%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : LCL943^24 : 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 10:31:06 AM UTC 2026
% Result : Theorem 0.08s 0.23s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 10
% Syntax : Number of formulae : 92 ( 47 unt; 0 typ; 8 def)
% Number of atoms : 930 ( 229 equ; 0 cnn)
% Maximal formula atoms : 24 ( 10 avg)
% Number of connectives : 1243 ( 131 ~; 288 |; 2 &; 766 @)
% ( 1 <=>; 55 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 19 usr; 7 con; 0-3 aty)
% Number of variables : 240 ( 19 ^; 220 !; 1 ?; 240 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_mworld,type,
mworld: $tType ).
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_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_p,type,
p: mworld > $o ).
thf(tp_q,type,
q: mworld > $o ).
thf(tp_r,type,
r: mworld > $o ).
thf(tp_sK1_SY87,type,
sK1_SY87: mworld ).
thf(tp_sK2_SX0,type,
sK2_SX0: mworld ).
thf(tp_sK3_SX0,type,
sK3_SX0: mworld ).
thf(tp_sK4_SY124,type,
sK4_SY124: mworld ).
thf(tp_sK5_SY119,type,
sK5_SY119: mworld > mworld ).
thf(tp_sK6_SY120,type,
sK6_SY120: mworld > mworld ).
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(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,
! [W: mworld,V: mworld] : ( mrel @ W @ V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_universal) ).
thf(2,conjecture,
mlocal @ ( mbox @ ( mimplies @ ( mbox @ ( mimplies @ ( mor @ ( mbox @ p ) @ ( mbox @ q ) ) @ ( mor @ ( mbox @ p ) @ ( mbox @ r ) ) ) ) @ ( mor @ ( mbox @ p ) @ ( mbox @ ( mimplies @ ( mbox @ q ) @ ( mbox @ r ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel5) ).
thf(3,negated_conjecture,
( ( mlocal @ ( mbox @ ( mimplies @ ( mbox @ ( mimplies @ ( mor @ ( mbox @ p ) @ ( mbox @ q ) ) @ ( mor @ ( mbox @ p ) @ ( mbox @ r ) ) ) ) @ ( mor @ ( mbox @ p ) @ ( mbox @ ( mimplies @ ( mbox @ q ) @ ( mbox @ r ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[2]) ).
thf(4,plain,
( ( ! [SY87: mworld] :
( ( mrel @ mactual @ SY87 )
=> ( ! [SY78: mworld] :
( ( mrel @ SY87 @ SY78 )
=> ( ( ! [SY31: mworld] :
( ( mrel @ SY78 @ SY31 )
=> ( p @ SY31 ) )
| ! [SY32: mworld] :
( ( mrel @ SY78 @ SY32 )
=> ( q @ SY32 ) ) )
=> ( ! [SY33: mworld] :
( ( mrel @ SY78 @ SY33 )
=> ( p @ SY33 ) )
| ! [SY34: mworld] :
( ( mrel @ SY78 @ SY34 )
=> ( r @ SY34 ) ) ) ) )
=> ( ! [SY83: mworld] :
( ( mrel @ SY87 @ SY83 )
=> ( p @ SY83 ) )
| ! [SY84: mworld] :
( ( mrel @ SY87 @ SY84 )
=> ( ! [SY59: mworld] :
( ( mrel @ SY84 @ SY59 )
=> ( q @ SY59 ) )
=> ! [SY60: mworld] :
( ( mrel @ SY84 @ SY60 )
=> ( r @ SY60 ) ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[3,mand,mbox,mdia,mequiv,mimplies,mlocal,mnot,mor]) ).
thf(5,plain,
( ( ! [W: mworld,V: mworld] : ( mrel @ W @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[1,mand,mbox,mdia,mequiv,mimplies,mlocal,mnot,mor]) ).
thf(6,plain,
( ( ( mrel @ mactual @ sK1_SY87 )
=> ( ! [SY109: mworld] :
( ( mrel @ sK1_SY87 @ SY109 )
=> ( ( ! [SY31: mworld] :
( ( mrel @ SY109 @ SY31 )
=> ( p @ SY31 ) )
| ! [SY32: mworld] :
( ( mrel @ SY109 @ SY32 )
=> ( q @ SY32 ) ) )
=> ( ! [SY33: mworld] :
( ( mrel @ SY109 @ SY33 )
=> ( p @ SY33 ) )
| ! [SY34: mworld] :
( ( mrel @ SY109 @ SY34 )
=> ( r @ SY34 ) ) ) ) )
=> ( ! [SY114: mworld] :
( ( mrel @ sK1_SY87 @ SY114 )
=> ( p @ SY114 ) )
| ! [SY115: mworld] :
( ( mrel @ sK1_SY87 @ SY115 )
=> ( ! [SY59: mworld] :
( ( mrel @ SY115 @ SY59 )
=> ( q @ SY59 ) )
=> ! [SY60: mworld] :
( ( mrel @ SY115 @ SY60 )
=> ( r @ SY60 ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[4]) ).
