%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU745^2 : 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 : n010.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 10:47:25 AM UTC 2026
% Result : Theorem 0.24s 0.29s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 3
% Syntax : Number of formulae : 58 ( 43 unt; 0 typ; 2 def)
% Number of atoms : 386 ( 87 equ; 0 cnn)
% Maximal formula atoms : 7 ( 6 avg)
% Number of connectives : 1004 ( 161 ~; 102 |; 8 &; 689 @)
% ( 0 <=>; 44 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 125 ( 0 ^; 125 !; 0 ?; 125 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_binunion,type,
binunion: $i > $i > $i ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_inComplementUnionImpNotIn1,type,
inComplementUnionImpNotIn1: $o ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY15,type,
sK2_SY15: $i ).
thf(tp_sK3_SY18,type,
sK3_SY18: $i ).
thf(tp_sK4_SY20,type,
sK4_SY20: $i ).
thf(tp_setminus,type,
setminus: $i > $i > $i ).
thf(tp_setminusI,type,
setminusI: $o ).
thf(inComplementUnionImpNotIn1,definition,
( inComplementUnionImpNotIn1
= ( ! [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 @ X ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inComplementUnionImpNotIn1) ).
thf(setminusI,definition,
( setminusI
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusI) ).
thf(1,conjecture,
( setminusI
=> ( inComplementUnionImpNotIn1
=> ! [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 @ X ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inComplementUnionImpInComplement1) ).
thf(2,negated_conjecture,
( ( setminusI
=> ( inComplementUnionImpNotIn1
=> ! [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 @ X ) ) ) ) ) ) ) )
= $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,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 @ X ) ) ) ) )
=> ! [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 @ X ) ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,inComplementUnionImpNotIn1,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,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 @ X ) ) ) ) ) )
= $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 @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
=> ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) )
= $false ),
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 @ X ) ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(8,plain,
( ( ( in @ sK2_SY15 @ ( powerset @ sK1_A ) )
& ( in @ sK3_SY18 @ ( powerset @ sK1_A ) )
& ( in @ sK4_SY20 @ sK1_A )
& ( in @ sK4_SY20 @ ( setminus @ sK1_A @ ( binunion @ sK2_SY15 @ sK3_SY18 ) ) )
& ~ ( in @ sK4_SY20 @ ( setminus @ sK1_A @ sK2_SY15 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(9,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ( in @ Xx @ B )
| ( in @ Xx @ ( setminus @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(10,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 @ X ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[5]) ).
thf(11,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 @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(12,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ( in @ Xx @ B )
| ( in @ Xx @ ( setminus @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(13,plain,
( ( ( in @ sK2_SY15 @ ( powerset @ sK1_A ) )
& ( in @ sK3_SY18 @ ( powerset @ sK1_A ) )
& ( in @ sK4_SY20 @ sK1_A )
& ( in @ sK4_SY20 @ ( setminus @ sK1_A @ ( binunion @ sK2_SY15 @ sK3_SY18 ) ) )
& ~ ( in @ sK4_SY20 @ ( setminus @ sK1_A @ sK2_SY15 ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(14,plain,
( ( ~ ( ~ ( in @ sK2_SY15 @ ( powerset @ sK1_A ) )
| ~ ~ ( ~ ( in @ sK3_SY18 @ ( powerset @ sK1_A ) )
| ~ ~ ( ~ ( in @ sK4_SY20 @ sK1_A )
| ~ ~ ( ~ ( in @ sK4_SY20 @ ( setminus @ sK1_A @ ( binunion @ sK2_SY15 @ sK3_SY18 ) ) )
| ~ ~ ( in @ sK4_SY20 @ ( setminus @ sK1_A @ sK2_SY15 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13,inComplementUnionImpNotIn1,setminusI]) ).
