%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET062+3 : TPTP v9.3.1. Released v2.2.0.
% 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 : 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 10:39:14 AM UTC 2026
% Result : Theorem 0.07s 0.24s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 4
% Syntax : Number of formulae : 40 ( 28 unt; 0 typ; 0 def)
% Number of atoms : 189 ( 48 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 298 ( 53 ~; 47 |; 0 &; 192 @)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 78 ( 0 ^; 78 !; 0 ?; 78 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_empty_set,type,
empty_set: $i ).
thf(tp_member,type,
member: $i > $i > $o ).
thf(tp_sK1_B,type,
sK1_B: $i ).
thf(tp_sK2_SY10,type,
sK2_SY10: $i > $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(2,axiom,
! [B: $i] : ( subset @ B @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_of_subset) ).
thf(3,axiom,
! [B: $i,C: $i] :
( ( subset @ B @ C )
<=> ! [D: $i] :
( ( member @ D @ B )
=> ( member @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
thf(4,axiom,
! [B: $i] :
~ ( member @ B @ empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_defn) ).
thf(5,conjecture,
! [B: $i] : ( subset @ empty_set @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_empty_set_subset) ).
thf(6,negated_conjecture,
( ( ! [B: $i] : ( subset @ empty_set @ B ) )
= $false ),
inference(negate_conjecture,[status(cth)],[5]) ).
thf(7,plain,
( ( ! [B: $i] : ( subset @ empty_set @ B ) )
= $false ),
inference(unfold_def,[status(thm)],[6]) ).
thf(8,plain,
( ( ! [B: $i] : ( subset @ B @ B ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(9,plain,
( ( ! [B: $i,C: $i] :
( ( subset @ B @ C )
<=> ! [D: $i] :
( ( member @ D @ B )
=> ( member @ D @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(10,plain,
( ( ! [B: $i] :
~ ( member @ B @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(11,plain,
( ( subset @ empty_set @ sK1_B )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[7]) ).
thf(12,plain,
( ( ~ ( subset @ empty_set @ sK1_B ) )
= $true ),
inference(polarity_switch,[status(thm)],[11]) ).
thf(13,plain,
( ( ! [B: $i] :
~ ( member @ B @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(14,plain,
( ( ! [B: $i,C: $i] :
( ( subset @ B @ C )
<=> ! [D: $i] :
( ( member @ D @ B )
=> ( member @ D @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(15,plain,
( ( ! [B: $i] : ( subset @ B @ B ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(16,plain,
( ( ~ ( subset @ empty_set @ sK1_B ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(17,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(18,plain,
! [SV1: $i] :
( ( ~ ( member @ SV1 @ empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[13]) ).
thf(19,plain,
! [SV2: $i] :
( ( subset @ SV2 @ SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(20,plain,
( ( subset @ empty_set @ sK1_B )
= $false ),
inference(extcnf_not_pos,[status(thm)],[16]) ).
thf(21,plain,
! [SV3: $i] :
( ( ! [SY6: $i] :
~ ( ~ ( ~ ( subset @ SV3 @ SY6 )
| ! [SY7: $i] :
( ~ ( member @ SY7 @ SV3 )
| ( member @ SY7 @ SY6 ) ) )
| ~ ( ~ ! [SY8: $i] :
( ~ ( member @ SY8 @ SV3 )
| ( member @ SY8 @ SY6 ) )
| ( subset @ SV3 @ SY6 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(22,plain,
! [SV1: $i] :
( ( member @ SV1 @ empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(23,plain,
! [SV4: $i,SV3: $i] :
( ( ~ ( ~ ( ~ ( subset @ SV3 @ SV4 )
| ! [SY9: $i] :
( ~ ( member @ SY9 @ SV3 )
| ( member @ SY9 @ SV4 ) ) )
| ~ ( ~ ! [SY10: $i] :
( ~ ( member @ SY10 @ SV3 )
| ( member @ SY10 @ SV4 ) )
| ( subset @ SV3 @ SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(24,plain,
! [SV4: $i,SV3: $i] :
( ( ~ ( ~ ( subset @ SV3 @ SV4 )
| ! [SY9: $i] :
( ~ ( member @ SY9 @ SV3 )
| ( member @ SY9 @ SV4 ) ) )
| ~ ( ~ ! [SY10: $i] :
( ~ ( member @ SY10 @ SV3 )
| ( member @ SY10 @ SV4 ) )
| ( subset @ SV3 @ SV4 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(25,plain,
! [SV4: $i,SV3: $i] :
( ( ~ ( ~ ( subset @ SV3 @ SV4 )
| ! [SY9: $i] :
( ~ ( member @ SY9 @ SV3 )
| ( member @ SY9 @ SV4 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[24]) ).
