%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET045-5 : 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 : n015.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 10:39:07 AM UTC 2026
% Result : Unsatisfiable 0.06s 0.20s
% Output : CNFRefutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 36 ( 24 unt; 0 typ; 0 def)
% Number of atoms : 148 ( 40 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 205 ( 29 ~; 32 |; 0 &; 144 @)
% ( 0 <=>; 0 =>; 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 : 6 ( 3 usr; 3 con; 0-2 aty)
% Number of variables : 52 ( 0 ^; 52 !; 0 ?; 52 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_element,type,
element: $i > $i > $o ).
thf(tp_f,type,
f: $i > $i ).
thf(1,axiom,
! [X: $i,Y: $i] :
( ~ ( element @ X @ Y )
| ( element @ X @ X )
| ( element @ X @ ( f @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_3) ).
thf(2,axiom,
! [X: $i,Y: $i] :
( ~ ( element @ X @ ( f @ Y ) )
| ~ ( element @ X @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2) ).
thf(3,axiom,
! [X: $i,Y: $i] :
( ~ ( element @ X @ ( f @ Y ) )
| ( element @ X @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1) ).
thf(4,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(5,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[4]) ).
thf(6,negated_conjecture,
! [X: $i] : ( element @ X @ a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_4) ).
thf(7,plain,
$false = $false,
inference(unfold_def,[status(thm)],[5]) ).
thf(8,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( element @ X @ Y )
| ( element @ X @ X )
| ( element @ X @ ( f @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(9,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( element @ X @ ( f @ Y ) )
| ~ ( element @ X @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(10,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( element @ X @ ( f @ Y ) )
| ( element @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(11,plain,
( ( ! [X: $i] : ( element @ X @ a ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(12,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(13,plain,
( ( ! [X: $i] :
( ! [Y: $i] :
~ ( element @ X @ ( f @ Y ) )
| ~ ( element @ X @ X ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[9]) ).
thf(14,plain,
( ( ! [X: $i] : ( element @ X @ a ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(15,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( element @ X @ ( f @ Y ) )
| ( element @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(16,plain,
( ( ! [X: $i] :
( ! [Y: $i] :
~ ( element @ X @ ( f @ Y ) )
| ~ ( element @ X @ X ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(17,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( element @ X @ Y )
| ( element @ X @ X )
| ( element @ X @ ( f @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(18,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[12]) ).
thf(19,plain,
! [SV1: $i] :
( ( element @ SV1 @ a )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(20,plain,
! [SV2: $i] :
( ( ! [SY7: $i] :
( ~ ( element @ SV2 @ ( f @ SY7 ) )
| ( element @ SV2 @ SY7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(21,plain,
! [SV3: $i] :
( ( ! [SY8: $i] :
~ ( element @ SV3 @ ( f @ SY8 ) )
| ~ ( element @ SV3 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(22,plain,
! [SV4: $i] :
( ( ! [SY9: $i] :
( ~ ( element @ SV4 @ SY9 )
| ( element @ SV4 @ SV4 )
| ( element @ SV4 @ ( f @ SY9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(23,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(24,plain,
! [SV5: $i,SV2: $i] :
( ( ~ ( element @ SV2 @ ( f @ SV5 ) )
| ( element @ SV2 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(25,plain,
! [SV3: $i] :
( ( ( ! [SY8: $i] :
~ ( element @ SV3 @ ( f @ SY8 ) ) )
= $true )
| ( ( ~ ( element @ SV3 @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[21]) ).
thf(26,plain,
! [SV6: $i,SV4: $i] :
( ( ~ ( element @ SV4 @ SV6 )
| ( element @ SV4 @ SV4 )
| ( element @ SV4 @ ( f @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(27,plain,
! [SV5: $i,SV2: $i] :
( ( ( ~ ( element @ SV2 @ ( f @ SV5 ) ) )
= $true )
| ( ( element @ SV2 @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[24]) ).
thf(28,plain,
! [SV7: $i,SV3: $i] :
( ( ( ~ ( element @ SV3 @ ( f @ SV7 ) ) )
= $true )
| ( ( ~ ( element @ SV3 @ SV3 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(29,plain,
! [SV6: $i,SV4: $i] :
( ( ( ~ ( element @ SV4 @ SV6 ) )
= $true )
| ( ( ( element @ SV4 @ SV4 )
| ( element @ SV4 @ ( f @ SV6 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[26]) ).
thf(30,plain,
! [SV5: $i,SV2: $i] :
( ( ( element @ SV2 @ ( f @ SV5 ) )
= $false )
| ( ( element @ SV2 @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(31,plain,
! [SV7: $i,SV3: $i] :
( ( ( element @ SV3 @ ( f @ SV7 ) )
= $false )
| ( ( ~ ( element @ SV3 @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(32,plain,
! [SV6: $i,SV4: $i] :
( ( ( element @ SV4 @ SV6 )
= $false )
| ( ( ( element @ SV4 @ SV4 )
| ( element @ SV4 @ ( f @ SV6 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[29]) ).
thf(33,plain,
! [SV7: $i,SV3: $i] :
( ( ( element @ SV3 @ SV3 )
= $false )
| ( ( element @ SV3 @ ( f @ SV7 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(34,plain,
! [SV6: $i,SV4: $i] :
( ( ( element @ SV4 @ SV4 )
= $true )
| ( ( element @ SV4 @ ( f @ SV6 ) )
= $true )
| ( ( element @ SV4 @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[32]) ).
thf(35,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[19,34,33,30,23]) ).
thf(36,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET045-5 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.17 % Computer : n015.cluster.edu
% 0.06/0.17 % Model : x86_64 x86_64
% 0.06/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.17 % Memory : 8046.5625MB
% 0.06/0.17 % OS : Linux 6.8.0-71-generic
% 0.06/0.17 % CPULimit : 300
% 0.06/0.17 % WCLimit : 300
% 0.06/0.17 % DateTime : Tue Oct 6 14:32:43 UTC 2026
% 0.06/0.18 % CPUTime :
% 0.06/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.20
% 0.06/0.20 No.of.Axioms: 4
% 0.06/0.20
% 0.06/0.20 Length.of.Defs: 0
% 0.06/0.20
% 0.06/0.20 Contains.Choice.Funs: false
% 0.06/0.20
% 0.06/0.20 ********************************
% 0.06/0.20 * All subproblems solved! *
% 0.06/0.20 ********************************
% 0.06/0.20 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:4,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:35,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.06/0.20
% 0.06/0.20 %**** Beginning of derivation protocol ****
% 0.06/0.20 % SZS output start CNFRefutation
% See solution above
% 0.06/0.20
% 0.06/0.20 %**** End of derivation protocol ****
% 0.06/0.20 %**** no. of clauses in derivation: 36 ****
% 0.06/0.20 %**** clause counter: 35 ****
% 0.06/0.20
% 0.06/0.20 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:4,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:35,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------