thf(7,plain,
( ( mrel @ mactual @ sK1_SY87 )
= $true ),
inference(standard_cnf,[status(thm)],[6]) ).
thf(8,plain,
( ( ! [SY109: mworld] :
( ( mrel @ sK1_SY87 @ SY109 )
=> ( ( ! [SY31: mworld] :
( ( mrel @ SY109 @ SY31 )
=> ( p @ SY31 ) )
| ! [SY32: mworld] :
( ( mrel @ SY109 @ SY32 )
=> ( q @ SY32 ) ) )
=> ( ! [SY33: mworld] :
( ( mrel @ SY109 @ SY33 )
=> ( p @ SY33 ) )
| ! [SY34: mworld] :
( ( mrel @ SY109 @ SY34 )
=> ( r @ SY34 ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[6]) ).
thf(9,plain,
( ( ! [SY114: mworld] :
( ( mrel @ sK1_SY87 @ SY114 )
=> ( p @ SY114 ) )
| ! [SY115: mworld] :
( ( mrel @ sK1_SY87 @ SY115 )
=> ( ! [SY59: mworld] :
( ( mrel @ SY115 @ SY59 )
=> ( q @ SY59 ) )
=> ! [SY60: mworld] :
( ( mrel @ SY115 @ SY60 )
=> ( r @ SY60 ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[6]) ).
thf(10,plain,
( ( ~ ( ! [SY114: mworld] :
( ( mrel @ sK1_SY87 @ SY114 )
=> ( p @ SY114 ) )
| ! [SY115: mworld] :
( ( mrel @ sK1_SY87 @ SY115 )
=> ( ! [SY59: mworld] :
( ( mrel @ SY115 @ SY59 )
=> ( q @ SY59 ) )
=> ! [SY60: mworld] :
( ( mrel @ SY115 @ SY60 )
=> ( r @ SY60 ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[9]) ).
thf(11,plain,
( ( ! [W: mworld,V: mworld] : ( mrel @ W @ V ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(12,plain,
( ( ! [SY109: mworld] :
( ( mrel @ sK1_SY87 @ SY109 )
=> ( ( ! [SY31: mworld] :
( ( mrel @ SY109 @ SY31 )
=> ( p @ SY31 ) )
| ! [SY32: mworld] :
( ( mrel @ SY109 @ SY32 )
=> ( q @ SY32 ) ) )
=> ( ! [SY33: mworld] :
( ( mrel @ SY109 @ SY33 )
=> ( p @ SY33 ) )
| ! [SY34: mworld] :
( ( mrel @ SY109 @ SY34 )
=> ( r @ SY34 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(13,plain,
( ( mrel @ mactual @ sK1_SY87 )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(14,plain,
( ( ~ ( ! [SY114: mworld] :
( ( mrel @ sK1_SY87 @ SY114 )
=> ( p @ SY114 ) )
| ! [SY115: mworld] :
( ( mrel @ sK1_SY87 @ SY115 )
=> ( ! [SY59: mworld] :
( ( mrel @ SY115 @ SY59 )
=> ( q @ SY59 ) )
=> ! [SY60: mworld] :
( ( mrel @ SY115 @ SY60 )
=> ( r @ SY60 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(15,plain,
( ( ~ ( ! [SX0: mworld] :
( ~ ( mrel @ sK1_SY87 @ SX0 )
| ( p @ SX0 ) )
| ! [SX0: mworld] :
( ~ ( mrel @ sK1_SY87 @ SX0 )
| ~ ! [SX1: mworld] :
( ~ ( mrel @ SX0 @ SX1 )
| ( q @ SX1 ) )
| ! [SX1: mworld] :
( ~ ( mrel @ SX0 @ SX1 )
| ( r @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14,mand,mbox,mdia,mequiv,mimplies,mlocal,mnot,mor]) ).
thf(16,plain,
( ( ! [SX0: mworld] :
( ~ ( mrel @ sK1_SY87 @ SX0 )
| ~ ( ! [SX1: mworld] :
( ~ ( mrel @ SX0 @ SX1 )
| ( p @ SX1 ) )
| ! [SX1: mworld] :
( ~ ( mrel @ SX0 @ SX1 )
| ( q @ SX1 ) ) )
| ! [SX1: mworld] :
( ~ ( mrel @ SX0 @ SX1 )
| ( p @ SX1 ) )
| ! [SX1: mworld] :
( ~ ( mrel @ SX0 @ SX1 )
| ( r @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12,mand,mbox,mdia,mequiv,mimplies,mlocal,mnot,mor]) ).
