%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU737^2 : 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 : 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 10:47:09 AM UTC 2026
% Result : Theorem 0.09s 0.25s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 4
% Syntax : Number of formulae : 68 ( 39 unt; 0 typ; 3 def)
% Number of atoms : 582 ( 136 equ; 0 cnn)
% Maximal formula atoms : 7 ( 8 avg)
% Number of connectives : 1270 ( 118 ~; 171 |; 0 &; 910 @)
% ( 0 <=>; 71 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 8 con; 0-3 aty)
% Number of variables : 199 ( 0 ^; 199 !; 0 ?; 199 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_complementT_lem,type,
complementT_lem: $o ).
thf(tp_contraSubsetComplement,type,
contraSubsetComplement: $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_sK1_SX0,type,
sK1_SX0: $i ).
thf(tp_sK2_SY23,type,
sK2_SY23: $i ).
thf(tp_sK3_SY29,type,
sK3_SY29: $i ).
thf(tp_sK4_SY31,type,
sK4_SY31: $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(complementT_lem,definition,
( complementT_lem
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementT_lem) ).
thf(contraSubsetComplement,definition,
( contraSubsetComplement
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( ( subset @ X @ ( setminus @ A @ Y ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ Y )
=> ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',contraSubsetComplement) ).
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/sandbox2/benchmark/theBenchmark.p',subsetTI) ).
thf(1,conjecture,
( complementT_lem
=> ( subsetTI
=> ( contraSubsetComplement
=> ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( ( subset @ X @ ( setminus @ A @ Y ) )
=> ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementTcontraSubset) ).
thf(2,negated_conjecture,
( ( complementT_lem
=> ( subsetTI
=> ( contraSubsetComplement
=> ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( ( subset @ X @ ( setminus @ A @ Y ) )
=> ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [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 ) )
=> ( ( subset @ X @ ( setminus @ A @ Y ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ Y )
=> ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) )
=> ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( ( subset @ X @ ( setminus @ A @ Y ) )
=> ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,complementT_lem,contraSubsetComplement,subsetTI]) ).
thf(4,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,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(6,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( ( subset @ X @ ( setminus @ A @ Y ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ Y )
=> ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( ( subset @ X @ ( setminus @ A @ Y ) )
=> ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(8,plain,
( ( ~ ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( ( subset @ X @ ( setminus @ A @ Y ) )
=> ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(9,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( ( subset @ X @ ( setminus @ A @ Y ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ Y )
=> ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(10,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(copy,[status(thm)],[5]) ).
thf(11,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(12,plain,
( ( ~ ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( ( subset @ X @ ( setminus @ A @ Y ) )
=> ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(13,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ~ ( subset @ SX1 @ ( setminus @ SX0 @ SX2 ) )
| ( subset @ SX2 @ ( setminus @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12,complementT_lem,contraSubsetComplement,subsetTI]) ).
thf(14,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ~ ( subset @ SX1 @ ( setminus @ SX0 @ SX2 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ ( setminus @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9,complementT_lem,contraSubsetComplement,subsetTI]) ).
thf(15,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ( in @ ( setminus @ SX0 @ SX1 ) @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11,complementT_lem,contraSubsetComplement,subsetTI]) ).
thf(16,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ SX1 )
| ( in @ SX3 @ SX2 ) )
| ( subset @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10,complementT_lem,contraSubsetComplement,subsetTI]) ).
thf(17,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ~ ( subset @ SX1 @ ( setminus @ SX0 @ SX2 ) )
| ( subset @ SX2 @ ( setminus @ SX0 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[13]) ).
