%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU709^2 : 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 : n013.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 10:46:29 AM UTC 2026
% Result : Theorem 0.09s 0.24s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 6
% Syntax : Number of formulae : 118 ( 57 unt; 0 typ; 5 def)
% Number of atoms : 928 ( 346 equ; 0 cnn)
% Maximal formula atoms : 8 ( 7 avg)
% Number of connectives : 1501 ( 233 ~; 269 |; 0 &; 936 @)
% ( 4 <=>; 59 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 12 con; 0-4 aty)
% Number of variables : 389 ( 0 ^; 389 !; 0 ?; 389 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_emptyset,type,
emptyset: $i ).
thf(tp_if,type,
if: $i > $o > $i > $i > $i ).
thf(tp_iffalse,type,
iffalse: $o ).
thf(tp_iftrue,type,
iftrue: $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_in__Cong,type,
in__Cong: $o ).
thf(tp_sK1_SX0,type,
sK1_SX0: $i ).
thf(tp_sK2_SY37,type,
sK2_SY37: $o ).
thf(tp_sK3_SY44,type,
sK3_SY44: $i ).
thf(tp_sK4_SY52,type,
sK4_SY52: $i ).
thf(tp_secondinupair,type,
secondinupair: $o ).
thf(tp_setadjoin,type,
setadjoin: $i > $i > $i ).
thf(tp_setadjoinIL,type,
setadjoinIL: $o ).
thf(iffalse,definition,
( iffalse
= ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ~ Xphi
=> ( ( if @ A @ Xphi @ Xx @ Xy )
= Xy ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iffalse) ).
thf(iftrue,definition,
( iftrue
= ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( Xphi
=> ( ( if @ A @ Xphi @ Xx @ Xy )
= Xx ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iftrue) ).
thf(in__Cong,definition,
( in__Cong
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
<=> ( in @ Xy @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',in__Cong) ).
thf(secondinupair,definition,
( secondinupair
= ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',secondinupair) ).
thf(setadjoinIL,definition,
( setadjoinIL
= ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinIL) ).
thf(1,conjecture,
( setadjoinIL
=> ( in__Cong
=> ( secondinupair
=> ( iftrue
=> ( iffalse
=> ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iftrueorfalse) ).
thf(2,negated_conjecture,
( ( setadjoinIL
=> ( in__Cong
=> ( secondinupair
=> ( iftrue
=> ( iffalse
=> ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) )
=> ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
<=> ( in @ Xy @ B ) ) ) )
=> ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( Xphi
=> ( ( if @ A @ Xphi @ Xx @ Xy )
= Xx ) ) ) )
=> ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ~ Xphi
=> ( ( if @ A @ Xphi @ Xx @ Xy )
= Xy ) ) ) )
=> ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,iffalse,iftrue,in__Cong,secondinupair,setadjoinIL]) ).
thf(4,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
<=> ( in @ Xy @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( Xphi
=> ( ( if @ A @ Xphi @ Xx @ Xy )
= Xx ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(8,plain,
( ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ~ Xphi
=> ( ( if @ A @ Xphi @ Xx @ Xy )
= Xy ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(9,plain,
( ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(10,plain,
( ( ~ ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[9]) ).
thf(11,plain,
( ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ~ Xphi
=> ( ( if @ A @ Xphi @ Xx @ Xy )
= Xy ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(12,plain,
( ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( Xphi
=> ( ( if @ A @ Xphi @ Xx @ Xy )
= Xx ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(13,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(14,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
<=> ( in @ Xy @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(15,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(16,plain,
( ( ~ ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(17,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ! [SX2: $i,SX3: $i] :
( ( SX2 != SX3 )
| ~ ( ~ ( ~ ( in @ SX2 @ SX0 )
| ( in @ SX3 @ SX1 ) )
| ~ ( ~ ( in @ SX3 @ SX1 )
| ( in @ SX2 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14,iffalse,iftrue,in__Cong,secondinupair,setadjoinIL]) ).
thf(18,plain,
( ( ~ ! [SX0: $i,SX1: $o,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ ( if @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( setadjoin @ SX2 @ ( setadjoin @ SX3 @ emptyset ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16,iffalse,iftrue,in__Cong,secondinupair,setadjoinIL]) ).
thf(19,plain,
( ( ! [SX0: $i,SX1: $o,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ SX1
| ( ( if @ SX0 @ SX1 @ SX2 @ SX3 )
= SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12,iffalse,iftrue,in__Cong,secondinupair,setadjoinIL]) ).
