%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET027^3 : 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 : n009.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 10:39:03 AM UTC 2026
% Result : Theorem 0.08s 0.23s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 13
% Syntax : Number of formulae : 52 ( 38 unt; 0 typ; 10 def)
% Number of atoms : 251 ( 61 equ; 0 cnn)
% Maximal formula atoms : 9 ( 4 avg)
% Number of connectives : 476 ( 50 ~; 48 |; 6 &; 361 @)
% ( 3 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 18 usr; 6 con; 0-3 aty)
% Number of variables : 109 ( 33 ^; 74 !; 2 ?; 109 :)
% 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_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_sK1_SY24,type,
sK1_SY24: $i ).
thf(tp_sK2_SY66,type,
sK2_SY66: $i ).
thf(tp_sK3_SY68,type,
sK3_SY68: $i ).
thf(tp_sK4_SY73,type,
sK4_SY73: $i > $i > $i ).
thf(tp_subset,type,
subset: $i > $i > mworld > $o ).
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,
( mlocal
@ ( mforall_di
@ ^ [B: $i] : ( subset @ B @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_of_subset) ).
thf(2,axiom,
( mlocal
@ ( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] :
( mequiv @ ( subset @ B @ C )
@ ( mforall_di
@ ^ [D: $i] : ( mimplies @ ( member @ D @ B ) @ ( member @ D @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
thf(4,conjecture,
( mlocal
@ ( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] :
( mforall_di
@ ^ [D: $i] : ( mimplies @ ( mand @ ( subset @ B @ C ) @ ( subset @ C @ D ) ) @ ( subset @ B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_transitivity_of_subset) ).
thf(5,negated_conjecture,
( ( mlocal
@ ( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] :
( mforall_di
@ ^ [D: $i] : ( mimplies @ ( mand @ ( subset @ B @ C ) @ ( subset @ C @ D ) ) @ ( subset @ B @ D ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[4]) ).
thf(6,plain,
( ( ! [SY24: $i,SY25: $i,SY26: $i] :
( ( ( subset @ SY24 @ SY25 @ mactual )
& ( subset @ SY25 @ SY26 @ mactual ) )
=> ( subset @ SY24 @ SY26 @ mactual ) ) )
= $false ),
inference(unfold_def,[status(thm)],[5,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(7,plain,
( ( ! [SY33: $i] : ( subset @ SY33 @ SY33 @ mactual ) )
= $true ),
inference(unfold_def,[status(thm)],[1,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(8,plain,
( ( ! [SY60: $i,SY61: $i] :
( ( subset @ SY60 @ SY61 @ mactual )
<=> ! [SY62: $i] :
( ( member @ SY62 @ SY60 @ mactual )
=> ( member @ SY62 @ SY61 @ mactual ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(9,plain,
( ( ! [SY66: $i,SY67: $i] :
( ( ( subset @ sK1_SY24 @ SY66 @ mactual )
& ( subset @ SY66 @ SY67 @ mactual ) )
=> ( subset @ sK1_SY24 @ SY67 @ mactual ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[6]) ).
thf(10,plain,
( ( ! [SY68: $i] :
( ( ( subset @ sK1_SY24 @ sK2_SY66 @ mactual )
& ( subset @ sK2_SY66 @ SY68 @ mactual ) )
=> ( subset @ sK1_SY24 @ SY68 @ mactual ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[9]) ).
thf(11,plain,
( ( ( ( subset @ sK1_SY24 @ sK2_SY66 @ mactual )
& ( subset @ sK2_SY66 @ sK3_SY68 @ mactual ) )
=> ( subset @ sK1_SY24 @ sK3_SY68 @ mactual ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[10]) ).
thf(12,plain,
( ( subset @ sK1_SY24 @ sK2_SY66 @ mactual )
= $true ),
inference(standard_cnf,[status(thm)],[11]) ).
thf(13,plain,
( ( subset @ sK2_SY66 @ sK3_SY68 @ mactual )
= $true ),
inference(standard_cnf,[status(thm)],[11]) ).
thf(14,plain,
( ( subset @ sK1_SY24 @ sK3_SY68 @ mactual )
= $false ),
inference(standard_cnf,[status(thm)],[11]) ).