thf(18,plain,
! [SV1: $i] :
( ( ! [SY16: $i] :
( ~ ( in @ SY16 @ ( powerset @ SV1 ) )
| ! [SY17: $i] :
( ~ ( in @ SY17 @ ( powerset @ SV1 ) )
| ~ ( subset @ SY16 @ ( setminus @ SV1 @ SY17 ) )
| ! [SY18: $i] :
( ~ ( in @ SY18 @ SV1 )
| ~ ( in @ SY18 @ SY17 )
| ( in @ SY18 @ ( setminus @ SV1 @ SY16 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(19,plain,
! [SV2: $i] :
( ( ! [SY19: $i] :
( ~ ( in @ SY19 @ ( powerset @ SV2 ) )
| ( in @ ( setminus @ SV2 @ SY19 ) @ ( powerset @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(20,plain,
! [SV3: $i] :
( ( ! [SY20: $i] :
( ~ ( in @ SY20 @ ( powerset @ SV3 ) )
| ! [SY21: $i] :
( ~ ( in @ SY21 @ ( powerset @ SV3 ) )
| ~ ! [SY22: $i] :
( ~ ( in @ SY22 @ SV3 )
| ~ ( in @ SY22 @ SY20 )
| ( in @ SY22 @ SY21 ) )
| ( subset @ SY20 @ SY21 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(21,plain,
( ( ! [SY23: $i] :
( ~ ( in @ SY23 @ ( powerset @ sK1_SX0 ) )
| ! [SY24: $i] :
( ~ ( in @ SY24 @ ( powerset @ sK1_SX0 ) )
| ~ ( subset @ SY23 @ ( setminus @ sK1_SX0 @ SY24 ) )
| ( subset @ SY24 @ ( setminus @ sK1_SX0 @ SY23 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[17]) ).
thf(22,plain,
! [SV1: $i,SV4: $i] :
( ( ~ ( in @ SV4 @ ( powerset @ SV1 ) )
| ! [SY25: $i] :
( ~ ( in @ SY25 @ ( powerset @ SV1 ) )
| ~ ( subset @ SV4 @ ( setminus @ SV1 @ SY25 ) )
| ! [SY26: $i] :
( ~ ( in @ SY26 @ SV1 )
| ~ ( in @ SY26 @ SY25 )
| ( in @ SY26 @ ( setminus @ SV1 @ SV4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(23,plain,
! [SV2: $i,SV5: $i] :
( ( ~ ( in @ SV5 @ ( powerset @ SV2 ) )
| ( in @ ( setminus @ SV2 @ SV5 ) @ ( powerset @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(24,plain,
! [SV3: $i,SV6: $i] :
( ( ~ ( in @ SV6 @ ( powerset @ SV3 ) )
| ! [SY27: $i] :
( ~ ( in @ SY27 @ ( powerset @ SV3 ) )
| ~ ! [SY28: $i] :
( ~ ( in @ SY28 @ SV3 )
| ~ ( in @ SY28 @ SV6 )
| ( in @ SY28 @ SY27 ) )
| ( subset @ SV6 @ SY27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(25,plain,
( ( ~ ( in @ sK2_SY23 @ ( powerset @ sK1_SX0 ) )
| ! [SY29: $i] :
( ~ ( in @ SY29 @ ( powerset @ sK1_SX0 ) )
| ~ ( subset @ sK2_SY23 @ ( setminus @ sK1_SX0 @ SY29 ) )
| ( subset @ SY29 @ ( setminus @ sK1_SX0 @ sK2_SY23 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[21]) ).
thf(26,plain,
! [SV1: $i,SV4: $i] :
( ( ( ~ ( in @ SV4 @ ( powerset @ SV1 ) ) )
= $true )
| ( ( ! [SY25: $i] :
( ~ ( in @ SY25 @ ( powerset @ SV1 ) )
| ~ ( subset @ SV4 @ ( setminus @ SV1 @ SY25 ) )
| ! [SY26: $i] :
( ~ ( in @ SY26 @ SV1 )
| ~ ( in @ SY26 @ SY25 )
| ( in @ SY26 @ ( setminus @ SV1 @ SV4 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[22]) ).
thf(27,plain,
! [SV2: $i,SV5: $i] :
( ( ( ~ ( in @ SV5 @ ( powerset @ SV2 ) ) )
= $true )
| ( ( in @ ( setminus @ SV2 @ SV5 ) @ ( powerset @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[23]) ).
thf(28,plain,
! [SV3: $i,SV6: $i] :
( ( ( ~ ( in @ SV6 @ ( powerset @ SV3 ) ) )
= $true )
| ( ( ! [SY27: $i] :
( ~ ( in @ SY27 @ ( powerset @ SV3 ) )
| ~ ! [SY28: $i] :
( ~ ( in @ SY28 @ SV3 )
| ~ ( in @ SY28 @ SV6 )
| ( in @ SY28 @ SY27 ) )
| ( subset @ SV6 @ SY27 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[24]) ).