thf(17,plain,
! [SV1: mworld] :
( ( ! [SY118: mworld] : ( mrel @ SV1 @ SY118 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(18,plain,
( ( ! [SX0: mworld] :
( ~ ( mrel @ sK1_SY87 @ SX0 )
| ( p @ SX0 ) )
| ! [SX0: mworld] :
( ~ ( mrel @ sK1_SY87 @ SX0 )
| ~ ! [SX1: mworld] :
( ~ ( mrel @ SX0 @ SX1 )
| ( q @ SX1 ) )
| ! [SX1: mworld] :
( ~ ( mrel @ SX0 @ SX1 )
| ( r @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[15]) ).
thf(19,plain,
! [SV2: mworld] :
( ( ~ ( mrel @ sK1_SY87 @ SV2 )
| ~ ( ! [SY119: mworld] :
( ~ ( mrel @ SV2 @ SY119 )
| ( p @ SY119 ) )
| ! [SY120: mworld] :
( ~ ( mrel @ SV2 @ SY120 )
| ( q @ SY120 ) ) )
| ! [SY121: mworld] :
( ~ ( mrel @ SV2 @ SY121 )
| ( p @ SY121 ) )
| ! [SY122: mworld] :
( ~ ( mrel @ SV2 @ SY122 )
| ( r @ SY122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(20,plain,
! [SV3: mworld,SV1: mworld] :
( ( mrel @ SV1 @ SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(21,plain,
( ( ! [SX0: mworld] :
( ~ ( mrel @ sK1_SY87 @ SX0 )
| ( p @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[18]) ).
thf(22,plain,
( ( ! [SX0: mworld] :
( ~ ( mrel @ sK1_SY87 @ SX0 )
| ~ ! [SX1: mworld] :
( ~ ( mrel @ SX0 @ SX1 )
| ( q @ SX1 ) )
| ! [SX1: mworld] :
( ~ ( mrel @ SX0 @ SX1 )
| ( r @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[18]) ).
thf(23,plain,
! [SV2: mworld] :
( ( ( ~ ( mrel @ sK1_SY87 @ SV2 ) )
= $true )
| ( ( ~ ( ! [SY119: mworld] :
( ~ ( mrel @ SV2 @ SY119 )
| ( p @ SY119 ) )
| ! [SY120: mworld] :
( ~ ( mrel @ SV2 @ SY120 )
| ( q @ SY120 ) ) )
| ! [SY121: mworld] :
( ~ ( mrel @ SV2 @ SY121 )
| ( p @ SY121 ) )
| ! [SY122: mworld] :
( ~ ( mrel @ SV2 @ SY122 )
| ( r @ SY122 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[19]) ).
thf(24,plain,
( ( ~ ( mrel @ sK1_SY87 @ sK2_SX0 )
| ( p @ sK2_SX0 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[21]) ).
thf(25,plain,
( ( ~ ( mrel @ sK1_SY87 @ sK3_SX0 )
| ~ ! [SY123: mworld] :
( ~ ( mrel @ sK3_SX0 @ SY123 )
| ( q @ SY123 ) )
| ! [SY124: mworld] :
( ~ ( mrel @ sK3_SX0 @ SY124 )
| ( r @ SY124 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[22]) ).
thf(26,plain,
! [SV2: mworld] :
( ( ( mrel @ sK1_SY87 @ SV2 )
= $false )
| ( ( ~ ( ! [SY119: mworld] :
( ~ ( mrel @ SV2 @ SY119 )
| ( p @ SY119 ) )
| ! [SY120: mworld] :
( ~ ( mrel @ SV2 @ SY120 )
| ( q @ SY120 ) ) )
| ! [SY121: mworld] :
( ~ ( mrel @ SV2 @ SY121 )
| ( p @ SY121 ) )
| ! [SY122: mworld] :
( ~ ( mrel @ SV2 @ SY122 )
| ( r @ SY122 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(27,plain,
( ( ~ ( mrel @ sK1_SY87 @ sK2_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[24]) ).
thf(28,plain,
( ( p @ sK2_SX0 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[24]) ).
thf(29,plain,
( ( ~ ( mrel @ sK1_SY87 @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[25]) ).
thf(30,plain,
( ( ~ ! [SY123: mworld] :
( ~ ( mrel @ sK3_SX0 @ SY123 )
| ( q @ SY123 ) )
| ! [SY124: mworld] :
( ~ ( mrel @ sK3_SX0 @ SY124 )
| ( r @ SY124 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[25]) ).
