%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : LAT388+1 : TPTP v9.3.1. Released v4.0.0.
% 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 : 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 10:27:43 AM UTC 2026
% Result : Theorem 0.11s 0.28s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 5
% Syntax : Number of formulae : 45 ( 30 unt; 0 typ; 0 def)
% Number of atoms : 264 ( 92 equ; 0 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 386 ( 73 ~; 62 |; 6 &; 236 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 26 usr; 8 con; 0-3 aty)
% Number of variables : 82 ( 0 ^; 77 !; 5 ?; 82 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_aCompleteLattice0,type,
aCompleteLattice0: $i > $o ).
thf(tp_aElement0,type,
aElement0: $i > $o ).
thf(tp_aElementOf0,type,
aElementOf0: $i > $i > $o ).
thf(tp_aFixedPointOf0,type,
aFixedPointOf0: $i > $i > $o ).
thf(tp_aFunction0,type,
aFunction0: $i > $o ).
thf(tp_aInfimumOfIn0,type,
aInfimumOfIn0: $i > $i > $i > $o ).
thf(tp_aLowerBoundOfIn0,type,
aLowerBoundOfIn0: $i > $i > $i > $o ).
thf(tp_aSet0,type,
aSet0: $i > $o ).
thf(tp_aSubsetOf0,type,
aSubsetOf0: $i > $i > $o ).
thf(tp_aSupremumOfIn0,type,
aSupremumOfIn0: $i > $i > $i > $o ).
thf(tp_aUpperBoundOfIn0,type,
aUpperBoundOfIn0: $i > $i > $i > $o ).
thf(tp_cS1142,type,
cS1142: $i > $i ).
thf(tp_cS1241,type,
cS1241: $i > $i > $i > $i ).
thf(tp_isEmpty0,type,
isEmpty0: $i > $o ).
thf(tp_isMonotone0,type,
isMonotone0: $i > $o ).
thf(tp_isOn0,type,
isOn0: $i > $i > $o ).
thf(tp_sdtlpdtrp0,type,
sdtlpdtrp0: $i > $i > $i ).
thf(tp_sdtlseqdt0,type,
sdtlseqdt0: $i > $i > $o ).
thf(tp_szDzozmdt0,type,
szDzozmdt0: $i > $i ).
thf(tp_szRzazndt0,type,
szRzazndt0: $i > $i ).
thf(tp_xP,type,
xP: $i ).
thf(tp_xS,type,
xS: $i ).
thf(tp_xT,type,
xT: $i ).
thf(tp_xU,type,
xU: $i ).
thf(tp_xf,type,
xf: $i ).
thf(tp_xp,type,
xp: $i ).
thf(6,axiom,
! [W0: $i] :
( ( aSet0 @ W0 )
=> ! [W1: $i] :
( ( aSubsetOf0 @ W1 @ W0 )
=> ! [W2: $i,W3: $i] :
( ( ( aSupremumOfIn0 @ W2 @ W1 @ W0 )
& ( aSupremumOfIn0 @ W3 @ W1 @ W0 ) )
=> ( W2 = W3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSupUn) ).
thf(14,axiom,
( ( aFixedPointOf0 @ xp @ xf )
& ( aSupremumOfIn0 @ xp @ xT @ xS ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1330) ).
thf(18,axiom,
aSubsetOf0 @ xT @ xS,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1173) ).
thf(19,axiom,
( xS
= ( cS1142 @ xf ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1144) ).
thf(21,conjecture,
? [W0: $i] : ( aSupremumOfIn0 @ W0 @ xT @ xS ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
thf(22,negated_conjecture,
( ( ? [W0: $i] : ( aSupremumOfIn0 @ W0 @ xT @ xS ) )
= $false ),
inference(negate_conjecture,[status(cth)],[21]) ).
thf(23,plain,
( ( ? [W0: $i] : ( aSupremumOfIn0 @ W0 @ xT @ xS ) )
= $false ),
inference(unfold_def,[status(thm)],[22]) ).
