%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : PLA054^4 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.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 10:36:25 AM UTC 2026
% Result : Theorem 0.09s 0.24s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 18
% Syntax : Number of formulae : 150 ( 69 unt; 0 typ; 10 def)
% Number of atoms : 1359 ( 319 equ; 0 cnn)
% Maximal formula atoms : 25 ( 9 avg)
% Number of connectives : 2721 ( 619 ~; 458 |; 22 &;1577 @)
% ( 1 <=>; 44 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 23 usr; 9 con; 0-3 aty)
% Number of variables : 488 ( 32 ^; 440 !; 16 ?; 488 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_mworld,type,
mworld: $tType ).
thf(tp_closed,type,
closed: $i > mworld > $o ).
thf(tp_combo,type,
combo: $i > $i > mworld > $o ).
thf(tp_d,type,
d: $i ).
thf(tp_h,type,
h: $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_n,type,
n: $i ).
thf(tp_o,type,
o: $i ).
thf(tp_open,type,
open: $i > mworld > $o ).
thf(tp_sK1_SY37,type,
sK1_SY37: mworld ).
thf(tp_sK2_SX0,type,
sK2_SX0: $i ).
thf(tp_sK3_SY222,type,
sK3_SY222: $i > $i > mworld > $i ).
thf(tp_sK4_SX2,type,
sK4_SX2: mworld ).
thf(mand,definition,
( mand
= ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
( ( A @ W )
& ( B @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mand_def) ).
thf(mbox,definition,
( mbox
= ( ^ [Phi: mworld > $o,W: mworld] :
! [V: mworld] :
( ( mrel @ W @ V )
=> ( Phi @ V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_def) ).
thf(mdia,definition,
( mdia
= ( ^ [Phi: mworld > $o,W: mworld] :
? [V: mworld] :
( ( mrel @ W @ V )
& ( Phi @ V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia_def) ).
thf(mequiv,definition,
( mequiv
= ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
( ( A @ W )
<=> ( B @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mequiv_def) ).
thf(mexists_di,definition,
( mexists_di
= ( ^ [A: $i > mworld > $o,W: mworld] :
? [X: $i] : ( A @ X @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mexists_di_def) ).
thf(mforall_di,definition,
( mforall_di
= ( ^ [A: $i > mworld > $o,W: mworld] :
! [X: $i] : ( A @ X @ W ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mimplies_def) ).
thf(mlocal,definition,
( mlocal
= ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mlocal_def) ).
thf(mnot,definition,
( mnot
= ( ^ [A: mworld > $o,W: mworld] :
~ ( A @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot_def) ).
thf(mor,definition,
( mor
= ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
( ( A @ W )
| ( B @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor_def) ).
thf(1,axiom,
( mlocal
@ ( mexists_di
@ ^ [V: $i] : ( mbox @ ( combo @ d @ V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax5) ).
thf(2,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [S: $i] : ( mnot @ ( mand @ ( open @ S ) @ ( closed @ S ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
thf(3,axiom,
mlocal @ ( mbox @ ( mor @ ( combo @ d @ n ) @ ( mnot @ ( combo @ d @ n ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
thf(4,axiom,
mlocal @ ( mbox @ ( closed @ d ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
thf(5,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [S: $i] :
( mforall_di
@ ^ [V: $i] :
( mexists_di
@ ^ [O: $i] : ( mand @ ( mbox @ ( mimplies @ ( mand @ ( closed @ S ) @ ( mand @ ( combo @ S @ V ) @ ( h @ O ) ) ) @ ( mbox @ ( open @ S ) ) ) ) @ ( mbox @ ( mimplies @ ( mand @ ( closed @ S ) @ ( mand @ ( mnot @ ( combo @ S @ V ) ) @ ( h @ o ) ) ) @ ( mbox @ ( closed @ S ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
thf(6,axiom,
! [W: mworld,V: mworld,U: mworld] :
( ( ( mrel @ W @ V )
& ( mrel @ V @ U ) )
=> ( mrel @ W @ U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_transitive) ).
thf(7,axiom,
! [W: mworld] : ( mrel @ W @ W ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_reflexive) ).
thf(8,conjecture,
( mlocal
@ ( mbox
@ ( mexists_di
@ ^ [V: $i] :
( mexists_di
@ ^ [O: $i] : ( mimplies @ ( mbox @ ( mand @ ( combo @ d @ V ) @ ( h @ O ) ) ) @ ( mbox @ ( open @ d ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(9,negated_conjecture,
( ( mlocal
@ ( mbox
@ ( mexists_di
@ ^ [V: $i] :
( mexists_di
@ ^ [O: $i] : ( mimplies @ ( mbox @ ( mand @ ( combo @ d @ V ) @ ( h @ O ) ) ) @ ( mbox @ ( open @ d ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[8]) ).
thf(10,plain,
( ( ! [SY37: mworld] :
( ( mrel @ mactual @ SY37 )
=> ? [SY33: $i,SY34: $i] :
( ! [SY35: mworld] :
( ( mrel @ SY37 @ SY35 )
=> ( ( combo @ d @ SY33 @ SY35 )
& ( h @ SY34 @ SY35 ) ) )
=> ! [SY36: mworld] :
( ( mrel @ SY37 @ SY36 )
=> ( open @ d @ SY36 ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[9,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(11,plain,
( ( ? [SY55: $i] :
! [SY56: mworld] :
( ( mrel @ mactual @ SY56 )
=> ( combo @ d @ SY55 @ SY56 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(12,plain,
( ( ! [SY70: mworld] :
( ( mrel @ mactual @ SY70 )
=> ! [SY69: $i] :
~ ( ( open @ SY69 @ SY70 )
& ( closed @ SY69 @ SY70 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(13,plain,
( ( ! [SY80: mworld] :
( ( mrel @ mactual @ SY80 )
=> ( ( combo @ d @ n @ SY80 )
| ~ ( combo @ d @ n @ SY80 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(14,plain,
( ( ! [SY84: mworld] :
( ( mrel @ mactual @ SY84 )
=> ( closed @ d @ SY84 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(15,plain,
( ( ! [SY177: mworld] :
( ( mrel @ mactual @ SY177 )
=> ! [SY170: $i,SY171: $i] :
? [SY172: $i] :
( ! [SY173: mworld] :
( ( mrel @ SY177 @ SY173 )
=> ( ( ( closed @ SY170 @ SY173 )
& ( combo @ SY170 @ SY171 @ SY173 )
& ( h @ SY172 @ SY173 ) )
=> ! [SY159: mworld] :
( ( mrel @ SY173 @ SY159 )
=> ( open @ SY170 @ SY159 ) ) ) )
& ! [SY175: mworld] :
( ( mrel @ SY177 @ SY175 )
=> ( ( ( closed @ SY170 @ SY175 )
& ~ ( combo @ SY170 @ SY171 @ SY175 )
& ( h @ o @ SY175 ) )
=> ! [SY161: mworld] :
( ( mrel @ SY175 @ SY161 )
=> ( closed @ SY170 @ SY161 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(16,plain,
( ( ! [W: mworld,V: mworld,U: mworld] :
( ( ( mrel @ W @ V )
& ( mrel @ V @ U ) )
=> ( mrel @ W @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(17,plain,
( ( ! [W: mworld] : ( mrel @ W @ W ) )
= $true ),
inference(unfold_def,[status(thm)],[7,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(18,plain,
( ( ( mrel @ mactual @ sK1_SY37 )
=> ? [SY197: $i,SY198: $i] :
( ! [SY199: mworld] :
( ( mrel @ sK1_SY37 @ SY199 )
=> ( ( combo @ d @ SY197 @ SY199 )
& ( h @ SY198 @ SY199 ) ) )
=> ! [SY200: mworld] :
( ( mrel @ sK1_SY37 @ SY200 )
=> ( open @ d @ SY200 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[10]) ).
thf(19,plain,
( ( mrel @ mactual @ sK1_SY37 )
= $true ),
inference(standard_cnf,[status(thm)],[18]) ).
