%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU592^2 : 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 : n004.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 10:45:23 AM UTC 2026
% Result : Theorem 269.05s 45.35s
% Output : CNFRefutation 269.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 4
% Syntax : Number of formulae : 44 ( 28 unt; 0 typ; 3 def)
% Number of atoms : 239 ( 61 equ; 0 cnn)
% Maximal formula atoms : 3 ( 5 avg)
% Number of connectives : 433 ( 34 ~; 30 |; 2 &; 352 @)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 117 ( 30 ^; 87 !; 0 ?; 117 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_binintersect,type,
binintersect: $i > $i > $i ).
thf(tp_binintersectEL,type,
binintersectEL: $o ).
thf(tp_dsetconstr,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_sK1_SY0,type,
sK1_SY0: $i ).
thf(tp_sK2_SY27,type,
sK2_SY27: $i ).
thf(tp_sK3_Xx,type,
sK3_Xx: $i > $i > $i ).
thf(tp_sK4_E,type,
sK4_E: $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_subsetI2,type,
subsetI2: $o ).
thf(binintersect,definition,
( binintersect
= ( ^ [A: $i,B: $i] :
( dsetconstr @ A
@ ^ [Xx: $i] : ( in @ Xx @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersect) ).
thf(binintersectEL,definition,
( binintersectEL
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectEL) ).
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,
( subsetI2
=> ( binintersectEL
=> ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectLsub) ).
thf(2,negated_conjecture,
( ( subsetI2
=> ( binintersectEL
=> ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) )
=> ( ! [SY8: $i,SY9: $i,SY10: $i] :
( ( in @ SY10
@ ( dsetconstr @ SY8
@ ^ [SY13: $i] : ( in @ SY13 @ SY9 ) ) )
=> ( in @ SY10 @ SY8 ) )
=> ! [SY0: $i,SY1: $i] :
( subset
@ ( dsetconstr @ SY0
@ ^ [SY4: $i] : ( in @ SY4 @ SY1 ) )
@ SY0 ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,binintersect,binintersectEL,subsetI2]) ).
thf(4,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [SY8: $i,SY9: $i,SY10: $i] :
( ( in @ SY10
@ ( dsetconstr @ SY8
@ ^ [SY13: $i] : ( in @ SY13 @ SY9 ) ) )
=> ( in @ SY10 @ SY8 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [SY0: $i,SY1: $i] :
( subset
@ ( dsetconstr @ SY0
@ ^ [SY4: $i] : ( in @ SY4 @ SY1 ) )
@ SY0 ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ~ ! [SY0: $i,SY1: $i] :
( subset
@ ( dsetconstr @ SY0
@ ^ [SY4: $i] : ( in @ SY4 @ SY1 ) )
@ SY0 ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(8,plain,
( ( ~ ( subset
@ ( dsetconstr @ sK1_SY0
@ ^ [SY29: $i] : ( in @ SY29 @ sK2_SY27 ) )
@ sK1_SY0 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(9,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK3_Xx @ B @ A ) @ A )
& ~ ( in @ ( sK3_Xx @ B @ A ) @ B ) )
| ( subset @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(10,plain,
( ( ! [SY8: $i,SY9: $i,SY10: $i] :
( ~ ( in @ SY10
@ ( dsetconstr @ SY8
@ ^ [SY13: $i] : ( in @ SY13 @ SY9 ) ) )
| ( in @ SY10 @ SY8 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[5]) ).
thf(11,plain,
( ( ! [SY8: $i,SY9: $i,SY10: $i] :
( ~ ( in @ SY10
@ ( dsetconstr @ SY8
@ ^ [SY13: $i] : ( in @ SY13 @ SY9 ) ) )
| ( in @ SY10 @ SY8 ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(12,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK3_Xx @ B @ A ) @ A )
& ~ ( in @ ( sK3_Xx @ B @ A ) @ B ) )
| ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(13,plain,
( ( ~ ( subset
@ ( dsetconstr @ sK1_SY0
@ ^ [SY29: $i] : ( in @ SY29 @ sK2_SY27 ) )
@ sK1_SY0 ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(14,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK3_Xx @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK3_Xx @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12,binintersect,binintersectEL,subsetI2]) ).
thf(15,plain,
! [SV1: $i] :
( ( ! [SY30: $i,SY31: $i] :
( ~ ( in @ SY31
@ ( dsetconstr @ SV1
@ ^ [SY13: $i] : ( in @ SY13 @ SY30 ) ) )
| ( in @ SY31 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(16,plain,
( ( subset
@ ( dsetconstr @ sK1_SY0
@ ^ [SY29: $i] : ( in @ SY29 @ sK2_SY27 ) )
@ sK1_SY0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[13]) ).