thf(15,plain,
! [SV1: $i] :
( ( ! [SY21: $i] :
( ~ ( in @ SY21 @ ( powerset @ SV1 ) )
| ! [SY22: $i] :
( ~ ( in @ SY22 @ ( powerset @ SV1 ) )
| ! [SY23: $i] :
( ~ ( in @ SY23 @ SV1 )
| ~ ( in @ SY23 @ ( setminus @ SV1 @ ( binunion @ SY21 @ SY22 ) ) )
| ~ ( in @ SY23 @ SY21 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(16,plain,
! [SV2: $i] :
( ( ! [SY24: $i,SY25: $i] :
( ~ ( in @ SY25 @ SV2 )
| ( in @ SY25 @ SY24 )
| ( in @ SY25 @ ( setminus @ SV2 @ SY24 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(17,plain,
( ( ~ ( in @ sK2_SY15 @ ( powerset @ sK1_A ) )
| ~ ~ ( ~ ( in @ sK3_SY18 @ ( powerset @ sK1_A ) )
| ~ ~ ( ~ ( in @ sK4_SY20 @ sK1_A )
| ~ ~ ( ~ ( in @ sK4_SY20 @ ( setminus @ sK1_A @ ( binunion @ sK2_SY15 @ sK3_SY18 ) ) )
| ~ ~ ( in @ sK4_SY20 @ ( setminus @ sK1_A @ sK2_SY15 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[14]) ).
thf(18,plain,
! [SV1: $i,SV3: $i] :
( ( ~ ( in @ SV3 @ ( powerset @ SV1 ) )
| ! [SY26: $i] :
( ~ ( in @ SY26 @ ( powerset @ SV1 ) )
| ! [SY27: $i] :
( ~ ( in @ SY27 @ SV1 )
| ~ ( in @ SY27 @ ( setminus @ SV1 @ ( binunion @ SV3 @ SY26 ) ) )
| ~ ( in @ SY27 @ SV3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(19,plain,
! [SV4: $i,SV2: $i] :
( ( ! [SY28: $i] :
( ~ ( in @ SY28 @ SV2 )
| ( in @ SY28 @ SV4 )
| ( in @ SY28 @ ( setminus @ SV2 @ SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(20,plain,
( ( ~ ( in @ sK2_SY15 @ ( powerset @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(21,plain,
( ( ~ ~ ( ~ ( in @ sK3_SY18 @ ( powerset @ sK1_A ) )
| ~ ~ ( ~ ( in @ sK4_SY20 @ sK1_A )
| ~ ~ ( ~ ( in @ sK4_SY20 @ ( setminus @ sK1_A @ ( binunion @ sK2_SY15 @ sK3_SY18 ) ) )
| ~ ~ ( in @ sK4_SY20 @ ( setminus @ sK1_A @ sK2_SY15 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(22,plain,
! [SV1: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ ( powerset @ SV1 ) ) )
= $true )
| ( ( ! [SY26: $i] :
( ~ ( in @ SY26 @ ( powerset @ SV1 ) )
| ! [SY27: $i] :
( ~ ( in @ SY27 @ SV1 )
| ~ ( in @ SY27 @ ( setminus @ SV1 @ ( binunion @ SV3 @ SY26 ) ) )
| ~ ( in @ SY27 @ SV3 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[18]) ).
thf(23,plain,
! [SV4: $i,SV2: $i,SV5: $i] :
( ( ~ ( in @ SV5 @ SV2 )
| ( in @ SV5 @ SV4 )
| ( in @ SV5 @ ( setminus @ SV2 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(24,plain,
( ( in @ sK2_SY15 @ ( powerset @ sK1_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[20]) ).
thf(25,plain,
( ( ~ ( ~ ( in @ sK3_SY18 @ ( powerset @ sK1_A ) )
| ~ ~ ( ~ ( in @ sK4_SY20 @ sK1_A )
| ~ ~ ( ~ ( in @ sK4_SY20 @ ( setminus @ sK1_A @ ( binunion @ sK2_SY15 @ sK3_SY18 ) ) )
| ~ ~ ( in @ sK4_SY20 @ ( setminus @ sK1_A @ sK2_SY15 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[21]) ).