thf(20,plain,
( ( ? [SY197: $i,SY198: $i] :
( ! [SY199: mworld] :
( ( mrel @ sK1_SY37 @ SY199 )
=> ( ( combo @ d @ SY197 @ SY199 )
& ( h @ SY198 @ SY199 ) ) )
=> ! [SY200: mworld] :
( ( mrel @ sK1_SY37 @ SY200 )
=> ( open @ d @ SY200 ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[18]) ).
thf(21,plain,
( ( ~ ? [SY197: $i,SY198: $i] :
( ! [SY199: mworld] :
( ( mrel @ sK1_SY37 @ SY199 )
=> ( ( combo @ d @ SY197 @ SY199 )
& ( h @ SY198 @ SY199 ) ) )
=> ! [SY200: mworld] :
( ( mrel @ sK1_SY37 @ SY200 )
=> ( open @ d @ SY200 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[20]) ).
thf(22,plain,
( ( ! [W: mworld] : ( mrel @ W @ W ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(23,plain,
( ( ! [W: mworld,V: mworld,U: mworld] :
( ( ( mrel @ W @ V )
& ( mrel @ V @ U ) )
=> ( mrel @ W @ U ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(24,plain,
( ( ! [SY177: mworld] :
( ( mrel @ mactual @ SY177 )
=> ! [SY170: $i,SY171: $i] :
? [SY172: $i] :
( ! [SY173: mworld] :
( ( mrel @ SY177 @ SY173 )
=> ( ( ( closed @ SY170 @ SY173 )
& ( combo @ SY170 @ SY171 @ SY173 )
& ( h @ SY172 @ SY173 ) )
=> ! [SY159: mworld] :
( ( mrel @ SY173 @ SY159 )
=> ( open @ SY170 @ SY159 ) ) ) )
& ! [SY175: mworld] :
( ( mrel @ SY177 @ SY175 )
=> ( ( ( closed @ SY170 @ SY175 )
& ~ ( combo @ SY170 @ SY171 @ SY175 )
& ( h @ o @ SY175 ) )
=> ! [SY161: mworld] :
( ( mrel @ SY175 @ SY161 )
=> ( closed @ SY170 @ SY161 ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(25,plain,
( ( ! [SY84: mworld] :
( ( mrel @ mactual @ SY84 )
=> ( closed @ d @ SY84 ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(26,plain,
( ( ! [SY80: mworld] :
( ( mrel @ mactual @ SY80 )
=> ( ( combo @ d @ n @ SY80 )
| ~ ( combo @ d @ n @ SY80 ) ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(27,plain,
( ( ! [SY70: mworld] :
( ( mrel @ mactual @ SY70 )
=> ! [SY69: $i] :
~ ( ( open @ SY69 @ SY70 )
& ( closed @ SY69 @ SY70 ) ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(28,plain,
( ( ? [SY55: $i] :
! [SY56: mworld] :
( ( mrel @ mactual @ SY56 )
=> ( combo @ d @ SY55 @ SY56 ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(29,plain,
( ( mrel @ mactual @ sK1_SY37 )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(30,plain,
( ( ~ ? [SY197: $i,SY198: $i] :
( ! [SY199: mworld] :
( ( mrel @ sK1_SY37 @ SY199 )
=> ( ( combo @ d @ SY197 @ SY199 )
& ( h @ SY198 @ SY199 ) ) )
=> ! [SY200: mworld] :
( ( mrel @ sK1_SY37 @ SY200 )
=> ( open @ d @ SY200 ) ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(31,plain,
( ( ! [SX0: mworld] :
( ~ ( mrel @ mactual @ SX0 )
| ( combo @ d @ n @ SX0 )
| ~ ( combo @ d @ n @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(32,plain,
( ( ! [SX0: mworld] :
( ~ ( mrel @ mactual @ SX0 )
| ! [SX1: $i] :
~ ~ ( ~ ( open @ SX1 @ SX0 )
| ~ ( closed @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(33,plain,
( ( ! [SX0: mworld] :
( ~ ( mrel @ mactual @ SX0 )
| ! [SX1: $i,SX2: $i] :
~ ! [SX3: $i] :
~ ~ ( ~ ! [SX4: mworld] :
( ~ ( mrel @ SX0 @ SX4 )
| ~ ~ ( ~ ( closed @ SX1 @ SX4 )
| ~ ~ ( ~ ( combo @ SX1 @ SX2 @ SX4 )
| ~ ( h @ SX3 @ SX4 ) ) )
| ! [SX5: mworld] :
( ~ ( mrel @ SX4 @ SX5 )
| ( open @ SX1 @ SX5 ) ) )
| ~ ! [SX4: mworld] :
( ~ ( mrel @ SX0 @ SX4 )
| ~ ~ ( ~ ( closed @ SX1 @ SX4 )
| ~ ~ ( ~ ~ ( combo @ SX1 @ SX2 @ SX4 )
| ~ ( h @ o @ SX4 ) ) )
| ! [SX5: mworld] :
( ~ ( mrel @ SX4 @ SX5 )
| ( closed @ SX1 @ SX5 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(34,plain,
( ( ~ ~ ! [SX0: $i] :
~ ~ ! [SX1: $i] :
~ ( ~ ! [SX2: mworld] :
( ~ ( mrel @ sK1_SY37 @ SX2 )
| ~ ( ~ ( combo @ d @ SX0 @ SX2 )
| ~ ( h @ SX1 @ SX2 ) ) )
| ! [SX2: mworld] :
( ~ ( mrel @ sK1_SY37 @ SX2 )
| ( open @ d @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(35,plain,
( ( ! [SX0: mworld] :
( ~ ( mrel @ mactual @ SX0 )
| ( closed @ d @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(36,plain,
( ( ! [SX0: mworld,SX1: mworld,SX2: mworld] :
( ~ ~ ( ~ ( mrel @ SX0 @ SX1 )
| ~ ( mrel @ SX1 @ SX2 ) )
| ( mrel @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(37,plain,
( ( ~ ! [SX0: $i] :
~ ! [SX1: mworld] :
( ~ ( mrel @ mactual @ SX1 )
| ( combo @ d @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(38,plain,
! [SV1: mworld] :
( ( mrel @ SV1 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(39,plain,
! [SV2: mworld] :
( ( ~ ( mrel @ mactual @ SV2 )
| ( combo @ d @ n @ SV2 )
| ~ ( combo @ d @ n @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(40,plain,
! [SV3: mworld] :
( ( ~ ( mrel @ mactual @ SV3 )
| ! [SY201: $i] :
~ ~ ( ~ ( open @ SY201 @ SV3 )
| ~ ( closed @ SY201 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(41,plain,
! [SV4: mworld] :
( ( ~ ( mrel @ mactual @ SV4 )
| ! [SY202: $i,SY203: $i] :
~ ! [SY204: $i] :
~ ~ ( ~ ! [SY205: mworld] :
( ~ ( mrel @ SV4 @ SY205 )
| ~ ~ ( ~ ( closed @ SY202 @ SY205 )
| ~ ~ ( ~ ( combo @ SY202 @ SY203 @ SY205 )
| ~ ( h @ SY204 @ SY205 ) ) )
| ! [SX5: mworld] :
( ~ ( mrel @ SY205 @ SX5 )
| ( open @ SY202 @ SX5 ) ) )
| ~ ! [SY207: mworld] :
( ~ ( mrel @ SV4 @ SY207 )
| ~ ~ ( ~ ( closed @ SY202 @ SY207 )
| ~ ~ ( ~ ~ ( combo @ SY202 @ SY203 @ SY207 )
| ~ ( h @ o @ SY207 ) ) )
| ! [SX5: mworld] :
( ~ ( mrel @ SY207 @ SX5 )
| ( closed @ SY202 @ SX5 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(42,plain,
( ( ~ ! [SX0: $i] :
~ ~ ! [SX1: $i] :
~ ( ~ ! [SX2: mworld] :
( ~ ( mrel @ sK1_SY37 @ SX2 )
| ~ ( ~ ( combo @ d @ SX0 @ SX2 )
| ~ ( h @ SX1 @ SX2 ) ) )
| ! [SX2: mworld] :
( ~ ( mrel @ sK1_SY37 @ SX2 )
| ( open @ d @ SX2 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(43,plain,
! [SV5: mworld] :
( ( ~ ( mrel @ mactual @ SV5 )
| ( closed @ d @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(44,plain,
! [SV6: mworld] :
( ( ! [SY209: mworld,SY210: mworld] :
( ~ ~ ( ~ ( mrel @ SV6 @ SY209 )
| ~ ( mrel @ SY209 @ SY210 ) )
| ( mrel @ SV6 @ SY210 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(45,plain,
( ( ! [SX0: $i] :
~ ! [SX1: mworld] :
( ~ ( mrel @ mactual @ SX1 )
| ( combo @ d @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(46,plain,
! [SV2: mworld] :
( ( ( ~ ( mrel @ mactual @ SV2 ) )
= $true )
| ( ( ( combo @ d @ n @ SV2 )
| ~ ( combo @ d @ n @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[39]) ).
