%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU500^2 : 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 : n016.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 10:44:37 AM UTC 2026
% Result : Theorem 0.07s 0.27s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 3
% Syntax : Number of formulae : 30 ( 25 unt; 0 typ; 2 def)
% Number of atoms : 109 ( 34 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 186 ( 13 ~; 12 |; 0 &; 148 @)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 87 ( 28 ^; 59 !; 0 ?; 87 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_dsetconstr,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(tp_dsetconstrER,type,
dsetconstrER: $o ).
thf(tp_emptyset,type,
emptyset: $i ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_prop2set,type,
prop2set: $o > $i ).
thf(tp_sK1_SX0,type,
sK1_SX0: $o ).
thf(tp_sK2_SY13,type,
sK2_SY13: $i ).
thf(tp_sK3_E,type,
sK3_E: ( $i > $o ) > $i ).
thf(tp_sK4_E,type,
sK4_E: $i ).
thf(dsetconstrER,definition,
( dsetconstrER
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( Xphi @ Xx ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrER) ).
thf(prop2set,definition,
( prop2set
= ( ^ [Xphi: $o] :
( dsetconstr @ ( powerset @ emptyset )
@ ^ [Xx: $i] : Xphi ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2set) ).
thf(1,conjecture,
( dsetconstrER
=> ! [Xphi: $o,Xx: $i] :
( ( in @ Xx @ ( prop2set @ Xphi ) )
=> Xphi ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2setE) ).
thf(2,negated_conjecture,
( ( dsetconstrER
=> ! [Xphi: $o,Xx: $i] :
( ( in @ Xx @ ( prop2set @ Xphi ) )
=> Xphi ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( Xphi @ Xx ) )
=> ! [SY0: $o,SY1: $i] :
( ( in @ SY1
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SY2: $i] : SY0 ) )
=> SY0 ) )
= $false ),
inference(unfold_def,[status(thm)],[2,dsetconstrER,prop2set]) ).
thf(4,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( Xphi @ Xx ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [SY0: $o,SY1: $i] :
( ( in @ SY1
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SY2: $i] : SY0 ) )
=> SY0 ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ~ ! [SY0: $o,SY1: $i] :
( ( in @ SY1
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SY2: $i] : SY0 ) )
=> SY0 ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(7,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( Xphi @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(8,plain,
( ( ~ ! [SY0: $o,SY1: $i] :
( ( in @ SY1
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SY2: $i] : SY0 ) )
=> SY0 ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(9,plain,
( ( ~ ! [SX0: $o,SX1: $i] :
( ~ ( in @ SX1
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SX2: $i] : SX0 ) )
| SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[8,dsetconstrER,prop2set]) ).
thf(10,plain,
( ( ! [SX0: $i,SX1: $i > $o,SX2: $i] :
( ~ ( in @ SX2
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) )
| ( SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7,dsetconstrER,prop2set]) ).
thf(11,plain,
( ( ! [SX0: $o,SX1: $i] :
( ~ ( in @ SX1
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SX2: $i] : SX0 ) )
| SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[9]) ).
thf(12,plain,
! [SV1: $i] :
( ( ! [SY10: $i > $o,SY11: $i] :
( ~ ( in @ SY11
@ ( dsetconstr @ SV1
@ ^ [SX3: $i] : ( SY10 @ SX3 ) ) )
| ( SY10 @ SY11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[10]) ).
thf(13,plain,
( ( ! [SY13: $i] :
( ~ ( in @ SY13
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SY14: $i] : sK1_SX0 ) )
| sK1_SX0 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[11]) ).
thf(14,plain,
! [SV2: $i > $o,SV1: $i] :
( ( ! [SY15: $i] :
( ~ ( in @ SY15
@ ( dsetconstr @ SV1
@ ^ [SY16: $i] : ( SV2 @ SY16 ) ) )
| ( SV2 @ SY15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(15,plain,
( ( ~ ( in @ sK2_SY13
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SY14: $i] : sK1_SX0 ) )
| sK1_SX0 )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[13]) ).
thf(16,plain,
! [SV2: $i > $o,SV1: $i,SV3: $i] :
( ( ~ ( in @ SV3
@ ( dsetconstr @ SV1
@ ^ [SY16: $i] : ( SV2 @ SY16 ) ) )
| ( SV2 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(17,plain,
( ( ~ ( in @ sK2_SY13
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SY14: $i] : sK1_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[15]) ).
