%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU734^2 : 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 : n007.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 10:47:07 AM UTC 2026
% Result : Theorem 0.10s 0.23s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 5
% Syntax : Number of formulae : 80 ( 45 unt; 0 typ; 4 def)
% Number of atoms : 628 ( 153 equ; 0 cnn)
% Maximal formula atoms : 7 ( 7 avg)
% Number of connectives : 1601 ( 191 ~; 176 |; 8 &;1168 @)
% ( 0 <=>; 58 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 9 con; 0-3 aty)
% Number of variables : 215 ( 0 ^; 215 !; 0 ?; 215 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_binintersect,type,
binintersect: $i > $i > $i ).
thf(tp_binintersectT_lem,type,
binintersectT_lem: $o ).
thf(tp_complementImpComplementIntersect,type,
complementImpComplementIntersect: $o ).
thf(tp_complementT_lem,type,
complementT_lem: $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY19,type,
sK2_SY19: $i ).
thf(tp_sK3_SY21,type,
sK3_SY21: $i ).
thf(tp_sK4_Xx,type,
sK4_Xx: $i > $i > $i > $i ).
thf(tp_setminus,type,
setminus: $i > $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_subsetTI,type,
subsetTI: $o ).
thf(binintersectT_lem,definition,
( binintersectT_lem
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectT_lem) ).
thf(complementImpComplementIntersect,definition,
( complementImpComplementIntersect
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( setminus @ A @ X ) )
=> ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementImpComplementIntersect) ).
thf(complementT_lem,definition,
( complementT_lem
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementT_lem) ).
thf(subsetTI,definition,
( subsetTI
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ X )
=> ( in @ Xx @ Y ) ) )
=> ( subset @ X @ Y ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetTI) ).
thf(1,conjecture,
( binintersectT_lem
=> ( complementT_lem
=> ( subsetTI
=> ( complementImpComplementIntersect
=> ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( subset @ ( setminus @ A @ X ) @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementSubsetComplementIntersect) ).
thf(2,negated_conjecture,
( ( binintersectT_lem
=> ( complementT_lem
=> ( subsetTI
=> ( complementImpComplementIntersect
=> ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( subset @ ( setminus @ A @ X ) @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ X )
=> ( in @ Xx @ Y ) ) )
=> ( subset @ X @ Y ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( setminus @ A @ X ) )
=> ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) )
=> ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( subset @ ( setminus @ A @ X ) @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,binintersectT_lem,complementImpComplementIntersect,complementT_lem,subsetTI]) ).
thf(4,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ X )
=> ( in @ Xx @ Y ) ) )
=> ( subset @ X @ Y ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( setminus @ A @ X ) )
=> ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(8,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( subset @ ( setminus @ A @ X ) @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(9,plain,
( ( ~ ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( subset @ ( setminus @ A @ X ) @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[8]) ).
thf(10,plain,
( ( ( in @ sK2_SY19 @ ( powerset @ sK1_A ) )
& ( in @ sK3_SY21 @ ( powerset @ sK1_A ) )
& ~ ( subset @ ( setminus @ sK1_A @ sK2_SY19 ) @ ( setminus @ sK1_A @ ( binintersect @ sK2_SY19 @ sK3_SY21 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[9]) ).
thf(11,plain,
( ( ! [A: $i,X: $i] :
( ~ ( in @ X @ ( powerset @ A ) )
| ! [Y: $i] :
( ~ ( in @ Y @ ( powerset @ A ) )
| ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(12,plain,
( ( ! [A: $i,X: $i] :
( ~ ( in @ X @ ( powerset @ A ) )
| ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[5]) ).
