%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : NUM615+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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 10:34:38 AM UTC 2026
% Result : Theorem 1.20s 0.40s
% Output : CNFRefutation 1.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 3
% Syntax : Number of formulae : 38 ( 26 unt; 0 typ; 0 def)
% Number of atoms : 195 ( 98 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 455 ( 87 ~; 48 |; 13 &; 307 @)
% ( 0 <=>; 0 =>; 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 : 43 ( 40 usr; 19 con; 0-2 aty)
% Number of variables : 26 ( 0 ^; 18 !; 8 ?; 26 :)
% 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_sK1_SX0,type,
sK1_SX0: $i ).
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_xp,type,
xp: $i ).
thf(66,axiom,
? [W0: $i] :
( ( aElementOf0 @ W0 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
& ( ( sdtlpdtrp0 @ xe @ W0 )
= xp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5182) ).
thf(67,axiom,
aElementOf0 @ xp @ xQ,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5173) ).
thf(100,conjecture,
? [W0: $i] :
( ( ( ( aElementOf0 @ W0 @ ( szDzozmdt0 @ xd ) )
& ( ( sdtlpdtrp0 @ xd @ W0 )
= ( szDzizrdt0 @ xd ) ) )
| ( aElementOf0 @ W0 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) ) )
& ( ( sdtlpdtrp0 @ xe @ W0 )
= xp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
thf(101,negated_conjecture,
( ( ? [W0: $i] :
( ( ( ( aElementOf0 @ W0 @ ( szDzozmdt0 @ xd ) )
& ( ( sdtlpdtrp0 @ xd @ W0 )
= ( szDzizrdt0 @ xd ) ) )
| ( aElementOf0 @ W0 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) ) )
& ( ( sdtlpdtrp0 @ xe @ W0 )
= xp ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[100]) ).
thf(102,plain,
( ( ? [W0: $i] :
( ( ( ( aElementOf0 @ W0 @ ( szDzozmdt0 @ xd ) )
& ( ( sdtlpdtrp0 @ xd @ W0 )
= ( szDzizrdt0 @ xd ) ) )
| ( aElementOf0 @ W0 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) ) )
& ( ( sdtlpdtrp0 @ xe @ W0 )
= xp ) ) )
= $false ),
inference(unfold_def,[status(thm)],[101]) ).
thf(103,plain,
( ( ? [W0: $i] :
( ( aElementOf0 @ W0 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
& ( ( sdtlpdtrp0 @ xe @ W0 )
= xp ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(104,plain,
( ( aElementOf0 @ xp @ xQ )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(105,plain,
( ( ~ ? [W0: $i] :
( ( ( ( aElementOf0 @ W0 @ ( szDzozmdt0 @ xd ) )
& ( ( sdtlpdtrp0 @ xd @ W0 )
= ( szDzizrdt0 @ xd ) ) )
| ( aElementOf0 @ W0 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) ) )
& ( ( sdtlpdtrp0 @ xe @ W0 )
= xp ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[102]) ).
thf(106,plain,
( ( aElementOf0 @ xp @ xQ )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(107,plain,
( ( ? [W0: $i] :
( ( aElementOf0 @ W0 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
& ( ( sdtlpdtrp0 @ xe @ W0 )
= xp ) ) )
= $true ),
inference(copy,[status(thm)],[103]) ).
thf(108,plain,
( ( ~ ? [W0: $i] :
( ( ( ( aElementOf0 @ W0 @ ( szDzozmdt0 @ xd ) )
& ( ( sdtlpdtrp0 @ xd @ W0 )
= ( szDzizrdt0 @ xd ) ) )
| ( aElementOf0 @ W0 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) ) )
& ( ( sdtlpdtrp0 @ xe @ W0 )
= xp ) ) )
= $true ),
inference(copy,[status(thm)],[105]) ).
thf(109,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( aElementOf0 @ SX0 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
| ( ( sdtlpdtrp0 @ xe @ SX0 )
!= xp ) ) )
= $true ),
inference(unfold_def,[status(thm)],[107]) ).
thf(110,plain,
( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( ~ ( ~ ( aElementOf0 @ SX0 @ ( szDzozmdt0 @ xd ) )
| ( ( sdtlpdtrp0 @ xd @ SX0 )
!= ( szDzizrdt0 @ xd ) ) )
| ( aElementOf0 @ SX0 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) ) )
| ( ( sdtlpdtrp0 @ xe @ SX0 )
!= xp ) ) )
= $true ),
inference(unfold_def,[status(thm)],[108]) ).