thf(17,plain,
! [SV2: $i] :
( ( ! [SY33: $i] :
( ~ ( ~ ( in @ ( sK3_Xx @ SY33 @ SV2 ) @ SV2 )
| ~ ~ ( in @ ( sK3_Xx @ SY33 @ SV2 ) @ SY33 ) )
| ( subset @ SV2 @ SY33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(18,plain,
! [SV3: $i,SV1: $i] :
( ( ! [SY34: $i] :
( ~ ( in @ SY34
@ ( dsetconstr @ SV1
@ ^ [SY35: $i] : ( in @ SY35 @ SV3 ) ) )
| ( in @ SY34 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(19,plain,
! [SV2: $i,SV4: $i] :
( ( ~ ( ~ ( in @ ( sK3_Xx @ SV4 @ SV2 ) @ SV2 )
| ~ ~ ( in @ ( sK3_Xx @ SV4 @ SV2 ) @ SV4 ) )
| ( subset @ SV2 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(20,plain,
! [SV3: $i,SV1: $i,SV5: $i] :
( ( ~ ( in @ SV5
@ ( dsetconstr @ SV1
@ ^ [SY35: $i] : ( in @ SY35 @ SV3 ) ) )
| ( in @ SV5 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(21,plain,
! [SV2: $i,SV4: $i] :
( ( ( ~ ( ~ ( in @ ( sK3_Xx @ SV4 @ SV2 ) @ SV2 )
| ~ ~ ( in @ ( sK3_Xx @ SV4 @ SV2 ) @ SV4 ) ) )
= $true )
| ( ( subset @ SV2 @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[19]) ).
thf(22,plain,
! [SV3: $i,SV1: $i,SV5: $i] :
( ( ( ~ ( in @ SV5
@ ( dsetconstr @ SV1
@ ^ [SY35: $i] : ( in @ SY35 @ SV3 ) ) ) )
= $true )
| ( ( in @ SV5 @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[20]) ).
thf(23,plain,
! [SV2: $i,SV4: $i] :
( ( ( ~ ( in @ ( sK3_Xx @ SV4 @ SV2 ) @ SV2 )
| ~ ~ ( in @ ( sK3_Xx @ SV4 @ SV2 ) @ SV4 ) )
= $false )
| ( ( subset @ SV2 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(24,plain,
! [SV3: $i,SV1: $i,SV5: $i] :
( ( ( in @ SV5
@ ( dsetconstr @ SV1
@ ^ [SY35: $i] : ( in @ SY35 @ SV3 ) ) )
= $false )
| ( ( in @ SV5 @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[22]) ).
thf(25,plain,
! [SV2: $i,SV4: $i] :
( ( ( ~ ( in @ ( sK3_Xx @ SV4 @ SV2 ) @ SV2 ) )
= $false )
| ( ( subset @ SV2 @ SV4 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[23]) ).
thf(26,plain,
! [SV2: $i,SV4: $i] :
( ( ( ~ ~ ( in @ ( sK3_Xx @ SV4 @ SV2 ) @ SV4 ) )
= $false )
| ( ( subset @ SV2 @ SV4 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[23]) ).
thf(27,plain,
! [SV2: $i,SV4: $i] :
( ( ( in @ ( sK3_Xx @ SV4 @ SV2 ) @ SV2 )
= $true )
| ( ( subset @ SV2 @ SV4 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[25]) ).
thf(28,plain,
! [SV2: $i,SV4: $i] :
( ( ( ~ ( in @ ( sK3_Xx @ SV4 @ SV2 ) @ SV4 ) )
= $true )
| ( ( subset @ SV2 @ SV4 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[26]) ).
thf(29,plain,
! [SV2: $i,SV4: $i] :
( ( ( in @ ( sK3_Xx @ SV4 @ SV2 ) @ SV4 )
= $false )
| ( ( subset @ SV2 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(42,plain,
! [SV6: $i,SV7: $i,SV8: $i] :
( ( ( in @ SV8
@ ( dsetconstr @ SV7
@ ^ [SX0: $i] : ( in @ SX0 @ SV6 ) ) )
= $false )
| ( ( in @ SV8 @ SV7 )
= $true ) ),
inference(rename,[status(thm)],[24]) ).
thf(46,plain,
! [SV9: $i,SV10: $i] :
( ( ( in @ ( sK3_Xx @ SV10 @ SV9 ) @ SV9 )
= $true )
| ( ( subset @ SV9 @ SV10 )
= $true ) ),
inference(rename,[status(thm)],[27]) ).
thf(49,plain,
! [SV9: $i,SV10: $i] :
( ( ( ( subset @ SV9 @ SV10 )
= ( subset
@ ( dsetconstr @ sK1_SY0
@ ^ [SY29: $i] : ( in @ SY29 @ sK2_SY27 ) )
@ sK1_SY0 ) )
= $false )
| ( ( in @ ( sK3_Xx @ SV10 @ SV9 ) @ SV9 )
= $true ) ),
inference(res,[status(thm)],[46,16]) ).
