%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : NUM626+3 : 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/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 10:34:40 AM UTC 2026
% Result : Theorem 0.75s 0.40s
% Output : CNFRefutation 0.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 42 ( 28 unt; 0 typ; 0 def)
% Number of atoms : 205 ( 93 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 246 ( 53 ~; 40 |; 6 &; 138 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 45 ( 42 usr; 21 con; 0-2 aty)
% Number of variables : 36 ( 0 ^; 36 !; 0 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_aElement0,type,
aElement0: $i > $o ).
thf(tp_aElementOf0,type,
aElementOf0: $i > $i > $o ).
thf(tp_aFunction0,type,
aFunction0: $i > $o ).
thf(tp_aSet0,type,
aSet0: $i > $o ).
thf(tp_aSubsetOf0,type,
aSubsetOf0: $i > $i > $o ).
thf(tp_iLess0,type,
iLess0: $i > $i > $o ).
thf(tp_isCountable0,type,
isCountable0: $i > $o ).
thf(tp_isFinite0,type,
isFinite0: $i > $o ).
thf(tp_sbrdtbr0,type,
sbrdtbr0: $i > $i ).
thf(tp_sdtexdt0,type,
sdtexdt0: $i > $i > $i ).
thf(tp_sdtlbdtrb0,type,
sdtlbdtrb0: $i > $i > $i ).
thf(tp_sdtlcdtrc0,type,
sdtlcdtrc0: $i > $i > $i ).
thf(tp_sdtlpdtrp0,type,
sdtlpdtrp0: $i > $i > $i ).
thf(tp_sdtlseqdt0,type,
sdtlseqdt0: $i > $i > $o ).
thf(tp_sdtmndt0,type,
sdtmndt0: $i > $i > $i ).
thf(tp_sdtpldt0,type,
sdtpldt0: $i > $i > $i ).
thf(tp_slbdtrb0,type,
slbdtrb0: $i > $i ).
thf(tp_slbdtsldtrb0,type,
slbdtsldtrb0: $i > $i > $i ).
thf(tp_slcrc0,type,
slcrc0: $i ).
thf(tp_sz00,type,
sz00: $i ).
thf(tp_szDzizrdt0,type,
szDzizrdt0: $i > $i ).
thf(tp_szDzozmdt0,type,
szDzozmdt0: $i > $i ).
thf(tp_szNzAzT0,type,
szNzAzT0: $i ).
thf(tp_szmzazxdt0,type,
szmzazxdt0: $i > $i ).
thf(tp_szmzizndt0,type,
szmzizndt0: $i > $i ).
thf(tp_szszuzczcdt0,type,
szszuzczcdt0: $i > $i ).
thf(tp_xC,type,
xC: $i ).
thf(tp_xK,type,
xK: $i ).
thf(tp_xN,type,
xN: $i ).
thf(tp_xO,type,
xO: $i ).
thf(tp_xP,type,
xP: $i ).
thf(tp_xQ,type,
xQ: $i ).
thf(tp_xS,type,
xS: $i ).
thf(tp_xT,type,
xT: $i ).
thf(tp_xc,type,
xc: $i ).
thf(tp_xd,type,
xd: $i ).
thf(tp_xe,type,
xe: $i ).
thf(tp_xk,type,
xk: $i ).
thf(tp_xm,type,
xm: $i ).
thf(tp_xn,type,
xn: $i ).
thf(tp_xp,type,
xp: $i ).
thf(tp_xx,type,
xx: $i ).
thf(38,axiom,
! [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
=> ( W0
!= ( szszuzczcdt0 @ W0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNatNSucc) ).
thf(40,axiom,
! [W0: $i,W1: $i] :
( ( ( aElementOf0 @ W0 @ szNzAzT0 )
& ( aElementOf0 @ W1 @ szNzAzT0 ) )
=> ( ( ( szszuzczcdt0 @ W0 )
= ( szszuzczcdt0 @ W1 ) )
=> ( W0 = W1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSuccEquSucc) ).
thf(62,axiom,
( $false
& $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5538) ).
thf(63,axiom,
xp = xx,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5496) ).
