%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : LCL953^8 : TPTP v9.3.1. Released v8.1.0.
% 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 : n012.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 10:31:09 AM UTC 2026
% Result : Theorem 0.08s 0.17s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 14
% Syntax : Number of formulae : 161 ( 58 unt; 0 typ; 10 def)
% Number of atoms : 2412 ( 610 equ; 0 cnn)
% Maximal formula atoms : 13 ( 14 avg)
% Number of connectives : 4460 ( 545 ~; 886 |; 3 &;2928 @)
% ( 1 <=>; 97 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 32 ( 29 usr; 9 con; 0-6 aty)
% Number of variables : 885 ( 33 ^; 850 !; 2 ?; 885 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_mworld,type,
mworld: $tType ).
thf(tp_disjoint,type,
disjoint: $i > $i > mworld > $o ).
thf(tp_eiw_di,type,
eiw_di: $i > mworld > $o ).
thf(tp_empty,type,
empty: $i > mworld > $o ).
thf(tp_in,type,
in: $i > $i > mworld > $o ).
thf(tp_mactual,type,
mactual: mworld ).
thf(tp_mand,type,
mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(tp_mbox,type,
mbox: ( mworld > $o ) > mworld > $o ).
thf(tp_mdia,type,
mdia: ( mworld > $o ) > mworld > $o ).
thf(tp_mequiv,type,
mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(tp_mexists_di,type,
mexists_di: ( $i > mworld > $o ) > mworld > $o ).
thf(tp_mforall_di,type,
mforall_di: ( $i > mworld > $o ) > mworld > $o ).
thf(tp_mimplies,type,
mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(tp_mlocal,type,
mlocal: ( mworld > $o ) > $o ).
thf(tp_mnot,type,
mnot: ( mworld > $o ) > mworld > $o ).
thf(tp_mor,type,
mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(tp_mrel,type,
mrel: mworld > mworld > $o ).
thf(tp_sK10_SY405,type,
sK10_SY405: mworld > mworld > $i > $i > mworld > mworld ).
thf(tp_sK11_SY408,type,
sK11_SY408: mworld > mworld > mworld > $i > $i > mworld > mworld ).
thf(tp_sK12_SY409,type,
sK12_SY409: mworld > mworld > mworld > $i > $i > mworld > mworld ).
thf(tp_sK1_SY66,type,
sK1_SY66: mworld ).
thf(tp_sK2_SX0,type,
sK2_SX0: $i ).
thf(tp_sK3_SY338,type,
sK3_SY338: mworld ).
thf(tp_sK4_SY361,type,
sK4_SY361: $i ).
thf(tp_sK5_SY366,type,
sK5_SY366: mworld ).
thf(tp_sK6_SY386,type,
sK6_SY386: mworld ).
thf(tp_sK7_SY398,type,
sK7_SY398: mworld > mworld ).
thf(tp_sK8_SY399,type,
sK8_SY399: mworld > mworld > $i > $i > mworld > mworld ).
thf(tp_sK9_SY402,type,
sK9_SY402: mworld > mworld > $i > $i > mworld > mworld ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(mand,definition,
( mand
= ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
( ( A @ W )
& ( B @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mand_def) ).
thf(mbox,definition,
( mbox
= ( ^ [Phi: mworld > $o,W: mworld] :
! [V: mworld] :
( ( mrel @ W @ V )
=> ( Phi @ V ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_def) ).
thf(mdia,definition,
( mdia
= ( ^ [Phi: mworld > $o,W: mworld] :
? [V: mworld] :
( ( mrel @ W @ V )
& ( Phi @ V ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mdia_def) ).
thf(mequiv,definition,
( mequiv
= ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
( ( A @ W )
<=> ( B @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mequiv_def) ).
thf(mexists_di,definition,
( mexists_di
= ( ^ [A: $i > mworld > $o,W: mworld] :
? [X: $i] :
( ( eiw_di @ X @ W )
& ( A @ X @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mexists_di_def) ).
thf(mforall_di,definition,
( mforall_di
= ( ^ [A: $i > mworld > $o,W: mworld] :
! [X: $i] :
( ( eiw_di @ X @ W )
=> ( A @ X @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mforall_di_def) ).
thf(mimplies,definition,
( mimplies
= ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
( ( A @ W )
=> ( B @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies_def) ).
thf(mlocal,definition,
( mlocal
= ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mlocal_def) ).
thf(mnot,definition,
( mnot
= ( ^ [A: mworld > $o,W: mworld] :
~ ( A @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot_def) ).
thf(mor,definition,
( mor
= ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
( ( A @ W )
| ( B @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor_def) ).
thf(1,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( mnot @ ( mbox @ ( in @ A @ B ) ) ) ) @ ( mbox @ ( disjoint @ ( singleton @ A ) @ B ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l28_zfmisc_1) ).
thf(4,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( in @ A @ B ) ) @ ( mbox @ ( mnot @ ( mbox @ ( in @ B @ A ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(5,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( disjoint @ A @ B ) ) @ ( mbox @ ( disjoint @ B @ A ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
thf(8,conjecture,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( mnot @ ( mbox @ ( in @ A @ B ) ) ) ) @ ( mbox @ ( disjoint @ ( singleton @ A ) @ B ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_zfmisc_1) ).
thf(9,negated_conjecture,
( ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( mnot @ ( mbox @ ( in @ A @ B ) ) ) ) @ ( mbox @ ( disjoint @ ( singleton @ A ) @ B ) ) ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[8]) ).
thf(10,plain,
( ( ! [SY66: mworld] :
( ( mrel @ mactual @ SY66 )
=> ! [SY59: $i] :
( ( eiw_di @ SY59 @ SY66 )
=> ! [SY60: mworld] :
( ( mrel @ SY66 @ SY60 )
=> ! [SY46: $i] :
( ( eiw_di @ SY46 @ SY60 )
=> ! [SY47: mworld] :
( ( mrel @ SY60 @ SY47 )
=> ( ! [SY48: mworld] :
( ( mrel @ SY47 @ SY48 )
=> ~ ! [SY49: mworld] :
( ( mrel @ SY48 @ SY49 )
=> ( in @ SY59 @ SY46 @ SY49 ) ) )
=> ! [SY50: mworld] :
( ( mrel @ SY47 @ SY50 )
=> ( disjoint @ ( singleton @ SY59 ) @ SY46 @ SY50 ) ) ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[9,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(11,plain,
( ( ! [SY148: mworld] :
( ( mrel @ mactual @ SY148 )
=> ! [SY141: $i] :
( ( eiw_di @ SY141 @ SY148 )
=> ! [SY142: mworld] :
( ( mrel @ SY148 @ SY142 )
=> ! [SY128: $i] :
( ( eiw_di @ SY128 @ SY142 )
=> ! [SY129: mworld] :
( ( mrel @ SY142 @ SY129 )
=> ( ! [SY130: mworld] :
( ( mrel @ SY129 @ SY130 )
=> ~ ! [SY131: mworld] :
( ( mrel @ SY130 @ SY131 )
=> ( in @ SY141 @ SY128 @ SY131 ) ) )
=> ! [SY132: mworld] :
( ( mrel @ SY129 @ SY132 )
=> ( disjoint @ ( singleton @ SY141 ) @ SY128 @ SY132 ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(12,plain,
( ( ! [SY229: mworld] :
( ( mrel @ mactual @ SY229 )
=> ! [SY222: $i] :
( ( eiw_di @ SY222 @ SY229 )
=> ! [SY223: mworld] :
( ( mrel @ SY229 @ SY223 )
=> ! [SY209: $i] :
( ( eiw_di @ SY209 @ SY223 )
=> ! [SY210: mworld] :
( ( mrel @ SY223 @ SY210 )
=> ( ! [SY211: mworld] :
( ( mrel @ SY210 @ SY211 )
=> ( in @ SY222 @ SY209 @ SY211 ) )
=> ! [SY212: mworld] :
( ( mrel @ SY210 @ SY212 )
=> ~ ! [SY213: mworld] :
( ( mrel @ SY212 @ SY213 )
=> ( in @ SY209 @ SY222 @ SY213 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(13,plain,
( ( ! [SY297: mworld] :
( ( mrel @ mactual @ SY297 )
=> ! [SY291: $i] :
( ( eiw_di @ SY291 @ SY297 )
=> ! [SY292: mworld] :
( ( mrel @ SY297 @ SY292 )
=> ! [SY280: $i] :
( ( eiw_di @ SY280 @ SY292 )
=> ! [SY281: mworld] :
( ( mrel @ SY292 @ SY281 )
=> ( ! [SY282: mworld] :
( ( mrel @ SY281 @ SY282 )
=> ( disjoint @ SY291 @ SY280 @ SY282 ) )
=> ! [SY283: mworld] :
( ( mrel @ SY281 @ SY283 )
=> ( disjoint @ SY280 @ SY291 @ SY283 ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(14,plain,
( ( ( mrel @ mactual @ sK1_SY66 )
=> ! [SY311: $i] :
( ( eiw_di @ SY311 @ sK1_SY66 )
=> ! [SY312: mworld] :
( ( mrel @ sK1_SY66 @ SY312 )
=> ! [SY46: $i] :
( ( eiw_di @ SY46 @ SY312 )
=> ! [SY47: mworld] :
( ( mrel @ SY312 @ SY47 )
=> ( ! [SY48: mworld] :
( ( mrel @ SY47 @ SY48 )
=> ~ ! [SY49: mworld] :
( ( mrel @ SY48 @ SY49 )
=> ( in @ SY311 @ SY46 @ SY49 ) ) )
=> ! [SY50: mworld] :
( ( mrel @ SY47 @ SY50 )
=> ( disjoint @ ( singleton @ SY311 ) @ SY46 @ SY50 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[10]) ).
thf(15,plain,
( ( mrel @ mactual @ sK1_SY66 )
= $true ),
inference(standard_cnf,[status(thm)],[14]) ).
thf(16,plain,
( ( ! [SY311: $i] :
( ( eiw_di @ SY311 @ sK1_SY66 )
=> ! [SY312: mworld] :
( ( mrel @ sK1_SY66 @ SY312 )
=> ! [SY46: $i] :
( ( eiw_di @ SY46 @ SY312 )
=> ! [SY47: mworld] :
( ( mrel @ SY312 @ SY47 )
=> ( ! [SY48: mworld] :
( ( mrel @ SY47 @ SY48 )
=> ~ ! [SY49: mworld] :
( ( mrel @ SY48 @ SY49 )
=> ( in @ SY311 @ SY46 @ SY49 ) ) )
=> ! [SY50: mworld] :
( ( mrel @ SY47 @ SY50 )
=> ( disjoint @ ( singleton @ SY311 ) @ SY46 @ SY50 ) ) ) ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[14]) ).
thf(17,plain,
( ( ~ ! [SY311: $i] :
( ( eiw_di @ SY311 @ sK1_SY66 )
=> ! [SY312: mworld] :
( ( mrel @ sK1_SY66 @ SY312 )
=> ! [SY46: $i] :
( ( eiw_di @ SY46 @ SY312 )
=> ! [SY47: mworld] :
( ( mrel @ SY312 @ SY47 )
=> ( ! [SY48: mworld] :
( ( mrel @ SY47 @ SY48 )
=> ~ ! [SY49: mworld] :
( ( mrel @ SY48 @ SY49 )
=> ( in @ SY311 @ SY46 @ SY49 ) ) )
=> ! [SY50: mworld] :
( ( mrel @ SY47 @ SY50 )
=> ( disjoint @ ( singleton @ SY311 ) @ SY46 @ SY50 ) ) ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[16]) ).
