%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU750^2 : 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 : 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 10:47:36 AM UTC 2026
% Result : Theorem 0.08s 0.25s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 4
% Syntax : Number of formulae : 66 ( 45 unt; 0 typ; 3 def)
% Number of atoms : 451 ( 106 equ; 0 cnn)
% Maximal formula atoms : 8 ( 6 avg)
% Number of connectives : 1026 ( 141 ~; 112 |; 0 &; 712 @)
% ( 0 <=>; 61 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 189 ( 0 ^; 189 !; 0 ?; 189 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_binunion,type,
binunion: $i > $i > $i ).
thf(tp_binunionTIRcontra,type,
binunionTIRcontra: $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_SY25,type,
sK2_SY25: $i ).
thf(tp_sK3_SY32,type,
sK3_SY32: $i ).
thf(tp_sK4_SY34,type,
sK4_SY34: $i ).
thf(tp_setminus,type,
setminus: $i > $i > $i ).
thf(tp_setminusER,type,
setminusER: $o ).
thf(tp_setminusI,type,
setminusI: $o ).
thf(binunionTIRcontra,definition,
( binunionTIRcontra
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
=> ~ ( in @ Xx @ Y ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionTIRcontra) ).
thf(setminusER,definition,
( setminusER
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
=> ~ ( in @ Xx @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusER) ).
thf(setminusI,definition,
( setminusI
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusI) ).
thf(1,conjecture,
( setminusI
=> ( setminusER
=> ( binunionTIRcontra
=> ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
=> ( in @ Xx @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',demorgan2a2) ).
thf(2,negated_conjecture,
( ( setminusI
=> ( setminusER
=> ( binunionTIRcontra
=> ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
=> ( in @ Xx @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( in @ Xx @ ( setminus @ A @ B ) ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
=> ~ ( in @ Xx @ B ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
=> ~ ( in @ Xx @ Y ) ) ) ) )
=> ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
=> ( in @ Xx @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,binunionTIRcontra,setminusER,setminusI]) ).
thf(4,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( in @ Xx @ ( setminus @ A @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
=> ~ ( in @ Xx @ B ) ) )
= $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 @ ( binunion @ X @ Y ) )
=> ~ ( in @ Xx @ 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 @ ( binunion @ X @ Y ) ) )
=> ( in @ Xx @ ( setminus @ A @ Y ) ) ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(8,plain,
( ( ~ ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
=> ( in @ Xx @ ( setminus @ A @ Y ) ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(9,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
=> ~ ( in @ Xx @ Y ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(10,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
=> ~ ( in @ Xx @ B ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(11,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( in @ Xx @ ( setminus @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(12,plain,
( ( ~ ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
=> ( in @ Xx @ ( setminus @ A @ Y ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(13,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ ( setminus @ SX0 @ ( binunion @ SX1 @ SX2 ) ) )
| ( in @ SX3 @ ( setminus @ SX0 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12,binunionTIRcontra,setminusER,setminusI]) ).
thf(14,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ~ ( in @ SX3 @ ( binunion @ SX1 @ SX2 ) )
| ~ ( in @ SX3 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9,binunionTIRcontra,setminusER,setminusI]) ).
thf(15,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11,binunionTIRcontra,setminusER,setminusI]) ).
thf(16,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) )
| ~ ( in @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10,binunionTIRcontra,setminusER,setminusI]) ).
thf(17,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ ( setminus @ SX0 @ ( binunion @ SX1 @ SX2 ) ) )
| ( in @ SX3 @ ( setminus @ SX0 @ SX2 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[13]) ).