thf(111,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( aElementOf0 @ SX0 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
| ( ( sdtlpdtrp0 @ xe @ SX0 )
!= xp ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(112,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( ~ ( ~ ( aElementOf0 @ SX0 @ ( szDzozmdt0 @ xd ) )
| ( ( sdtlpdtrp0 @ xd @ SX0 )
!= ( szDzizrdt0 @ xd ) ) )
| ( aElementOf0 @ SX0 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) ) )
| ( ( sdtlpdtrp0 @ xe @ SX0 )
!= xp ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(113,plain,
( ( ~ ~ ( ~ ( aElementOf0 @ sK1_SX0 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
| ( ( sdtlpdtrp0 @ xe @ sK1_SX0 )
!= xp ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[111]) ).
thf(114,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( ~ ( ~ ( aElementOf0 @ SX0 @ ( szDzozmdt0 @ xd ) )
| ( ( sdtlpdtrp0 @ xd @ SX0 )
!= ( szDzizrdt0 @ xd ) ) )
| ( aElementOf0 @ SX0 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) ) )
| ( ( sdtlpdtrp0 @ xe @ SX0 )
!= xp ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[112]) ).
thf(115,plain,
( ( ~ ( ~ ( aElementOf0 @ sK1_SX0 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
| ( ( sdtlpdtrp0 @ xe @ sK1_SX0 )
!= xp ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[113]) ).
thf(116,plain,
! [SV1: $i] :
( ( ~ ~ ( ~ ( ~ ( ~ ( aElementOf0 @ SV1 @ ( szDzozmdt0 @ xd ) )
| ( ( sdtlpdtrp0 @ xd @ SV1 )
!= ( szDzizrdt0 @ xd ) ) )
| ( aElementOf0 @ SV1 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) ) )
| ( ( sdtlpdtrp0 @ xe @ SV1 )
!= xp ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(117,plain,
( ( ~ ( aElementOf0 @ sK1_SX0 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
| ( ( sdtlpdtrp0 @ xe @ sK1_SX0 )
!= xp ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(118,plain,
! [SV1: $i] :
( ( ~ ( ~ ( ~ ( ~ ( aElementOf0 @ SV1 @ ( szDzozmdt0 @ xd ) )
| ( ( sdtlpdtrp0 @ xd @ SV1 )
!= ( szDzizrdt0 @ xd ) ) )
| ( aElementOf0 @ SV1 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) ) )
| ( ( sdtlpdtrp0 @ xe @ SV1 )
!= xp ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(119,plain,
( ( ~ ( aElementOf0 @ sK1_SX0 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[117]) ).
thf(120,plain,
( ( ( sdtlpdtrp0 @ xe @ sK1_SX0 )
!= xp )
= $false ),
inference(extcnf_or_neg,[status(thm)],[117]) ).
thf(121,plain,
! [SV1: $i] :
( ( ~ ( ~ ( ~ ( aElementOf0 @ SV1 @ ( szDzozmdt0 @ xd ) )
| ( ( sdtlpdtrp0 @ xd @ SV1 )
!= ( szDzizrdt0 @ xd ) ) )
| ( aElementOf0 @ SV1 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) ) )
| ( ( sdtlpdtrp0 @ xe @ SV1 )
!= xp ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[118]) ).
thf(122,plain,
( ( aElementOf0 @ sK1_SX0 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[119]) ).
thf(123,plain,
( ( ( sdtlpdtrp0 @ xe @ sK1_SX0 )
= xp )
= $true ),
inference(extcnf_not_neg,[status(thm)],[120]) ).
thf(124,plain,
! [SV1: $i] :
( ( ( ~ ( ~ ( ~ ( aElementOf0 @ SV1 @ ( szDzozmdt0 @ xd ) )
| ( ( sdtlpdtrp0 @ xd @ SV1 )
!= ( szDzizrdt0 @ xd ) ) )
| ( aElementOf0 @ SV1 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) ) ) )
= $true )
| ( ( ( sdtlpdtrp0 @ xe @ SV1 )
!= xp )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[121]) ).
