%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYO886^6 : 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 : n003.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 11:09:15 AM UTC 2026
% Result : Theorem 0.06s 0.20s
% Output : CNFRefutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of formulae : 40 ( 37 unt; 0 typ; 10 def)
% Number of atoms : 140 ( 39 equ; 0 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 164 ( 18 ~; 9 |; 2 &; 124 @)
% ( 1 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 5 con; 0-3 aty)
% Number of variables : 75 ( 27 ^; 43 !; 5 ?; 75 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_mworld,type,
mworld: $tType ).
thf(tp_f,type,
f: $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_SX0,type,
sK1_SX0: mworld ).
thf(tp_sK2_SY33,type,
sK2_SY33: mworld > mworld ).
thf(tp_sK3_SY35,type,
sK3_SY35: $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,
! [W: mworld] :
? [V: mworld] : ( mrel @ W @ V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_serial) ).
thf(2,conjecture,
( mlocal
@ ( mimplies
@ ( mforall_di
@ ^ [X: $i] : ( mbox @ ( f @ X ) ) )
@ ( mbox
@ ( mforall_di
@ ^ [X: $i] : ( f @ X ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(3,negated_conjecture,
( ( mlocal
@ ( mimplies
@ ( mforall_di
@ ^ [X: $i] : ( mbox @ ( f @ X ) ) )
@ ( mbox
@ ( mforall_di
@ ^ [X: $i] : ( f @ X ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[2]) ).
thf(4,plain,
( ( ! [SY23: $i,SY24: mworld] :
( ( mrel @ mactual @ SY24 )
=> ( f @ SY23 @ SY24 ) )
=> ! [SY25: mworld] :
( ( mrel @ mactual @ SY25 )
=> ! [SY17: $i] : ( f @ SY17 @ SY25 ) ) )
= $false ),
inference(unfold_def,[status(thm)],[3,mand,mbox,mdia,mequiv,mexists_di,mforall_di,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,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(6,plain,
( ( ! [SY23: $i,SY24: mworld] :
( ( mrel @ mactual @ SY24 )
=> ( f @ SY23 @ SY24 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[4]) ).
thf(7,plain,
( ( ! [SY25: mworld] :
( ( mrel @ mactual @ SY25 )
=> ! [SY17: $i] : ( f @ SY17 @ SY25 ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[4]) ).
thf(8,plain,
( ( ~ ! [SY25: mworld] :
( ( mrel @ mactual @ SY25 )
=> ! [SY17: $i] : ( f @ SY17 @ SY25 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(9,plain,
( ( ! [W: mworld] :
? [V: mworld] : ( mrel @ W @ V ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(10,plain,
( ( ! [SY23: $i,SY24: mworld] :
( ( mrel @ mactual @ SY24 )
=> ( f @ SY23 @ SY24 ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(11,plain,
( ( ~ ! [SY25: mworld] :
( ( mrel @ mactual @ SY25 )
=> ! [SY17: $i] : ( f @ SY17 @ SY25 ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(12,plain,
( ( ! [SX0: mworld] :
~ ! [SX1: mworld] :
~ ( mrel @ SX0 @ SX1 ) )
= $true ),
inference(unfold_def,[status(thm)],[9,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(13,plain,
( ( ~ ! [SX0: mworld] :
( ~ ( mrel @ mactual @ SX0 )
| ! [SX1: $i] : ( f @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(14,plain,
( ( ! [SX0: $i,SX1: mworld] :
( ~ ( mrel @ mactual @ SX1 )
| ( f @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(15,plain,
! [SV1: mworld] :
( ( ~ ! [SY33: mworld] :
~ ( mrel @ SV1 @ SY33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(16,plain,
( ( ! [SX0: mworld] :
( ~ ( mrel @ mactual @ SX0 )
| ! [SX1: $i] : ( f @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[13]) ).
thf(17,plain,
! [SV2: $i] :
( ( ! [SY34: mworld] :
( ~ ( mrel @ mactual @ SY34 )
| ( f @ SV2 @ SY34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(18,plain,
! [SV1: mworld] :
( ( ! [SY33: mworld] :
~ ( mrel @ SV1 @ SY33 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[15]) ).
thf(19,plain,
( ( ~ ( mrel @ mactual @ sK1_SX0 )
| ! [SY35: $i] : ( f @ SY35 @ sK1_SX0 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[16]) ).
thf(20,plain,
! [SV2: $i,SV3: mworld] :
( ( ~ ( mrel @ mactual @ SV3 )
| ( f @ SV2 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(21,plain,
! [SV1: mworld] :
( ( ~ ( mrel @ SV1 @ ( sK2_SY33 @ SV1 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[18]) ).
thf(22,plain,
( ( ~ ( mrel @ mactual @ sK1_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[19]) ).
thf(23,plain,
( ( ! [SY35: $i] : ( f @ SY35 @ sK1_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[19]) ).
thf(24,plain,
! [SV2: $i,SV3: mworld] :
( ( ( ~ ( mrel @ mactual @ SV3 ) )
= $true )
| ( ( f @ SV2 @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[20]) ).
thf(25,plain,
! [SV1: mworld] :
( ( mrel @ SV1 @ ( sK2_SY33 @ SV1 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[21]) ).
thf(26,plain,
( ( mrel @ mactual @ sK1_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[22]) ).
thf(27,plain,
( ( f @ sK3_SY35 @ sK1_SX0 )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[23]) ).
thf(28,plain,
! [SV2: $i,SV3: mworld] :
( ( ( mrel @ mactual @ SV3 )
= $false )
| ( ( f @ SV2 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(29,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[25,28,27,26]) ).
thf(30,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO886^6 : 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
% 0.06/0.17 % Computer : n003.cluster.edu
% 0.06/0.17 % Model : x86_64 x86_64
% 0.06/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.17 % Memory : 8046.5625MB
% 0.06/0.17 % OS : Linux 6.8.0-71-generic
% 0.06/0.17 % CPULimit : 300
% 0.06/0.17 % WCLimit : 300
% 0.06/0.17 % DateTime : Tue Oct 6 17:55:09 UTC 2026
% 0.06/0.17 % CPUTime :
% 0.06/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.20
% 0.06/0.20 No.of.Axioms: 1
% 0.06/0.20
% 0.06/0.20 Length.of.Defs: 1614
% 0.06/0.20
% 0.06/0.20 Contains.Choice.Funs: false
% 0.06/0.20
% 0.06/0.20 ********************************
% 0.06/0.20 * All subproblems solved! *
% 0.06/0.20 ********************************
% 0.06/0.20 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:2,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:29,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.06/0.20
% 0.06/0.20 %**** Beginning of derivation protocol ****
% 0.06/0.20 % SZS output start CNFRefutation
% See solution above
% 0.06/0.20
% 0.06/0.20 %**** End of derivation protocol ****
% 0.06/0.20 %**** no. of clauses in derivation: 30 ****
% 0.06/0.20 %**** clause counter: 29 ****
% 0.06/0.20
% 0.06/0.20 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:2,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:29,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------