thf(47,plain,
! [SV3: mworld] :
( ( ( ~ ( mrel @ mactual @ SV3 ) )
= $true )
| ( ( ! [SY201: $i] :
~ ~ ( ~ ( open @ SY201 @ SV3 )
| ~ ( closed @ SY201 @ SV3 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[40]) ).
thf(48,plain,
! [SV4: mworld] :
( ( ( ~ ( mrel @ mactual @ SV4 ) )
= $true )
| ( ( ! [SY202: $i,SY203: $i] :
~ ! [SY204: $i] :
~ ~ ( ~ ! [SY205: mworld] :
( ~ ( mrel @ SV4 @ SY205 )
| ~ ~ ( ~ ( closed @ SY202 @ SY205 )
| ~ ~ ( ~ ( combo @ SY202 @ SY203 @ SY205 )
| ~ ( h @ SY204 @ SY205 ) ) )
| ! [SX5: mworld] :
( ~ ( mrel @ SY205 @ SX5 )
| ( open @ SY202 @ SX5 ) ) )
| ~ ! [SY207: mworld] :
( ~ ( mrel @ SV4 @ SY207 )
| ~ ~ ( ~ ( closed @ SY202 @ SY207 )
| ~ ~ ( ~ ~ ( combo @ SY202 @ SY203 @ SY207 )
| ~ ( h @ o @ SY207 ) ) )
| ! [SX5: mworld] :
( ~ ( mrel @ SY207 @ SX5 )
| ( closed @ SY202 @ SX5 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[41]) ).
thf(49,plain,
( ( ! [SX0: $i] :
~ ~ ! [SX1: $i] :
~ ( ~ ! [SX2: mworld] :
( ~ ( mrel @ sK1_SY37 @ SX2 )
| ~ ( ~ ( combo @ d @ SX0 @ SX2 )
| ~ ( h @ SX1 @ SX2 ) ) )
| ! [SX2: mworld] :
( ~ ( mrel @ sK1_SY37 @ SX2 )
| ( open @ d @ SX2 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[42]) ).
thf(50,plain,
! [SV5: mworld] :
( ( ( ~ ( mrel @ mactual @ SV5 ) )
= $true )
| ( ( closed @ d @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[43]) ).
thf(51,plain,
! [SV7: mworld,SV6: mworld] :
( ( ! [SY211: mworld] :
( ~ ~ ( ~ ( mrel @ SV6 @ SV7 )
| ~ ( mrel @ SV7 @ SY211 ) )
| ( mrel @ SV6 @ SY211 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(52,plain,
( ( ~ ! [SY212: mworld] :
( ~ ( mrel @ mactual @ SY212 )
| ( combo @ d @ sK2_SX0 @ SY212 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[45]) ).
thf(53,plain,
! [SV2: mworld] :
( ( ( mrel @ mactual @ SV2 )
= $false )
| ( ( ( combo @ d @ n @ SV2 )
| ~ ( combo @ d @ n @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(54,plain,
! [SV3: mworld] :
( ( ( mrel @ mactual @ SV3 )
= $false )
| ( ( ! [SY201: $i] :
~ ~ ( ~ ( open @ SY201 @ SV3 )
| ~ ( closed @ SY201 @ SV3 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(55,plain,
! [SV4: mworld] :
( ( ( mrel @ mactual @ SV4 )
= $false )
| ( ( ! [SY202: $i,SY203: $i] :
~ ! [SY204: $i] :
~ ~ ( ~ ! [SY205: mworld] :
( ~ ( mrel @ SV4 @ SY205 )
| ~ ~ ( ~ ( closed @ SY202 @ SY205 )
| ~ ~ ( ~ ( combo @ SY202 @ SY203 @ SY205 )
| ~ ( h @ SY204 @ SY205 ) ) )
| ! [SX5: mworld] :
( ~ ( mrel @ SY205 @ SX5 )
| ( open @ SY202 @ SX5 ) ) )
| ~ ! [SY207: mworld] :
( ~ ( mrel @ SV4 @ SY207 )
| ~ ~ ( ~ ( closed @ SY202 @ SY207 )
| ~ ~ ( ~ ~ ( combo @ SY202 @ SY203 @ SY207 )
| ~ ( h @ o @ SY207 ) ) )
| ! [SX5: mworld] :
( ~ ( mrel @ SY207 @ SX5 )
| ( closed @ SY202 @ SX5 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(56,plain,
! [SV8: $i] :
( ( ~ ~ ! [SY213: $i] :
~ ( ~ ! [SY214: mworld] :
( ~ ( mrel @ sK1_SY37 @ SY214 )
| ~ ( ~ ( combo @ d @ SV8 @ SY214 )
| ~ ( h @ SY213 @ SY214 ) ) )
| ! [SX2: mworld] :
( ~ ( mrel @ sK1_SY37 @ SX2 )
| ( open @ d @ SX2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(57,plain,
! [SV5: mworld] :
( ( ( mrel @ mactual @ SV5 )
= $false )
| ( ( closed @ d @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(58,plain,
! [SV9: mworld,SV7: mworld,SV6: mworld] :
( ( ~ ~ ( ~ ( mrel @ SV6 @ SV7 )
| ~ ( mrel @ SV7 @ SV9 ) )
| ( mrel @ SV6 @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(59,plain,
( ( ! [SY212: mworld] :
( ~ ( mrel @ mactual @ SY212 )
| ( combo @ d @ sK2_SX0 @ SY212 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[52]) ).
thf(60,plain,
! [SV2: mworld] :
( ( ( combo @ d @ n @ SV2 )
= $true )
| ( ( ~ ( combo @ d @ n @ SV2 ) )
= $true )
| ( ( mrel @ mactual @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[53]) ).
thf(61,plain,
! [SV3: mworld,SV10: $i] :
( ( ( ~ ~ ( ~ ( open @ SV10 @ SV3 )
| ~ ( closed @ SV10 @ SV3 ) ) )
= $true )
| ( ( mrel @ mactual @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(62,plain,
! [SV11: $i,SV4: mworld] :
( ( ( ! [SY216: $i] :
~ ! [SY217: $i] :
~ ~ ( ~ ! [SY218: mworld] :
( ~ ( mrel @ SV4 @ SY218 )
| ~ ~ ( ~ ( closed @ SV11 @ SY218 )
| ~ ~ ( ~ ( combo @ SV11 @ SY216 @ SY218 )
| ~ ( h @ SY217 @ SY218 ) ) )
| ! [SY219: mworld] :
( ~ ( mrel @ SY218 @ SY219 )
| ( open @ SV11 @ SY219 ) ) )
| ~ ! [SY220: mworld] :
( ~ ( mrel @ SV4 @ SY220 )
| ~ ~ ( ~ ( closed @ SV11 @ SY220 )
| ~ ~ ( ~ ~ ( combo @ SV11 @ SY216 @ SY220 )
| ~ ( h @ o @ SY220 ) ) )
| ! [SY221: mworld] :
( ~ ( mrel @ SY220 @ SY221 )
| ( closed @ SV11 @ SY221 ) ) ) ) )
= $true )
| ( ( mrel @ mactual @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(63,plain,
! [SV8: $i] :
( ( ~ ! [SY213: $i] :
~ ( ~ ! [SY214: mworld] :
( ~ ( mrel @ sK1_SY37 @ SY214 )
| ~ ( ~ ( combo @ d @ SV8 @ SY214 )
| ~ ( h @ SY213 @ SY214 ) ) )
| ! [SX2: mworld] :
( ~ ( mrel @ sK1_SY37 @ SX2 )
| ( open @ d @ SX2 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[56]) ).
