%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU764^2 : 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 : n006.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 10:47:59 AM UTC 2026
% Result : Theorem 0.08s 0.28s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 4
% Syntax : Number of formulae : 64 ( 48 unt; 0 typ; 3 def)
% Number of atoms : 365 ( 128 equ; 0 cnn)
% Maximal formula atoms : 8 ( 5 avg)
% Number of connectives : 1436 ( 137 ~; 80 |; 8 &;1164 @)
% ( 0 <=>; 47 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 10 con; 0-2 aty)
% Number of variables : 133 ( 0 ^; 133 !; 0 ?; 133 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_binintersect,type,
binintersect: $i > $i > $i ).
thf(tp_binunion,type,
binunion: $i > $i > $i ).
thf(tp_binunionT_lem,type,
binunionT_lem: $o ).
thf(tp_demorgan1,type,
demorgan1: $o ).
thf(tp_demorgan2,type,
demorgan2: $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_SY23,type,
sK3_SY23: $i ).
thf(tp_sK4_SY26,type,
sK4_SY26: $i ).
thf(tp_sK5_SY28,type,
sK5_SY28: $i ).
thf(tp_setminus,type,
setminus: $i > $i > $i ).
thf(binunionT_lem,definition,
( binunionT_lem
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionT_lem) ).
thf(demorgan1,definition,
( demorgan1
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( ( setminus @ A @ ( binintersect @ X @ Y ) )
= ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',demorgan1) ).
thf(demorgan2,definition,
( demorgan2
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( ( setminus @ A @ ( binunion @ X @ Y ) )
= ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',demorgan2) ).
thf(1,conjecture,
( binunionT_lem
=> ( demorgan1
=> ( demorgan2
=> ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Z: $i] :
( ( in @ Z @ ( powerset @ A ) )
=> ! [W: $i] :
( ( in @ W @ ( powerset @ A ) )
=> ( ( setminus @ A @ ( binintersect @ ( binunion @ X @ Y ) @ ( binunion @ Z @ W ) ) )
= ( binunion @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) @ ( binintersect @ ( setminus @ A @ Z ) @ ( setminus @ A @ W ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',woz1_2) ).
thf(2,negated_conjecture,
( ( binunionT_lem
=> ( demorgan1
=> ( demorgan2
=> ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Z: $i] :
( ( in @ Z @ ( powerset @ A ) )
=> ! [W: $i] :
( ( in @ W @ ( powerset @ A ) )
=> ( ( setminus @ A @ ( binintersect @ ( binunion @ X @ Y ) @ ( binunion @ Z @ W ) ) )
= ( binunion @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) @ ( binintersect @ ( setminus @ A @ Z ) @ ( setminus @ A @ W ) ) ) ) ) ) ) ) ) ) )
= $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 @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( ( setminus @ A @ ( binintersect @ X @ Y ) )
= ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( ( setminus @ A @ ( binunion @ X @ Y ) )
= ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) )
=> ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Z: $i] :
( ( in @ Z @ ( powerset @ A ) )
=> ! [W: $i] :
( ( in @ W @ ( powerset @ A ) )
=> ( ( setminus @ A @ ( binintersect @ ( binunion @ X @ Y ) @ ( binunion @ Z @ W ) ) )
= ( binunion @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) @ ( binintersect @ ( setminus @ A @ Z ) @ ( setminus @ A @ W ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,binunionT_lem,demorgan1,demorgan2]) ).
