%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU563^2 : 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 10:45:08 AM UTC 2026
% Result : Theorem 0.07s 0.21s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 4
% Syntax : Number of formulae : 41 ( 26 unt; 0 typ; 3 def)
% Number of atoms : 225 ( 57 equ; 0 cnn)
% Maximal formula atoms : 3 ( 5 avg)
% Number of connectives : 321 ( 35 ~; 44 |; 0 &; 216 @)
% ( 0 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 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 : 91 ( 2 ^; 89 !; 0 ?; 91 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_emptyset,type,
emptyset: $i ).
thf(tp_emptysetimpfalse,type,
emptysetimpfalse: $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_sK1_SX0,type,
sK1_SX0: $i ).
thf(tp_sK2_SY25,type,
sK2_SY25: $i ).
thf(tp_sK3_SY23,type,
sK3_SY23: $i > $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_subsetI2,type,
subsetI2: $o ).
thf(emptysetimpfalse,definition,
( emptysetimpfalse
= ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> $false ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetimpfalse) ).
thf(subset,definition,
( subset
= ( ^ [A: $i,B: $i] :
! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset) ).
thf(subsetI2,definition,
( subsetI2
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI2) ).
thf(1,conjecture,
( emptysetimpfalse
=> ( subsetI2
=> ! [A: $i] : ( subset @ emptyset @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetsubset) ).
thf(2,negated_conjecture,
( ( emptysetimpfalse
=> ( subsetI2
=> ! [A: $i] : ( subset @ emptyset @ A ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> $false )
=> ( ! [SY5: $i,SY6: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ SY5 )
=> ( in @ Xx @ SY6 ) )
=> ! [SY10: $i] :
( ( in @ SY10 @ SY5 )
=> ( in @ SY10 @ SY6 ) ) )
=> ! [SY0: $i,SY3: $i] :
( ( in @ SY3 @ emptyset )
=> ( in @ SY3 @ SY0 ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,emptysetimpfalse,subset,subsetI2]) ).
thf(4,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> $false ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [SY5: $i,SY6: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ SY5 )
=> ( in @ Xx @ SY6 ) )
=> ! [SY10: $i] :
( ( in @ SY10 @ SY5 )
=> ( in @ SY10 @ SY6 ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [SY0: $i,SY3: $i] :
( ( in @ SY3 @ emptyset )
=> ( in @ SY3 @ SY0 ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ~ ! [SY0: $i,SY3: $i] :
( ( in @ SY3 @ emptyset )
=> ( in @ SY3 @ SY0 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(8,plain,
( ( ! [SY5: $i,SY6: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ SY5 )
=> ( in @ Xx @ SY6 ) )
=> ! [SY10: $i] :
( ( in @ SY10 @ SY5 )
=> ( in @ SY10 @ SY6 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(9,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> $false ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(10,plain,
( ( ~ ! [SY0: $i,SY3: $i] :
( ( in @ SY3 @ emptyset )
=> ( in @ SY3 @ SY0 ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(11,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8,emptysetimpfalse,subset,subsetI2]) ).
thf(12,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ emptyset )
| $false ) )
= $true ),
inference(unfold_def,[status(thm)],[9,emptysetimpfalse,subset,subsetI2]) ).
thf(13,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ emptyset )
| ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10,emptysetimpfalse,subset,subsetI2]) ).
thf(14,plain,
! [SV1: $i] :
( ( ! [SY20: $i] :
( ~ ! [SY21: $i] :
( ~ ( in @ SY21 @ SV1 )
| ( in @ SY21 @ SY20 ) )
| ! [SY22: $i] :
( ~ ( in @ SY22 @ SV1 )
| ( in @ SY22 @ SY20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(15,plain,
! [SV2: $i] :
( ( ~ ( in @ SV2 @ emptyset )
| $false )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(16,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ emptyset )
| ( in @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[13]) ).
thf(17,plain,
! [SV3: $i,SV1: $i] :
( ( ~ ! [SY23: $i] :
( ~ ( in @ SY23 @ SV1 )
| ( in @ SY23 @ SV3 ) )
| ! [SY24: $i] :
( ~ ( in @ SY24 @ SV1 )
| ( in @ SY24 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(18,plain,
! [SV2: $i] :
( ( ( ~ ( in @ SV2 @ emptyset ) )
= $true )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[15]) ).
thf(19,plain,
( ( ! [SY25: $i] :
( ~ ( in @ SY25 @ emptyset )
| ( in @ SY25 @ sK1_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[16]) ).
thf(20,plain,
! [SV3: $i,SV1: $i] :
( ( ( ~ ! [SY23: $i] :
( ~ ( in @ SY23 @ SV1 )
| ( in @ SY23 @ SV3 ) ) )
= $true )
| ( ( ! [SY24: $i] :
( ~ ( in @ SY24 @ SV1 )
| ( in @ SY24 @ SV3 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[17]) ).
thf(21,plain,
! [SV2: $i] :
( ( ( in @ SV2 @ emptyset )
= $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(22,plain,
( ( ~ ( in @ sK2_SY25 @ emptyset )
| ( in @ sK2_SY25 @ sK1_SX0 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[19]) ).