thf(18,plain,
( ( ! [SY297: mworld] :
( ( mrel @ mactual @ SY297 )
=> ! [SY291: $i] :
( ( eiw_di @ SY291 @ SY297 )
=> ! [SY292: mworld] :
( ( mrel @ SY297 @ SY292 )
=> ! [SY280: $i] :
( ( eiw_di @ SY280 @ SY292 )
=> ! [SY281: mworld] :
( ( mrel @ SY292 @ SY281 )
=> ( ! [SY282: mworld] :
( ( mrel @ SY281 @ SY282 )
=> ( disjoint @ SY291 @ SY280 @ SY282 ) )
=> ! [SY283: mworld] :
( ( mrel @ SY281 @ SY283 )
=> ( disjoint @ SY280 @ SY291 @ SY283 ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(19,plain,
( ( ! [SY229: mworld] :
( ( mrel @ mactual @ SY229 )
=> ! [SY222: $i] :
( ( eiw_di @ SY222 @ SY229 )
=> ! [SY223: mworld] :
( ( mrel @ SY229 @ SY223 )
=> ! [SY209: $i] :
( ( eiw_di @ SY209 @ SY223 )
=> ! [SY210: mworld] :
( ( mrel @ SY223 @ SY210 )
=> ( ! [SY211: mworld] :
( ( mrel @ SY210 @ SY211 )
=> ( in @ SY222 @ SY209 @ SY211 ) )
=> ! [SY212: mworld] :
( ( mrel @ SY210 @ SY212 )
=> ~ ! [SY213: mworld] :
( ( mrel @ SY212 @ SY213 )
=> ( in @ SY209 @ SY222 @ SY213 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(20,plain,
( ( ! [SY148: mworld] :
( ( mrel @ mactual @ SY148 )
=> ! [SY141: $i] :
( ( eiw_di @ SY141 @ SY148 )
=> ! [SY142: mworld] :
( ( mrel @ SY148 @ SY142 )
=> ! [SY128: $i] :
( ( eiw_di @ SY128 @ SY142 )
=> ! [SY129: mworld] :
( ( mrel @ SY142 @ SY129 )
=> ( ! [SY130: mworld] :
( ( mrel @ SY129 @ SY130 )
=> ~ ! [SY131: mworld] :
( ( mrel @ SY130 @ SY131 )
=> ( in @ SY141 @ SY128 @ SY131 ) ) )
=> ! [SY132: mworld] :
( ( mrel @ SY129 @ SY132 )
=> ( disjoint @ ( singleton @ SY141 ) @ SY128 @ SY132 ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(21,plain,
( ( mrel @ mactual @ sK1_SY66 )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(22,plain,
( ( ~ ! [SY311: $i] :
( ( eiw_di @ SY311 @ sK1_SY66 )
=> ! [SY312: mworld] :
( ( mrel @ sK1_SY66 @ SY312 )
=> ! [SY46: $i] :
( ( eiw_di @ SY46 @ SY312 )
=> ! [SY47: mworld] :
( ( mrel @ SY312 @ SY47 )
=> ( ! [SY48: mworld] :
( ( mrel @ SY47 @ SY48 )
=> ~ ! [SY49: mworld] :
( ( mrel @ SY48 @ SY49 )
=> ( in @ SY311 @ SY46 @ SY49 ) ) )
=> ! [SY50: mworld] :
( ( mrel @ SY47 @ SY50 )
=> ( disjoint @ ( singleton @ SY311 ) @ SY46 @ SY50 ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(23,plain,
( ( ! [SX0: mworld] :
( ~ ( mrel @ mactual @ SX0 )
| ! [SX1: $i] :
( ~ ( eiw_di @ SX1 @ SX0 )
| ! [SX2: mworld] :
( ~ ( mrel @ SX0 @ SX2 )
| ! [SX3: $i] :
( ~ ( eiw_di @ SX3 @ SX2 )
| ! [SX4: mworld] :
( ~ ( mrel @ SX2 @ SX4 )
| ~ ! [SX5: mworld] :
( ~ ( mrel @ SX4 @ SX5 )
| ~ ! [SX6: mworld] :
( ~ ( mrel @ SX5 @ SX6 )
| ( in @ SX1 @ SX3 @ SX6 ) ) )
| ! [SX5: mworld] :
( ~ ( mrel @ SX4 @ SX5 )
| ( disjoint @ ( singleton @ SX1 ) @ SX3 @ SX5 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(24,plain,
( ( ! [SX0: mworld] :
( ~ ( mrel @ mactual @ SX0 )
| ! [SX1: $i] :
( ~ ( eiw_di @ SX1 @ SX0 )
| ! [SX2: mworld] :
( ~ ( mrel @ SX0 @ SX2 )
| ! [SX3: $i] :
( ~ ( eiw_di @ SX3 @ SX2 )
| ! [SX4: mworld] :
( ~ ( mrel @ SX2 @ SX4 )
| ~ ! [SX5: mworld] :
( ~ ( mrel @ SX4 @ SX5 )
| ( in @ SX1 @ SX3 @ SX5 ) )
| ! [SX5: mworld] :
( ~ ( mrel @ SX4 @ SX5 )
| ~ ! [SX6: mworld] :
( ~ ( mrel @ SX5 @ SX6 )
| ( in @ SX3 @ SX1 @ SX6 ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(25,plain,
( ( ! [SX0: mworld] :
( ~ ( mrel @ mactual @ SX0 )
| ! [SX1: $i] :
( ~ ( eiw_di @ SX1 @ SX0 )
| ! [SX2: mworld] :
( ~ ( mrel @ SX0 @ SX2 )
| ! [SX3: $i] :
( ~ ( eiw_di @ SX3 @ SX2 )
| ! [SX4: mworld] :
( ~ ( mrel @ SX2 @ SX4 )
| ~ ! [SX5: mworld] :
( ~ ( mrel @ SX4 @ SX5 )
| ( disjoint @ SX1 @ SX3 @ SX5 ) )
| ! [SX5: mworld] :
( ~ ( mrel @ SX4 @ SX5 )
| ( disjoint @ SX3 @ SX1 @ SX5 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(26,plain,
( ( ~ ! [SX0: $i] :
( ~ ( eiw_di @ SX0 @ sK1_SY66 )
| ! [SX1: mworld] :
( ~ ( mrel @ sK1_SY66 @ SX1 )
| ! [SX2: $i] :
( ~ ( eiw_di @ SX2 @ SX1 )
| ! [SX3: mworld] :
( ~ ( mrel @ SX1 @ SX3 )
| ~ ! [SX4: mworld] :
( ~ ( mrel @ SX3 @ SX4 )
| ~ ! [SX5: mworld] :
( ~ ( mrel @ SX4 @ SX5 )
| ( in @ SX0 @ SX2 @ SX5 ) ) )
| ! [SX4: mworld] :
( ~ ( mrel @ SX3 @ SX4 )
| ( disjoint @ ( singleton @ SX0 ) @ SX2 @ SX4 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(27,plain,
! [SV1: mworld] :
( ( ~ ( mrel @ mactual @ SV1 )
| ! [SY318: $i] :
( ~ ( eiw_di @ SY318 @ SV1 )
| ! [SY319: mworld] :
( ~ ( mrel @ SV1 @ SY319 )
| ! [SX3: $i] :
( ~ ( eiw_di @ SX3 @ SY319 )
| ! [SX4: mworld] :
( ~ ( mrel @ SY319 @ SX4 )
| ~ ! [SX5: mworld] :
( ~ ( mrel @ SX4 @ SX5 )
| ~ ! [SX6: mworld] :
( ~ ( mrel @ SX5 @ SX6 )
| ( in @ SY318 @ SX3 @ SX6 ) ) )
| ! [SX5: mworld] :
( ~ ( mrel @ SX4 @ SX5 )
| ( disjoint @ ( singleton @ SY318 ) @ SX3 @ SX5 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(28,plain,
! [SV2: mworld] :
( ( ~ ( mrel @ mactual @ SV2 )
| ! [SY325: $i] :
( ~ ( eiw_di @ SY325 @ SV2 )
| ! [SY326: mworld] :
( ~ ( mrel @ SV2 @ SY326 )
| ! [SX3: $i] :
( ~ ( eiw_di @ SX3 @ SY326 )
| ! [SX4: mworld] :
( ~ ( mrel @ SY326 @ SX4 )
| ~ ! [SX5: mworld] :
( ~ ( mrel @ SX4 @ SX5 )
| ( in @ SY325 @ SX3 @ SX5 ) )
| ! [SX5: mworld] :
( ~ ( mrel @ SX4 @ SX5 )
| ~ ! [SX6: mworld] :
( ~ ( mrel @ SX5 @ SX6 )
| ( in @ SX3 @ SY325 @ SX6 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(29,plain,
! [SV3: mworld] :
( ( ~ ( mrel @ mactual @ SV3 )
| ! [SY332: $i] :
( ~ ( eiw_di @ SY332 @ SV3 )
| ! [SY333: mworld] :
( ~ ( mrel @ SV3 @ SY333 )
| ! [SX3: $i] :
( ~ ( eiw_di @ SX3 @ SY333 )
| ! [SX4: mworld] :
( ~ ( mrel @ SY333 @ SX4 )
| ~ ! [SX5: mworld] :
( ~ ( mrel @ SX4 @ SX5 )
| ( disjoint @ SY332 @ SX3 @ SX5 ) )
| ! [SX5: mworld] :
( ~ ( mrel @ SX4 @ SX5 )
| ( disjoint @ SX3 @ SY332 @ SX5 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(30,plain,
( ( ! [SX0: $i] :
( ~ ( eiw_di @ SX0 @ sK1_SY66 )
| ! [SX1: mworld] :
( ~ ( mrel @ sK1_SY66 @ SX1 )
| ! [SX2: $i] :
( ~ ( eiw_di @ SX2 @ SX1 )
| ! [SX3: mworld] :
( ~ ( mrel @ SX1 @ SX3 )
| ~ ! [SX4: mworld] :
( ~ ( mrel @ SX3 @ SX4 )
| ~ ! [SX5: mworld] :
( ~ ( mrel @ SX4 @ SX5 )
| ( in @ SX0 @ SX2 @ SX5 ) ) )
| ! [SX4: mworld] :
( ~ ( mrel @ SX3 @ SX4 )
| ( disjoint @ ( singleton @ SX0 ) @ SX2 @ SX4 ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(31,plain,
! [SV1: mworld] :
( ( ( ~ ( mrel @ mactual @ SV1 ) )
= $true )
| ( ( ! [SY318: $i] :
( ~ ( eiw_di @ SY318 @ SV1 )
| ! [SY319: mworld] :
( ~ ( mrel @ SV1 @ SY319 )
| ! [SX3: $i] :
( ~ ( eiw_di @ SX3 @ SY319 )
| ! [SX4: mworld] :
( ~ ( mrel @ SY319 @ SX4 )
| ~ ! [SX5: mworld] :
( ~ ( mrel @ SX4 @ SX5 )
| ~ ! [SX6: mworld] :
( ~ ( mrel @ SX5 @ SX6 )
| ( in @ SY318 @ SX3 @ SX6 ) ) )
| ! [SX5: mworld] :
( ~ ( mrel @ SX4 @ SX5 )
| ( disjoint @ ( singleton @ SY318 ) @ SX3 @ SX5 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[27]) ).
thf(32,plain,
! [SV2: mworld] :
( ( ( ~ ( mrel @ mactual @ SV2 ) )
= $true )
| ( ( ! [SY325: $i] :
( ~ ( eiw_di @ SY325 @ SV2 )
| ! [SY326: mworld] :
( ~ ( mrel @ SV2 @ SY326 )
| ! [SX3: $i] :
( ~ ( eiw_di @ SX3 @ SY326 )
| ! [SX4: mworld] :
( ~ ( mrel @ SY326 @ SX4 )
| ~ ! [SX5: mworld] :
( ~ ( mrel @ SX4 @ SX5 )
| ( in @ SY325 @ SX3 @ SX5 ) )
| ! [SX5: mworld] :
( ~ ( mrel @ SX4 @ SX5 )
| ~ ! [SX6: mworld] :
( ~ ( mrel @ SX5 @ SX6 )
| ( in @ SX3 @ SY325 @ SX6 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[28]) ).
thf(33,plain,
! [SV3: mworld] :
( ( ( ~ ( mrel @ mactual @ SV3 ) )
= $true )
| ( ( ! [SY332: $i] :
( ~ ( eiw_di @ SY332 @ SV3 )
| ! [SY333: mworld] :
( ~ ( mrel @ SV3 @ SY333 )
| ! [SX3: $i] :
( ~ ( eiw_di @ SX3 @ SY333 )
| ! [SX4: mworld] :
( ~ ( mrel @ SY333 @ SX4 )
| ~ ! [SX5: mworld] :
( ~ ( mrel @ SX4 @ SX5 )
| ( disjoint @ SY332 @ SX3 @ SX5 ) )
| ! [SX5: mworld] :
( ~ ( mrel @ SX4 @ SX5 )
| ( disjoint @ SX3 @ SY332 @ SX5 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[29]) ).
thf(34,plain,
( ( ~ ( eiw_di @ sK2_SX0 @ sK1_SY66 )
| ! [SY338: mworld] :
( ~ ( mrel @ sK1_SY66 @ SY338 )
| ! [SY339: $i] :
( ~ ( eiw_di @ SY339 @ SY338 )
| ! [SY340: mworld] :
( ~ ( mrel @ SY338 @ SY340 )
| ~ ! [SY341: mworld] :
( ~ ( mrel @ SY340 @ SY341 )
| ~ ! [SY342: mworld] :
( ~ ( mrel @ SY341 @ SY342 )
| ( in @ sK2_SX0 @ SY339 @ SY342 ) ) )
| ! [SY343: mworld] :
( ~ ( mrel @ SY340 @ SY343 )
| ( disjoint @ ( singleton @ sK2_SX0 ) @ SY339 @ SY343 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[30]) ).
thf(35,plain,
! [SV1: mworld] :
( ( ( mrel @ mactual @ SV1 )
= $false )
| ( ( ! [SY318: $i] :
( ~ ( eiw_di @ SY318 @ SV1 )
| ! [SY319: mworld] :
( ~ ( mrel @ SV1 @ SY319 )
| ! [SX3: $i] :
( ~ ( eiw_di @ SX3 @ SY319 )
| ! [SX4: mworld] :
( ~ ( mrel @ SY319 @ SX4 )
| ~ ! [SX5: mworld] :
( ~ ( mrel @ SX4 @ SX5 )
| ~ ! [SX6: mworld] :
( ~ ( mrel @ SX5 @ SX6 )
| ( in @ SY318 @ SX3 @ SX6 ) ) )
| ! [SX5: mworld] :
( ~ ( mrel @ SX4 @ SX5 )
| ( disjoint @ ( singleton @ SY318 ) @ SX3 @ SX5 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(36,plain,
! [SV2: mworld] :
( ( ( mrel @ mactual @ SV2 )
= $false )
| ( ( ! [SY325: $i] :
( ~ ( eiw_di @ SY325 @ SV2 )
| ! [SY326: mworld] :
( ~ ( mrel @ SV2 @ SY326 )
| ! [SX3: $i] :
( ~ ( eiw_di @ SX3 @ SY326 )
| ! [SX4: mworld] :
( ~ ( mrel @ SY326 @ SX4 )
| ~ ! [SX5: mworld] :
( ~ ( mrel @ SX4 @ SX5 )
| ( in @ SY325 @ SX3 @ SX5 ) )
| ! [SX5: mworld] :
( ~ ( mrel @ SX4 @ SX5 )
| ~ ! [SX6: mworld] :
( ~ ( mrel @ SX5 @ SX6 )
| ( in @ SX3 @ SY325 @ SX6 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(37,plain,
! [SV3: mworld] :
( ( ( mrel @ mactual @ SV3 )
= $false )
| ( ( ! [SY332: $i] :
( ~ ( eiw_di @ SY332 @ SV3 )
| ! [SY333: mworld] :
( ~ ( mrel @ SV3 @ SY333 )
| ! [SX3: $i] :
( ~ ( eiw_di @ SX3 @ SY333 )
| ! [SX4: mworld] :
( ~ ( mrel @ SY333 @ SX4 )
| ~ ! [SX5: mworld] :
( ~ ( mrel @ SX4 @ SX5 )
| ( disjoint @ SY332 @ SX3 @ SX5 ) )
| ! [SX5: mworld] :
( ~ ( mrel @ SX4 @ SX5 )
| ( disjoint @ SX3 @ SY332 @ SX5 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(38,plain,
( ( ~ ( eiw_di @ sK2_SX0 @ sK1_SY66 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[34]) ).
thf(39,plain,
( ( ! [SY338: mworld] :
( ~ ( mrel @ sK1_SY66 @ SY338 )
| ! [SY339: $i] :
( ~ ( eiw_di @ SY339 @ SY338 )
| ! [SY340: mworld] :
( ~ ( mrel @ SY338 @ SY340 )
| ~ ! [SY341: mworld] :
( ~ ( mrel @ SY340 @ SY341 )
| ~ ! [SY342: mworld] :
( ~ ( mrel @ SY341 @ SY342 )
| ( in @ sK2_SX0 @ SY339 @ SY342 ) ) )
| ! [SY343: mworld] :
( ~ ( mrel @ SY340 @ SY343 )
| ( disjoint @ ( singleton @ sK2_SX0 ) @ SY339 @ SY343 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[34]) ).