thf(4,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( binunion @ X @ Y ) @ ( 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 ) )
=> ( ( setminus @ A @ ( binintersect @ X @ Y ) )
= ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ 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 ) )
=> ( ( setminus @ A @ ( binunion @ X @ Y ) )
= ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ 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 ) )
=> ! [Z: $i] :
( ( in @ Z @ ( powerset @ A ) )
=> ! [W: $i] :
( ( in @ W @ ( powerset @ A ) )
=> ( ( setminus @ A @ ( binintersect @ ( binunion @ X @ Y ) @ ( binunion @ Z @ W ) ) )
= ( binunion @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) @ ( binintersect @ ( setminus @ A @ Z ) @ ( setminus @ A @ W ) ) ) ) ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(8,plain,
( ( ~ ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Z: $i] :
( ( in @ Z @ ( powerset @ A ) )
=> ! [W: $i] :
( ( in @ W @ ( powerset @ A ) )
=> ( ( setminus @ A @ ( binintersect @ ( binunion @ X @ Y ) @ ( binunion @ Z @ W ) ) )
= ( binunion @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) @ ( binintersect @ ( setminus @ A @ Z ) @ ( setminus @ A @ W ) ) ) ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(9,plain,
( ( ( in @ sK2_SY19 @ ( powerset @ sK1_A ) )
& ( in @ sK3_SY23 @ ( powerset @ sK1_A ) )
& ( in @ sK4_SY26 @ ( powerset @ sK1_A ) )
& ( in @ sK5_SY28 @ ( powerset @ sK1_A ) )
& ( ( setminus @ sK1_A @ ( binintersect @ ( binunion @ sK2_SY19 @ sK3_SY23 ) @ ( binunion @ sK4_SY26 @ sK5_SY28 ) ) )
!= ( binunion @ ( binintersect @ ( setminus @ sK1_A @ sK2_SY19 ) @ ( setminus @ sK1_A @ sK3_SY23 ) ) @ ( binintersect @ ( setminus @ sK1_A @ sK4_SY26 ) @ ( setminus @ sK1_A @ sK5_SY28 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[8]) ).
thf(10,plain,
( ( ! [A: $i,X: $i] :
( ~ ( in @ X @ ( powerset @ A ) )
| ! [Y: $i] :
( ~ ( in @ Y @ ( powerset @ A ) )
| ( in @ ( binunion @ X @ Y ) @ ( 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 ) )
| ( ( setminus @ A @ ( binintersect @ X @ Y ) )
= ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[5]) ).
thf(12,plain,
( ( ! [A: $i,X: $i] :
( ~ ( in @ X @ ( powerset @ A ) )
| ! [Y: $i] :
( ~ ( in @ Y @ ( powerset @ A ) )
| ( ( setminus @ A @ ( binunion @ X @ Y ) )
= ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(13,plain,
( ( ! [A: $i,X: $i] :
( ~ ( in @ X @ ( powerset @ A ) )
| ! [Y: $i] :
( ~ ( in @ Y @ ( powerset @ A ) )
| ( ( setminus @ A @ ( binunion @ X @ Y ) )
= ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(14,plain,
( ( ! [A: $i,X: $i] :
( ~ ( in @ X @ ( powerset @ A ) )
| ! [Y: $i] :
( ~ ( in @ Y @ ( powerset @ A ) )
| ( ( setminus @ A @ ( binintersect @ X @ Y ) )
= ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(15,plain,
( ( ! [A: $i,X: $i] :
( ~ ( in @ X @ ( powerset @ A ) )
| ! [Y: $i] :
( ~ ( in @ Y @ ( powerset @ A ) )
| ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(16,plain,
( ( ( in @ sK2_SY19 @ ( powerset @ sK1_A ) )
& ( in @ sK3_SY23 @ ( powerset @ sK1_A ) )
& ( in @ sK4_SY26 @ ( powerset @ sK1_A ) )
& ( in @ sK5_SY28 @ ( powerset @ sK1_A ) )
& ( ( setminus @ sK1_A @ ( binintersect @ ( binunion @ sK2_SY19 @ sK3_SY23 ) @ ( binunion @ sK4_SY26 @ sK5_SY28 ) ) )
!= ( binunion @ ( binintersect @ ( setminus @ sK1_A @ sK2_SY19 ) @ ( setminus @ sK1_A @ sK3_SY23 ) ) @ ( binintersect @ ( setminus @ sK1_A @ sK4_SY26 ) @ ( setminus @ sK1_A @ sK5_SY28 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(17,plain,
( ( ~ ( ~ ( in @ sK2_SY19 @ ( powerset @ sK1_A ) )
| ~ ~ ( ~ ( in @ sK3_SY23 @ ( powerset @ sK1_A ) )
| ~ ~ ( ~ ( in @ sK4_SY26 @ ( powerset @ sK1_A ) )
| ~ ~ ( ~ ( in @ sK5_SY28 @ ( powerset @ sK1_A ) )
| ~ ( ( ( setminus @ sK1_A @ ( binintersect @ ( binunion @ sK2_SY19 @ sK3_SY23 ) @ ( binunion @ sK4_SY26 @ sK5_SY28 ) ) )
!= ( binunion @ ( binintersect @ ( setminus @ sK1_A @ sK2_SY19 ) @ ( setminus @ sK1_A @ sK3_SY23 ) ) @ ( binintersect @ ( setminus @ sK1_A @ sK4_SY26 ) @ ( setminus @ sK1_A @ sK5_SY28 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16,binunionT_lem,demorgan1,demorgan2]) ).