thf(24,plain,
( ( ! [W0: $i] :
( ( aSet0 @ W0 )
=> ! [W1: $i] :
( ( aSubsetOf0 @ W1 @ W0 )
=> ! [W2: $i,W3: $i] :
( ( ( aSupremumOfIn0 @ W2 @ W1 @ W0 )
& ( aSupremumOfIn0 @ W3 @ W1 @ W0 ) )
=> ( W2 = W3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(25,plain,
( ( ( aFixedPointOf0 @ xp @ xf )
& ( aSupremumOfIn0 @ xp @ xT @ xS ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(26,plain,
( ( aSubsetOf0 @ xT @ xS )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(27,plain,
( ( xS
= ( cS1142 @ xf ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(28,plain,
( ( ~ ? [W0: $i] : ( aSupremumOfIn0 @ W0 @ xT @ xS ) )
= $true ),
inference(polarity_switch,[status(thm)],[23]) ).
thf(29,plain,
( ( xS
= ( cS1142 @ xf ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(30,plain,
( ( aSubsetOf0 @ xT @ xS )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(31,plain,
( ( ( aFixedPointOf0 @ xp @ xf )
& ( aSupremumOfIn0 @ xp @ xT @ xS ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(32,plain,
( ( ! [W0: $i] :
( ( aSet0 @ W0 )
=> ! [W1: $i] :
( ( aSubsetOf0 @ W1 @ W0 )
=> ! [W2: $i,W3: $i] :
( ( ( aSupremumOfIn0 @ W2 @ W1 @ W0 )
& ( aSupremumOfIn0 @ W3 @ W1 @ W0 ) )
=> ( W2 = W3 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(33,plain,
( ( ~ ? [W0: $i] : ( aSupremumOfIn0 @ W0 @ xT @ xS ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(34,plain,
( ( ~ ~ ! [SX0: $i] :
~ ( aSupremumOfIn0 @ SX0 @ xT @ xS ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(35,plain,
( ( ~ ( ~ ( aFixedPointOf0 @ xp @ xf )
| ~ ( aSupremumOfIn0 @ xp @ xT @ xS ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(36,plain,
( ( ! [SX0: $i] :
( ~ ( aSet0 @ SX0 )
| ! [SX1: $i] :
( ~ ( aSubsetOf0 @ SX1 @ SX0 )
| ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( aSupremumOfIn0 @ SX2 @ SX1 @ SX0 )
| ~ ( aSupremumOfIn0 @ SX3 @ SX1 @ SX0 ) )
| ( SX2 = SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(37,plain,
( ( ~ ! [SX0: $i] :
~ ( aSupremumOfIn0 @ SX0 @ xT @ xS ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(38,plain,
( ( ~ ( aFixedPointOf0 @ xp @ xf )
| ~ ( aSupremumOfIn0 @ xp @ xT @ xS ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(39,plain,
! [SV1: $i] :
( ( ~ ( aSet0 @ SV1 )
| ! [SY5: $i] :
( ~ ( aSubsetOf0 @ SY5 @ SV1 )
| ! [SY6: $i,SY7: $i] :
( ~ ~ ( ~ ( aSupremumOfIn0 @ SY6 @ SY5 @ SV1 )
| ~ ( aSupremumOfIn0 @ SY7 @ SY5 @ SV1 ) )
| ( SY6 = SY7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(40,plain,
( ( ! [SX0: $i] :
~ ( aSupremumOfIn0 @ SX0 @ xT @ xS ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[37]) ).
thf(41,plain,
( ( ~ ( aFixedPointOf0 @ xp @ xf ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[38]) ).
thf(42,plain,
( ( ~ ( aSupremumOfIn0 @ xp @ xT @ xS ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[38]) ).
thf(43,plain,
! [SV1: $i] :
( ( ( ~ ( aSet0 @ SV1 ) )
= $true )
| ( ( ! [SY5: $i] :
( ~ ( aSubsetOf0 @ SY5 @ SV1 )
| ! [SY6: $i,SY7: $i] :
( ~ ~ ( ~ ( aSupremumOfIn0 @ SY6 @ SY5 @ SV1 )
| ~ ( aSupremumOfIn0 @ SY7 @ SY5 @ SV1 ) )
| ( SY6 = SY7 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[39]) ).
