TSTP Solution File: SEU811^2 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU811^2 : TPTP v8.1.0. Released v3.7.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 12:14:56 EDT 2022
% Result : Theorem 0.20s 0.43s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 16
% Syntax : Number of formulae : 144 ( 52 unt; 10 typ; 5 def)
% Number of atoms : 1009 ( 423 equ; 0 cnn)
% Maximal formula atoms : 8 ( 7 avg)
% Number of connectives : 1494 ( 334 ~; 404 |; 14 &; 688 @)
% ( 3 <=>; 51 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 9 con; 0-2 aty)
% Number of variables : 446 ( 1 ^ 445 !; 0 ?; 446 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_in__Cong,type,
in__Cong: $o ).
thf(tp_notinself2,type,
notinself2: $o ).
thf(tp_omega,type,
omega: $i ).
thf(tp_omegaS,type,
omegaS: $i > $i ).
thf(tp_sK1_SY0,type,
sK1_SY0: $i ).
thf(tp_sK2_SY16,type,
sK2_SY16: $i ).
thf(tp_setadjoin,type,
setadjoin: $i > $i > $i ).
thf(tp_setadjoinE,type,
setadjoinE: $o ).
thf(tp_setadjoinIL,type,
setadjoinIL: $o ).
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/sandbox/benchmark/theBenchmark.p',in__Cong) ).
thf(notinself2,definition,
( notinself2
= ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinself2) ).
thf(omegaS,definition,
( omegaS
= ( ^ [Xx: $i] : ( setadjoin @ Xx @ Xx ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaS) ).
thf(setadjoinE,definition,
( setadjoinE
= ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ! [Xphi: $o] :
( ( ( Xy = Xx )
=> Xphi )
=> ( ( ( in @ Xy @ A )
=> Xphi )
=> Xphi ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinE) ).
thf(setadjoinIL,definition,
( setadjoinIL
= ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIL) ).
thf(1,conjecture,
( setadjoinIL
=> ( setadjoinE
=> ( in__Cong
=> ( notinself2
=> ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ! [Xy: $i] :
( ( in @ Xy @ omega )
=> ( ( ( omegaS @ Xx )
= ( omegaS @ Xy ) )
=> ( Xx = Xy ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',peanoSinj) ).
thf(2,negated_conjecture,
( ( setadjoinIL
=> ( setadjoinE
=> ( in__Cong
=> ( notinself2
=> ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ! [Xy: $i] :
( ( in @ Xy @ omega )
=> ( ( ( omegaS @ Xx )
= ( omegaS @ Xy ) )
=> ( Xx = Xy ) ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) )
=> ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ! [Xphi: $o] :
( ( ( Xy = Xx )
=> Xphi )
=> ( ( ( in @ Xy @ A )
=> Xphi )
=> Xphi ) ) )
=> ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
<=> ( in @ Xy @ B ) ) ) )
=> ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) )
=> ! [SY0: $i] :
( ( in @ SY0 @ omega )
=> ! [SY1: $i] :
( ( in @ SY1 @ omega )
=> ( ( ( setadjoin @ SY0 @ SY0 )
= ( setadjoin @ SY1 @ SY1 ) )
=> ( SY0 = SY1 ) ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,in__Cong,notinself2,omegaS,setadjoinE,setadjoinIL]) ).
thf(4,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ! [Xphi: $o] :
( ( ( Xy = Xx )
=> Xphi )
=> ( ( ( in @ Xy @ A )
=> Xphi )
=> Xphi ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,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(7,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(8,plain,
( ( ! [SY0: $i] :
( ( in @ SY0 @ omega )
=> ! [SY1: $i] :
( ( in @ SY1 @ omega )
=> ( ( ( setadjoin @ SY0 @ SY0 )
= ( setadjoin @ SY1 @ SY1 ) )
=> ( SY0 = SY1 ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(9,plain,
( ( ~ ! [SY0: $i] :
( ( in @ SY0 @ omega )
=> ! [SY1: $i] :
( ( in @ SY1 @ omega )
=> ( ( ( setadjoin @ SY0 @ SY0 )
= ( setadjoin @ SY1 @ SY1 ) )
=> ( SY0 = SY1 ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[8]) ).
thf(10,plain,
( ( ( in @ sK1_SY0 @ omega )
& ( in @ sK2_SY16 @ omega )
& ( ( setadjoin @ sK1_SY0 @ sK1_SY0 )
= ( setadjoin @ sK2_SY16 @ sK2_SY16 ) )
& ( sK1_SY0 != sK2_SY16 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[9]) ).
thf(11,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ~ ( in @ Xy @ ( setadjoin @ Xx @ A ) )
| ( ( ( Xy = Xx )
| ( in @ Xy @ A )
| ! [Xphi: $o] : Xphi )
& ( ( Xy = Xx )
| ! [Xphi: $o] :
( ~ Xphi
| Xphi ) )
& ! [Xphi: $o] :
( ~ Xphi
| ( in @ Xy @ A )
| Xphi )
& ! [Xphi: $o] :
( ~ Xphi
| ~ Xphi
| Xphi ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[5]) ).
