%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU596^2 : 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 : n011.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 10:45:24 AM UTC 2026
% Result : Theorem 0.10s 0.21s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 4
% Syntax : Number of formulae : 50 ( 38 unt; 0 typ; 3 def)
% Number of atoms : 237 ( 80 equ; 0 cnn)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 406 ( 93 ~; 36 |; 6 &; 244 @)
% ( 0 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 8 con; 0-2 aty)
% Number of variables : 115 ( 0 ^; 109 !; 6 ?; 115 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_binintersect,type,
binintersect: $i > $i > $i ).
thf(tp_binintersectEL,type,
binintersectEL: $o ).
thf(tp_binintersectER,type,
binintersectER: $o ).
thf(tp_emptyI,type,
emptyI: $o ).
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_SY19,type,
sK2_SY19: $i ).
thf(tp_sK3_SY16,type,
sK3_SY16: $i > $i ).
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(binintersectER,definition,
( binintersectER
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectER) ).
thf(emptyI,definition,
( emptyI
= ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyI) ).
thf(1,conjecture,
( emptyI
=> ( binintersectEL
=> ( binintersectER
=> ! [A: $i,B: $i] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( in @ Xx @ B ) )
=> ( ( binintersect @ A @ B )
= emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',disjointsetsI1) ).
thf(2,negated_conjecture,
( ( emptyI
=> ( binintersectEL
=> ( binintersectER
=> ! [A: $i,B: $i] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( in @ Xx @ B ) )
=> ( ( binintersect @ A @ B )
= emptyset ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ A ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ B ) )
=> ! [A: $i,B: $i] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( in @ Xx @ B ) )
=> ( ( binintersect @ A @ B )
= emptyset ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,binintersectEL,binintersectER,emptyI]) ).
thf(4,plain,
( ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ! [A: $i,B: $i] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( in @ Xx @ B ) )
=> ( ( binintersect @ A @ B )
= emptyset ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(8,plain,
( ( ~ ! [A: $i,B: $i] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( in @ Xx @ B ) )
=> ( ( binintersect @ A @ B )
= emptyset ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(9,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ B ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(10,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ A ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(11,plain,
( ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(12,plain,
( ( ~ ! [A: $i,B: $i] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( in @ Xx @ B ) )
=> ( ( binintersect @ A @ B )
= emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(13,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ( ( binintersect @ SX0 @ SX1 )
= emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12,binintersectEL,binintersectER,emptyI]) ).
thf(14,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( binintersect @ SX0 @ SX1 ) )
| ( in @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9,binintersectEL,binintersectER,emptyI]) ).
thf(15,plain,
( ( ! [SX0: $i] :
( ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ( SX0 = emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11,binintersectEL,binintersectER,emptyI]) ).
thf(16,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( binintersect @ SX0 @ SX1 ) )
| ( in @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10,binintersectEL,binintersectER,emptyI]) ).
thf(17,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ( ( binintersect @ SX0 @ SX1 )
= emptyset ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[13]) ).
thf(18,plain,
! [SV1: $i] :
( ( ! [SY14: $i,SY15: $i] :
( ~ ( in @ SY15 @ ( binintersect @ SV1 @ SY14 ) )
| ( in @ SY15 @ SY14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(19,plain,
! [SV2: $i] :
( ( ~ ! [SY16: $i] :
~ ( in @ SY16 @ SV2 )
| ( SV2 = emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(20,plain,
! [SV3: $i] :
( ( ! [SY17: $i,SY18: $i] :
( ~ ( in @ SY18 @ ( binintersect @ SV3 @ SY17 ) )
| ( in @ SY18 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(21,plain,
( ( ! [SY19: $i] :
( ~ ~ ~ ! [SY20: $i] :
~ ~ ( ~ ( in @ SY20 @ sK1_SX0 )
| ~ ( in @ SY20 @ SY19 ) )
| ( ( binintersect @ sK1_SX0 @ SY19 )
= emptyset ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[17]) ).
thf(22,plain,
! [SV4: $i,SV1: $i] :
( ( ! [SY21: $i] :
( ~ ( in @ SY21 @ ( binintersect @ SV1 @ SV4 ) )
| ( in @ SY21 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(23,plain,
! [SV2: $i] :
( ( ( ~ ! [SY16: $i] :
~ ( in @ SY16 @ SV2 ) )
= $true )
| ( ( SV2 = emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[19]) ).
thf(24,plain,
! [SV5: $i,SV3: $i] :
( ( ! [SY22: $i] :
( ~ ( in @ SY22 @ ( binintersect @ SV3 @ SV5 ) )
| ( in @ SY22 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(25,plain,
( ( ~ ~ ~ ! [SY23: $i] :
~ ~ ( ~ ( in @ SY23 @ sK1_SX0 )
| ~ ( in @ SY23 @ sK2_SY19 ) )
| ( ( binintersect @ sK1_SX0 @ sK2_SY19 )
= emptyset ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[21]) ).