thf(40,plain,
! [SV1: mworld,SV4: $i] :
( ( ( ~ ( eiw_di @ SV4 @ SV1 )
| ! [SY344: mworld] :
( ~ ( mrel @ SV1 @ SY344 )
| ! [SY345: $i] :
( ~ ( eiw_di @ SY345 @ SY344 )
| ! [SY346: mworld] :
( ~ ( mrel @ SY344 @ SY346 )
| ~ ! [SY347: mworld] :
( ~ ( mrel @ SY346 @ SY347 )
| ~ ! [SY348: mworld] :
( ~ ( mrel @ SY347 @ SY348 )
| ( in @ SV4 @ SY345 @ SY348 ) ) )
| ! [SY349: mworld] :
( ~ ( mrel @ SY346 @ SY349 )
| ( disjoint @ ( singleton @ SV4 ) @ SY345 @ SY349 ) ) ) ) ) )
= $true )
| ( ( mrel @ mactual @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(41,plain,
! [SV2: mworld,SV5: $i] :
( ( ( ~ ( eiw_di @ SV5 @ SV2 )
| ! [SY350: mworld] :
( ~ ( mrel @ SV2 @ SY350 )
| ! [SY351: $i] :
( ~ ( eiw_di @ SY351 @ SY350 )
| ! [SY352: mworld] :
( ~ ( mrel @ SY350 @ SY352 )
| ~ ! [SY353: mworld] :
( ~ ( mrel @ SY352 @ SY353 )
| ( in @ SV5 @ SY351 @ SY353 ) )
| ! [SY354: mworld] :
( ~ ( mrel @ SY352 @ SY354 )
| ~ ! [SY355: mworld] :
( ~ ( mrel @ SY354 @ SY355 )
| ( in @ SY351 @ SV5 @ SY355 ) ) ) ) ) ) )
= $true )
| ( ( mrel @ mactual @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(42,plain,
! [SV3: mworld,SV6: $i] :
( ( ( ~ ( eiw_di @ SV6 @ SV3 )
| ! [SY356: mworld] :
( ~ ( mrel @ SV3 @ SY356 )
| ! [SY357: $i] :
( ~ ( eiw_di @ SY357 @ SY356 )
| ! [SY358: mworld] :
( ~ ( mrel @ SY356 @ SY358 )
| ~ ! [SY359: mworld] :
( ~ ( mrel @ SY358 @ SY359 )
| ( disjoint @ SV6 @ SY357 @ SY359 ) )
| ! [SY360: mworld] :
( ~ ( mrel @ SY358 @ SY360 )
| ( disjoint @ SY357 @ SV6 @ SY360 ) ) ) ) ) )
= $true )
| ( ( mrel @ mactual @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(43,plain,
( ( eiw_di @ sK2_SX0 @ sK1_SY66 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[38]) ).
thf(44,plain,
( ( ~ ( mrel @ sK1_SY66 @ sK3_SY338 )
| ! [SY361: $i] :
( ~ ( eiw_di @ SY361 @ sK3_SY338 )
| ! [SY362: mworld] :
( ~ ( mrel @ sK3_SY338 @ SY362 )
| ~ ! [SY341: mworld] :
( ~ ( mrel @ SY362 @ SY341 )
| ~ ! [SY342: mworld] :
( ~ ( mrel @ SY341 @ SY342 )
| ( in @ sK2_SX0 @ SY361 @ SY342 ) ) )
| ! [SY343: mworld] :
( ~ ( mrel @ SY362 @ SY343 )
| ( disjoint @ ( singleton @ sK2_SX0 ) @ SY361 @ SY343 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[39]) ).
thf(45,plain,
! [SV1: mworld,SV4: $i] :
( ( ( ~ ( eiw_di @ SV4 @ SV1 ) )
= $true )
| ( ( ! [SY344: mworld] :
( ~ ( mrel @ SV1 @ SY344 )
| ! [SY345: $i] :
( ~ ( eiw_di @ SY345 @ SY344 )
| ! [SY346: mworld] :
( ~ ( mrel @ SY344 @ SY346 )
| ~ ! [SY347: mworld] :
( ~ ( mrel @ SY346 @ SY347 )
| ~ ! [SY348: mworld] :
( ~ ( mrel @ SY347 @ SY348 )
| ( in @ SV4 @ SY345 @ SY348 ) ) )
| ! [SY349: mworld] :
( ~ ( mrel @ SY346 @ SY349 )
| ( disjoint @ ( singleton @ SV4 ) @ SY345 @ SY349 ) ) ) ) ) )
= $true )
| ( ( mrel @ mactual @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[40]) ).
thf(46,plain,
! [SV2: mworld,SV5: $i] :
( ( ( ~ ( eiw_di @ SV5 @ SV2 ) )
= $true )
| ( ( ! [SY350: mworld] :
( ~ ( mrel @ SV2 @ SY350 )
| ! [SY351: $i] :
( ~ ( eiw_di @ SY351 @ SY350 )
| ! [SY352: mworld] :
( ~ ( mrel @ SY350 @ SY352 )
| ~ ! [SY353: mworld] :
( ~ ( mrel @ SY352 @ SY353 )
| ( in @ SV5 @ SY351 @ SY353 ) )
| ! [SY354: mworld] :
( ~ ( mrel @ SY352 @ SY354 )
| ~ ! [SY355: mworld] :
( ~ ( mrel @ SY354 @ SY355 )
| ( in @ SY351 @ SV5 @ SY355 ) ) ) ) ) ) )
= $true )
| ( ( mrel @ mactual @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[41]) ).
thf(47,plain,
! [SV3: mworld,SV6: $i] :
( ( ( ~ ( eiw_di @ SV6 @ SV3 ) )
= $true )
| ( ( ! [SY356: mworld] :
( ~ ( mrel @ SV3 @ SY356 )
| ! [SY357: $i] :
( ~ ( eiw_di @ SY357 @ SY356 )
| ! [SY358: mworld] :
( ~ ( mrel @ SY356 @ SY358 )
| ~ ! [SY359: mworld] :
( ~ ( mrel @ SY358 @ SY359 )
| ( disjoint @ SV6 @ SY357 @ SY359 ) )
| ! [SY360: mworld] :
( ~ ( mrel @ SY358 @ SY360 )
| ( disjoint @ SY357 @ SV6 @ SY360 ) ) ) ) ) )
= $true )
| ( ( mrel @ mactual @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[42]) ).
thf(48,plain,
( ( ~ ( mrel @ sK1_SY66 @ sK3_SY338 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[44]) ).
thf(49,plain,
( ( ! [SY361: $i] :
( ~ ( eiw_di @ SY361 @ sK3_SY338 )
| ! [SY362: mworld] :
( ~ ( mrel @ sK3_SY338 @ SY362 )
| ~ ! [SY341: mworld] :
( ~ ( mrel @ SY362 @ SY341 )
| ~ ! [SY342: mworld] :
( ~ ( mrel @ SY341 @ SY342 )
| ( in @ sK2_SX0 @ SY361 @ SY342 ) ) )
| ! [SY343: mworld] :
( ~ ( mrel @ SY362 @ SY343 )
| ( disjoint @ ( singleton @ sK2_SX0 ) @ SY361 @ SY343 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[44]) ).
thf(50,plain,
! [SV1: mworld,SV4: $i] :
( ( ( eiw_di @ SV4 @ SV1 )
= $false )
| ( ( ! [SY344: mworld] :
( ~ ( mrel @ SV1 @ SY344 )
| ! [SY345: $i] :
( ~ ( eiw_di @ SY345 @ SY344 )
| ! [SY346: mworld] :
( ~ ( mrel @ SY344 @ SY346 )
| ~ ! [SY347: mworld] :
( ~ ( mrel @ SY346 @ SY347 )
| ~ ! [SY348: mworld] :
( ~ ( mrel @ SY347 @ SY348 )
| ( in @ SV4 @ SY345 @ SY348 ) ) )
| ! [SY349: mworld] :
( ~ ( mrel @ SY346 @ SY349 )
| ( disjoint @ ( singleton @ SV4 ) @ SY345 @ SY349 ) ) ) ) ) )
= $true )
| ( ( mrel @ mactual @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(51,plain,
! [SV2: mworld,SV5: $i] :
( ( ( eiw_di @ SV5 @ SV2 )
= $false )
| ( ( ! [SY350: mworld] :
( ~ ( mrel @ SV2 @ SY350 )
| ! [SY351: $i] :
( ~ ( eiw_di @ SY351 @ SY350 )
| ! [SY352: mworld] :
( ~ ( mrel @ SY350 @ SY352 )
| ~ ! [SY353: mworld] :
( ~ ( mrel @ SY352 @ SY353 )
| ( in @ SV5 @ SY351 @ SY353 ) )
| ! [SY354: mworld] :
( ~ ( mrel @ SY352 @ SY354 )
| ~ ! [SY355: mworld] :
( ~ ( mrel @ SY354 @ SY355 )
| ( in @ SY351 @ SV5 @ SY355 ) ) ) ) ) ) )
= $true )
| ( ( mrel @ mactual @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(52,plain,
! [SV3: mworld,SV6: $i] :
( ( ( eiw_di @ SV6 @ SV3 )
= $false )
| ( ( ! [SY356: mworld] :
( ~ ( mrel @ SV3 @ SY356 )
| ! [SY357: $i] :
( ~ ( eiw_di @ SY357 @ SY356 )
| ! [SY358: mworld] :
( ~ ( mrel @ SY356 @ SY358 )
| ~ ! [SY359: mworld] :
( ~ ( mrel @ SY358 @ SY359 )
| ( disjoint @ SV6 @ SY357 @ SY359 ) )
| ! [SY360: mworld] :
( ~ ( mrel @ SY358 @ SY360 )
| ( disjoint @ SY357 @ SV6 @ SY360 ) ) ) ) ) )
= $true )
| ( ( mrel @ mactual @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(53,plain,
( ( mrel @ sK1_SY66 @ sK3_SY338 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[48]) ).
thf(54,plain,
( ( ~ ( eiw_di @ sK4_SY361 @ sK3_SY338 )
| ! [SY366: mworld] :
( ~ ( mrel @ sK3_SY338 @ SY366 )
| ~ ! [SY367: mworld] :
( ~ ( mrel @ SY366 @ SY367 )
| ~ ! [SY368: mworld] :
( ~ ( mrel @ SY367 @ SY368 )
| ( in @ sK2_SX0 @ sK4_SY361 @ SY368 ) ) )
| ! [SY369: mworld] :
( ~ ( mrel @ SY366 @ SY369 )
| ( disjoint @ ( singleton @ sK2_SX0 ) @ sK4_SY361 @ SY369 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[49]) ).
thf(55,plain,
! [SV4: $i,SV7: mworld,SV1: mworld] :
( ( ( ~ ( mrel @ SV1 @ SV7 )
| ! [SY370: $i] :
( ~ ( eiw_di @ SY370 @ SV7 )
| ! [SY371: mworld] :
( ~ ( mrel @ SV7 @ SY371 )
| ~ ! [SY347: mworld] :
( ~ ( mrel @ SY371 @ SY347 )
| ~ ! [SY348: mworld] :
( ~ ( mrel @ SY347 @ SY348 )
| ( in @ SV4 @ SY370 @ SY348 ) ) )
| ! [SY349: mworld] :
( ~ ( mrel @ SY371 @ SY349 )
| ( disjoint @ ( singleton @ SV4 ) @ SY370 @ SY349 ) ) ) ) )
= $true )
| ( ( eiw_di @ SV4 @ SV1 )
= $false )
| ( ( mrel @ mactual @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(56,plain,
! [SV5: $i,SV8: mworld,SV2: mworld] :
( ( ( ~ ( mrel @ SV2 @ SV8 )
| ! [SY375: $i] :
( ~ ( eiw_di @ SY375 @ SV8 )
| ! [SY376: mworld] :
( ~ ( mrel @ SV8 @ SY376 )
| ~ ! [SY353: mworld] :
( ~ ( mrel @ SY376 @ SY353 )
| ( in @ SV5 @ SY375 @ SY353 ) )
| ! [SY354: mworld] :
( ~ ( mrel @ SY376 @ SY354 )
| ~ ! [SY355: mworld] :
( ~ ( mrel @ SY354 @ SY355 )
| ( in @ SY375 @ SV5 @ SY355 ) ) ) ) ) )
= $true )
| ( ( eiw_di @ SV5 @ SV2 )
= $false )
| ( ( mrel @ mactual @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(57,plain,
! [SV6: $i,SV9: mworld,SV3: mworld] :
( ( ( ~ ( mrel @ SV3 @ SV9 )
| ! [SY380: $i] :
( ~ ( eiw_di @ SY380 @ SV9 )
| ! [SY381: mworld] :
( ~ ( mrel @ SV9 @ SY381 )
| ~ ! [SY359: mworld] :
( ~ ( mrel @ SY381 @ SY359 )
| ( disjoint @ SV6 @ SY380 @ SY359 ) )
| ! [SY360: mworld] :
( ~ ( mrel @ SY381 @ SY360 )
| ( disjoint @ SY380 @ SV6 @ SY360 ) ) ) ) )
= $true )
| ( ( eiw_di @ SV6 @ SV3 )
= $false )
| ( ( mrel @ mactual @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(58,plain,
( ( ~ ( eiw_di @ sK4_SY361 @ sK3_SY338 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[54]) ).
thf(59,plain,
( ( ! [SY366: mworld] :
( ~ ( mrel @ sK3_SY338 @ SY366 )
| ~ ! [SY367: mworld] :
( ~ ( mrel @ SY366 @ SY367 )
| ~ ! [SY368: mworld] :
( ~ ( mrel @ SY367 @ SY368 )
| ( in @ sK2_SX0 @ sK4_SY361 @ SY368 ) ) )
| ! [SY369: mworld] :
( ~ ( mrel @ SY366 @ SY369 )
| ( disjoint @ ( singleton @ sK2_SX0 ) @ sK4_SY361 @ SY369 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[54]) ).
