%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : PLA053^4 : 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:36:25 AM UTC 2026
% Result : Theorem 0.07s 0.22s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 16
% Syntax : Number of formulae : 87 ( 56 unt; 0 typ; 10 def)
% Number of atoms : 551 ( 137 equ; 0 cnn)
% Maximal formula atoms : 10 ( 6 avg)
% Number of connectives : 848 ( 118 ~; 135 |; 14 &; 563 @)
% ( 1 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 20 usr; 6 con; 0-3 aty)
% Number of variables : 185 ( 32 ^; 144 !; 9 ?; 185 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_mworld,type,
mworld: $tType ).
thf(tp_bomb,type,
bomb: $i > mworld > $o ).
thf(tp_defused,type,
defused: $i > mworld > $o ).
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_sK1_SY20,type,
sK1_SY20: mworld ).
thf(tp_sK2_SY112,type,
sK2_SY112: $i ).
thf(tp_sK3_SY51,type,
sK3_SY51: $i > mworld > $i ).
thf(tp_sK4_SY90,type,
sK4_SY90: $i ).
thf(tp_sK5_SY103,type,
sK5_SY103: mworld > $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] : ( 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] : ( 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
@ ^ [X: $i] :
( mexists_di
@ ^ [D: $i] : ( mbox @ ( mimplies @ ( mand @ ( bomb @ X ) @ ( h @ D ) ) @ ( defused @ X ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
thf(2,axiom,
( mlocal
@ ( mexists_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [X: $i] : ( mimplies @ ( mand @ ( bomb @ X ) @ ( h @ A ) ) @ ( mbox @ ( bomb @ X ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).
thf(3,axiom,
( mlocal
@ ( mbox
@ ( mexists_di
@ ^ [B: $i] : ( bomb @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).
thf(4,axiom,
! [W: mworld,V: mworld,U: mworld] :
( ( ( mrel @ W @ V )
& ( mrel @ V @ U ) )
=> ( mrel @ W @ U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_transitive) ).
thf(5,axiom,
! [W: mworld] : ( mrel @ W @ W ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_reflexive) ).
thf(6,conjecture,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [X: $i] :
( mexists_di
@ ^ [D: $i] : ( mimplies @ ( mand @ ( bomb @ X ) @ ( h @ D ) ) @ ( defused @ X ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(7,negated_conjecture,
( ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [X: $i] :
( mexists_di
@ ^ [D: $i] : ( mimplies @ ( mand @ ( bomb @ X ) @ ( h @ D ) ) @ ( defused @ X ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[6]) ).
thf(8,plain,
( ( ! [SY20: mworld] :
( ( mrel @ mactual @ SY20 )
=> ! [SY18: $i] :
? [SY19: $i] :
( ( ( bomb @ SY18 @ SY20 )
& ( h @ SY19 @ SY20 ) )
=> ( defused @ SY18 @ SY20 ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[7,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(9,plain,
( ( ! [SY53: mworld] :
( ( mrel @ mactual @ SY53 )
=> ! [SY50: $i] :
? [SY51: $i] :
! [SY52: mworld] :
( ( mrel @ SY53 @ SY52 )
=> ( ( ( bomb @ SY50 @ SY52 )
& ( h @ SY51 @ SY52 ) )
=> ( defused @ SY50 @ SY52 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(10,plain,
( ( ? [SY90: $i] :
! [SY91: mworld] :
( ( mrel @ mactual @ SY91 )
=> ! [SY85: $i] :
( ( ( bomb @ SY85 @ SY91 )
& ( h @ SY90 @ SY91 ) )
=> ! [SY80: mworld] :
( ( mrel @ SY91 @ SY80 )
=> ( bomb @ SY85 @ SY80 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(11,plain,
( ( ! [SY104: mworld] :
( ( mrel @ mactual @ SY104 )
=> ? [SY103: $i] : ( bomb @ SY103 @ SY104 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(12,plain,
( ( ! [W: mworld,V: mworld,U: mworld] :
( ( ( mrel @ W @ V )
& ( mrel @ V @ U ) )
=> ( mrel @ W @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(13,plain,
( ( ! [W: mworld] : ( mrel @ W @ W ) )
= $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_SY20 )
=> ! [SY112: $i] :
? [SY113: $i] :
( ( ( bomb @ SY112 @ sK1_SY20 )
& ( h @ SY113 @ sK1_SY20 ) )
=> ( defused @ SY112 @ sK1_SY20 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[8]) ).