thf(29,plain,
( ( ~ ( in @ sK2_SY23 @ ( powerset @ sK1_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[25]) ).
thf(30,plain,
( ( ! [SY29: $i] :
( ~ ( in @ SY29 @ ( powerset @ sK1_SX0 ) )
| ~ ( subset @ sK2_SY23 @ ( setminus @ sK1_SX0 @ SY29 ) )
| ( subset @ SY29 @ ( setminus @ sK1_SX0 @ sK2_SY23 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[25]) ).
thf(31,plain,
! [SV1: $i,SV4: $i] :
( ( ( in @ SV4 @ ( powerset @ SV1 ) )
= $false )
| ( ( ! [SY25: $i] :
( ~ ( in @ SY25 @ ( powerset @ SV1 ) )
| ~ ( subset @ SV4 @ ( setminus @ SV1 @ SY25 ) )
| ! [SY26: $i] :
( ~ ( in @ SY26 @ SV1 )
| ~ ( in @ SY26 @ SY25 )
| ( in @ SY26 @ ( setminus @ SV1 @ SV4 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(32,plain,
! [SV2: $i,SV5: $i] :
( ( ( in @ SV5 @ ( powerset @ SV2 ) )
= $false )
| ( ( in @ ( setminus @ SV2 @ SV5 ) @ ( powerset @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(33,plain,
! [SV3: $i,SV6: $i] :
( ( ( in @ SV6 @ ( powerset @ SV3 ) )
= $false )
| ( ( ! [SY27: $i] :
( ~ ( in @ SY27 @ ( powerset @ SV3 ) )
| ~ ! [SY28: $i] :
( ~ ( in @ SY28 @ SV3 )
| ~ ( in @ SY28 @ SV6 )
| ( in @ SY28 @ SY27 ) )
| ( subset @ SV6 @ SY27 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(34,plain,
( ( in @ sK2_SY23 @ ( powerset @ sK1_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[29]) ).
thf(35,plain,
( ( ~ ( in @ sK3_SY29 @ ( powerset @ sK1_SX0 ) )
| ~ ( subset @ sK2_SY23 @ ( setminus @ sK1_SX0 @ sK3_SY29 ) )
| ( subset @ sK3_SY29 @ ( setminus @ sK1_SX0 @ sK2_SY23 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[30]) ).
thf(36,plain,
! [SV4: $i,SV1: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ ( powerset @ SV1 ) )
| ~ ( subset @ SV4 @ ( setminus @ SV1 @ SV7 ) )
| ! [SY30: $i] :
( ~ ( in @ SY30 @ SV1 )
| ~ ( in @ SY30 @ SV7 )
| ( in @ SY30 @ ( setminus @ SV1 @ SV4 ) ) ) )
= $true )
| ( ( in @ SV4 @ ( powerset @ SV1 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(37,plain,
! [SV6: $i,SV3: $i,SV8: $i] :
( ( ( ~ ( in @ SV8 @ ( powerset @ SV3 ) )
| ~ ! [SY31: $i] :
( ~ ( in @ SY31 @ SV3 )
| ~ ( in @ SY31 @ SV6 )
| ( in @ SY31 @ SV8 ) )
| ( subset @ SV6 @ SV8 ) )
= $true )
| ( ( in @ SV6 @ ( powerset @ SV3 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(38,plain,
( ( ~ ( in @ sK3_SY29 @ ( powerset @ sK1_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[35]) ).
thf(39,plain,
( ( ~ ( subset @ sK2_SY23 @ ( setminus @ sK1_SX0 @ sK3_SY29 ) )
| ( subset @ sK3_SY29 @ ( setminus @ sK1_SX0 @ sK2_SY23 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[35]) ).
