%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU812^2 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 10:48:43 AM UTC 2026
% Result : Theorem 0.09s 0.21s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 2
% Syntax : Number of formulae : 22 ( 19 unt; 0 typ; 1 def)
% Number of atoms : 89 ( 22 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 117 ( 10 ~; 7 |; 0 &; 84 @)
% ( 0 <=>; 16 =>; 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 : 8 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 22 ( 1 ^; 21 !; 0 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_sK1_SY0,type,
sK1_SY0: $i ).
thf(tp_sK2_SX0,type,
sK2_SX0: $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_transitiveset,type,
transitiveset: $i > $o ).
thf(transitiveset,definition,
( transitiveset
= ( ^ [A: $i] :
! [X: $i] :
( ( in @ X @ A )
=> ( subset @ X @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitiveset) ).
thf(1,conjecture,
! [X: $i] :
( ( transitiveset @ X )
=> ! [A: $i] :
( ( in @ A @ X )
=> ( subset @ A @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivesetOp1) ).
thf(2,negated_conjecture,
( ( ! [X: $i] :
( ( transitiveset @ X )
=> ! [A: $i] :
( ( in @ A @ X )
=> ( subset @ A @ X ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [SY0: $i] :
( ! [SY1: $i] :
( ( in @ SY1 @ SY0 )
=> ( subset @ SY1 @ SY0 ) )
=> ! [A: $i] :
( ( in @ A @ SY0 )
=> ( subset @ A @ SY0 ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,transitiveset]) ).
thf(4,plain,
( ( ! [SY6: $i] :
( ( in @ SY6 @ sK1_SY0 )
=> ( subset @ SY6 @ sK1_SY0 ) )
=> ! [SY7: $i] :
( ( in @ SY7 @ sK1_SY0 )
=> ( subset @ SY7 @ sK1_SY0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ! [SY6: $i] :
( ( in @ SY6 @ sK1_SY0 )
=> ( subset @ SY6 @ sK1_SY0 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[4]) ).
thf(6,plain,
( ( ! [SY7: $i] :
( ( in @ SY7 @ sK1_SY0 )
=> ( subset @ SY7 @ sK1_SY0 ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[4]) ).
thf(7,plain,
( ( ~ ! [SY7: $i] :
( ( in @ SY7 @ sK1_SY0 )
=> ( subset @ SY7 @ sK1_SY0 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(8,plain,
( ( ! [SY6: $i] :
( ( in @ SY6 @ sK1_SY0 )
=> ( subset @ SY6 @ sK1_SY0 ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(9,plain,
( ( ~ ! [SY7: $i] :
( ( in @ SY7 @ sK1_SY0 )
=> ( subset @ SY7 @ sK1_SY0 ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(10,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_SY0 )
| ( subset @ SX0 @ sK1_SY0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8,transitiveset]) ).
thf(11,plain,
( ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_SY0 )
| ( subset @ SX0 @ sK1_SY0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9,transitiveset]) ).
thf(12,plain,
! [SV1: $i] :
( ( ~ ( in @ SV1 @ sK1_SY0 )
| ( subset @ SV1 @ sK1_SY0 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[10]) ).
thf(13,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_SY0 )
| ( subset @ SX0 @ sK1_SY0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[11]) ).
thf(14,plain,
! [SV1: $i] :
( ( ( ~ ( in @ SV1 @ sK1_SY0 ) )
= $true )
| ( ( subset @ SV1 @ sK1_SY0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[12]) ).
thf(15,plain,
( ( ~ ( in @ sK2_SX0 @ sK1_SY0 )
| ( subset @ sK2_SX0 @ sK1_SY0 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[13]) ).
thf(16,plain,
! [SV1: $i] :
( ( ( in @ SV1 @ sK1_SY0 )
= $false )
| ( ( subset @ SV1 @ sK1_SY0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[14]) ).
thf(17,plain,
( ( ~ ( in @ sK2_SX0 @ sK1_SY0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[15]) ).
thf(18,plain,
( ( subset @ sK2_SX0 @ sK1_SY0 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[15]) ).
thf(19,plain,
( ( in @ sK2_SX0 @ sK1_SY0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[17]) ).
thf(20,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[16,19,18]) ).
thf(21,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU812^2 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.18 % Computer : n008.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Oct 6 15:37:33 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.21
% 0.09/0.21 No.of.Axioms: 0
% 0.09/0.21
% 0.09/0.21 Length.of.Defs: 176
% 0.09/0.21
% 0.09/0.21 Contains.Choice.Funs: false
% 0.09/0.21
% 0.09/0.21 ********************************
% 0.09/0.21 * All subproblems solved! *
% 0.09/0.21 ********************************
% 0.09/0.21 % SZS status Theorem for /export/starexec/sandbox2/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:20,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.09/0.21
% 0.09/0.21 %**** Beginning of derivation protocol ****
% 0.09/0.21 % SZS output start CNFRefutation
% See solution above
% 0.09/0.21
% 0.09/0.21 %**** End of derivation protocol ****
% 0.09/0.21 %**** no. of clauses in derivation: 21 ****
% 0.09/0.21 %**** clause counter: 20 ****
% 0.09/0.21
% 0.09/0.21 % SZS status Theorem for /export/starexec/sandbox2/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:20,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------