thf(20,plain,
( ( ! [SX0: $i,SX1: $o,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ~ SX1
| ( ( if @ SX0 @ SX1 @ SX2 @ SX3 )
= SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11,iffalse,iftrue,in__Cong,secondinupair,setadjoinIL]) ).
thf(21,plain,
! [SV1: $i] :
( ( ! [SY24: $i] : ( in @ SY24 @ ( setadjoin @ SV1 @ ( setadjoin @ SY24 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[13]) ).
thf(22,plain,
! [SV2: $i] :
( ( ! [SY25: $i] : ( in @ SV2 @ ( setadjoin @ SV2 @ SY25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(23,plain,
! [SV3: $i] :
( ( ! [SY26: $i] :
( ( SV3 != SY26 )
| ! [SY27: $i,SY28: $i] :
( ( SY27 != SY28 )
| ~ ( ~ ( ~ ( in @ SY27 @ SV3 )
| ( in @ SY28 @ SY26 ) )
| ~ ( ~ ( in @ SY28 @ SY26 )
| ( in @ SY27 @ SV3 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(24,plain,
( ( ! [SX0: $i,SX1: $o,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ ( if @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( setadjoin @ SX2 @ ( setadjoin @ SX3 @ emptyset ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(25,plain,
! [SV4: $i] :
( ( ! [SY29: $o,SY30: $i] :
( ~ ( in @ SY30 @ SV4 )
| ! [SY31: $i] :
( ~ ( in @ SY31 @ SV4 )
| ~ SY29
| ( ( if @ SV4 @ SY29 @ SY30 @ SY31 )
= SY30 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(26,plain,
! [SV5: $i] :
( ( ! [SY32: $o,SY33: $i] :
( ~ ( in @ SY33 @ SV5 )
| ! [SY34: $i] :
( ~ ( in @ SY34 @ SV5 )
| ~ ~ SY32
| ( ( if @ SV5 @ SY32 @ SY33 @ SY34 )
= SY34 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(27,plain,
! [SV1: $i,SV6: $i] :
( ( in @ SV6 @ ( setadjoin @ SV1 @ ( setadjoin @ SV6 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(28,plain,
! [SV7: $i,SV2: $i] :
( ( in @ SV2 @ ( setadjoin @ SV2 @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(29,plain,
! [SV8: $i,SV3: $i] :
( ( ( SV3 != SV8 )
| ! [SY35: $i,SY36: $i] :
( ( SY35 != SY36 )
| ~ ( ~ ( ~ ( in @ SY35 @ SV3 )
| ( in @ SY36 @ SV8 ) )
| ~ ( ~ ( in @ SY36 @ SV8 )
| ( in @ SY35 @ SV3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(30,plain,
( ( ! [SY37: $o,SY38: $i] :
( ~ ( in @ SY38 @ sK1_SX0 )
| ! [SY39: $i] :
( ~ ( in @ SY39 @ sK1_SX0 )
| ( in @ ( if @ sK1_SX0 @ SY37 @ SY38 @ SY39 ) @ ( setadjoin @ SY38 @ ( setadjoin @ SY39 @ emptyset ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[24]) ).
thf(31,plain,
! [SV9: $o,SV4: $i] :
( ( ! [SY40: $i] :
( ~ ( in @ SY40 @ SV4 )
| ! [SY41: $i] :
( ~ ( in @ SY41 @ SV4 )
| ~ SV9
| ( ( if @ SV4 @ SV9 @ SY40 @ SY41 )
= SY40 ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[25]) ).
thf(32,plain,
! [SV4: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV4 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV4 )
| ~ $true
| ( ( if @ SV4 @ $true @ SX0 @ SX1 )
= SX0 ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[25]) ).
thf(33,plain,
! [SV4: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV4 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV4 )
| ~ $false
| ( ( if @ SV4 @ $false @ SX0 @ SX1 )
= SX0 ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[25]) ).
thf(34,plain,
! [SV10: $o,SV5: $i] :
( ( ! [SY42: $i] :
( ~ ( in @ SY42 @ SV5 )
| ! [SY43: $i] :
( ~ ( in @ SY43 @ SV5 )
| ~ ~ SV10
| ( ( if @ SV5 @ SV10 @ SY42 @ SY43 )
= SY43 ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[26]) ).
thf(35,plain,
! [SV5: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV5 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV5 )
| ~ ~ $true
| ( ( if @ SV5 @ $true @ SX0 @ SX1 )
= SX1 ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[26]) ).