thf(26,plain,
! [SV4: $i,SV1: $i,SV6: $i] :
( ( ~ ( in @ SV6 @ ( binintersect @ SV1 @ SV4 ) )
| ( in @ SV6 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(27,plain,
! [SV2: $i] :
( ( ( ! [SY16: $i] :
~ ( in @ SY16 @ SV2 ) )
= $false )
| ( ( SV2 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(28,plain,
! [SV5: $i,SV3: $i,SV7: $i] :
( ( ~ ( in @ SV7 @ ( binintersect @ SV3 @ SV5 ) )
| ( in @ SV7 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(29,plain,
( ( ~ ~ ~ ! [SY23: $i] :
~ ~ ( ~ ( in @ SY23 @ sK1_SX0 )
| ~ ( in @ SY23 @ sK2_SY19 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[25]) ).
thf(30,plain,
( ( ( binintersect @ sK1_SX0 @ sK2_SY19 )
= emptyset )
= $false ),
inference(extcnf_or_neg,[status(thm)],[25]) ).
thf(31,plain,
! [SV4: $i,SV1: $i,SV6: $i] :
( ( ( ~ ( in @ SV6 @ ( binintersect @ SV1 @ SV4 ) ) )
= $true )
| ( ( in @ SV6 @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[26]) ).
thf(32,plain,
! [SV2: $i] :
( ( ( ~ ( in @ ( sK3_SY16 @ SV2 ) @ SV2 ) )
= $false )
| ( ( SV2 = emptyset )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[27]) ).
thf(33,plain,
! [SV5: $i,SV3: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ ( binintersect @ SV3 @ SV5 ) ) )
= $true )
| ( ( in @ SV7 @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[28]) ).
thf(34,plain,
( ( ~ ~ ! [SY23: $i] :
~ ~ ( ~ ( in @ SY23 @ sK1_SX0 )
| ~ ( in @ SY23 @ sK2_SY19 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[29]) ).
thf(35,plain,
! [SV4: $i,SV1: $i,SV6: $i] :
( ( ( in @ SV6 @ ( binintersect @ SV1 @ SV4 ) )
= $false )
| ( ( in @ SV6 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(36,plain,
! [SV2: $i] :
( ( ( in @ ( sK3_SY16 @ SV2 ) @ SV2 )
= $true )
| ( ( SV2 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[32]) ).
thf(37,plain,
! [SV5: $i,SV3: $i,SV7: $i] :
( ( ( in @ SV7 @ ( binintersect @ SV3 @ SV5 ) )
= $false )
| ( ( in @ SV7 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(38,plain,
( ( ~ ! [SY23: $i] :
~ ~ ( ~ ( in @ SY23 @ sK1_SX0 )
| ~ ( in @ SY23 @ sK2_SY19 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(39,plain,
( ( ! [SY23: $i] :
~ ~ ( ~ ( in @ SY23 @ sK1_SX0 )
| ~ ( in @ SY23 @ sK2_SY19 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[38]) ).
thf(40,plain,
! [SV8: $i] :
( ( ~ ~ ( ~ ( in @ SV8 @ sK1_SX0 )
| ~ ( in @ SV8 @ sK2_SY19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(41,plain,
! [SV8: $i] :
( ( ~ ( ~ ( in @ SV8 @ sK1_SX0 )
| ~ ( in @ SV8 @ sK2_SY19 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(42,plain,
! [SV8: $i] :
( ( ~ ( in @ SV8 @ sK1_SX0 )
| ~ ( in @ SV8 @ sK2_SY19 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[41]) ).
thf(43,plain,
! [SV8: $i] :
( ( ( ~ ( in @ SV8 @ sK1_SX0 ) )
= $true )
| ( ( ~ ( in @ SV8 @ sK2_SY19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[42]) ).
thf(44,plain,
! [SV8: $i] :
( ( ( in @ SV8 @ sK1_SX0 )
= $false )
| ( ( ~ ( in @ SV8 @ sK2_SY19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(45,plain,
! [SV8: $i] :
( ( ( in @ SV8 @ sK2_SY19 )
= $false )
| ( ( in @ SV8 @ sK1_SX0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(46,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[30,45,37,36,35]) ).
thf(47,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU596^2 : 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
% 0.10/0.18 % Computer : n011.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Tue Oct 6 15:28:51 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.21
% 0.10/0.21 No.of.Axioms: 0
% 0.10/0.21
% 0.10/0.21 Length.of.Defs: 550
% 0.10/0.21
% 0.10/0.21 Contains.Choice.Funs: false
% 0.10/0.21 .
% 0.10/0.21
% 0.10/0.21 ********************************
% 0.10/0.21 * All subproblems solved! *
% 0.10/0.21 ********************************
% 0.10/0.21 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:3,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:46,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.10/0.21
% 0.10/0.21 %**** Beginning of derivation protocol ****
% 0.10/0.21 % SZS output start CNFRefutation
% See solution above
% 0.10/0.21
% 0.10/0.21 %**** End of derivation protocol ****
% 0.10/0.21 %**** no. of clauses in derivation: 47 ****
% 0.10/0.21 %**** clause counter: 46 ****
% 0.10/0.21
% 0.10/0.21 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:3,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:46,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------