thf(60,plain,
! [SV4: $i,SV7: mworld,SV1: mworld] :
( ( ( ~ ( mrel @ SV1 @ SV7 ) )
= $true )
| ( ( ! [SY370: $i] :
( ~ ( eiw_di @ SY370 @ SV7 )
| ! [SY371: mworld] :
( ~ ( mrel @ SV7 @ SY371 )
| ~ ! [SY347: mworld] :
( ~ ( mrel @ SY371 @ SY347 )
| ~ ! [SY348: mworld] :
( ~ ( mrel @ SY347 @ SY348 )
| ( in @ SV4 @ SY370 @ SY348 ) ) )
| ! [SY349: mworld] :
( ~ ( mrel @ SY371 @ SY349 )
| ( disjoint @ ( singleton @ SV4 ) @ SY370 @ SY349 ) ) ) ) )
= $true )
| ( ( eiw_di @ SV4 @ SV1 )
= $false )
| ( ( mrel @ mactual @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[55]) ).
thf(61,plain,
! [SV5: $i,SV8: mworld,SV2: mworld] :
( ( ( ~ ( mrel @ SV2 @ SV8 ) )
= $true )
| ( ( ! [SY375: $i] :
( ~ ( eiw_di @ SY375 @ SV8 )
| ! [SY376: mworld] :
( ~ ( mrel @ SV8 @ SY376 )
| ~ ! [SY353: mworld] :
( ~ ( mrel @ SY376 @ SY353 )
| ( in @ SV5 @ SY375 @ SY353 ) )
| ! [SY354: mworld] :
( ~ ( mrel @ SY376 @ SY354 )
| ~ ! [SY355: mworld] :
( ~ ( mrel @ SY354 @ SY355 )
| ( in @ SY375 @ SV5 @ SY355 ) ) ) ) ) )
= $true )
| ( ( eiw_di @ SV5 @ SV2 )
= $false )
| ( ( mrel @ mactual @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[56]) ).
thf(62,plain,
! [SV6: $i,SV9: mworld,SV3: mworld] :
( ( ( ~ ( mrel @ SV3 @ SV9 ) )
= $true )
| ( ( ! [SY380: $i] :
( ~ ( eiw_di @ SY380 @ SV9 )
| ! [SY381: mworld] :
( ~ ( mrel @ SV9 @ SY381 )
| ~ ! [SY359: mworld] :
( ~ ( mrel @ SY381 @ SY359 )
| ( disjoint @ SV6 @ SY380 @ SY359 ) )
| ! [SY360: mworld] :
( ~ ( mrel @ SY381 @ SY360 )
| ( disjoint @ SY380 @ SV6 @ SY360 ) ) ) ) )
= $true )
| ( ( eiw_di @ SV6 @ SV3 )
= $false )
| ( ( mrel @ mactual @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[57]) ).
thf(63,plain,
( ( eiw_di @ sK4_SY361 @ sK3_SY338 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[58]) ).
thf(64,plain,
( ( ~ ( mrel @ sK3_SY338 @ sK5_SY366 )
| ~ ! [SY384: mworld] :
( ~ ( mrel @ sK5_SY366 @ SY384 )
| ~ ! [SY368: mworld] :
( ~ ( mrel @ SY384 @ SY368 )
| ( in @ sK2_SX0 @ sK4_SY361 @ SY368 ) ) )
| ! [SY386: mworld] :
( ~ ( mrel @ sK5_SY366 @ SY386 )
| ( disjoint @ ( singleton @ sK2_SX0 ) @ sK4_SY361 @ SY386 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[59]) ).
thf(65,plain,
! [SV4: $i,SV7: mworld,SV1: mworld] :
( ( ( mrel @ SV1 @ SV7 )
= $false )
| ( ( ! [SY370: $i] :
( ~ ( eiw_di @ SY370 @ SV7 )
| ! [SY371: mworld] :
( ~ ( mrel @ SV7 @ SY371 )
| ~ ! [SY347: mworld] :
( ~ ( mrel @ SY371 @ SY347 )
| ~ ! [SY348: mworld] :
( ~ ( mrel @ SY347 @ SY348 )
| ( in @ SV4 @ SY370 @ SY348 ) ) )
| ! [SY349: mworld] :
( ~ ( mrel @ SY371 @ SY349 )
| ( disjoint @ ( singleton @ SV4 ) @ SY370 @ SY349 ) ) ) ) )
= $true )
| ( ( eiw_di @ SV4 @ SV1 )
= $false )
| ( ( mrel @ mactual @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(66,plain,
! [SV5: $i,SV8: mworld,SV2: mworld] :
( ( ( mrel @ SV2 @ SV8 )
= $false )
| ( ( ! [SY375: $i] :
( ~ ( eiw_di @ SY375 @ SV8 )
| ! [SY376: mworld] :
( ~ ( mrel @ SV8 @ SY376 )
| ~ ! [SY353: mworld] :
( ~ ( mrel @ SY376 @ SY353 )
| ( in @ SV5 @ SY375 @ SY353 ) )
| ! [SY354: mworld] :
( ~ ( mrel @ SY376 @ SY354 )
| ~ ! [SY355: mworld] :
( ~ ( mrel @ SY354 @ SY355 )
| ( in @ SY375 @ SV5 @ SY355 ) ) ) ) ) )
= $true )
| ( ( eiw_di @ SV5 @ SV2 )
= $false )
| ( ( mrel @ mactual @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(67,plain,
! [SV6: $i,SV9: mworld,SV3: mworld] :
( ( ( mrel @ SV3 @ SV9 )
= $false )
| ( ( ! [SY380: $i] :
( ~ ( eiw_di @ SY380 @ SV9 )
| ! [SY381: mworld] :
( ~ ( mrel @ SV9 @ SY381 )
| ~ ! [SY359: mworld] :
( ~ ( mrel @ SY381 @ SY359 )
| ( disjoint @ SV6 @ SY380 @ SY359 ) )
| ! [SY360: mworld] :
( ~ ( mrel @ SY381 @ SY360 )
| ( disjoint @ SY380 @ SV6 @ SY360 ) ) ) ) )
= $true )
| ( ( eiw_di @ SV6 @ SV3 )
= $false )
| ( ( mrel @ mactual @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(68,plain,
( ( ~ ( mrel @ sK3_SY338 @ sK5_SY366 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[64]) ).
thf(69,plain,
( ( ~ ! [SY384: mworld] :
( ~ ( mrel @ sK5_SY366 @ SY384 )
| ~ ! [SY368: mworld] :
( ~ ( mrel @ SY384 @ SY368 )
| ( in @ sK2_SX0 @ sK4_SY361 @ SY368 ) ) )
| ! [SY386: mworld] :
( ~ ( mrel @ sK5_SY366 @ SY386 )
| ( disjoint @ ( singleton @ sK2_SX0 ) @ sK4_SY361 @ SY386 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[64]) ).
thf(70,plain,
! [SV1: mworld,SV4: $i,SV7: mworld,SV10: $i] :
( ( ( ~ ( eiw_di @ SV10 @ SV7 )
| ! [SY387: mworld] :
( ~ ( mrel @ SV7 @ SY387 )
| ~ ! [SY388: mworld] :
( ~ ( mrel @ SY387 @ SY388 )
| ~ ! [SY389: mworld] :
( ~ ( mrel @ SY388 @ SY389 )
| ( in @ SV4 @ SV10 @ SY389 ) ) )
| ! [SY390: mworld] :
( ~ ( mrel @ SY387 @ SY390 )
| ( disjoint @ ( singleton @ SV4 ) @ SV10 @ SY390 ) ) ) )
= $true )
| ( ( mrel @ SV1 @ SV7 )
= $false )
| ( ( eiw_di @ SV4 @ SV1 )
= $false )
| ( ( mrel @ mactual @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(71,plain,
! [SV2: mworld,SV5: $i,SV8: mworld,SV11: $i] :
( ( ( ~ ( eiw_di @ SV11 @ SV8 )
| ! [SY391: mworld] :
( ~ ( mrel @ SV8 @ SY391 )
| ~ ! [SY392: mworld] :
( ~ ( mrel @ SY391 @ SY392 )
| ( in @ SV5 @ SV11 @ SY392 ) )
| ! [SY393: mworld] :
( ~ ( mrel @ SY391 @ SY393 )
| ~ ! [SY394: mworld] :
( ~ ( mrel @ SY393 @ SY394 )
| ( in @ SV11 @ SV5 @ SY394 ) ) ) ) )
= $true )
| ( ( mrel @ SV2 @ SV8 )
= $false )
| ( ( eiw_di @ SV5 @ SV2 )
= $false )
| ( ( mrel @ mactual @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(72,plain,
! [SV3: mworld,SV6: $i,SV9: mworld,SV12: $i] :
( ( ( ~ ( eiw_di @ SV12 @ SV9 )
| ! [SY395: mworld] :
( ~ ( mrel @ SV9 @ SY395 )
| ~ ! [SY396: mworld] :
( ~ ( mrel @ SY395 @ SY396 )
| ( disjoint @ SV6 @ SV12 @ SY396 ) )
| ! [SY397: mworld] :
( ~ ( mrel @ SY395 @ SY397 )
| ( disjoint @ SV12 @ SV6 @ SY397 ) ) ) )
= $true )
| ( ( mrel @ SV3 @ SV9 )
= $false )
| ( ( eiw_di @ SV6 @ SV3 )
= $false )
| ( ( mrel @ mactual @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(73,plain,
( ( mrel @ sK3_SY338 @ sK5_SY366 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[68]) ).
thf(74,plain,
( ( ~ ! [SY384: mworld] :
( ~ ( mrel @ sK5_SY366 @ SY384 )
| ~ ! [SY368: mworld] :
( ~ ( mrel @ SY384 @ SY368 )
| ( in @ sK2_SX0 @ sK4_SY361 @ SY368 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[69]) ).
thf(75,plain,
( ( ! [SY386: mworld] :
( ~ ( mrel @ sK5_SY366 @ SY386 )
| ( disjoint @ ( singleton @ sK2_SX0 ) @ sK4_SY361 @ SY386 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[69]) ).
thf(76,plain,
! [SV1: mworld,SV4: $i,SV7: mworld,SV10: $i] :
( ( ( ~ ( eiw_di @ SV10 @ SV7 ) )
= $true )
| ( ( ! [SY387: mworld] :
( ~ ( mrel @ SV7 @ SY387 )
| ~ ! [SY388: mworld] :
( ~ ( mrel @ SY387 @ SY388 )
| ~ ! [SY389: mworld] :
( ~ ( mrel @ SY388 @ SY389 )
| ( in @ SV4 @ SV10 @ SY389 ) ) )
| ! [SY390: mworld] :
( ~ ( mrel @ SY387 @ SY390 )
| ( disjoint @ ( singleton @ SV4 ) @ SV10 @ SY390 ) ) ) )
= $true )
| ( ( mrel @ SV1 @ SV7 )
= $false )
| ( ( eiw_di @ SV4 @ SV1 )
= $false )
| ( ( mrel @ mactual @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[70]) ).
thf(77,plain,
! [SV2: mworld,SV5: $i,SV8: mworld,SV11: $i] :
( ( ( ~ ( eiw_di @ SV11 @ SV8 ) )
= $true )
| ( ( ! [SY391: mworld] :
( ~ ( mrel @ SV8 @ SY391 )
| ~ ! [SY392: mworld] :
( ~ ( mrel @ SY391 @ SY392 )
| ( in @ SV5 @ SV11 @ SY392 ) )
| ! [SY393: mworld] :
( ~ ( mrel @ SY391 @ SY393 )
| ~ ! [SY394: mworld] :
( ~ ( mrel @ SY393 @ SY394 )
| ( in @ SV11 @ SV5 @ SY394 ) ) ) ) )
= $true )
| ( ( mrel @ SV2 @ SV8 )
= $false )
| ( ( eiw_di @ SV5 @ SV2 )
= $false )
| ( ( mrel @ mactual @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[71]) ).
thf(78,plain,
! [SV3: mworld,SV6: $i,SV9: mworld,SV12: $i] :
( ( ( ~ ( eiw_di @ SV12 @ SV9 ) )
= $true )
| ( ( ! [SY395: mworld] :
( ~ ( mrel @ SV9 @ SY395 )
| ~ ! [SY396: mworld] :
( ~ ( mrel @ SY395 @ SY396 )
| ( disjoint @ SV6 @ SV12 @ SY396 ) )
| ! [SY397: mworld] :
( ~ ( mrel @ SY395 @ SY397 )
| ( disjoint @ SV12 @ SV6 @ SY397 ) ) ) )
= $true )
| ( ( mrel @ SV3 @ SV9 )
= $false )
| ( ( eiw_di @ SV6 @ SV3 )
= $false )
| ( ( mrel @ mactual @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[72]) ).
thf(79,plain,
( ( ! [SY384: mworld] :
( ~ ( mrel @ sK5_SY366 @ SY384 )
| ~ ! [SY368: mworld] :
( ~ ( mrel @ SY384 @ SY368 )
| ( in @ sK2_SX0 @ sK4_SY361 @ SY368 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[74]) ).
thf(80,plain,
( ( ~ ( mrel @ sK5_SY366 @ sK6_SY386 )
| ( disjoint @ ( singleton @ sK2_SX0 ) @ sK4_SY361 @ sK6_SY386 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[75]) ).