thf(64,plain,
! [SV9: mworld,SV7: mworld,SV6: mworld] :
( ( ( ~ ~ ( ~ ( mrel @ SV6 @ SV7 )
| ~ ( mrel @ SV7 @ SV9 ) ) )
= $true )
| ( ( mrel @ SV6 @ SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[58]) ).
thf(65,plain,
! [SV12: mworld] :
( ( ~ ( mrel @ mactual @ SV12 )
| ( combo @ d @ sK2_SX0 @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(66,plain,
! [SV2: mworld] :
( ( ( combo @ d @ n @ SV2 )
= $false )
| ( ( combo @ d @ n @ SV2 )
= $true )
| ( ( mrel @ mactual @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(67,plain,
! [SV3: mworld,SV10: $i] :
( ( ( ~ ( ~ ( open @ SV10 @ SV3 )
| ~ ( closed @ SV10 @ SV3 ) ) )
= $false )
| ( ( mrel @ mactual @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(68,plain,
! [SV13: $i,SV11: $i,SV4: mworld] :
( ( ( ~ ! [SY222: $i] :
~ ~ ( ~ ! [SY223: mworld] :
( ~ ( mrel @ SV4 @ SY223 )
| ~ ~ ( ~ ( closed @ SV11 @ SY223 )
| ~ ~ ( ~ ( combo @ SV11 @ SV13 @ SY223 )
| ~ ( h @ SY222 @ SY223 ) ) )
| ! [SY219: mworld] :
( ~ ( mrel @ SY223 @ SY219 )
| ( open @ SV11 @ SY219 ) ) )
| ~ ! [SY225: mworld] :
( ~ ( mrel @ SV4 @ SY225 )
| ~ ~ ( ~ ( closed @ SV11 @ SY225 )
| ~ ~ ( ~ ~ ( combo @ SV11 @ SV13 @ SY225 )
| ~ ( h @ o @ SY225 ) ) )
| ! [SY221: mworld] :
( ~ ( mrel @ SY225 @ SY221 )
| ( closed @ SV11 @ SY221 ) ) ) ) )
= $true )
| ( ( mrel @ mactual @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(69,plain,
! [SV8: $i] :
( ( ! [SY213: $i] :
~ ( ~ ! [SY214: mworld] :
( ~ ( mrel @ sK1_SY37 @ SY214 )
| ~ ( ~ ( combo @ d @ SV8 @ SY214 )
| ~ ( h @ SY213 @ SY214 ) ) )
| ! [SX2: mworld] :
( ~ ( mrel @ sK1_SY37 @ SX2 )
| ( open @ d @ SX2 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[63]) ).
thf(70,plain,
! [SV9: mworld,SV7: mworld,SV6: mworld] :
( ( ( ~ ( ~ ( mrel @ SV6 @ SV7 )
| ~ ( mrel @ SV7 @ SV9 ) ) )
= $false )
| ( ( mrel @ SV6 @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(71,plain,
! [SV12: mworld] :
( ( ( ~ ( mrel @ mactual @ SV12 ) )
= $true )
| ( ( combo @ d @ sK2_SX0 @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[65]) ).
thf(72,plain,
! [SV3: mworld,SV10: $i] :
( ( ( ~ ( open @ SV10 @ SV3 )
| ~ ( closed @ SV10 @ SV3 ) )
= $true )
| ( ( mrel @ mactual @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[67]) ).
thf(73,plain,
! [SV13: $i,SV11: $i,SV4: mworld] :
( ( ( ! [SY222: $i] :
~ ~ ( ~ ! [SY223: mworld] :
( ~ ( mrel @ SV4 @ SY223 )
| ~ ~ ( ~ ( closed @ SV11 @ SY223 )
| ~ ~ ( ~ ( combo @ SV11 @ SV13 @ SY223 )
| ~ ( h @ SY222 @ SY223 ) ) )
| ! [SY219: mworld] :
( ~ ( mrel @ SY223 @ SY219 )
| ( open @ SV11 @ SY219 ) ) )
| ~ ! [SY225: mworld] :
( ~ ( mrel @ SV4 @ SY225 )
| ~ ~ ( ~ ( closed @ SV11 @ SY225 )
| ~ ~ ( ~ ~ ( combo @ SV11 @ SV13 @ SY225 )
| ~ ( h @ o @ SY225 ) ) )
| ! [SY221: mworld] :
( ~ ( mrel @ SY225 @ SY221 )
| ( closed @ SV11 @ SY221 ) ) ) ) )
= $false )
| ( ( mrel @ mactual @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[68]) ).
thf(74,plain,
! [SV14: $i,SV8: $i] :
( ( ~ ( ~ ! [SY227: mworld] :
( ~ ( mrel @ sK1_SY37 @ SY227 )
| ~ ( ~ ( combo @ d @ SV8 @ SY227 )
| ~ ( h @ SV14 @ SY227 ) ) )
| ! [SX2: mworld] :
( ~ ( mrel @ sK1_SY37 @ SX2 )
| ( open @ d @ SX2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(75,plain,
! [SV9: mworld,SV7: mworld,SV6: mworld] :
( ( ( ~ ( mrel @ SV6 @ SV7 )
| ~ ( mrel @ SV7 @ SV9 ) )
= $true )
| ( ( mrel @ SV6 @ SV9 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[70]) ).
thf(76,plain,
! [SV12: mworld] :
( ( ( mrel @ mactual @ SV12 )
= $false )
| ( ( combo @ d @ sK2_SX0 @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(77,plain,
! [SV3: mworld,SV10: $i] :
( ( ( ~ ( open @ SV10 @ SV3 ) )
= $true )
| ( ( ~ ( closed @ SV10 @ SV3 ) )
= $true )
| ( ( mrel @ mactual @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[72]) ).
thf(78,plain,
! [SV13: $i,SV11: $i,SV4: mworld] :
( ( ( ~ ~ ( ~ ! [SY229: mworld] :
( ~ ( mrel @ SV4 @ SY229 )
| ~ ~ ( ~ ( closed @ SV11 @ SY229 )
| ~ ~ ( ~ ( combo @ SV11 @ SV13 @ SY229 )
| ~ ( h @ ( sK3_SY222 @ SV13 @ SV11 @ SV4 ) @ SY229 ) ) )
| ! [SY219: mworld] :
( ~ ( mrel @ SY229 @ SY219 )
| ( open @ SV11 @ SY219 ) ) )
| ~ ! [SY225: mworld] :
( ~ ( mrel @ SV4 @ SY225 )
| ~ ~ ( ~ ( closed @ SV11 @ SY225 )
| ~ ~ ( ~ ~ ( combo @ SV11 @ SV13 @ SY225 )
| ~ ( h @ o @ SY225 ) ) )
| ! [SY221: mworld] :
( ~ ( mrel @ SY225 @ SY221 )
| ( closed @ SV11 @ SY221 ) ) ) ) )
= $false )
| ( ( mrel @ mactual @ SV4 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[73]) ).
thf(79,plain,
! [SV14: $i,SV8: $i] :
( ( ~ ! [SY227: mworld] :
( ~ ( mrel @ sK1_SY37 @ SY227 )
| ~ ( ~ ( combo @ d @ SV8 @ SY227 )
| ~ ( h @ SV14 @ SY227 ) ) )
| ! [SX2: mworld] :
( ~ ( mrel @ sK1_SY37 @ SX2 )
| ( open @ d @ SX2 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(80,plain,
! [SV9: mworld,SV7: mworld,SV6: mworld] :
( ( ( ~ ( mrel @ SV6 @ SV7 ) )
= $true )
| ( ( ~ ( mrel @ SV7 @ SV9 ) )
= $true )
| ( ( mrel @ SV6 @ SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[75]) ).
