%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU730^2 : 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 : n009.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 10:46:59 AM UTC 2026
% Result : Theorem 0.12s 0.27s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 4
% Syntax : Number of formulae : 61 ( 34 unt; 0 typ; 3 def)
% Number of atoms : 472 ( 117 equ; 0 cnn)
% Maximal formula atoms : 5 ( 7 avg)
% Number of connectives : 1144 ( 145 ~; 130 |; 6 &; 822 @)
% ( 0 <=>; 41 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 7 con; 0-3 aty)
% Number of variables : 148 ( 0 ^; 148 !; 0 ?; 148 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_complementT_lem,type,
complementT_lem: $o ).
thf(tp_doubleComplementE1,type,
doubleComplementE1: $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_SY13,type,
sK2_SY13: $i ).
thf(tp_sK3_Xx,type,
sK3_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(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(doubleComplementE1,definition,
( doubleComplementE1
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) )
=> ( in @ Xx @ X ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',doubleComplementE1) ).
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,
( complementT_lem
=> ( subsetTI
=> ( doubleComplementE1
=> ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ( subset @ ( setminus @ A @ ( setminus @ A @ X ) ) @ X ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',doubleComplementSub2) ).
thf(2,negated_conjecture,
( ( complementT_lem
=> ( subsetTI
=> ( doubleComplementE1
=> ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ( subset @ ( setminus @ A @ ( setminus @ A @ X ) ) @ 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 ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) )
=> ( in @ Xx @ X ) ) ) )
=> ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ( subset @ ( setminus @ A @ ( setminus @ A @ X ) ) @ X ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,complementT_lem,doubleComplementE1,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 ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) )
=> ( in @ Xx @ X ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ( subset @ ( setminus @ A @ ( setminus @ A @ X ) ) @ X ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(8,plain,
( ( ~ ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ( subset @ ( setminus @ A @ ( setminus @ A @ X ) ) @ X ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(9,plain,
( ( ( in @ sK2_SY13 @ ( powerset @ sK1_A ) )
& ~ ( subset @ ( setminus @ sK1_A @ ( setminus @ sK1_A @ sK2_SY13 ) ) @ sK2_SY13 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[8]) ).
thf(10,plain,
( ( ! [A: $i,X: $i] :
( ~ ( in @ X @ ( powerset @ A ) )
| ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(11,plain,
( ( ! [A: $i,X: $i] :
( ~ ( in @ X @ ( powerset @ A ) )
| ! [Y: $i] :
( ~ ( in @ Y @ ( powerset @ A ) )
| ( ( in @ ( sK3_Xx @ Y @ X @ A ) @ A )
& ( in @ ( sK3_Xx @ Y @ X @ A ) @ X )
& ~ ( in @ ( sK3_Xx @ Y @ X @ A ) @ Y ) )
| ( subset @ X @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[5]) ).
thf(12,plain,
( ( ! [A: $i,X: $i] :
( ~ ( in @ X @ ( powerset @ A ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ A )
| ~ ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) )
| ( in @ Xx @ X ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(13,plain,
( ( ! [A: $i,X: $i] :
( ~ ( in @ X @ ( powerset @ A ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ A )
| ~ ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) )
| ( in @ Xx @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(14,plain,
( ( ! [A: $i,X: $i] :
( ~ ( in @ X @ ( powerset @ A ) )
| ! [Y: $i] :
( ~ ( in @ Y @ ( powerset @ A ) )
| ( ( in @ ( sK3_Xx @ Y @ X @ A ) @ A )
& ( in @ ( sK3_Xx @ Y @ X @ A ) @ X )
& ~ ( in @ ( sK3_Xx @ Y @ X @ A ) @ Y ) )
| ( subset @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(15,plain,
( ( ! [A: $i,X: $i] :
( ~ ( in @ X @ ( powerset @ A ) )
| ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(16,plain,
( ( ( in @ sK2_SY13 @ ( powerset @ sK1_A ) )
& ~ ( subset @ ( setminus @ sK1_A @ ( setminus @ sK1_A @ sK2_SY13 ) ) @ sK2_SY13 ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(17,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ~ ( ~ ( in @ ( sK3_Xx @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( ~ ( in @ ( sK3_Xx @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( in @ ( sK3_Xx @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) )
| ( subset @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14,complementT_lem,doubleComplementE1,subsetTI]) ).