thf(111,conjecture,
aElementOf0 @ xx @ ( sdtlpdtrp0 @ xN @ ( szszuzczcdt0 @ xn ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
thf(112,negated_conjecture,
( ( aElementOf0 @ xx @ ( sdtlpdtrp0 @ xN @ ( szszuzczcdt0 @ xn ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[111]) ).
thf(113,plain,
( ( aElementOf0 @ xx @ ( sdtlpdtrp0 @ xN @ ( szszuzczcdt0 @ xn ) ) )
= $false ),
inference(unfold_def,[status(thm)],[112]) ).
thf(114,plain,
( ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
=> ( W0
!= ( szszuzczcdt0 @ W0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(115,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aElementOf0 @ W0 @ szNzAzT0 )
& ( aElementOf0 @ W1 @ szNzAzT0 ) )
=> ( ( ( szszuzczcdt0 @ W0 )
= ( szszuzczcdt0 @ W1 ) )
=> ( W0 = W1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(116,plain,
( ( $false
& $false )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(117,plain,
( ( xp = xx )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(118,plain,
( ( ~ ( aElementOf0 @ xx @ ( sdtlpdtrp0 @ xN @ ( szszuzczcdt0 @ xn ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[113]) ).
thf(119,plain,
( ( xp = xx )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(120,plain,
( ( $false
& $false )
= $true ),
inference(copy,[status(thm)],[116]) ).
thf(121,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aElementOf0 @ W0 @ szNzAzT0 )
& ( aElementOf0 @ W1 @ szNzAzT0 ) )
=> ( ( ( szszuzczcdt0 @ W0 )
= ( szszuzczcdt0 @ W1 ) )
=> ( W0 = W1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[115]) ).
thf(122,plain,
( ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
=> ( W0
!= ( szszuzczcdt0 @ W0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[114]) ).
thf(123,plain,
( ( ~ ( aElementOf0 @ xx @ ( sdtlpdtrp0 @ xN @ ( szszuzczcdt0 @ xn ) ) ) )
= $true ),
inference(copy,[status(thm)],[118]) ).
thf(124,plain,
( ( ~ ( ~ $false
| ~ $false ) )
= $true ),
inference(unfold_def,[status(thm)],[120]) ).
thf(125,plain,
( ( ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ szNzAzT0 )
| ( SX0
!= ( szszuzczcdt0 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[122]) ).
thf(126,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SX0 @ szNzAzT0 )
| ~ ( aElementOf0 @ SX1 @ szNzAzT0 ) )
| ( ( szszuzczcdt0 @ SX0 )
!= ( szszuzczcdt0 @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[121]) ).
thf(127,plain,
( ( aElementOf0 @ xx @ ( sdtlpdtrp0 @ xN @ ( szszuzczcdt0 @ xn ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(128,plain,
( ( ~ $false
| ~ $false )
= $false ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(129,plain,
! [SV1: $i] :
( ( ~ ( aElementOf0 @ SV1 @ szNzAzT0 )
| ( SV1
!= ( szszuzczcdt0 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(130,plain,
! [SV2: $i] :
( ( ! [SY3: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SV2 @ szNzAzT0 )
| ~ ( aElementOf0 @ SY3 @ szNzAzT0 ) )
| ( ( szszuzczcdt0 @ SV2 )
!= ( szszuzczcdt0 @ SY3 ) )
| ( SV2 = SY3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(131,plain,
( ( ~ $false ) = $false ),
inference(extcnf_or_neg,[status(thm)],[128]) ).
thf(132,plain,
( ( ~ $false ) = $false ),
inference(extcnf_or_neg,[status(thm)],[128]) ).
thf(133,plain,
! [SV1: $i] :
( ( ( ~ ( aElementOf0 @ SV1 @ szNzAzT0 ) )
= $true )
| ( ( SV1
!= ( szszuzczcdt0 @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[129]) ).
thf(134,plain,
! [SV3: $i,SV2: $i] :
( ( ~ ~ ( ~ ( aElementOf0 @ SV2 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV3 @ szNzAzT0 ) )
| ( ( szszuzczcdt0 @ SV2 )
!= ( szszuzczcdt0 @ SV3 ) )
| ( SV2 = SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(135,plain,
$false = $true,
inference(extcnf_not_neg,[status(thm)],[131]) ).
thf(136,plain,
$false = $true,
inference(extcnf_not_neg,[status(thm)],[132]) ).