thf(15,plain,
( ( mrel @ mactual @ sK1_SY20 )
= $true ),
inference(standard_cnf,[status(thm)],[14]) ).
thf(16,plain,
( ( ! [SY112: $i] :
? [SY113: $i] :
( ( ( bomb @ SY112 @ sK1_SY20 )
& ( h @ SY113 @ sK1_SY20 ) )
=> ( defused @ SY112 @ sK1_SY20 ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[14]) ).
thf(17,plain,
( ( ~ ! [SY112: $i] :
? [SY113: $i] :
( ( ( bomb @ SY112 @ sK1_SY20 )
& ( h @ SY113 @ sK1_SY20 ) )
=> ( defused @ SY112 @ sK1_SY20 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[16]) ).
thf(18,plain,
( ( ( bomb @ sK2_SY112 @ sK1_SY20 )
& ! [SY113: $i] : ( h @ SY113 @ sK1_SY20 )
& ~ ( defused @ sK2_SY112 @ sK1_SY20 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[17]) ).
thf(19,plain,
( ( ! [SY53: mworld] :
( ~ ( mrel @ mactual @ SY53 )
| ! [SY50: $i,SY115: mworld] :
( ~ ( mrel @ SY53 @ SY115 )
| ~ ( bomb @ SY50 @ SY115 )
| ~ ( h @ ( sK3_SY51 @ SY50 @ SY53 ) @ SY115 )
| ( defused @ SY50 @ SY115 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[9]) ).
thf(20,plain,
( ( ! [SY116: mworld] :
( ~ ( mrel @ mactual @ SY116 )
| ! [SY117: $i] :
( ~ ( bomb @ SY117 @ SY116 )
| ~ ( h @ sK4_SY90 @ SY116 )
| ! [SY80: mworld] :
( ~ ( mrel @ SY116 @ SY80 )
| ( bomb @ SY117 @ SY80 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[10]) ).
thf(21,plain,
( ( ! [SY104: mworld] :
( ~ ( mrel @ mactual @ SY104 )
| ( bomb @ ( sK5_SY103 @ SY104 ) @ SY104 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[11]) ).
thf(22,plain,
( ( ! [W: mworld,V: mworld,U: mworld] :
( ~ ( mrel @ W @ V )
| ~ ( mrel @ V @ U )
| ( mrel @ W @ U ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[12]) ).
thf(23,plain,
( ( ! [W: mworld] : ( mrel @ W @ W ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(24,plain,
( ( ! [W: mworld,V: mworld,U: mworld] :
( ~ ( mrel @ W @ V )
| ~ ( mrel @ V @ U )
| ( mrel @ W @ U ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(25,plain,
( ( ! [SY104: mworld] :
( ~ ( mrel @ mactual @ SY104 )
| ( bomb @ ( sK5_SY103 @ SY104 ) @ SY104 ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(26,plain,
( ( ! [SY116: mworld] :
( ~ ( mrel @ mactual @ SY116 )
| ! [SY117: $i] :
( ~ ( bomb @ SY117 @ SY116 )
| ~ ( h @ sK4_SY90 @ SY116 )
| ! [SY80: mworld] :
( ~ ( mrel @ SY116 @ SY80 )
| ( bomb @ SY117 @ SY80 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(27,plain,
( ( ! [SY53: mworld] :
( ~ ( mrel @ mactual @ SY53 )
| ! [SY50: $i,SY115: mworld] :
( ~ ( mrel @ SY53 @ SY115 )
| ~ ( bomb @ SY50 @ SY115 )
| ~ ( h @ ( sK3_SY51 @ SY50 @ SY53 ) @ SY115 )
| ( defused @ SY50 @ SY115 ) ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(28,plain,
( ( mrel @ mactual @ sK1_SY20 )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(29,plain,
( ( ( bomb @ sK2_SY112 @ sK1_SY20 )