thf(81,plain,
! [SV1: mworld,SV4: $i,SV7: mworld,SV10: $i] :
( ( ( eiw_di @ SV10 @ SV7 )
= $false )
| ( ( ! [SY387: mworld] :
( ~ ( mrel @ SV7 @ SY387 )
| ~ ! [SY388: mworld] :
( ~ ( mrel @ SY387 @ SY388 )
| ~ ! [SY389: mworld] :
( ~ ( mrel @ SY388 @ SY389 )
| ( in @ SV4 @ SV10 @ SY389 ) ) )
| ! [SY390: mworld] :
( ~ ( mrel @ SY387 @ SY390 )
| ( disjoint @ ( singleton @ SV4 ) @ SV10 @ SY390 ) ) ) )
= $true )
| ( ( mrel @ SV1 @ SV7 )
= $false )
| ( ( eiw_di @ SV4 @ SV1 )
= $false )
| ( ( mrel @ mactual @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(82,plain,
! [SV2: mworld,SV5: $i,SV8: mworld,SV11: $i] :
( ( ( eiw_di @ SV11 @ SV8 )
= $false )
| ( ( ! [SY391: mworld] :
( ~ ( mrel @ SV8 @ SY391 )
| ~ ! [SY392: mworld] :
( ~ ( mrel @ SY391 @ SY392 )
| ( in @ SV5 @ SV11 @ SY392 ) )
| ! [SY393: mworld] :
( ~ ( mrel @ SY391 @ SY393 )
| ~ ! [SY394: mworld] :
( ~ ( mrel @ SY393 @ SY394 )
| ( in @ SV11 @ SV5 @ SY394 ) ) ) ) )
= $true )
| ( ( mrel @ SV2 @ SV8 )
= $false )
| ( ( eiw_di @ SV5 @ SV2 )
= $false )
| ( ( mrel @ mactual @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(83,plain,
! [SV3: mworld,SV6: $i,SV9: mworld,SV12: $i] :
( ( ( eiw_di @ SV12 @ SV9 )
= $false )
| ( ( ! [SY395: mworld] :
( ~ ( mrel @ SV9 @ SY395 )
| ~ ! [SY396: mworld] :
( ~ ( mrel @ SY395 @ SY396 )
| ( disjoint @ SV6 @ SV12 @ SY396 ) )
| ! [SY397: mworld] :
( ~ ( mrel @ SY395 @ SY397 )
| ( disjoint @ SV12 @ SV6 @ SY397 ) ) ) )
= $true )
| ( ( mrel @ SV3 @ SV9 )
= $false )
| ( ( eiw_di @ SV6 @ SV3 )
= $false )
| ( ( mrel @ mactual @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(84,plain,
! [SV13: mworld] :
( ( ~ ( mrel @ sK5_SY366 @ SV13 )
| ~ ! [SY398: mworld] :
( ~ ( mrel @ SV13 @ SY398 )
| ( in @ sK2_SX0 @ sK4_SY361 @ SY398 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(85,plain,
( ( ~ ( mrel @ sK5_SY366 @ sK6_SY386 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[80]) ).
thf(86,plain,
( ( disjoint @ ( singleton @ sK2_SX0 ) @ sK4_SY361 @ sK6_SY386 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[80]) ).
thf(87,plain,
! [SV1: mworld,SV10: $i,SV4: $i,SV14: mworld,SV7: mworld] :
( ( ( ~ ( mrel @ SV7 @ SV14 )
| ~ ! [SY399: mworld] :
( ~ ( mrel @ SV14 @ SY399 )
| ~ ! [SY389: mworld] :
( ~ ( mrel @ SY399 @ SY389 )
| ( in @ SV4 @ SV10 @ SY389 ) ) )
| ! [SY401: mworld] :
( ~ ( mrel @ SV14 @ SY401 )
| ( disjoint @ ( singleton @ SV4 ) @ SV10 @ SY401 ) ) )
= $true )
| ( ( eiw_di @ SV10 @ SV7 )
= $false )
| ( ( mrel @ SV1 @ SV7 )
= $false )
| ( ( eiw_di @ SV4 @ SV1 )
= $false )
| ( ( mrel @ mactual @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(88,plain,
! [SV2: mworld,SV11: $i,SV5: $i,SV15: mworld,SV8: mworld] :
( ( ( ~ ( mrel @ SV8 @ SV15 )
| ~ ! [SY402: mworld] :
( ~ ( mrel @ SV15 @ SY402 )
| ( in @ SV5 @ SV11 @ SY402 ) )
| ! [SY403: mworld] :
( ~ ( mrel @ SV15 @ SY403 )
| ~ ! [SY394: mworld] :
( ~ ( mrel @ SY403 @ SY394 )
| ( in @ SV11 @ SV5 @ SY394 ) ) ) )
= $true )
| ( ( eiw_di @ SV11 @ SV8 )
= $false )
| ( ( mrel @ SV2 @ SV8 )
= $false )
| ( ( eiw_di @ SV5 @ SV2 )
= $false )
| ( ( mrel @ mactual @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(89,plain,
! [SV3: mworld,SV12: $i,SV6: $i,SV16: mworld,SV9: mworld] :
( ( ( ~ ( mrel @ SV9 @ SV16 )
| ~ ! [SY405: mworld] :
( ~ ( mrel @ SV16 @ SY405 )
| ( disjoint @ SV6 @ SV12 @ SY405 ) )
| ! [SY406: mworld] :
( ~ ( mrel @ SV16 @ SY406 )
| ( disjoint @ SV12 @ SV6 @ SY406 ) ) )
= $true )
| ( ( eiw_di @ SV12 @ SV9 )
= $false )
| ( ( mrel @ SV3 @ SV9 )
= $false )
| ( ( eiw_di @ SV6 @ SV3 )
= $false )
| ( ( mrel @ mactual @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(90,plain,
! [SV13: mworld] :
( ( ( ~ ( mrel @ sK5_SY366 @ SV13 ) )
= $true )
| ( ( ~ ! [SY398: mworld] :
( ~ ( mrel @ SV13 @ SY398 )
| ( in @ sK2_SX0 @ sK4_SY361 @ SY398 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[84]) ).
thf(91,plain,
( ( mrel @ sK5_SY366 @ sK6_SY386 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[85]) ).
thf(92,plain,
! [SV1: mworld,SV10: $i,SV4: $i,SV14: mworld,SV7: mworld] :
( ( ( ~ ( mrel @ SV7 @ SV14 ) )
= $true )
| ( ( ~ ! [SY399: mworld] :
( ~ ( mrel @ SV14 @ SY399 )
| ~ ! [SY389: mworld] :
( ~ ( mrel @ SY399 @ SY389 )
| ( in @ SV4 @ SV10 @ SY389 ) ) )
| ! [SY401: mworld] :
( ~ ( mrel @ SV14 @ SY401 )
| ( disjoint @ ( singleton @ SV4 ) @ SV10 @ SY401 ) ) )
= $true )
| ( ( eiw_di @ SV10 @ SV7 )
= $false )
| ( ( mrel @ SV1 @ SV7 )
= $false )
| ( ( eiw_di @ SV4 @ SV1 )
= $false )
| ( ( mrel @ mactual @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[87]) ).
thf(93,plain,
! [SV2: mworld,SV11: $i,SV5: $i,SV15: mworld,SV8: mworld] :
( ( ( ~ ( mrel @ SV8 @ SV15 ) )
= $true )
| ( ( ~ ! [SY402: mworld] :
( ~ ( mrel @ SV15 @ SY402 )
| ( in @ SV5 @ SV11 @ SY402 ) )
| ! [SY403: mworld] :
( ~ ( mrel @ SV15 @ SY403 )
| ~ ! [SY394: mworld] :
( ~ ( mrel @ SY403 @ SY394 )
| ( in @ SV11 @ SV5 @ SY394 ) ) ) )
= $true )
| ( ( eiw_di @ SV11 @ SV8 )
= $false )
| ( ( mrel @ SV2 @ SV8 )
= $false )
| ( ( eiw_di @ SV5 @ SV2 )
= $false )
| ( ( mrel @ mactual @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[88]) ).
thf(94,plain,
! [SV3: mworld,SV12: $i,SV6: $i,SV16: mworld,SV9: mworld] :
( ( ( ~ ( mrel @ SV9 @ SV16 ) )
= $true )
| ( ( ~ ! [SY405: mworld] :
( ~ ( mrel @ SV16 @ SY405 )
| ( disjoint @ SV6 @ SV12 @ SY405 ) )
| ! [SY406: mworld] :
( ~ ( mrel @ SV16 @ SY406 )
| ( disjoint @ SV12 @ SV6 @ SY406 ) ) )
= $true )
| ( ( eiw_di @ SV12 @ SV9 )
= $false )
| ( ( mrel @ SV3 @ SV9 )
= $false )
| ( ( eiw_di @ SV6 @ SV3 )
= $false )
| ( ( mrel @ mactual @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[89]) ).
thf(95,plain,
! [SV13: mworld] :
( ( ( mrel @ sK5_SY366 @ SV13 )
= $false )
| ( ( ~ ! [SY398: mworld] :
( ~ ( mrel @ SV13 @ SY398 )
| ( in @ sK2_SX0 @ sK4_SY361 @ SY398 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(96,plain,
! [SV1: mworld,SV10: $i,SV4: $i,SV14: mworld,SV7: mworld] :
( ( ( mrel @ SV7 @ SV14 )
= $false )
| ( ( ~ ! [SY399: mworld] :
( ~ ( mrel @ SV14 @ SY399 )
| ~ ! [SY389: mworld] :
( ~ ( mrel @ SY399 @ SY389 )
| ( in @ SV4 @ SV10 @ SY389 ) ) )
| ! [SY401: mworld] :
( ~ ( mrel @ SV14 @ SY401 )
| ( disjoint @ ( singleton @ SV4 ) @ SV10 @ SY401 ) ) )
= $true )
| ( ( eiw_di @ SV10 @ SV7 )
= $false )
| ( ( mrel @ SV1 @ SV7 )
= $false )
| ( ( eiw_di @ SV4 @ SV1 )
= $false )
| ( ( mrel @ mactual @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(97,plain,
! [SV2: mworld,SV11: $i,SV5: $i,SV15: mworld,SV8: mworld] :
( ( ( mrel @ SV8 @ SV15 )
= $false )
| ( ( ~ ! [SY402: mworld] :
( ~ ( mrel @ SV15 @ SY402 )
| ( in @ SV5 @ SV11 @ SY402 ) )
| ! [SY403: mworld] :
( ~ ( mrel @ SV15 @ SY403 )
| ~ ! [SY394: mworld] :
( ~ ( mrel @ SY403 @ SY394 )
| ( in @ SV11 @ SV5 @ SY394 ) ) ) )
= $true )
| ( ( eiw_di @ SV11 @ SV8 )
= $false )
| ( ( mrel @ SV2 @ SV8 )
= $false )
| ( ( eiw_di @ SV5 @ SV2 )
= $false )
| ( ( mrel @ mactual @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(98,plain,
! [SV3: mworld,SV12: $i,SV6: $i,SV16: mworld,SV9: mworld] :
( ( ( mrel @ SV9 @ SV16 )
= $false )
| ( ( ~ ! [SY405: mworld] :
( ~ ( mrel @ SV16 @ SY405 )
| ( disjoint @ SV6 @ SV12 @ SY405 ) )
| ! [SY406: mworld] :
( ~ ( mrel @ SV16 @ SY406 )
| ( disjoint @ SV12 @ SV6 @ SY406 ) ) )
= $true )
| ( ( eiw_di @ SV12 @ SV9 )
= $false )
| ( ( mrel @ SV3 @ SV9 )
= $false )
| ( ( eiw_di @ SV6 @ SV3 )
= $false )
| ( ( mrel @ mactual @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(99,plain,
! [SV13: mworld] :
( ( ( ! [SY398: mworld] :
( ~ ( mrel @ SV13 @ SY398 )
| ( in @ sK2_SX0 @ sK4_SY361 @ SY398 ) ) )
= $false )
| ( ( mrel @ sK5_SY366 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(100,plain,
! [SV1: mworld,SV7: mworld,SV10: $i,SV4: $i,SV14: mworld] :
( ( ( ~ ! [SY399: mworld] :
( ~ ( mrel @ SV14 @ SY399 )
| ~ ! [SY389: mworld] :
( ~ ( mrel @ SY399 @ SY389 )
| ( in @ SV4 @ SV10 @ SY389 ) ) ) )
= $true )
| ( ( ! [SY401: mworld] :
( ~ ( mrel @ SV14 @ SY401 )
| ( disjoint @ ( singleton @ SV4 ) @ SV10 @ SY401 ) ) )
= $true )
| ( ( mrel @ SV7 @ SV14 )
= $false )
| ( ( eiw_di @ SV10 @ SV7 )
= $false )
| ( ( mrel @ SV1 @ SV7 )
= $false )
| ( ( eiw_di @ SV4 @ SV1 )
= $false )
| ( ( mrel @ mactual @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[96]) ).
thf(101,plain,
! [SV2: mworld,SV8: mworld,SV11: $i,SV5: $i,SV15: mworld] :
( ( ( ~ ! [SY402: mworld] :
( ~ ( mrel @ SV15 @ SY402 )
| ( in @ SV5 @ SV11 @ SY402 ) ) )
= $true )
| ( ( ! [SY403: mworld] :
( ~ ( mrel @ SV15 @ SY403 )
| ~ ! [SY394: mworld] :
( ~ ( mrel @ SY403 @ SY394 )
| ( in @ SV11 @ SV5 @ SY394 ) ) ) )
= $true )
| ( ( mrel @ SV8 @ SV15 )
= $false )
| ( ( eiw_di @ SV11 @ SV8 )
= $false )
| ( ( mrel @ SV2 @ SV8 )
= $false )
| ( ( eiw_di @ SV5 @ SV2 )
= $false )
| ( ( mrel @ mactual @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[97]) ).
thf(102,plain,
! [SV3: mworld,SV9: mworld,SV12: $i,SV6: $i,SV16: mworld] :
( ( ( ~ ! [SY405: mworld] :
( ~ ( mrel @ SV16 @ SY405 )
| ( disjoint @ SV6 @ SV12 @ SY405 ) ) )
= $true )
| ( ( ! [SY406: mworld] :
( ~ ( mrel @ SV16 @ SY406 )
| ( disjoint @ SV12 @ SV6 @ SY406 ) ) )
= $true )
| ( ( mrel @ SV9 @ SV16 )
= $false )
| ( ( eiw_di @ SV12 @ SV9 )
= $false )
| ( ( mrel @ SV3 @ SV9 )
= $false )
| ( ( eiw_di @ SV6 @ SV3 )
= $false )
| ( ( mrel @ mactual @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[98]) ).
thf(103,plain,
! [SV13: mworld] :
( ( ( ~ ( mrel @ SV13 @ ( sK7_SY398 @ SV13 ) )
| ( in @ sK2_SX0 @ sK4_SY361 @ ( sK7_SY398 @ SV13 ) ) )
= $false )
| ( ( mrel @ sK5_SY366 @ SV13 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[99]) ).