thf(36,plain,
! [SV5: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV5 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV5 )
| ~ ~ $false
| ( ( if @ SV5 @ $false @ SX0 @ SX1 )
= SX1 ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[26]) ).
thf(37,plain,
! [SV8: $i,SV3: $i] :
( ( ( SV3 != SV8 )
= $true )
| ( ( ! [SY35: $i,SY36: $i] :
( ( SY35 != SY36 )
| ~ ( ~ ( ~ ( in @ SY35 @ SV3 )
| ( in @ SY36 @ SV8 ) )
| ~ ( ~ ( in @ SY36 @ SV8 )
| ( in @ SY35 @ SV3 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[29]) ).
thf(38,plain,
( ( ! [SY44: $i] :
( ~ ( in @ SY44 @ sK1_SX0 )
| ! [SY45: $i] :
( ~ ( in @ SY45 @ sK1_SX0 )
| ( in @ ( if @ sK1_SX0 @ sK2_SY37 @ SY44 @ SY45 ) @ ( setadjoin @ SY44 @ ( setadjoin @ SY45 @ emptyset ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[30]) ).
thf(39,plain,
! [SV9: $o,SV4: $i,SV11: $i] :
( ( ~ ( in @ SV11 @ SV4 )
| ! [SY46: $i] :
( ~ ( in @ SY46 @ SV4 )
| ~ SV9
| ( ( if @ SV4 @ SV9 @ SV11 @ SY46 )
= SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(40,plain,
! [SV4: $i,SV12: $i] :
( ( ~ ( in @ SV12 @ SV4 )
| ! [SY47: $i] :
( ~ ( in @ SY47 @ SV4 )
| ~ $true
| ( ( if @ SV4 @ $true @ SV12 @ SY47 )
= SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(41,plain,
! [SV4: $i,SV13: $i] :
( ( ~ ( in @ SV13 @ SV4 )
| ! [SY48: $i] :
( ~ ( in @ SY48 @ SV4 )
| ~ $false
| ( ( if @ SV4 @ $false @ SV13 @ SY48 )
= SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(42,plain,
! [SV10: $o,SV5: $i,SV14: $i] :
( ( ~ ( in @ SV14 @ SV5 )
| ! [SY49: $i] :
( ~ ( in @ SY49 @ SV5 )
| ~ ~ SV10
| ( ( if @ SV5 @ SV10 @ SV14 @ SY49 )
= SY49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(43,plain,
! [SV5: $i,SV15: $i] :
( ( ~ ( in @ SV15 @ SV5 )
| ! [SY50: $i] :
( ~ ( in @ SY50 @ SV5 )
| ~ ~ $true
| ( ( if @ SV5 @ $true @ SV15 @ SY50 )
= SY50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(44,plain,
! [SV5: $i,SV16: $i] :
( ( ~ ( in @ SV16 @ SV5 )
| ! [SY51: $i] :
( ~ ( in @ SY51 @ SV5 )
| ~ ~ $false
| ( ( if @ SV5 @ $false @ SV16 @ SY51 )
= SY51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(45,plain,
! [SV8: $i,SV3: $i] :
( ( ( SV3 = SV8 )
= $false )
| ( ( ! [SY35: $i,SY36: $i] :
( ( SY35 != SY36 )
| ~ ( ~ ( ~ ( in @ SY35 @ SV3 )
| ( in @ SY36 @ SV8 ) )
| ~ ( ~ ( in @ SY36 @ SV8 )
| ( in @ SY35 @ SV3 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(46,plain,
( ( ~ ( in @ sK3_SY44 @ sK1_SX0 )
| ! [SY52: $i] :
( ~ ( in @ SY52 @ sK1_SX0 )
| ( in @ ( if @ sK1_SX0 @ sK2_SY37 @ sK3_SY44 @ SY52 ) @ ( setadjoin @ sK3_SY44 @ ( setadjoin @ SY52 @ emptyset ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[38]) ).
thf(47,plain,
! [SV9: $o,SV4: $i,SV11: $i] :
( ( ( ~ ( in @ SV11 @ SV4 ) )
= $true )
| ( ( ! [SY46: $i] :
( ~ ( in @ SY46 @ SV4 )
| ~ SV9
| ( ( if @ SV4 @ SV9 @ SV11 @ SY46 )
= SV11 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[39]) ).