thf(31,plain,
! [SV2: mworld] :
( ( ( ~ ( ! [SY119: mworld] :
( ~ ( mrel @ SV2 @ SY119 )
| ( p @ SY119 ) )
| ! [SY120: mworld] :
( ~ ( mrel @ SV2 @ SY120 )
| ( q @ SY120 ) ) ) )
= $true )
| ( ( ! [SY121: mworld] :
( ~ ( mrel @ SV2 @ SY121 )
| ( p @ SY121 ) )
| ! [SY122: mworld] :
( ~ ( mrel @ SV2 @ SY122 )
| ( r @ SY122 ) ) )
= $true )
| ( ( mrel @ sK1_SY87 @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[26]) ).
thf(32,plain,
( ( mrel @ sK1_SY87 @ sK2_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[27]) ).
thf(33,plain,
( ( mrel @ sK1_SY87 @ sK3_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[29]) ).
thf(34,plain,
( ( ~ ! [SY123: mworld] :
( ~ ( mrel @ sK3_SX0 @ SY123 )
| ( q @ SY123 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[30]) ).
thf(35,plain,
( ( ! [SY124: mworld] :
( ~ ( mrel @ sK3_SX0 @ SY124 )
| ( r @ SY124 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[30]) ).
thf(36,plain,
! [SV2: mworld] :
( ( ( ! [SY119: mworld] :
( ~ ( mrel @ SV2 @ SY119 )
| ( p @ SY119 ) )
| ! [SY120: mworld] :
( ~ ( mrel @ SV2 @ SY120 )
| ( q @ SY120 ) ) )
= $false )
| ( ( ! [SY121: mworld] :
( ~ ( mrel @ SV2 @ SY121 )
| ( p @ SY121 ) )
| ! [SY122: mworld] :
( ~ ( mrel @ SV2 @ SY122 )
| ( r @ SY122 ) ) )
= $true )
| ( ( mrel @ sK1_SY87 @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(37,plain,
( ( ! [SY123: mworld] :
( ~ ( mrel @ sK3_SX0 @ SY123 )
| ( q @ SY123 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[34]) ).
thf(38,plain,
( ( ~ ( mrel @ sK3_SX0 @ sK4_SY124 )
| ( r @ sK4_SY124 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[35]) ).
thf(39,plain,
! [SV2: mworld] :
( ( ( ! [SY119: mworld] :
( ~ ( mrel @ SV2 @ SY119 )
| ( p @ SY119 ) ) )
= $false )
| ( ( ! [SY121: mworld] :
( ~ ( mrel @ SV2 @ SY121 )
| ( p @ SY121 ) )
| ! [SY122: mworld] :
( ~ ( mrel @ SV2 @ SY122 )
| ( r @ SY122 ) ) )
= $true )
| ( ( mrel @ sK1_SY87 @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[36]) ).
thf(40,plain,
! [SV2: mworld] :
( ( ( ! [SY120: mworld] :
( ~ ( mrel @ SV2 @ SY120 )
| ( q @ SY120 ) ) )
= $false )
| ( ( ! [SY121: mworld] :
( ~ ( mrel @ SV2 @ SY121 )
| ( p @ SY121 ) )
| ! [SY122: mworld] :
( ~ ( mrel @ SV2 @ SY122 )
| ( r @ SY122 ) ) )
= $true )
| ( ( mrel @ sK1_SY87 @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[36]) ).
thf(41,plain,
! [SV4: mworld] :
( ( ~ ( mrel @ sK3_SX0 @ SV4 )
| ( q @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(42,plain,
( ( ~ ( mrel @ sK3_SX0 @ sK4_SY124 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[38]) ).
thf(43,plain,
( ( r @ sK4_SY124 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[38]) ).
thf(44,plain,
! [SV2: mworld] :
( ( ( ~ ( mrel @ SV2 @ ( sK5_SY119 @ SV2 ) )
| ( p @ ( sK5_SY119 @ SV2 ) ) )
= $false )
| ( ( ! [SY121: mworld] :
( ~ ( mrel @ SV2 @ SY121 )
| ( p @ SY121 ) )
| ! [SY122: mworld] :
( ~ ( mrel @ SV2 @ SY122 )
| ( r @ SY122 ) ) )
= $true )
| ( ( mrel @ sK1_SY87 @ SV2 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[39]) ).
