%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU519^2 : TPTP v9.3.1. Released v3.7.0.
% 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 : n018.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 10:44:44 AM UTC 2026
% Result : Theorem 0.18s 0.28s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 32 ( 20 unt; 0 typ; 2 def)
% Number of atoms : 145 ( 41 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 197 ( 16 ~; 22 |; 0 &; 141 @)
% ( 0 <=>; 18 =>; 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 : 10 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 62 ( 0 ^; 62 !; 0 ?; 62 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_emptyset,type,
emptyset: $i ).
thf(tp_emptysetE,type,
emptysetE: $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_powersetI,type,
powersetI: $o ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY10,type,
sK2_SY10: $i > $i > $i ).
thf(emptysetE,definition,
( emptysetE
= ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> ! [Xphi: $o] : Xphi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetE) ).
thf(powersetI,definition,
( powersetI
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( in @ B @ ( powerset @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI) ).
thf(1,conjecture,
( emptysetE
=> ( powersetI
=> ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyinPowerset) ).
thf(2,negated_conjecture,
( ( emptysetE
=> ( powersetI
=> ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> ! [Xphi: $o] : Xphi )
=> ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( in @ B @ ( powerset @ A ) ) )
=> ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,emptysetE,powersetI]) ).
thf(4,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> ! [Xphi: $o] : Xphi ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( in @ B @ ( powerset @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ~ ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(8,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( in @ B @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(9,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> ! [Xphi: $o] : Xphi ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(10,plain,
( ( ~ ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(11,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) )
| ( in @ SX1 @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8,emptysetE,powersetI]) ).
thf(12,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ emptyset )
| ! [SX1: $o] : SX1 ) )
= $true ),
inference(unfold_def,[status(thm)],[9,emptysetE,powersetI]) ).
thf(13,plain,
( ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[10]) ).
thf(14,plain,
! [SV1: $i] :
( ( ! [SY7: $i] :
( ~ ! [SY8: $i] :
( ~ ( in @ SY8 @ SY7 )
| ( in @ SY8 @ SV1 ) )
| ( in @ SY7 @ ( powerset @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(15,plain,
! [SV2: $i] :
( ( ~ ( in @ SV2 @ emptyset )
| ! [SX1: $o] : SX1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(16,plain,
( ( in @ emptyset @ ( powerset @ sK1_A ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[13]) ).
thf(17,plain,
! [SV1: $i,SV3: $i] :
( ( ~ ! [SY10: $i] :
( ~ ( in @ SY10 @ SV3 )
| ( in @ SY10 @ SV1 ) )
| ( in @ SV3 @ ( powerset @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(18,plain,
! [SV2: $i] :
( ( ( ~ ( in @ SV2 @ emptyset ) )
= $true )
| ( ( ! [SX1: $o] : SX1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[15]) ).
thf(19,plain,
! [SV1: $i,SV3: $i] :
( ( ( ~ ! [SY10: $i] :
( ~ ( in @ SY10 @ SV3 )
| ( in @ SY10 @ SV1 ) ) )
= $true )
| ( ( in @ SV3 @ ( powerset @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[17]) ).
thf(20,plain,
! [SV2: $i] :
( ( ( in @ SV2 @ emptyset )
= $false )
| ( ( ! [SX1: $o] : SX1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(21,plain,
! [SV1: $i,SV3: $i] :
( ( ( ! [SY10: $i] :
( ~ ( in @ SY10 @ SV3 )
| ( in @ SY10 @ SV1 ) ) )
= $false )
| ( ( in @ SV3 @ ( powerset @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[19]) ).
thf(22,plain,
! [SV2: $i,SV4: $o] :
( ( SV4 = $true )
| ( ( in @ SV2 @ emptyset )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[20]) ).
thf(23,plain,
! [SV2: $i] :
( ( $true = $true )
| ( ( in @ SV2 @ emptyset )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[20]) ).
thf(24,plain,
! [SV2: $i] :
( ( $false = $true )
| ( ( in @ SV2 @ emptyset )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[20]) ).
thf(25,plain,
! [SV3: $i,SV1: $i] :
( ( ( ~ ( in @ ( sK2_SY10 @ SV1 @ SV3 ) @ SV3 )
| ( in @ ( sK2_SY10 @ SV1 @ SV3 ) @ SV1 ) )
= $false )
| ( ( in @ SV3 @ ( powerset @ SV1 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[21]) ).
thf(26,plain,
! [SV3: $i,SV1: $i] :
( ( ( ~ ( in @ ( sK2_SY10 @ SV1 @ SV3 ) @ SV3 ) )
= $false )
| ( ( in @ SV3 @ ( powerset @ SV1 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[25]) ).
thf(27,plain,
! [SV3: $i,SV1: $i] :
( ( ( in @ ( sK2_SY10 @ SV1 @ SV3 ) @ SV1 )
= $false )
| ( ( in @ SV3 @ ( powerset @ SV1 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[25]) ).
thf(28,plain,
! [SV3: $i,SV1: $i] :
( ( ( in @ ( sK2_SY10 @ SV1 @ SV3 ) @ SV3 )
= $true )
| ( ( in @ SV3 @ ( powerset @ SV1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[26]) ).
thf(29,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[16,28,27,24,23,22]) ).
thf(30,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU519^2 : TPTP v9.3.1. Released v3.7.0.
% 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
% 0.07/0.25 % Computer : n018.cluster.edu
% 0.07/0.25 % Model : x86_64 x86_64
% 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.25 % Memory : 8046.5625MB
% 0.07/0.25 % OS : Linux 6.8.0-71-generic
% 0.07/0.25 % CPULimit : 300
% 0.07/0.25 % WCLimit : 300
% 0.07/0.25 % DateTime : Tue Oct 6 15:29:52 UTC 2026
% 0.07/0.26 % CPUTime :
% 0.07/0.26 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.28
% 0.18/0.28 No.of.Axioms: 0
% 0.18/0.28
% 0.18/0.28 Length.of.Defs: 359
% 0.18/0.28
% 0.18/0.28 Contains.Choice.Funs: false
% 0.18/0.28
% 0.18/0.28 ********************************
% 0.18/0.28 * All subproblems solved! *
% 0.18/0.28 ********************************
% 0.18/0.28 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:2,ps:3,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:29,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.18/0.28
% 0.18/0.28 %**** Beginning of derivation protocol ****
% 0.18/0.28 % SZS output start CNFRefutation
% See solution above
% 0.18/0.28
% 0.18/0.28 %**** End of derivation protocol ****
% 0.18/0.28 %**** no. of clauses in derivation: 30 ****
% 0.18/0.28 %**** clause counter: 29 ****
% 0.18/0.28
% 0.18/0.28 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:2,ps:3,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:29,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------