thf(52,plain,
( ( in
@ ( sK3_Xx @ sK1_SY0
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( in @ SX0 @ sK2_SY27 ) ) )
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( in @ SX0 @ sK2_SY27 ) ) )
= $true ),
inference(extuni,[status(esa)],[49:[bind(SV10,$thf( sK1_SY0 )),bind(SV9,$thf( dsetconstr @ sK1_SY0 @ ^ [SX0: $i] : ( in @ SX0 @ sK2_SY27 ) ))]]) ).
thf(54,plain,
! [SV6: $i,SV7: $i,SV8: $i] :
( ( ( ( in
@ ( sK3_Xx @ sK1_SY0
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( in @ SX0 @ sK2_SY27 ) ) )
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( in @ SX0 @ sK2_SY27 ) ) )
= ( in @ SV8
@ ( dsetconstr @ SV7
@ ^ [SX0: $i] : ( in @ SX0 @ SV6 ) ) ) )
= $false )
| ( ( in @ SV8 @ SV7 )
= $true ) ),
inference(res,[status(thm)],[52,42]) ).
thf(56,plain,
( ( in
@ ( sK3_Xx @ sK1_SY0
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( in @ SX0 @ sK2_SY27 ) ) )
@ sK1_SY0 )
= $true ),
inference(extuni,[status(esa)],[54:[bind(SV6,$thf( sK2_SY27 )),bind(SV7,$thf( sK1_SY0 )),bind(SV8,$thf( sK3_Xx @ sK1_SY0 @ ( dsetconstr @ sK1_SY0 @ ^ [SX0: $i] : ( in @ SX0 @ sK2_SY27 ) ) ))]]) ).
thf(60,plain,
! [SV11: $i,SV12: $i] :
( ( ( in @ ( sK3_Xx @ SV12 @ SV11 ) @ SV12 )
= $false )
| ( ( subset @ SV11 @ SV12 )
= $true ) ),
inference(rename,[status(thm)],[29]) ).
thf(68,plain,
! [SV11: $i,SV12: $i] :
( ( ( ( subset @ SV11 @ SV12 )
= ( subset
@ ( dsetconstr @ sK1_SY0
@ ^ [SY29: $i] : ( in @ SY29 @ sK2_SY27 ) )
@ sK1_SY0 ) )
= $false )
| ( ( in @ ( sK3_Xx @ SV12 @ SV11 ) @ SV12 )
= $false ) ),
inference(res,[status(thm)],[60,16]) ).
thf(69,plain,
( ( in
@ ( sK3_Xx @ sK1_SY0
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( in @ SX0 @ sK2_SY27 ) ) )
@ sK1_SY0 )
= $false ),
inference(extuni,[status(esa)],[68:[bind(SV12,$thf( sK1_SY0 )),bind(SV11,$thf( dsetconstr @ sK1_SY0 @ ^ [SX0: $i] : ( in @ SX0 @ sK2_SY27 ) ))]]) ).
thf(83,plain,
( ( ( in
@ ( sK3_Xx @ sK1_SY0
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( in @ SX0 @ sK2_SY27 ) ) )
@ sK1_SY0 )
= ( in
@ ( sK3_Xx @ sK1_SY0
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( in @ SX0 @ sK2_SY27 ) ) )
@ sK1_SY0 ) )
= $false ),
inference(res,[status(thm)],[69,56]) ).
thf(92,plain,
$false = $true,
inference(extuni,[status(esa)],[83]) ).
thf(93,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[92]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU592^2 : 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
% 0.09/0.18 % Computer : n004.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Oct 6 15:28:39 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 269.05/45.35
% 269.05/45.35 No.of.Axioms: 0
% 269.05/45.35
% 269.05/45.35 Length.of.Defs: 555
% 269.05/45.35
% 269.05/45.35 Contains.Choice.Funs: false
% 269.05/45.35 .eprover: CPU time limit exceeded, terminating
% 269.05/45.35 eprover: CPU time limit exceeded, terminating
% 269.05/45.35 eprover: CPU time limit exceeded, terminating
% 269.05/45.35 .
% 269.05/45.35
% 269.05/45.35 ********************************
% 269.05/45.35 * All subproblems solved! *
% 269.05/45.35 ********************************
% 269.05/45.35 % 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:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:92,loop_count:7,foatp_calls:3,translation:fof_experiment)
% 269.05/45.35
% 269.05/45.35 %**** Beginning of derivation protocol ****
% 269.05/45.35 % SZS output start CNFRefutation
% See solution above
% 269.05/45.35
% 269.05/45.35 %**** End of derivation protocol ****
% 269.05/45.35 %**** no. of clauses in derivation: 41 ****
% 269.05/45.35 %**** clause counter: 92 ****
% 269.05/45.35
% 269.05/45.35 % 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:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:92,loop_count:7,foatp_calls:3,translation:fof_experiment)
%------------------------------------------------------------------------------