%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : LCL691^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 10:30:01 AM UTC 2026
% Result : Theorem 0.06s 0.23s
% Output : CNFRefutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 30
% Syntax : Number of formulae : 161 ( 71 unt; 0 typ; 24 def)
% Number of atoms : 1011 ( 294 equ; 0 cnn)
% Maximal formula atoms : 10 ( 6 avg)
% Number of connectives : 1733 ( 233 ~; 338 |; 2 &;1103 @)
% ( 0 <=>; 57 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 143 ( 143 >; 0 *; 0 +; 0 <<)
% Number of symbols : 43 ( 40 usr; 6 con; 0-3 aty)
% Number of variables : 533 ( 38 ^; 491 !; 4 ?; 533 :)
% 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_SY284,type,
sK10_SY284: $i > ( $i > $o ) > $i ).
thf(tp_sK1_SY0,type,
sK1_SY0: $i > $o ).
thf(tp_sK2_SY238,type,
sK2_SY238: $i ).
thf(tp_sK3_SY244,type,
sK3_SY244: $i ).
thf(tp_sK4_SX0,type,
sK4_SX0: $i ).
thf(tp_sK5_SY270,type,
sK5_SY270: ( $i > $o ) > $i > $i ).
thf(tp_sK6_SY271,type,
sK6_SY271: ( $i > $o ) > $i > $i ).
thf(tp_sK7_SY272,type,
sK7_SY272: ( $i > $o ) > $i > $i ).
thf(tp_sK8_SY276,type,
sK8_SY276: ( $i > $o ) > $i > $i ).
thf(tp_sK9_SY279,type,
sK9_SY279: ( $i > $o ) > $i > $i ).
thf(cs4_all,definition,
( cs4_all
= ( ^ [A: individuals > $i > $o] : ( mbox @ reli @ ( mall @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cs4_all) ).
thf(cs4_and,definition,
( cs4_and
= ( ^ [A: $i > $o,B: $i > $o] : ( mand @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cs4_and) ).
thf(cs4_atom,definition,
( cs4_atom
= ( ^ [P: $i > $o] : ( mbox @ reli @ P ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cs4_atom) ).
thf(cs4_box,definition,
( cs4_box
= ( ^ [A: $i > $o] : ( mbox @ reli @ ( mbox @ relr @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cs4_box) ).
thf(cs4_false,definition,
cs4_false = mfalse,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cs4_false) ).
thf(cs4_impl,definition,
( cs4_impl
= ( ^ [A: $i > $o,B: $i > $o] : ( mbox @ reli @ ( mimpl @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cs4_impl) ).
thf(cs4_or,definition,
( cs4_or
= ( ^ [A: $i > $o,B: $i > $o] : ( mor @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cs4_or) ).
thf(cs4_true,definition,
cs4_true = mtrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cs4_true) ).
thf(cs4_valid,definition,
( cs4_valid
= ( ^ [A: $i > $o] : ( mvalid @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cs4_valid_def) ).
thf(mall,definition,
( mall
= ( ^ [P: individuals > $i > $o,W: $i] :
! [X: individuals] : ( P @ X @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mall) ).
thf(mand,definition,
( mand
= ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
( ( X @ U )
& ( Y @ U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mand) ).
thf(mbox,definition,
( mbox
= ( ^ [R: $i > $i > $o,P: $i > $o,X: $i] :
! [Y: $i] :
( ( R @ X @ Y )
=> ( P @ Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox) ).
thf(mcountersatisfiable,definition,
( mcountersatisfiable
= ( ^ [P: $i > $o] :
? [W: $i] :
~ ( P @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mcountersatisfiable) ).
thf(mdia,definition,
( mdia
= ( ^ [R: $i > $i > $o,P: $i > $o,X: $i] :
? [Y: $i] :
( ( R @ X @ Y )
& ( P @ Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',individuals_decl) ).
thf(mexists,definition,
( mexists
= ( ^ [P: individuals > $i > $o,W: $i] :
? [X: individuals] : ( P @ X @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mexists) ).
thf(mfalse,definition,
( mfalse
= ( ^ [X: $i] : $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mfalse) ).
thf(miff,definition,
( miff
= ( ^ [U: $i > $o,V: $i > $o] : ( mand @ ( mimpl @ U @ V ) @ ( mimpl @ V @ U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',miff) ).
thf(mimpl,definition,
( mimpl
= ( ^ [U: $i > $o,V: $i > $o] : ( mor @ ( mnot @ U ) @ V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimpl) ).
thf(minvalid,definition,
( minvalid
= ( ^ [P: $i > $o] :
! [W: $i] :
~ ( P @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',minvalid) ).
thf(mnot,definition,
( mnot
= ( ^ [X: $i > $o,U: $i] :
~ ( X @ U ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot) ).
thf(mor,definition,
( mor
= ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
( ( X @ U )
| ( Y @ U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor) ).
thf(msatisfiable,definition,
( msatisfiable
= ( ^ [P: $i > $o] :
? [W: $i] : ( P @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',msatisfiable) ).
thf(mtrue,definition,
( mtrue
= ( ^ [X: $i] : $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mtrue) ).
thf(mvalid,definition,
( mvalid
= ( ^ [P: $i > $o] :
! [W: $i] : ( P @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mvalid) ).
thf(1,axiom,
! [A: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ reli @ ( mbox @ relr @ A ) ) @ ( mbox @ relr @ ( mbox @ reli @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_i_r_commute) ).
thf(2,axiom,
! [A: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ relr @ A ) @ ( mbox @ relr @ ( mbox @ relr @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',trans_axiom_r) ).
thf(3,axiom,
! [A: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ reli @ A ) @ ( mbox @ reli @ ( mbox @ reli @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',trans_axiom_i) ).
thf(4,axiom,
! [A: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ relr @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',refl_axiom_r) ).
thf(5,axiom,
! [A: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ reli @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',refl_axiom_i) ).
thf(6,conjecture,
! [A: $i > $o] : ( cs4_valid @ ( cs4_impl @ ( cs4_box @ ( cs4_atom @ A ) ) @ ( cs4_atom @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cs4_refl) ).
thf(7,negated_conjecture,
( ( ! [A: $i > $o] : ( cs4_valid @ ( cs4_impl @ ( cs4_box @ ( cs4_atom @ A ) ) @ ( cs4_atom @ A ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[6]) ).