thf(48,plain,
! [SV4: $i,SV12: $i] :
( ( ( ~ ( in @ SV12 @ SV4 ) )
= $true )
| ( ( ! [SY47: $i] :
( ~ ( in @ SY47 @ SV4 )
| ~ $true
| ( ( if @ SV4 @ $true @ SV12 @ SY47 )
= SV12 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[40]) ).
thf(49,plain,
! [SV4: $i,SV13: $i] :
( ( ( ~ ( in @ SV13 @ SV4 ) )
= $true )
| ( ( ! [SY48: $i] :
( ~ ( in @ SY48 @ SV4 )
| ~ $false
| ( ( if @ SV4 @ $false @ SV13 @ SY48 )
= SV13 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[41]) ).
thf(50,plain,
! [SV10: $o,SV5: $i,SV14: $i] :
( ( ( ~ ( in @ SV14 @ SV5 ) )
= $true )
| ( ( ! [SY49: $i] :
( ~ ( in @ SY49 @ SV5 )
| ~ ~ SV10
| ( ( if @ SV5 @ SV10 @ SV14 @ SY49 )
= SY49 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[42]) ).
thf(51,plain,
! [SV5: $i,SV15: $i] :
( ( ( ~ ( in @ SV15 @ SV5 ) )
= $true )
| ( ( ! [SY50: $i] :
( ~ ( in @ SY50 @ SV5 )
| ~ ~ $true
| ( ( if @ SV5 @ $true @ SV15 @ SY50 )
= SY50 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[43]) ).
thf(52,plain,
! [SV5: $i,SV16: $i] :
( ( ( ~ ( in @ SV16 @ SV5 ) )
= $true )
| ( ( ! [SY51: $i] :
( ~ ( in @ SY51 @ SV5 )
| ~ ~ $false
| ( ( if @ SV5 @ $false @ SV16 @ SY51 )
= SY51 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[44]) ).
thf(53,plain,
! [SV8: $i,SV3: $i,SV17: $i] :
( ( ( ! [SY53: $i] :
( ( SV17 != SY53 )
| ~ ( ~ ( ~ ( in @ SV17 @ SV3 )
| ( in @ SY53 @ SV8 ) )
| ~ ( ~ ( in @ SY53 @ SV8 )
| ( in @ SV17 @ SV3 ) ) ) ) )
= $true )
| ( ( SV3 = SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(54,plain,
( ( ~ ( in @ sK3_SY44 @ sK1_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[46]) ).
thf(55,plain,
( ( ! [SY52: $i] :
( ~ ( in @ SY52 @ sK1_SX0 )
| ( in @ ( if @ sK1_SX0 @ sK2_SY37 @ sK3_SY44 @ SY52 ) @ ( setadjoin @ sK3_SY44 @ ( setadjoin @ SY52 @ emptyset ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[46]) ).
thf(56,plain,
! [SV9: $o,SV4: $i,SV11: $i] :
( ( ( in @ SV11 @ SV4 )
= $false )
| ( ( ! [SY46: $i] :
( ~ ( in @ SY46 @ SV4 )
| ~ SV9
| ( ( if @ SV4 @ SV9 @ SV11 @ SY46 )
= SV11 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(57,plain,
! [SV4: $i,SV12: $i] :
( ( ( in @ SV12 @ SV4 )
= $false )
| ( ( ! [SY47: $i] :
( ~ ( in @ SY47 @ SV4 )
| ~ $true
| ( ( if @ SV4 @ $true @ SV12 @ SY47 )
= SV12 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(58,plain,
! [SV4: $i,SV13: $i] :
( ( ( in @ SV13 @ SV4 )
= $false )
| ( ( ! [SY48: $i] :
( ~ ( in @ SY48 @ SV4 )
| ~ $false
| ( ( if @ SV4 @ $false @ SV13 @ SY48 )
= SV13 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(59,plain,
! [SV10: $o,SV5: $i,SV14: $i] :
( ( ( in @ SV14 @ SV5 )
= $false )
| ( ( ! [SY49: $i] :
( ~ ( in @ SY49 @ SV5 )
| ~ ~ SV10
| ( ( if @ SV5 @ SV10 @ SV14 @ SY49 )
= SY49 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(60,plain,
! [SV5: $i,SV15: $i] :
( ( ( in @ SV15 @ SV5 )
= $false )
| ( ( ! [SY50: $i] :
( ~ ( in @ SY50 @ SV5 )
| ~ ~ $true
| ( ( if @ SV5 @ $true @ SV15 @ SY50 )
= SY50 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(61,plain,
! [SV5: $i,SV16: $i] :
( ( ( in @ SV16 @ SV5 )
= $false )
| ( ( ! [SY51: $i] :
( ~ ( in @ SY51 @ SV5 )
| ~ ~ $false
| ( ( if @ SV5 @ $false @ SV16 @ SY51 )
= SY51 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(62,plain,
! [SV8: $i,SV3: $i,SV18: $i,SV17: $i] :
( ( ( ( SV17 != SV18 )
| ~ ( ~ ( ~ ( in @ SV17 @ SV3 )
| ( in @ SV18 @ SV8 ) )
| ~ ( ~ ( in @ SV18 @ SV8 )
| ( in @ SV17 @ SV3 ) ) ) )
= $true )
| ( ( SV3 = SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(63,plain,
( ( in @ sK3_SY44 @ sK1_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[54]) ).