thf(81,plain,
! [SV3: mworld,SV10: $i] :
( ( ( open @ SV10 @ SV3 )
= $false )
| ( ( ~ ( closed @ SV10 @ SV3 ) )
= $true )
| ( ( mrel @ mactual @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(82,plain,
! [SV13: $i,SV11: $i,SV4: mworld] :
( ( ( ~ ( ~ ! [SY229: mworld] :
( ~ ( mrel @ SV4 @ SY229 )
| ~ ~ ( ~ ( closed @ SV11 @ SY229 )
| ~ ~ ( ~ ( combo @ SV11 @ SV13 @ SY229 )
| ~ ( h @ ( sK3_SY222 @ SV13 @ SV11 @ SV4 ) @ SY229 ) ) )
| ! [SY219: mworld] :
( ~ ( mrel @ SY229 @ SY219 )
| ( open @ SV11 @ SY219 ) ) )
| ~ ! [SY225: mworld] :
( ~ ( mrel @ SV4 @ SY225 )
| ~ ~ ( ~ ( closed @ SV11 @ SY225 )
| ~ ~ ( ~ ~ ( combo @ SV11 @ SV13 @ SY225 )
| ~ ( h @ o @ SY225 ) ) )
| ! [SY221: mworld] :
( ~ ( mrel @ SY225 @ SY221 )
| ( closed @ SV11 @ SY221 ) ) ) ) )
= $true )
| ( ( mrel @ mactual @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[78]) ).
thf(83,plain,
! [SV14: $i,SV8: $i] :
( ( ~ ! [SY227: mworld] :
( ~ ( mrel @ sK1_SY37 @ SY227 )
| ~ ( ~ ( combo @ d @ SV8 @ SY227 )
| ~ ( h @ SV14 @ SY227 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[79]) ).
thf(84,plain,
( ( ! [SX2: mworld] :
( ~ ( mrel @ sK1_SY37 @ SX2 )
| ( open @ d @ SX2 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[79]) ).
thf(85,plain,
! [SV9: mworld,SV7: mworld,SV6: mworld] :
( ( ( mrel @ SV6 @ SV7 )
= $false )
| ( ( ~ ( mrel @ SV7 @ SV9 ) )
= $true )
| ( ( mrel @ SV6 @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(86,plain,
! [SV3: mworld,SV10: $i] :
( ( ( closed @ SV10 @ SV3 )
= $false )
| ( ( open @ SV10 @ SV3 )
= $false )
| ( ( mrel @ mactual @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(87,plain,
! [SV13: $i,SV11: $i,SV4: mworld] :
( ( ( ~ ! [SY229: mworld] :
( ~ ( mrel @ SV4 @ SY229 )
| ~ ~ ( ~ ( closed @ SV11 @ SY229 )
| ~ ~ ( ~ ( combo @ SV11 @ SV13 @ SY229 )
| ~ ( h @ ( sK3_SY222 @ SV13 @ SV11 @ SV4 ) @ SY229 ) ) )
| ! [SY219: mworld] :
( ~ ( mrel @ SY229 @ SY219 )
| ( open @ SV11 @ SY219 ) ) )
| ~ ! [SY225: mworld] :
( ~ ( mrel @ SV4 @ SY225 )
| ~ ~ ( ~ ( closed @ SV11 @ SY225 )
| ~ ~ ( ~ ~ ( combo @ SV11 @ SV13 @ SY225 )
| ~ ( h @ o @ SY225 ) ) )
| ! [SY221: mworld] :
( ~ ( mrel @ SY225 @ SY221 )
| ( closed @ SV11 @ SY221 ) ) ) )
= $false )
| ( ( mrel @ mactual @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(88,plain,
! [SV14: $i,SV8: $i] :
( ( ! [SY227: mworld] :
( ~ ( mrel @ sK1_SY37 @ SY227 )
| ~ ( ~ ( combo @ d @ SV8 @ SY227 )
| ~ ( h @ SV14 @ SY227 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[83]) ).
thf(89,plain,
( ( ~ ( mrel @ sK1_SY37 @ sK4_SX2 )
| ( open @ d @ sK4_SX2 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[84]) ).
thf(90,plain,
! [SV6: mworld,SV9: mworld,SV7: mworld] :
( ( ( mrel @ SV7 @ SV9 )
= $false )
| ( ( mrel @ SV6 @ SV7 )
= $false )
| ( ( mrel @ SV6 @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[85]) ).
thf(91,plain,
! [SV13: $i,SV11: $i,SV4: mworld] :
( ( ( ~ ! [SY229: mworld] :
( ~ ( mrel @ SV4 @ SY229 )
| ~ ~ ( ~ ( closed @ SV11 @ SY229 )
| ~ ~ ( ~ ( combo @ SV11 @ SV13 @ SY229 )
| ~ ( h @ ( sK3_SY222 @ SV13 @ SV11 @ SV4 ) @ SY229 ) ) )
| ! [SY219: mworld] :
( ~ ( mrel @ SY229 @ SY219 )
| ( open @ SV11 @ SY219 ) ) ) )
= $false )
| ( ( mrel @ mactual @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[87]) ).
thf(92,plain,
! [SV13: $i,SV11: $i,SV4: mworld] :
( ( ( ~ ! [SY225: mworld] :
( ~ ( mrel @ SV4 @ SY225 )
| ~ ~ ( ~ ( closed @ SV11 @ SY225 )
| ~ ~ ( ~ ~ ( combo @ SV11 @ SV13 @ SY225 )
| ~ ( h @ o @ SY225 ) ) )
| ! [SY221: mworld] :
( ~ ( mrel @ SY225 @ SY221 )
| ( closed @ SV11 @ SY221 ) ) ) )
= $false )
| ( ( mrel @ mactual @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[87]) ).
thf(93,plain,
! [SV14: $i,SV8: $i,SV15: mworld] :
( ( ~ ( mrel @ sK1_SY37 @ SV15 )
| ~ ( ~ ( combo @ d @ SV8 @ SV15 )
| ~ ( h @ SV14 @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(94,plain,
( ( ~ ( mrel @ sK1_SY37 @ sK4_SX2 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[89]) ).
thf(95,plain,
( ( open @ d @ sK4_SX2 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[89]) ).
thf(96,plain,
! [SV13: $i,SV11: $i,SV4: mworld] :
( ( ( ! [SY229: mworld] :
( ~ ( mrel @ SV4 @ SY229 )
| ~ ~ ( ~ ( closed @ SV11 @ SY229 )
| ~ ~ ( ~ ( combo @ SV11 @ SV13 @ SY229 )
| ~ ( h @ ( sK3_SY222 @ SV13 @ SV11 @ SV4 ) @ SY229 ) ) )
| ! [SY219: mworld] :
( ~ ( mrel @ SY229 @ SY219 )
| ( open @ SV11 @ SY219 ) ) ) )
= $true )
| ( ( mrel @ mactual @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[91]) ).
thf(97,plain,
! [SV13: $i,SV11: $i,SV4: mworld] :
( ( ( ! [SY225: mworld] :
( ~ ( mrel @ SV4 @ SY225 )
| ~ ~ ( ~ ( closed @ SV11 @ SY225 )
| ~ ~ ( ~ ~ ( combo @ SV11 @ SV13 @ SY225 )
| ~ ( h @ o @ SY225 ) ) )
| ! [SY221: mworld] :
( ~ ( mrel @ SY225 @ SY221 )
| ( closed @ SV11 @ SY221 ) ) ) )
= $true )
| ( ( mrel @ mactual @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[92]) ).
thf(98,plain,
! [SV14: $i,SV8: $i,SV15: mworld] :
( ( ( ~ ( mrel @ sK1_SY37 @ SV15 ) )
= $true )
| ( ( ~ ( ~ ( combo @ d @ SV8 @ SV15 )
| ~ ( h @ SV14 @ SV15 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[93]) ).