thf(40,plain,
! [SV4: $i,SV1: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ ( powerset @ SV1 ) ) )
= $true )
| ( ( ~ ( subset @ SV4 @ ( setminus @ SV1 @ SV7 ) )
| ! [SY30: $i] :
( ~ ( in @ SY30 @ SV1 )
| ~ ( in @ SY30 @ SV7 )
| ( in @ SY30 @ ( setminus @ SV1 @ SV4 ) ) ) )
= $true )
| ( ( in @ SV4 @ ( powerset @ SV1 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[36]) ).
thf(41,plain,
! [SV6: $i,SV3: $i,SV8: $i] :
( ( ( ~ ( in @ SV8 @ ( powerset @ SV3 ) ) )
= $true )
| ( ( ~ ! [SY31: $i] :
( ~ ( in @ SY31 @ SV3 )
| ~ ( in @ SY31 @ SV6 )
| ( in @ SY31 @ SV8 ) )
| ( subset @ SV6 @ SV8 ) )
= $true )
| ( ( in @ SV6 @ ( powerset @ SV3 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[37]) ).
thf(42,plain,
( ( in @ sK3_SY29 @ ( powerset @ sK1_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[38]) ).
thf(43,plain,
( ( ~ ( subset @ sK2_SY23 @ ( setminus @ sK1_SX0 @ sK3_SY29 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[39]) ).
thf(44,plain,
( ( subset @ sK3_SY29 @ ( setminus @ sK1_SX0 @ sK2_SY23 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[39]) ).
thf(45,plain,
! [SV4: $i,SV1: $i,SV7: $i] :
( ( ( in @ SV7 @ ( powerset @ SV1 ) )
= $false )
| ( ( ~ ( subset @ SV4 @ ( setminus @ SV1 @ SV7 ) )
| ! [SY30: $i] :
( ~ ( in @ SY30 @ SV1 )
| ~ ( in @ SY30 @ SV7 )
| ( in @ SY30 @ ( setminus @ SV1 @ SV4 ) ) ) )
= $true )
| ( ( in @ SV4 @ ( powerset @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(46,plain,
! [SV6: $i,SV3: $i,SV8: $i] :
( ( ( in @ SV8 @ ( powerset @ SV3 ) )
= $false )
| ( ( ~ ! [SY31: $i] :
( ~ ( in @ SY31 @ SV3 )
| ~ ( in @ SY31 @ SV6 )
| ( in @ SY31 @ SV8 ) )
| ( subset @ SV6 @ SV8 ) )
= $true )
| ( ( in @ SV6 @ ( powerset @ SV3 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[41]) ).
thf(47,plain,
( ( subset @ sK2_SY23 @ ( setminus @ sK1_SX0 @ sK3_SY29 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[43]) ).
thf(48,plain,
! [SV7: $i,SV1: $i,SV4: $i] :
( ( ( ~ ( subset @ SV4 @ ( setminus @ SV1 @ SV7 ) ) )
= $true )
| ( ( ! [SY30: $i] :
( ~ ( in @ SY30 @ SV1 )
| ~ ( in @ SY30 @ SV7 )
| ( in @ SY30 @ ( setminus @ SV1 @ SV4 ) ) ) )
= $true )
| ( ( in @ SV7 @ ( powerset @ SV1 ) )
= $false )
| ( ( in @ SV4 @ ( powerset @ SV1 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[45]) ).
thf(49,plain,
! [SV8: $i,SV6: $i,SV3: $i] :
( ( ( ~ ! [SY31: $i] :
( ~ ( in @ SY31 @ SV3 )
| ~ ( in @ SY31 @ SV6 )
| ( in @ SY31 @ SV8 ) ) )
= $true )
| ( ( subset @ SV6 @ SV8 )
= $true )
| ( ( in @ SV8 @ ( powerset @ SV3 ) )
= $false )
| ( ( in @ SV6 @ ( powerset @ SV3 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[46]) ).
