%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU621^2 : 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 : n017.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 10:45:39 AM UTC 2026
% Result : Theorem 0.07s 0.24s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 35 ( 26 unt; 0 typ; 2 def)
% Number of atoms : 165 ( 50 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 257 ( 23 ~; 24 |; 0 &; 186 @)
% ( 0 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 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 : 70 ( 0 ^; 70 !; 0 ?; 70 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_emptyset,type,
emptyset: $i ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_sK1_SX0,type,
sK1_SX0: $i ).
thf(tp_sK2_SY13,type,
sK2_SY13: $i ).
thf(tp_sK3_SY12,type,
sK3_SY12: $i > $i > $i ).
thf(tp_setadjoin,type,
setadjoin: $i > $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_subsetI2,type,
subsetI2: $o ).
thf(tp_uniqinunit,type,
uniqinunit: $o ).
thf(subsetI2,definition,
( subsetI2
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI2) ).
thf(uniqinunit,definition,
( uniqinunit
= ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uniqinunit) ).
thf(1,conjecture,
( uniqinunit
=> ( subsetI2
=> ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletonsubset) ).
thf(2,negated_conjecture,
( ( uniqinunit
=> ( subsetI2
=> ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) )
=> ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) )
=> ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,subsetI2,uniqinunit]) ).
thf(4,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ~ ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(8,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(9,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(10,plain,
( ( ~ ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(11,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8,subsetI2,uniqinunit]) ).
thf(12,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ ( setadjoin @ SX1 @ emptyset ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9,subsetI2,uniqinunit]) ).
thf(13,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( subset @ ( setadjoin @ SX1 @ emptyset ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10,subsetI2,uniqinunit]) ).
thf(14,plain,
! [SV1: $i] :
( ( ! [SY9: $i] :
( ~ ! [SY10: $i] :
( ~ ( in @ SY10 @ SV1 )
| ( in @ SY10 @ SY9 ) )
| ( subset @ SV1 @ SY9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(15,plain,
! [SV2: $i] :
( ( ! [SY11: $i] :
( ~ ( in @ SV2 @ ( setadjoin @ SY11 @ emptyset ) )
| ( SV2 = SY11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(16,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( subset @ ( setadjoin @ SX1 @ emptyset ) @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[13]) ).
thf(17,plain,
! [SV3: $i,SV1: $i] :
( ( ~ ! [SY12: $i] :
( ~ ( in @ SY12 @ SV1 )
| ( in @ SY12 @ SV3 ) )
| ( subset @ SV1 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(18,plain,
! [SV4: $i,SV2: $i] :
( ( ~ ( in @ SV2 @ ( setadjoin @ SV4 @ emptyset ) )
| ( SV2 = SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(19,plain,
( ( ! [SY13: $i] :
( ~ ( in @ SY13 @ sK1_SX0 )
| ( subset @ ( setadjoin @ SY13 @ emptyset ) @ sK1_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[16]) ).
thf(20,plain,
! [SV3: $i,SV1: $i] :
( ( ( ~ ! [SY12: $i] :
( ~ ( in @ SY12 @ SV1 )
| ( in @ SY12 @ SV3 ) ) )
= $true )
| ( ( subset @ SV1 @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[17]) ).
thf(21,plain,
! [SV4: $i,SV2: $i] :
( ( ( ~ ( in @ SV2 @ ( setadjoin @ SV4 @ emptyset ) ) )
= $true )
| ( ( SV2 = SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[18]) ).
thf(22,plain,
( ( ~ ( in @ sK2_SY13 @ sK1_SX0 )
| ( subset @ ( setadjoin @ sK2_SY13 @ emptyset ) @ sK1_SX0 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[19]) ).
thf(23,plain,
! [SV3: $i,SV1: $i] :
( ( ( ! [SY12: $i] :
( ~ ( in @ SY12 @ SV1 )
| ( in @ SY12 @ SV3 ) ) )
= $false )
| ( ( subset @ SV1 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(24,plain,
! [SV4: $i,SV2: $i] :
( ( ( in @ SV2 @ ( setadjoin @ SV4 @ emptyset ) )
= $false )
| ( ( SV2 = SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(25,plain,
( ( ~ ( in @ sK2_SY13 @ sK1_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[22]) ).
thf(26,plain,
( ( subset @ ( setadjoin @ sK2_SY13 @ emptyset ) @ sK1_SX0 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[22]) ).
thf(27,plain,
! [SV1: $i,SV3: $i] :
( ( ( ~ ( in @ ( sK3_SY12 @ SV3 @ SV1 ) @ SV1 )
| ( in @ ( sK3_SY12 @ SV3 @ SV1 ) @ SV3 ) )
= $false )
| ( ( subset @ SV1 @ SV3 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[23]) ).
thf(28,plain,
( ( in @ sK2_SY13 @ sK1_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[25]) ).
thf(29,plain,
! [SV1: $i,SV3: $i] :
( ( ( ~ ( in @ ( sK3_SY12 @ SV3 @ SV1 ) @ SV1 ) )
= $false )
| ( ( subset @ SV1 @ SV3 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[27]) ).
thf(30,plain,
! [SV1: $i,SV3: $i] :
( ( ( in @ ( sK3_SY12 @ SV3 @ SV1 ) @ SV3 )
= $false )
| ( ( subset @ SV1 @ SV3 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[27]) ).
thf(31,plain,
! [SV1: $i,SV3: $i] :
( ( ( in @ ( sK3_SY12 @ SV3 @ SV1 ) @ SV1 )
= $true )
| ( ( subset @ SV1 @ SV3 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[29]) ).
thf(32,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[24,31,30,28,26]) ).
thf(33,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU621^2 : 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
% 0.07/0.18 % Computer : n017.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 15:25:00 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.24
% 0.07/0.24 No.of.Axioms: 0
% 0.07/0.24
% 0.07/0.24 Length.of.Defs: 368
% 0.07/0.24
% 0.07/0.24 Contains.Choice.Funs: false
% 0.07/0.24
% 0.07/0.24 ********************************
% 0.07/0.24 * All subproblems solved! *
% 0.07/0.24 ********************************
% 0.07/0.24 % SZS status Theorem for /export/starexec/sandbox2/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:32,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.07/0.24
% 0.07/0.24 %**** Beginning of derivation protocol ****
% 0.07/0.24 % SZS output start CNFRefutation
% See solution above
% 0.07/0.24
% 0.07/0.24 %**** End of derivation protocol ****
% 0.07/0.24 %**** no. of clauses in derivation: 33 ****
% 0.07/0.24 %**** clause counter: 32 ****
% 0.07/0.24
% 0.07/0.24 % SZS status Theorem for /export/starexec/sandbox2/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:32,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------