thf(44,plain,
! [SV2: $i] :
( ( ~ ( aSupremumOfIn0 @ SV2 @ xT @ xS ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(45,plain,
( ( aFixedPointOf0 @ xp @ xf )
= $true ),
inference(extcnf_not_neg,[status(thm)],[41]) ).
thf(46,plain,
( ( aSupremumOfIn0 @ xp @ xT @ xS )
= $true ),
inference(extcnf_not_neg,[status(thm)],[42]) ).
thf(47,plain,
! [SV1: $i] :
( ( ( aSet0 @ SV1 )
= $false )
| ( ( ! [SY5: $i] :
( ~ ( aSubsetOf0 @ SY5 @ SV1 )
| ! [SY6: $i,SY7: $i] :
( ~ ~ ( ~ ( aSupremumOfIn0 @ SY6 @ SY5 @ SV1 )
| ~ ( aSupremumOfIn0 @ SY7 @ SY5 @ SV1 ) )
| ( SY6 = SY7 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(48,plain,
! [SV2: $i] :
( ( aSupremumOfIn0 @ SV2 @ xT @ xS )
= $false ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(49,plain,
! [SV1: $i,SV3: $i] :
( ( ( ~ ( aSubsetOf0 @ SV3 @ SV1 )
| ! [SY8: $i,SY9: $i] :
( ~ ~ ( ~ ( aSupremumOfIn0 @ SY8 @ SV3 @ SV1 )
| ~ ( aSupremumOfIn0 @ SY9 @ SV3 @ SV1 ) )
| ( SY8 = SY9 ) ) )
= $true )
| ( ( aSet0 @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(50,plain,
! [SV1: $i,SV3: $i] :
( ( ( ~ ( aSubsetOf0 @ SV3 @ SV1 ) )
= $true )
| ( ( ! [SY8: $i,SY9: $i] :
( ~ ~ ( ~ ( aSupremumOfIn0 @ SY8 @ SV3 @ SV1 )
| ~ ( aSupremumOfIn0 @ SY9 @ SV3 @ SV1 ) )
| ( SY8 = SY9 ) ) )
= $true )
| ( ( aSet0 @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[49]) ).
thf(51,plain,
! [SV1: $i,SV3: $i] :
( ( ( aSubsetOf0 @ SV3 @ SV1 )
= $false )
| ( ( ! [SY8: $i,SY9: $i] :
( ~ ~ ( ~ ( aSupremumOfIn0 @ SY8 @ SV3 @ SV1 )
| ~ ( aSupremumOfIn0 @ SY9 @ SV3 @ SV1 ) )
| ( SY8 = SY9 ) ) )
= $true )
| ( ( aSet0 @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(52,plain,
! [SV1: $i,SV3: $i,SV4: $i] :
( ( ( ! [SY10: $i] :
( ~ ~ ( ~ ( aSupremumOfIn0 @ SV4 @ SV3 @ SV1 )
| ~ ( aSupremumOfIn0 @ SY10 @ SV3 @ SV1 ) )
| ( SV4 = SY10 ) ) )
= $true )
| ( ( aSubsetOf0 @ SV3 @ SV1 )
= $false )
| ( ( aSet0 @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(53,plain,
! [SV5: $i,SV1: $i,SV3: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ( aSupremumOfIn0 @ SV4 @ SV3 @ SV1 )
| ~ ( aSupremumOfIn0 @ SV5 @ SV3 @ SV1 ) )
| ( SV4 = SV5 ) )
= $true )
| ( ( aSubsetOf0 @ SV3 @ SV1 )
= $false )
| ( ( aSet0 @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(54,plain,
! [SV5: $i,SV1: $i,SV3: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ( aSupremumOfIn0 @ SV4 @ SV3 @ SV1 )
| ~ ( aSupremumOfIn0 @ SV5 @ SV3 @ SV1 ) ) )
= $true )
| ( ( SV4 = SV5 )
= $true )
| ( ( aSubsetOf0 @ SV3 @ SV1 )
= $false )
| ( ( aSet0 @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[53]) ).