thf(18,plain,
sK1_SX0 = $false,
inference(extcnf_or_neg,[status(thm)],[15]) ).
thf(19,plain,
! [SV2: $i > $o,SV1: $i,SV3: $i] :
( ( ( ~ ( in @ SV3
@ ( dsetconstr @ SV1
@ ^ [SY16: $i] : ( SV2 @ SY16 ) ) ) )
= $true )
| ( ( SV2 @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[16]) ).
thf(20,plain,
( ( in @ sK2_SY13
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SY14: $i] : sK1_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[17]) ).
thf(21,plain,
! [SV2: $i > $o,SV1: $i,SV3: $i] :
( ( ( in @ SV3
@ ( dsetconstr @ SV1
@ ^ [SY16: $i] : ( SV2 @ SY16 ) ) )
= $false )
| ( ( SV2 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[19]) ).
thf(51,plain,
! [SV11: $i > $o,SV12: $i,SV13: $i] :
( ( ( in @ SV13
@ ( dsetconstr @ SV12
@ ^ [SX0: $i] : ( SV11 @ SX0 ) ) )
= $false )
| ( ( SV11 @ SV13 )
= $true ) ),
inference(rename,[status(thm)],[21]) ).
thf(55,plain,
! [SV11: $i > $o,SV12: $i,SV13: $i] :
( ( ( ( SV11 @ SV13 )
= sK1_SX0 )
= $false )
| ( ( in @ SV13
@ ( dsetconstr @ SV12
@ ^ [SX0: $i] : ( SV11 @ SX0 ) ) )
= $false ) ),
inference(res,[status(thm)],[51,18]) ).
thf(57,plain,
! [SV12: $i,SV13: $i] :
( ( in @ SV13
@ ( dsetconstr @ SV12
@ ^ [SX0: $i] : sK1_SX0 ) )
= $false ),
inference(extuni,[status(esa)],[55:[bind(SV11,$thf( ^ [SX0: $i] : sK1_SX0 ))]]) ).
thf(76,plain,
! [SV29: $i,SV30: $i] :
( ( in @ SV30
@ ( dsetconstr @ SV29
@ ^ [SX0: $i] : sK1_SX0 ) )
= $false ),
inference(rename,[status(thm)],[57]) ).
thf(78,plain,
! [SV29: $i,SV30: $i] :
( ( ( in @ SV30
@ ( dsetconstr @ SV29
@ ^ [SX0: $i] : sK1_SX0 ) )
= ( in @ sK2_SY13
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [SY14: $i] : sK1_SX0 ) ) )
= $false ),
inference(res,[status(thm)],[76,20]) ).
thf(79,plain,
$false = $true,
inference(extuni,[status(esa)],[78:[bind(SV29,$thf( powerset @ emptyset )),bind(SV30,$thf( sK2_SY13 ))]]) ).
thf(80,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[79]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU500^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.20 % Computer : n016.cluster.edu
% 0.07/0.20 % Model : x86_64 x86_64
% 0.07/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.20 % Memory : 8046.5625MB
% 0.07/0.20 % OS : Linux 6.8.0-71-generic
% 0.07/0.20 % CPULimit : 300
% 0.07/0.20 % WCLimit : 300
% 0.07/0.20 % DateTime : Tue Oct 6 15:31:14 UTC 2026
% 0.07/0.20 % CPUTime :
% 0.07/0.20 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.27
% 0.07/0.27 No.of.Axioms: 0
% 0.07/0.27
% 0.07/0.27 Length.of.Defs: 388
% 0.07/0.27
% 0.07/0.27 Contains.Choice.Funs: false
% 0.07/0.27 .
% 0.07/0.27
% 0.07/0.27 ********************************
% 0.07/0.27 * All subproblems solved! *
% 0.07/0.27 ********************************
% 0.07/0.27 % 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:79,loop_count:4,foatp_calls:2,translation:fof_full)
% 0.07/0.27
% 0.07/0.27 %**** Beginning of derivation protocol ****
% 0.07/0.27 % SZS output start CNFRefutation
% See solution above
% 0.07/0.28
% 0.07/0.28 %**** End of derivation protocol ****
% 0.07/0.28 %**** no. of clauses in derivation: 28 ****
% 0.07/0.28 %**** clause counter: 79 ****
% 0.07/0.28
% 0.07/0.28 % 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:79,loop_count:4,foatp_calls:2,translation:fof_full)
%------------------------------------------------------------------------------