thf(13,plain,
( ( ! [A: $i,X: $i] :
( ~ ( in @ X @ ( powerset @ A ) )
| ! [Y: $i] :
( ~ ( in @ Y @ ( powerset @ A ) )
| ( ( in @ ( sK4_Xx @ Y @ X @ A ) @ A )
& ( in @ ( sK4_Xx @ Y @ X @ A ) @ X )
& ~ ( in @ ( sK4_Xx @ Y @ X @ A ) @ Y ) )
| ( subset @ X @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(14,plain,
( ( ! [A: $i,X: $i] :
( ~ ( in @ X @ ( powerset @ A ) )
| ! [Y: $i] :
( ~ ( in @ Y @ ( powerset @ A ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ A )
| ~ ( in @ Xx @ ( setminus @ A @ X ) )
| ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(15,plain,
( ( ! [A: $i,X: $i] :
( ~ ( in @ X @ ( powerset @ A ) )
| ! [Y: $i] :
( ~ ( in @ Y @ ( powerset @ A ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ A )
| ~ ( in @ Xx @ ( setminus @ A @ X ) )
| ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(16,plain,
( ( ! [A: $i,X: $i] :
( ~ ( in @ X @ ( powerset @ A ) )
| ! [Y: $i] :
( ~ ( in @ Y @ ( powerset @ A ) )
| ( ( in @ ( sK4_Xx @ Y @ X @ A ) @ A )
& ( in @ ( sK4_Xx @ Y @ X @ A ) @ X )
& ~ ( in @ ( sK4_Xx @ Y @ X @ A ) @ Y ) )
| ( subset @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(17,plain,
( ( ! [A: $i,X: $i] :
( ~ ( in @ X @ ( powerset @ A ) )
| ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(18,plain,
( ( ! [A: $i,X: $i] :
( ~ ( in @ X @ ( powerset @ A ) )
| ! [Y: $i] :
( ~ ( in @ Y @ ( powerset @ A ) )
| ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(19,plain,
( ( ( in @ sK2_SY19 @ ( powerset @ sK1_A ) )
& ( in @ sK3_SY21 @ ( powerset @ sK1_A ) )
& ~ ( subset @ ( setminus @ sK1_A @ sK2_SY19 ) @ ( setminus @ sK1_A @ ( binintersect @ sK2_SY19 @ sK3_SY21 ) ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(20,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ~ ( ~ ( in @ ( sK4_Xx @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( ~ ( in @ ( sK4_Xx @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( in @ ( sK4_Xx @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) )
| ( subset @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16,binintersectT_lem,complementImpComplementIntersect,complementT_lem,subsetTI]) ).
thf(21,plain,
( ( ~ ( ~ ( in @ sK2_SY19 @ ( powerset @ sK1_A ) )
| ~ ~ ( ~ ( in @ sK3_SY21 @ ( powerset @ sK1_A ) )
| ~ ~ ( subset @ ( setminus @ sK1_A @ sK2_SY19 ) @ ( setminus @ sK1_A @ ( binintersect @ sK2_SY19 @ sK3_SY21 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19,binintersectT_lem,complementImpComplementIntersect,complementT_lem,subsetTI]) ).
thf(22,plain,
! [SV1: $i] :
( ( ! [SY22: $i] :
( ~ ( in @ SY22 @ ( powerset @ SV1 ) )
| ! [SY23: $i] :
( ~ ( in @ SY23 @ ( powerset @ SV1 ) )
| ! [SY24: $i] :
( ~ ( in @ SY24 @ SV1 )
| ~ ( in @ SY24 @ ( setminus @ SV1 @ SY22 ) )
| ( in @ SY24 @ ( setminus @ SV1 @ ( binintersect @ SY22 @ SY23 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(23,plain,
! [SV2: $i] :
( ( ! [SY25: $i] :