thf(15,plain,
( ( ~ ( subset @ sK1_SY24 @ sK3_SY68 @ mactual ) )
= $true ),
inference(polarity_switch,[status(thm)],[14]) ).
thf(16,plain,
( ( ! [SY60: $i,SY61: $i] :
( ( subset @ SY60 @ SY61 @ mactual )
<=> ! [SY62: $i] :
( ( member @ SY62 @ SY60 @ mactual )
=> ( member @ SY62 @ SY61 @ mactual ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(17,plain,
( ( ! [SY33: $i] : ( subset @ SY33 @ SY33 @ mactual ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(18,plain,
( ( subset @ sK2_SY66 @ sK3_SY68 @ mactual )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(19,plain,
( ( subset @ sK1_SY24 @ sK2_SY66 @ mactual )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(20,plain,
( ( ~ ( subset @ sK1_SY24 @ sK3_SY68 @ mactual ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(21,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( subset @ SX0 @ SX1 @ mactual )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 @ mactual )
| ( member @ SX2 @ SX1 @ mactual ) ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 @ mactual )
| ( member @ SX2 @ SX1 @ mactual ) )
| ( subset @ SX0 @ SX1 @ mactual ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(22,plain,
! [SV1: $i] :
( ( subset @ SV1 @ SV1 @ mactual )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(23,plain,
( ( subset @ sK1_SY24 @ sK3_SY68 @ mactual )
= $false ),
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(24,plain,
! [SV2: $i] :
( ( ! [SY69: $i] :
~ ( ~ ( ~ ( subset @ SV2 @ SY69 @ mactual )
| ! [SY70: $i] :
( ~ ( member @ SY70 @ SV2 @ mactual )
| ( member @ SY70 @ SY69 @ mactual ) ) )
| ~ ( ~ ! [SY71: $i] :
( ~ ( member @ SY71 @ SV2 @ mactual )
| ( member @ SY71 @ SY69 @ mactual ) )
| ( subset @ SV2 @ SY69 @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(25,plain,
! [SV3: $i,SV2: $i] :
( ( ~ ( ~ ( ~ ( subset @ SV2 @ SV3 @ mactual )
| ! [SY72: $i] :
( ~ ( member @ SY72 @ SV2 @ mactual )
| ( member @ SY72 @ SV3 @ mactual ) ) )
| ~ ( ~ ! [SY73: $i] :
( ~ ( member @ SY73 @ SV2 @ mactual )
| ( member @ SY73 @ SV3 @ mactual ) )
| ( subset @ SV2 @ SV3 @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(26,plain,
! [SV3: $i,SV2: $i] :
( ( ~ ( ~ ( subset @ SV2 @ SV3 @ mactual )
| ! [SY72: $i] :
( ~ ( member @ SY72 @ SV2 @ mactual )
| ( member @ SY72 @ SV3 @ mactual ) ) )
| ~ ( ~ ! [SY73: $i] :
( ~ ( member @ SY73 @ SV2 @ mactual )
| ( member @ SY73 @ SV3 @ mactual ) )
| ( subset @ SV2 @ SV3 @ mactual ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(27,plain,
! [SV3: $i,SV2: $i] :
( ( ~ ( ~ ( subset @ SV2 @ SV3 @ mactual )
| ! [SY72: $i] :
( ~ ( member @ SY72 @ SV2 @ mactual )
| ( member @ SY72 @ SV3 @ mactual ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[26]) ).
thf(28,plain,
! [SV3: $i,SV2: $i] :
( ( ~ ( ~ ! [SY73: $i] :
( ~ ( member @ SY73 @ SV2 @ mactual )
| ( member @ SY73 @ SV3 @ mactual ) )
| ( subset @ SV2 @ SV3 @ mactual ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[26]) ).
thf(29,plain,
! [SV3: $i,SV2: $i] :
( ( ~ ( subset @ SV2 @ SV3 @ mactual )
| ! [SY72: $i] :
( ~ ( member @ SY72 @ SV2 @ mactual )
| ( member @ SY72 @ SV3 @ mactual ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[27]) ).
