%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET001-1 : TPTP v9.3.1. Released v1.0.0.
% 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 : n006.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 10:38:48 AM UTC 2026
% Result : Unsatisfiable 0.08s 0.19s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 66 ( 44 unt; 0 typ; 0 def)
% Number of atoms : 284 ( 75 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 402 ( 54 ~; 68 |; 0 &; 280 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 107 ( 0 ^; 107 !; 0 ?; 107 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_b,type,
b: $i ).
thf(tp_bb,type,
bb: $i ).
thf(tp_element_of_b,type,
element_of_b: $i ).
thf(tp_equal_sets,type,
equal_sets: $i > $i > $o ).
thf(tp_member,type,
member: $i > $i > $o ).
thf(tp_member_of_1_not_of_2,type,
member_of_1_not_of_2: $i > $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(1,axiom,
! [Set1: $i,Set2: $i] :
( ~ ( subset @ Set1 @ Set2 )
| ~ ( subset @ Set2 @ Set1 )
| ( equal_sets @ Set2 @ Set1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsets_are_set_equal_sets) ).
thf(2,axiom,
! [Superset: $i,Subset: $i] :
( ~ ( equal_sets @ Superset @ Subset )
| ( subset @ Subset @ Superset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_equal_sets_are_subsets2) ).
thf(3,axiom,
! [Subset: $i,Superset: $i] :
( ~ ( equal_sets @ Subset @ Superset )
| ( subset @ Subset @ Superset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_equal_sets_are_subsets1) ).
thf(4,axiom,
! [Subset: $i,Superset: $i] :
( ~ ( member @ ( member_of_1_not_of_2 @ Subset @ Superset ) @ Superset )
| ( subset @ Subset @ Superset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsets_axiom2) ).
thf(5,axiom,
! [Subset: $i,Superset: $i] :
( ( subset @ Subset @ Superset )
| ( member @ ( member_of_1_not_of_2 @ Subset @ Superset ) @ Subset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsets_axiom1) ).
thf(6,axiom,
! [Element: $i,Subset: $i,Superset: $i] :
( ~ ( member @ Element @ Subset )
| ~ ( subset @ Subset @ Superset )
| ( member @ Element @ Superset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',membership_in_subsets) ).
thf(7,axiom,
member @ element_of_b @ b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_of_b) ).
thf(8,axiom,
equal_sets @ b @ bb,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_equals_bb) ).
thf(9,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(10,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[9]) ).
thf(11,negated_conjecture,
~ ( member @ element_of_b @ bb ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_element_of_bb) ).
thf(12,plain,
$false = $false,
inference(unfold_def,[status(thm)],[10]) ).
thf(13,plain,
( ( ! [Set1: $i,Set2: $i] :
( ~ ( subset @ Set1 @ Set2 )
| ~ ( subset @ Set2 @ Set1 )
| ( equal_sets @ Set2 @ Set1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(14,plain,
( ( ! [Superset: $i,Subset: $i] :
( ~ ( equal_sets @ Superset @ Subset )
| ( subset @ Subset @ Superset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(15,plain,
( ( ! [Subset: $i,Superset: $i] :
( ~ ( equal_sets @ Subset @ Superset )
| ( subset @ Subset @ Superset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(16,plain,
( ( ! [Subset: $i,Superset: $i] :
( ~ ( member @ ( member_of_1_not_of_2 @ Subset @ Superset ) @ Superset )
| ( subset @ Subset @ Superset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(17,plain,
( ( ! [Subset: $i,Superset: $i] :
( ( subset @ Subset @ Superset )
| ( member @ ( member_of_1_not_of_2 @ Subset @ Superset ) @ Subset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(18,plain,
( ( ! [Element: $i,Subset: $i,Superset: $i] :
( ~ ( member @ Element @ Subset )
| ~ ( subset @ Subset @ Superset )
| ( member @ Element @ Superset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(19,plain,
( ( member @ element_of_b @ b )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(20,plain,
( ( equal_sets @ b @ bb )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(21,plain,
( ( ~ ( member @ element_of_b @ bb ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(22,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[12]) ).
thf(23,plain,
( ( ! [Subset: $i,Superset: $i] :
( ( member @ ( member_of_1_not_of_2 @ Subset @ Superset ) @ Subset )
| ( subset @ Subset @ Superset ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[17]) ).
thf(24,plain,
( ( ! [Element: $i,Subset: $i] :
( ~ ( member @ Element @ Subset )
| ! [Superset: $i] :
( ~ ( subset @ Subset @ Superset )
| ( member @ Element @ Superset ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[18]) ).