( ~ ( in @ SY25 @ ( powerset @ SV2 ) )
| ( in @ ( setminus @ SV2 @ SY25 ) @ ( powerset @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(24,plain,
! [SV3: $i] :
( ( ! [SY26: $i] :
( ~ ( in @ SY26 @ ( powerset @ SV3 ) )
| ! [SY27: $i] :
( ~ ( in @ SY27 @ ( powerset @ SV3 ) )
| ( in @ ( binintersect @ SY26 @ SY27 ) @ ( powerset @ SV3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(25,plain,
! [SV4: $i] :
( ( ! [SY28: $i] :
( ~ ( in @ SY28 @ ( powerset @ SV4 ) )
| ! [SY29: $i] :
( ~ ( in @ SY29 @ ( powerset @ SV4 ) )
| ~ ( ~ ( in @ ( sK4_Xx @ SY29 @ SY28 @ SV4 ) @ SV4 )
| ~ ~ ( ~ ( in @ ( sK4_Xx @ SY29 @ SY28 @ SV4 ) @ SY28 )
| ~ ~ ( in @ ( sK4_Xx @ SY29 @ SY28 @ SV4 ) @ SY29 ) ) )
| ( subset @ SY28 @ SY29 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(26,plain,
( ( ~ ( in @ sK2_SY19 @ ( powerset @ sK1_A ) )
| ~ ~ ( ~ ( in @ sK3_SY21 @ ( powerset @ sK1_A ) )
| ~ ~ ( subset @ ( setminus @ sK1_A @ sK2_SY19 ) @ ( setminus @ sK1_A @ ( binintersect @ sK2_SY19 @ sK3_SY21 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(27,plain,
! [SV1: $i,SV5: $i] :
( ( ~ ( in @ SV5 @ ( powerset @ SV1 ) )
| ! [SY30: $i] :
( ~ ( in @ SY30 @ ( powerset @ SV1 ) )
| ! [SY31: $i] :
( ~ ( in @ SY31 @ SV1 )
| ~ ( in @ SY31 @ ( setminus @ SV1 @ SV5 ) )
| ( in @ SY31 @ ( setminus @ SV1 @ ( binintersect @ SV5 @ SY30 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(28,plain,
! [SV2: $i,SV6: $i] :
( ( ~ ( in @ SV6 @ ( powerset @ SV2 ) )
| ( in @ ( setminus @ SV2 @ SV6 ) @ ( powerset @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(29,plain,
! [SV3: $i,SV7: $i] :
( ( ~ ( in @ SV7 @ ( powerset @ SV3 ) )
| ! [SY32: $i] :
( ~ ( in @ SY32 @ ( powerset @ SV3 ) )
| ( in @ ( binintersect @ SV7 @ SY32 ) @ ( powerset @ SV3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(30,plain,
! [SV4: $i,SV8: $i] :
( ( ~ ( in @ SV8 @ ( powerset @ SV4 ) )
| ! [SY33: $i] :
( ~ ( in @ SY33 @ ( powerset @ SV4 ) )
| ~ ( ~ ( in @ ( sK4_Xx @ SY33 @ SV8 @ SV4 ) @ SV4 )
| ~ ~ ( ~ ( in @ ( sK4_Xx @ SY33 @ SV8 @ SV4 ) @ SV8 )
| ~ ~ ( in @ ( sK4_Xx @ SY33 @ SV8 @ SV4 ) @ SY33 ) ) )
| ( subset @ SV8 @ SY33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(31,plain,
( ( ~ ( in @ sK2_SY19 @ ( powerset @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[26]) ).
thf(32,plain,
( ( ~ ~ ( ~ ( in @ sK3_SY21 @ ( powerset @ sK1_A ) )
| ~ ~ ( subset @ ( setminus @ sK1_A @ sK2_SY19 ) @ ( setminus @ sK1_A @ ( binintersect @ sK2_SY19 @ sK3_SY21 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[26]) ).
thf(33,plain,
! [SV1: $i,SV5: $i] :
( ( ( ~ ( in @ SV5 @ ( powerset @ SV1 ) ) )
= $true )
| ( ( ! [SY30: $i] :
( ~ ( in @ SY30 @ ( powerset @ SV1 ) )
| ! [SY31: $i] :
( ~ ( in @ SY31 @ SV1 )
| ~ ( in @ SY31 @ ( setminus @ SV1 @ SV5 ) )
| ( in @ SY31 @ ( setminus @ SV1 @ ( binintersect @ SV5 @ SY30 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[27]) ).