thf(18,plain,
! [SV1: $i] :
( ( ! [SY29: $i] :
( ~ ( in @ SY29 @ ( powerset @ SV1 ) )
| ! [SY30: $i] :
( ~ ( in @ SY30 @ ( powerset @ SV1 ) )
| ( ( setminus @ SV1 @ ( binunion @ SY29 @ SY30 ) )
= ( binintersect @ ( setminus @ SV1 @ SY29 ) @ ( setminus @ SV1 @ SY30 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[13]) ).
thf(19,plain,
! [SV2: $i] :
( ( ! [SY31: $i] :
( ~ ( in @ SY31 @ ( powerset @ SV2 ) )
| ! [SY32: $i] :
( ~ ( in @ SY32 @ ( powerset @ SV2 ) )
| ( ( setminus @ SV2 @ ( binintersect @ SY31 @ SY32 ) )
= ( binunion @ ( setminus @ SV2 @ SY31 ) @ ( setminus @ SV2 @ SY32 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(20,plain,
! [SV3: $i] :
( ( ! [SY33: $i] :
( ~ ( in @ SY33 @ ( powerset @ SV3 ) )
| ! [SY34: $i] :
( ~ ( in @ SY34 @ ( powerset @ SV3 ) )
| ( in @ ( binunion @ SY33 @ SY34 ) @ ( powerset @ SV3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(21,plain,
( ( ~ ( in @ sK2_SY19 @ ( powerset @ sK1_A ) )
| ~ ~ ( ~ ( in @ sK3_SY23 @ ( powerset @ sK1_A ) )
| ~ ~ ( ~ ( in @ sK4_SY26 @ ( powerset @ sK1_A ) )
| ~ ~ ( ~ ( in @ sK5_SY28 @ ( powerset @ sK1_A ) )
| ~ ( ( ( setminus @ sK1_A @ ( binintersect @ ( binunion @ sK2_SY19 @ sK3_SY23 ) @ ( binunion @ sK4_SY26 @ sK5_SY28 ) ) )
!= ( binunion @ ( binintersect @ ( setminus @ sK1_A @ sK2_SY19 ) @ ( setminus @ sK1_A @ sK3_SY23 ) ) @ ( binintersect @ ( setminus @ sK1_A @ sK4_SY26 ) @ ( setminus @ sK1_A @ sK5_SY28 ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[17]) ).
thf(22,plain,
! [SV1: $i,SV4: $i] :
( ( ~ ( in @ SV4 @ ( powerset @ SV1 ) )
| ! [SY35: $i] :
( ~ ( in @ SY35 @ ( powerset @ SV1 ) )
| ( ( setminus @ SV1 @ ( binunion @ SV4 @ SY35 ) )
= ( binintersect @ ( setminus @ SV1 @ SV4 ) @ ( setminus @ SV1 @ SY35 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(23,plain,
! [SV2: $i,SV5: $i] :
( ( ~ ( in @ SV5 @ ( powerset @ SV2 ) )
| ! [SY36: $i] :
( ~ ( in @ SY36 @ ( powerset @ SV2 ) )
| ( ( setminus @ SV2 @ ( binintersect @ SV5 @ SY36 ) )
= ( binunion @ ( setminus @ SV2 @ SV5 ) @ ( setminus @ SV2 @ SY36 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(24,plain,
! [SV3: $i,SV6: $i] :
( ( ~ ( in @ SV6 @ ( powerset @ SV3 ) )
| ! [SY37: $i] :
( ~ ( in @ SY37 @ ( powerset @ SV3 ) )
| ( in @ ( binunion @ SV6 @ SY37 ) @ ( powerset @ SV3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(25,plain,
( ( ~ ( in @ sK2_SY19 @ ( powerset @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(26,plain,
( ( ~ ~ ( ~ ( in @ sK3_SY23 @ ( powerset @ sK1_A ) )
| ~ ~ ( ~ ( in @ sK4_SY26 @ ( powerset @ sK1_A ) )
| ~ ~ ( ~ ( in @ sK5_SY28 @ ( powerset @ sK1_A ) )
| ~ ( ( ( setminus @ sK1_A @ ( binintersect @ ( binunion @ sK2_SY19 @ sK3_SY23 ) @ ( binunion @ sK4_SY26 @ sK5_SY28 ) ) )
!= ( binunion @ ( binintersect @ ( setminus @ sK1_A @ sK2_SY19 ) @ ( setminus @ sK1_A @ sK3_SY23 ) ) @ ( binintersect @ ( setminus @ sK1_A @ sK4_SY26 ) @ ( setminus @ sK1_A @ sK5_SY28 ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(27,plain,
! [SV1: $i,SV4: $i] :
( ( ( ~ ( in @ SV4 @ ( powerset @ SV1 ) ) )
= $true )
| ( ( ! [SY35: $i] :
( ~ ( in @ SY35 @ ( powerset @ SV1 ) )
| ( ( setminus @ SV1 @ ( binunion @ SV4 @ SY35 ) )
= ( binintersect @ ( setminus @ SV1 @ SV4 ) @ ( setminus @ SV1 @ SY35 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[22]) ).