thf(25,plain,
( ( ~ ( member @ element_of_b @ bb ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(26,plain,
( ( equal_sets @ b @ bb )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(27,plain,
( ( member @ element_of_b @ b )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(28,plain,
( ( ! [Element: $i,Subset: $i] :
( ~ ( member @ Element @ Subset )
| ! [Superset: $i] :
( ~ ( subset @ Subset @ Superset )
| ( member @ Element @ Superset ) ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(29,plain,
( ( ! [Subset: $i,Superset: $i] :
( ( member @ ( member_of_1_not_of_2 @ Subset @ Superset ) @ Subset )
| ( subset @ Subset @ Superset ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(30,plain,
( ( ! [Subset: $i,Superset: $i] :
( ~ ( member @ ( member_of_1_not_of_2 @ Subset @ Superset ) @ Superset )
| ( subset @ Subset @ Superset ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(31,plain,
( ( ! [Subset: $i,Superset: $i] :
( ~ ( equal_sets @ Subset @ Superset )
| ( subset @ Subset @ Superset ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(32,plain,
( ( ! [Superset: $i,Subset: $i] :
( ~ ( equal_sets @ Superset @ Subset )
| ( subset @ Subset @ Superset ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(33,plain,
( ( ! [Set1: $i,Set2: $i] :
( ~ ( subset @ Set1 @ Set2 )
| ~ ( subset @ Set2 @ Set1 )
| ( equal_sets @ Set2 @ Set1 ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(34,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[22]) ).
thf(35,plain,
( ( member @ element_of_b @ bb )
= $false ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(36,plain,
! [SV1: $i] :
( ( ! [SY13: $i] :
( ~ ( member @ SV1 @ SY13 )
| ! [SY14: $i] :
( ~ ( subset @ SY13 @ SY14 )
| ( member @ SV1 @ SY14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(37,plain,
! [SV2: $i] :
( ( ! [SY15: $i] :
( ( member @ ( member_of_1_not_of_2 @ SV2 @ SY15 ) @ SV2 )
| ( subset @ SV2 @ SY15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(38,plain,
! [SV3: $i] :
( ( ! [SY16: $i] :
( ~ ( member @ ( member_of_1_not_of_2 @ SV3 @ SY16 ) @ SY16 )
| ( subset @ SV3 @ SY16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(39,plain,
! [SV4: $i] :
( ( ! [SY17: $i] :
( ~ ( equal_sets @ SV4 @ SY17 )
| ( subset @ SV4 @ SY17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(40,plain,
! [SV5: $i] :
( ( ! [SY18: $i] :
( ~ ( equal_sets @ SV5 @ SY18 )
| ( subset @ SY18 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(41,plain,
! [SV6: $i] :
( ( ! [SY19: $i] :
( ~ ( subset @ SV6 @ SY19 )
| ~ ( subset @ SY19 @ SV6 )
| ( equal_sets @ SY19 @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(42,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(43,plain,
! [SV7: $i,SV1: $i] :
( ( ~ ( member @ SV1 @ SV7 )
| ! [SY20: $i] :
( ~ ( subset @ SV7 @ SY20 )
| ( member @ SV1 @ SY20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(44,plain,
! [SV8: $i,SV2: $i] :
( ( ( member @ ( member_of_1_not_of_2 @ SV2 @ SV8 ) @ SV2 )
| ( subset @ SV2 @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(45,plain,
! [SV9: $i,SV3: $i] :
( ( ~ ( member @ ( member_of_1_not_of_2 @ SV3 @ SV9 ) @ SV9 )
| ( subset @ SV3 @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(46,plain,
! [SV10: $i,SV4: $i] :
( ( ~ ( equal_sets @ SV4 @ SV10 )
| ( subset @ SV4 @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(47,plain,
! [SV11: $i,SV5: $i] :
( ( ~ ( equal_sets @ SV5 @ SV11 )
| ( subset @ SV11 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(48,plain,
! [SV12: $i,SV6: $i] :
( ( ~ ( subset @ SV6 @ SV12 )
| ~ ( subset @ SV12 @ SV6 )
| ( equal_sets @ SV12 @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(49,plain,
! [SV7: $i,SV1: $i] :
( ( ( ~ ( member @ SV1 @ SV7 ) )
= $true )
| ( ( ! [SY20: $i] :
( ~ ( subset @ SV7 @ SY20 )
| ( member @ SV1 @ SY20 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[43]) ).
thf(50,plain,
! [SV8: $i,SV2: $i] :
( ( ( member @ ( member_of_1_not_of_2 @ SV2 @ SV8 ) @ SV2 )
= $true )
| ( ( subset @ SV2 @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[44]) ).
thf(51,plain,
! [SV9: $i,SV3: $i] :
( ( ( ~ ( member @ ( member_of_1_not_of_2 @ SV3 @ SV9 ) @ SV9 ) )
= $true )
| ( ( subset @ SV3 @ SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[45]) ).