thf(45,plain,
! [SV2: mworld] :
( ( ( ~ ( mrel @ SV2 @ ( sK6_SY120 @ SV2 ) )
| ( q @ ( sK6_SY120 @ SV2 ) ) )
= $false )
| ( ( ! [SY121: mworld] :
( ~ ( mrel @ SV2 @ SY121 )
| ( p @ SY121 ) )
| ! [SY122: mworld] :
( ~ ( mrel @ SV2 @ SY122 )
| ( r @ SY122 ) ) )
= $true )
| ( ( mrel @ sK1_SY87 @ SV2 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[40]) ).
thf(46,plain,
! [SV4: mworld] :
( ( ( ~ ( mrel @ sK3_SX0 @ SV4 ) )
= $true )
| ( ( q @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[41]) ).
thf(47,plain,
( ( mrel @ sK3_SX0 @ sK4_SY124 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[42]) ).
thf(48,plain,
! [SV2: mworld] :
( ( ( ~ ( mrel @ SV2 @ ( sK5_SY119 @ SV2 ) ) )
= $false )
| ( ( ! [SY121: mworld] :
( ~ ( mrel @ SV2 @ SY121 )
| ( p @ SY121 ) )
| ! [SY122: mworld] :
( ~ ( mrel @ SV2 @ SY122 )
| ( r @ SY122 ) ) )
= $true )
| ( ( mrel @ sK1_SY87 @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[44]) ).
thf(49,plain,
! [SV2: mworld] :
( ( ( p @ ( sK5_SY119 @ SV2 ) )
= $false )
| ( ( ! [SY121: mworld] :
( ~ ( mrel @ SV2 @ SY121 )
| ( p @ SY121 ) )
| ! [SY122: mworld] :
( ~ ( mrel @ SV2 @ SY122 )
| ( r @ SY122 ) ) )
= $true )
| ( ( mrel @ sK1_SY87 @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[44]) ).
thf(50,plain,
! [SV2: mworld] :
( ( ( ~ ( mrel @ SV2 @ ( sK6_SY120 @ SV2 ) ) )
= $false )
| ( ( ! [SY121: mworld] :
( ~ ( mrel @ SV2 @ SY121 )
| ( p @ SY121 ) )
| ! [SY122: mworld] :
( ~ ( mrel @ SV2 @ SY122 )
| ( r @ SY122 ) ) )
= $true )
| ( ( mrel @ sK1_SY87 @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[45]) ).
thf(51,plain,
! [SV2: mworld] :
( ( ( q @ ( sK6_SY120 @ SV2 ) )
= $false )
| ( ( ! [SY121: mworld] :
( ~ ( mrel @ SV2 @ SY121 )
| ( p @ SY121 ) )
| ! [SY122: mworld] :
( ~ ( mrel @ SV2 @ SY122 )
| ( r @ SY122 ) ) )
= $true )
| ( ( mrel @ sK1_SY87 @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[45]) ).
thf(52,plain,
! [SV4: mworld] :
( ( ( mrel @ sK3_SX0 @ SV4 )
= $false )
| ( ( q @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(53,plain,
! [SV2: mworld] :
( ( ( mrel @ SV2 @ ( sK5_SY119 @ SV2 ) )
= $true )
| ( ( ! [SY121: mworld] :
( ~ ( mrel @ SV2 @ SY121 )
| ( p @ SY121 ) )
| ! [SY122: mworld] :
( ~ ( mrel @ SV2 @ SY122 )
| ( r @ SY122 ) ) )
= $true )
| ( ( mrel @ sK1_SY87 @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[48]) ).
thf(54,plain,
! [SV2: mworld] :
( ( ( ! [SY121: mworld] :
( ~ ( mrel @ SV2 @ SY121 )
| ( p @ SY121 ) ) )
= $true )
| ( ( ! [SY122: mworld] :
( ~ ( mrel @ SV2 @ SY122 )
| ( r @ SY122 ) ) )
= $true )
| ( ( p @ ( sK5_SY119 @ SV2 ) )
= $false )
| ( ( mrel @ sK1_SY87 @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[49]) ).
thf(55,plain,
! [SV2: mworld] :
( ( ( mrel @ SV2 @ ( sK6_SY120 @ SV2 ) )
= $true )
| ( ( ! [SY121: mworld] :
( ~ ( mrel @ SV2 @ SY121 )
| ( p @ SY121 ) )
| ! [SY122: mworld] :
( ~ ( mrel @ SV2 @ SY122 )
| ( r @ SY122 ) ) )
= $true )
| ( ( mrel @ sK1_SY87 @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[50]) ).
thf(56,plain,
! [SV2: mworld] :
( ( ( ! [SY121: mworld] :
( ~ ( mrel @ SV2 @ SY121 )
| ( p @ SY121 ) ) )
= $true )
| ( ( ! [SY122: mworld] :
( ~ ( mrel @ SV2 @ SY122 )
| ( r @ SY122 ) ) )
= $true )
| ( ( q @ ( sK6_SY120 @ SV2 ) )
= $false )
| ( ( mrel @ sK1_SY87 @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[51]) ).
