%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU809^2 : 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 : 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 10:48:35 AM UTC 2026
% Result : Theorem 0.11s 0.18s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 2
% Syntax : Number of formulae : 21 ( 18 unt; 0 typ; 1 def)
% Number of atoms : 83 ( 21 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 140 ( 10 ~; 7 |; 0 &; 110 @)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 5 con; 0-2 aty)
% Number of variables : 16 ( 0 ^; 16 !; 0 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_omega,type,
omega: $i ).
thf(tp_omegaSAx,type,
omegaSAx: $o ).
thf(tp_sK1_SX0,type,
sK1_SX0: $i ).
thf(tp_setadjoin,type,
setadjoin: $i > $i > $i ).
thf(omegaSAx,definition,
( omegaSAx
= ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaSAx) ).
thf(1,conjecture,
( omegaSAx
=> ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaSclos) ).
thf(2,negated_conjecture,
( ( omegaSAx
=> ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) )
=> ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,omegaSAx]) ).
thf(4,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ~ ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(7,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(8,plain,
( ( ~ ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(9,plain,
( ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ omega )
| ( in @ ( setadjoin @ SX0 @ SX0 ) @ omega ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8,omegaSAx]) ).
thf(10,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ omega )
| ( in @ ( setadjoin @ SX0 @ SX0 ) @ omega ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7,omegaSAx]) ).
thf(11,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ omega )
| ( in @ ( setadjoin @ SX0 @ SX0 ) @ omega ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[9]) ).
thf(12,plain,
! [SV1: $i] :
( ( ~ ( in @ SV1 @ omega )
| ( in @ ( setadjoin @ SV1 @ SV1 ) @ omega ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[10]) ).
thf(13,plain,
( ( ~ ( in @ sK1_SX0 @ omega )
| ( in @ ( setadjoin @ sK1_SX0 @ sK1_SX0 ) @ omega ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[11]) ).
thf(14,plain,
! [SV1: $i] :
( ( ( ~ ( in @ SV1 @ omega ) )
= $true )
| ( ( in @ ( setadjoin @ SV1 @ SV1 ) @ omega )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[12]) ).
thf(15,plain,
( ( ~ ( in @ sK1_SX0 @ omega ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[13]) ).
thf(16,plain,
( ( in @ ( setadjoin @ sK1_SX0 @ sK1_SX0 ) @ omega )
= $false ),
inference(extcnf_or_neg,[status(thm)],[13]) ).
thf(17,plain,
! [SV1: $i] :
( ( ( in @ SV1 @ omega )
= $false )
| ( ( in @ ( setadjoin @ SV1 @ SV1 ) @ omega )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[14]) ).
thf(18,plain,
( ( in @ sK1_SX0 @ omega )
= $true ),
inference(extcnf_not_neg,[status(thm)],[15]) ).
thf(19,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[16,18,17]) ).
thf(20,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU809^2 : 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
% 0.11/0.15 % Computer : n006.cluster.edu
% 0.11/0.15 % Model : x86_64 x86_64
% 0.11/0.15 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.15 % Memory : 8046.5625MB
% 0.11/0.15 % OS : Linux 6.8.0-71-generic
% 0.11/0.15 % CPULimit : 300
% 0.11/0.15 % WCLimit : 300
% 0.11/0.15 % DateTime : Tue Oct 6 15:35:07 UTC 2026
% 0.11/0.16 % CPUTime :
% 0.11/0.16 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.18
% 0.11/0.18 No.of.Axioms: 0
% 0.11/0.18
% 0.11/0.18 Length.of.Defs: 173
% 0.11/0.18
% 0.11/0.18 Contains.Choice.Funs: false
% 0.11/0.18
% 0.11/0.18 ********************************
% 0.11/0.18 * All subproblems solved! *
% 0.11/0.18 ********************************
% 0.11/0.18 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:1,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:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:19,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.11/0.18
% 0.11/0.18 %**** Beginning of derivation protocol ****
% 0.11/0.18 % SZS output start CNFRefutation
% See solution above
% 0.11/0.18
% 0.11/0.18 %**** End of derivation protocol ****
% 0.11/0.18 %**** no. of clauses in derivation: 20 ****
% 0.11/0.18 %**** clause counter: 19 ****
% 0.11/0.18
% 0.11/0.18 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:1,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:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:19,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------