thf(52,plain,
! [SV10: $i,SV4: $i] :
( ( ( ~ ( equal_sets @ SV4 @ SV10 ) )
= $true )
| ( ( subset @ SV4 @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[46]) ).
thf(53,plain,
! [SV11: $i,SV5: $i] :
( ( ( ~ ( equal_sets @ SV5 @ SV11 ) )
= $true )
| ( ( subset @ SV11 @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[47]) ).
thf(54,plain,
! [SV12: $i,SV6: $i] :
( ( ( ~ ( subset @ SV6 @ SV12 ) )
= $true )
| ( ( ~ ( subset @ SV12 @ SV6 )
| ( equal_sets @ SV12 @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[48]) ).
thf(55,plain,
! [SV7: $i,SV1: $i] :
( ( ( member @ SV1 @ SV7 )
= $false )
| ( ( ! [SY20: $i] :
( ~ ( subset @ SV7 @ SY20 )
| ( member @ SV1 @ SY20 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(56,plain,
! [SV9: $i,SV3: $i] :
( ( ( member @ ( member_of_1_not_of_2 @ SV3 @ SV9 ) @ SV9 )
= $false )
| ( ( subset @ SV3 @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(57,plain,
! [SV10: $i,SV4: $i] :
( ( ( equal_sets @ SV4 @ SV10 )
= $false )
| ( ( subset @ SV4 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(58,plain,
! [SV11: $i,SV5: $i] :
( ( ( equal_sets @ SV5 @ SV11 )
= $false )
| ( ( subset @ SV11 @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(59,plain,
! [SV12: $i,SV6: $i] :
( ( ( subset @ SV6 @ SV12 )
= $false )
| ( ( ~ ( subset @ SV12 @ SV6 )
| ( equal_sets @ SV12 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(60,plain,
! [SV1: $i,SV13: $i,SV7: $i] :
( ( ( ~ ( subset @ SV7 @ SV13 )
| ( member @ SV1 @ SV13 ) )
= $true )
| ( ( member @ SV1 @ SV7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(61,plain,
! [SV6: $i,SV12: $i] :
( ( ( ~ ( subset @ SV12 @ SV6 ) )
= $true )
| ( ( equal_sets @ SV12 @ SV6 )
= $true )
| ( ( subset @ SV6 @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[59]) ).
thf(62,plain,
! [SV1: $i,SV13: $i,SV7: $i] :
( ( ( ~ ( subset @ SV7 @ SV13 ) )
= $true )
| ( ( member @ SV1 @ SV13 )
= $true )
| ( ( member @ SV1 @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[60]) ).
thf(63,plain,
! [SV6: $i,SV12: $i] :
( ( ( subset @ SV12 @ SV6 )
= $false )
| ( ( equal_sets @ SV12 @ SV6 )
= $true )
| ( ( subset @ SV6 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(64,plain,
! [SV1: $i,SV13: $i,SV7: $i] :
( ( ( subset @ SV7 @ SV13 )
= $false )
| ( ( member @ SV1 @ SV13 )
= $true )
| ( ( member @ SV1 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(65,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[26,64,63,58,57,56,50,42,35,27]) ).
thf(66,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET001-1 : TPTP v9.3.1. Released v1.0.0.
% 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
% 0.08/0.16 % Computer : n006.cluster.edu
% 0.08/0.16 % Model : x86_64 x86_64
% 0.08/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.16 % Memory : 8046.5625MB
% 0.08/0.16 % OS : Linux 6.8.0-71-generic
% 0.08/0.16 % CPULimit : 300
% 0.08/0.16 % WCLimit : 300
% 0.08/0.16 % DateTime : Tue Oct 6 14:25:37 UTC 2026
% 0.08/0.16 % CPUTime :
% 0.08/0.16 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.19
% 0.08/0.19 No.of.Axioms: 9
% 0.08/0.19
% 0.08/0.19 Length.of.Defs: 0
% 0.08/0.19
% 0.08/0.19 Contains.Choice.Funs: false
% 0.08/0.19 .
% 0.08/0.19
% 0.08/0.19 ********************************
% 0.08/0.19 * All subproblems solved! *
% 0.08/0.19 ********************************
% 0.08/0.19 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:9,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:65,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.08/0.19
% 0.08/0.19 %**** Beginning of derivation protocol ****
% 0.08/0.19 % SZS output start CNFRefutation
% See solution above
% 0.08/0.20
% 0.08/0.20 %**** End of derivation protocol ****
% 0.08/0.20 %**** no. of clauses in derivation: 66 ****
% 0.08/0.20 %**** clause counter: 65 ****
% 0.08/0.20
% 0.08/0.20 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:9,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:65,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------