thf(57,plain,
! [SV2: mworld] :
( ( ( ! [SY121: mworld] :
( ~ ( mrel @ SV2 @ SY121 )
| ( p @ SY121 ) ) )
= $true )
| ( ( ! [SY122: mworld] :
( ~ ( mrel @ SV2 @ SY122 )
| ( r @ SY122 ) ) )
= $true )
| ( ( mrel @ SV2 @ ( sK5_SY119 @ SV2 ) )
= $true )
| ( ( mrel @ sK1_SY87 @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[53]) ).
thf(58,plain,
! [SV5: mworld,SV2: mworld] :
( ( ( ~ ( mrel @ SV2 @ SV5 )
| ( p @ SV5 ) )
= $true )
| ( ( ! [SY122: mworld] :
( ~ ( mrel @ SV2 @ SY122 )
| ( r @ SY122 ) ) )
= $true )
| ( ( p @ ( sK5_SY119 @ SV2 ) )
= $false )
| ( ( mrel @ sK1_SY87 @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(59,plain,
! [SV2: mworld] :
( ( ( ! [SY121: mworld] :
( ~ ( mrel @ SV2 @ SY121 )
| ( p @ SY121 ) ) )
= $true )
| ( ( ! [SY122: mworld] :
( ~ ( mrel @ SV2 @ SY122 )
| ( r @ SY122 ) ) )
= $true )
| ( ( mrel @ SV2 @ ( sK6_SY120 @ SV2 ) )
= $true )
| ( ( mrel @ sK1_SY87 @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[55]) ).
thf(60,plain,
! [SV6: mworld,SV2: mworld] :
( ( ( ~ ( mrel @ SV2 @ SV6 )
| ( p @ SV6 ) )
= $true )
| ( ( ! [SY122: mworld] :
( ~ ( mrel @ SV2 @ SY122 )
| ( r @ SY122 ) ) )
= $true )
| ( ( q @ ( sK6_SY120 @ SV2 ) )
= $false )
| ( ( mrel @ sK1_SY87 @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(61,plain,
! [SV7: mworld,SV2: mworld] :
( ( ( ~ ( mrel @ SV2 @ SV7 )
| ( p @ SV7 ) )
= $true )
| ( ( ! [SY122: mworld] :
( ~ ( mrel @ SV2 @ SY122 )
| ( r @ SY122 ) ) )
= $true )
| ( ( mrel @ SV2 @ ( sK5_SY119 @ SV2 ) )
= $true )
| ( ( mrel @ sK1_SY87 @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(62,plain,
! [SV5: mworld,SV2: mworld] :
( ( ( ~ ( mrel @ SV2 @ SV5 ) )
= $true )
| ( ( p @ SV5 )
= $true )
| ( ( ! [SY122: mworld] :
( ~ ( mrel @ SV2 @ SY122 )
| ( r @ SY122 ) ) )
= $true )
| ( ( p @ ( sK5_SY119 @ SV2 ) )
= $false )
| ( ( mrel @ sK1_SY87 @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[58]) ).
thf(63,plain,
! [SV8: mworld,SV2: mworld] :
( ( ( ~ ( mrel @ SV2 @ SV8 )
| ( p @ SV8 ) )
= $true )
| ( ( ! [SY122: mworld] :
( ~ ( mrel @ SV2 @ SY122 )
| ( r @ SY122 ) ) )
= $true )
| ( ( mrel @ SV2 @ ( sK6_SY120 @ SV2 ) )
= $true )
| ( ( mrel @ sK1_SY87 @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(64,plain,
! [SV6: mworld,SV2: mworld] :
( ( ( ~ ( mrel @ SV2 @ SV6 ) )
= $true )
| ( ( p @ SV6 )
= $true )
| ( ( ! [SY122: mworld] :
( ~ ( mrel @ SV2 @ SY122 )
| ( r @ SY122 ) ) )
= $true )
| ( ( q @ ( sK6_SY120 @ SV2 ) )
= $false )
| ( ( mrel @ sK1_SY87 @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[60]) ).
thf(65,plain,
! [SV7: mworld,SV2: mworld] :
( ( ( ~ ( mrel @ SV2 @ SV7 ) )
= $true )
| ( ( p @ SV7 )
= $true )
| ( ( ! [SY122: mworld] :
( ~ ( mrel @ SV2 @ SY122 )
| ( r @ SY122 ) ) )
= $true )
| ( ( mrel @ SV2 @ ( sK5_SY119 @ SV2 ) )
= $true )
| ( ( mrel @ sK1_SY87 @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[61]) ).
