%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET055^12 : 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 : n017.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 10:39:10 AM UTC 2026
% Result : Theorem 0.04s 0.26s
% Output : CNFRefutation 0.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 13
% Syntax : Number of formulae : 41 ( 29 unt; 0 typ; 10 def)
% Number of atoms : 191 ( 52 equ; 0 cnn)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 283 ( 23 ~; 32 |; 3 &; 211 @)
% ( 1 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 49 ( 46 usr; 9 con; 0-3 aty)
% Number of variables : 61 ( 28 ^; 31 !; 2 ?; 61 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_mworld,type,
mworld: $tType ).
thf(tp_apply,type,
apply: $i > $i > $i ).
thf(tp_complement,type,
complement: $i > $i ).
thf(tp_compose,type,
compose: $i > $i > $i ).
thf(tp_cross_product,type,
cross_product: $i > $i > $i ).
thf(tp_disjoint,type,
disjoint: $i > $i > mworld > $o ).
thf(tp_domain_of,type,
domain_of: $i > $i ).
thf(tp_eiw_di,type,
eiw_di: $i > mworld > $o ).
thf(tp_element_relation,type,
element_relation: $i ).
thf(tp_first,type,
first: $i > $i ).
thf(tp_flip,type,
flip: $i > $i ).
thf(tp_function,type,
function: $i > mworld > $o ).
thf(tp_identity_relation,type,
identity_relation: $i ).
thf(tp_image,type,
image: $i > $i > $i ).
thf(tp_inductive,type,
inductive: $i > mworld > $o ).
thf(tp_intersection,type,
intersection: $i > $i > $i ).
thf(tp_inverse,type,
inverse: $i > $i ).
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_member,type,
member: $i > $i > 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_null_class,type,
null_class: $i ).
thf(tp_ordered_pair,type,
ordered_pair: $i > $i > $i ).
thf(tp_power_class,type,
power_class: $i > $i ).
thf(tp_qmltpeq,type,
qmltpeq: $i > $i > mworld > $o ).
thf(tp_range_of,type,
range_of: $i > $i ).
thf(tp_restrict,type,
restrict: $i > $i > $i > $i ).
thf(tp_rotate,type,
rotate: $i > $i ).
thf(tp_sK1_SY3,type,
sK1_SY3: $i ).
thf(tp_second,type,
second: $i > $i ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(tp_subclass,type,
subclass: $i > $i > mworld > $o ).
thf(tp_successor,type,
successor: $i > $i ).
thf(tp_successor_relation,type,
successor_relation: $i ).
thf(tp_sum_class,type,
sum_class: $i > $i ).
thf(tp_union,type,
union: $i > $i > $i ).
thf(tp_universal_class,type,
universal_class: $i ).
thf(tp_unordered_pair,type,
unordered_pair: $i > $i > $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] :
( ( eiw_di @ X @ W )
& ( 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] :
( ( eiw_di @ X @ W )
=> ( 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(82,axiom,
( mlocal
@ ( mforall_di
@ ^ [X: $i] :
( mforall_di
@ ^ [Y: $i] : ( mimplies @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ X ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry) ).
thf(83,axiom,
( mlocal
@ ( mforall_di
@ ^ [X: $i] : ( qmltpeq @ X @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).
thf(86,conjecture,
( mlocal
@ ( mforall_di
@ ^ [X: $i] : ( qmltpeq @ X @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_0) ).
thf(87,negated_conjecture,
( ( mlocal
@ ( mforall_di
@ ^ [X: $i] : ( qmltpeq @ X @ X ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[86]) ).
