%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYO896^7 : 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 : n013.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 11:09:17 AM UTC 2026
% Result : Theorem 0.07s 0.20s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 40 ( 30 unt; 0 typ; 8 def)
% Number of atoms : 213 ( 52 equ; 0 cnn)
% Maximal formula atoms : 15 ( 5 avg)
% Number of connectives : 239 ( 39 ~; 33 |; 8 &; 147 @)
% ( 1 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 43 ( 19 ^; 20 !; 4 ?; 43 :)
% 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_SY31,type,
sK1_SY31: 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,conjecture,
mlocal @ ( mimplies @ ( mand @ ( mbox @ ( mimplies @ p @ q ) ) @ ( mbox @ ( mimplies @ p @ ( mnot @ q ) ) ) ) @ ( mnot @ ( mdia @ p ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(2,negated_conjecture,
( ( mlocal @ ( mimplies @ ( mand @ ( mbox @ ( mimplies @ p @ q ) ) @ ( mbox @ ( mimplies @ p @ ( mnot @ q ) ) ) ) @ ( mnot @ ( mdia @ p ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ( ! [SY29: mworld] :
( ( mrel @ mactual @ SY29 )
=> ( ( p @ SY29 )
=> ( q @ SY29 ) ) )
& ! [SY30: mworld] :
( ( mrel @ mactual @ SY30 )
=> ( ( p @ SY30 )
=> ~ ( q @ SY30 ) ) ) )
=> ~ ? [SY31: mworld] :
( ( mrel @ mactual @ SY31 )
& ( p @ SY31 ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,mand,mbox,mdia,mequiv,mimplies,mlocal,mnot,mor]) ).
thf(4,plain,
( ( ! [SY29: mworld] :
( ( mrel @ mactual @ SY29 )
=> ( ( p @ SY29 )
=> ( q @ SY29 ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [SY30: mworld] :
( ( mrel @ mactual @ SY30 )
=> ( ( p @ SY30 )
=> ~ ( q @ SY30 ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ~ ? [SY31: mworld] :
( ( mrel @ mactual @ SY31 )
& ( p @ SY31 ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ? [SY31: mworld] :
( ( mrel @ mactual @ SY31 )
& ( p @ SY31 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(8,plain,
( ( ( mrel @ mactual @ sK1_SY31 )
& ( p @ sK1_SY31 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(9,plain,
( ( ! [SY29: mworld] :
( ~ ( mrel @ mactual @ SY29 )
| ~ ( p @ SY29 )
| ( q @ SY29 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(10,plain,
( ( ! [SY30: mworld] :
( ~ ( mrel @ mactual @ SY30 )
| ~ ( p @ SY30 )
| ~ ( q @ SY30 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[5]) ).
thf(11,plain,
( ( ! [SY30: mworld] :
( ~ ( mrel @ mactual @ SY30 )
| ~ ( p @ SY30 )
| ~ ( q @ SY30 ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(12,plain,
( ( ! [SY29: mworld] :
( ~ ( mrel @ mactual @ SY29 )
| ~ ( p @ SY29 )
| ( q @ SY29 ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(13,plain,
( ( ( mrel @ mactual @ sK1_SY31 )
& ( p @ sK1_SY31 ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(14,plain,
( ( ~ ( ~ ( mrel @ mactual @ sK1_SY31 )
| ~ ( p @ sK1_SY31 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13,mand,mbox,mdia,mequiv,mimplies,mlocal,mnot,mor]) ).
thf(15,plain,
! [SV1: mworld] :
( ( ~ ( mrel @ mactual @ SV1 )
| ~ ( p @ SV1 )
| ~ ( q @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(16,plain,
! [SV2: mworld] :
( ( ~ ( mrel @ mactual @ SV2 )
| ~ ( p @ SV2 )
| ( q @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(17,plain,
( ( ~ ( mrel @ mactual @ sK1_SY31 )
| ~ ( p @ sK1_SY31 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[14]) ).
thf(18,plain,
! [SV1: mworld] :
( ( ( ~ ( mrel @ mactual @ SV1 ) )
= $true )
| ( ( ~ ( p @ SV1 )
| ~ ( q @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[15]) ).
thf(19,plain,
! [SV2: mworld] :
( ( ( ~ ( mrel @ mactual @ SV2 ) )
= $true )
| ( ( ~ ( p @ SV2 )
| ( q @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[16]) ).
thf(20,plain,
( ( ~ ( mrel @ mactual @ sK1_SY31 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(21,plain,
( ( ~ ( p @ sK1_SY31 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(22,plain,
! [SV1: mworld] :
( ( ( mrel @ mactual @ SV1 )
= $false )
| ( ( ~ ( p @ SV1 )
| ~ ( q @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(23,plain,
! [SV2: mworld] :
( ( ( mrel @ mactual @ SV2 )
= $false )
| ( ( ~ ( p @ SV2 )
| ( q @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[19]) ).
thf(24,plain,
( ( mrel @ mactual @ sK1_SY31 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[20]) ).
thf(25,plain,
( ( p @ sK1_SY31 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[21]) ).
thf(26,plain,
! [SV1: mworld] :
( ( ( ~ ( p @ SV1 ) )
= $true )
| ( ( ~ ( q @ SV1 ) )
= $true )
| ( ( mrel @ mactual @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[22]) ).
thf(27,plain,
! [SV2: mworld] :
( ( ( ~ ( p @ SV2 ) )
= $true )
| ( ( q @ SV2 )
= $true )
| ( ( mrel @ mactual @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[23]) ).
thf(28,plain,
! [SV1: mworld] :
( ( ( p @ SV1 )
= $false )
| ( ( ~ ( q @ SV1 ) )
= $true )
| ( ( mrel @ mactual @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(29,plain,
! [SV2: mworld] :
( ( ( p @ SV2 )
= $false )
| ( ( q @ SV2 )
= $true )
| ( ( mrel @ mactual @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(30,plain,
! [SV1: mworld] :
( ( ( q @ SV1 )
= $false )
| ( ( p @ SV1 )
= $false )
| ( ( mrel @ mactual @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(31,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[24,30,29,25]) ).
thf(32,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO896^7 : 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
% 0.07/0.17 % Computer : n013.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Oct 6 17:52:51 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.20
% 0.07/0.20 No.of.Axioms: 0
% 0.07/0.20
% 0.07/0.20 Length.of.Defs: 1270
% 0.07/0.20
% 0.07/0.20 Contains.Choice.Funs: false
% 0.07/0.20
% 0.07/0.20 ********************************
% 0.07/0.20 * All subproblems solved! *
% 0.07/0.20 ********************************
% 0.07/0.20 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:2,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:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:31,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.07/0.20
% 0.07/0.20 %**** Beginning of derivation protocol ****
% 0.07/0.20 % SZS output start CNFRefutation
% See solution above
% 0.07/0.20
% 0.07/0.20 %**** End of derivation protocol ****
% 0.07/0.20 %**** no. of clauses in derivation: 32 ****
% 0.07/0.20 %**** clause counter: 31 ****
% 0.07/0.20
% 0.07/0.20 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:2,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:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:31,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------