%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU644^2 : 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 : n014.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 10:45:51 AM UTC 2026
% Result : Theorem 0.06s 0.20s
% Output : CNFRefutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 4
% Syntax : Number of formulae : 35 ( 32 unt; 0 typ; 3 def)
% Number of atoms : 143 ( 65 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 236 ( 51 ~; 17 |; 5 &; 147 @)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 43 ( 1 ^; 37 !; 5 ?; 43 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_emptyset,type,
emptyset: $i ).
thf(tp_eqinunit,type,
eqinunit: $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_sK1_SX0,type,
sK1_SX0: $i ).
thf(tp_sK2_SY8,type,
sK2_SY8: $i ).
thf(tp_setadjoin,type,
setadjoin: $i > $i > $i ).
thf(tp_setunion,type,
setunion: $i > $i ).
thf(tp_setunionsingleton,type,
setunionsingleton: $o ).
thf(tp_singleton,type,
singleton: $i > $o ).
thf(eqinunit,definition,
( eqinunit
= ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqinunit) ).
thf(setunionsingleton,definition,
( setunionsingleton
= ( ! [Xx: $i] :
( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
= Xx ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionsingleton) ).
thf(singleton,definition,
( singleton
= ( ^ [A: $i] :
? [Xx: $i] :
( ( in @ Xx @ A )
& ( A
= ( setadjoin @ Xx @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton) ).
thf(1,conjecture,
( eqinunit
=> ( setunionsingleton
=> ! [X: $i] :
( ( singleton @ X )
=> ( in @ ( setunion @ X ) @ X ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',theprop) ).
thf(2,negated_conjecture,
( ( eqinunit
=> ( setunionsingleton
=> ! [X: $i] :
( ( singleton @ X )
=> ( in @ ( setunion @ X ) @ X ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ! [Xx: $i] :
( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
= Xx )
=> ! [SY0: $i] :
( ? [SY1: $i] :
( ( in @ SY1 @ SY0 )
& ( SY0
= ( setadjoin @ SY1 @ emptyset ) ) )
=> ( in @ ( setunion @ SY0 ) @ SY0 ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,eqinunit,setunionsingleton,singleton]) ).
thf(4,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [Xx: $i] :
( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
= Xx ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [SY0: $i] :
( ? [SY1: $i] :
( ( in @ SY1 @ SY0 )
& ( SY0
= ( setadjoin @ SY1 @ emptyset ) ) )
=> ( in @ ( setunion @ SY0 ) @ SY0 ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ~ ! [SY0: $i] :
( ? [SY1: $i] :
( ( in @ SY1 @ SY0 )
& ( SY0
= ( setadjoin @ SY1 @ emptyset ) ) )
=> ( in @ ( setunion @ SY0 ) @ SY0 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(8,plain,
( ( ! [Xx: $i] :
( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
= Xx ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(9,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(10,plain,
( ( ~ ! [SY0: $i] :
( ? [SY1: $i] :
( ( in @ SY1 @ SY0 )
& ( SY0
= ( setadjoin @ SY1 @ emptyset ) ) )
=> ( in @ ( setunion @ SY0 ) @ SY0 ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(11,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( in @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9,eqinunit,setunionsingleton,singleton]) ).
thf(12,plain,
( ( ~ ! [SX0: $i] :
( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( in @ SX1 @ SX0 )
| ( SX0
!= ( setadjoin @ SX1 @ emptyset ) ) )
| ( in @ ( setunion @ SX0 ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10,eqinunit,setunionsingleton,singleton]) ).
thf(13,plain,
! [SV1: $i] :
( ( ( setunion @ ( setadjoin @ SV1 @ emptyset ) )
= SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8]) ).
thf(14,plain,
! [SV2: $i] :
( ( ! [SY7: $i] :
( ( SV2 != SY7 )
| ( in @ SV2 @ ( setadjoin @ SY7 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(15,plain,
( ( ! [SX0: $i] :
( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( in @ SX1 @ SX0 )
| ( SX0
!= ( setadjoin @ SX1 @ emptyset ) ) )
| ( in @ ( setunion @ SX0 ) @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[12]) ).
thf(16,plain,
! [SV3: $i,SV2: $i] :
( ( ( SV2 != SV3 )
| ( in @ SV2 @ ( setadjoin @ SV3 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(17,plain,
( ( ~ ~ ! [SY8: $i] :
~ ~ ( ~ ( in @ SY8 @ sK1_SX0 )
| ( sK1_SX0
!= ( setadjoin @ SY8 @ emptyset ) ) )
| ( in @ ( setunion @ sK1_SX0 ) @ sK1_SX0 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[15]) ).
thf(18,plain,
! [SV3: $i,SV2: $i] :
( ( ( SV2 != SV3 )
= $true )
| ( ( in @ SV2 @ ( setadjoin @ SV3 @ emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[16]) ).
thf(19,plain,
( ( ~ ~ ! [SY8: $i] :
~ ~ ( ~ ( in @ SY8 @ sK1_SX0 )
| ( sK1_SX0
!= ( setadjoin @ SY8 @ emptyset ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(20,plain,
( ( in @ ( setunion @ sK1_SX0 ) @ sK1_SX0 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(21,plain,
! [SV3: $i,SV2: $i] :
( ( ( SV2 = SV3 )
= $false )
| ( ( in @ SV2 @ ( setadjoin @ SV3 @ emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(22,plain,
( ( ~ ! [SY8: $i] :
~ ~ ( ~ ( in @ SY8 @ sK1_SX0 )
| ( sK1_SX0
!= ( setadjoin @ SY8 @ emptyset ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[19]) ).
thf(23,plain,
( ( ! [SY8: $i] :
~ ~ ( ~ ( in @ SY8 @ sK1_SX0 )
| ( sK1_SX0
!= ( setadjoin @ SY8 @ emptyset ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[22]) ).
thf(24,plain,
( ( ~ ~ ( ~ ( in @ sK2_SY8 @ sK1_SX0 )
| ( sK1_SX0
!= ( setadjoin @ sK2_SY8 @ emptyset ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[23]) ).
thf(25,plain,
( ( ~ ( ~ ( in @ sK2_SY8 @ sK1_SX0 )
| ( sK1_SX0
!= ( setadjoin @ sK2_SY8 @ emptyset ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[24]) ).
thf(26,plain,
( ( ~ ( in @ sK2_SY8 @ sK1_SX0 )
| ( sK1_SX0
!= ( setadjoin @ sK2_SY8 @ emptyset ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(27,plain,
( ( ~ ( in @ sK2_SY8 @ sK1_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[26]) ).
thf(28,plain,
( ( sK1_SX0
!= ( setadjoin @ sK2_SY8 @ emptyset ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[26]) ).
thf(29,plain,
( ( in @ sK2_SY8 @ sK1_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[27]) ).
thf(30,plain,
( ( sK1_SX0
= ( setadjoin @ sK2_SY8 @ emptyset ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[28]) ).
thf(31,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[13,30,29,21,20]) ).
thf(32,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU644^2 : 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
% 0.06/0.17 % Computer : n014.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 15:29:41 UTC 2026
% 0.06/0.17 % CPUTime :
% 0.06/0.17 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: 0
% 0.06/0.20
% 0.06/0.20 Length.of.Defs: 547
% 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 Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:2,ps:3,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:31,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: 32 ****
% 0.06/0.20 %**** clause counter: 31 ****
% 0.06/0.20
% 0.06/0.20 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:2,ps:3,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:31,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------