thf(18,plain,
! [SV1: $i] :
( ( ! [SY18: $i] :
( ~ ( in @ SY18 @ ( powerset @ SV1 ) )
| ! [SY19: $i] :
( ~ ( in @ SY19 @ ( powerset @ SV1 ) )
| ! [SY20: $i] :
( ~ ( in @ SY20 @ SV1 )
| ~ ~ ( in @ SY20 @ ( binunion @ SY18 @ SY19 ) )
| ~ ( in @ SY20 @ SY19 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(19,plain,
! [SV2: $i] :
( ( ! [SY21: $i,SY22: $i] :
( ~ ( in @ SY22 @ SV2 )
| ~ ~ ( in @ SY22 @ SY21 )
| ( in @ SY22 @ ( setminus @ SV2 @ SY21 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(20,plain,
! [SV3: $i] :
( ( ! [SY23: $i,SY24: $i] :
( ~ ( in @ SY24 @ ( setminus @ SV3 @ SY23 ) )
| ~ ( in @ SY24 @ SY23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(21,plain,
( ( ! [SY25: $i] :
( ~ ( in @ SY25 @ ( powerset @ sK1_SX0 ) )
| ! [SY26: $i] :
( ~ ( in @ SY26 @ ( powerset @ sK1_SX0 ) )
| ! [SY27: $i] :
( ~ ( in @ SY27 @ sK1_SX0 )
| ~ ( in @ SY27 @ ( setminus @ sK1_SX0 @ ( binunion @ SY25 @ SY26 ) ) )
| ( in @ SY27 @ ( setminus @ sK1_SX0 @ SY26 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[17]) ).
thf(22,plain,
! [SV1: $i,SV4: $i] :
( ( ~ ( in @ SV4 @ ( powerset @ SV1 ) )
| ! [SY28: $i] :
( ~ ( in @ SY28 @ ( powerset @ SV1 ) )
| ! [SY29: $i] :
( ~ ( in @ SY29 @ SV1 )
| ~ ~ ( in @ SY29 @ ( binunion @ SV4 @ SY28 ) )
| ~ ( in @ SY29 @ SY28 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(23,plain,
! [SV5: $i,SV2: $i] :
( ( ! [SY30: $i] :
( ~ ( in @ SY30 @ SV2 )
| ~ ~ ( in @ SY30 @ SV5 )
| ( in @ SY30 @ ( setminus @ SV2 @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(24,plain,
! [SV6: $i,SV3: $i] :
( ( ! [SY31: $i] :
( ~ ( in @ SY31 @ ( setminus @ SV3 @ SV6 ) )
| ~ ( in @ SY31 @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(25,plain,
( ( ~ ( in @ sK2_SY25 @ ( powerset @ sK1_SX0 ) )
| ! [SY32: $i] :
( ~ ( in @ SY32 @ ( powerset @ sK1_SX0 ) )
| ! [SY33: $i] :
( ~ ( in @ SY33 @ sK1_SX0 )
| ~ ( in @ SY33 @ ( setminus @ sK1_SX0 @ ( binunion @ sK2_SY25 @ SY32 ) ) )
| ( in @ SY33 @ ( setminus @ sK1_SX0 @ SY32 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[21]) ).
thf(26,plain,
! [SV1: $i,SV4: $i] :
( ( ( ~ ( in @ SV4 @ ( powerset @ SV1 ) ) )
= $true )
| ( ( ! [SY28: $i] :
( ~ ( in @ SY28 @ ( powerset @ SV1 ) )
| ! [SY29: $i] :
( ~ ( in @ SY29 @ SV1 )
| ~ ~ ( in @ SY29 @ ( binunion @ SV4 @ SY28 ) )
| ~ ( in @ SY29 @ SY28 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[22]) ).
thf(27,plain,
! [SV5: $i,SV2: $i,SV7: $i] :
( ( ~ ( in @ SV7 @ SV2 )
| ~ ~ ( in @ SV7 @ SV5 )
| ( in @ SV7 @ ( setminus @ SV2 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(28,plain,
! [SV6: $i,SV3: $i,SV8: $i] :
( ( ~ ( in @ SV8 @ ( setminus @ SV3 @ SV6 ) )
| ~ ( in @ SV8 @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(29,plain,
( ( ~ ( in @ sK2_SY25 @ ( powerset @ sK1_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[25]) ).