thf(64,plain,
( ( ~ ( in @ sK4_SY52 @ sK1_SX0 )
| ( in @ ( if @ sK1_SX0 @ sK2_SY37 @ sK3_SY44 @ sK4_SY52 ) @ ( setadjoin @ sK3_SY44 @ ( setadjoin @ sK4_SY52 @ emptyset ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[55]) ).
thf(65,plain,
! [SV11: $i,SV9: $o,SV4: $i,SV19: $i] :
( ( ( ~ ( in @ SV19 @ SV4 )
| ~ SV9
| ( ( if @ SV4 @ SV9 @ SV11 @ SV19 )
= SV11 ) )
= $true )
| ( ( in @ SV11 @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(66,plain,
! [SV12: $i,SV4: $i,SV20: $i] :
( ( ( ~ ( in @ SV20 @ SV4 )
| ~ $true
| ( ( if @ SV4 @ $true @ SV12 @ SV20 )
= SV12 ) )
= $true )
| ( ( in @ SV12 @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(67,plain,
! [SV13: $i,SV4: $i,SV21: $i] :
( ( ( ~ ( in @ SV21 @ SV4 )
| ~ $false
| ( ( if @ SV4 @ $false @ SV13 @ SV21 )
= SV13 ) )
= $true )
| ( ( in @ SV13 @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(68,plain,
! [SV14: $i,SV10: $o,SV5: $i,SV22: $i] :
( ( ( ~ ( in @ SV22 @ SV5 )
| ~ ~ SV10
| ( ( if @ SV5 @ SV10 @ SV14 @ SV22 )
= SV22 ) )
= $true )
| ( ( in @ SV14 @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(69,plain,
! [SV15: $i,SV5: $i,SV23: $i] :
( ( ( ~ ( in @ SV23 @ SV5 )
| ~ ~ $true
| ( ( if @ SV5 @ $true @ SV15 @ SV23 )
= SV23 ) )
= $true )
| ( ( in @ SV15 @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(70,plain,
! [SV16: $i,SV5: $i,SV24: $i] :
( ( ( ~ ( in @ SV24 @ SV5 )
| ~ ~ $false
| ( ( if @ SV5 @ $false @ SV16 @ SV24 )
= SV24 ) )
= $true )
| ( ( in @ SV16 @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(71,plain,
! [SV8: $i,SV3: $i,SV18: $i,SV17: $i] :
( ( ( SV17 != SV18 )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ SV17 @ SV3 )
| ( in @ SV18 @ SV8 ) )
| ~ ( ~ ( in @ SV18 @ SV8 )
| ( in @ SV17 @ SV3 ) ) ) )
= $true )
| ( ( SV3 = SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[62]) ).
thf(72,plain,
( ( ~ ( in @ sK4_SY52 @ sK1_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[64]) ).
thf(73,plain,
( ( in @ ( if @ sK1_SX0 @ sK2_SY37 @ sK3_SY44 @ sK4_SY52 ) @ ( setadjoin @ sK3_SY44 @ ( setadjoin @ sK4_SY52 @ emptyset ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[64]) ).
thf(74,plain,
! [SV11: $i,SV9: $o,SV4: $i,SV19: $i] :
( ( ( ~ ( in @ SV19 @ SV4 ) )
= $true )
| ( ( ~ SV9
| ( ( if @ SV4 @ SV9 @ SV11 @ SV19 )
= SV11 ) )
= $true )
| ( ( in @ SV11 @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[65]) ).
thf(75,plain,
! [SV12: $i,SV4: $i,SV20: $i] :
( ( ( ~ ( in @ SV20 @ SV4 ) )
= $true )
| ( ( ~ $true
| ( ( if @ SV4 @ $true @ SV12 @ SV20 )
= SV12 ) )
= $true )
| ( ( in @ SV12 @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[66]) ).