& ! [SY113: $i] : ( h @ SY113 @ sK1_SY20 )
& ~ ( defused @ sK2_SY112 @ sK1_SY20 ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(30,plain,
( ( ~ ( ~ ~ ( ~ ( bomb @ sK2_SY112 @ sK1_SY20 )
| ~ ! [SX0: $i] : ( h @ SX0 @ sK1_SY20 ) )
| ~ ~ ( defused @ sK2_SY112 @ sK1_SY20 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(31,plain,
! [SV1: mworld] :
( ( mrel @ SV1 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(32,plain,
! [SV2: mworld] :
( ( ! [SY119: mworld,SY120: mworld] :
( ~ ( mrel @ SV2 @ SY119 )
| ~ ( mrel @ SY119 @ SY120 )
| ( mrel @ SV2 @ SY120 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(33,plain,
! [SV3: mworld] :
( ( ~ ( mrel @ mactual @ SV3 )
| ( bomb @ ( sK5_SY103 @ SV3 ) @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(34,plain,
! [SV4: mworld] :
( ( ~ ( mrel @ mactual @ SV4 )
| ! [SY121: $i] :
( ~ ( bomb @ SY121 @ SV4 )
| ~ ( h @ sK4_SY90 @ SV4 )
| ! [SY122: mworld] :
( ~ ( mrel @ SV4 @ SY122 )
| ( bomb @ SY121 @ SY122 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(35,plain,
! [SV5: mworld] :
( ( ~ ( mrel @ mactual @ SV5 )
| ! [SY123: $i,SY124: mworld] :
( ~ ( mrel @ SV5 @ SY124 )
| ~ ( bomb @ SY123 @ SY124 )
| ~ ( h @ ( sK3_SY51 @ SY123 @ SV5 ) @ SY124 )
| ( defused @ SY123 @ SY124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(36,plain,
( ( ~ ~ ( ~ ( bomb @ sK2_SY112 @ sK1_SY20 )
| ~ ! [SX0: $i] : ( h @ SX0 @ sK1_SY20 ) )
| ~ ~ ( defused @ sK2_SY112 @ sK1_SY20 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(37,plain,
! [SV6: mworld,SV2: mworld] :
( ( ! [SY125: mworld] :
( ~ ( mrel @ SV2 @ SV6 )
| ~ ( mrel @ SV6 @ SY125 )
| ( mrel @ SV2 @ SY125 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(38,plain,
! [SV3: mworld] :
( ( ( ~ ( mrel @ mactual @ SV3 ) )
= $true )
| ( ( bomb @ ( sK5_SY103 @ SV3 ) @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[33]) ).
thf(39,plain,
! [SV4: mworld] :
( ( ( ~ ( mrel @ mactual @ SV4 ) )
= $true )
| ( ( ! [SY121: $i] :
( ~ ( bomb @ SY121 @ SV4 )
| ~ ( h @ sK4_SY90 @ SV4 )
| ! [SY122: mworld] :
( ~ ( mrel @ SV4 @ SY122 )
| ( bomb @ SY121 @ SY122 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[34]) ).
thf(40,plain,
! [SV5: mworld] :
( ( ( ~ ( mrel @ mactual @ SV5 ) )
= $true )
| ( ( ! [SY123: $i,SY124: mworld] :
( ~ ( mrel @ SV5 @ SY124 )
| ~ ( bomb @ SY123 @ SY124 )
| ~ ( h @ ( sK3_SY51 @ SY123 @ SV5 ) @ SY124 )
| ( defused @ SY123 @ SY124 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[35]) ).
thf(41,plain,
( ( ~ ~ ( ~ ( bomb @ sK2_SY112 @ sK1_SY20 )
| ~ ! [SX0: $i] : ( h @ SX0 @ sK1_SY20 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[36]) ).
thf(42,plain,
( ( ~ ~ ( defused @ sK2_SY112 @ sK1_SY20 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[36]) ).