thf(104,plain,
! [SV1: mworld,SV7: mworld,SV10: $i,SV4: $i,SV14: mworld] :
( ( ( ! [SY399: mworld] :
( ~ ( mrel @ SV14 @ SY399 )
| ~ ! [SY389: mworld] :
( ~ ( mrel @ SY399 @ SY389 )
| ( in @ SV4 @ SV10 @ SY389 ) ) ) )
= $false )
| ( ( ! [SY401: mworld] :
( ~ ( mrel @ SV14 @ SY401 )
| ( disjoint @ ( singleton @ SV4 ) @ SV10 @ SY401 ) ) )
= $true )
| ( ( mrel @ SV7 @ SV14 )
= $false )
| ( ( eiw_di @ SV10 @ SV7 )
= $false )
| ( ( mrel @ SV1 @ SV7 )
= $false )
| ( ( eiw_di @ SV4 @ SV1 )
= $false )
| ( ( mrel @ mactual @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(105,plain,
! [SV2: mworld,SV8: mworld,SV11: $i,SV5: $i,SV15: mworld] :
( ( ( ! [SY402: mworld] :
( ~ ( mrel @ SV15 @ SY402 )
| ( in @ SV5 @ SV11 @ SY402 ) ) )
= $false )
| ( ( ! [SY403: mworld] :
( ~ ( mrel @ SV15 @ SY403 )
| ~ ! [SY394: mworld] :
( ~ ( mrel @ SY403 @ SY394 )
| ( in @ SV11 @ SV5 @ SY394 ) ) ) )
= $true )
| ( ( mrel @ SV8 @ SV15 )
= $false )
| ( ( eiw_di @ SV11 @ SV8 )
= $false )
| ( ( mrel @ SV2 @ SV8 )
= $false )
| ( ( eiw_di @ SV5 @ SV2 )
= $false )
| ( ( mrel @ mactual @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(106,plain,
! [SV3: mworld,SV9: mworld,SV12: $i,SV6: $i,SV16: mworld] :
( ( ( ! [SY405: mworld] :
( ~ ( mrel @ SV16 @ SY405 )
| ( disjoint @ SV6 @ SV12 @ SY405 ) ) )
= $false )
| ( ( ! [SY406: mworld] :
( ~ ( mrel @ SV16 @ SY406 )
| ( disjoint @ SV12 @ SV6 @ SY406 ) ) )
= $true )
| ( ( mrel @ SV9 @ SV16 )
= $false )
| ( ( eiw_di @ SV12 @ SV9 )
= $false )
| ( ( mrel @ SV3 @ SV9 )
= $false )
| ( ( eiw_di @ SV6 @ SV3 )
= $false )
| ( ( mrel @ mactual @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(107,plain,
! [SV13: mworld] :
( ( ( ~ ( mrel @ SV13 @ ( sK7_SY398 @ SV13 ) ) )
= $false )
| ( ( mrel @ sK5_SY366 @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[103]) ).
thf(108,plain,
! [SV13: mworld] :
( ( ( in @ sK2_SX0 @ sK4_SY361 @ ( sK7_SY398 @ SV13 ) )
= $false )
| ( ( mrel @ sK5_SY366 @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[103]) ).
thf(109,plain,
! [SV4: $i,SV10: $i,SV7: mworld,SV1: mworld,SV14: mworld] :
( ( ( ~ ( mrel @ SV14 @ ( sK8_SY399 @ SV1 @ SV7 @ SV10 @ SV4 @ SV14 ) )
| ~ ! [SY407: mworld] :
( ~ ( mrel @ ( sK8_SY399 @ SV1 @ SV7 @ SV10 @ SV4 @ SV14 ) @ SY407 )
| ( in @ SV4 @ SV10 @ SY407 ) ) )
= $false )
| ( ( ! [SY401: mworld] :
( ~ ( mrel @ SV14 @ SY401 )
| ( disjoint @ ( singleton @ SV4 ) @ SV10 @ SY401 ) ) )
= $true )
| ( ( mrel @ SV7 @ SV14 )
= $false )
| ( ( eiw_di @ SV10 @ SV7 )
= $false )
| ( ( mrel @ SV1 @ SV7 )
= $false )
| ( ( eiw_di @ SV4 @ SV1 )
= $false )
| ( ( mrel @ mactual @ SV1 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[104]) ).
thf(110,plain,
! [SV5: $i,SV11: $i,SV8: mworld,SV2: mworld,SV15: mworld] :
( ( ( ~ ( mrel @ SV15 @ ( sK9_SY402 @ SV2 @ SV8 @ SV11 @ SV5 @ SV15 ) )
| ( in @ SV5 @ SV11 @ ( sK9_SY402 @ SV2 @ SV8 @ SV11 @ SV5 @ SV15 ) ) )
= $false )
| ( ( ! [SY403: mworld] :
( ~ ( mrel @ SV15 @ SY403 )
| ~ ! [SY394: mworld] :
( ~ ( mrel @ SY403 @ SY394 )
| ( in @ SV11 @ SV5 @ SY394 ) ) ) )
= $true )
| ( ( mrel @ SV8 @ SV15 )
= $false )
| ( ( eiw_di @ SV11 @ SV8 )
= $false )
| ( ( mrel @ SV2 @ SV8 )
= $false )
| ( ( eiw_di @ SV5 @ SV2 )
= $false )
| ( ( mrel @ mactual @ SV2 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[105]) ).
thf(111,plain,
! [SV6: $i,SV12: $i,SV9: mworld,SV3: mworld,SV16: mworld] :
( ( ( ~ ( mrel @ SV16 @ ( sK10_SY405 @ SV3 @ SV9 @ SV12 @ SV6 @ SV16 ) )
| ( disjoint @ SV6 @ SV12 @ ( sK10_SY405 @ SV3 @ SV9 @ SV12 @ SV6 @ SV16 ) ) )
= $false )
| ( ( ! [SY406: mworld] :
( ~ ( mrel @ SV16 @ SY406 )
| ( disjoint @ SV12 @ SV6 @ SY406 ) ) )
= $true )
| ( ( mrel @ SV9 @ SV16 )
= $false )
| ( ( eiw_di @ SV12 @ SV9 )
= $false )
| ( ( mrel @ SV3 @ SV9 )
= $false )
| ( ( eiw_di @ SV6 @ SV3 )
= $false )
| ( ( mrel @ mactual @ SV3 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[106]) ).
thf(112,plain,
! [SV13: mworld] :
( ( ( mrel @ SV13 @ ( sK7_SY398 @ SV13 ) )
= $true )
| ( ( mrel @ sK5_SY366 @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[107]) ).
thf(113,plain,
! [SV4: $i,SV10: $i,SV7: mworld,SV1: mworld,SV14: mworld] :
( ( ( ~ ( mrel @ SV14 @ ( sK8_SY399 @ SV1 @ SV7 @ SV10 @ SV4 @ SV14 ) ) )
= $false )
| ( ( ! [SY401: mworld] :
( ~ ( mrel @ SV14 @ SY401 )
| ( disjoint @ ( singleton @ SV4 ) @ SV10 @ SY401 ) ) )
= $true )
| ( ( mrel @ SV7 @ SV14 )
= $false )
| ( ( eiw_di @ SV10 @ SV7 )
= $false )
| ( ( mrel @ SV1 @ SV7 )
= $false )
| ( ( eiw_di @ SV4 @ SV1 )
= $false )
| ( ( mrel @ mactual @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[109]) ).
thf(114,plain,
! [SV14: mworld,SV4: $i,SV10: $i,SV7: mworld,SV1: mworld] :
( ( ( ~ ! [SY407: mworld] :
( ~ ( mrel @ ( sK8_SY399 @ SV1 @ SV7 @ SV10 @ SV4 @ SV14 ) @ SY407 )
| ( in @ SV4 @ SV10 @ SY407 ) ) )
= $false )
| ( ( ! [SY401: mworld] :
( ~ ( mrel @ SV14 @ SY401 )
| ( disjoint @ ( singleton @ SV4 ) @ SV10 @ SY401 ) ) )
= $true )
| ( ( mrel @ SV7 @ SV14 )
= $false )
| ( ( eiw_di @ SV10 @ SV7 )
= $false )
| ( ( mrel @ SV1 @ SV7 )
= $false )
| ( ( eiw_di @ SV4 @ SV1 )
= $false )
| ( ( mrel @ mactual @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[109]) ).
thf(115,plain,
! [SV5: $i,SV11: $i,SV8: mworld,SV2: mworld,SV15: mworld] :
( ( ( ~ ( mrel @ SV15 @ ( sK9_SY402 @ SV2 @ SV8 @ SV11 @ SV5 @ SV15 ) ) )
= $false )
| ( ( ! [SY403: mworld] :
( ~ ( mrel @ SV15 @ SY403 )
| ~ ! [SY394: mworld] :
( ~ ( mrel @ SY403 @ SY394 )
| ( in @ SV11 @ SV5 @ SY394 ) ) ) )
= $true )
| ( ( mrel @ SV8 @ SV15 )
= $false )
| ( ( eiw_di @ SV11 @ SV8 )
= $false )
| ( ( mrel @ SV2 @ SV8 )
= $false )
| ( ( eiw_di @ SV5 @ SV2 )
= $false )
| ( ( mrel @ mactual @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[110]) ).
thf(116,plain,
! [SV15: mworld,SV8: mworld,SV2: mworld,SV11: $i,SV5: $i] :
( ( ( in @ SV5 @ SV11 @ ( sK9_SY402 @ SV2 @ SV8 @ SV11 @ SV5 @ SV15 ) )
= $false )
| ( ( ! [SY403: mworld] :
( ~ ( mrel @ SV15 @ SY403 )
| ~ ! [SY394: mworld] :
( ~ ( mrel @ SY403 @ SY394 )
| ( in @ SV11 @ SV5 @ SY394 ) ) ) )
= $true )
| ( ( mrel @ SV8 @ SV15 )
= $false )
| ( ( eiw_di @ SV11 @ SV8 )
= $false )
| ( ( mrel @ SV2 @ SV8 )
= $false )
| ( ( eiw_di @ SV5 @ SV2 )
= $false )
| ( ( mrel @ mactual @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[110]) ).
thf(117,plain,
! [SV6: $i,SV12: $i,SV9: mworld,SV3: mworld,SV16: mworld] :
( ( ( ~ ( mrel @ SV16 @ ( sK10_SY405 @ SV3 @ SV9 @ SV12 @ SV6 @ SV16 ) ) )
= $false )
| ( ( ! [SY406: mworld] :
( ~ ( mrel @ SV16 @ SY406 )
| ( disjoint @ SV12 @ SV6 @ SY406 ) ) )
= $true )
| ( ( mrel @ SV9 @ SV16 )
= $false )
| ( ( eiw_di @ SV12 @ SV9 )
= $false )
| ( ( mrel @ SV3 @ SV9 )
= $false )
| ( ( eiw_di @ SV6 @ SV3 )
= $false )
| ( ( mrel @ mactual @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[111]) ).
thf(118,plain,
! [SV16: mworld,SV9: mworld,SV3: mworld,SV12: $i,SV6: $i] :
( ( ( disjoint @ SV6 @ SV12 @ ( sK10_SY405 @ SV3 @ SV9 @ SV12 @ SV6 @ SV16 ) )
= $false )
| ( ( ! [SY406: mworld] :
( ~ ( mrel @ SV16 @ SY406 )
| ( disjoint @ SV12 @ SV6 @ SY406 ) ) )
= $true )
| ( ( mrel @ SV9 @ SV16 )
= $false )
| ( ( eiw_di @ SV12 @ SV9 )
= $false )
| ( ( mrel @ SV3 @ SV9 )
= $false )
| ( ( eiw_di @ SV6 @ SV3 )
= $false )
| ( ( mrel @ mactual @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[111]) ).
thf(119,plain,
! [SV4: $i,SV10: $i,SV7: mworld,SV1: mworld,SV14: mworld] :
( ( ( mrel @ SV14 @ ( sK8_SY399 @ SV1 @ SV7 @ SV10 @ SV4 @ SV14 ) )
= $true )
| ( ( ! [SY401: mworld] :
( ~ ( mrel @ SV14 @ SY401 )
| ( disjoint @ ( singleton @ SV4 ) @ SV10 @ SY401 ) ) )
= $true )
| ( ( mrel @ SV7 @ SV14 )
= $false )
| ( ( eiw_di @ SV10 @ SV7 )
= $false )
| ( ( mrel @ SV1 @ SV7 )
= $false )
| ( ( eiw_di @ SV4 @ SV1 )
= $false )
| ( ( mrel @ mactual @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[113]) ).
thf(120,plain,
! [SV14: mworld,SV4: $i,SV10: $i,SV7: mworld,SV1: mworld] :
( ( ( ! [SY407: mworld] :
( ~ ( mrel @ ( sK8_SY399 @ SV1 @ SV7 @ SV10 @ SV4 @ SV14 ) @ SY407 )
| ( in @ SV4 @ SV10 @ SY407 ) ) )
= $true )
| ( ( ! [SY401: mworld] :
( ~ ( mrel @ SV14 @ SY401 )
| ( disjoint @ ( singleton @ SV4 ) @ SV10 @ SY401 ) ) )
= $true )
| ( ( mrel @ SV7 @ SV14 )
= $false )
| ( ( eiw_di @ SV10 @ SV7 )
= $false )
| ( ( mrel @ SV1 @ SV7 )
= $false )
| ( ( eiw_di @ SV4 @ SV1 )
= $false )
| ( ( mrel @ mactual @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[114]) ).
thf(121,plain,
! [SV5: $i,SV11: $i,SV8: mworld,SV2: mworld,SV15: mworld] :
( ( ( mrel @ SV15 @ ( sK9_SY402 @ SV2 @ SV8 @ SV11 @ SV5 @ SV15 ) )
= $true )
| ( ( ! [SY403: mworld] :
( ~ ( mrel @ SV15 @ SY403 )
| ~ ! [SY394: mworld] :
( ~ ( mrel @ SY403 @ SY394 )
| ( in @ SV11 @ SV5 @ SY394 ) ) ) )
= $true )
| ( ( mrel @ SV8 @ SV15 )
= $false )
| ( ( eiw_di @ SV11 @ SV8 )
= $false )
| ( ( mrel @ SV2 @ SV8 )
= $false )
| ( ( eiw_di @ SV5 @ SV2 )
= $false )
| ( ( mrel @ mactual @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[115]) ).
