ( ( relr @ SV11 @ SV12 )
= $false )
| ( ( reli @ sK3_SY327 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[150]) ).
thf(153,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[25,152,151,149,146,145,142,140,138,133,124,113,93,85,81,74,70,63]) ).
thf(154,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[153]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO932^9 : 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
% 0.09/0.16 % Computer : n001.cluster.edu
% 0.09/0.16 % Model : x86_64 x86_64
% 0.09/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.16 % Memory : 8046.5625MB
% 0.09/0.16 % OS : Linux 6.8.0-71-generic
% 0.09/0.16 % CPULimit : 300
% 0.09/0.16 % WCLimit : 300
% 0.09/0.16 % DateTime : Tue Oct 6 17:59:54 UTC 2026
% 0.09/0.16 % CPUTime :
% 0.09/0.16 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.57/0.28
% 0.57/0.28 No.of.Axioms: 5
% 0.57/0.28
% 0.57/0.28 Length.of.Defs: 3503
% 0.57/0.28
% 0.57/0.28 Contains.Choice.Funs: false
% 0.57/0.28 ........
% 0.57/0.28
% 0.57/0.28 ********************************
% 0.57/0.28 * All subproblems solved! *
% 0.57/0.28 ********************************
% 0.57/0.28 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:6,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:153,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.57/0.28
% 0.57/0.28 %**** Beginning of derivation protocol ****
% 0.57/0.28 % SZS output start CNFRefutation
% See solution above
% 0.57/0.28
% 0.57/0.28 %**** End of derivation protocol ****
% 0.57/0.28 %**** no. of clauses in derivation: 154 ****
% 0.57/0.28 %**** clause counter: 153 ****
% 0.57/0.28
% 0.57/0.28 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:6,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:153,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------