thf(34,plain,
! [SV2: $i,SV6: $i] :
( ( ( ~ ( in @ SV6 @ ( powerset @ SV2 ) ) )
= $true )
| ( ( in @ ( setminus @ SV2 @ SV6 ) @ ( powerset @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[28]) ).
thf(35,plain,
! [SV3: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ ( powerset @ SV3 ) ) )
= $true )
| ( ( ! [SY32: $i] :
( ~ ( in @ SY32 @ ( powerset @ SV3 ) )
| ( in @ ( binintersect @ SV7 @ SY32 ) @ ( powerset @ SV3 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[29]) ).
thf(36,plain,
! [SV4: $i,SV8: $i] :
( ( ( ~ ( in @ SV8 @ ( powerset @ SV4 ) ) )
= $true )
| ( ( ! [SY33: $i] :
( ~ ( in @ SY33 @ ( powerset @ SV4 ) )
| ~ ( ~ ( in @ ( sK4_Xx @ SY33 @ SV8 @ SV4 ) @ SV4 )
| ~ ~ ( ~ ( in @ ( sK4_Xx @ SY33 @ SV8 @ SV4 ) @ SV8 )
| ~ ~ ( in @ ( sK4_Xx @ SY33 @ SV8 @ SV4 ) @ SY33 ) ) )
| ( subset @ SV8 @ SY33 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[30]) ).
thf(37,plain,
( ( in @ sK2_SY19 @ ( powerset @ sK1_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[31]) ).
thf(38,plain,
( ( ~ ( ~ ( in @ sK3_SY21 @ ( powerset @ sK1_A ) )
| ~ ~ ( subset @ ( setminus @ sK1_A @ sK2_SY19 ) @ ( setminus @ sK1_A @ ( binintersect @ sK2_SY19 @ sK3_SY21 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[32]) ).
thf(39,plain,
! [SV1: $i,SV5: $i] :
( ( ( in @ SV5 @ ( powerset @ SV1 ) )
= $false )
| ( ( ! [SY30: $i] :
( ~ ( in @ SY30 @ ( powerset @ SV1 ) )
| ! [SY31: $i] :
( ~ ( in @ SY31 @ SV1 )
| ~ ( in @ SY31 @ ( setminus @ SV1 @ SV5 ) )
| ( in @ SY31 @ ( setminus @ SV1 @ ( binintersect @ SV5 @ SY30 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(40,plain,
! [SV2: $i,SV6: $i] :
( ( ( in @ SV6 @ ( powerset @ SV2 ) )
= $false )
| ( ( in @ ( setminus @ SV2 @ SV6 ) @ ( powerset @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(41,plain,
! [SV3: $i,SV7: $i] :
( ( ( in @ SV7 @ ( powerset @ SV3 ) )
= $false )
| ( ( ! [SY32: $i] :
( ~ ( in @ SY32 @ ( powerset @ SV3 ) )
| ( in @ ( binintersect @ SV7 @ SY32 ) @ ( powerset @ SV3 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(42,plain,
! [SV4: $i,SV8: $i] :
( ( ( in @ SV8 @ ( powerset @ SV4 ) )
= $false )
| ( ( ! [SY33: $i] :
( ~ ( in @ SY33 @ ( powerset @ SV4 ) )
| ~ ( ~ ( in @ ( sK4_Xx @ SY33 @ SV8 @ SV4 ) @ SV4 )
| ~ ~ ( ~ ( in @ ( sK4_Xx @ SY33 @ SV8 @ SV4 ) @ SV8 )
| ~ ~ ( in @ ( sK4_Xx @ SY33 @ SV8 @ SV4 ) @ SY33 ) ) )
| ( subset @ SV8 @ SY33 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(43,plain,
( ( ~ ( in @ sK3_SY21 @ ( powerset @ sK1_A ) )
| ~ ~ ( subset @ ( setminus @ sK1_A @ sK2_SY19 ) @ ( setminus @ sK1_A @ ( binintersect @ sK2_SY19 @ sK3_SY21 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(44,plain,