thf(30,plain,
( ( ! [SY32: $i] :
( ~ ( in @ SY32 @ ( powerset @ sK1_SX0 ) )
| ! [SY33: $i] :
( ~ ( in @ SY33 @ sK1_SX0 )
| ~ ( in @ SY33 @ ( setminus @ sK1_SX0 @ ( binunion @ sK2_SY25 @ SY32 ) ) )
| ( in @ SY33 @ ( setminus @ sK1_SX0 @ SY32 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[25]) ).
thf(31,plain,
! [SV1: $i,SV4: $i] :
( ( ( in @ SV4 @ ( powerset @ SV1 ) )
= $false )
| ( ( ! [SY28: $i] :
( ~ ( in @ SY28 @ ( powerset @ SV1 ) )
| ! [SY29: $i] :
( ~ ( in @ SY29 @ SV1 )
| ~ ~ ( in @ SY29 @ ( binunion @ SV4 @ SY28 ) )
| ~ ( in @ SY29 @ SY28 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(32,plain,
! [SV5: $i,SV2: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ SV2 ) )
= $true )
| ( ( ~ ~ ( in @ SV7 @ SV5 )
| ( in @ SV7 @ ( setminus @ SV2 @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[27]) ).
thf(33,plain,
! [SV6: $i,SV3: $i,SV8: $i] :
( ( ( ~ ( in @ SV8 @ ( setminus @ SV3 @ SV6 ) ) )
= $true )
| ( ( ~ ( in @ SV8 @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[28]) ).
thf(34,plain,
( ( in @ sK2_SY25 @ ( powerset @ sK1_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[29]) ).
thf(35,plain,
( ( ~ ( in @ sK3_SY32 @ ( powerset @ sK1_SX0 ) )
| ! [SY34: $i] :
( ~ ( in @ SY34 @ sK1_SX0 )
| ~ ( in @ SY34 @ ( setminus @ sK1_SX0 @ ( binunion @ sK2_SY25 @ sK3_SY32 ) ) )
| ( in @ SY34 @ ( setminus @ sK1_SX0 @ sK3_SY32 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[30]) ).
thf(36,plain,
! [SV4: $i,SV1: $i,SV9: $i] :
( ( ( ~ ( in @ SV9 @ ( powerset @ SV1 ) )
| ! [SY35: $i] :
( ~ ( in @ SY35 @ SV1 )
| ~ ~ ( in @ SY35 @ ( binunion @ SV4 @ SV9 ) )
| ~ ( in @ SY35 @ SV9 ) ) )
= $true )
| ( ( in @ SV4 @ ( powerset @ SV1 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(37,plain,
! [SV5: $i,SV2: $i,SV7: $i] :
( ( ( in @ SV7 @ SV2 )
= $false )
| ( ( ~ ~ ( in @ SV7 @ SV5 )
| ( in @ SV7 @ ( setminus @ SV2 @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(38,plain,
! [SV6: $i,SV3: $i,SV8: $i] :
( ( ( in @ SV8 @ ( setminus @ SV3 @ SV6 ) )
= $false )
| ( ( ~ ( in @ SV8 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(39,plain,
( ( ~ ( in @ sK3_SY32 @ ( powerset @ sK1_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[35]) ).
thf(40,plain,
( ( ! [SY34: $i] :
( ~ ( in @ SY34 @ sK1_SX0 )
| ~ ( in @ SY34 @ ( setminus @ sK1_SX0 @ ( binunion @ sK2_SY25 @ sK3_SY32 ) ) )
| ( in @ SY34 @ ( setminus @ sK1_SX0 @ sK3_SY32 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[35]) ).
thf(41,plain,
! [SV4: $i,SV1: $i,SV9: $i] :
( ( ( ~ ( in @ SV9 @ ( powerset @ SV1 ) ) )
= $true )
| ( ( ! [SY35: $i] :
( ~ ( in @ SY35 @ SV1 )
| ~ ~ ( in @ SY35 @ ( binunion @ SV4 @ SV9 ) )
| ~ ( in @ SY35 @ SV9 ) ) )
= $true )
| ( ( in @ SV4 @ ( powerset @ SV1 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[36]) ).