thf(18,plain,
( ( ~ ( ~ ( in @ sK2_SY13 @ ( powerset @ sK1_A ) )
| ~ ~ ( subset @ ( setminus @ sK1_A @ ( setminus @ sK1_A @ sK2_SY13 ) ) @ sK2_SY13 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16,complementT_lem,doubleComplementE1,subsetTI]) ).
thf(19,plain,
! [SV1: $i] :
( ( ! [SY14: $i] :
( ~ ( in @ SY14 @ ( powerset @ SV1 ) )
| ! [SY15: $i] :
( ~ ( in @ SY15 @ SV1 )
| ~ ( in @ SY15 @ ( setminus @ SV1 @ ( setminus @ SV1 @ SY14 ) ) )
| ( in @ SY15 @ SY14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[13]) ).
thf(20,plain,
! [SV2: $i] :
( ( ! [SY16: $i] :
( ~ ( in @ SY16 @ ( powerset @ SV2 ) )
| ( in @ ( setminus @ SV2 @ SY16 ) @ ( powerset @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(21,plain,
! [SV3: $i] :
( ( ! [SY17: $i] :
( ~ ( in @ SY17 @ ( powerset @ SV3 ) )
| ! [SY18: $i] :
( ~ ( in @ SY18 @ ( powerset @ SV3 ) )
| ~ ( ~ ( in @ ( sK3_Xx @ SY18 @ SY17 @ SV3 ) @ SV3 )
| ~ ~ ( ~ ( in @ ( sK3_Xx @ SY18 @ SY17 @ SV3 ) @ SY17 )
| ~ ~ ( in @ ( sK3_Xx @ SY18 @ SY17 @ SV3 ) @ SY18 ) ) )
| ( subset @ SY17 @ SY18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(22,plain,
( ( ~ ( in @ sK2_SY13 @ ( powerset @ sK1_A ) )
| ~ ~ ( subset @ ( setminus @ sK1_A @ ( setminus @ sK1_A @ sK2_SY13 ) ) @ sK2_SY13 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(23,plain,
! [SV1: $i,SV4: $i] :
( ( ~ ( in @ SV4 @ ( powerset @ SV1 ) )
| ! [SY19: $i] :
( ~ ( in @ SY19 @ SV1 )
| ~ ( in @ SY19 @ ( setminus @ SV1 @ ( setminus @ SV1 @ SV4 ) ) )
| ( in @ SY19 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(24,plain,
! [SV2: $i,SV5: $i] :
( ( ~ ( in @ SV5 @ ( powerset @ SV2 ) )
| ( in @ ( setminus @ SV2 @ SV5 ) @ ( powerset @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(25,plain,
! [SV3: $i,SV6: $i] :
( ( ~ ( in @ SV6 @ ( powerset @ SV3 ) )
| ! [SY20: $i] :
( ~ ( in @ SY20 @ ( powerset @ SV3 ) )
| ~ ( ~ ( in @ ( sK3_Xx @ SY20 @ SV6 @ SV3 ) @ SV3 )
| ~ ~ ( ~ ( in @ ( sK3_Xx @ SY20 @ SV6 @ SV3 ) @ SV6 )
| ~ ~ ( in @ ( sK3_Xx @ SY20 @ SV6 @ SV3 ) @ SY20 ) ) )
| ( subset @ SV6 @ SY20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(26,plain,
( ( ~ ( in @ sK2_SY13 @ ( powerset @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[22]) ).
thf(27,plain,
( ( ~ ~ ( subset @ ( setminus @ sK1_A @ ( setminus @ sK1_A @ sK2_SY13 ) ) @ sK2_SY13 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[22]) ).
thf(28,plain,
! [SV1: $i,SV4: $i] :
( ( ( ~ ( in @ SV4 @ ( powerset @ SV1 ) ) )
= $true )
| ( ( ! [SY19: $i] :
( ~ ( in @ SY19 @ SV1 )
| ~ ( in @ SY19 @ ( setminus @ SV1 @ ( setminus @ SV1 @ SV4 ) ) )
| ( in @ SY19 @ SV4 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[23]) ).