thf(76,plain,
! [SV13: $i,SV4: $i,SV21: $i] :
( ( ( ~ ( in @ SV21 @ SV4 ) )
= $true )
| ( ( ~ $false
| ( ( if @ SV4 @ $false @ SV13 @ SV21 )
= SV13 ) )
= $true )
| ( ( in @ SV13 @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[67]) ).
thf(77,plain,
! [SV14: $i,SV10: $o,SV5: $i,SV22: $i] :
( ( ( ~ ( in @ SV22 @ SV5 ) )
= $true )
| ( ( ~ ~ SV10
| ( ( if @ SV5 @ SV10 @ SV14 @ SV22 )
= SV22 ) )
= $true )
| ( ( in @ SV14 @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[68]) ).
thf(78,plain,
! [SV15: $i,SV5: $i,SV23: $i] :
( ( ( ~ ( in @ SV23 @ SV5 ) )
= $true )
| ( ( ~ ~ $true
| ( ( if @ SV5 @ $true @ SV15 @ SV23 )
= SV23 ) )
= $true )
| ( ( in @ SV15 @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[69]) ).
thf(79,plain,
! [SV16: $i,SV5: $i,SV24: $i] :
( ( ( ~ ( in @ SV24 @ SV5 ) )
= $true )
| ( ( ~ ~ $false
| ( ( if @ SV5 @ $false @ SV16 @ SV24 )
= SV24 ) )
= $true )
| ( ( in @ SV16 @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[70]) ).
thf(80,plain,
! [SV8: $i,SV3: $i,SV18: $i,SV17: $i] :
( ( ( SV17 = SV18 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ SV17 @ SV3 )
| ( in @ SV18 @ SV8 ) )
| ~ ( ~ ( in @ SV18 @ SV8 )
| ( in @ SV17 @ SV3 ) ) ) )
= $true )
| ( ( SV3 = SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(81,plain,
( ( in @ sK4_SY52 @ sK1_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[72]) ).
thf(82,plain,
! [SV11: $i,SV9: $o,SV4: $i,SV19: $i] :
( ( ( in @ SV19 @ SV4 )
= $false )
| ( ( ~ SV9
| ( ( if @ SV4 @ SV9 @ SV11 @ SV19 )
= SV11 ) )
= $true )
| ( ( in @ SV11 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(83,plain,
! [SV12: $i,SV4: $i,SV20: $i] :
( ( ( in @ SV20 @ SV4 )
= $false )
| ( ( ~ $true
| ( ( if @ SV4 @ $true @ SV12 @ SV20 )
= SV12 ) )
= $true )
| ( ( in @ SV12 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(84,plain,
! [SV13: $i,SV4: $i,SV21: $i] :
( ( ( in @ SV21 @ SV4 )
= $false )
| ( ( ~ $false
| ( ( if @ SV4 @ $false @ SV13 @ SV21 )
= SV13 ) )
= $true )
| ( ( in @ SV13 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(85,plain,
! [SV14: $i,SV10: $o,SV5: $i,SV22: $i] :
( ( ( in @ SV22 @ SV5 )
= $false )
| ( ( ~ ~ SV10
| ( ( if @ SV5 @ SV10 @ SV14 @ SV22 )
= SV22 ) )
= $true )
| ( ( in @ SV14 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(86,plain,
! [SV15: $i,SV5: $i,SV23: $i] :
( ( ( in @ SV23 @ SV5 )
= $false )
| ( ( ~ ~ $true
| ( ( if @ SV5 @ $true @ SV15 @ SV23 )
= SV23 ) )
= $true )
| ( ( in @ SV15 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(87,plain,
! [SV16: $i,SV5: $i,SV24: $i] :
( ( ( in @ SV24 @ SV5 )
= $false )
| ( ( ~ ~ $false
| ( ( if @ SV5 @ $false @ SV16 @ SV24 )
= SV24 ) )
= $true )
| ( ( in @ SV16 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(88,plain,
! [SV8: $i,SV18: $i,SV3: $i,SV17: $i] :
( ( ( ~ ( ~ ( in @ SV17 @ SV3 )
| ( in @ SV18 @ SV8 ) )
| ~ ( ~ ( in @ SV18 @ SV8 )
| ( in @ SV17 @ SV3 ) ) )
= $false )
| ( ( SV17 = SV18 )
= $false )
| ( ( SV3 = SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(89,plain,
! [SV19: $i,SV11: $i,SV4: $i,SV9: $o] :
( ( ( ~ SV9 ) = $true )
| ( ( ( if @ SV4 @ SV9 @ SV11 @ SV19 )
= SV11 )
= $true )
| ( ( in @ SV19 @ SV4 )
= $false )
| ( ( in @ SV11 @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[82]) ).