thf(99,plain,
( ( mrel @ sK1_SY37 @ sK4_SX2 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[94]) ).
thf(100,plain,
! [SV13: $i,SV11: $i,SV16: mworld,SV4: mworld] :
( ( ( ~ ( mrel @ SV4 @ SV16 )
| ~ ~ ( ~ ( closed @ SV11 @ SV16 )
| ~ ~ ( ~ ( combo @ SV11 @ SV13 @ SV16 )
| ~ ( h @ ( sK3_SY222 @ SV13 @ SV11 @ SV4 ) @ SV16 ) ) )
| ! [SY233: mworld] :
( ~ ( mrel @ SV16 @ SY233 )
| ( open @ SV11 @ SY233 ) ) )
= $true )
| ( ( mrel @ mactual @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(101,plain,
! [SV13: $i,SV11: $i,SV17: mworld,SV4: mworld] :
( ( ( ~ ( mrel @ SV4 @ SV17 )
| ~ ~ ( ~ ( closed @ SV11 @ SV17 )
| ~ ~ ( ~ ~ ( combo @ SV11 @ SV13 @ SV17 )
| ~ ( h @ o @ SV17 ) ) )
| ! [SY234: mworld] :
( ~ ( mrel @ SV17 @ SY234 )
| ( closed @ SV11 @ SY234 ) ) )
= $true )
| ( ( mrel @ mactual @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(102,plain,
! [SV14: $i,SV8: $i,SV15: mworld] :
( ( ( mrel @ sK1_SY37 @ SV15 )
= $false )
| ( ( ~ ( ~ ( combo @ d @ SV8 @ SV15 )
| ~ ( h @ SV14 @ SV15 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(103,plain,
! [SV13: $i,SV11: $i,SV16: mworld,SV4: mworld] :
( ( ( ~ ( mrel @ SV4 @ SV16 ) )
= $true )
| ( ( ~ ~ ( ~ ( closed @ SV11 @ SV16 )
| ~ ~ ( ~ ( combo @ SV11 @ SV13 @ SV16 )
| ~ ( h @ ( sK3_SY222 @ SV13 @ SV11 @ SV4 ) @ SV16 ) ) )
| ! [SY233: mworld] :
( ~ ( mrel @ SV16 @ SY233 )
| ( open @ SV11 @ SY233 ) ) )
= $true )
| ( ( mrel @ mactual @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[100]) ).
thf(104,plain,
! [SV13: $i,SV11: $i,SV17: mworld,SV4: mworld] :
( ( ( ~ ( mrel @ SV4 @ SV17 ) )
= $true )
| ( ( ~ ~ ( ~ ( closed @ SV11 @ SV17 )
| ~ ~ ( ~ ~ ( combo @ SV11 @ SV13 @ SV17 )
| ~ ( h @ o @ SV17 ) ) )
| ! [SY234: mworld] :
( ~ ( mrel @ SV17 @ SY234 )
| ( closed @ SV11 @ SY234 ) ) )
= $true )
| ( ( mrel @ mactual @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[101]) ).
thf(105,plain,
! [SV14: $i,SV15: mworld,SV8: $i] :
( ( ( ~ ( combo @ d @ SV8 @ SV15 )
| ~ ( h @ SV14 @ SV15 ) )
= $false )
| ( ( mrel @ sK1_SY37 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(106,plain,
! [SV13: $i,SV11: $i,SV16: mworld,SV4: mworld] :
( ( ( mrel @ SV4 @ SV16 )
= $false )
| ( ( ~ ~ ( ~ ( closed @ SV11 @ SV16 )
| ~ ~ ( ~ ( combo @ SV11 @ SV13 @ SV16 )
| ~ ( h @ ( sK3_SY222 @ SV13 @ SV11 @ SV4 ) @ SV16 ) ) )
| ! [SY233: mworld] :
( ~ ( mrel @ SV16 @ SY233 )
| ( open @ SV11 @ SY233 ) ) )
= $true )
| ( ( mrel @ mactual @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(107,plain,
! [SV13: $i,SV11: $i,SV17: mworld,SV4: mworld] :
( ( ( mrel @ SV4 @ SV17 )
= $false )
| ( ( ~ ~ ( ~ ( closed @ SV11 @ SV17 )
| ~ ~ ( ~ ~ ( combo @ SV11 @ SV13 @ SV17 )
| ~ ( h @ o @ SV17 ) ) )
| ! [SY234: mworld] :
( ~ ( mrel @ SV17 @ SY234 )
| ( closed @ SV11 @ SY234 ) ) )
= $true )
| ( ( mrel @ mactual @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[104]) ).
thf(108,plain,
! [SV15: mworld,SV8: $i] :
( ( ( ~ ( combo @ d @ SV8 @ SV15 ) )
= $false )
| ( ( mrel @ sK1_SY37 @ SV15 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[105]) ).
thf(109,plain,
! [SV15: mworld,SV14: $i] :
( ( ( ~ ( h @ SV14 @ SV15 ) )
= $false )
| ( ( mrel @ sK1_SY37 @ SV15 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[105]) ).
thf(110,plain,
! [SV4: mworld,SV13: $i,SV16: mworld,SV11: $i] :
( ( ( ~ ~ ( ~ ( closed @ SV11 @ SV16 )
| ~ ~ ( ~ ( combo @ SV11 @ SV13 @ SV16 )
| ~ ( h @ ( sK3_SY222 @ SV13 @ SV11 @ SV4 ) @ SV16 ) ) ) )
= $true )
| ( ( ! [SY233: mworld] :
( ~ ( mrel @ SV16 @ SY233 )
| ( open @ SV11 @ SY233 ) ) )
= $true )
| ( ( mrel @ SV4 @ SV16 )
= $false )
| ( ( mrel @ mactual @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[106]) ).
thf(111,plain,
! [SV4: mworld,SV13: $i,SV17: mworld,SV11: $i] :
( ( ( ~ ~ ( ~ ( closed @ SV11 @ SV17 )
| ~ ~ ( ~ ~ ( combo @ SV11 @ SV13 @ SV17 )
| ~ ( h @ o @ SV17 ) ) ) )
= $true )
| ( ( ! [SY234: mworld] :
( ~ ( mrel @ SV17 @ SY234 )
| ( closed @ SV11 @ SY234 ) ) )
= $true )
| ( ( mrel @ SV4 @ SV17 )
= $false )
| ( ( mrel @ mactual @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[107]) ).
thf(112,plain,
! [SV15: mworld,SV8: $i] :
( ( ( combo @ d @ SV8 @ SV15 )
= $true )
| ( ( mrel @ sK1_SY37 @ SV15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[108]) ).
thf(113,plain,
! [SV15: mworld,SV14: $i] :
( ( ( h @ SV14 @ SV15 )
= $true )
| ( ( mrel @ sK1_SY37 @ SV15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[109]) ).
thf(114,plain,
! [SV4: mworld,SV13: $i,SV16: mworld,SV11: $i] :
( ( ( ~ ( ~ ( closed @ SV11 @ SV16 )
| ~ ~ ( ~ ( combo @ SV11 @ SV13 @ SV16 )
| ~ ( h @ ( sK3_SY222 @ SV13 @ SV11 @ SV4 ) @ SV16 ) ) ) )
= $false )
| ( ( ! [SY233: mworld] :
( ~ ( mrel @ SV16 @ SY233 )
| ( open @ SV11 @ SY233 ) ) )
= $true )
| ( ( mrel @ SV4 @ SV16 )
= $false )
| ( ( mrel @ mactual @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(115,plain,
! [SV4: mworld,SV13: $i,SV17: mworld,SV11: $i] :
( ( ( ~ ( ~ ( closed @ SV11 @ SV17 )
| ~ ~ ( ~ ~ ( combo @ SV11 @ SV13 @ SV17 )
| ~ ( h @ o @ SV17 ) ) ) )
= $false )
| ( ( ! [SY234: mworld] :
( ~ ( mrel @ SV17 @ SY234 )
| ( closed @ SV11 @ SY234 ) ) )
= $true )
| ( ( mrel @ SV4 @ SV17 )
= $false )
| ( ( mrel @ mactual @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(116,plain,
! [SV4: mworld,SV13: $i,SV16: mworld,SV11: $i] :
( ( ( ~ ( closed @ SV11 @ SV16 )
| ~ ~ ( ~ ( combo @ SV11 @ SV13 @ SV16 )
| ~ ( h @ ( sK3_SY222 @ SV13 @ SV11 @ SV4 ) @ SV16 ) ) )
= $true )
| ( ( ! [SY233: mworld] :
( ~ ( mrel @ SV16 @ SY233 )
| ( open @ SV11 @ SY233 ) ) )
= $true )
| ( ( mrel @ SV4 @ SV16 )
= $false )
| ( ( mrel @ mactual @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[114]) ).