thf(8,plain,
( ( ! [SY0: $i > $o,SY57: $i,SY58: $i] :
( ( reli @ SY57 @ SY58 )
=> ( ~ ! [SY43: $i] :
( ( reli @ SY58 @ SY43 )
=> ! [SY17: $i] :
( ( relr @ SY43 @ SY17 )
=> ! [SY14: $i] :
( ( reli @ SY17 @ SY14 )
=> ( SY0 @ SY14 ) ) ) )
| ! [SY56: $i] :
( ( reli @ SY58 @ SY56 )
=> ( SY0 @ SY56 ) ) ) ) )
= $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,
( ( ! [SY70: $i > $o,SY109: $i] :
( ~ ! [SY110: $i] :
( ( reli @ SY109 @ SY110 )
=> ! [SY81: $i] :
( ( relr @ SY110 @ SY81 )
=> ( SY70 @ SY81 ) ) )
| ! [SY112: $i] :
( ( relr @ SY109 @ SY112 )
=> ! [SY103: $i] :
( ( reli @ SY112 @ SY103 )
=> ( SY70 @ SY103 ) ) ) ) )
= $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,
( ( ! [SY120: $i > $o,SY149: $i] :
( ~ ! [SY150: $i] :
( ( relr @ SY149 @ SY150 )
=> ( SY120 @ SY150 ) )
| ! [SY151: $i] :
( ( relr @ SY149 @ SY151 )
=> ! [SY144: $i] :
( ( relr @ SY151 @ SY144 )
=> ( SY120 @ SY144 ) ) ) ) )
= $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,
( ( ! [SY158: $i > $o,SY187: $i] :
( ~ ! [SY188: $i] :
( ( reli @ SY187 @ SY188 )
=> ( SY158 @ SY188 ) )
| ! [SY189: $i] :
( ( reli @ SY187 @ SY189 )
=> ! [SY182: $i] :
( ( reli @ SY189 @ SY182 )
=> ( SY158 @ SY182 ) ) ) ) )
= $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,
( ( ! [SY196: $i > $o,SY212: $i] :
( ~ ! [SY213: $i] :
( ( relr @ SY212 @ SY213 )
=> ( SY196 @ SY213 ) )
| ( SY196 @ SY212 ) ) )
= $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,
( ( ! [SY217: $i > $o,SY233: $i] :
( ~ ! [SY234: $i] :
( ( reli @ SY233 @ SY234 )
=> ( SY217 @ SY234 ) )
| ( SY217 @ SY233 ) ) )
= $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,
( ( ! [SY238: $i,SY239: $i] :
( ( reli @ SY238 @ SY239 )
=> ( ~ ! [SY240: $i] :
( ( reli @ SY239 @ SY240 )
=> ! [SY241: $i] :
( ( relr @ SY240 @ SY241 )
=> ! [SY242: $i] :
( ( reli @ SY241 @ SY242 )
=> ( sK1_SY0 @ SY242 ) ) ) )
| ! [SY243: $i] :
( ( reli @ SY239 @ SY243 )
=> ( sK1_SY0 @ SY243 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[8]) ).
thf(15,plain,
( ( ! [SY244: $i] :
( ( reli @ sK2_SY238 @ SY244 )
=> ( ~ ! [SY240: $i] :
( ( reli @ SY244 @ SY240 )
=> ! [SY241: $i] :
( ( relr @ SY240 @ SY241 )
=> ! [SY242: $i] :
( ( reli @ SY241 @ SY242 )
=> ( sK1_SY0 @ SY242 ) ) ) )
| ! [SY243: $i] :
( ( reli @ SY244 @ SY243 )
=> ( sK1_SY0 @ SY243 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[14]) ).
thf(16,plain,
( ( ( reli @ sK2_SY238 @ sK3_SY244 )
=> ( ~ ! [SY249: $i] :
( ( reli @ sK3_SY244 @ SY249 )
=> ! [SY241: $i] :
( ( relr @ SY249 @ SY241 )
=> ! [SY242: $i] :
( ( reli @ SY241 @ SY242 )
=> ( sK1_SY0 @ SY242 ) ) ) )
| ! [SY252: $i] :
( ( reli @ sK3_SY244 @ SY252 )
=> ( sK1_SY0 @ SY252 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[15]) ).
thf(17,plain,
( ( reli @ sK2_SY238 @ sK3_SY244 )
= $true ),
inference(standard_cnf,[status(thm)],[16]) ).
thf(18,plain,
( ( ~ ! [SY249: $i] :
( ( reli @ sK3_SY244 @ SY249 )
=> ! [SY241: $i] :
( ( relr @ SY249 @ SY241 )
=> ! [SY242: $i] :
( ( reli @ SY241 @ SY242 )
=> ( sK1_SY0 @ SY242 ) ) ) )
| ! [SY252: $i] :
( ( reli @ sK3_SY244 @ SY252 )
=> ( sK1_SY0 @ SY252 ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[16]) ).
thf(19,plain,
( ( ~ ( ~ ! [SY249: $i] :
( ( reli @ sK3_SY244 @ SY249 )
=> ! [SY241: $i] :
( ( relr @ SY249 @ SY241 )
=> ! [SY242: $i] :
( ( reli @ SY241 @ SY242 )
=> ( sK1_SY0 @ SY242 ) ) ) )
| ! [SY252: $i] :
( ( reli @ sK3_SY244 @ SY252 )
=> ( sK1_SY0 @ SY252 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[18]) ).
thf(20,plain,
( ( ! [SY217: $i > $o,SY233: $i] :
( ~ ! [SY234: $i] :
( ( reli @ SY233 @ SY234 )
=> ( SY217 @ SY234 ) )
| ( SY217 @ SY233 ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(21,plain,
( ( ! [SY196: $i > $o,SY212: $i] :
( ~ ! [SY213: $i] :
( ( relr @ SY212 @ SY213 )
=> ( SY196 @ SY213 ) )
| ( SY196 @ SY212 ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(22,plain,
( ( ! [SY158: $i > $o,SY187: $i] :
( ~ ! [SY188: $i] :
( ( reli @ SY187 @ SY188 )
=> ( SY158 @ SY188 ) )
| ! [SY189: $i] :
( ( reli @ SY187 @ SY189 )
=> ! [SY182: $i] :
( ( reli @ SY189 @ SY182 )
=> ( SY158 @ SY182 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(23,plain,
( ( ! [SY120: $i > $o,SY149: $i] :
( ~ ! [SY150: $i] :
( ( relr @ SY149 @ SY150 )
=> ( SY120 @ SY150 ) )
| ! [SY151: $i] :
( ( relr @ SY149 @ SY151 )
=> ! [SY144: $i] :
( ( relr @ SY151 @ SY144 )
=> ( SY120 @ SY144 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(24,plain,
( ( ! [SY70: $i > $o,SY109: $i] :
( ~ ! [SY110: $i] :
( ( reli @ SY109 @ SY110 )
=> ! [SY81: $i] :
( ( relr @ SY110 @ SY81 )
=> ( SY70 @ SY81 ) ) )
| ! [SY112: $i] :
( ( relr @ SY109 @ SY112 )
=> ! [SY103: $i] :
( ( reli @ SY112 @ SY103 )
=> ( SY70 @ SY103 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(25,plain,
( ( reli @ sK2_SY238 @ sK3_SY244 )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(26,plain,