thf(42,plain,
! [SV2: $i,SV5: $i,SV7: $i] :
( ( ( ~ ~ ( in @ SV7 @ SV5 ) )
= $true )
| ( ( in @ SV7 @ ( setminus @ SV2 @ SV5 ) )
= $true )
| ( ( in @ SV7 @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[37]) ).
thf(43,plain,
! [SV3: $i,SV6: $i,SV8: $i] :
( ( ( in @ SV8 @ SV6 )
= $false )
| ( ( in @ SV8 @ ( setminus @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(44,plain,
( ( in @ sK3_SY32 @ ( powerset @ sK1_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[39]) ).
thf(45,plain,
( ( ~ ( in @ sK4_SY34 @ sK1_SX0 )
| ~ ( in @ sK4_SY34 @ ( setminus @ sK1_SX0 @ ( binunion @ sK2_SY25 @ sK3_SY32 ) ) )
| ( in @ sK4_SY34 @ ( setminus @ sK1_SX0 @ sK3_SY32 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[40]) ).
thf(46,plain,
! [SV4: $i,SV1: $i,SV9: $i] :
( ( ( in @ SV9 @ ( powerset @ SV1 ) )
= $false )
| ( ( ! [SY35: $i] :
( ~ ( in @ SY35 @ SV1 )
| ~ ~ ( in @ SY35 @ ( binunion @ SV4 @ SV9 ) )
| ~ ( in @ SY35 @ SV9 ) ) )
= $true )
| ( ( in @ SV4 @ ( powerset @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[41]) ).
thf(47,plain,
! [SV2: $i,SV5: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ SV5 ) )
= $false )
| ( ( in @ SV7 @ ( setminus @ SV2 @ SV5 ) )
= $true )
| ( ( in @ SV7 @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(48,plain,
( ( ~ ( in @ sK4_SY34 @ sK1_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[45]) ).
thf(49,plain,
( ( ~ ( in @ sK4_SY34 @ ( setminus @ sK1_SX0 @ ( binunion @ sK2_SY25 @ sK3_SY32 ) ) )
| ( in @ sK4_SY34 @ ( setminus @ sK1_SX0 @ sK3_SY32 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[45]) ).
thf(50,plain,
! [SV9: $i,SV4: $i,SV1: $i,SV10: $i] :
( ( ( ~ ( in @ SV10 @ SV1 )
| ~ ~ ( in @ SV10 @ ( binunion @ SV4 @ SV9 ) )
| ~ ( in @ SV10 @ SV9 ) )
= $true )
| ( ( in @ SV9 @ ( powerset @ SV1 ) )
= $false )
| ( ( in @ SV4 @ ( powerset @ SV1 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(51,plain,
! [SV2: $i,SV5: $i,SV7: $i] :
( ( ( in @ SV7 @ SV5 )
= $true )
| ( ( in @ SV7 @ ( setminus @ SV2 @ SV5 ) )
= $true )
| ( ( in @ SV7 @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[47]) ).
thf(52,plain,
( ( in @ sK4_SY34 @ sK1_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[48]) ).
thf(53,plain,
( ( ~ ( in @ sK4_SY34 @ ( setminus @ sK1_SX0 @ ( binunion @ sK2_SY25 @ sK3_SY32 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[49]) ).
thf(54,plain,
( ( in @ sK4_SY34 @ ( setminus @ sK1_SX0 @ sK3_SY32 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[49]) ).
thf(55,plain,
! [SV9: $i,SV4: $i,SV1: $i,SV10: $i] :
( ( ( ~ ( in @ SV10 @ SV1 ) )
= $true )
| ( ( ~ ~ ( in @ SV10 @ ( binunion @ SV4 @ SV9 ) )
| ~ ( in @ SV10 @ SV9 ) )
= $true )
| ( ( in @ SV9 @ ( powerset @ SV1 ) )
= $false )
| ( ( in @ SV4 @ ( powerset @ SV1 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[50]) ).