thf(137,plain,
! [SV1: $i] :
( ( ( aElementOf0 @ SV1 @ szNzAzT0 )
= $false )
| ( ( SV1
!= ( szszuzczcdt0 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(138,plain,
! [SV3: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ SV2 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV3 @ szNzAzT0 ) ) )
= $true )
| ( ( ( ( szszuzczcdt0 @ SV2 )
!= ( szszuzczcdt0 @ SV3 ) )
| ( SV2 = SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[134]) ).
thf(139,plain,
! [SV1: $i] :
( ( ( SV1
= ( szszuzczcdt0 @ SV1 ) )
= $false )
| ( ( aElementOf0 @ SV1 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(140,plain,
! [SV3: $i,SV2: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ SV2 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV3 @ szNzAzT0 ) ) )
= $false )
| ( ( ( ( szszuzczcdt0 @ SV2 )
!= ( szszuzczcdt0 @ SV3 ) )
| ( SV2 = SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(141,plain,
! [SV3: $i,SV2: $i] :
( ( ( ~ ( aElementOf0 @ SV2 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV3 @ szNzAzT0 ) )
= $true )
| ( ( ( ( szszuzczcdt0 @ SV2 )
!= ( szszuzczcdt0 @ SV3 ) )
| ( SV2 = SV3 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[140]) ).
thf(142,plain,
! [SV3: $i,SV2: $i] :
( ( ( ~ ( aElementOf0 @ SV2 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( aElementOf0 @ SV3 @ szNzAzT0 ) )
= $true )
| ( ( ( ( szszuzczcdt0 @ SV2 )
!= ( szszuzczcdt0 @ SV3 ) )
| ( SV2 = SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[141]) ).
thf(143,plain,
! [SV3: $i,SV2: $i] :
( ( ( aElementOf0 @ SV2 @ szNzAzT0 )
= $false )
| ( ( ~ ( aElementOf0 @ SV3 @ szNzAzT0 ) )
= $true )
| ( ( ( ( szszuzczcdt0 @ SV2 )
!= ( szszuzczcdt0 @ SV3 ) )
| ( SV2 = SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(144,plain,
! [SV2: $i,SV3: $i] :
( ( ( aElementOf0 @ SV3 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV2 @ szNzAzT0 )
= $false )
| ( ( ( ( szszuzczcdt0 @ SV2 )
!= ( szszuzczcdt0 @ SV3 ) )
| ( SV2 = SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[143]) ).
thf(145,plain,
! [SV3: $i,SV2: $i] :
( ( ( ( szszuzczcdt0 @ SV2 )
!= ( szszuzczcdt0 @ SV3 ) )
= $true )
| ( ( SV2 = SV3 )
= $true )
| ( ( aElementOf0 @ SV2 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV3 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[144]) ).
thf(146,plain,
! [SV3: $i,SV2: $i] :
( ( ( ( szszuzczcdt0 @ SV2 )
= ( szszuzczcdt0 @ SV3 ) )
= $false )
| ( ( SV2 = SV3 )
= $true )
| ( ( aElementOf0 @ SV2 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV3 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[145]) ).
thf(147,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[119,146,139,136,135,127]) ).
thf(148,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[147]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM626+3 : 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.18 % Computer : n017.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Tue Oct 6 13:26:32 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.75/0.40 .
% 0.75/0.40
% 0.75/0.40 No.of.Axioms: 4
% 0.75/0.40
% 0.75/0.40 Length.of.Defs: 0
% 0.75/0.40
% 0.75/0.40 Contains.Choice.Funs: false
% 0.75/0.40 .
% 0.75/0.40
% 0.75/0.40 ********************************
% 0.75/0.40 * All subproblems solved! *
% 0.75/0.40 ********************************
% 0.75/0.40 % 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:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:147,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.75/0.40
% 0.75/0.40 %**** Beginning of derivation protocol ****
% 0.75/0.40 % SZS output start CNFRefutation
% See solution above
% 0.75/0.40
% 0.75/0.40 %**** End of derivation protocol ****
% 0.75/0.40 %**** no. of clauses in derivation: 42 ****
% 0.75/0.40 %**** clause counter: 147 ****
% 0.75/0.40
% 0.75/0.40 % 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:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:147,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------