( ( ~ ( ~ ! [SY249: $i] :
( ( reli @ sK3_SY244 @ SY249 )
=> ! [SY241: $i] :
( ( relr @ SY249 @ SY241 )
=> ! [SY242: $i] :
( ( reli @ SY241 @ SY242 )
=> ( sK1_SY0 @ SY242 ) ) ) )
| ! [SY252: $i] :
( ( reli @ sK3_SY244 @ SY252 )
=> ( sK1_SY0 @ SY252 ) ) ) )
= $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_SY244 @ SX0 )
| ! [SX1: $i] :
( ~ ( relr @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( reli @ SX1 @ SX2 )
| ( sK1_SY0 @ SX2 ) ) ) )
| ! [SX0: $i] :
( ~ ( reli @ sK3_SY244 @ SX0 )
| ( sK1_SY0 @ SX0 ) ) ) )
= $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] :
( ( ! [SY253: $i] :
( ~ ! [SY254: $i] :
( ~ ( reli @ SY253 @ SY254 )
| ( SV1 @ SY254 ) )
| ( SV1 @ SY253 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(34,plain,
( ( ~ ! [SX0: $i] :
( ~ ( reli @ sK3_SY244 @ SX0 )
| ! [SX1: $i] :
( ~ ( relr @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( reli @ SX1 @ SX2 )
| ( sK1_SY0 @ SX2 ) ) ) )
| ! [SX0: $i] :
( ~ ( reli @ sK3_SY244 @ SX0 )
| ( sK1_SY0 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(35,plain,
! [SV2: $i > $o] :
( ( ! [SY255: $i] :
( ~ ! [SY256: $i] :
( ~ ( relr @ SY255 @ SY256 )
| ( SV2 @ SY256 ) )
| ( SV2 @ SY255 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(36,plain,
! [SV3: $i > $o] :
( ( ! [SY257: $i] :
( ~ ! [SY258: $i] :
( ~ ( reli @ SY257 @ SY258 )
| ! [SY259: $i] :
( ~ ( relr @ SY258 @ SY259 )
| ( SV3 @ SY259 ) ) )
| ! [SY260: $i] :
( ~ ( relr @ SY257 @ SY260 )
| ! [SY261: $i] :
( ~ ( reli @ SY260 @ SY261 )
| ( SV3 @ SY261 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(37,plain,
! [SV4: $i > $o] :
( ( ! [SY262: $i] :
( ~ ! [SY263: $i] :
( ~ ( relr @ SY262 @ SY263 )
| ( SV4 @ SY263 ) )
| ! [SY264: $i] :
( ~ ( relr @ SY262 @ SY264 )
| ! [SY265: $i] :
( ~ ( relr @ SY264 @ SY265 )
| ( SV4 @ SY265 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(38,plain,
! [SV5: $i > $o] :
( ( ! [SY266: $i] :
( ~ ! [SY267: $i] :
( ~ ( reli @ SY266 @ SY267 )
| ( SV5 @ SY267 ) )
| ! [SY268: $i] :
( ~ ( reli @ SY266 @ SY268 )
| ! [SY269: $i] :
( ~ ( reli @ SY268 @ SY269 )
| ( SV5 @ SY269 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(39,plain,
! [SV1: $i > $o,SV6: $i] :
( ( ~ ! [SY270: $i] :
( ~ ( reli @ SV6 @ SY270 )
| ( SV1 @ SY270 ) )
| ( SV1 @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(40,plain,
( ( ~ ! [SX0: $i] :
( ~ ( reli @ sK3_SY244 @ SX0 )
| ! [SX1: $i] :
( ~ ( relr @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( reli @ SX1 @ SX2 )
| ( sK1_SY0 @ SX2 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[34]) ).
thf(41,plain,
( ( ! [SX0: $i] :
( ~ ( reli @ sK3_SY244 @ SX0 )
| ( sK1_SY0 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[34]) ).
thf(42,plain,
! [SV2: $i > $o,SV7: $i] :
( ( ~ ! [SY271: $i] :
( ~ ( relr @ SV7 @ SY271 )
| ( SV2 @ SY271 ) )
| ( SV2 @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(43,plain,
! [SV3: $i > $o,SV8: $i] :
( ( ~ ! [SY272: $i] :
( ~ ( reli @ SV8 @ SY272 )
| ! [SY259: $i] :
( ~ ( relr @ SY272 @ SY259 )
| ( SV3 @ SY259 ) ) )
| ! [SY274: $i] :
( ~ ( relr @ SV8 @ SY274 )
| ! [SY261: $i] :
( ~ ( reli @ SY274 @ SY261 )
| ( SV3 @ SY261 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(44,plain,
! [SV4: $i > $o,SV9: $i] :
( ( ~ ! [SY276: $i] :
( ~ ( relr @ SV9 @ SY276 )
| ( SV4 @ SY276 ) )
| ! [SY277: $i] :
( ~ ( relr @ SV9 @ SY277 )
| ! [SY265: $i] :
( ~ ( relr @ SY277 @ SY265 )
| ( SV4 @ SY265 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(45,plain,
! [SV5: $i > $o,SV10: $i] :
( ( ~ ! [SY279: $i] :
( ~ ( reli @ SV10 @ SY279 )
| ( SV5 @ SY279 ) )
| ! [SY280: $i] :
( ~ ( reli @ SV10 @ SY280 )
| ! [SY269: $i] :
( ~ ( reli @ SY280 @ SY269 )
| ( SV5 @ SY269 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(46,plain,
! [SV1: $i > $o,SV6: $i] :
( ( ( ~ ! [SY270: $i] :
( ~ ( reli @ SV6 @ SY270 )
| ( SV1 @ SY270 ) ) )
= $true )
| ( ( SV1 @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[39]) ).
thf(47,plain,
( ( ! [SX0: $i] :
( ~ ( reli @ sK3_SY244 @ SX0 )
| ! [SX1: $i] :
( ~ ( relr @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( reli @ SX1 @ SX2 )
| ( sK1_SY0 @ SX2 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[40]) ).
thf(48,plain,
( ( ~ ( reli @ sK3_SY244 @ sK4_SX0 )
| ( sK1_SY0 @ sK4_SX0 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[41]) ).
thf(49,plain,
! [SV2: $i > $o,SV7: $i] :
( ( ( ~ ! [SY271: $i] :
( ~ ( relr @ SV7 @ SY271 )
| ( SV2 @ SY271 ) ) )
= $true )
| ( ( SV2 @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[42]) ).
thf(50,plain,
! [SV3: $i > $o,SV8: $i] :
( ( ( ~ ! [SY272: $i] :
( ~ ( reli @ SV8 @ SY272 )
| ! [SY259: $i] :
( ~ ( relr @ SY272 @ SY259 )
| ( SV3 @ SY259 ) ) ) )
= $true )
| ( ( ! [SY274: $i] :
( ~ ( relr @ SV8 @ SY274 )
| ! [SY261: $i] :
( ~ ( reli @ SY274 @ SY261 )
| ( SV3 @ SY261 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[43]) ).