thf(117,plain,
! [SV4: mworld,SV13: $i,SV17: mworld,SV11: $i] :
( ( ( ~ ( closed @ SV11 @ SV17 )
| ~ ~ ( ~ ~ ( combo @ SV11 @ SV13 @ SV17 )
| ~ ( h @ o @ SV17 ) ) )
= $true )
| ( ( ! [SY234: mworld] :
( ~ ( mrel @ SV17 @ SY234 )
| ( closed @ SV11 @ SY234 ) ) )
= $true )
| ( ( mrel @ SV4 @ SV17 )
= $false )
| ( ( mrel @ mactual @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[115]) ).
thf(118,plain,
! [SV4: mworld,SV13: $i,SV16: mworld,SV11: $i] :
( ( ( ~ ( closed @ SV11 @ SV16 ) )
= $true )
| ( ( ~ ~ ( ~ ( combo @ SV11 @ SV13 @ SV16 )
| ~ ( h @ ( sK3_SY222 @ SV13 @ SV11 @ SV4 ) @ SV16 ) ) )
= $true )
| ( ( ! [SY233: mworld] :
( ~ ( mrel @ SV16 @ SY233 )
| ( open @ SV11 @ SY233 ) ) )
= $true )
| ( ( mrel @ SV4 @ SV16 )
= $false )
| ( ( mrel @ mactual @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[116]) ).
thf(119,plain,
! [SV4: mworld,SV13: $i,SV17: mworld,SV11: $i] :
( ( ( ~ ( closed @ SV11 @ SV17 ) )
= $true )
| ( ( ~ ~ ( ~ ~ ( combo @ SV11 @ SV13 @ SV17 )
| ~ ( h @ o @ SV17 ) ) )
= $true )
| ( ( ! [SY234: mworld] :
( ~ ( mrel @ SV17 @ SY234 )
| ( closed @ SV11 @ SY234 ) ) )
= $true )
| ( ( mrel @ SV4 @ SV17 )
= $false )
| ( ( mrel @ mactual @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[117]) ).
thf(120,plain,
! [SV4: mworld,SV13: $i,SV16: mworld,SV11: $i] :
( ( ( closed @ SV11 @ SV16 )
= $false )
| ( ( ~ ~ ( ~ ( combo @ SV11 @ SV13 @ SV16 )
| ~ ( h @ ( sK3_SY222 @ SV13 @ SV11 @ SV4 ) @ SV16 ) ) )
= $true )
| ( ( ! [SY233: mworld] :
( ~ ( mrel @ SV16 @ SY233 )
| ( open @ SV11 @ SY233 ) ) )
= $true )
| ( ( mrel @ SV4 @ SV16 )
= $false )
| ( ( mrel @ mactual @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(121,plain,
! [SV4: mworld,SV13: $i,SV17: mworld,SV11: $i] :
( ( ( closed @ SV11 @ SV17 )
= $false )
| ( ( ~ ~ ( ~ ~ ( combo @ SV11 @ SV13 @ SV17 )
| ~ ( h @ o @ SV17 ) ) )
= $true )
| ( ( ! [SY234: mworld] :
( ~ ( mrel @ SV17 @ SY234 )
| ( closed @ SV11 @ SY234 ) ) )
= $true )
| ( ( mrel @ SV4 @ SV17 )
= $false )
| ( ( mrel @ mactual @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(122,plain,
! [SV4: mworld,SV16: mworld,SV13: $i,SV11: $i] :
( ( ( ~ ( ~ ( combo @ SV11 @ SV13 @ SV16 )
| ~ ( h @ ( sK3_SY222 @ SV13 @ SV11 @ SV4 ) @ SV16 ) ) )
= $false )
| ( ( closed @ SV11 @ SV16 )
= $false )
| ( ( ! [SY233: mworld] :
( ~ ( mrel @ SV16 @ SY233 )
| ( open @ SV11 @ SY233 ) ) )
= $true )
| ( ( mrel @ SV4 @ SV16 )
= $false )
| ( ( mrel @ mactual @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(123,plain,
! [SV4: mworld,SV17: mworld,SV13: $i,SV11: $i] :
( ( ( ~ ( ~ ~ ( combo @ SV11 @ SV13 @ SV17 )
| ~ ( h @ o @ SV17 ) ) )
= $false )
| ( ( closed @ SV11 @ SV17 )
= $false )
| ( ( ! [SY234: mworld] :
( ~ ( mrel @ SV17 @ SY234 )
| ( closed @ SV11 @ SY234 ) ) )
= $true )
| ( ( mrel @ SV4 @ SV17 )
= $false )
| ( ( mrel @ mactual @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[121]) ).
thf(124,plain,
! [SV4: mworld,SV16: mworld,SV13: $i,SV11: $i] :
( ( ( ~ ( combo @ SV11 @ SV13 @ SV16 )
| ~ ( h @ ( sK3_SY222 @ SV13 @ SV11 @ SV4 ) @ SV16 ) )
= $true )
| ( ( closed @ SV11 @ SV16 )
= $false )
| ( ( ! [SY233: mworld] :
( ~ ( mrel @ SV16 @ SY233 )
| ( open @ SV11 @ SY233 ) ) )
= $true )
| ( ( mrel @ SV4 @ SV16 )
= $false )
| ( ( mrel @ mactual @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[122]) ).
thf(125,plain,
! [SV4: mworld,SV17: mworld,SV13: $i,SV11: $i] :
( ( ( ~ ~ ( combo @ SV11 @ SV13 @ SV17 )
| ~ ( h @ o @ SV17 ) )
= $true )
| ( ( closed @ SV11 @ SV17 )
= $false )
| ( ( ! [SY234: mworld] :
( ~ ( mrel @ SV17 @ SY234 )
| ( closed @ SV11 @ SY234 ) ) )
= $true )
| ( ( mrel @ SV4 @ SV17 )
= $false )
| ( ( mrel @ mactual @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[123]) ).
thf(126,plain,
! [SV4: mworld,SV16: mworld,SV13: $i,SV11: $i] :
( ( ( ~ ( combo @ SV11 @ SV13 @ SV16 ) )
= $true )
| ( ( ~ ( h @ ( sK3_SY222 @ SV13 @ SV11 @ SV4 ) @ SV16 ) )
= $true )
| ( ( closed @ SV11 @ SV16 )
= $false )
| ( ( ! [SY233: mworld] :
( ~ ( mrel @ SV16 @ SY233 )
| ( open @ SV11 @ SY233 ) ) )
= $true )
| ( ( mrel @ SV4 @ SV16 )
= $false )
| ( ( mrel @ mactual @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[124]) ).
thf(127,plain,
! [SV4: mworld,SV17: mworld,SV13: $i,SV11: $i] :
( ( ( ~ ~ ( combo @ SV11 @ SV13 @ SV17 ) )
= $true )
| ( ( ~ ( h @ o @ SV17 ) )
= $true )
| ( ( closed @ SV11 @ SV17 )
= $false )
| ( ( ! [SY234: mworld] :
( ~ ( mrel @ SV17 @ SY234 )
| ( closed @ SV11 @ SY234 ) ) )
= $true )
| ( ( mrel @ SV4 @ SV17 )
= $false )
| ( ( mrel @ mactual @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[125]) ).