thf(122,plain,
! [SV8: mworld,SV2: mworld,SV5: $i,SV11: $i,SV17: mworld,SV15: mworld] :
( ( ( ~ ( mrel @ SV15 @ SV17 )
| ~ ! [SY408: mworld] :
( ~ ( mrel @ SV17 @ SY408 )
| ( in @ SV11 @ SV5 @ SY408 ) ) )
= $true )
| ( ( in @ SV5 @ SV11 @ ( sK9_SY402 @ SV2 @ SV8 @ SV11 @ SV5 @ SV15 ) )
= $false )
| ( ( mrel @ SV8 @ SV15 )
= $false )
| ( ( eiw_di @ SV11 @ SV8 )
= $false )
| ( ( mrel @ SV2 @ SV8 )
= $false )
| ( ( eiw_di @ SV5 @ SV2 )
= $false )
| ( ( mrel @ mactual @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(123,plain,
! [SV6: $i,SV12: $i,SV9: mworld,SV3: mworld,SV16: mworld] :
( ( ( mrel @ SV16 @ ( sK10_SY405 @ SV3 @ SV9 @ SV12 @ SV6 @ SV16 ) )
= $true )
| ( ( ! [SY406: mworld] :
( ~ ( mrel @ SV16 @ SY406 )
| ( disjoint @ SV12 @ SV6 @ SY406 ) ) )
= $true )
| ( ( mrel @ SV9 @ SV16 )
= $false )
| ( ( eiw_di @ SV12 @ SV9 )
= $false )
| ( ( mrel @ SV3 @ SV9 )
= $false )
| ( ( eiw_di @ SV6 @ SV3 )
= $false )
| ( ( mrel @ mactual @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[117]) ).
thf(124,plain,
! [SV9: mworld,SV3: mworld,SV6: $i,SV12: $i,SV18: mworld,SV16: mworld] :
( ( ( ~ ( mrel @ SV16 @ SV18 )
| ( disjoint @ SV12 @ SV6 @ SV18 ) )
= $true )
| ( ( disjoint @ SV6 @ SV12 @ ( sK10_SY405 @ SV3 @ SV9 @ SV12 @ SV6 @ SV16 ) )
= $false )
| ( ( mrel @ SV9 @ SV16 )
= $false )
| ( ( eiw_di @ SV12 @ SV9 )
= $false )
| ( ( mrel @ SV3 @ SV9 )
= $false )
| ( ( eiw_di @ SV6 @ SV3 )
= $false )
| ( ( mrel @ mactual @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(125,plain,
! [SV7: mworld,SV1: mworld,SV10: $i,SV4: $i,SV19: mworld,SV14: mworld] :
( ( ( ~ ( mrel @ SV14 @ SV19 )
| ( disjoint @ ( singleton @ SV4 ) @ SV10 @ SV19 ) )
= $true )
| ( ( mrel @ SV14 @ ( sK8_SY399 @ SV1 @ SV7 @ SV10 @ SV4 @ SV14 ) )
= $true )
| ( ( mrel @ SV7 @ SV14 )
= $false )
| ( ( eiw_di @ SV10 @ SV7 )
= $false )
| ( ( mrel @ SV1 @ SV7 )
= $false )
| ( ( eiw_di @ SV4 @ SV1 )
= $false )
| ( ( mrel @ mactual @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(126,plain,
! [SV20: mworld,SV14: mworld,SV4: $i,SV10: $i,SV7: mworld,SV1: mworld] :
( ( ( ~ ( mrel @ ( sK8_SY399 @ SV1 @ SV7 @ SV10 @ SV4 @ SV14 ) @ SV20 )
| ( in @ SV4 @ SV10 @ SV20 ) )
= $true )
| ( ( ! [SY401: mworld] :
( ~ ( mrel @ SV14 @ SY401 )
| ( disjoint @ ( singleton @ SV4 ) @ SV10 @ SY401 ) ) )
= $true )
| ( ( mrel @ SV7 @ SV14 )
= $false )
| ( ( eiw_di @ SV10 @ SV7 )
= $false )
| ( ( mrel @ SV1 @ SV7 )
= $false )
| ( ( eiw_di @ SV4 @ SV1 )
= $false )
| ( ( mrel @ mactual @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(127,plain,
! [SV8: mworld,SV2: mworld,SV5: $i,SV11: $i,SV21: mworld,SV15: mworld] :
( ( ( ~ ( mrel @ SV15 @ SV21 )
| ~ ! [SY409: mworld] :
( ~ ( mrel @ SV21 @ SY409 )
| ( in @ SV11 @ SV5 @ SY409 ) ) )
= $true )
| ( ( mrel @ SV15 @ ( sK9_SY402 @ SV2 @ SV8 @ SV11 @ SV5 @ SV15 ) )
= $true )
| ( ( mrel @ SV8 @ SV15 )
= $false )
| ( ( eiw_di @ SV11 @ SV8 )
= $false )
| ( ( mrel @ SV2 @ SV8 )
= $false )
| ( ( eiw_di @ SV5 @ SV2 )
= $false )
| ( ( mrel @ mactual @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(128,plain,
! [SV8: mworld,SV2: mworld,SV5: $i,SV11: $i,SV17: mworld,SV15: mworld] :
( ( ( ~ ( mrel @ SV15 @ SV17 ) )
= $true )
| ( ( ~ ! [SY408: mworld] :
( ~ ( mrel @ SV17 @ SY408 )
| ( in @ SV11 @ SV5 @ SY408 ) ) )
= $true )
| ( ( in @ SV5 @ SV11 @ ( sK9_SY402 @ SV2 @ SV8 @ SV11 @ SV5 @ SV15 ) )
= $false )
| ( ( mrel @ SV8 @ SV15 )
= $false )
| ( ( eiw_di @ SV11 @ SV8 )
= $false )
| ( ( mrel @ SV2 @ SV8 )
= $false )
| ( ( eiw_di @ SV5 @ SV2 )
= $false )
| ( ( mrel @ mactual @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[122]) ).
thf(129,plain,
! [SV9: mworld,SV3: mworld,SV6: $i,SV12: $i,SV22: mworld,SV16: mworld] :
( ( ( ~ ( mrel @ SV16 @ SV22 )
| ( disjoint @ SV12 @ SV6 @ SV22 ) )
= $true )
| ( ( mrel @ SV16 @ ( sK10_SY405 @ SV3 @ SV9 @ SV12 @ SV6 @ SV16 ) )
= $true )
| ( ( mrel @ SV9 @ SV16 )
= $false )
| ( ( eiw_di @ SV12 @ SV9 )
= $false )
| ( ( mrel @ SV3 @ SV9 )
= $false )
| ( ( eiw_di @ SV6 @ SV3 )
= $false )
| ( ( mrel @ mactual @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(130,plain,
! [SV9: mworld,SV3: mworld,SV6: $i,SV12: $i,SV18: mworld,SV16: mworld] :
( ( ( ~ ( mrel @ SV16 @ SV18 ) )
= $true )
| ( ( disjoint @ SV12 @ SV6 @ SV18 )
= $true )
| ( ( disjoint @ SV6 @ SV12 @ ( sK10_SY405 @ SV3 @ SV9 @ SV12 @ SV6 @ SV16 ) )
= $false )
| ( ( mrel @ SV9 @ SV16 )
= $false )
| ( ( eiw_di @ SV12 @ SV9 )
= $false )
| ( ( mrel @ SV3 @ SV9 )
= $false )
| ( ( eiw_di @ SV6 @ SV3 )
= $false )
| ( ( mrel @ mactual @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[124]) ).
thf(131,plain,
! [SV7: mworld,SV1: mworld,SV10: $i,SV4: $i,SV19: mworld,SV14: mworld] :
( ( ( ~ ( mrel @ SV14 @ SV19 ) )
= $true )
| ( ( disjoint @ ( singleton @ SV4 ) @ SV10 @ SV19 )
= $true )
| ( ( mrel @ SV14 @ ( sK8_SY399 @ SV1 @ SV7 @ SV10 @ SV4 @ SV14 ) )
= $true )
| ( ( mrel @ SV7 @ SV14 )
= $false )
| ( ( eiw_di @ SV10 @ SV7 )
= $false )
| ( ( mrel @ SV1 @ SV7 )
= $false )
| ( ( eiw_di @ SV4 @ SV1 )
= $false )
| ( ( mrel @ mactual @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[125]) ).
thf(132,plain,
! [SV20: mworld,SV14: mworld,SV4: $i,SV10: $i,SV7: mworld,SV1: mworld] :
( ( ( ~ ( mrel @ ( sK8_SY399 @ SV1 @ SV7 @ SV10 @ SV4 @ SV14 ) @ SV20 ) )
= $true )
| ( ( in @ SV4 @ SV10 @ SV20 )
= $true )
| ( ( ! [SY401: mworld] :
( ~ ( mrel @ SV14 @ SY401 )
| ( disjoint @ ( singleton @ SV4 ) @ SV10 @ SY401 ) ) )
= $true )
| ( ( mrel @ SV7 @ SV14 )
= $false )
| ( ( eiw_di @ SV10 @ SV7 )
= $false )
| ( ( mrel @ SV1 @ SV7 )
= $false )
| ( ( eiw_di @ SV4 @ SV1 )
= $false )
| ( ( mrel @ mactual @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[126]) ).
thf(133,plain,
! [SV8: mworld,SV2: mworld,SV5: $i,SV11: $i,SV21: mworld,SV15: mworld] :
( ( ( ~ ( mrel @ SV15 @ SV21 ) )
= $true )
| ( ( ~ ! [SY409: mworld] :
( ~ ( mrel @ SV21 @ SY409 )
| ( in @ SV11 @ SV5 @ SY409 ) ) )
= $true )
| ( ( mrel @ SV15 @ ( sK9_SY402 @ SV2 @ SV8 @ SV11 @ SV5 @ SV15 ) )
= $true )
| ( ( mrel @ SV8 @ SV15 )
= $false )
| ( ( eiw_di @ SV11 @ SV8 )
= $false )
| ( ( mrel @ SV2 @ SV8 )
= $false )
| ( ( eiw_di @ SV5 @ SV2 )
= $false )
| ( ( mrel @ mactual @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[127]) ).
thf(134,plain,
! [SV8: mworld,SV2: mworld,SV5: $i,SV11: $i,SV17: mworld,SV15: mworld] :
( ( ( mrel @ SV15 @ SV17 )
= $false )
| ( ( ~ ! [SY408: mworld] :
( ~ ( mrel @ SV17 @ SY408 )
| ( in @ SV11 @ SV5 @ SY408 ) ) )
= $true )
| ( ( in @ SV5 @ SV11 @ ( sK9_SY402 @ SV2 @ SV8 @ SV11 @ SV5 @ SV15 ) )
= $false )
| ( ( mrel @ SV8 @ SV15 )
= $false )
| ( ( eiw_di @ SV11 @ SV8 )
= $false )
| ( ( mrel @ SV2 @ SV8 )
= $false )
| ( ( eiw_di @ SV5 @ SV2 )
= $false )
| ( ( mrel @ mactual @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(135,plain,
! [SV9: mworld,SV3: mworld,SV6: $i,SV12: $i,SV22: mworld,SV16: mworld] :
( ( ( ~ ( mrel @ SV16 @ SV22 ) )
= $true )
| ( ( disjoint @ SV12 @ SV6 @ SV22 )
= $true )
| ( ( mrel @ SV16 @ ( sK10_SY405 @ SV3 @ SV9 @ SV12 @ SV6 @ SV16 ) )
= $true )
| ( ( mrel @ SV9 @ SV16 )
= $false )
| ( ( eiw_di @ SV12 @ SV9 )
= $false )
| ( ( mrel @ SV3 @ SV9 )
= $false )
| ( ( eiw_di @ SV6 @ SV3 )
= $false )
| ( ( mrel @ mactual @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[129]) ).
thf(136,plain,
! [SV9: mworld,SV3: mworld,SV6: $i,SV12: $i,SV18: mworld,SV16: mworld] :
( ( ( mrel @ SV16 @ SV18 )
= $false )
| ( ( disjoint @ SV12 @ SV6 @ SV18 )
= $true )
| ( ( disjoint @ SV6 @ SV12 @ ( sK10_SY405 @ SV3 @ SV9 @ SV12 @ SV6 @ SV16 ) )
= $false )
| ( ( mrel @ SV9 @ SV16 )
= $false )
| ( ( eiw_di @ SV12 @ SV9 )
= $false )
| ( ( mrel @ SV3 @ SV9 )
= $false )
| ( ( eiw_di @ SV6 @ SV3 )
= $false )
| ( ( mrel @ mactual @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[130]) ).