thf(66,plain,
! [SV5: mworld,SV2: mworld] :
( ( ( mrel @ SV2 @ SV5 )
= $false )
| ( ( p @ SV5 )
= $true )
| ( ( ! [SY122: mworld] :
( ~ ( mrel @ SV2 @ SY122 )
| ( r @ SY122 ) ) )
= $true )
| ( ( p @ ( sK5_SY119 @ SV2 ) )
= $false )
| ( ( mrel @ sK1_SY87 @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(67,plain,
! [SV8: mworld,SV2: mworld] :
( ( ( ~ ( mrel @ SV2 @ SV8 ) )
= $true )
| ( ( p @ SV8 )
= $true )
| ( ( ! [SY122: mworld] :
( ~ ( mrel @ SV2 @ SY122 )
| ( r @ SY122 ) ) )
= $true )
| ( ( mrel @ SV2 @ ( sK6_SY120 @ SV2 ) )
= $true )
| ( ( mrel @ sK1_SY87 @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[63]) ).
thf(68,plain,
! [SV6: mworld,SV2: mworld] :
( ( ( mrel @ SV2 @ SV6 )
= $false )
| ( ( p @ SV6 )
= $true )
| ( ( ! [SY122: mworld] :
( ~ ( mrel @ SV2 @ SY122 )
| ( r @ SY122 ) ) )
= $true )
| ( ( q @ ( sK6_SY120 @ SV2 ) )
= $false )
| ( ( mrel @ sK1_SY87 @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(69,plain,
! [SV7: mworld,SV2: mworld] :
( ( ( mrel @ SV2 @ SV7 )
= $false )
| ( ( p @ SV7 )
= $true )
| ( ( ! [SY122: mworld] :
( ~ ( mrel @ SV2 @ SY122 )
| ( r @ SY122 ) ) )
= $true )
| ( ( mrel @ SV2 @ ( sK5_SY119 @ SV2 ) )
= $true )
| ( ( mrel @ sK1_SY87 @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(70,plain,
! [SV5: mworld,SV9: mworld,SV2: mworld] :
( ( ( ~ ( mrel @ SV2 @ SV9 )
| ( r @ SV9 ) )
= $true )
| ( ( p @ SV5 )
= $true )
| ( ( mrel @ SV2 @ SV5 )
= $false )
| ( ( p @ ( sK5_SY119 @ SV2 ) )
= $false )
| ( ( mrel @ sK1_SY87 @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(71,plain,
! [SV8: mworld,SV2: mworld] :
( ( ( mrel @ SV2 @ SV8 )
= $false )
| ( ( p @ SV8 )
= $true )
| ( ( ! [SY122: mworld] :
( ~ ( mrel @ SV2 @ SY122 )
| ( r @ SY122 ) ) )
= $true )
| ( ( mrel @ SV2 @ ( sK6_SY120 @ SV2 ) )
= $true )
| ( ( mrel @ sK1_SY87 @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(72,plain,
! [SV6: mworld,SV10: mworld,SV2: mworld] :
( ( ( ~ ( mrel @ SV2 @ SV10 )
| ( r @ SV10 ) )
= $true )
| ( ( p @ SV6 )
= $true )
| ( ( mrel @ SV2 @ SV6 )
= $false )
| ( ( q @ ( sK6_SY120 @ SV2 ) )
= $false )
| ( ( mrel @ sK1_SY87 @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(73,plain,
! [SV7: mworld,SV11: mworld,SV2: mworld] :
( ( ( ~ ( mrel @ SV2 @ SV11 )
| ( r @ SV11 ) )
= $true )
| ( ( p @ SV7 )
= $true )
| ( ( mrel @ SV2 @ SV7 )
= $false )
| ( ( mrel @ SV2 @ ( sK5_SY119 @ SV2 ) )
= $true )
| ( ( mrel @ sK1_SY87 @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(74,plain,
! [SV5: mworld,SV9: mworld,SV2: mworld] :
( ( ( ~ ( mrel @ SV2 @ SV9 ) )
= $true )
| ( ( r @ SV9 )
= $true )
| ( ( p @ SV5 )
= $true )
| ( ( mrel @ SV2 @ SV5 )
= $false )
| ( ( p @ ( sK5_SY119 @ SV2 ) )
= $false )
| ( ( mrel @ sK1_SY87 @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[70]) ).
