%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : NUM561+2 : 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 10:34:27 AM UTC 2026
% Result : Theorem 0.08s 0.25s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 3
% Syntax : Number of formulae : 24 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 92 ( 38 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 229 ( 34 ~; 17 |; 5 &; 173 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 26 usr; 7 con; 0-2 aty)
% Number of variables : 15 ( 0 ^; 10 !; 5 ?; 15 :)
% 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_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_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_xF,type,
xF: $i ).
thf(tp_xx,type,
xx: $i ).
thf(59,axiom,
aElementOf0 @ xx @ ( szDzozmdt0 @ xF ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2911_02) ).
thf(60,axiom,
aFunction0 @ xF,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2911) ).
thf(61,conjecture,
( ? [W0: $i] :
( ( aElementOf0 @ W0 @ ( szDzozmdt0 @ xF ) )
& ( ( sdtlpdtrp0 @ xF @ W0 )
= ( sdtlpdtrp0 @ xF @ xx ) ) )
| ( aElementOf0 @ ( sdtlpdtrp0 @ xF @ xx ) @ ( sdtlcdtrc0 @ xF @ ( szDzozmdt0 @ xF ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
thf(62,negated_conjecture,
( ( ? [W0: $i] :
( ( aElementOf0 @ W0 @ ( szDzozmdt0 @ xF ) )
& ( ( sdtlpdtrp0 @ xF @ W0 )
= ( sdtlpdtrp0 @ xF @ xx ) ) )
| ( aElementOf0 @ ( sdtlpdtrp0 @ xF @ xx ) @ ( sdtlcdtrc0 @ xF @ ( szDzozmdt0 @ xF ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[61]) ).
thf(63,plain,
( ( ? [W0: $i] :
( ( aElementOf0 @ W0 @ ( szDzozmdt0 @ xF ) )
& ( ( sdtlpdtrp0 @ xF @ W0 )
= ( sdtlpdtrp0 @ xF @ xx ) ) )
| ( aElementOf0 @ ( sdtlpdtrp0 @ xF @ xx ) @ ( sdtlcdtrc0 @ xF @ ( szDzozmdt0 @ xF ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[62]) ).
thf(64,plain,
( ( aElementOf0 @ xx @ ( szDzozmdt0 @ xF ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(65,plain,
( ( aFunction0 @ xF )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(66,plain,
( ( ~ ( ? [W0: $i] :
( ( aElementOf0 @ W0 @ ( szDzozmdt0 @ xF ) )
& ( ( sdtlpdtrp0 @ xF @ W0 )
= ( sdtlpdtrp0 @ xF @ xx ) ) )
| ( aElementOf0 @ ( sdtlpdtrp0 @ xF @ xx ) @ ( sdtlcdtrc0 @ xF @ ( szDzozmdt0 @ xF ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[63]) ).
thf(67,plain,
( ( aFunction0 @ xF )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(68,plain,
( ( aElementOf0 @ xx @ ( szDzozmdt0 @ xF ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(69,plain,
( ( ~ ( ? [W0: $i] :
( ( aElementOf0 @ W0 @ ( szDzozmdt0 @ xF ) )
& ( ( sdtlpdtrp0 @ xF @ W0 )
= ( sdtlpdtrp0 @ xF @ xx ) ) )
| ( aElementOf0 @ ( sdtlpdtrp0 @ xF @ xx ) @ ( sdtlcdtrc0 @ xF @ ( szDzozmdt0 @ xF ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(70,plain,
( ( ~ ( ~ ! [SX0: $i] :
~ ~ ( ~ ( aElementOf0 @ SX0 @ ( szDzozmdt0 @ xF ) )
| ( ( sdtlpdtrp0 @ xF @ SX0 )
!= ( sdtlpdtrp0 @ xF @ xx ) ) )
| ( aElementOf0 @ ( sdtlpdtrp0 @ xF @ xx ) @ ( sdtlcdtrc0 @ xF @ ( szDzozmdt0 @ xF ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(71,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( aElementOf0 @ SX0 @ ( szDzozmdt0 @ xF ) )
| ( ( sdtlpdtrp0 @ xF @ SX0 )
!= ( sdtlpdtrp0 @ xF @ xx ) ) )
| ( aElementOf0 @ ( sdtlpdtrp0 @ xF @ xx ) @ ( sdtlcdtrc0 @ xF @ ( szDzozmdt0 @ xF ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(72,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( aElementOf0 @ SX0 @ ( szDzozmdt0 @ xF ) )
| ( ( sdtlpdtrp0 @ xF @ SX0 )
!= ( sdtlpdtrp0 @ xF @ xx ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[71]) ).