thf(56,plain,
( ( in @ sK4_SY34 @ ( setminus @ sK1_SX0 @ ( binunion @ sK2_SY25 @ sK3_SY32 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[53]) ).
thf(57,plain,
! [SV9: $i,SV4: $i,SV1: $i,SV10: $i] :
( ( ( in @ SV10 @ SV1 )
= $false )
| ( ( ~ ~ ( in @ SV10 @ ( binunion @ SV4 @ SV9 ) )
| ~ ( in @ SV10 @ SV9 ) )
= $true )
| ( ( in @ SV9 @ ( powerset @ SV1 ) )
= $false )
| ( ( in @ SV4 @ ( powerset @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(58,plain,
! [SV1: $i,SV9: $i,SV4: $i,SV10: $i] :
( ( ( ~ ~ ( in @ SV10 @ ( binunion @ SV4 @ SV9 ) ) )
= $true )
| ( ( ~ ( in @ SV10 @ SV9 ) )
= $true )
| ( ( in @ SV10 @ SV1 )
= $false )
| ( ( in @ SV9 @ ( powerset @ SV1 ) )
= $false )
| ( ( in @ SV4 @ ( powerset @ SV1 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[57]) ).
thf(59,plain,
! [SV1: $i,SV9: $i,SV4: $i,SV10: $i] :
( ( ( ~ ( in @ SV10 @ ( binunion @ SV4 @ SV9 ) ) )
= $false )
| ( ( ~ ( in @ SV10 @ SV9 ) )
= $true )
| ( ( in @ SV10 @ SV1 )
= $false )
| ( ( in @ SV9 @ ( powerset @ SV1 ) )
= $false )
| ( ( in @ SV4 @ ( powerset @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(60,plain,
! [SV1: $i,SV9: $i,SV4: $i,SV10: $i] :
( ( ( in @ SV10 @ ( binunion @ SV4 @ SV9 ) )
= $true )
| ( ( ~ ( in @ SV10 @ SV9 ) )
= $true )
| ( ( in @ SV10 @ SV1 )
= $false )
| ( ( in @ SV9 @ ( powerset @ SV1 ) )
= $false )
| ( ( in @ SV4 @ ( powerset @ SV1 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[59]) ).
thf(61,plain,
! [SV1: $i,SV4: $i,SV9: $i,SV10: $i] :
( ( ( in @ SV10 @ SV9 )
= $false )
| ( ( in @ SV10 @ ( binunion @ SV4 @ SV9 ) )
= $true )
| ( ( in @ SV10 @ SV1 )
= $false )
| ( ( in @ SV9 @ ( powerset @ SV1 ) )
= $false )
| ( ( in @ SV4 @ ( powerset @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(62,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[34,61,56,54,52,51,44,43]) ).
thf(63,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU750^2 : 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
% 0.08/0.19 % Computer : n004.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Oct 6 15:33:39 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.25
% 0.08/0.25 No.of.Axioms: 0
% 0.08/0.25
% 0.08/0.25 Length.of.Defs: 679
% 0.08/0.25
% 0.08/0.25 Contains.Choice.Funs: false
% 0.08/0.25 ..
% 0.08/0.25
% 0.08/0.25 ********************************
% 0.08/0.25 * All subproblems solved! *
% 0.08/0.25 ********************************
% 0.08/0.25 % 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:62,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.08/0.25
% 0.08/0.25 %**** Beginning of derivation protocol ****
% 0.08/0.25 % SZS output start CNFRefutation
% See solution above
% 0.08/0.25
% 0.08/0.25 %**** End of derivation protocol ****
% 0.08/0.25 %**** no. of clauses in derivation: 63 ****
% 0.08/0.25 %**** clause counter: 62 ****
% 0.08/0.25
% 0.08/0.25 % 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:62,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------