thf(51,plain,
! [SV4: $i > $o,SV9: $i] :
( ( ( ~ ! [SY276: $i] :
( ~ ( relr @ SV9 @ SY276 )
| ( SV4 @ SY276 ) ) )
= $true )
| ( ( ! [SY277: $i] :
( ~ ( relr @ SV9 @ SY277 )
| ! [SY265: $i] :
( ~ ( relr @ SY277 @ SY265 )
| ( SV4 @ SY265 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[44]) ).
thf(52,plain,
! [SV5: $i > $o,SV10: $i] :
( ( ( ~ ! [SY279: $i] :
( ~ ( reli @ SV10 @ SY279 )
| ( SV5 @ SY279 ) ) )
= $true )
| ( ( ! [SY280: $i] :
( ~ ( reli @ SV10 @ SY280 )
| ! [SY269: $i] :
( ~ ( reli @ SY280 @ SY269 )
| ( SV5 @ SY269 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[45]) ).
thf(53,plain,
! [SV1: $i > $o,SV6: $i] :
( ( ( ! [SY270: $i] :
( ~ ( reli @ SV6 @ SY270 )
| ( SV1 @ SY270 ) ) )
= $false )
| ( ( SV1 @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(54,plain,
! [SV11: $i] :
( ( ~ ( reli @ sK3_SY244 @ SV11 )
| ! [SY282: $i] :
( ~ ( relr @ SV11 @ SY282 )
| ! [SX2: $i] :
( ~ ( reli @ SY282 @ SX2 )
| ( sK1_SY0 @ SX2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(55,plain,
( ( ~ ( reli @ sK3_SY244 @ sK4_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[48]) ).
thf(56,plain,
( ( sK1_SY0 @ sK4_SX0 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[48]) ).
thf(57,plain,
! [SV2: $i > $o,SV7: $i] :
( ( ( ! [SY271: $i] :
( ~ ( relr @ SV7 @ SY271 )
| ( SV2 @ SY271 ) ) )
= $false )
| ( ( SV2 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(58,plain,
! [SV3: $i > $o,SV8: $i] :
( ( ( ! [SY272: $i] :
( ~ ( reli @ SV8 @ SY272 )
| ! [SY259: $i] :
( ~ ( relr @ SY272 @ SY259 )
| ( SV3 @ SY259 ) ) ) )
= $false )
| ( ( ! [SY274: $i] :
( ~ ( relr @ SV8 @ SY274 )
| ! [SY261: $i] :
( ~ ( reli @ SY274 @ SY261 )
| ( SV3 @ SY261 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(59,plain,
! [SV4: $i > $o,SV9: $i] :
( ( ( ! [SY276: $i] :
( ~ ( relr @ SV9 @ SY276 )
| ( SV4 @ SY276 ) ) )
= $false )
| ( ( ! [SY277: $i] :
( ~ ( relr @ SV9 @ SY277 )
| ! [SY265: $i] :
( ~ ( relr @ SY277 @ SY265 )
| ( SV4 @ SY265 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(60,plain,
! [SV5: $i > $o,SV10: $i] :
( ( ( ! [SY279: $i] :
( ~ ( reli @ SV10 @ SY279 )
| ( SV5 @ SY279 ) ) )
= $false )
| ( ( ! [SY280: $i] :
( ~ ( reli @ SV10 @ SY280 )
| ! [SY269: $i] :
( ~ ( reli @ SY280 @ SY269 )
| ( SV5 @ SY269 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(61,plain,
! [SV1: $i > $o,SV6: $i] :
( ( ( ~ ( reli @ SV6 @ ( sK5_SY270 @ SV1 @ SV6 ) )
| ( SV1 @ ( sK5_SY270 @ SV1 @ SV6 ) ) )
= $false )
| ( ( SV1 @ SV6 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[53]) ).
thf(62,plain,
! [SV11: $i] :
( ( ( ~ ( reli @ sK3_SY244 @ SV11 ) )
= $true )
| ( ( ! [SY282: $i] :
( ~ ( relr @ SV11 @ SY282 )
| ! [SX2: $i] :
( ~ ( reli @ SY282 @ SX2 )
| ( sK1_SY0 @ SX2 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[54]) ).
thf(63,plain,
( ( reli @ sK3_SY244 @ sK4_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[55]) ).
thf(64,plain,
! [SV2: $i > $o,SV7: $i] :
( ( ( ~ ( relr @ SV7 @ ( sK6_SY271 @ SV2 @ SV7 ) )
| ( SV2 @ ( sK6_SY271 @ SV2 @ SV7 ) ) )
= $false )
| ( ( SV2 @ SV7 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[57]) ).
thf(65,plain,
! [SV3: $i > $o,SV8: $i] :
( ( ( ~ ( reli @ SV8 @ ( sK7_SY272 @ SV3 @ SV8 ) )
| ! [SY284: $i] :
( ~ ( relr @ ( sK7_SY272 @ SV3 @ SV8 ) @ SY284 )
| ( SV3 @ SY284 ) ) )
= $false )
| ( ( ! [SY274: $i] :
( ~ ( relr @ SV8 @ SY274 )
| ! [SY261: $i] :
( ~ ( reli @ SY274 @ SY261 )
| ( SV3 @ SY261 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[58]) ).
thf(66,plain,
! [SV4: $i > $o,SV9: $i] :
( ( ( ~ ( relr @ SV9 @ ( sK8_SY276 @ SV4 @ SV9 ) )
| ( SV4 @ ( sK8_SY276 @ SV4 @ SV9 ) ) )
= $false )
| ( ( ! [SY277: $i] :
( ~ ( relr @ SV9 @ SY277 )
| ! [SY265: $i] :
( ~ ( relr @ SY277 @ SY265 )
| ( SV4 @ SY265 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[59]) ).
thf(67,plain,
! [SV5: $i > $o,SV10: $i] :
( ( ( ~ ( reli @ SV10 @ ( sK9_SY279 @ SV5 @ SV10 ) )
| ( SV5 @ ( sK9_SY279 @ SV5 @ SV10 ) ) )
= $false )
| ( ( ! [SY280: $i] :
( ~ ( reli @ SV10 @ SY280 )
| ! [SY269: $i] :
( ~ ( reli @ SY280 @ SY269 )
| ( SV5 @ SY269 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[60]) ).
thf(68,plain,
! [SV1: $i > $o,SV6: $i] :
( ( ( ~ ( reli @ SV6 @ ( sK5_SY270 @ SV1 @ SV6 ) ) )
= $false )
| ( ( SV1 @ SV6 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[61]) ).
thf(69,plain,
! [SV6: $i,SV1: $i > $o] :
( ( ( SV1 @ ( sK5_SY270 @ SV1 @ SV6 ) )
= $false )
| ( ( SV1 @ SV6 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[61]) ).