thf(50,plain,
! [SV7: $i,SV1: $i,SV4: $i] :
( ( ( subset @ SV4 @ ( setminus @ SV1 @ SV7 ) )
= $false )
| ( ( ! [SY30: $i] :
( ~ ( in @ SY30 @ SV1 )
| ~ ( in @ SY30 @ SV7 )
| ( in @ SY30 @ ( setminus @ SV1 @ SV4 ) ) ) )
= $true )
| ( ( in @ SV7 @ ( powerset @ SV1 ) )
= $false )
| ( ( in @ SV4 @ ( powerset @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(51,plain,
! [SV8: $i,SV6: $i,SV3: $i] :
( ( ( ! [SY31: $i] :
( ~ ( in @ SY31 @ SV3 )
| ~ ( in @ SY31 @ SV6 )
| ( in @ SY31 @ SV8 ) ) )
= $false )
| ( ( subset @ SV6 @ SV8 )
= $true )
| ( ( in @ SV8 @ ( powerset @ SV3 ) )
= $false )
| ( ( in @ SV6 @ ( powerset @ SV3 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(52,plain,
! [SV4: $i,SV7: $i,SV1: $i,SV9: $i] :
( ( ( ~ ( in @ SV9 @ SV1 )
| ~ ( in @ SV9 @ SV7 )
| ( in @ SV9 @ ( setminus @ SV1 @ SV4 ) ) )
= $true )
| ( ( subset @ SV4 @ ( setminus @ SV1 @ SV7 ) )
= $false )
| ( ( in @ SV7 @ ( powerset @ SV1 ) )
= $false )
| ( ( in @ SV4 @ ( powerset @ SV1 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(53,plain,
! [SV3: $i,SV6: $i,SV8: $i] :
( ( ( ~ ( in @ ( sK4_SY31 @ SV8 @ SV6 @ SV3 ) @ SV3 )
| ~ ( in @ ( sK4_SY31 @ SV8 @ SV6 @ SV3 ) @ SV6 )
| ( in @ ( sK4_SY31 @ SV8 @ SV6 @ SV3 ) @ SV8 ) )
= $false )
| ( ( subset @ SV6 @ SV8 )
= $true )
| ( ( in @ SV8 @ ( powerset @ SV3 ) )
= $false )
| ( ( in @ SV6 @ ( powerset @ SV3 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[51]) ).
thf(54,plain,
! [SV4: $i,SV7: $i,SV1: $i,SV9: $i] :
( ( ( ~ ( in @ SV9 @ SV1 ) )
= $true )
| ( ( ~ ( in @ SV9 @ SV7 )
| ( in @ SV9 @ ( setminus @ SV1 @ SV4 ) ) )
= $true )
| ( ( subset @ SV4 @ ( setminus @ SV1 @ SV7 ) )
= $false )
| ( ( in @ SV7 @ ( powerset @ SV1 ) )
= $false )
| ( ( in @ SV4 @ ( powerset @ SV1 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[52]) ).
thf(55,plain,
! [SV3: $i,SV6: $i,SV8: $i] :
( ( ( ~ ( in @ ( sK4_SY31 @ SV8 @ SV6 @ SV3 ) @ SV3 ) )
= $false )
| ( ( subset @ SV6 @ SV8 )
= $true )
| ( ( in @ SV8 @ ( powerset @ SV3 ) )
= $false )
| ( ( in @ SV6 @ ( powerset @ SV3 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[53]) ).
thf(56,plain,
! [SV3: $i,SV6: $i,SV8: $i] :
( ( ( ~ ( in @ ( sK4_SY31 @ SV8 @ SV6 @ SV3 ) @ SV6 )
| ( in @ ( sK4_SY31 @ SV8 @ SV6 @ SV3 ) @ SV8 ) )
= $false )
| ( ( subset @ SV6 @ SV8 )
= $true )
| ( ( in @ SV8 @ ( powerset @ SV3 ) )
= $false )
| ( ( in @ SV6 @ ( powerset @ SV3 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[53]) ).
thf(57,plain,
! [SV4: $i,SV7: $i,SV1: $i,SV9: $i] :
( ( ( in @ SV9 @ SV1 )
= $false )
| ( ( ~ ( in @ SV9 @ SV7 )
| ( in @ SV9 @ ( setminus @ SV1 @ SV4 ) ) )
= $true )
| ( ( subset @ SV4 @ ( setminus @ SV1 @ SV7 ) )
= $false )
| ( ( in @ SV7 @ ( powerset @ SV1 ) )
= $false )
| ( ( in @ SV4 @ ( powerset @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(58,plain,
! [SV3: $i,SV6: $i,SV8: $i] :
( ( ( in @ ( sK4_SY31 @ SV8 @ SV6 @ SV3 ) @ SV3 )
= $true )
| ( ( subset @ SV6 @ SV8 )
= $true )
| ( ( in @ SV8 @ ( powerset @ SV3 ) )
= $false )
| ( ( in @ SV6 @ ( powerset @ SV3 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[55]) ).