thf(43,plain,
! [SV7: mworld,SV6: mworld,SV2: mworld] :
( ( ~ ( mrel @ SV2 @ SV6 )
| ~ ( mrel @ SV6 @ SV7 )
| ( mrel @ SV2 @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(44,plain,
! [SV3: mworld] :
( ( ( mrel @ mactual @ SV3 )
= $false )
| ( ( bomb @ ( sK5_SY103 @ SV3 ) @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(45,plain,
! [SV4: mworld] :
( ( ( mrel @ mactual @ SV4 )
= $false )
| ( ( ! [SY121: $i] :
( ~ ( bomb @ SY121 @ SV4 )
| ~ ( h @ sK4_SY90 @ SV4 )
| ! [SY122: mworld] :
( ~ ( mrel @ SV4 @ SY122 )
| ( bomb @ SY121 @ SY122 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(46,plain,
! [SV5: mworld] :
( ( ( mrel @ mactual @ SV5 )
= $false )
| ( ( ! [SY123: $i,SY124: mworld] :
( ~ ( mrel @ SV5 @ SY124 )
| ~ ( bomb @ SY123 @ SY124 )
| ~ ( h @ ( sK3_SY51 @ SY123 @ SV5 ) @ SY124 )
| ( defused @ SY123 @ SY124 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(47,plain,
( ( ~ ( ~ ( bomb @ sK2_SY112 @ sK1_SY20 )
| ~ ! [SX0: $i] : ( h @ SX0 @ sK1_SY20 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[41]) ).
thf(48,plain,
( ( ~ ( defused @ sK2_SY112 @ sK1_SY20 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[42]) ).
thf(49,plain,
! [SV7: mworld,SV6: mworld,SV2: mworld] :
( ( ( ~ ( mrel @ SV2 @ SV6 )
| ~ ( mrel @ SV6 @ SV7 ) )
= $true )
| ( ( mrel @ SV2 @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[43]) ).
thf(50,plain,
! [SV4: mworld,SV8: $i] :
( ( ( ~ ( bomb @ SV8 @ SV4 )
| ~ ( h @ sK4_SY90 @ SV4 )
| ! [SY126: mworld] :
( ~ ( mrel @ SV4 @ SY126 )
| ( bomb @ SV8 @ SY126 ) ) )
= $true )
| ( ( mrel @ mactual @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(51,plain,
! [SV9: $i,SV5: mworld] :
( ( ( ! [SY127: mworld] :
( ~ ( mrel @ SV5 @ SY127 )
| ~ ( bomb @ SV9 @ SY127 )
| ~ ( h @ ( sK3_SY51 @ SV9 @ SV5 ) @ SY127 )
| ( defused @ SV9 @ SY127 ) ) )
= $true )
| ( ( mrel @ mactual @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(52,plain,
( ( ~ ( bomb @ sK2_SY112 @ sK1_SY20 )
| ~ ! [SX0: $i] : ( h @ SX0 @ sK1_SY20 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(53,plain,
( ( defused @ sK2_SY112 @ sK1_SY20 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(54,plain,
! [SV7: mworld,SV6: mworld,SV2: mworld] :
( ( ( ~ ( mrel @ SV2 @ SV6 ) )
= $true )
| ( ( ~ ( mrel @ SV6 @ SV7 ) )
= $true )
| ( ( mrel @ SV2 @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[49]) ).
thf(55,plain,
! [SV4: mworld,SV8: $i] :
( ( ( ~ ( bomb @ SV8 @ SV4 )
| ~ ( h @ sK4_SY90 @ SV4 ) )
= $true )
| ( ( ! [SY126: mworld] :
( ~ ( mrel @ SV4 @ SY126 )
| ( bomb @ SV8 @ SY126 ) ) )
= $true )
| ( ( mrel @ mactual @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[50]) ).
thf(56,plain,
! [SV9: $i,SV10: mworld,SV5: mworld] :
( ( ( ~ ( mrel @ SV5 @ SV10 )
| ~ ( bomb @ SV9 @ SV10 )
| ~ ( h @ ( sK3_SY51 @ SV9 @ SV5 ) @ SV10 )
| ( defused @ SV9 @ SV10 ) )
= $true )
| ( ( mrel @ mactual @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(57,plain,
( ( ~ ( bomb @ sK2_SY112 @ sK1_SY20 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[52]) ).