thf(70,plain,
! [SV11: $i] :
( ( ( reli @ sK3_SY244 @ SV11 )
= $false )
| ( ( ! [SY282: $i] :
( ~ ( relr @ SV11 @ SY282 )
| ! [SX2: $i] :
( ~ ( reli @ SY282 @ SX2 )
| ( sK1_SY0 @ SX2 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(71,plain,
! [SV2: $i > $o,SV7: $i] :
( ( ( ~ ( relr @ SV7 @ ( sK6_SY271 @ SV2 @ SV7 ) ) )
= $false )
| ( ( SV2 @ SV7 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[64]) ).
thf(72,plain,
! [SV7: $i,SV2: $i > $o] :
( ( ( SV2 @ ( sK6_SY271 @ SV2 @ SV7 ) )
= $false )
| ( ( SV2 @ SV7 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[64]) ).
thf(73,plain,
! [SV3: $i > $o,SV8: $i] :
( ( ( ~ ( reli @ SV8 @ ( sK7_SY272 @ SV3 @ SV8 ) ) )
= $false )
| ( ( ! [SY274: $i] :
( ~ ( relr @ SV8 @ SY274 )
| ! [SY261: $i] :
( ~ ( reli @ SY274 @ SY261 )
| ( SV3 @ SY261 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[65]) ).
thf(74,plain,
! [SV8: $i,SV3: $i > $o] :
( ( ( ! [SY284: $i] :
( ~ ( relr @ ( sK7_SY272 @ SV3 @ SV8 ) @ SY284 )
| ( SV3 @ SY284 ) ) )
= $false )
| ( ( ! [SY274: $i] :
( ~ ( relr @ SV8 @ SY274 )
| ! [SY261: $i] :
( ~ ( reli @ SY274 @ SY261 )
| ( SV3 @ SY261 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[65]) ).
thf(75,plain,
! [SV4: $i > $o,SV9: $i] :
( ( ( ~ ( relr @ SV9 @ ( sK8_SY276 @ SV4 @ SV9 ) ) )
= $false )
| ( ( ! [SY277: $i] :
( ~ ( relr @ SV9 @ SY277 )
| ! [SY265: $i] :
( ~ ( relr @ SY277 @ SY265 )
| ( SV4 @ SY265 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[66]) ).
thf(76,plain,
! [SV9: $i,SV4: $i > $o] :
( ( ( SV4 @ ( sK8_SY276 @ SV4 @ SV9 ) )
= $false )
| ( ( ! [SY277: $i] :
( ~ ( relr @ SV9 @ SY277 )
| ! [SY265: $i] :
( ~ ( relr @ SY277 @ SY265 )
| ( SV4 @ SY265 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[66]) ).
thf(77,plain,
! [SV5: $i > $o,SV10: $i] :
( ( ( ~ ( reli @ SV10 @ ( sK9_SY279 @ SV5 @ SV10 ) ) )
= $false )
| ( ( ! [SY280: $i] :
( ~ ( reli @ SV10 @ SY280 )
| ! [SY269: $i] :
( ~ ( reli @ SY280 @ SY269 )
| ( SV5 @ SY269 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[67]) ).
thf(78,plain,
! [SV10: $i,SV5: $i > $o] :
( ( ( SV5 @ ( sK9_SY279 @ SV5 @ SV10 ) )
= $false )
| ( ( ! [SY280: $i] :
( ~ ( reli @ SV10 @ SY280 )
| ! [SY269: $i] :
( ~ ( reli @ SY280 @ SY269 )
| ( SV5 @ SY269 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[67]) ).
thf(79,plain,
! [SV1: $i > $o,SV6: $i] :
( ( ( reli @ SV6 @ ( sK5_SY270 @ SV1 @ SV6 ) )
= $true )
| ( ( SV1 @ SV6 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[68]) ).
thf(80,plain,
! [SV12: $i,SV11: $i] :
( ( ( ~ ( relr @ SV11 @ SV12 )
| ! [SY285: $i] :
( ~ ( reli @ SV12 @ SY285 )
| ( sK1_SY0 @ SY285 ) ) )
= $true )
| ( ( reli @ sK3_SY244 @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(81,plain,
! [SV2: $i > $o,SV7: $i] :
( ( ( relr @ SV7 @ ( sK6_SY271 @ SV2 @ SV7 ) )
= $true )
| ( ( SV2 @ SV7 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[71]) ).
thf(82,plain,
! [SV3: $i > $o,SV8: $i] :
( ( ( reli @ SV8 @ ( sK7_SY272 @ SV3 @ SV8 ) )
= $true )
| ( ( ! [SY274: $i] :
( ~ ( relr @ SV8 @ SY274 )
| ! [SY261: $i] :
( ~ ( reli @ SY274 @ SY261 )
| ( SV3 @ SY261 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[73]) ).
thf(83,plain,
! [SV8: $i,SV3: $i > $o] :
( ( ( ~ ( relr @ ( sK7_SY272 @ SV3 @ SV8 ) @ ( sK10_SY284 @ SV8 @ SV3 ) )
| ( SV3 @ ( sK10_SY284 @ SV8 @ SV3 ) ) )
= $false )
| ( ( ! [SY274: $i] :
( ~ ( relr @ SV8 @ SY274 )
| ! [SY261: $i] :
( ~ ( reli @ SY274 @ SY261 )
| ( SV3 @ SY261 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[74]) ).
thf(84,plain,
! [SV4: $i > $o,SV9: $i] :
( ( ( relr @ SV9 @ ( sK8_SY276 @ SV4 @ SV9 ) )
= $true )
| ( ( ! [SY277: $i] :
( ~ ( relr @ SV9 @ SY277 )
| ! [SY265: $i] :
( ~ ( relr @ SY277 @ SY265 )
| ( SV4 @ SY265 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[75]) ).
thf(85,plain,
! [SV4: $i > $o,SV13: $i,SV9: $i] :
( ( ( ~ ( relr @ SV9 @ SV13 )
| ! [SY286: $i] :
( ~ ( relr @ SV13 @ SY286 )
| ( SV4 @ SY286 ) ) )
= $true )
| ( ( SV4 @ ( sK8_SY276 @ SV4 @ SV9 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(86,plain,
! [SV5: $i > $o,SV10: $i] :
( ( ( reli @ SV10 @ ( sK9_SY279 @ SV5 @ SV10 ) )
= $true )
| ( ( ! [SY280: $i] :
( ~ ( reli @ SV10 @ SY280 )
| ! [SY269: $i] :
( ~ ( reli @ SY280 @ SY269 )
| ( SV5 @ SY269 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[77]) ).
thf(87,plain,
! [SV5: $i > $o,SV14: $i,SV10: $i] :
( ( ( ~ ( reli @ SV10 @ SV14 )
| ! [SY287: $i] :
( ~ ( reli @ SV14 @ SY287 )
| ( SV5 @ SY287 ) ) )
= $true )
| ( ( SV5 @ ( sK9_SY279 @ SV5 @ SV10 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(88,plain,
! [SV12: $i,SV11: $i] :
( ( ( ~ ( relr @ SV11 @ SV12 ) )
= $true )
| ( ( ! [SY285: $i] :
( ~ ( reli @ SV12 @ SY285 )
| ( sK1_SY0 @ SY285 ) ) )
= $true )
| ( ( reli @ sK3_SY244 @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[80]) ).
