%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYO899^8 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 11:09:18 AM UTC 2026
% Result : Theorem 0.11s 0.21s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 45 ( 34 unt; 0 typ; 8 def)
% Number of atoms : 219 ( 54 equ; 0 cnn)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 257 ( 39 ~; 36 |; 9 &; 162 @)
% ( 1 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 4 con; 0-3 aty)
% Number of variables : 56 ( 19 ^; 31 !; 6 ?; 56 :)
% 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_sK1_SY28,type,
sK1_SY28: 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(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,
! [W: mworld] : ( mrel @ W @ W ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_reflexive) ).
thf(2,conjecture,
mlocal @ ( mimplies @ ( mdia @ ( mimplies @ p @ ( mbox @ q ) ) ) @ ( mimplies @ ( mbox @ p ) @ ( mdia @ q ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(3,negated_conjecture,
( ( mlocal @ ( mimplies @ ( mdia @ ( mimplies @ p @ ( mbox @ q ) ) ) @ ( mimplies @ ( mbox @ p ) @ ( mdia @ q ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[2]) ).
thf(4,plain,
( ( ? [SY28: mworld] :
( ( mrel @ mactual @ SY28 )
& ( ( p @ SY28 )
=> ! [SY8: mworld] :
( ( mrel @ SY28 @ SY8 )
=> ( q @ SY8 ) ) ) )
=> ( ! [SY30: mworld] :
( ( mrel @ mactual @ SY30 )
=> ( p @ SY30 ) )
=> ? [SY31: mworld] :
( ( mrel @ mactual @ SY31 )
& ( q @ SY31 ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[3,mand,mbox,mdia,mequiv,mimplies,mlocal,mnot,mor]) ).
thf(5,plain,
( ( ! [W: mworld] : ( mrel @ W @ W ) )
= $true ),
inference(unfold_def,[status(thm)],[1,mand,mbox,mdia,mequiv,mimplies,mlocal,mnot,mor]) ).
thf(6,plain,
( ( ? [SY28: mworld] :
( ( mrel @ mactual @ SY28 )
& ( ( p @ SY28 )
=> ! [SY8: mworld] :
( ( mrel @ SY28 @ SY8 )
=> ( q @ SY8 ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[4]) ).
thf(7,plain,
( ( ! [SY30: mworld] :
( ( mrel @ mactual @ SY30 )
=> ( p @ SY30 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[4]) ).
thf(8,plain,
( ( ? [SY31: mworld] :
( ( mrel @ mactual @ SY31 )
& ( q @ SY31 ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[4]) ).
thf(9,plain,
( ( ~ ? [SY31: mworld] :
( ( mrel @ mactual @ SY31 )
& ( q @ SY31 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[8]) ).
thf(10,plain,
( ( ! [SY31: mworld] :
( ~ ( mrel @ mactual @ SY31 )
| ~ ( q @ SY31 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[9]) ).
thf(11,plain,
( ( ( ~ ( p @ sK1_SY28 )
| ! [SY37: mworld] :
( ~ ( mrel @ sK1_SY28 @ SY37 )
| ( q @ SY37 ) ) )
& ( mrel @ mactual @ sK1_SY28 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(12,plain,
( ( ! [SY30: mworld] :
( ~ ( mrel @ mactual @ SY30 )
| ( p @ SY30 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(13,plain,
( ( ! [W: mworld] : ( mrel @ W @ W ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(14,plain,
( ( ! [SY30: mworld] :
( ~ ( mrel @ mactual @ SY30 )
| ( p @ SY30 ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(15,plain,
( ( ( ~ ( p @ sK1_SY28 )
| ! [SY37: mworld] :
( ~ ( mrel @ sK1_SY28 @ SY37 )
| ( q @ SY37 ) ) )
& ( mrel @ mactual @ sK1_SY28 ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(16,plain,
( ( ! [SY31: mworld] :
( ~ ( mrel @ mactual @ SY31 )
| ~ ( q @ SY31 ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(17,plain,
( ( ~ ( ~ ( ~ ( p @ sK1_SY28 )
| ! [SX0: mworld] :
( ~ ( mrel @ sK1_SY28 @ SX0 )
| ( q @ SX0 ) ) )
| ~ ( mrel @ mactual @ sK1_SY28 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15,mand,mbox,mdia,mequiv,mimplies,mlocal,mnot,mor]) ).
thf(18,plain,
! [SV1: mworld] :
( ( mrel @ SV1 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[13]) ).