thf(30,plain,
! [SV3: $i,SV2: $i] :
( ( ~ ! [SY73: $i] :
( ~ ( member @ SY73 @ SV2 @ mactual )
| ( member @ SY73 @ SV3 @ mactual ) )
| ( subset @ SV2 @ SV3 @ mactual ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[28]) ).
thf(31,plain,
! [SV3: $i,SV2: $i] :
( ( ( ~ ( subset @ SV2 @ SV3 @ mactual ) )
= $true )
| ( ( ! [SY72: $i] :
( ~ ( member @ SY72 @ SV2 @ mactual )
| ( member @ SY72 @ SV3 @ mactual ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[29]) ).
thf(32,plain,
! [SV3: $i,SV2: $i] :
( ( ( ~ ! [SY73: $i] :
( ~ ( member @ SY73 @ SV2 @ mactual )
| ( member @ SY73 @ SV3 @ mactual ) ) )
= $true )
| ( ( subset @ SV2 @ SV3 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[30]) ).
thf(33,plain,
! [SV3: $i,SV2: $i] :
( ( ( subset @ SV2 @ SV3 @ mactual )
= $false )
| ( ( ! [SY72: $i] :
( ~ ( member @ SY72 @ SV2 @ mactual )
| ( member @ SY72 @ SV3 @ mactual ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(34,plain,
! [SV3: $i,SV2: $i] :
( ( ( ! [SY73: $i] :
( ~ ( member @ SY73 @ SV2 @ mactual )
| ( member @ SY73 @ SV3 @ mactual ) ) )
= $false )
| ( ( subset @ SV2 @ SV3 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(35,plain,
! [SV3: $i,SV2: $i,SV4: $i] :
( ( ( ~ ( member @ SV4 @ SV2 @ mactual )
| ( member @ SV4 @ SV3 @ mactual ) )
= $true )
| ( ( subset @ SV2 @ SV3 @ mactual )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(36,plain,
! [SV2: $i,SV3: $i] :
( ( ( ~ ( member @ ( sK4_SY73 @ SV3 @ SV2 ) @ SV2 @ mactual )
| ( member @ ( sK4_SY73 @ SV3 @ SV2 ) @ SV3 @ mactual ) )
= $false )
| ( ( subset @ SV2 @ SV3 @ mactual )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[34]) ).
thf(37,plain,
! [SV3: $i,SV2: $i,SV4: $i] :
( ( ( ~ ( member @ SV4 @ SV2 @ mactual ) )
= $true )
| ( ( member @ SV4 @ SV3 @ mactual )
= $true )
| ( ( subset @ SV2 @ SV3 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[35]) ).
thf(38,plain,
! [SV2: $i,SV3: $i] :
( ( ( ~ ( member @ ( sK4_SY73 @ SV3 @ SV2 ) @ SV2 @ mactual ) )
= $false )
| ( ( subset @ SV2 @ SV3 @ mactual )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[36]) ).
thf(39,plain,
! [SV2: $i,SV3: $i] :
( ( ( member @ ( sK4_SY73 @ SV3 @ SV2 ) @ SV3 @ mactual )
= $false )
| ( ( subset @ SV2 @ SV3 @ mactual )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[36]) ).
thf(40,plain,
! [SV3: $i,SV2: $i,SV4: $i] :
( ( ( member @ SV4 @ SV2 @ mactual )
= $false )
| ( ( member @ SV4 @ SV3 @ mactual )
= $true )
| ( ( subset @ SV2 @ SV3 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(41,plain,
! [SV2: $i,SV3: $i] :
( ( ( member @ ( sK4_SY73 @ SV3 @ SV2 ) @ SV2 @ mactual )
= $true )
| ( ( subset @ SV2 @ SV3 @ mactual )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[38]) ).
thf(42,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[18,41,40,39,23,22,19]) ).
thf(43,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET027^3 : 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 : n009.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 14:27:17 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: 2
% 0.08/0.23
% 0.08/0.23 Length.of.Defs: 1614
% 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:4,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:42,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: 42 ****
% 0.08/0.23 %**** clause counter: 42 ****
% 0.08/0.23
% 0.08/0.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:4,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:42,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------