%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU116+1 : TPTP v9.3.1. Released v3.2.0.
% 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 : n004.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 10:42:55 AM UTC 2026
% Result : Theorem 0.08s 0.23s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 71 ( 54 unt; 0 typ; 0 def)
% Number of atoms : 277 ( 75 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 319 ( 58 ~; 33 |; 3 &; 205 @)
% ( 0 <=>; 20 =>; 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 : 26 ( 23 usr; 6 con; 0-2 aty)
% Number of variables : 89 ( 0 ^; 83 !; 6 ?; 89 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_cap_closed,type,
cap_closed: $i > $o ).
thf(tp_cup_closed,type,
cup_closed: $i > $o ).
thf(tp_diff_closed,type,
diff_closed: $i > $o ).
thf(tp_element,type,
element: $i > $i > $o ).
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_empty_set,type,
empty_set: $i ).
thf(tp_epsilon_connected,type,
epsilon_connected: $i > $o ).
thf(tp_epsilon_transitive,type,
epsilon_transitive: $i > $o ).
thf(tp_finite,type,
finite: $i > $o ).
thf(tp_finite_subsets,type,
finite_subsets: $i > $i ).
thf(tp_function,type,
function: $i > $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_natural,type,
natural: $i > $o ).
thf(tp_one_to_one,type,
one_to_one: $i > $o ).
thf(tp_ordinal,type,
ordinal: $i > $o ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_preboolean,type,
preboolean: $i > $o ).
thf(tp_relation,type,
relation: $i > $o ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY13,type,
sK2_SY13: $i ).
thf(tp_sK3_SX0,type,
sK3_SX0: $i ).
thf(tp_sK4_SY17,type,
sK4_SY17: $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(8,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( finite @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( finite_subsets @ A ) )
=> ( finite @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_finsub_1) ).
thf(12,axiom,
! [A: $i] : ( preboolean @ ( finite_subsets @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_finsub_1) ).
thf(13,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(19,axiom,
! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_finset_1) ).
thf(20,axiom,
! [A: $i] :
( ( empty @ A )
=> ( finite @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(31,conjecture,
! [A: $i,B: $i] :
( ( element @ B @ ( finite_subsets @ A ) )
=> ( finite @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_finsub_1) ).
thf(32,negated_conjecture,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( finite_subsets @ A ) )
=> ( finite @ B ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[31]) ).
thf(33,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( finite_subsets @ A ) )
=> ( finite @ B ) ) )
= $false ),
inference(unfold_def,[status(thm)],[32]) ).
thf(34,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( finite @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(35,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( finite_subsets @ A ) )
=> ( finite @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(36,plain,
( ( ! [A: $i] : ( preboolean @ ( finite_subsets @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(37,plain,
( ( ! [A: $i] :
? [B: $i] : ( element @ B @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(38,plain,
( ( ! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(39,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( finite @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(40,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(41,plain,
( ( ! [SY13: $i] :
( ( element @ SY13 @ ( finite_subsets @ sK1_A ) )
=> ( finite @ SY13 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[33]) ).
thf(42,plain,
( ( ( element @ sK2_SY13 @ ( finite_subsets @ sK1_A ) )
=> ( finite @ sK2_SY13 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[41]) ).
thf(43,plain,
( ( element @ sK2_SY13 @ ( finite_subsets @ sK1_A ) )
= $true ),
inference(standard_cnf,[status(thm)],[42]) ).
thf(44,plain,
( ( finite @ sK2_SY13 )
= $false ),
inference(standard_cnf,[status(thm)],[42]) ).
thf(45,plain,
( ( ~ ( finite @ sK2_SY13 ) )
= $true ),
inference(polarity_switch,[status(thm)],[44]) ).
thf(46,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(47,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( finite @ A ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(48,plain,
( ( ! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(49,plain,
( ( ! [A: $i] :
? [B: $i] : ( element @ B @ A ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(50,plain,
( ( ! [A: $i] : ( preboolean @ ( finite_subsets @ A ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(51,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( finite_subsets @ A ) )
=> ( finite @ B ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(52,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( finite @ A ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(53,plain,
( ( element @ sK2_SY13 @ ( finite_subsets @ sK1_A ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(54,plain,
( ( ~ ( finite @ sK2_SY13 ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(55,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( finite_subsets @ SX0 ) )
| ( finite @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(56,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( element @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(57,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( finite @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(58,plain,
( ( ! [SX0: $i] :
( ~ ( finite @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ( finite @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(59,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( finite @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(60,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ( element @ SX1 @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(61,plain,
! [SV1: $i] :
( ( preboolean @ ( finite_subsets @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(62,plain,
( ( finite @ sK2_SY13 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(63,plain,
! [SV2: $i] :
( ( ! [SY14: $i] :
( ~ ( element @ SY14 @ ( finite_subsets @ SV2 ) )
| ( finite @ SY14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(64,plain,
! [SV3: $i] :
( ( ! [SY15: $i] :
( ~ ( in @ SV3 @ SY15 )
| ( element @ SV3 @ SY15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(65,plain,
! [SV4: $i] :
( ( ~ ( empty @ SV4 )
| ( finite @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(66,plain,
! [SV5: $i] :
( ( ~ ( finite @ SV5 )
| ! [SY16: $i] :
( ~ ( element @ SY16 @ ( powerset @ SV5 ) )
| ( finite @ SY16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(67,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( finite @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(68,plain,
! [SV6: $i] :
( ( ~ ! [SY17: $i] :
~ ( element @ SY17 @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(69,plain,
! [SV2: $i,SV7: $i] :
( ( ~ ( element @ SV7 @ ( finite_subsets @ SV2 ) )
| ( finite @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(70,plain,
! [SV8: $i,SV3: $i] :
( ( ~ ( in @ SV3 @ SV8 )
| ( element @ SV3 @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(71,plain,
! [SV4: $i] :
( ( ( ~ ( empty @ SV4 ) )
= $true )
| ( ( finite @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[65]) ).