thf(58,plain,
( ( ~ ! [SX0: $i] : ( h @ SX0 @ sK1_SY20 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[52]) ).
thf(59,plain,
! [SV7: mworld,SV6: mworld,SV2: mworld] :
( ( ( mrel @ SV2 @ SV6 )
= $false )
| ( ( ~ ( mrel @ SV6 @ SV7 ) )
= $true )
| ( ( mrel @ SV2 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(60,plain,
! [SV4: mworld,SV8: $i] :
( ( ( ~ ( bomb @ SV8 @ SV4 ) )
= $true )
| ( ( ~ ( h @ sK4_SY90 @ SV4 ) )
= $true )
| ( ( ! [SY126: mworld] :
( ~ ( mrel @ SV4 @ SY126 )
| ( bomb @ SV8 @ SY126 ) ) )
= $true )
| ( ( mrel @ mactual @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[55]) ).
thf(61,plain,
! [SV9: $i,SV10: mworld,SV5: mworld] :
( ( ( ~ ( mrel @ SV5 @ SV10 ) )
= $true )
| ( ( ~ ( bomb @ SV9 @ SV10 )
| ~ ( h @ ( sK3_SY51 @ SV9 @ SV5 ) @ SV10 )
| ( defused @ SV9 @ SV10 ) )
= $true )
| ( ( mrel @ mactual @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[56]) ).
thf(62,plain,
( ( bomb @ sK2_SY112 @ sK1_SY20 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[57]) ).
thf(63,plain,
( ( ! [SX0: $i] : ( h @ SX0 @ sK1_SY20 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[58]) ).
thf(64,plain,
! [SV2: mworld,SV7: mworld,SV6: mworld] :
( ( ( mrel @ SV6 @ SV7 )
= $false )
| ( ( mrel @ SV2 @ SV6 )
= $false )
| ( ( mrel @ SV2 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(65,plain,
! [SV4: mworld,SV8: $i] :
( ( ( bomb @ SV8 @ SV4 )
= $false )
| ( ( ~ ( h @ sK4_SY90 @ SV4 ) )
= $true )
| ( ( ! [SY126: mworld] :
( ~ ( mrel @ SV4 @ SY126 )
| ( bomb @ SV8 @ SY126 ) ) )
= $true )
| ( ( mrel @ mactual @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(66,plain,
! [SV9: $i,SV10: mworld,SV5: mworld] :
( ( ( mrel @ SV5 @ SV10 )
= $false )
| ( ( ~ ( bomb @ SV9 @ SV10 )
| ~ ( h @ ( sK3_SY51 @ SV9 @ SV5 ) @ SV10 )
| ( defused @ SV9 @ SV10 ) )
= $true )
| ( ( mrel @ mactual @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(67,plain,
! [SV11: $i] :
( ( h @ SV11 @ sK1_SY20 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(68,plain,
! [SV8: $i,SV4: mworld] :
( ( ( h @ sK4_SY90 @ SV4 )
= $false )
| ( ( bomb @ SV8 @ SV4 )
= $false )
| ( ( ! [SY126: mworld] :
( ~ ( mrel @ SV4 @ SY126 )
| ( bomb @ SV8 @ SY126 ) ) )
= $true )
| ( ( mrel @ mactual @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(69,plain,
! [SV5: mworld,SV10: mworld,SV9: $i] :
( ( ( ~ ( bomb @ SV9 @ SV10 )
| ~ ( h @ ( sK3_SY51 @ SV9 @ SV5 ) @ SV10 ) )
= $true )
| ( ( defused @ SV9 @ SV10 )
= $true )
| ( ( mrel @ SV5 @ SV10 )
= $false )
| ( ( mrel @ mactual @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[66]) ).