thf(75,plain,
! [SV8: mworld,SV12: mworld,SV2: mworld] :
( ( ( ~ ( mrel @ SV2 @ SV12 )
| ( r @ SV12 ) )
= $true )
| ( ( p @ SV8 )
= $true )
| ( ( mrel @ SV2 @ SV8 )
= $false )
| ( ( mrel @ SV2 @ ( sK6_SY120 @ SV2 ) )
= $true )
| ( ( mrel @ sK1_SY87 @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(76,plain,
! [SV6: mworld,SV10: mworld,SV2: mworld] :
( ( ( ~ ( mrel @ SV2 @ SV10 ) )
= $true )
| ( ( r @ SV10 )
= $true )
| ( ( p @ SV6 )
= $true )
| ( ( mrel @ SV2 @ SV6 )
= $false )
| ( ( q @ ( sK6_SY120 @ SV2 ) )
= $false )
| ( ( mrel @ sK1_SY87 @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[72]) ).
thf(77,plain,
! [SV7: mworld,SV11: mworld,SV2: mworld] :
( ( ( ~ ( mrel @ SV2 @ SV11 ) )
= $true )
| ( ( r @ SV11 )
= $true )
| ( ( p @ SV7 )
= $true )
| ( ( mrel @ SV2 @ SV7 )
= $false )
| ( ( mrel @ SV2 @ ( sK5_SY119 @ SV2 ) )
= $true )
| ( ( mrel @ sK1_SY87 @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[73]) ).
thf(78,plain,
! [SV5: mworld,SV9: mworld,SV2: mworld] :
( ( ( mrel @ SV2 @ SV9 )
= $false )
| ( ( r @ SV9 )
= $true )
| ( ( p @ SV5 )
= $true )
| ( ( mrel @ SV2 @ SV5 )
= $false )
| ( ( p @ ( sK5_SY119 @ SV2 ) )
= $false )
| ( ( mrel @ sK1_SY87 @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(79,plain,
! [SV8: mworld,SV12: mworld,SV2: mworld] :
( ( ( ~ ( mrel @ SV2 @ SV12 ) )
= $true )
| ( ( r @ SV12 )
= $true )
| ( ( p @ SV8 )
= $true )
| ( ( mrel @ SV2 @ SV8 )
= $false )
| ( ( mrel @ SV2 @ ( sK6_SY120 @ SV2 ) )
= $true )
| ( ( mrel @ sK1_SY87 @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[75]) ).
thf(80,plain,
! [SV6: mworld,SV10: mworld,SV2: mworld] :
( ( ( mrel @ SV2 @ SV10 )
= $false )
| ( ( r @ SV10 )
= $true )
| ( ( p @ SV6 )
= $true )
| ( ( mrel @ SV2 @ SV6 )
= $false )
| ( ( q @ ( sK6_SY120 @ SV2 ) )
= $false )
| ( ( mrel @ sK1_SY87 @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(81,plain,
! [SV7: mworld,SV11: mworld,SV2: mworld] :
( ( ( mrel @ SV2 @ SV11 )
= $false )
| ( ( r @ SV11 )
= $true )
| ( ( p @ SV7 )
= $true )
| ( ( mrel @ SV2 @ SV7 )
= $false )
| ( ( mrel @ SV2 @ ( sK5_SY119 @ SV2 ) )
= $true )
| ( ( mrel @ sK1_SY87 @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(82,plain,
! [SV8: mworld,SV12: mworld,SV2: mworld] :
( ( ( mrel @ SV2 @ SV12 )
= $false )
| ( ( r @ SV12 )
= $true )
| ( ( p @ SV8 )
= $true )
| ( ( mrel @ SV2 @ SV8 )
= $false )
| ( ( mrel @ SV2 @ ( sK6_SY120 @ SV2 ) )
= $true )
| ( ( mrel @ sK1_SY87 @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(83,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[13,82,81,80,78,52,47,43,33,32,28,20]) ).
thf(84,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL943^24 : 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
% 0.08/0.18 % Computer : n001.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Oct 6 12:43:39 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.23
% 0.08/0.23 No.of.Axioms: 1
% 0.08/0.23
% 0.08/0.23 Length.of.Defs: 1270
% 0.08/0.23
% 0.08/0.23 Contains.Choice.Funs: false
% 0.08/0.23 ...
% 0.08/0.23
% 0.08/0.23 ********************************
% 0.08/0.23 * All subproblems solved! *
% 0.08/0.23 ********************************
% 0.08/0.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:3,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:83,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.08/0.23
% 0.08/0.23 %**** Beginning of derivation protocol ****
% 0.08/0.23 % SZS output start CNFRefutation
% See solution above
% 0.08/0.23
% 0.08/0.23 %**** End of derivation protocol ****
% 0.08/0.23 %**** no. of clauses in derivation: 84 ****
% 0.08/0.23 %**** clause counter: 83 ****
% 0.08/0.23
% 0.08/0.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:3,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:83,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------