thf(128,plain,
! [SV4: mworld,SV16: mworld,SV13: $i,SV11: $i] :
( ( ( combo @ SV11 @ SV13 @ SV16 )
= $false )
| ( ( ~ ( h @ ( sK3_SY222 @ SV13 @ SV11 @ SV4 ) @ SV16 ) )
= $true )
| ( ( closed @ SV11 @ SV16 )
= $false )
| ( ( ! [SY233: mworld] :
( ~ ( mrel @ SV16 @ SY233 )
| ( open @ SV11 @ SY233 ) ) )
= $true )
| ( ( mrel @ SV4 @ SV16 )
= $false )
| ( ( mrel @ mactual @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[126]) ).
thf(129,plain,
! [SV4: mworld,SV17: mworld,SV13: $i,SV11: $i] :
( ( ( ~ ( combo @ SV11 @ SV13 @ SV17 ) )
= $false )
| ( ( ~ ( h @ o @ SV17 ) )
= $true )
| ( ( closed @ SV11 @ SV17 )
= $false )
| ( ( ! [SY234: mworld] :
( ~ ( mrel @ SV17 @ SY234 )
| ( closed @ SV11 @ SY234 ) ) )
= $true )
| ( ( mrel @ SV4 @ SV17 )
= $false )
| ( ( mrel @ mactual @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[127]) ).
thf(130,plain,
! [SV16: mworld,SV4: mworld,SV11: $i,SV13: $i] :
( ( ( h @ ( sK3_SY222 @ SV13 @ SV11 @ SV4 ) @ SV16 )
= $false )
| ( ( combo @ SV11 @ SV13 @ SV16 )
= $false )
| ( ( closed @ SV11 @ SV16 )
= $false )
| ( ( ! [SY233: mworld] :
( ~ ( mrel @ SV16 @ SY233 )
| ( open @ SV11 @ SY233 ) ) )
= $true )
| ( ( mrel @ SV4 @ SV16 )
= $false )
| ( ( mrel @ mactual @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(131,plain,
! [SV4: mworld,SV17: mworld,SV13: $i,SV11: $i] :
( ( ( combo @ SV11 @ SV13 @ SV17 )
= $true )
| ( ( ~ ( h @ o @ SV17 ) )
= $true )
| ( ( closed @ SV11 @ SV17 )
= $false )
| ( ( ! [SY234: mworld] :
( ~ ( mrel @ SV17 @ SY234 )
| ( closed @ SV11 @ SY234 ) ) )
= $true )
| ( ( mrel @ SV4 @ SV17 )
= $false )
| ( ( mrel @ mactual @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[129]) ).
thf(132,plain,
! [SV4: mworld,SV13: $i,SV11: $i,SV18: mworld,SV16: mworld] :
( ( ( ~ ( mrel @ SV16 @ SV18 )
| ( open @ SV11 @ SV18 ) )
= $true )
| ( ( closed @ SV11 @ SV16 )
= $false )
| ( ( combo @ SV11 @ SV13 @ SV16 )
= $false )
| ( ( h @ ( sK3_SY222 @ SV13 @ SV11 @ SV4 ) @ SV16 )
= $false )
| ( ( mrel @ SV4 @ SV16 )
= $false )
| ( ( mrel @ mactual @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(133,plain,
! [SV4: mworld,SV13: $i,SV11: $i,SV17: mworld] :
( ( ( h @ o @ SV17 )
= $false )
| ( ( combo @ SV11 @ SV13 @ SV17 )
= $true )
| ( ( closed @ SV11 @ SV17 )
= $false )
| ( ( ! [SY234: mworld] :
( ~ ( mrel @ SV17 @ SY234 )
| ( closed @ SV11 @ SY234 ) ) )
= $true )
| ( ( mrel @ SV4 @ SV17 )
= $false )
| ( ( mrel @ mactual @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(134,plain,
! [SV4: mworld,SV13: $i,SV11: $i,SV18: mworld,SV16: mworld] :
( ( ( ~ ( mrel @ SV16 @ SV18 ) )
= $true )
| ( ( open @ SV11 @ SV18 )
= $true )
| ( ( closed @ SV11 @ SV16 )
= $false )
| ( ( combo @ SV11 @ SV13 @ SV16 )
= $false )
| ( ( h @ ( sK3_SY222 @ SV13 @ SV11 @ SV4 ) @ SV16 )
= $false )
| ( ( mrel @ SV4 @ SV16 )
= $false )
| ( ( mrel @ mactual @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[132]) ).
thf(135,plain,
! [SV4: mworld,SV13: $i,SV11: $i,SV19: mworld,SV17: mworld] :
( ( ( ~ ( mrel @ SV17 @ SV19 )
| ( closed @ SV11 @ SV19 ) )
= $true )
| ( ( closed @ SV11 @ SV17 )
= $false )
| ( ( combo @ SV11 @ SV13 @ SV17 )
= $true )
| ( ( h @ o @ SV17 )
= $false )
| ( ( mrel @ SV4 @ SV17 )
= $false )
| ( ( mrel @ mactual @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(136,plain,
! [SV4: mworld,SV13: $i,SV11: $i,SV18: mworld,SV16: mworld] :
( ( ( mrel @ SV16 @ SV18 )
= $false )
| ( ( open @ SV11 @ SV18 )
= $true )
| ( ( closed @ SV11 @ SV16 )
= $false )
| ( ( combo @ SV11 @ SV13 @ SV16 )
= $false )
| ( ( h @ ( sK3_SY222 @ SV13 @ SV11 @ SV4 ) @ SV16 )
= $false )
| ( ( mrel @ SV4 @ SV16 )
= $false )
| ( ( mrel @ mactual @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(137,plain,
! [SV4: mworld,SV13: $i,SV11: $i,SV19: mworld,SV17: mworld] :
( ( ( ~ ( mrel @ SV17 @ SV19 ) )
= $true )
| ( ( closed @ SV11 @ SV19 )
= $true )
| ( ( closed @ SV11 @ SV17 )
= $false )
| ( ( combo @ SV11 @ SV13 @ SV17 )
= $true )
| ( ( h @ o @ SV17 )
= $false )
| ( ( mrel @ SV4 @ SV17 )
= $false )
| ( ( mrel @ mactual @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[135]) ).
thf(138,plain,
! [SV4: mworld,SV13: $i,SV11: $i,SV19: mworld,SV17: mworld] :
( ( ( mrel @ SV17 @ SV19 )
= $false )
| ( ( closed @ SV11 @ SV19 )
= $true )
| ( ( closed @ SV11 @ SV17 )
= $false )
| ( ( combo @ SV11 @ SV13 @ SV17 )
= $true )
| ( ( h @ o @ SV17 )
= $false )
| ( ( mrel @ SV4 @ SV17 )
= $false )
| ( ( mrel @ mactual @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(139,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[29,138,136,113,112,99,95,90,86,76,66,57,38]) ).
thf(140,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[139]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PLA054^4 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.18 % Computer : n006.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Oct 6 13:52:37 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.24
% 0.09/0.24 No.of.Axioms: 7
% 0.09/0.24
% 0.09/0.24 Length.of.Defs: 1624
% 0.09/0.24
% 0.09/0.24 Contains.Choice.Funs: false
% 0.09/0.24 .......
% 0.09/0.24
% 0.09/0.24 ********************************
% 0.09/0.24 * All subproblems solved! *
% 0.09/0.24 ********************************
% 0.09/0.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:8,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:139,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.09/0.24
% 0.09/0.24 %**** Beginning of derivation protocol ****
% 0.09/0.24 % SZS output start CNFRefutation
% See solution above
% 0.09/0.25
% 0.09/0.25 %**** End of derivation protocol ****
% 0.09/0.25 %**** no. of clauses in derivation: 140 ****
% 0.09/0.25 %**** clause counter: 139 ****
% 0.09/0.25
% 0.09/0.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:8,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:139,loop_count:0,foatp_calls:1,translation:fof_full)
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