thf(88,plain,
( ( ! [SY3: $i] :
( ( eiw_di @ SY3 @ mactual )
=> ( qmltpeq @ SY3 @ SY3 @ mactual ) ) )
= $false ),
inference(unfold_def,[status(thm)],[87,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(89,plain,
( ( ! [SY18: $i] :
( ( eiw_di @ SY18 @ mactual )
=> ! [SY19: $i] :
( ( eiw_di @ SY19 @ mactual )
=> ( ( qmltpeq @ SY18 @ SY19 @ mactual )
=> ( qmltpeq @ SY19 @ SY18 @ mactual ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[82,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(90,plain,
( ( ! [SY25: $i] :
( ( eiw_di @ SY25 @ mactual )
=> ( qmltpeq @ SY25 @ SY25 @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(91,plain,
( ( ( eiw_di @ sK1_SY3 @ mactual )
=> ( qmltpeq @ sK1_SY3 @ sK1_SY3 @ mactual ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[88]) ).
thf(92,plain,
( ( eiw_di @ sK1_SY3 @ mactual )
= $true ),
inference(standard_cnf,[status(thm)],[91]) ).
thf(93,plain,
( ( qmltpeq @ sK1_SY3 @ sK1_SY3 @ mactual )
= $false ),
inference(standard_cnf,[status(thm)],[91]) ).
thf(94,plain,
( ( ~ ( qmltpeq @ sK1_SY3 @ sK1_SY3 @ mactual ) )
= $true ),
inference(polarity_switch,[status(thm)],[93]) ).
thf(95,plain,
( ( ! [SY25: $i] :
( ( eiw_di @ SY25 @ mactual )
=> ( qmltpeq @ SY25 @ SY25 @ mactual ) ) )
= $true ),
inference(copy,[status(thm)],[90]) ).
thf(96,plain,
( ( ! [SY18: $i] :
( ( eiw_di @ SY18 @ mactual )
=> ! [SY19: $i] :
( ( eiw_di @ SY19 @ mactual )
=> ( ( qmltpeq @ SY18 @ SY19 @ mactual )
=> ( qmltpeq @ SY19 @ SY18 @ mactual ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[89]) ).
thf(97,plain,
( ( eiw_di @ sK1_SY3 @ mactual )
= $true ),
inference(copy,[status(thm)],[92]) ).
thf(98,plain,
( ( ~ ( qmltpeq @ sK1_SY3 @ sK1_SY3 @ mactual ) )
= $true ),
inference(copy,[status(thm)],[94]) ).
thf(99,plain,
( ( ! [SX0: $i] :
( ~ ( eiw_di @ SX0 @ mactual )
| ( qmltpeq @ SX0 @ SX0 @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(100,plain,
( ( ! [SX0: $i] :
( ~ ( eiw_di @ SX0 @ mactual )
| ! [SX1: $i] :
( ~ ( eiw_di @ SX1 @ mactual )
| ~ ( qmltpeq @ SX0 @ SX1 @ mactual )
| ( qmltpeq @ SX1 @ SX0 @ mactual ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(101,plain,
( ( qmltpeq @ sK1_SY3 @ sK1_SY3 @ mactual )
= $false ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(102,plain,
! [SV1: $i] :
( ( ~ ( eiw_di @ SV1 @ mactual )
| ( qmltpeq @ SV1 @ SV1 @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(103,plain,
! [SV2: $i] :
( ( ~ ( eiw_di @ SV2 @ mactual )
| ! [SY27: $i] :
( ~ ( eiw_di @ SY27 @ mactual )
| ~ ( qmltpeq @ SV2 @ SY27 @ mactual )
| ( qmltpeq @ SY27 @ SV2 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(104,plain,
! [SV1: $i] :
( ( ( ~ ( eiw_di @ SV1 @ mactual ) )
= $true )
| ( ( qmltpeq @ SV1 @ SV1 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[102]) ).
thf(105,plain,
! [SV2: $i] :
( ( ( ~ ( eiw_di @ SV2 @ mactual ) )
= $true )
| ( ( ! [SY27: $i] :
( ~ ( eiw_di @ SY27 @ mactual )
| ~ ( qmltpeq @ SV2 @ SY27 @ mactual )
| ( qmltpeq @ SY27 @ SV2 @ mactual ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[103]) ).