thf(28,plain,
! [SV2: $i,SV5: $i] :
( ( ( ~ ( in @ SV5 @ ( powerset @ SV2 ) ) )
= $true )
| ( ( ! [SY36: $i] :
( ~ ( in @ SY36 @ ( powerset @ SV2 ) )
| ( ( setminus @ SV2 @ ( binintersect @ SV5 @ SY36 ) )
= ( binunion @ ( setminus @ SV2 @ SV5 ) @ ( setminus @ SV2 @ SY36 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[23]) ).
thf(29,plain,
! [SV3: $i,SV6: $i] :
( ( ( ~ ( in @ SV6 @ ( powerset @ SV3 ) ) )
= $true )
| ( ( ! [SY37: $i] :
( ~ ( in @ SY37 @ ( powerset @ SV3 ) )
| ( in @ ( binunion @ SV6 @ SY37 ) @ ( powerset @ SV3 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[24]) ).
thf(30,plain,
( ( in @ sK2_SY19 @ ( powerset @ sK1_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[25]) ).
thf(31,plain,
( ( ~ ( ~ ( in @ sK3_SY23 @ ( powerset @ sK1_A ) )
| ~ ~ ( ~ ( in @ sK4_SY26 @ ( powerset @ sK1_A ) )
| ~ ~ ( ~ ( in @ sK5_SY28 @ ( powerset @ sK1_A ) )
| ~ ( ( ( setminus @ sK1_A @ ( binintersect @ ( binunion @ sK2_SY19 @ sK3_SY23 ) @ ( binunion @ sK4_SY26 @ sK5_SY28 ) ) )
!= ( binunion @ ( binintersect @ ( setminus @ sK1_A @ sK2_SY19 ) @ ( setminus @ sK1_A @ sK3_SY23 ) ) @ ( binintersect @ ( setminus @ sK1_A @ sK4_SY26 ) @ ( setminus @ sK1_A @ sK5_SY28 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[26]) ).
thf(32,plain,
! [SV1: $i,SV4: $i] :
( ( ( in @ SV4 @ ( powerset @ SV1 ) )
= $false )
| ( ( ! [SY35: $i] :
( ~ ( in @ SY35 @ ( powerset @ SV1 ) )
| ( ( setminus @ SV1 @ ( binunion @ SV4 @ SY35 ) )
= ( binintersect @ ( setminus @ SV1 @ SV4 ) @ ( setminus @ SV1 @ SY35 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(33,plain,
! [SV2: $i,SV5: $i] :
( ( ( in @ SV5 @ ( powerset @ SV2 ) )
= $false )
| ( ( ! [SY36: $i] :
( ~ ( in @ SY36 @ ( powerset @ SV2 ) )
| ( ( setminus @ SV2 @ ( binintersect @ SV5 @ SY36 ) )
= ( binunion @ ( setminus @ SV2 @ SV5 ) @ ( setminus @ SV2 @ SY36 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(34,plain,
! [SV3: $i,SV6: $i] :
( ( ( in @ SV6 @ ( powerset @ SV3 ) )
= $false )
| ( ( ! [SY37: $i] :
( ~ ( in @ SY37 @ ( powerset @ SV3 ) )
| ( in @ ( binunion @ SV6 @ SY37 ) @ ( powerset @ SV3 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[29]) ).