thf(26,plain,
! [SV1: $i,SV3: $i] :
( ( ( in @ SV3 @ ( powerset @ SV1 ) )
= $false )
| ( ( ! [SY26: $i] :
( ~ ( in @ SY26 @ ( powerset @ SV1 ) )
| ! [SY27: $i] :
( ~ ( in @ SY27 @ SV1 )
| ~ ( in @ SY27 @ ( setminus @ SV1 @ ( binunion @ SV3 @ SY26 ) ) )
| ~ ( in @ SY27 @ SV3 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[22]) ).
thf(27,plain,
! [SV4: $i,SV2: $i,SV5: $i] :
( ( ( ~ ( in @ SV5 @ SV2 ) )
= $true )
| ( ( ( in @ SV5 @ SV4 )
| ( in @ SV5 @ ( setminus @ SV2 @ SV4 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[23]) ).
thf(28,plain,
( ( ~ ( in @ sK3_SY18 @ ( powerset @ sK1_A ) )
| ~ ~ ( ~ ( in @ sK4_SY20 @ sK1_A )
| ~ ~ ( ~ ( in @ sK4_SY20 @ ( setminus @ sK1_A @ ( binunion @ sK2_SY15 @ sK3_SY18 ) ) )
| ~ ~ ( in @ sK4_SY20 @ ( setminus @ sK1_A @ sK2_SY15 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(29,plain,
! [SV3: $i,SV1: $i,SV6: $i] :
( ( ( ~ ( in @ SV6 @ ( powerset @ SV1 ) )
| ! [SY29: $i] :
( ~ ( in @ SY29 @ SV1 )
| ~ ( in @ SY29 @ ( setminus @ SV1 @ ( binunion @ SV3 @ SV6 ) ) )
| ~ ( in @ SY29 @ SV3 ) ) )
= $true )
| ( ( in @ SV3 @ ( powerset @ SV1 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(30,plain,
! [SV4: $i,SV2: $i,SV5: $i] :
( ( ( in @ SV5 @ SV2 )
= $false )
| ( ( ( in @ SV5 @ SV4 )
| ( in @ SV5 @ ( setminus @ SV2 @ SV4 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(31,plain,
( ( ~ ( in @ sK3_SY18 @ ( powerset @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[28]) ).
thf(32,plain,
( ( ~ ~ ( ~ ( in @ sK4_SY20 @ sK1_A )
| ~ ~ ( ~ ( in @ sK4_SY20 @ ( setminus @ sK1_A @ ( binunion @ sK2_SY15 @ sK3_SY18 ) ) )
| ~ ~ ( in @ sK4_SY20 @ ( setminus @ sK1_A @ sK2_SY15 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[28]) ).
thf(33,plain,
! [SV3: $i,SV1: $i,SV6: $i] :
( ( ( ~ ( in @ SV6 @ ( powerset @ SV1 ) ) )
= $true )
| ( ( ! [SY29: $i] :
( ~ ( in @ SY29 @ SV1 )
| ~ ( in @ SY29 @ ( setminus @ SV1 @ ( binunion @ SV3 @ SV6 ) ) )
| ~ ( in @ SY29 @ SV3 ) ) )
= $true )
| ( ( in @ SV3 @ ( powerset @ SV1 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[29]) ).
thf(34,plain,
! [SV2: $i,SV4: $i,SV5: $i] :
( ( ( in @ SV5 @ SV4 )
= $true )
| ( ( in @ SV5 @ ( setminus @ SV2 @ SV4 ) )
= $true )
| ( ( in @ SV5 @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[30]) ).
thf(35,plain,
( ( in @ sK3_SY18 @ ( powerset @ sK1_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[31]) ).