thf(70,plain,
! [SV8: $i,SV12: mworld,SV4: mworld] :
( ( ( ~ ( mrel @ SV4 @ SV12 )
| ( bomb @ SV8 @ SV12 ) )
= $true )
| ( ( bomb @ SV8 @ SV4 )
= $false )
| ( ( h @ sK4_SY90 @ SV4 )
= $false )
| ( ( mrel @ mactual @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(71,plain,
! [SV5: mworld,SV10: mworld,SV9: $i] :
( ( ( ~ ( bomb @ SV9 @ SV10 ) )
= $true )
| ( ( ~ ( h @ ( sK3_SY51 @ SV9 @ SV5 ) @ SV10 ) )
= $true )
| ( ( defused @ SV9 @ SV10 )
= $true )
| ( ( mrel @ SV5 @ SV10 )
= $false )
| ( ( mrel @ mactual @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[69]) ).
thf(72,plain,
! [SV8: $i,SV12: mworld,SV4: mworld] :
( ( ( ~ ( mrel @ SV4 @ SV12 ) )
= $true )
| ( ( bomb @ SV8 @ SV12 )
= $true )
| ( ( bomb @ SV8 @ SV4 )
= $false )
| ( ( h @ sK4_SY90 @ SV4 )
= $false )
| ( ( mrel @ mactual @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[70]) ).
thf(73,plain,
! [SV5: mworld,SV10: mworld,SV9: $i] :
( ( ( bomb @ SV9 @ SV10 )
= $false )
| ( ( ~ ( h @ ( sK3_SY51 @ SV9 @ SV5 ) @ SV10 ) )
= $true )
| ( ( defused @ SV9 @ SV10 )
= $true )
| ( ( mrel @ SV5 @ SV10 )
= $false )
| ( ( mrel @ mactual @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(74,plain,
! [SV8: $i,SV12: mworld,SV4: mworld] :
( ( ( mrel @ SV4 @ SV12 )
= $false )
| ( ( bomb @ SV8 @ SV12 )
= $true )
| ( ( bomb @ SV8 @ SV4 )
= $false )
| ( ( h @ sK4_SY90 @ SV4 )
= $false )
| ( ( mrel @ mactual @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(75,plain,
! [SV10: mworld,SV5: mworld,SV9: $i] :
( ( ( h @ ( sK3_SY51 @ SV9 @ SV5 ) @ SV10 )
= $false )
| ( ( bomb @ SV9 @ SV10 )
= $false )
| ( ( defused @ SV9 @ SV10 )
= $true )
| ( ( mrel @ SV5 @ SV10 )
= $false )
| ( ( mrel @ mactual @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(76,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[28,75,74,67,64,62,53,44,31]) ).
thf(77,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[76]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PLA053^4 : 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.16 % Computer : n001.cluster.edu
% 0.07/0.16 % Model : x86_64 x86_64
% 0.07/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.16 % Memory : 8046.5625MB
% 0.07/0.16 % OS : Linux 6.8.0-71-generic
% 0.07/0.16 % CPULimit : 300
% 0.07/0.16 % WCLimit : 300
% 0.07/0.16 % DateTime : Tue Oct 6 13:58:54 UTC 2026
% 0.07/0.16 % CPUTime :
% 0.07/0.16 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.22
% 0.07/0.22 No.of.Axioms: 5
% 0.07/0.22
% 0.07/0.22 Length.of.Defs: 1614
% 0.07/0.22
% 0.07/0.22 Contains.Choice.Funs: false
% 0.07/0.22 ...
% 0.07/0.22
% 0.07/0.22 ********************************
% 0.07/0.22 * All subproblems solved! *
% 0.07/0.22 ********************************
% 0.07/0.22 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:6,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:76,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.07/0.22
% 0.07/0.22 %**** Beginning of derivation protocol ****
% 0.07/0.22 % SZS output start CNFRefutation
% See solution above
% 0.07/0.22
% 0.07/0.22 %**** End of derivation protocol ****
% 0.07/0.22 %**** no. of clauses in derivation: 77 ****
% 0.07/0.22 %**** clause counter: 76 ****
% 0.07/0.22
% 0.07/0.22 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:6,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:76,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------