thf(35,plain,
( ( ~ ( in @ sK3_SY23 @ ( powerset @ sK1_A ) )
| ~ ~ ( ~ ( in @ sK4_SY26 @ ( powerset @ sK1_A ) )
| ~ ~ ( ~ ( in @ sK5_SY28 @ ( powerset @ sK1_A ) )
| ~ ( ( ( setminus @ sK1_A @ ( binintersect @ ( binunion @ sK2_SY19 @ sK3_SY23 ) @ ( binunion @ sK4_SY26 @ sK5_SY28 ) ) )
!= ( binunion @ ( binintersect @ ( setminus @ sK1_A @ sK2_SY19 ) @ ( setminus @ sK1_A @ sK3_SY23 ) ) @ ( binintersect @ ( setminus @ sK1_A @ sK4_SY26 ) @ ( setminus @ sK1_A @ sK5_SY28 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(36,plain,
! [SV4: $i,SV1: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ ( powerset @ SV1 ) )
| ( ( setminus @ SV1 @ ( binunion @ SV4 @ SV7 ) )
= ( binintersect @ ( setminus @ SV1 @ SV4 ) @ ( setminus @ SV1 @ SV7 ) ) ) )
= $true )
| ( ( in @ SV4 @ ( powerset @ SV1 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(37,plain,
! [SV5: $i,SV2: $i,SV8: $i] :
( ( ( ~ ( in @ SV8 @ ( powerset @ SV2 ) )
| ( ( setminus @ SV2 @ ( binintersect @ SV5 @ SV8 ) )
= ( binunion @ ( setminus @ SV2 @ SV5 ) @ ( setminus @ SV2 @ SV8 ) ) ) )
= $true )
| ( ( in @ SV5 @ ( powerset @ SV2 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(38,plain,
! [SV6: $i,SV3: $i,SV9: $i] :
( ( ( ~ ( in @ SV9 @ ( powerset @ SV3 ) )
| ( in @ ( binunion @ SV6 @ SV9 ) @ ( powerset @ SV3 ) ) )
= $true )
| ( ( in @ SV6 @ ( powerset @ SV3 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(39,plain,
( ( ~ ( in @ sK3_SY23 @ ( powerset @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[35]) ).
thf(40,plain,
( ( ~ ~ ( ~ ( in @ sK4_SY26 @ ( powerset @ sK1_A ) )
| ~ ~ ( ~ ( in @ sK5_SY28 @ ( powerset @ sK1_A ) )
| ~ ( ( ( setminus @ sK1_A @ ( binintersect @ ( binunion @ sK2_SY19 @ sK3_SY23 ) @ ( binunion @ sK4_SY26 @ sK5_SY28 ) ) )
!= ( binunion @ ( binintersect @ ( setminus @ sK1_A @ sK2_SY19 ) @ ( setminus @ sK1_A @ sK3_SY23 ) ) @ ( binintersect @ ( setminus @ sK1_A @ sK4_SY26 ) @ ( setminus @ sK1_A @ sK5_SY28 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[35]) ).
thf(41,plain,
! [SV4: $i,SV1: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ ( powerset @ SV1 ) ) )
= $true )
| ( ( ( setminus @ SV1 @ ( binunion @ SV4 @ SV7 ) )
= ( binintersect @ ( setminus @ SV1 @ SV4 ) @ ( setminus @ SV1 @ SV7 ) ) )
= $true )
| ( ( in @ SV4 @ ( powerset @ SV1 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[36]) ).
thf(42,plain,
! [SV5: $i,SV2: $i,SV8: $i] :
( ( ( ~ ( in @ SV8 @ ( powerset @ SV2 ) ) )
= $true )
| ( ( ( setminus @ SV2 @ ( binintersect @ SV5 @ SV8 ) )
= ( binunion @ ( setminus @ SV2 @ SV5 ) @ ( setminus @ SV2 @ SV8 ) ) )
= $true )
| ( ( in @ SV5 @ ( powerset @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[37]) ).
thf(43,plain,
! [SV6: $i,SV3: $i,SV9: $i] :
( ( ( ~ ( in @ SV9 @ ( powerset @ SV3 ) ) )
= $true )
| ( ( in @ ( binunion @ SV6 @ SV9 ) @ ( powerset @ SV3 ) )
= $true )
| ( ( in @ SV6 @ ( powerset @ SV3 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[38]) ).
thf(44,plain,
( ( in @ sK3_SY23 @ ( powerset @ sK1_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[39]) ).