thf(29,plain,
! [SV2: $i,SV5: $i] :
( ( ( ~ ( in @ SV5 @ ( powerset @ SV2 ) ) )
= $true )
| ( ( in @ ( setminus @ SV2 @ SV5 ) @ ( powerset @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[24]) ).
thf(30,plain,
! [SV3: $i,SV6: $i] :
( ( ( ~ ( in @ SV6 @ ( powerset @ SV3 ) ) )
= $true )
| ( ( ! [SY20: $i] :
( ~ ( in @ SY20 @ ( powerset @ SV3 ) )
| ~ ( ~ ( in @ ( sK3_Xx @ SY20 @ SV6 @ SV3 ) @ SV3 )
| ~ ~ ( ~ ( in @ ( sK3_Xx @ SY20 @ SV6 @ SV3 ) @ SV6 )
| ~ ~ ( in @ ( sK3_Xx @ SY20 @ SV6 @ SV3 ) @ SY20 ) ) )
| ( subset @ SV6 @ SY20 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[25]) ).
thf(31,plain,
( ( in @ sK2_SY13 @ ( powerset @ sK1_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[26]) ).
thf(32,plain,
( ( ~ ( subset @ ( setminus @ sK1_A @ ( setminus @ sK1_A @ sK2_SY13 ) ) @ sK2_SY13 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[27]) ).
thf(33,plain,
! [SV1: $i,SV4: $i] :
( ( ( in @ SV4 @ ( powerset @ SV1 ) )
= $false )
| ( ( ! [SY19: $i] :
( ~ ( in @ SY19 @ SV1 )
| ~ ( in @ SY19 @ ( setminus @ SV1 @ ( setminus @ SV1 @ SV4 ) ) )
| ( in @ SY19 @ SV4 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(34,plain,
! [SV2: $i,SV5: $i] :
( ( ( in @ SV5 @ ( powerset @ SV2 ) )
= $false )
| ( ( in @ ( setminus @ SV2 @ SV5 ) @ ( powerset @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[29]) ).
thf(35,plain,
! [SV3: $i,SV6: $i] :
( ( ( in @ SV6 @ ( powerset @ SV3 ) )
= $false )
| ( ( ! [SY20: $i] :
( ~ ( in @ SY20 @ ( powerset @ SV3 ) )
| ~ ( ~ ( in @ ( sK3_Xx @ SY20 @ SV6 @ SV3 ) @ SV3 )
| ~ ~ ( ~ ( in @ ( sK3_Xx @ SY20 @ SV6 @ SV3 ) @ SV6 )
| ~ ~ ( in @ ( sK3_Xx @ SY20 @ SV6 @ SV3 ) @ SY20 ) ) )
| ( subset @ SV6 @ SY20 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(36,plain,
( ( subset @ ( setminus @ sK1_A @ ( setminus @ sK1_A @ sK2_SY13 ) ) @ sK2_SY13 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(37,plain,
! [SV4: $i,SV1: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ SV1 )
| ~ ( in @ SV7 @ ( setminus @ SV1 @ ( setminus @ SV1 @ SV4 ) ) )
| ( in @ SV7 @ SV4 ) )
= $true )
| ( ( in @ SV4 @ ( powerset @ SV1 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(38,plain,
! [SV6: $i,SV3: $i,SV8: $i] :
( ( ( ~ ( in @ SV8 @ ( powerset @ SV3 ) )
| ~ ( ~ ( in @ ( sK3_Xx @ SV8 @ SV6 @ SV3 ) @ SV3 )
| ~ ~ ( ~ ( in @ ( sK3_Xx @ SV8 @ SV6 @ SV3 ) @ SV6 )
| ~ ~ ( in @ ( sK3_Xx @ SV8 @ SV6 @ SV3 ) @ SV8 ) ) )
| ( subset @ SV6 @ SV8 ) )
= $true )
| ( ( in @ SV6 @ ( powerset @ SV3 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(39,plain,
! [SV4: $i,SV1: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ SV1 ) )
= $true )
| ( ( ~ ( in @ SV7 @ ( setminus @ SV1 @ ( setminus @ SV1 @ SV4 ) ) )
| ( in @ SV7 @ SV4 ) )
= $true )
| ( ( in @ SV4 @ ( powerset @ SV1 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[37]) ).