thf(72,plain,
! [SV5: $i] :
( ( ( ~ ( finite @ SV5 ) )
= $true )
| ( ( ! [SY16: $i] :
( ~ ( element @ SY16 @ ( powerset @ SV5 ) )
| ( finite @ SY16 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[66]) ).
thf(73,plain,
( ( ~ ~ ( ~ ~ ( empty @ sK3_SX0 )
| ~ ( finite @ sK3_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[67]) ).
thf(74,plain,
! [SV6: $i] :
( ( ! [SY17: $i] :
~ ( element @ SY17 @ SV6 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[68]) ).
thf(75,plain,
! [SV2: $i,SV7: $i] :
( ( ( ~ ( element @ SV7 @ ( finite_subsets @ SV2 ) ) )
= $true )
| ( ( finite @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[69]) ).
thf(76,plain,
! [SV8: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ SV8 ) )
= $true )
| ( ( element @ SV3 @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[70]) ).
thf(77,plain,
! [SV4: $i] :
( ( ( empty @ SV4 )
= $false )
| ( ( finite @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(78,plain,
! [SV5: $i] :
( ( ( finite @ SV5 )
= $false )
| ( ( ! [SY16: $i] :
( ~ ( element @ SY16 @ ( powerset @ SV5 ) )
| ( finite @ SY16 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(79,plain,
( ( ~ ( ~ ~ ( empty @ sK3_SX0 )
| ~ ( finite @ sK3_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[73]) ).
thf(80,plain,
! [SV6: $i] :
( ( ~ ( element @ ( sK4_SY17 @ SV6 ) @ SV6 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[74]) ).
thf(81,plain,
! [SV2: $i,SV7: $i] :
( ( ( element @ SV7 @ ( finite_subsets @ SV2 ) )
= $false )
| ( ( finite @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(82,plain,
! [SV8: $i,SV3: $i] :
( ( ( in @ SV3 @ SV8 )
= $false )
| ( ( element @ SV3 @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(83,plain,
! [SV5: $i,SV9: $i] :
( ( ( ~ ( element @ SV9 @ ( powerset @ SV5 ) )
| ( finite @ SV9 ) )
= $true )
| ( ( finite @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(84,plain,
( ( ~ ~ ( empty @ sK3_SX0 )
| ~ ( finite @ sK3_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(85,plain,
! [SV6: $i] :
( ( element @ ( sK4_SY17 @ SV6 ) @ SV6 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[80]) ).
thf(86,plain,
! [SV5: $i,SV9: $i] :
( ( ( ~ ( element @ SV9 @ ( powerset @ SV5 ) ) )
= $true )
| ( ( finite @ SV9 )
= $true )
| ( ( finite @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[83]) ).
thf(87,plain,
( ( ~ ~ ( empty @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[84]) ).
thf(88,plain,
( ( ~ ( finite @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[84]) ).
thf(89,plain,
! [SV5: $i,SV9: $i] :
( ( ( element @ SV9 @ ( powerset @ SV5 ) )
= $false )
| ( ( finite @ SV9 )
= $true )
| ( ( finite @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(90,plain,
( ( ~ ( empty @ sK3_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[87]) ).
thf(91,plain,
( ( finite @ sK3_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[88]) ).
thf(92,plain,
( ( empty @ sK3_SX0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(93,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[53,92,91,89,85,82,81,77,62,61]) ).
thf(94,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[93]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU116+1 : TPTP v9.3.1. Released v3.2.0.
% 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
% 0.08/0.18 % Computer : n004.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Oct 6 15:00:24 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.23
% 0.08/0.23 No.of.Axioms: 7
% 0.08/0.23
% 0.08/0.23 Length.of.Defs: 0
% 0.08/0.23
% 0.08/0.23 Contains.Choice.Funs: false
% 0.08/0.23 .
% 0.08/0.23
% 0.08/0.23 ********************************
% 0.08/0.23 * All subproblems solved! *
% 0.08/0.23 ********************************
% 0.08/0.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:8,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:93,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.08/0.23
% 0.08/0.23 %**** Beginning of derivation protocol ****
% 0.08/0.23 % SZS output start CNFRefutation
% See solution above
% 0.08/0.23
% 0.08/0.23 %**** End of derivation protocol ****
% 0.08/0.23 %**** no. of clauses in derivation: 71 ****
% 0.08/0.23 %**** clause counter: 93 ****
% 0.08/0.23
% 0.08/0.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:8,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:93,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------