thf(36,plain,
( ( ~ ( ~ ( in @ sK4_SY20 @ sK1_A )
| ~ ~ ( ~ ( in @ sK4_SY20 @ ( setminus @ sK1_A @ ( binunion @ sK2_SY15 @ sK3_SY18 ) ) )
| ~ ~ ( in @ sK4_SY20 @ ( setminus @ sK1_A @ sK2_SY15 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[32]) ).
thf(37,plain,
! [SV3: $i,SV1: $i,SV6: $i] :
( ( ( in @ SV6 @ ( powerset @ SV1 ) )
= $false )
| ( ( ! [SY29: $i] :
( ~ ( in @ SY29 @ SV1 )
| ~ ( in @ SY29 @ ( setminus @ SV1 @ ( binunion @ SV3 @ SV6 ) ) )
| ~ ( in @ SY29 @ SV3 ) ) )
= $true )
| ( ( in @ SV3 @ ( powerset @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(38,plain,
( ( ~ ( in @ sK4_SY20 @ sK1_A )
| ~ ~ ( ~ ( in @ sK4_SY20 @ ( setminus @ sK1_A @ ( binunion @ sK2_SY15 @ sK3_SY18 ) ) )
| ~ ~ ( in @ sK4_SY20 @ ( setminus @ sK1_A @ sK2_SY15 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(39,plain,
! [SV6: $i,SV3: $i,SV1: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ SV1 )
| ~ ( in @ SV7 @ ( setminus @ SV1 @ ( binunion @ SV3 @ SV6 ) ) )
| ~ ( in @ SV7 @ SV3 ) )
= $true )
| ( ( in @ SV6 @ ( powerset @ SV1 ) )
= $false )
| ( ( in @ SV3 @ ( powerset @ SV1 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(40,plain,
( ( ~ ( in @ sK4_SY20 @ sK1_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[38]) ).
thf(41,plain,
( ( ~ ~ ( ~ ( in @ sK4_SY20 @ ( setminus @ sK1_A @ ( binunion @ sK2_SY15 @ sK3_SY18 ) ) )
| ~ ~ ( in @ sK4_SY20 @ ( setminus @ sK1_A @ sK2_SY15 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[38]) ).
thf(42,plain,
! [SV6: $i,SV3: $i,SV1: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ SV1 ) )
= $true )
| ( ( ~ ( in @ SV7 @ ( setminus @ SV1 @ ( binunion @ SV3 @ SV6 ) ) )
| ~ ( in @ SV7 @ SV3 ) )
= $true )
| ( ( in @ SV6 @ ( powerset @ SV1 ) )
= $false )
| ( ( in @ SV3 @ ( powerset @ SV1 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[39]) ).
thf(43,plain,
( ( in @ sK4_SY20 @ sK1_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[40]) ).
thf(44,plain,
( ( ~ ( ~ ( in @ sK4_SY20 @ ( setminus @ sK1_A @ ( binunion @ sK2_SY15 @ sK3_SY18 ) ) )
| ~ ~ ( in @ sK4_SY20 @ ( setminus @ sK1_A @ sK2_SY15 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[41]) ).
thf(45,plain,
! [SV6: $i,SV3: $i,SV1: $i,SV7: $i] :
( ( ( in @ SV7 @ SV1 )
= $false )
| ( ( ~ ( in @ SV7 @ ( setminus @ SV1 @ ( binunion @ SV3 @ SV6 ) ) )
| ~ ( in @ SV7 @ SV3 ) )
= $true )
| ( ( in @ SV6 @ ( powerset @ SV1 ) )
= $false )
| ( ( in @ SV3 @ ( powerset @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(46,plain,
( ( ~ ( in @ sK4_SY20 @ ( setminus @ sK1_A @ ( binunion @ sK2_SY15 @ sK3_SY18 ) ) )
| ~ ~ ( in @ sK4_SY20 @ ( setminus @ sK1_A @ sK2_SY15 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(47,plain,
! [SV6: $i,SV3: $i,SV1: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ ( setminus @ SV1 @ ( binunion @ SV3 @ SV6 ) ) ) )
= $true )
| ( ( ~ ( in @ SV7 @ SV3 ) )
= $true )
| ( ( in @ SV7 @ SV1 )
= $false )
| ( ( in @ SV6 @ ( powerset @ SV1 ) )
= $false )
| ( ( in @ SV3 @ ( powerset @ SV1 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[45]) ).