thf(40,plain,
! [SV6: $i,SV3: $i,SV8: $i] :
( ( ( ~ ( in @ SV8 @ ( powerset @ SV3 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK3_Xx @ SV8 @ SV6 @ SV3 ) @ SV3 )
| ~ ~ ( ~ ( in @ ( sK3_Xx @ SV8 @ SV6 @ SV3 ) @ SV6 )
| ~ ~ ( in @ ( sK3_Xx @ SV8 @ SV6 @ SV3 ) @ SV8 ) ) )
| ( subset @ SV6 @ SV8 ) )
= $true )
| ( ( in @ SV6 @ ( powerset @ SV3 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[38]) ).
thf(41,plain,
! [SV4: $i,SV1: $i,SV7: $i] :
( ( ( in @ SV7 @ SV1 )
= $false )
| ( ( ~ ( in @ SV7 @ ( setminus @ SV1 @ ( setminus @ SV1 @ SV4 ) ) )
| ( in @ SV7 @ SV4 ) )
= $true )
| ( ( in @ SV4 @ ( powerset @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(42,plain,
! [SV6: $i,SV3: $i,SV8: $i] :
( ( ( in @ SV8 @ ( powerset @ SV3 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK3_Xx @ SV8 @ SV6 @ SV3 ) @ SV3 )
| ~ ~ ( ~ ( in @ ( sK3_Xx @ SV8 @ SV6 @ SV3 ) @ SV6 )
| ~ ~ ( in @ ( sK3_Xx @ SV8 @ SV6 @ SV3 ) @ SV8 ) ) )
| ( subset @ SV6 @ SV8 ) )
= $true )
| ( ( in @ SV6 @ ( powerset @ SV3 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(43,plain,
! [SV4: $i,SV1: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ ( setminus @ SV1 @ ( setminus @ SV1 @ SV4 ) ) ) )
= $true )
| ( ( in @ SV7 @ SV4 )
= $true )
| ( ( in @ SV7 @ SV1 )
= $false )
| ( ( in @ SV4 @ ( powerset @ SV1 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[41]) ).
thf(44,plain,
! [SV3: $i,SV6: $i,SV8: $i] :
( ( ( ~ ( ~ ( in @ ( sK3_Xx @ SV8 @ SV6 @ SV3 ) @ SV3 )
| ~ ~ ( ~ ( in @ ( sK3_Xx @ SV8 @ SV6 @ SV3 ) @ SV6 )
| ~ ~ ( in @ ( sK3_Xx @ SV8 @ SV6 @ SV3 ) @ SV8 ) ) ) )
= $true )
| ( ( subset @ SV6 @ SV8 )
= $true )
| ( ( in @ SV8 @ ( powerset @ SV3 ) )
= $false )
| ( ( in @ SV6 @ ( powerset @ SV3 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[42]) ).
thf(45,plain,
! [SV4: $i,SV1: $i,SV7: $i] :
( ( ( in @ SV7 @ ( setminus @ SV1 @ ( setminus @ SV1 @ SV4 ) ) )
= $false )
| ( ( in @ SV7 @ SV4 )
= $true )
| ( ( in @ SV7 @ SV1 )
= $false )
| ( ( in @ SV4 @ ( powerset @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(46,plain,
! [SV3: $i,SV6: $i,SV8: $i] :
( ( ( ~ ( in @ ( sK3_Xx @ SV8 @ SV6 @ SV3 ) @ SV3 )
| ~ ~ ( ~ ( in @ ( sK3_Xx @ SV8 @ SV6 @ SV3 ) @ SV6 )
| ~ ~ ( in @ ( sK3_Xx @ SV8 @ SV6 @ SV3 ) @ SV8 ) ) )
= $false )
| ( ( subset @ SV6 @ SV8 )
= $true )
| ( ( in @ SV8 @ ( powerset @ SV3 ) )
= $false )
| ( ( in @ SV6 @ ( powerset @ SV3 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(47,plain,
! [SV3: $i,SV6: $i,SV8: $i] :
( ( ( ~ ( in @ ( sK3_Xx @ 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)],[46]) ).
thf(48,plain,
! [SV3: $i,SV6: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK3_Xx @ SV8 @ SV6 @ SV3 ) @ SV6 )
| ~ ~ ( in @ ( sK3_Xx @ 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)],[46]) ).