thf(89,plain,
! [SV3: $i > $o,SV15: $i,SV8: $i] :
( ( ( ~ ( relr @ SV8 @ SV15 )
| ! [SY288: $i] :
( ~ ( reli @ SV15 @ SY288 )
| ( SV3 @ SY288 ) ) )
= $true )
| ( ( reli @ SV8 @ ( sK7_SY272 @ SV3 @ SV8 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(90,plain,
! [SV8: $i,SV3: $i > $o] :
( ( ( ~ ( relr @ ( sK7_SY272 @ SV3 @ SV8 ) @ ( sK10_SY284 @ SV8 @ SV3 ) ) )
= $false )
| ( ( ! [SY274: $i] :
( ~ ( relr @ SV8 @ SY274 )
| ! [SY261: $i] :
( ~ ( reli @ SY274 @ SY261 )
| ( SV3 @ SY261 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[83]) ).
thf(91,plain,
! [SV8: $i,SV3: $i > $o] :
( ( ( SV3 @ ( sK10_SY284 @ SV8 @ SV3 ) )
= $false )
| ( ( ! [SY274: $i] :
( ~ ( relr @ SV8 @ SY274 )
| ! [SY261: $i] :
( ~ ( reli @ SY274 @ SY261 )
| ( SV3 @ SY261 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[83]) ).
thf(92,plain,
! [SV4: $i > $o,SV16: $i,SV9: $i] :
( ( ( ~ ( relr @ SV9 @ SV16 )
| ! [SY289: $i] :
( ~ ( relr @ SV16 @ SY289 )
| ( SV4 @ SY289 ) ) )
= $true )
| ( ( relr @ SV9 @ ( sK8_SY276 @ SV4 @ SV9 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(93,plain,
! [SV4: $i > $o,SV13: $i,SV9: $i] :
( ( ( ~ ( relr @ SV9 @ SV13 ) )
= $true )
| ( ( ! [SY286: $i] :
( ~ ( relr @ SV13 @ SY286 )
| ( SV4 @ SY286 ) ) )
= $true )
| ( ( SV4 @ ( sK8_SY276 @ SV4 @ SV9 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[85]) ).
thf(94,plain,
! [SV5: $i > $o,SV17: $i,SV10: $i] :
( ( ( ~ ( reli @ SV10 @ SV17 )
| ! [SY290: $i] :
( ~ ( reli @ SV17 @ SY290 )
| ( SV5 @ SY290 ) ) )
= $true )
| ( ( reli @ SV10 @ ( sK9_SY279 @ SV5 @ SV10 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(95,plain,
! [SV5: $i > $o,SV14: $i,SV10: $i] :
( ( ( ~ ( reli @ SV10 @ SV14 ) )
= $true )
| ( ( ! [SY287: $i] :
( ~ ( reli @ SV14 @ SY287 )
| ( SV5 @ SY287 ) ) )
= $true )
| ( ( SV5 @ ( sK9_SY279 @ SV5 @ SV10 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[87]) ).
thf(96,plain,
! [SV12: $i,SV11: $i] :
( ( ( relr @ SV11 @ SV12 )
= $false )
| ( ( ! [SY285: $i] :
( ~ ( reli @ SV12 @ SY285 )
| ( sK1_SY0 @ SY285 ) ) )
= $true )
| ( ( reli @ sK3_SY244 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(97,plain,
! [SV3: $i > $o,SV15: $i,SV8: $i] :
( ( ( ~ ( relr @ SV8 @ SV15 ) )
= $true )
| ( ( ! [SY288: $i] :
( ~ ( reli @ SV15 @ SY288 )
| ( SV3 @ SY288 ) ) )
= $true )
| ( ( reli @ SV8 @ ( sK7_SY272 @ SV3 @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[89]) ).
thf(98,plain,
! [SV8: $i,SV3: $i > $o] :
( ( ( relr @ ( sK7_SY272 @ SV3 @ SV8 ) @ ( sK10_SY284 @ SV8 @ SV3 ) )
= $true )
| ( ( ! [SY274: $i] :
( ~ ( relr @ SV8 @ SY274 )
| ! [SY261: $i] :
( ~ ( reli @ SY274 @ SY261 )
| ( SV3 @ SY261 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[90]) ).
thf(99,plain,
! [SV3: $i > $o,SV18: $i,SV8: $i] :
( ( ( ~ ( relr @ SV8 @ SV18 )
| ! [SY291: $i] :
( ~ ( reli @ SV18 @ SY291 )
| ( SV3 @ SY291 ) ) )
= $true )
| ( ( SV3 @ ( sK10_SY284 @ SV8 @ SV3 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(100,plain,
! [SV4: $i > $o,SV16: $i,SV9: $i] :
( ( ( ~ ( relr @ SV9 @ SV16 ) )
= $true )
| ( ( ! [SY289: $i] :
( ~ ( relr @ SV16 @ SY289 )
| ( SV4 @ SY289 ) ) )
= $true )
| ( ( relr @ SV9 @ ( sK8_SY276 @ SV4 @ SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[92]) ).
thf(101,plain,
! [SV4: $i > $o,SV13: $i,SV9: $i] :
( ( ( relr @ SV9 @ SV13 )
= $false )
| ( ( ! [SY286: $i] :
( ~ ( relr @ SV13 @ SY286 )
| ( SV4 @ SY286 ) ) )
= $true )
| ( ( SV4 @ ( sK8_SY276 @ SV4 @ SV9 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(102,plain,
! [SV5: $i > $o,SV17: $i,SV10: $i] :
( ( ( ~ ( reli @ SV10 @ SV17 ) )
= $true )
| ( ( ! [SY290: $i] :
( ~ ( reli @ SV17 @ SY290 )
| ( SV5 @ SY290 ) ) )
= $true )
| ( ( reli @ SV10 @ ( sK9_SY279 @ SV5 @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(103,plain,
! [SV5: $i > $o,SV14: $i,SV10: $i] :
( ( ( reli @ SV10 @ SV14 )
= $false )
| ( ( ! [SY287: $i] :
( ~ ( reli @ SV14 @ SY287 )
| ( SV5 @ SY287 ) ) )
= $true )
| ( ( SV5 @ ( sK9_SY279 @ SV5 @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(104,plain,
! [SV11: $i,SV19: $i,SV12: $i] :
( ( ( ~ ( reli @ SV12 @ SV19 )
| ( sK1_SY0 @ SV19 ) )
= $true )
| ( ( relr @ SV11 @ SV12 )
= $false )
| ( ( reli @ sK3_SY244 @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(105,plain,
! [SV3: $i > $o,SV15: $i,SV8: $i] :
( ( ( relr @ SV8 @ SV15 )
= $false )
| ( ( ! [SY288: $i] :
( ~ ( reli @ SV15 @ SY288 )
| ( SV3 @ SY288 ) ) )
= $true )
| ( ( reli @ SV8 @ ( sK7_SY272 @ SV3 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[97]) ).