thf(23,plain,
! [SV3: $i,SV1: $i] :
( ( ( ! [SY23: $i] :
( ~ ( in @ SY23 @ SV1 )
| ( in @ SY23 @ SV3 ) ) )
= $false )
| ( ( ! [SY24: $i] :
( ~ ( in @ SY24 @ SV1 )
| ( in @ SY24 @ SV3 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(24,plain,
( ( ~ ( in @ sK2_SY25 @ emptyset ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[22]) ).
thf(25,plain,
( ( in @ sK2_SY25 @ sK1_SX0 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[22]) ).
thf(26,plain,
! [SV1: $i,SV3: $i] :
( ( ( ~ ( in @ ( sK3_SY23 @ SV3 @ SV1 ) @ SV1 )
| ( in @ ( sK3_SY23 @ SV3 @ SV1 ) @ SV3 ) )
= $false )
| ( ( ! [SY24: $i] :
( ~ ( in @ SY24 @ SV1 )
| ( in @ SY24 @ SV3 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[23]) ).
thf(27,plain,
( ( in @ sK2_SY25 @ emptyset )
= $true ),
inference(extcnf_not_neg,[status(thm)],[24]) ).
thf(28,plain,
! [SV1: $i,SV3: $i] :
( ( ( ~ ( in @ ( sK3_SY23 @ SV3 @ SV1 ) @ SV1 ) )
= $false )
| ( ( ! [SY24: $i] :
( ~ ( in @ SY24 @ SV1 )
| ( in @ SY24 @ SV3 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[26]) ).
thf(29,plain,
! [SV1: $i,SV3: $i] :
( ( ( in @ ( sK3_SY23 @ SV3 @ SV1 ) @ SV3 )
= $false )
| ( ( ! [SY24: $i] :
( ~ ( in @ SY24 @ SV1 )
| ( in @ SY24 @ SV3 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[26]) ).
thf(30,plain,
! [SV1: $i,SV3: $i] :
( ( ( in @ ( sK3_SY23 @ SV3 @ SV1 ) @ SV1 )
= $true )
| ( ( ! [SY24: $i] :
( ~ ( in @ SY24 @ SV1 )
| ( in @ SY24 @ SV3 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[28]) ).
thf(31,plain,
! [SV3: $i,SV1: $i,SV4: $i] :
( ( ( ~ ( in @ SV4 @ SV1 )
| ( in @ SV4 @ SV3 ) )
= $true )
| ( ( in @ ( sK3_SY23 @ SV3 @ SV1 ) @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(32,plain,
! [SV3: $i,SV1: $i,SV5: $i] :
( ( ( ~ ( in @ SV5 @ SV1 )
| ( in @ SV5 @ SV3 ) )
= $true )
| ( ( in @ ( sK3_SY23 @ SV3 @ SV1 ) @ SV1 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(33,plain,
! [SV3: $i,SV1: $i,SV4: $i] :
( ( ( ~ ( in @ SV4 @ SV1 ) )
= $true )
| ( ( in @ SV4 @ SV3 )
= $true )
| ( ( in @ ( sK3_SY23 @ SV3 @ SV1 ) @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[31]) ).
thf(34,plain,
! [SV3: $i,SV1: $i,SV5: $i] :
( ( ( ~ ( in @ SV5 @ SV1 ) )
= $true )
| ( ( in @ SV5 @ SV3 )
= $true )
| ( ( in @ ( sK3_SY23 @ SV3 @ SV1 ) @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[32]) ).
thf(35,plain,
! [SV3: $i,SV1: $i,SV4: $i] :
( ( ( in @ SV4 @ SV1 )
= $false )
| ( ( in @ SV4 @ SV3 )
= $true )
| ( ( in @ ( sK3_SY23 @ SV3 @ SV1 ) @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(36,plain,
! [SV3: $i,SV1: $i,SV5: $i] :
( ( ( in @ SV5 @ SV1 )
= $false )
| ( ( in @ SV5 @ SV3 )
= $true )
| ( ( in @ ( sK3_SY23 @ SV3 @ SV1 ) @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(37,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[21,36,35,27,25]) ).
thf(38,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU563^2 : 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
% 0.07/0.18 % Computer : n014.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Oct 6 15:27:56 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.21
% 0.07/0.21 No.of.Axioms: 0
% 0.07/0.21
% 0.07/0.21 Length.of.Defs: 516
% 0.07/0.21
% 0.07/0.21 Contains.Choice.Funs: false
% 0.07/0.21 .
% 0.07/0.21
% 0.07/0.21 ********************************
% 0.07/0.21 * All subproblems solved! *
% 0.07/0.21 ********************************
% 0.07/0.21 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:2,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:37,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.07/0.21
% 0.07/0.21 %**** Beginning of derivation protocol ****
% 0.07/0.21 % SZS output start CNFRefutation
% See solution above
% 0.07/0.21
% 0.07/0.21 %**** End of derivation protocol ****
% 0.07/0.21 %**** no. of clauses in derivation: 38 ****
% 0.07/0.21 %**** clause counter: 37 ****
% 0.07/0.21
% 0.07/0.21 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:2,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:37,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------