thf(49,plain,
! [SV3: $i,SV6: $i,SV8: $i] :
( ( ( in @ ( sK3_Xx @ 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)],[47]) ).
thf(50,plain,
! [SV3: $i,SV6: $i,SV8: $i] :
( ( ( ~ ( ~ ( in @ ( sK3_Xx @ SV8 @ SV6 @ SV3 ) @ SV6 )
| ~ ~ ( in @ ( sK3_Xx @ SV8 @ SV6 @ SV3 ) @ SV8 ) ) )
= $true )
| ( ( subset @ SV6 @ SV8 )
= $true )
| ( ( in @ SV8 @ ( powerset @ SV3 ) )
= $false )
| ( ( in @ SV6 @ ( powerset @ SV3 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[48]) ).
thf(51,plain,
! [SV3: $i,SV6: $i,SV8: $i] :
( ( ( ~ ( in @ ( sK3_Xx @ SV8 @ SV6 @ SV3 ) @ SV6 )
| ~ ~ ( in @ ( sK3_Xx @ SV8 @ SV6 @ SV3 ) @ SV8 ) )
= $false )
| ( ( subset @ SV6 @ SV8 )
= $true )
| ( ( in @ SV8 @ ( powerset @ SV3 ) )
= $false )
| ( ( in @ SV6 @ ( powerset @ SV3 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(52,plain,
! [SV3: $i,SV6: $i,SV8: $i] :
( ( ( ~ ( in @ ( sK3_Xx @ 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)],[51]) ).
thf(53,plain,
! [SV3: $i,SV6: $i,SV8: $i] :
( ( ( ~ ~ ( in @ ( sK3_Xx @ 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)],[51]) ).
thf(54,plain,
! [SV3: $i,SV6: $i,SV8: $i] :
( ( ( in @ ( sK3_Xx @ 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)],[52]) ).
thf(55,plain,
! [SV3: $i,SV6: $i,SV8: $i] :
( ( ( ~ ( in @ ( sK3_Xx @ SV8 @ SV6 @ SV3 ) @ SV8 ) )
= $true )
| ( ( subset @ SV6 @ SV8 )
= $true )
| ( ( in @ SV8 @ ( powerset @ SV3 ) )
= $false )
| ( ( in @ SV6 @ ( powerset @ SV3 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[53]) ).
thf(56,plain,
! [SV3: $i,SV6: $i,SV8: $i] :
( ( ( in @ ( sK3_Xx @ SV8 @ SV6 @ SV3 ) @ SV8 )
= $false )
| ( ( subset @ SV6 @ SV8 )
= $true )
| ( ( in @ SV8 @ ( powerset @ SV3 ) )
= $false )
| ( ( in @ SV6 @ ( powerset @ SV3 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(57,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[31,56,54,49,45,36,34]) ).
thf(58,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU730^2 : 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.20 % Computer : n009.cluster.edu
% 0.12/0.20 % Model : x86_64 x86_64
% 0.12/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.20 % Memory : 8046.5625MB
% 0.12/0.20 % OS : Linux 6.8.0-71-generic
% 0.12/0.20 % CPULimit : 300
% 0.12/0.20 % WCLimit : 300
% 0.12/0.20 % DateTime : Tue Oct 6 15:33:17 UTC 2026
% 0.12/0.21 % CPUTime :
% 0.12/0.21 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.27
% 0.12/0.27 No.of.Axioms: 0
% 0.12/0.27
% 0.12/0.27 Length.of.Defs: 742
% 0.12/0.27
% 0.12/0.27 Contains.Choice.Funs: false
% 0.12/0.27 ..
% 0.12/0.27
% 0.12/0.27 ********************************
% 0.12/0.27 * All subproblems solved! *
% 0.12/0.27 ********************************
% 0.12/0.27 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:3,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:57,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.12/0.27
% 0.12/0.27 %**** Beginning of derivation protocol ****
% 0.12/0.27 % SZS output start CNFRefutation
% See solution above
% 0.12/0.27
% 0.12/0.27 %**** End of derivation protocol ****
% 0.12/0.27 %**** no. of clauses in derivation: 58 ****
% 0.12/0.27 %**** clause counter: 57 ****
% 0.12/0.27
% 0.12/0.27 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:3,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:57,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------