thf(106,plain,
! [SV3: $i > $o,SV20: $i,SV8: $i] :
( ( ( ~ ( relr @ SV8 @ SV20 )
| ! [SY292: $i] :
( ~ ( reli @ SV20 @ SY292 )
| ( SV3 @ SY292 ) ) )
= $true )
| ( ( relr @ ( sK7_SY272 @ SV3 @ SV8 ) @ ( sK10_SY284 @ SV8 @ SV3 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(107,plain,
! [SV3: $i > $o,SV18: $i,SV8: $i] :
( ( ( ~ ( relr @ SV8 @ SV18 ) )
= $true )
| ( ( ! [SY291: $i] :
( ~ ( reli @ SV18 @ SY291 )
| ( SV3 @ SY291 ) ) )
= $true )
| ( ( SV3 @ ( sK10_SY284 @ SV8 @ SV3 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[99]) ).
thf(108,plain,
! [SV4: $i > $o,SV16: $i,SV9: $i] :
( ( ( relr @ SV9 @ SV16 )
= $false )
| ( ( ! [SY289: $i] :
( ~ ( relr @ SV16 @ SY289 )
| ( SV4 @ SY289 ) ) )
= $true )
| ( ( relr @ SV9 @ ( sK8_SY276 @ SV4 @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(109,plain,
! [SV9: $i,SV4: $i > $o,SV21: $i,SV13: $i] :
( ( ( ~ ( relr @ SV13 @ SV21 )
| ( SV4 @ SV21 ) )
= $true )
| ( ( relr @ SV9 @ SV13 )
= $false )
| ( ( SV4 @ ( sK8_SY276 @ SV4 @ SV9 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(110,plain,
! [SV5: $i > $o,SV17: $i,SV10: $i] :
( ( ( reli @ SV10 @ SV17 )
= $false )
| ( ( ! [SY290: $i] :
( ~ ( reli @ SV17 @ SY290 )
| ( SV5 @ SY290 ) ) )
= $true )
| ( ( reli @ SV10 @ ( sK9_SY279 @ SV5 @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(111,plain,
! [SV10: $i,SV5: $i > $o,SV22: $i,SV14: $i] :
( ( ( ~ ( reli @ SV14 @ SV22 )
| ( SV5 @ SV22 ) )
= $true )
| ( ( reli @ SV10 @ SV14 )
= $false )
| ( ( SV5 @ ( sK9_SY279 @ SV5 @ SV10 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(112,plain,
! [SV11: $i,SV19: $i,SV12: $i] :
( ( ( ~ ( reli @ SV12 @ SV19 ) )
= $true )
| ( ( sK1_SY0 @ SV19 )
= $true )
| ( ( relr @ SV11 @ SV12 )
= $false )
| ( ( reli @ sK3_SY244 @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[104]) ).
thf(113,plain,
! [SV8: $i,SV3: $i > $o,SV23: $i,SV15: $i] :
( ( ( ~ ( reli @ SV15 @ SV23 )
| ( SV3 @ SV23 ) )
= $true )
| ( ( relr @ SV8 @ SV15 )
= $false )
| ( ( reli @ SV8 @ ( sK7_SY272 @ SV3 @ SV8 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(114,plain,
! [SV3: $i > $o,SV20: $i,SV8: $i] :
( ( ( ~ ( relr @ SV8 @ SV20 ) )
= $true )
| ( ( ! [SY292: $i] :
( ~ ( reli @ SV20 @ SY292 )
| ( SV3 @ SY292 ) ) )
= $true )
| ( ( relr @ ( sK7_SY272 @ SV3 @ SV8 ) @ ( sK10_SY284 @ SV8 @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[106]) ).
thf(115,plain,
! [SV3: $i > $o,SV18: $i,SV8: $i] :
( ( ( relr @ SV8 @ SV18 )
= $false )
| ( ( ! [SY291: $i] :
( ~ ( reli @ SV18 @ SY291 )
| ( SV3 @ SY291 ) ) )
= $true )
| ( ( SV3 @ ( sK10_SY284 @ SV8 @ SV3 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(116,plain,
! [SV9: $i,SV4: $i > $o,SV24: $i,SV16: $i] :
( ( ( ~ ( relr @ SV16 @ SV24 )
| ( SV4 @ SV24 ) )
= $true )
| ( ( relr @ SV9 @ SV16 )
= $false )
| ( ( relr @ SV9 @ ( sK8_SY276 @ SV4 @ SV9 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(117,plain,
! [SV9: $i,SV4: $i > $o,SV21: $i,SV13: $i] :
( ( ( ~ ( relr @ SV13 @ SV21 ) )
= $true )
| ( ( SV4 @ SV21 )
= $true )
| ( ( relr @ SV9 @ SV13 )
= $false )
| ( ( SV4 @ ( sK8_SY276 @ SV4 @ SV9 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[109]) ).
thf(118,plain,
! [SV10: $i,SV5: $i > $o,SV25: $i,SV17: $i] :
( ( ( ~ ( reli @ SV17 @ SV25 )
| ( SV5 @ SV25 ) )
= $true )
| ( ( reli @ SV10 @ SV17 )
= $false )
| ( ( reli @ SV10 @ ( sK9_SY279 @ SV5 @ SV10 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(119,plain,
! [SV10: $i,SV5: $i > $o,SV22: $i,SV14: $i] :
( ( ( ~ ( reli @ SV14 @ SV22 ) )
= $true )
| ( ( SV5 @ SV22 )
= $true )
| ( ( reli @ SV10 @ SV14 )
= $false )
| ( ( SV5 @ ( sK9_SY279 @ SV5 @ SV10 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[111]) ).
thf(120,plain,
! [SV11: $i,SV19: $i,SV12: $i] :
( ( ( reli @ SV12 @ SV19 )
= $false )
| ( ( sK1_SY0 @ SV19 )
= $true )
| ( ( relr @ SV11 @ SV12 )
= $false )
| ( ( reli @ sK3_SY244 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(121,plain,
! [SV8: $i,SV3: $i > $o,SV23: $i,SV15: $i] :
( ( ( ~ ( reli @ SV15 @ SV23 ) )
= $true )
| ( ( SV3 @ SV23 )
= $true )
| ( ( relr @ SV8 @ SV15 )
= $false )
| ( ( reli @ SV8 @ ( sK7_SY272 @ SV3 @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[113]) ).
thf(122,plain,
! [SV3: $i > $o,SV20: $i,SV8: $i] :
( ( ( relr @ SV8 @ SV20 )
= $false )
| ( ( ! [SY292: $i] :
( ~ ( reli @ SV20 @ SY292 )
| ( SV3 @ SY292 ) ) )
= $true )
| ( ( relr @ ( sK7_SY272 @ SV3 @ SV8 ) @ ( sK10_SY284 @ SV8 @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[114]) ).