! [SV5: $i,SV1: $i,SV9: $i] :
( ( ( ~ ( in @ SV9 @ ( powerset @ SV1 ) )
| ! [SY34: $i] :
( ~ ( in @ SY34 @ SV1 )
| ~ ( in @ SY34 @ ( setminus @ SV1 @ SV5 ) )
| ( in @ SY34 @ ( setminus @ SV1 @ ( binintersect @ SV5 @ SV9 ) ) ) ) )
= $true )
| ( ( in @ SV5 @ ( powerset @ SV1 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(45,plain,
! [SV7: $i,SV3: $i,SV10: $i] :
( ( ( ~ ( in @ SV10 @ ( powerset @ SV3 ) )
| ( in @ ( binintersect @ SV7 @ SV10 ) @ ( powerset @ SV3 ) ) )
= $true )
| ( ( in @ SV7 @ ( powerset @ SV3 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(46,plain,
! [SV8: $i,SV4: $i,SV11: $i] :
( ( ( ~ ( in @ SV11 @ ( powerset @ SV4 ) )
| ~ ( ~ ( in @ ( sK4_Xx @ SV11 @ SV8 @ SV4 ) @ SV4 )
| ~ ~ ( ~ ( in @ ( sK4_Xx @ SV11 @ SV8 @ SV4 ) @ SV8 )
| ~ ~ ( in @ ( sK4_Xx @ SV11 @ SV8 @ SV4 ) @ SV11 ) ) )
| ( subset @ SV8 @ SV11 ) )
= $true )
| ( ( in @ SV8 @ ( powerset @ SV4 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(47,plain,
( ( ~ ( in @ sK3_SY21 @ ( powerset @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[43]) ).
thf(48,plain,
( ( ~ ~ ( subset @ ( setminus @ sK1_A @ sK2_SY19 ) @ ( setminus @ sK1_A @ ( binintersect @ sK2_SY19 @ sK3_SY21 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[43]) ).
thf(49,plain,
! [SV5: $i,SV1: $i,SV9: $i] :
( ( ( ~ ( in @ SV9 @ ( powerset @ SV1 ) ) )
= $true )
| ( ( ! [SY34: $i] :
( ~ ( in @ SY34 @ SV1 )
| ~ ( in @ SY34 @ ( setminus @ SV1 @ SV5 ) )
| ( in @ SY34 @ ( setminus @ SV1 @ ( binintersect @ SV5 @ SV9 ) ) ) ) )
= $true )
| ( ( in @ SV5 @ ( powerset @ SV1 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[44]) ).
thf(50,plain,
! [SV7: $i,SV3: $i,SV10: $i] :
( ( ( ~ ( in @ SV10 @ ( powerset @ SV3 ) ) )
= $true )
| ( ( in @ ( binintersect @ SV7 @ SV10 ) @ ( powerset @ SV3 ) )
= $true )
| ( ( in @ SV7 @ ( powerset @ SV3 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[45]) ).
thf(51,plain,
! [SV8: $i,SV4: $i,SV11: $i] :
( ( ( ~ ( in @ SV11 @ ( powerset @ SV4 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK4_Xx @ SV11 @ SV8 @ SV4 ) @ SV4 )
| ~ ~ ( ~ ( in @ ( sK4_Xx @ SV11 @ SV8 @ SV4 ) @ SV8 )
| ~ ~ ( in @ ( sK4_Xx @ SV11 @ SV8 @ SV4 ) @ SV11 ) ) )
| ( subset @ SV8 @ SV11 ) )
= $true )
| ( ( in @ SV8 @ ( powerset @ SV4 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[46]) ).
thf(52,plain,
( ( in @ sK3_SY21 @ ( powerset @ sK1_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[47]) ).
thf(53,plain,
( ( ~ ( subset @ ( setminus @ sK1_A @ sK2_SY19 ) @ ( setminus @ sK1_A @ ( binintersect @ sK2_SY19 @ sK3_SY21 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[48]) ).