thf(137,plain,
! [SV7: mworld,SV1: mworld,SV10: $i,SV4: $i,SV19: mworld,SV14: mworld] :
( ( ( mrel @ SV14 @ SV19 )
= $false )
| ( ( disjoint @ ( singleton @ SV4 ) @ SV10 @ SV19 )
= $true )
| ( ( mrel @ SV14 @ ( sK8_SY399 @ SV1 @ SV7 @ SV10 @ SV4 @ SV14 ) )
= $true )
| ( ( mrel @ SV7 @ SV14 )
= $false )
| ( ( eiw_di @ SV10 @ SV7 )
= $false )
| ( ( mrel @ SV1 @ SV7 )
= $false )
| ( ( eiw_di @ SV4 @ SV1 )
= $false )
| ( ( mrel @ mactual @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(138,plain,
! [SV20: mworld,SV14: mworld,SV4: $i,SV10: $i,SV7: mworld,SV1: mworld] :
( ( ( mrel @ ( sK8_SY399 @ SV1 @ SV7 @ SV10 @ SV4 @ SV14 ) @ SV20 )
= $false )
| ( ( in @ SV4 @ SV10 @ SV20 )
= $true )
| ( ( ! [SY401: mworld] :
( ~ ( mrel @ SV14 @ SY401 )
| ( disjoint @ ( singleton @ SV4 ) @ SV10 @ SY401 ) ) )
= $true )
| ( ( mrel @ SV7 @ SV14 )
= $false )
| ( ( eiw_di @ SV10 @ SV7 )
= $false )
| ( ( mrel @ SV1 @ SV7 )
= $false )
| ( ( eiw_di @ SV4 @ SV1 )
= $false )
| ( ( mrel @ mactual @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(139,plain,
! [SV8: mworld,SV2: mworld,SV5: $i,SV11: $i,SV21: mworld,SV15: mworld] :
( ( ( mrel @ SV15 @ SV21 )
= $false )
| ( ( ~ ! [SY409: mworld] :
( ~ ( mrel @ SV21 @ SY409 )
| ( in @ SV11 @ SV5 @ SY409 ) ) )
= $true )
| ( ( mrel @ SV15 @ ( sK9_SY402 @ SV2 @ SV8 @ SV11 @ SV5 @ SV15 ) )
= $true )
| ( ( mrel @ SV8 @ SV15 )
= $false )
| ( ( eiw_di @ SV11 @ SV8 )
= $false )
| ( ( mrel @ SV2 @ SV8 )
= $false )
| ( ( eiw_di @ SV5 @ SV2 )
= $false )
| ( ( mrel @ mactual @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(140,plain,
! [SV8: mworld,SV2: mworld,SV15: mworld,SV5: $i,SV11: $i,SV17: mworld] :
( ( ( ! [SY408: mworld] :
( ~ ( mrel @ SV17 @ SY408 )
| ( in @ SV11 @ SV5 @ SY408 ) ) )
= $false )
| ( ( mrel @ SV15 @ SV17 )
= $false )
| ( ( in @ SV5 @ SV11 @ ( sK9_SY402 @ SV2 @ SV8 @ SV11 @ SV5 @ SV15 ) )
= $false )
| ( ( mrel @ SV8 @ SV15 )
= $false )
| ( ( eiw_di @ SV11 @ SV8 )
= $false )
| ( ( mrel @ SV2 @ SV8 )
= $false )
| ( ( eiw_di @ SV5 @ SV2 )
= $false )
| ( ( mrel @ mactual @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(141,plain,
! [SV9: mworld,SV3: mworld,SV6: $i,SV12: $i,SV22: mworld,SV16: mworld] :
( ( ( mrel @ SV16 @ SV22 )
= $false )
| ( ( disjoint @ SV12 @ SV6 @ SV22 )
= $true )
| ( ( mrel @ SV16 @ ( sK10_SY405 @ SV3 @ SV9 @ SV12 @ SV6 @ SV16 ) )
= $true )
| ( ( mrel @ SV9 @ SV16 )
= $false )
| ( ( eiw_di @ SV12 @ SV9 )
= $false )
| ( ( mrel @ SV3 @ SV9 )
= $false )
| ( ( eiw_di @ SV6 @ SV3 )
= $false )
| ( ( mrel @ mactual @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(142,plain,
! [SV7: mworld,SV1: mworld,SV20: mworld,SV10: $i,SV4: $i,SV23: mworld,SV14: mworld] :
( ( ( ~ ( mrel @ SV14 @ SV23 )
| ( disjoint @ ( singleton @ SV4 ) @ SV10 @ SV23 ) )
= $true )
| ( ( in @ SV4 @ SV10 @ SV20 )
= $true )
| ( ( mrel @ ( sK8_SY399 @ SV1 @ SV7 @ SV10 @ SV4 @ SV14 ) @ SV20 )
= $false )
| ( ( mrel @ SV7 @ SV14 )
= $false )
| ( ( eiw_di @ SV10 @ SV7 )
= $false )
| ( ( mrel @ SV1 @ SV7 )
= $false )
| ( ( eiw_di @ SV4 @ SV1 )
= $false )
| ( ( mrel @ mactual @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(143,plain,
! [SV8: mworld,SV2: mworld,SV15: mworld,SV5: $i,SV11: $i,SV21: mworld] :
( ( ( ! [SY409: mworld] :
( ~ ( mrel @ SV21 @ SY409 )
| ( in @ SV11 @ SV5 @ SY409 ) ) )
= $false )
| ( ( mrel @ SV15 @ SV21 )
= $false )
| ( ( mrel @ SV15 @ ( sK9_SY402 @ SV2 @ SV8 @ SV11 @ SV5 @ SV15 ) )
= $true )
| ( ( mrel @ SV8 @ SV15 )
= $false )
| ( ( eiw_di @ SV11 @ SV8 )
= $false )
| ( ( mrel @ SV2 @ SV8 )
= $false )
| ( ( eiw_di @ SV5 @ SV2 )
= $false )
| ( ( mrel @ mactual @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(144,plain,
! [SV11: $i,SV5: $i,SV15: mworld,SV2: mworld,SV8: mworld,SV17: mworld] :
( ( ( ~ ( mrel @ SV17 @ ( sK11_SY408 @ SV8 @ SV2 @ SV15 @ SV5 @ SV11 @ SV17 ) )
| ( in @ SV11 @ SV5 @ ( sK11_SY408 @ SV8 @ SV2 @ SV15 @ SV5 @ SV11 @ SV17 ) ) )
= $false )
| ( ( mrel @ SV15 @ SV17 )
= $false )
| ( ( in @ SV5 @ SV11 @ ( sK9_SY402 @ SV2 @ SV8 @ SV11 @ SV5 @ SV15 ) )
= $false )
| ( ( mrel @ SV8 @ SV15 )
= $false )
| ( ( eiw_di @ SV11 @ SV8 )
= $false )
| ( ( mrel @ SV2 @ SV8 )
= $false )
| ( ( eiw_di @ SV5 @ SV2 )
= $false )
| ( ( mrel @ mactual @ SV2 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[140]) ).
thf(145,plain,
! [SV7: mworld,SV1: mworld,SV20: mworld,SV10: $i,SV4: $i,SV23: mworld,SV14: mworld] :
( ( ( ~ ( mrel @ SV14 @ SV23 ) )
= $true )
| ( ( disjoint @ ( singleton @ SV4 ) @ SV10 @ SV23 )
= $true )
| ( ( in @ SV4 @ SV10 @ SV20 )
= $true )
| ( ( mrel @ ( sK8_SY399 @ SV1 @ SV7 @ SV10 @ SV4 @ SV14 ) @ SV20 )
= $false )
| ( ( mrel @ SV7 @ SV14 )
= $false )
| ( ( eiw_di @ SV10 @ SV7 )
= $false )
| ( ( mrel @ SV1 @ SV7 )
= $false )
| ( ( eiw_di @ SV4 @ SV1 )
= $false )
| ( ( mrel @ mactual @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[142]) ).
thf(146,plain,
! [SV11: $i,SV5: $i,SV15: mworld,SV2: mworld,SV8: mworld,SV21: mworld] :
( ( ( ~ ( mrel @ SV21 @ ( sK12_SY409 @ SV8 @ SV2 @ SV15 @ SV5 @ SV11 @ SV21 ) )
| ( in @ SV11 @ SV5 @ ( sK12_SY409 @ SV8 @ SV2 @ SV15 @ SV5 @ SV11 @ SV21 ) ) )
= $false )
| ( ( mrel @ SV15 @ SV21 )
= $false )
| ( ( mrel @ SV15 @ ( sK9_SY402 @ SV2 @ SV8 @ SV11 @ SV5 @ SV15 ) )
= $true )
| ( ( mrel @ SV8 @ SV15 )
= $false )
| ( ( eiw_di @ SV11 @ SV8 )
= $false )
| ( ( mrel @ SV2 @ SV8 )
= $false )
| ( ( eiw_di @ SV5 @ SV2 )
= $false )
| ( ( mrel @ mactual @ SV2 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[143]) ).
thf(147,plain,
! [SV11: $i,SV5: $i,SV15: mworld,SV2: mworld,SV8: mworld,SV17: mworld] :
( ( ( ~ ( mrel @ SV17 @ ( sK11_SY408 @ SV8 @ SV2 @ SV15 @ SV5 @ SV11 @ SV17 ) ) )
= $false )
| ( ( mrel @ SV15 @ SV17 )
= $false )
| ( ( in @ SV5 @ SV11 @ ( sK9_SY402 @ SV2 @ SV8 @ SV11 @ SV5 @ SV15 ) )
= $false )
| ( ( mrel @ SV8 @ SV15 )
= $false )
| ( ( eiw_di @ SV11 @ SV8 )
= $false )
| ( ( mrel @ SV2 @ SV8 )
= $false )
| ( ( eiw_di @ SV5 @ SV2 )
= $false )
| ( ( mrel @ mactual @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[144]) ).
thf(148,plain,
! [SV17: mworld,SV15: mworld,SV2: mworld,SV8: mworld,SV5: $i,SV11: $i] :
( ( ( in @ SV11 @ SV5 @ ( sK11_SY408 @ SV8 @ SV2 @ SV15 @ SV5 @ SV11 @ SV17 ) )
= $false )
| ( ( mrel @ SV15 @ SV17 )
= $false )
| ( ( in @ SV5 @ SV11 @ ( sK9_SY402 @ SV2 @ SV8 @ SV11 @ SV5 @ SV15 ) )
= $false )
| ( ( mrel @ SV8 @ SV15 )
= $false )
| ( ( eiw_di @ SV11 @ SV8 )
= $false )
| ( ( mrel @ SV2 @ SV8 )
= $false )
| ( ( eiw_di @ SV5 @ SV2 )
= $false )
| ( ( mrel @ mactual @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[144]) ).
thf(149,plain,
! [SV7: mworld,SV1: mworld,SV20: mworld,SV10: $i,SV4: $i,SV23: mworld,SV14: mworld] :
( ( ( mrel @ SV14 @ SV23 )
= $false )
| ( ( disjoint @ ( singleton @ SV4 ) @ SV10 @ SV23 )
= $true )
| ( ( in @ SV4 @ SV10 @ SV20 )
= $true )
| ( ( mrel @ ( sK8_SY399 @ SV1 @ SV7 @ SV10 @ SV4 @ SV14 ) @ SV20 )
= $false )
| ( ( mrel @ SV7 @ SV14 )
= $false )
| ( ( eiw_di @ SV10 @ SV7 )
= $false )
| ( ( mrel @ SV1 @ SV7 )
= $false )
| ( ( eiw_di @ SV4 @ SV1 )
= $false )
| ( ( mrel @ mactual @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[145]) ).
thf(150,plain,
! [SV11: $i,SV5: $i,SV15: mworld,SV2: mworld,SV8: mworld,SV21: mworld] :
( ( ( ~ ( mrel @ SV21 @ ( sK12_SY409 @ SV8 @ SV2 @ SV15 @ SV5 @ SV11 @ SV21 ) ) )
= $false )
| ( ( mrel @ SV15 @ SV21 )
= $false )
| ( ( mrel @ SV15 @ ( sK9_SY402 @ SV2 @ SV8 @ SV11 @ SV5 @ SV15 ) )
= $true )
| ( ( mrel @ SV8 @ SV15 )
= $false )
| ( ( eiw_di @ SV11 @ SV8 )
= $false )
| ( ( mrel @ SV2 @ SV8 )
= $false )
| ( ( eiw_di @ SV5 @ SV2 )
= $false )
| ( ( mrel @ mactual @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[146]) ).
thf(151,plain,
! [SV21: mworld,SV15: mworld,SV2: mworld,SV8: mworld,SV5: $i,SV11: $i] :
( ( ( in @ SV11 @ SV5 @ ( sK12_SY409 @ SV8 @ SV2 @ SV15 @ SV5 @ SV11 @ SV21 ) )
= $false )
| ( ( mrel @ SV15 @ SV21 )
= $false )
| ( ( mrel @ SV15 @ ( sK9_SY402 @ SV2 @ SV8 @ SV11 @ SV5 @ SV15 ) )
= $true )
| ( ( mrel @ SV8 @ SV15 )
= $false )
| ( ( eiw_di @ SV11 @ SV8 )
= $false )
| ( ( mrel @ SV2 @ SV8 )
= $false )
| ( ( eiw_di @ SV5 @ SV2 )
= $false )
| ( ( mrel @ mactual @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[146]) ).
thf(152,plain,
! [SV11: $i,SV5: $i,SV15: mworld,SV2: mworld,SV8: mworld,SV17: mworld] :
( ( ( mrel @ SV17 @ ( sK11_SY408 @ SV8 @ SV2 @ SV15 @ SV5 @ SV11 @ SV17 ) )
= $true )
| ( ( mrel @ SV15 @ SV17 )
= $false )
| ( ( in @ SV5 @ SV11 @ ( sK9_SY402 @ SV2 @ SV8 @ SV11 @ SV5 @ SV15 ) )
= $false )
| ( ( mrel @ SV8 @ SV15 )
= $false )
| ( ( eiw_di @ SV11 @ SV8 )
= $false )
| ( ( mrel @ SV2 @ SV8 )
= $false )
| ( ( eiw_di @ SV5 @ SV2 )
= $false )
| ( ( mrel @ mactual @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[147]) ).
thf(153,plain,
! [SV11: $i,SV5: $i,SV15: mworld,SV2: mworld,SV8: mworld,SV21: mworld] :
( ( ( mrel @ SV21 @ ( sK12_SY409 @ SV8 @ SV2 @ SV15 @ SV5 @ SV11 @ SV21 ) )
= $true )
| ( ( mrel @ SV15 @ SV21 )
= $false )
| ( ( mrel @ SV15 @ ( sK9_SY402 @ SV2 @ SV8 @ SV11 @ SV5 @ SV15 ) )
= $true )
| ( ( mrel @ SV8 @ SV15 )
= $false )
| ( ( eiw_di @ SV11 @ SV8 )
= $false )
| ( ( mrel @ SV2 @ SV8 )
= $false )
| ( ( eiw_di @ SV5 @ SV2 )
= $false )
| ( ( mrel @ mactual @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[150]) ).
thf(154,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[21,153,152,151,149,148,141,137,136,112,108,91,86,73,63,53,43]) ).
thf(155,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[154]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL953^8 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.02 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Oct 6 12:37:16 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.17
% 0.08/0.17 No.of.Axioms: 3
% 0.08/0.17
% 0.08/0.17 Length.of.Defs: 1653
% 0.08/0.17
% 0.08/0.17 Contains.Choice.Funs: false
% 0.08/0.17 ...........
% 0.08/0.17
% 0.08/0.17 ********************************
% 0.08/0.17 * All subproblems solved! *
% 0.08/0.17 ********************************
% 0.08/0.17 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:4,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:154,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.08/0.17
% 0.08/0.17 %**** Beginning of derivation protocol ****
% 0.08/0.17 % SZS output start CNFRefutation
% See solution above
% 0.08/0.17
% 0.08/0.17 %**** End of derivation protocol ****
% 0.08/0.17 %**** no. of clauses in derivation: 151 ****
% 0.08/0.17 %**** clause counter: 154 ****
% 0.08/0.17
% 0.08/0.17 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:4,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:154,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------