thf(73,plain,
( ( aElementOf0 @ ( sdtlpdtrp0 @ xF @ xx ) @ ( sdtlcdtrc0 @ xF @ ( szDzozmdt0 @ xF ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[71]) ).
thf(74,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( aElementOf0 @ SX0 @ ( szDzozmdt0 @ xF ) )
| ( ( sdtlpdtrp0 @ xF @ SX0 )
!= ( sdtlpdtrp0 @ xF @ xx ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[72]) ).
thf(75,plain,
! [SV1: $i] :
( ( ~ ~ ( ~ ( aElementOf0 @ SV1 @ ( szDzozmdt0 @ xF ) )
| ( ( sdtlpdtrp0 @ xF @ SV1 )
!= ( sdtlpdtrp0 @ xF @ xx ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(76,plain,
! [SV1: $i] :
( ( ~ ( ~ ( aElementOf0 @ SV1 @ ( szDzozmdt0 @ xF ) )
| ( ( sdtlpdtrp0 @ xF @ SV1 )
!= ( sdtlpdtrp0 @ xF @ xx ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(77,plain,
! [SV1: $i] :
( ( ~ ( aElementOf0 @ SV1 @ ( szDzozmdt0 @ xF ) )
| ( ( sdtlpdtrp0 @ xF @ SV1 )
!= ( sdtlpdtrp0 @ xF @ xx ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[76]) ).
thf(78,plain,
! [SV1: $i] :
( ( ( ~ ( aElementOf0 @ SV1 @ ( szDzozmdt0 @ xF ) ) )
= $true )
| ( ( ( sdtlpdtrp0 @ xF @ SV1 )
!= ( sdtlpdtrp0 @ xF @ xx ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[77]) ).
thf(79,plain,
! [SV1: $i] :
( ( ( aElementOf0 @ SV1 @ ( szDzozmdt0 @ xF ) )
= $false )
| ( ( ( sdtlpdtrp0 @ xF @ SV1 )
!= ( sdtlpdtrp0 @ xF @ xx ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(80,plain,
! [SV1: $i] :
( ( ( ( sdtlpdtrp0 @ xF @ SV1 )
= ( sdtlpdtrp0 @ xF @ xx ) )
= $false )
| ( ( aElementOf0 @ SV1 @ ( szDzozmdt0 @ xF ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(81,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[67,80,73,68]) ).
thf(82,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[81]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM561+2 : 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
% 0.08/0.19 % Computer : n013.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Oct 6 13:24:36 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.25
% 0.08/0.25 No.of.Axioms: 2
% 0.08/0.25
% 0.08/0.25 Length.of.Defs: 0
% 0.08/0.25
% 0.08/0.25 Contains.Choice.Funs: false
% 0.08/0.25 .
% 0.08/0.25
% 0.08/0.25 ********************************
% 0.08/0.25 * All subproblems solved! *
% 0.08/0.25 ********************************
% 0.08/0.25 % 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:81,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.08/0.25
% 0.08/0.25 %**** Beginning of derivation protocol ****
% 0.08/0.25 % SZS output start CNFRefutation
% See solution above
% 0.08/0.25
% 0.08/0.25 %**** End of derivation protocol ****
% 0.08/0.25 %**** no. of clauses in derivation: 24 ****
% 0.08/0.25 %**** clause counter: 81 ****
% 0.08/0.25
% 0.08/0.25 % 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:81,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------