thf(54,plain,
! [SV5: $i,SV1: $i,SV9: $i] :
( ( ( in @ SV9 @ ( powerset @ SV1 ) )
= $false )
| ( ( ! [SY34: $i] :
( ~ ( in @ SY34 @ SV1 )
| ~ ( in @ SY34 @ ( setminus @ SV1 @ SV5 ) )
| ( in @ SY34 @ ( setminus @ SV1 @ ( binintersect @ SV5 @ SV9 ) ) ) ) )
= $true )
| ( ( in @ SV5 @ ( powerset @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(55,plain,
! [SV7: $i,SV3: $i,SV10: $i] :
( ( ( in @ SV10 @ ( powerset @ SV3 ) )
= $false )
| ( ( in @ ( binintersect @ SV7 @ SV10 ) @ ( powerset @ SV3 ) )
= $true )
| ( ( in @ SV7 @ ( powerset @ SV3 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(56,plain,
! [SV8: $i,SV4: $i,SV11: $i] :
( ( ( in @ SV11 @ ( powerset @ SV4 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK4_Xx @ SV11 @ SV8 @ SV4 ) @ SV4 )
| ~ ~ ( ~ ( in @ ( sK4_Xx @ SV11 @ SV8 @ SV4 ) @ SV8 )
| ~ ~ ( in @ ( sK4_Xx @ SV11 @ SV8 @ SV4 ) @ SV11 ) ) )
| ( subset @ SV8 @ SV11 ) )
= $true )
| ( ( in @ SV8 @ ( powerset @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(57,plain,
( ( subset @ ( setminus @ sK1_A @ sK2_SY19 ) @ ( setminus @ sK1_A @ ( binintersect @ sK2_SY19 @ sK3_SY21 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(58,plain,
! [SV9: $i,SV5: $i,SV1: $i,SV12: $i] :
( ( ( ~ ( in @ SV12 @ SV1 )
| ~ ( in @ SV12 @ ( setminus @ SV1 @ SV5 ) )
| ( in @ SV12 @ ( setminus @ SV1 @ ( binintersect @ SV5 @ SV9 ) ) ) )
= $true )
| ( ( in @ SV9 @ ( powerset @ SV1 ) )
= $false )
| ( ( in @ SV5 @ ( powerset @ SV1 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(59,plain,
! [SV4: $i,SV8: $i,SV11: $i] :
( ( ( ~ ( ~ ( in @ ( sK4_Xx @ SV11 @ SV8 @ SV4 ) @ SV4 )
| ~ ~ ( ~ ( in @ ( sK4_Xx @ SV11 @ SV8 @ SV4 ) @ SV8 )
| ~ ~ ( in @ ( sK4_Xx @ SV11 @ SV8 @ SV4 ) @ SV11 ) ) ) )
= $true )
| ( ( subset @ SV8 @ SV11 )
= $true )
| ( ( in @ SV11 @ ( powerset @ SV4 ) )
= $false )
| ( ( in @ SV8 @ ( powerset @ SV4 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[56]) ).
thf(60,plain,
! [SV9: $i,SV5: $i,SV1: $i,SV12: $i] :
( ( ( ~ ( in @ SV12 @ SV1 ) )
= $true )
| ( ( ~ ( in @ SV12 @ ( setminus @ SV1 @ SV5 ) )
| ( in @ SV12 @ ( setminus @ SV1 @ ( binintersect @ SV5 @ SV9 ) ) ) )
= $true )
| ( ( in @ SV9 @ ( powerset @ SV1 ) )
= $false )
| ( ( in @ SV5 @ ( powerset @ SV1 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[58]) ).