thf(90,plain,
! [SV20: $i,SV12: $i,SV4: $i] :
( ( ( ~ $true ) = $true )
| ( ( ( if @ SV4 @ $true @ SV12 @ SV20 )
= SV12 )
= $true )
| ( ( in @ SV20 @ SV4 )
= $false )
| ( ( in @ SV12 @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[83]) ).
thf(91,plain,
! [SV21: $i,SV13: $i,SV4: $i] :
( ( ( ~ $false ) = $true )
| ( ( ( if @ SV4 @ $false @ SV13 @ SV21 )
= SV13 )
= $true )
| ( ( in @ SV21 @ SV4 )
= $false )
| ( ( in @ SV13 @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[84]) ).
thf(92,plain,
! [SV22: $i,SV14: $i,SV5: $i,SV10: $o] :
( ( ( ~ ~ SV10 )
= $true )
| ( ( ( if @ SV5 @ SV10 @ SV14 @ SV22 )
= SV22 )
= $true )
| ( ( in @ SV22 @ SV5 )
= $false )
| ( ( in @ SV14 @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[85]) ).
thf(93,plain,
! [SV23: $i,SV15: $i,SV5: $i] :
( ( ( ~ ~ $true )
= $true )
| ( ( ( if @ SV5 @ $true @ SV15 @ SV23 )
= SV23 )
= $true )
| ( ( in @ SV23 @ SV5 )
= $false )
| ( ( in @ SV15 @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[86]) ).
thf(94,plain,
! [SV24: $i,SV16: $i,SV5: $i] :
( ( ( ~ ~ $false )
= $true )
| ( ( ( if @ SV5 @ $false @ SV16 @ SV24 )
= SV24 )
= $true )
| ( ( in @ SV24 @ SV5 )
= $false )
| ( ( in @ SV16 @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[87]) ).
thf(95,plain,
! [SV8: $i,SV18: $i,SV3: $i,SV17: $i] :
( ( ( ~ ( ~ ( in @ SV17 @ SV3 )
| ( in @ SV18 @ SV8 ) ) )
= $false )
| ( ( SV17 = SV18 )
= $false )
| ( ( SV3 = SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[88]) ).
thf(96,plain,
! [SV3: $i,SV17: $i,SV8: $i,SV18: $i] :
( ( ( ~ ( ~ ( in @ SV18 @ SV8 )
| ( in @ SV17 @ SV3 ) ) )
= $false )
| ( ( SV17 = SV18 )
= $false )
| ( ( SV3 = SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[88]) ).
thf(97,plain,
! [SV19: $i,SV11: $i,SV4: $i,SV9: $o] :
( ( SV9 = $false )
| ( ( ( if @ SV4 @ SV9 @ SV11 @ SV19 )
= SV11 )
= $true )
| ( ( in @ SV19 @ SV4 )
= $false )
| ( ( in @ SV11 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(98,plain,
! [SV20: $i,SV12: $i,SV4: $i] :
( ( $true = $false )
| ( ( ( if @ SV4 @ $true @ SV12 @ SV20 )
= SV12 )
= $true )
| ( ( in @ SV20 @ SV4 )
= $false )
| ( ( in @ SV12 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(99,plain,
! [SV21: $i,SV13: $i,SV4: $i] :
( ( $false = $false )
| ( ( ( if @ SV4 @ $false @ SV13 @ SV21 )
= SV13 )
= $true )
| ( ( in @ SV21 @ SV4 )
= $false )
| ( ( in @ SV13 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(100,plain,
! [SV22: $i,SV14: $i,SV5: $i,SV10: $o] :
( ( ( ~ SV10 ) = $false )
| ( ( ( if @ SV5 @ SV10 @ SV14 @ SV22 )
= SV22 )
= $true )
| ( ( in @ SV22 @ SV5 )
= $false )
| ( ( in @ SV14 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(101,plain,
! [SV23: $i,SV15: $i,SV5: $i] :
( ( ( ~ $true ) = $false )
| ( ( ( if @ SV5 @ $true @ SV15 @ SV23 )
= SV23 )
= $true )
| ( ( in @ SV23 @ SV5 )
= $false )
| ( ( in @ SV15 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(102,plain,
! [SV24: $i,SV16: $i,SV5: $i] :
( ( ( ~ $false ) = $false )
| ( ( ( if @ SV5 @ $false @ SV16 @ SV24 )
= SV24 )
= $true )
| ( ( in @ SV24 @ SV5 )
= $false )
| ( ( in @ SV16 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(103,plain,
! [SV8: $i,SV18: $i,SV3: $i,SV17: $i] :
( ( ( ~ ( in @ SV17 @ SV3 )
| ( in @ SV18 @ SV8 ) )
= $true )
| ( ( SV17 = SV18 )
= $false )
| ( ( SV3 = SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[95]) ).