thf(59,plain,
! [SV3: $i,SV6: $i,SV8: $i] :
( ( ( ~ ( in @ ( sK4_SY31 @ SV8 @ SV6 @ SV3 ) @ SV6 ) )
= $false )
| ( ( subset @ SV6 @ SV8 )
= $true )
| ( ( in @ SV8 @ ( powerset @ SV3 ) )
= $false )
| ( ( in @ SV6 @ ( powerset @ SV3 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[56]) ).
thf(60,plain,
! [SV3: $i,SV6: $i,SV8: $i] :
( ( ( in @ ( sK4_SY31 @ SV8 @ SV6 @ SV3 ) @ SV8 )
= $false )
| ( ( subset @ SV6 @ SV8 )
= $true )
| ( ( in @ SV8 @ ( powerset @ SV3 ) )
= $false )
| ( ( in @ SV6 @ ( powerset @ SV3 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[56]) ).
thf(61,plain,
! [SV4: $i,SV1: $i,SV7: $i,SV9: $i] :
( ( ( ~ ( in @ SV9 @ SV7 ) )
= $true )
| ( ( in @ SV9 @ ( setminus @ SV1 @ SV4 ) )
= $true )
| ( ( in @ SV9 @ SV1 )
= $false )
| ( ( subset @ SV4 @ ( setminus @ SV1 @ SV7 ) )
= $false )
| ( ( in @ SV7 @ ( powerset @ SV1 ) )
= $false )
| ( ( in @ SV4 @ ( powerset @ SV1 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[57]) ).
thf(62,plain,
! [SV3: $i,SV6: $i,SV8: $i] :
( ( ( in @ ( sK4_SY31 @ SV8 @ SV6 @ SV3 ) @ SV6 )
= $true )
| ( ( subset @ SV6 @ SV8 )
= $true )
| ( ( in @ SV8 @ ( powerset @ SV3 ) )
= $false )
| ( ( in @ SV6 @ ( powerset @ SV3 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[59]) ).
thf(63,plain,
! [SV4: $i,SV1: $i,SV7: $i,SV9: $i] :
( ( ( in @ SV9 @ SV7 )
= $false )
| ( ( in @ SV9 @ ( setminus @ SV1 @ SV4 ) )
= $true )
| ( ( in @ SV9 @ SV1 )
= $false )
| ( ( subset @ SV4 @ ( setminus @ SV1 @ SV7 ) )
= $false )
| ( ( in @ SV7 @ ( powerset @ SV1 ) )
= $false )
| ( ( in @ SV4 @ ( powerset @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(64,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[32,63,62,60,58,47,44,42,34]) ).
thf(65,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU737^2 : 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
% 0.09/0.18 % Computer : n011.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 15:33:36 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.25
% 0.09/0.25 No.of.Axioms: 0
% 0.09/0.25
% 0.09/0.25 Length.of.Defs: 815
% 0.09/0.25
% 0.09/0.25 Contains.Choice.Funs: false
% 0.09/0.25 ..
% 0.09/0.25
% 0.09/0.25 ********************************
% 0.09/0.25 * All subproblems solved! *
% 0.09/0.25 ********************************
% 0.09/0.25 % SZS status Theorem for /export/starexec/sandbox2/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:64,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.09/0.25
% 0.09/0.25 %**** Beginning of derivation protocol ****
% 0.09/0.25 % SZS output start CNFRefutation
% See solution above
% 0.09/0.25
% 0.09/0.25 %**** End of derivation protocol ****
% 0.09/0.25 %**** no. of clauses in derivation: 65 ****
% 0.09/0.25 %**** clause counter: 64 ****
% 0.09/0.25
% 0.09/0.25 % SZS status Theorem for /export/starexec/sandbox2/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:64,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------