thf(26,plain,
! [SV4: $i,SV3: $i] :
( ( ~ ( ~ ! [SY10: $i] :
( ~ ( member @ SY10 @ SV3 )
| ( member @ SY10 @ SV4 ) )
| ( subset @ SV3 @ SV4 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[24]) ).
thf(27,plain,
! [SV4: $i,SV3: $i] :
( ( ~ ( subset @ SV3 @ SV4 )
| ! [SY9: $i] :
( ~ ( member @ SY9 @ SV3 )
| ( member @ SY9 @ SV4 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[25]) ).
thf(28,plain,
! [SV4: $i,SV3: $i] :
( ( ~ ! [SY10: $i] :
( ~ ( member @ SY10 @ SV3 )
| ( member @ SY10 @ SV4 ) )
| ( subset @ SV3 @ SV4 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[26]) ).
thf(29,plain,
! [SV4: $i,SV3: $i] :
( ( ( ~ ( subset @ SV3 @ SV4 ) )
= $true )
| ( ( ! [SY9: $i] :
( ~ ( member @ SY9 @ SV3 )
| ( member @ SY9 @ SV4 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[27]) ).
thf(30,plain,
! [SV4: $i,SV3: $i] :
( ( ( ~ ! [SY10: $i] :
( ~ ( member @ SY10 @ SV3 )
| ( member @ SY10 @ SV4 ) ) )
= $true )
| ( ( subset @ SV3 @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[28]) ).
thf(31,plain,
! [SV4: $i,SV3: $i] :
( ( ( subset @ SV3 @ SV4 )
= $false )
| ( ( ! [SY9: $i] :
( ~ ( member @ SY9 @ SV3 )
| ( member @ SY9 @ SV4 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[29]) ).
thf(32,plain,
! [SV4: $i,SV3: $i] :
( ( ( ! [SY10: $i] :
( ~ ( member @ SY10 @ SV3 )
| ( member @ SY10 @ SV4 ) ) )
= $false )
| ( ( subset @ SV3 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(33,plain,
! [SV4: $i,SV3: $i,SV5: $i] :
( ( ( ~ ( member @ SV5 @ SV3 )
| ( member @ SV5 @ SV4 ) )
= $true )
| ( ( subset @ SV3 @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(34,plain,
! [SV3: $i,SV4: $i] :
( ( ( ~ ( member @ ( sK2_SY10 @ SV4 @ SV3 ) @ SV3 )
| ( member @ ( sK2_SY10 @ SV4 @ SV3 ) @ SV4 ) )
= $false )
| ( ( subset @ SV3 @ SV4 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[32]) ).
thf(35,plain,
! [SV4: $i,SV3: $i,SV5: $i] :
( ( ( ~ ( member @ SV5 @ SV3 ) )
= $true )
| ( ( member @ SV5 @ SV4 )
= $true )
| ( ( subset @ SV3 @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[33]) ).
thf(36,plain,
! [SV3: $i,SV4: $i] :
( ( ( ~ ( member @ ( sK2_SY10 @ SV4 @ SV3 ) @ SV3 ) )
= $false )
| ( ( subset @ SV3 @ SV4 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[34]) ).
thf(37,plain,
! [SV3: $i,SV4: $i] :
( ( ( member @ ( sK2_SY10 @ SV4 @ SV3 ) @ SV4 )
= $false )
| ( ( subset @ SV3 @ SV4 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[34]) ).
thf(38,plain,
! [SV4: $i,SV3: $i,SV5: $i] :
( ( ( member @ SV5 @ SV3 )
= $false )
| ( ( member @ SV5 @ SV4 )
= $true )
| ( ( subset @ SV3 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(39,plain,
! [SV3: $i,SV4: $i] :
( ( ( member @ ( sK2_SY10 @ SV4 @ SV3 ) @ SV3 )
= $true )
| ( ( subset @ SV3 @ SV4 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[36]) ).
thf(40,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[19,39,38,37,22,20]) ).
thf(41,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET062+3 : TPTP v9.3.1. Released v2.2.0.
% 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
% 0.07/0.19 % Computer : n018.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Oct 6 14:31:52 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.24
% 0.07/0.24 No.of.Axioms: 3
% 0.07/0.24
% 0.07/0.24 Length.of.Defs: 0
% 0.07/0.24
% 0.07/0.24 Contains.Choice.Funs: false
% 0.07/0.24
% 0.07/0.24 ********************************
% 0.07/0.24 * All subproblems solved! *
% 0.07/0.24 ********************************
% 0.07/0.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:3,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:40,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.07/0.24
% 0.07/0.24 %**** Beginning of derivation protocol ****
% 0.07/0.24 % SZS output start CNFRefutation
% See solution above
% 0.07/0.24
% 0.07/0.24 %**** End of derivation protocol ****
% 0.07/0.24 %**** no. of clauses in derivation: 40 ****
% 0.07/0.24 %**** clause counter: 40 ****
% 0.07/0.24
% 0.07/0.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:3,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:40,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------