thf(104,plain,
! [SV3: $i,SV17: $i,SV8: $i,SV18: $i] :
( ( ( ~ ( in @ SV18 @ SV8 )
| ( in @ SV17 @ SV3 ) )
= $true )
| ( ( SV17 = SV18 )
= $false )
| ( ( SV3 = SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[96]) ).
thf(105,plain,
! [SV22: $i,SV14: $i,SV5: $i,SV10: $o] :
( ( SV10 = $true )
| ( ( ( if @ SV5 @ SV10 @ SV14 @ SV22 )
= SV22 )
= $true )
| ( ( in @ SV22 @ SV5 )
= $false )
| ( ( in @ SV14 @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[100]) ).
thf(106,plain,
! [SV23: $i,SV15: $i,SV5: $i] :
( ( $true = $true )
| ( ( ( if @ SV5 @ $true @ SV15 @ SV23 )
= SV23 )
= $true )
| ( ( in @ SV23 @ SV5 )
= $false )
| ( ( in @ SV15 @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[101]) ).
thf(107,plain,
! [SV24: $i,SV16: $i,SV5: $i] :
( ( $false = $true )
| ( ( ( if @ SV5 @ $false @ SV16 @ SV24 )
= SV24 )
= $true )
| ( ( in @ SV24 @ SV5 )
= $false )
| ( ( in @ SV16 @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[102]) ).
thf(108,plain,
! [SV8: $i,SV18: $i,SV3: $i,SV17: $i] :
( ( ( ~ ( in @ SV17 @ SV3 ) )
= $true )
| ( ( in @ SV18 @ SV8 )
= $true )
| ( ( SV17 = SV18 )
= $false )
| ( ( SV3 = SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[103]) ).
thf(109,plain,
! [SV3: $i,SV17: $i,SV8: $i,SV18: $i] :
( ( ( ~ ( in @ SV18 @ SV8 ) )
= $true )
| ( ( in @ SV17 @ SV3 )
= $true )
| ( ( SV17 = SV18 )
= $false )
| ( ( SV3 = SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[104]) ).
thf(110,plain,
! [SV8: $i,SV18: $i,SV3: $i,SV17: $i] :
( ( ( in @ SV17 @ SV3 )
= $false )
| ( ( in @ SV18 @ SV8 )
= $true )
| ( ( SV17 = SV18 )
= $false )
| ( ( SV3 = SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(111,plain,
! [SV3: $i,SV17: $i,SV8: $i,SV18: $i] :
( ( ( in @ SV18 @ SV8 )
= $false )
| ( ( in @ SV17 @ SV3 )
= $true )
| ( ( SV17 = SV18 )
= $false )
| ( ( SV3 = SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(112,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[27,111,110,107,106,105,99,98,97,81,73,63,28]) ).
thf(113,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[112]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU709^2 : 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 : n013.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
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Oct 6 15:32:06 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
% 0.09/0.24
% 0.09/0.24 No.of.Axioms: 0
% 0.09/0.24
% 0.09/0.24 Length.of.Defs: 996
% 0.09/0.24
% 0.09/0.24 Contains.Choice.Funs: false
% 0.09/0.24 ...
% 0.09/0.24
% 0.09/0.24 ********************************
% 0.09/0.24 * All subproblems solved! *
% 0.09/0.24 ********************************
% 0.09/0.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:5,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:112,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.09/0.24
% 0.09/0.24 %**** Beginning of derivation protocol ****
% 0.09/0.24 % SZS output start CNFRefutation
% See solution above
% 0.09/0.24
% 0.09/0.24 %**** End of derivation protocol ****
% 0.09/0.24 %**** no. of clauses in derivation: 113 ****
% 0.09/0.24 %**** clause counter: 112 ****
% 0.09/0.24
% 0.09/0.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:5,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:112,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------