thf(19,plain,
! [SV2: mworld] :
( ( ~ ( mrel @ mactual @ SV2 )
| ( p @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(20,plain,
! [SV3: mworld] :
( ( ~ ( mrel @ mactual @ SV3 )
| ~ ( q @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(21,plain,
( ( ~ ( ~ ( p @ sK1_SY28 )
| ! [SX0: mworld] :
( ~ ( mrel @ sK1_SY28 @ SX0 )
| ( q @ SX0 ) ) )
| ~ ( mrel @ mactual @ sK1_SY28 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[17]) ).
thf(22,plain,
! [SV2: mworld] :
( ( ( ~ ( mrel @ mactual @ SV2 ) )
= $true )
| ( ( p @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[19]) ).
thf(23,plain,
! [SV3: mworld] :
( ( ( ~ ( mrel @ mactual @ SV3 ) )
= $true )
| ( ( ~ ( q @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[20]) ).
thf(24,plain,
( ( ~ ( ~ ( p @ sK1_SY28 )
| ! [SX0: mworld] :
( ~ ( mrel @ sK1_SY28 @ SX0 )
| ( q @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(25,plain,
( ( ~ ( mrel @ mactual @ sK1_SY28 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(26,plain,
! [SV2: mworld] :
( ( ( mrel @ mactual @ SV2 )
= $false )
| ( ( p @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[22]) ).
thf(27,plain,
! [SV3: mworld] :
( ( ( mrel @ mactual @ SV3 )
= $false )
| ( ( ~ ( q @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(28,plain,
( ( ~ ( p @ sK1_SY28 )
| ! [SX0: mworld] :
( ~ ( mrel @ sK1_SY28 @ SX0 )
| ( q @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[24]) ).
thf(29,plain,
( ( mrel @ mactual @ sK1_SY28 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[25]) ).
thf(30,plain,
! [SV3: mworld] :
( ( ( q @ SV3 )
= $false )
| ( ( mrel @ mactual @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(31,plain,
( ( ( ~ ( p @ sK1_SY28 ) )
= $true )
| ( ( ! [SX0: mworld] :
( ~ ( mrel @ sK1_SY28 @ SX0 )
| ( q @ SX0 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[28]) ).
thf(32,plain,
( ( ( p @ sK1_SY28 )
= $false )
| ( ( ! [SX0: mworld] :
( ~ ( mrel @ sK1_SY28 @ SX0 )
| ( q @ SX0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(33,plain,
! [SV4: mworld] :
( ( ( ~ ( mrel @ sK1_SY28 @ SV4 )
| ( q @ SV4 ) )
= $true )
| ( ( p @ sK1_SY28 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(34,plain,
! [SV4: mworld] :
( ( ( ~ ( mrel @ sK1_SY28 @ SV4 ) )
= $true )
| ( ( q @ SV4 )
= $true )
| ( ( p @ sK1_SY28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[33]) ).
thf(35,plain,
! [SV4: mworld] :
( ( ( mrel @ sK1_SY28 @ SV4 )
= $false )
| ( ( q @ SV4 )
= $true )
| ( ( p @ sK1_SY28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(36,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[18,35,30,29,26]) ).
thf(37,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO899^8 : 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
% 0.11/0.18 % Computer : n019.cluster.edu
% 0.11/0.18 % Model : x86_64 x86_64
% 0.11/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.18 % Memory : 8046.5625MB
% 0.11/0.18 % OS : Linux 6.8.0-71-generic
% 0.11/0.18 % CPULimit : 300
% 0.11/0.18 % WCLimit : 300
% 0.11/0.18 % DateTime : Tue Oct 6 17:53:31 UTC 2026
% 0.11/0.18 % CPUTime :
% 0.11/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.21
% 0.11/0.21 No.of.Axioms: 1
% 0.11/0.21
% 0.11/0.21 Length.of.Defs: 1278
% 0.11/0.21
% 0.11/0.21 Contains.Choice.Funs: false
% 0.11/0.21 .
% 0.11/0.21
% 0.11/0.21 ********************************
% 0.11/0.21 * All subproblems solved! *
% 0.11/0.21 ********************************
% 0.11/0.21 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:3,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:36,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.11/0.21
% 0.11/0.21 %**** Beginning of derivation protocol ****
% 0.11/0.21 % SZS output start CNFRefutation
% See solution above
% 0.11/0.21
% 0.11/0.21 %**** End of derivation protocol ****
% 0.11/0.21 %**** no. of clauses in derivation: 37 ****
% 0.11/0.21 %**** clause counter: 36 ****
% 0.11/0.21
% 0.11/0.21 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:3,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:36,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------