thf(125,plain,
! [SV1: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ SV1 @ ( szDzozmdt0 @ xd ) )
| ( ( sdtlpdtrp0 @ xd @ SV1 )
!= ( szDzizrdt0 @ xd ) ) )
| ( aElementOf0 @ SV1 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) ) )
= $false )
| ( ( ( sdtlpdtrp0 @ xe @ SV1 )
!= xp )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(126,plain,
! [SV1: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ SV1 @ ( szDzozmdt0 @ xd ) )
| ( ( sdtlpdtrp0 @ xd @ SV1 )
!= ( szDzizrdt0 @ xd ) ) ) )
= $false )
| ( ( ( sdtlpdtrp0 @ xe @ SV1 )
!= xp )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[125]) ).
thf(127,plain,
! [SV1: $i] :
( ( ( aElementOf0 @ SV1 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
= $false )
| ( ( ( sdtlpdtrp0 @ xe @ SV1 )
!= xp )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[125]) ).
thf(128,plain,
! [SV1: $i] :
( ( ( ~ ( aElementOf0 @ SV1 @ ( szDzozmdt0 @ xd ) )
| ( ( sdtlpdtrp0 @ xd @ SV1 )
!= ( szDzizrdt0 @ xd ) ) )
= $true )
| ( ( ( sdtlpdtrp0 @ xe @ SV1 )
!= xp )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[126]) ).
thf(129,plain,
! [SV1: $i] :
( ( ( ( sdtlpdtrp0 @ xe @ SV1 )
= xp )
= $false )
| ( ( aElementOf0 @ SV1 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[127]) ).
thf(130,plain,
! [SV1: $i] :
( ( ( ~ ( aElementOf0 @ SV1 @ ( szDzozmdt0 @ xd ) ) )
= $true )
| ( ( ( sdtlpdtrp0 @ xd @ SV1 )
!= ( szDzizrdt0 @ xd ) )
= $true )
| ( ( ( sdtlpdtrp0 @ xe @ SV1 )
!= xp )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[128]) ).
thf(131,plain,
! [SV1: $i] :
( ( ( aElementOf0 @ SV1 @ ( szDzozmdt0 @ xd ) )
= $false )
| ( ( ( sdtlpdtrp0 @ xd @ SV1 )
!= ( szDzizrdt0 @ xd ) )
= $true )
| ( ( ( sdtlpdtrp0 @ xe @ SV1 )
!= xp )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[130]) ).
thf(132,plain,
! [SV1: $i] :
( ( ( ( sdtlpdtrp0 @ xd @ SV1 )
= ( szDzizrdt0 @ xd ) )
= $false )
| ( ( aElementOf0 @ SV1 @ ( szDzozmdt0 @ xd ) )
= $false )
| ( ( ( sdtlpdtrp0 @ xe @ SV1 )
!= xp )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(133,plain,
! [SV1: $i] :
( ( ( ( sdtlpdtrp0 @ xe @ SV1 )
= xp )
= $false )
| ( ( aElementOf0 @ SV1 @ ( szDzozmdt0 @ xd ) )
= $false )
| ( ( ( sdtlpdtrp0 @ xd @ SV1 )
= ( szDzizrdt0 @ xd ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(134,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[106,133,129,123,122]) ).
thf(135,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[134]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM615+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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.18 % Computer : n020.cluster.edu
% 0.11/0.18 % Model : x86_64 x86_64
% 0.11/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.18 % Memory : 8046.5625MB
% 0.11/0.18 % OS : Linux 6.8.0-71-generic
% 0.11/0.18 % CPULimit : 300
% 0.11/0.18 % WCLimit : 300
% 0.11/0.18 % DateTime : Tue Oct 6 13:30:27 UTC 2026
% 0.11/0.19 % CPUTime :
% 0.11/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.20/0.40
% 1.20/0.40 No.of.Axioms: 2
% 1.20/0.40
% 1.20/0.40 Length.of.Defs: 0
% 1.20/0.40
% 1.20/0.40 Contains.Choice.Funs: false
% 1.20/0.40 ..
% 1.20/0.40
% 1.20/0.40 ********************************
% 1.20/0.40 * All subproblems solved! *
% 1.20/0.40 ********************************
% 1.20/0.40 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:2,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:134,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.20/0.40
% 1.20/0.40 %**** Beginning of derivation protocol ****
% 1.20/0.40 % SZS output start CNFRefutation
% See solution above
% 1.20/0.41
% 1.20/0.41 %**** End of derivation protocol ****
% 1.20/0.41 %**** no. of clauses in derivation: 38 ****
% 1.20/0.41 %**** clause counter: 134 ****
% 1.20/0.41
% 1.20/0.41 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:2,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:134,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------