thf(123,plain,
! [SV8: $i,SV3: $i > $o,SV26: $i,SV18: $i] :
( ( ( ~ ( reli @ SV18 @ SV26 )
| ( SV3 @ SV26 ) )
= $true )
| ( ( relr @ SV8 @ SV18 )
= $false )
| ( ( SV3 @ ( sK10_SY284 @ SV8 @ SV3 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(124,plain,
! [SV9: $i,SV4: $i > $o,SV24: $i,SV16: $i] :
( ( ( ~ ( relr @ SV16 @ SV24 ) )
= $true )
| ( ( SV4 @ SV24 )
= $true )
| ( ( relr @ SV9 @ SV16 )
= $false )
| ( ( relr @ SV9 @ ( sK8_SY276 @ SV4 @ SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[116]) ).
thf(125,plain,
! [SV9: $i,SV4: $i > $o,SV21: $i,SV13: $i] :
( ( ( relr @ SV13 @ SV21 )
= $false )
| ( ( SV4 @ SV21 )
= $true )
| ( ( relr @ SV9 @ SV13 )
= $false )
| ( ( SV4 @ ( sK8_SY276 @ SV4 @ SV9 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(126,plain,
! [SV10: $i,SV5: $i > $o,SV25: $i,SV17: $i] :
( ( ( ~ ( reli @ SV17 @ SV25 ) )
= $true )
| ( ( SV5 @ SV25 )
= $true )
| ( ( reli @ SV10 @ SV17 )
= $false )
| ( ( reli @ SV10 @ ( sK9_SY279 @ SV5 @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[118]) ).
thf(127,plain,
! [SV10: $i,SV5: $i > $o,SV22: $i,SV14: $i] :
( ( ( reli @ SV14 @ SV22 )
= $false )
| ( ( SV5 @ SV22 )
= $true )
| ( ( reli @ SV10 @ SV14 )
= $false )
| ( ( SV5 @ ( sK9_SY279 @ SV5 @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(128,plain,
! [SV8: $i,SV3: $i > $o,SV23: $i,SV15: $i] :
( ( ( reli @ SV15 @ SV23 )
= $false )
| ( ( SV3 @ SV23 )
= $true )
| ( ( relr @ SV8 @ SV15 )
= $false )
| ( ( reli @ SV8 @ ( sK7_SY272 @ SV3 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[121]) ).
thf(129,plain,
! [SV8: $i,SV3: $i > $o,SV27: $i,SV20: $i] :
( ( ( ~ ( reli @ SV20 @ SV27 )
| ( SV3 @ SV27 ) )
= $true )
| ( ( relr @ SV8 @ SV20 )
= $false )
| ( ( relr @ ( sK7_SY272 @ SV3 @ SV8 ) @ ( sK10_SY284 @ SV8 @ SV3 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(130,plain,
! [SV8: $i,SV3: $i > $o,SV26: $i,SV18: $i] :
( ( ( ~ ( reli @ SV18 @ SV26 ) )
= $true )
| ( ( SV3 @ SV26 )
= $true )
| ( ( relr @ SV8 @ SV18 )
= $false )
| ( ( SV3 @ ( sK10_SY284 @ SV8 @ SV3 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[123]) ).
thf(131,plain,
! [SV9: $i,SV4: $i > $o,SV24: $i,SV16: $i] :
( ( ( relr @ SV16 @ SV24 )
= $false )
| ( ( SV4 @ SV24 )
= $true )
| ( ( relr @ SV9 @ SV16 )
= $false )
| ( ( relr @ SV9 @ ( sK8_SY276 @ SV4 @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(132,plain,
! [SV10: $i,SV5: $i > $o,SV25: $i,SV17: $i] :
( ( ( reli @ SV17 @ SV25 )
= $false )
| ( ( SV5 @ SV25 )
= $true )
| ( ( reli @ SV10 @ SV17 )
= $false )
| ( ( reli @ SV10 @ ( sK9_SY279 @ SV5 @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[126]) ).
thf(133,plain,
! [SV8: $i,SV3: $i > $o,SV27: $i,SV20: $i] :
( ( ( ~ ( reli @ SV20 @ SV27 ) )
= $true )
| ( ( SV3 @ SV27 )
= $true )
| ( ( relr @ SV8 @ SV20 )
= $false )
| ( ( relr @ ( sK7_SY272 @ SV3 @ SV8 ) @ ( sK10_SY284 @ SV8 @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[129]) ).
thf(134,plain,
! [SV8: $i,SV3: $i > $o,SV26: $i,SV18: $i] :
( ( ( reli @ SV18 @ SV26 )
= $false )
| ( ( SV3 @ SV26 )
= $true )
| ( ( relr @ SV8 @ SV18 )
= $false )
| ( ( SV3 @ ( sK10_SY284 @ SV8 @ SV3 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[130]) ).
thf(135,plain,
! [SV8: $i,SV3: $i > $o,SV27: $i,SV20: $i] :
( ( ( reli @ SV20 @ SV27 )
= $false )
| ( ( SV3 @ SV27 )
= $true )
| ( ( relr @ SV8 @ SV20 )
= $false )
| ( ( relr @ ( sK7_SY272 @ SV3 @ SV8 ) @ ( sK10_SY284 @ SV8 @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(136,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[25,135,134,132,131,128,127,125,120,81,79,72,69,63,56]) ).
thf(137,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[136]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL691^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.18 % Computer : n013.cluster.edu
% 0.06/0.18 % Model : x86_64 x86_64
% 0.06/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.18 % Memory : 8046.5625MB
% 0.06/0.18 % OS : Linux 6.8.0-71-generic
% 0.06/0.18 % CPULimit : 300
% 0.06/0.18 % WCLimit : 300
% 0.06/0.18 % DateTime : Tue Oct 6 12:31:36 UTC 2026
% 0.06/0.18 % CPUTime :
% 0.06/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
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% 0.06/0.23 No.of.Axioms: 5
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% 0.06/0.23 Length.of.Defs: 3479
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% 0.06/0.23 Contains.Choice.Funs: false
% 0.06/0.23 ......
% 0.06/0.23
% 0.06/0.23 ********************************
% 0.06/0.23 * All subproblems solved! *
% 0.06/0.23 ********************************
% 0.06/0.23 % SZS status Theorem for /export/starexec/sandbox/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:136,loop_count:0,foatp_calls:1,translation:fof_full)
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% 0.06/0.23 %**** Beginning of derivation protocol ****
% 0.06/0.23 % SZS output start CNFRefutation
% See solution above
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% 0.06/0.23 %**** End of derivation protocol ****
% 0.06/0.23 %**** no. of clauses in derivation: 137 ****
% 0.06/0.23 %**** clause counter: 136 ****
% 0.06/0.23
% 0.06/0.23 % SZS status Theorem for /export/starexec/sandbox/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:136,loop_count:0,foatp_calls:1,translation:fof_full)
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