thf(61,plain,
! [SV4: $i,SV8: $i,SV11: $i] :
( ( ( ~ ( in @ ( sK4_Xx @ SV11 @ SV8 @ SV4 ) @ SV4 )
| ~ ~ ( ~ ( in @ ( sK4_Xx @ SV11 @ SV8 @ SV4 ) @ SV8 )
| ~ ~ ( in @ ( sK4_Xx @ SV11 @ SV8 @ SV4 ) @ SV11 ) ) )
= $false )
| ( ( subset @ SV8 @ SV11 )
= $true )
| ( ( in @ SV11 @ ( powerset @ SV4 ) )
= $false )
| ( ( in @ SV8 @ ( powerset @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(62,plain,
! [SV9: $i,SV5: $i,SV1: $i,SV12: $i] :
( ( ( in @ SV12 @ SV1 )
= $false )
| ( ( ~ ( in @ SV12 @ ( setminus @ SV1 @ SV5 ) )
| ( in @ SV12 @ ( setminus @ SV1 @ ( binintersect @ SV5 @ SV9 ) ) ) )
= $true )
| ( ( in @ SV9 @ ( powerset @ SV1 ) )
= $false )
| ( ( in @ SV5 @ ( powerset @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(63,plain,
! [SV4: $i,SV8: $i,SV11: $i] :
( ( ( ~ ( in @ ( sK4_Xx @ SV11 @ SV8 @ SV4 ) @ SV4 ) )
= $false )
| ( ( subset @ SV8 @ SV11 )
= $true )
| ( ( in @ SV11 @ ( powerset @ SV4 ) )
= $false )
| ( ( in @ SV8 @ ( powerset @ SV4 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[61]) ).
thf(64,plain,
! [SV4: $i,SV8: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK4_Xx @ SV11 @ SV8 @ SV4 ) @ SV8 )
| ~ ~ ( in @ ( sK4_Xx @ SV11 @ SV8 @ SV4 ) @ SV11 ) ) )
= $false )
| ( ( subset @ SV8 @ SV11 )
= $true )
| ( ( in @ SV11 @ ( powerset @ SV4 ) )
= $false )
| ( ( in @ SV8 @ ( powerset @ SV4 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[61]) ).
thf(65,plain,
! [SV9: $i,SV5: $i,SV1: $i,SV12: $i] :
( ( ( ~ ( in @ SV12 @ ( setminus @ SV1 @ SV5 ) ) )
= $true )
| ( ( in @ SV12 @ ( setminus @ SV1 @ ( binintersect @ SV5 @ SV9 ) ) )
= $true )
| ( ( in @ SV12 @ SV1 )
= $false )
| ( ( in @ SV9 @ ( powerset @ SV1 ) )
= $false )
| ( ( in @ SV5 @ ( powerset @ SV1 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[62]) ).
thf(66,plain,
! [SV4: $i,SV8: $i,SV11: $i] :
( ( ( in @ ( sK4_Xx @ SV11 @ SV8 @ SV4 ) @ SV4 )
= $true )
| ( ( subset @ SV8 @ SV11 )
= $true )
| ( ( in @ SV11 @ ( powerset @ SV4 ) )
= $false )
| ( ( in @ SV8 @ ( powerset @ SV4 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[63]) ).
thf(67,plain,
! [SV4: $i,SV8: $i,SV11: $i] :
( ( ( ~ ( ~ ( in @ ( sK4_Xx @ SV11 @ SV8 @ SV4 ) @ SV8 )
| ~ ~ ( in @ ( sK4_Xx @ SV11 @ SV8 @ SV4 ) @ SV11 ) ) )
= $true )
| ( ( subset @ SV8 @ SV11 )
= $true )
| ( ( in @ SV11 @ ( powerset @ SV4 ) )
= $false )
| ( ( in @ SV8 @ ( powerset @ SV4 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[64]) ).