thf(55,plain,
! [SV5: $i,SV1: $i,SV3: $i,SV4: $i] :
( ( ( ~ ( ~ ( aSupremumOfIn0 @ SV4 @ SV3 @ SV1 )
| ~ ( aSupremumOfIn0 @ SV5 @ SV3 @ SV1 ) ) )
= $false )
| ( ( SV4 = SV5 )
= $true )
| ( ( aSubsetOf0 @ SV3 @ SV1 )
= $false )
| ( ( aSet0 @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(56,plain,
! [SV5: $i,SV1: $i,SV3: $i,SV4: $i] :
( ( ( ~ ( aSupremumOfIn0 @ SV4 @ SV3 @ SV1 )
| ~ ( aSupremumOfIn0 @ SV5 @ SV3 @ SV1 ) )
= $true )
| ( ( SV4 = SV5 )
= $true )
| ( ( aSubsetOf0 @ SV3 @ SV1 )
= $false )
| ( ( aSet0 @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[55]) ).
thf(57,plain,
! [SV5: $i,SV1: $i,SV3: $i,SV4: $i] :
( ( ( ~ ( aSupremumOfIn0 @ SV4 @ SV3 @ SV1 ) )
= $true )
| ( ( ~ ( aSupremumOfIn0 @ SV5 @ SV3 @ SV1 ) )
= $true )
| ( ( SV4 = SV5 )
= $true )
| ( ( aSubsetOf0 @ SV3 @ SV1 )
= $false )
| ( ( aSet0 @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[56]) ).
thf(58,plain,
! [SV5: $i,SV1: $i,SV3: $i,SV4: $i] :
( ( ( aSupremumOfIn0 @ SV4 @ SV3 @ SV1 )
= $false )
| ( ( ~ ( aSupremumOfIn0 @ SV5 @ SV3 @ SV1 ) )
= $true )
| ( ( SV4 = SV5 )
= $true )
| ( ( aSubsetOf0 @ SV3 @ SV1 )
= $false )
| ( ( aSet0 @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(59,plain,
! [SV4: $i,SV1: $i,SV3: $i,SV5: $i] :
( ( ( aSupremumOfIn0 @ SV5 @ SV3 @ SV1 )
= $false )
| ( ( aSupremumOfIn0 @ SV4 @ SV3 @ SV1 )
= $false )
| ( ( SV4 = SV5 )
= $true )
| ( ( aSubsetOf0 @ SV3 @ SV1 )
= $false )
| ( ( aSet0 @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(60,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[29,59,48,46,45,30]) ).
thf(61,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT388+1 : TPTP v9.3.1. Released v4.0.0.
% 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
% 0.11/0.20 % Computer : n013.cluster.edu
% 0.11/0.20 % Model : x86_64 x86_64
% 0.11/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.20 % Memory : 8046.5625MB
% 0.11/0.20 % OS : Linux 6.8.0-71-generic
% 0.11/0.20 % CPULimit : 300
% 0.11/0.20 % WCLimit : 300
% 0.11/0.20 % DateTime : Tue Oct 6 12:04:36 UTC 2026
% 0.11/0.20 % CPUTime :
% 0.11/0.20 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.28
% 0.11/0.28 No.of.Axioms: 4
% 0.11/0.28
% 0.11/0.28 Length.of.Defs: 0
% 0.11/0.28
% 0.11/0.28 Contains.Choice.Funs: false
% 0.11/0.28 .
% 0.11/0.28
% 0.11/0.28 ********************************
% 0.11/0.28 * All subproblems solved! *
% 0.11/0.28 ********************************
% 0.11/0.28 % SZS status Theorem for /export/starexec/sandbox2/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:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:60,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.11/0.28
% 0.11/0.28 %**** Beginning of derivation protocol ****
% 0.11/0.28 % SZS output start CNFRefutation
% See solution above
% 0.11/0.28
% 0.11/0.28 %**** End of derivation protocol ****
% 0.11/0.28 %**** no. of clauses in derivation: 45 ****
% 0.11/0.28 %**** clause counter: 60 ****
% 0.11/0.28
% 0.11/0.28 % SZS status Theorem for /export/starexec/sandbox2/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:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:60,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------