%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU636^2 : 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 : 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 10:45:47 AM UTC 2026
% Result : Theorem 0.10s 0.20s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 28 ( 23 unt; 0 typ; 3 def)
% Number of atoms : 123 ( 51 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 164 ( 15 ~; 16 |; 0 &; 118 @)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 37 ( 0 ^; 37 !; 0 ?; 37 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_emptyset,type,
emptyset: $i ).
thf(tp_sK1_Xx,type,
sK1_Xx: $i ).
thf(tp_setadjoin,type,
setadjoin: $i > $i > $i ).
thf(tp_setextsub,type,
setextsub: $o ).
thf(tp_setunion,type,
setunion: $i > $i ).
thf(tp_setunionsingleton1,type,
setunionsingleton1: $o ).
thf(tp_setunionsingleton2,type,
setunionsingleton2: $o ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(setextsub,definition,
( setextsub
= ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ A )
=> ( A = B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setextsub) ).
thf(setunionsingleton1,definition,
( setunionsingleton1
= ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionsingleton1) ).
thf(setunionsingleton2,definition,
( setunionsingleton2
= ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionsingleton2) ).
thf(1,conjecture,
( setextsub
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ! [Xx: $i] :
( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
= Xx ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionsingleton) ).
thf(2,negated_conjecture,
( ( setextsub
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ! [Xx: $i] :
( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
= Xx ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ A )
=> ( A = B ) ) )
=> ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A )
=> ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) )
=> ! [Xx: $i] :
( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
= Xx ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,setextsub,setunionsingleton1,setunionsingleton2]) ).
thf(4,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ A )
=> ( A = B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ! [Xx: $i] :
( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
= Xx ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(8,plain,
( ( ~ ! [Xx: $i] :
( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
= Xx ) )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(9,plain,
( ( ( setunion @ ( setadjoin @ sK1_Xx @ emptyset ) )
!= sK1_Xx )
= $true ),
inference(extcnf_combined,[status(esa)],[8]) ).
thf(10,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(11,plain,
( ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(12,plain,
( ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(13,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(14,plain,
( ( ( setunion @ ( setadjoin @ sK1_Xx @ emptyset ) )
!= sK1_Xx )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(15,plain,
! [SV1: $i] :
( ( subset @ SV1 @ ( setunion @ ( setadjoin @ SV1 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(16,plain,
! [SV2: $i] :
( ( subset @ ( setunion @ ( setadjoin @ SV2 @ emptyset ) ) @ SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(17,plain,
! [SV3: $i] :
( ( ! [SY6: $i] :
( ~ ( subset @ SV3 @ SY6 )
| ~ ( subset @ SY6 @ SV3 )
| ( SV3 = SY6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[13]) ).
thf(18,plain,
( ( ( setunion @ ( setadjoin @ sK1_Xx @ emptyset ) )
= sK1_Xx )
= $false ),
inference(extcnf_not_pos,[status(thm)],[14]) ).
thf(19,plain,
! [SV4: $i,SV3: $i] :
( ( ~ ( subset @ SV3 @ SV4 )
| ~ ( subset @ SV4 @ SV3 )
| ( SV3 = SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(20,plain,
! [SV4: $i,SV3: $i] :
( ( ( ~ ( subset @ SV3 @ SV4 ) )
= $true )
| ( ( ~ ( subset @ SV4 @ SV3 )
| ( SV3 = SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[19]) ).
thf(21,plain,
! [SV4: $i,SV3: $i] :
( ( ( subset @ SV3 @ SV4 )
= $false )
| ( ( ~ ( subset @ SV4 @ SV3 )
| ( SV3 = SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(22,plain,
! [SV3: $i,SV4: $i] :
( ( ( ~ ( subset @ SV4 @ SV3 ) )
= $true )
| ( ( SV3 = SV4 )
= $true )
| ( ( subset @ SV3 @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[21]) ).
thf(23,plain,
! [SV3: $i,SV4: $i] :
( ( ( subset @ SV4 @ SV3 )
= $false )
| ( ( SV3 = SV4 )
= $true )
| ( ( subset @ SV3 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[22]) ).
thf(24,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[15,23,18,16]) ).
thf(25,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU636^2 : 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
% 0.10/0.17 % Computer : n014.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Tue Oct 6 15:29:26 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.20
% 0.10/0.20 No.of.Axioms: 0
% 0.10/0.20
% 0.10/0.20 Length.of.Defs: 571
% 0.10/0.20
% 0.10/0.20 Contains.Choice.Funs: false
% 0.10/0.20
% 0.10/0.20 ********************************
% 0.10/0.20 * All subproblems solved! *
% 0.10/0.20 ********************************
% 0.10/0.20 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:3,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:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:24,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.10/0.20
% 0.10/0.20 %**** Beginning of derivation protocol ****
% 0.10/0.20 % SZS output start CNFRefutation
% See solution above
% 0.10/0.20
% 0.10/0.20 %**** End of derivation protocol ****
% 0.10/0.20 %**** no. of clauses in derivation: 25 ****
% 0.10/0.20 %**** clause counter: 24 ****
% 0.10/0.20
% 0.10/0.20 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:3,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:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:24,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------