thf(68,plain,
! [SV9: $i,SV5: $i,SV1: $i,SV12: $i] :
( ( ( in @ SV12 @ ( setminus @ SV1 @ SV5 ) )
= $false )
| ( ( in @ SV12 @ ( setminus @ SV1 @ ( binintersect @ SV5 @ SV9 ) ) )
= $true )
| ( ( in @ SV12 @ SV1 )
= $false )
| ( ( in @ SV9 @ ( powerset @ SV1 ) )
= $false )
| ( ( in @ SV5 @ ( powerset @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(69,plain,
! [SV4: $i,SV8: $i,SV11: $i] :
( ( ( ~ ( in @ ( sK4_Xx @ SV11 @ SV8 @ SV4 ) @ SV8 )
| ~ ~ ( in @ ( sK4_Xx @ SV11 @ SV8 @ SV4 ) @ SV11 ) )
= $false )
| ( ( subset @ SV8 @ SV11 )
= $true )
| ( ( in @ SV11 @ ( powerset @ SV4 ) )
= $false )
| ( ( in @ SV8 @ ( powerset @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(70,plain,
! [SV4: $i,SV8: $i,SV11: $i] :
( ( ( ~ ( in @ ( sK4_Xx @ SV11 @ SV8 @ SV4 ) @ SV8 ) )
= $false )
| ( ( subset @ SV8 @ SV11 )
= $true )
| ( ( in @ SV11 @ ( powerset @ SV4 ) )
= $false )
| ( ( in @ SV8 @ ( powerset @ SV4 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[69]) ).
thf(71,plain,
! [SV4: $i,SV8: $i,SV11: $i] :
( ( ( ~ ~ ( in @ ( sK4_Xx @ SV11 @ SV8 @ SV4 ) @ SV11 ) )
= $false )
| ( ( subset @ SV8 @ SV11 )
= $true )
| ( ( in @ SV11 @ ( powerset @ SV4 ) )
= $false )
| ( ( in @ SV8 @ ( powerset @ SV4 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[69]) ).
thf(72,plain,
! [SV4: $i,SV8: $i,SV11: $i] :
( ( ( in @ ( sK4_Xx @ SV11 @ SV8 @ SV4 ) @ SV8 )
= $true )
| ( ( subset @ SV8 @ SV11 )
= $true )
| ( ( in @ SV11 @ ( powerset @ SV4 ) )
= $false )
| ( ( in @ SV8 @ ( powerset @ SV4 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[70]) ).
thf(73,plain,
! [SV4: $i,SV8: $i,SV11: $i] :
( ( ( ~ ( in @ ( sK4_Xx @ SV11 @ SV8 @ SV4 ) @ SV11 ) )
= $true )
| ( ( subset @ SV8 @ SV11 )
= $true )
| ( ( in @ SV11 @ ( powerset @ SV4 ) )
= $false )
| ( ( in @ SV8 @ ( powerset @ SV4 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[71]) ).
thf(74,plain,
! [SV4: $i,SV8: $i,SV11: $i] :
( ( ( in @ ( sK4_Xx @ SV11 @ SV8 @ SV4 ) @ SV11 )
= $false )
| ( ( subset @ SV8 @ SV11 )
= $true )
| ( ( in @ SV11 @ ( powerset @ SV4 ) )
= $false )
| ( ( in @ SV8 @ ( powerset @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(75,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[37,74,72,68,66,57,55,52,40]) ).
thf(76,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[75]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU734^2 : 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
% 0.10/0.17 % Computer : n007.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Tue Oct 6 15:31:15 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
% 0.10/0.23
% 0.10/0.23 No.of.Axioms: 0
% 0.10/0.23
% 0.10/0.23 Length.of.Defs: 1097
% 0.10/0.23
% 0.10/0.23 Contains.Choice.Funs: false
% 0.10/0.23 ..
% 0.10/0.23
% 0.10/0.23 ********************************
% 0.10/0.23 * All subproblems solved! *
% 0.10/0.23 ********************************
% 0.10/0.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:4,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:75,loop_count:0,foatp_calls:1,translation:fof_experiment)
% 0.10/0.23
% 0.10/0.23 %**** Beginning of derivation protocol ****
% 0.10/0.23 % SZS output start CNFRefutation
% See solution above
% 0.10/0.23
% 0.10/0.23 %**** End of derivation protocol ****
% 0.10/0.23 %**** no. of clauses in derivation: 76 ****
% 0.10/0.23 %**** clause counter: 75 ****
% 0.10/0.23
% 0.10/0.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:4,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:75,loop_count:0,foatp_calls:1,translation:fof_experiment)
%------------------------------------------------------------------------------