thf(45,plain,
( ( ~ ( ~ ( in @ sK4_SY26 @ ( powerset @ sK1_A ) )
| ~ ~ ( ~ ( in @ sK5_SY28 @ ( powerset @ sK1_A ) )
| ~ ( ( ( setminus @ sK1_A @ ( binintersect @ ( binunion @ sK2_SY19 @ sK3_SY23 ) @ ( binunion @ sK4_SY26 @ sK5_SY28 ) ) )
!= ( binunion @ ( binintersect @ ( setminus @ sK1_A @ sK2_SY19 ) @ ( setminus @ sK1_A @ sK3_SY23 ) ) @ ( binintersect @ ( setminus @ sK1_A @ sK4_SY26 ) @ ( setminus @ sK1_A @ sK5_SY28 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[40]) ).
thf(46,plain,
! [SV4: $i,SV1: $i,SV7: $i] :
( ( ( in @ SV7 @ ( powerset @ SV1 ) )
= $false )
| ( ( ( setminus @ SV1 @ ( binunion @ SV4 @ SV7 ) )
= ( binintersect @ ( setminus @ SV1 @ SV4 ) @ ( setminus @ SV1 @ SV7 ) ) )
= $true )
| ( ( in @ SV4 @ ( powerset @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[41]) ).
thf(47,plain,
! [SV5: $i,SV2: $i,SV8: $i] :
( ( ( in @ SV8 @ ( powerset @ SV2 ) )
= $false )
| ( ( ( setminus @ SV2 @ ( binintersect @ SV5 @ SV8 ) )
= ( binunion @ ( setminus @ SV2 @ SV5 ) @ ( setminus @ SV2 @ SV8 ) ) )
= $true )
| ( ( in @ SV5 @ ( powerset @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(48,plain,
! [SV6: $i,SV3: $i,SV9: $i] :
( ( ( in @ SV9 @ ( powerset @ SV3 ) )
= $false )
| ( ( in @ ( binunion @ SV6 @ SV9 ) @ ( powerset @ SV3 ) )
= $true )
| ( ( in @ SV6 @ ( powerset @ SV3 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(49,plain,
( ( ~ ( in @ sK4_SY26 @ ( powerset @ sK1_A ) )
| ~ ~ ( ~ ( in @ sK5_SY28 @ ( powerset @ sK1_A ) )
| ~ ( ( ( setminus @ sK1_A @ ( binintersect @ ( binunion @ sK2_SY19 @ sK3_SY23 ) @ ( binunion @ sK4_SY26 @ sK5_SY28 ) ) )
!= ( binunion @ ( binintersect @ ( setminus @ sK1_A @ sK2_SY19 ) @ ( setminus @ sK1_A @ sK3_SY23 ) ) @ ( binintersect @ ( setminus @ sK1_A @ sK4_SY26 ) @ ( setminus @ sK1_A @ sK5_SY28 ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(50,plain,
( ( ~ ( in @ sK4_SY26 @ ( powerset @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[49]) ).
thf(51,plain,
( ( ~ ~ ( ~ ( in @ sK5_SY28 @ ( powerset @ sK1_A ) )
| ~ ( ( ( setminus @ sK1_A @ ( binintersect @ ( binunion @ sK2_SY19 @ sK3_SY23 ) @ ( binunion @ sK4_SY26 @ sK5_SY28 ) ) )
!= ( binunion @ ( binintersect @ ( setminus @ sK1_A @ sK2_SY19 ) @ ( setminus @ sK1_A @ sK3_SY23 ) ) @ ( binintersect @ ( setminus @ sK1_A @ sK4_SY26 ) @ ( setminus @ sK1_A @ sK5_SY28 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[49]) ).
thf(52,plain,
( ( in @ sK4_SY26 @ ( powerset @ sK1_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[50]) ).
thf(53,plain,
( ( ~ ( ~ ( in @ sK5_SY28 @ ( powerset @ sK1_A ) )
| ~ ( ( ( setminus @ sK1_A @ ( binintersect @ ( binunion @ sK2_SY19 @ sK3_SY23 ) @ ( binunion @ sK4_SY26 @ sK5_SY28 ) ) )
!= ( binunion @ ( binintersect @ ( setminus @ sK1_A @ sK2_SY19 ) @ ( setminus @ sK1_A @ sK3_SY23 ) ) @ ( binintersect @ ( setminus @ sK1_A @ sK4_SY26 ) @ ( setminus @ sK1_A @ sK5_SY28 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[51]) ).