thf(106,plain,
! [SV1: $i] :
( ( ( eiw_di @ SV1 @ mactual )
= $false )
| ( ( qmltpeq @ SV1 @ SV1 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[104]) ).
thf(107,plain,
! [SV2: $i] :
( ( ( eiw_di @ SV2 @ mactual )
= $false )
| ( ( ! [SY27: $i] :
( ~ ( eiw_di @ SY27 @ mactual )
| ~ ( qmltpeq @ SV2 @ SY27 @ mactual )
| ( qmltpeq @ SY27 @ SV2 @ mactual ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(108,plain,
! [SV2: $i,SV3: $i] :
( ( ( ~ ( eiw_di @ SV3 @ mactual )
| ~ ( qmltpeq @ SV2 @ SV3 @ mactual )
| ( qmltpeq @ SV3 @ SV2 @ mactual ) )
= $true )
| ( ( eiw_di @ SV2 @ mactual )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(109,plain,
! [SV2: $i,SV3: $i] :
( ( ( ~ ( eiw_di @ SV3 @ mactual ) )
= $true )
| ( ( ~ ( qmltpeq @ SV2 @ SV3 @ mactual )
| ( qmltpeq @ SV3 @ SV2 @ mactual ) )
= $true )
| ( ( eiw_di @ SV2 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[108]) ).
thf(110,plain,
! [SV2: $i,SV3: $i] :
( ( ( eiw_di @ SV3 @ mactual )
= $false )
| ( ( ~ ( qmltpeq @ SV2 @ SV3 @ mactual )
| ( qmltpeq @ SV3 @ SV2 @ mactual ) )
= $true )
| ( ( eiw_di @ SV2 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(111,plain,
! [SV3: $i,SV2: $i] :
( ( ( ~ ( qmltpeq @ SV2 @ SV3 @ mactual ) )
= $true )
| ( ( qmltpeq @ SV3 @ SV2 @ mactual )
= $true )
| ( ( eiw_di @ SV3 @ mactual )
= $false )
| ( ( eiw_di @ SV2 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[110]) ).
thf(112,plain,
! [SV3: $i,SV2: $i] :
( ( ( qmltpeq @ SV2 @ SV3 @ mactual )
= $false )
| ( ( qmltpeq @ SV3 @ SV2 @ mactual )
= $true )
| ( ( eiw_di @ SV3 @ mactual )
= $false )
| ( ( eiw_di @ SV2 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(113,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[97,112,106,101]) ).
thf(114,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[113]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET055^12 : 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
% 0.04/0.17 % Computer : n017.cluster.edu
% 0.04/0.17 % Model : x86_64 x86_64
% 0.04/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.17 % Memory : 8046.5625MB
% 0.04/0.17 % OS : Linux 6.8.0-71-generic
% 0.04/0.17 % CPULimit : 300
% 0.04/0.17 % WCLimit : 300
% 0.04/0.17 % DateTime : Tue Oct 6 14:24:46 UTC 2026
% 0.04/0.18 % CPUTime :
% 0.04/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.04/0.26
% 0.04/0.26 No.of.Axioms: 2
% 0.04/0.26
% 0.04/0.26 Length.of.Defs: 1653
% 0.04/0.26
% 0.04/0.26 Contains.Choice.Funs: false
% 0.04/0.26 .
% 0.04/0.26
% 0.04/0.26 ********************************
% 0.04/0.26 * All subproblems solved! *
% 0.04/0.26 ********************************
% 0.04/0.26 % 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:113,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.04/0.26
% 0.04/0.26 %**** Beginning of derivation protocol ****
% 0.04/0.26 % SZS output start CNFRefutation
% See solution above
% 0.04/0.26
% 0.04/0.26 %**** End of derivation protocol ****
% 0.04/0.26 %**** no. of clauses in derivation: 31 ****
% 0.04/0.26 %**** clause counter: 113 ****
% 0.04/0.26
% 0.04/0.26 % 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:113,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------