thf(48,plain,
( ( ~ ( in @ sK4_SY20 @ ( setminus @ sK1_A @ ( binunion @ sK2_SY15 @ sK3_SY18 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[46]) ).
thf(49,plain,
( ( ~ ~ ( in @ sK4_SY20 @ ( setminus @ sK1_A @ sK2_SY15 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[46]) ).
thf(50,plain,
! [SV6: $i,SV3: $i,SV1: $i,SV7: $i] :
( ( ( in @ SV7 @ ( setminus @ SV1 @ ( binunion @ SV3 @ SV6 ) ) )
= $false )
| ( ( ~ ( in @ SV7 @ SV3 ) )
= $true )
| ( ( in @ SV7 @ SV1 )
= $false )
| ( ( in @ SV6 @ ( powerset @ SV1 ) )
= $false )
| ( ( in @ SV3 @ ( powerset @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(51,plain,
( ( in @ sK4_SY20 @ ( setminus @ sK1_A @ ( binunion @ sK2_SY15 @ sK3_SY18 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[48]) ).
thf(52,plain,
( ( ~ ( in @ sK4_SY20 @ ( setminus @ sK1_A @ sK2_SY15 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[49]) ).
thf(53,plain,
! [SV6: $i,SV1: $i,SV3: $i,SV7: $i] :
( ( ( in @ SV7 @ SV3 )
= $false )
| ( ( in @ SV7 @ ( setminus @ SV1 @ ( binunion @ SV3 @ SV6 ) ) )
= $false )
| ( ( in @ SV7 @ SV1 )
= $false )
| ( ( in @ SV6 @ ( powerset @ SV1 ) )
= $false )
| ( ( in @ SV3 @ ( powerset @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(54,plain,
( ( in @ sK4_SY20 @ ( setminus @ sK1_A @ sK2_SY15 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(55,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[24,54,53,51,43,35,34]) ).
thf(56,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU745^2 : 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
% 0.10/0.23 % Computer : n010.cluster.edu
% 0.10/0.23 % Model : x86_64 x86_64
% 0.10/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.23 % Memory : 8046.5625MB
% 0.10/0.23 % OS : Linux 6.8.0-71-generic
% 0.10/0.23 % CPULimit : 300
% 0.10/0.23 % WCLimit : 300
% 0.10/0.23 % DateTime : Tue Oct 6 15:33:55 UTC 2026
% 0.10/0.24 % CPUTime :
% 0.10/0.24 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.24/0.29
% 0.24/0.29 No.of.Axioms: 0
% 0.24/0.29
% 0.24/0.29 Length.of.Defs: 531
% 0.24/0.29
% 0.24/0.29 Contains.Choice.Funs: false
% 0.24/0.29 .
% 0.24/0.29
% 0.24/0.29 ********************************
% 0.24/0.29 * All subproblems solved! *
% 0.24/0.29 ********************************
% 0.24/0.29 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:2,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:55,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.24/0.29
% 0.24/0.29 %**** Beginning of derivation protocol ****
% 0.24/0.29 % SZS output start CNFRefutation
% See solution above
% 0.24/0.29
% 0.24/0.29 %**** End of derivation protocol ****
% 0.24/0.29 %**** no. of clauses in derivation: 56 ****
% 0.24/0.29 %**** clause counter: 55 ****
% 0.24/0.29
% 0.24/0.29 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:2,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:55,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------