thf(54,plain,
( ( ~ ( in @ sK5_SY28 @ ( powerset @ sK1_A ) )
| ~ ( ( ( setminus @ sK1_A @ ( binintersect @ ( binunion @ sK2_SY19 @ sK3_SY23 ) @ ( binunion @ sK4_SY26 @ sK5_SY28 ) ) )
!= ( binunion @ ( binintersect @ ( setminus @ sK1_A @ sK2_SY19 ) @ ( setminus @ sK1_A @ sK3_SY23 ) ) @ ( binintersect @ ( setminus @ sK1_A @ sK4_SY26 ) @ ( setminus @ sK1_A @ sK5_SY28 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(55,plain,
( ( ~ ( in @ sK5_SY28 @ ( powerset @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[54]) ).
thf(56,plain,
( ( ~ ( ( ( setminus @ sK1_A @ ( binintersect @ ( binunion @ sK2_SY19 @ sK3_SY23 ) @ ( binunion @ sK4_SY26 @ sK5_SY28 ) ) )
!= ( binunion @ ( binintersect @ ( setminus @ sK1_A @ sK2_SY19 ) @ ( setminus @ sK1_A @ sK3_SY23 ) ) @ ( binintersect @ ( setminus @ sK1_A @ sK4_SY26 ) @ ( setminus @ sK1_A @ sK5_SY28 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[54]) ).
thf(57,plain,
( ( in @ sK5_SY28 @ ( powerset @ sK1_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[55]) ).
thf(58,plain,
( ( ( setminus @ sK1_A @ ( binintersect @ ( binunion @ sK2_SY19 @ sK3_SY23 ) @ ( binunion @ sK4_SY26 @ sK5_SY28 ) ) )
!= ( binunion @ ( binintersect @ ( setminus @ sK1_A @ sK2_SY19 ) @ ( setminus @ sK1_A @ sK3_SY23 ) ) @ ( binintersect @ ( setminus @ sK1_A @ sK4_SY26 ) @ ( setminus @ sK1_A @ sK5_SY28 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[56]) ).
thf(59,plain,
( ( ( setminus @ sK1_A @ ( binintersect @ ( binunion @ sK2_SY19 @ sK3_SY23 ) @ ( binunion @ sK4_SY26 @ sK5_SY28 ) ) )
= ( binunion @ ( binintersect @ ( setminus @ sK1_A @ sK2_SY19 ) @ ( setminus @ sK1_A @ sK3_SY23 ) ) @ ( binintersect @ ( setminus @ sK1_A @ sK4_SY26 ) @ ( setminus @ sK1_A @ sK5_SY28 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(60,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[30,59,57,52,48,47,46,44]) ).
thf(61,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU764^2 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.21 % Computer : n006.cluster.edu
% 0.08/0.21 % Model : x86_64 x86_64
% 0.08/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.21 % Memory : 8046.5625MB
% 0.08/0.21 % OS : Linux 6.8.0-71-generic
% 0.08/0.21 % CPULimit : 300
% 0.08/0.21 % WCLimit : 300
% 0.08/0.21 % DateTime : Tue Oct 6 15:33:37 UTC 2026
% 0.08/0.21 % CPUTime :
% 0.08/0.21 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.28
% 0.08/0.28 No.of.Axioms: 0
% 0.08/0.28
% 0.08/0.28 Length.of.Defs: 799
% 0.08/0.28
% 0.08/0.28 Contains.Choice.Funs: false
% 0.08/0.28 ..
% 0.08/0.28
% 0.08/0.28 ********************************
% 0.08/0.28 * All subproblems solved! *
% 0.08/0.28 ********************************
% 0.08/0.28 % SZS status Theorem for /export/starexec/sandbox2/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:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:60,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.08/0.28
% 0.08/0.28 %**** Beginning of derivation protocol ****
% 0.08/0.28 % SZS output start CNFRefutation
% See solution above
% 0.08/0.28
% 0.08/0.28 %**** End of derivation protocol ****
% 0.08/0.28 %**** no. of clauses in derivation: 61 ****
% 0.08/0.28 %**** clause counter: 60 ****
% 0.08/0.28
% 0.08/0.28 % SZS status Theorem for /export/starexec/sandbox2/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:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:60,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------