thf(12,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ( ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
| ~ ( in @ Xx @ A )
| ( in @ Xy @ B ) )
& ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
| ~ ( in @ Xy @ B )
| ( in @ Xx @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(13,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(14,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(15,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ( ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
| ~ ( in @ Xx @ A )
| ( in @ Xy @ B ) )
& ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
| ~ ( in @ Xy @ B )
| ( in @ Xx @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(16,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ~ ( in @ Xy @ ( setadjoin @ Xx @ A ) )
| ( ( ( Xy = Xx )
| ( in @ Xy @ A )
| ! [Xphi: $o] : Xphi )
& ( ( Xy = Xx )
| ! [Xphi: $o] :
( ~ Xphi
| Xphi ) )
& ! [Xphi: $o] :
( ~ Xphi
| ( in @ Xy @ A )
| Xphi )
& ! [Xphi: $o] :
( ~ Xphi
| ~ Xphi
| Xphi ) ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(17,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(18,plain,
( ( ( in @ sK1_SY0 @ omega )
& ( in @ sK2_SY16 @ omega )
& ( ( setadjoin @ sK1_SY0 @ sK1_SY0 )
= ( setadjoin @ sK2_SY16 @ sK2_SY16 ) )
& ( sK1_SY0 != sK2_SY16 ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(19,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ( ~ ! [SX2: $i,SX3: $i] :
( ( SX2 != SX3 )
| ~ ( in @ SX2 @ SX0 )
| ( in @ SX3 @ SX1 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ( SX2 != SX3 )
| ~ ( in @ SX3 @ SX1 )
| ( in @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15,in__Cong,notinself2,omegaS,setadjoinE,setadjoinIL]) ).
thf(20,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setadjoin @ SX0 @ SX1 ) )
| ~ ( ~ ~ ( ~ ( ( SX2 = SX0 )
| ( in @ SX2 @ SX1 )
| ! [SX3: $o] : SX3 )
| ~ ( ( SX2 = SX0 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
| ~ ~ ( ~ ! [SX3: $o] :
( ~ SX3
| ( in @ SX2 @ SX1 )
| SX3 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16,in__Cong,notinself2,omegaS,setadjoinE,setadjoinIL]) ).
thf(21,plain,
( ( ~ ( ~ ( in @ sK1_SY0 @ omega )
| ~ ~ ( ~ ( in @ sK2_SY16 @ omega )
| ~ ~ ( ( ( setadjoin @ sK1_SY0 @ sK1_SY0 )
!= ( setadjoin @ sK2_SY16 @ sK2_SY16 ) )
| ~ ( ( sK1_SY0 != sK2_SY16 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18,in__Cong,notinself2,omegaS,setadjoinE,setadjoinIL]) ).
thf(22,plain,
! [SV1: $i] :
( ( ! [SY17: $i] :
( ~ ( in @ SV1 @ SY17 )
| ~ ( in @ SY17 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(23,plain,
! [SV2: $i] :
( ( ! [SY18: $i] : ( in @ SV2 @ ( setadjoin @ SV2 @ SY18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(24,plain,
! [SV3: $i] :
( ( ! [SY19: $i] :
( ( SV3 != SY19 )
| ~ ( ~ ! [SY20: $i,SY21: $i] :
( ( SY20 != SY21 )
| ~ ( in @ SY20 @ SV3 )
| ( in @ SY21 @ SY19 ) )
| ~ ! [SY22: $i,SY23: $i] :
( ( SY22 != SY23 )
| ~ ( in @ SY23 @ SY19 )
| ( in @ SY22 @ SV3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(25,plain,
! [SV4: $i] :
( ( ! [SY24: $i,SY25: $i] :
( ~ ( in @ SY25 @ ( setadjoin @ SV4 @ SY24 ) )
| ~ ( ~ ~ ( ~ ( ( SY25 = SV4 )
| ( in @ SY25 @ SY24 )
| ! [SX3: $o] : SX3 )
| ~ ( ( SY25 = SV4 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
| ~ ~ ( ~ ! [SX3: $o] :
( ~ SX3
| ( in @ SY25 @ SY24 )
| SX3 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(26,plain,
( ( ~ ( in @ sK1_SY0 @ omega )
| ~ ~ ( ~ ( in @ sK2_SY16 @ omega )
| ~ ~ ( ( ( setadjoin @ sK1_SY0 @ sK1_SY0 )
!= ( setadjoin @ sK2_SY16 @ sK2_SY16 ) )
| ~ ( ( sK1_SY0 != sK2_SY16 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(27,plain,
! [SV5: $i,SV1: $i] :
( ( ~ ( in @ SV1 @ SV5 )
| ~ ( in @ SV5 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(28,plain,
! [SV6: $i,SV2: $i] :
( ( in @ SV2 @ ( setadjoin @ SV2 @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(29,plain,
! [SV7: $i,SV3: $i] :
( ( ( SV3 != SV7 )
| ~ ( ~ ! [SY30: $i,SY31: $i] :
( ( SY30 != SY31 )
| ~ ( in @ SY30 @ SV3 )
| ( in @ SY31 @ SV7 ) )
| ~ ! [SY32: $i,SY33: $i] :
( ( SY32 != SY33 )
| ~ ( in @ SY33 @ SV7 )
| ( in @ SY32 @ SV3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(30,plain,
! [SV8: $i,SV4: $i] :
( ( ! [SY34: $i] :
( ~ ( in @ SY34 @ ( setadjoin @ SV4 @ SV8 ) )
| ~ ( ~ ~ ( ~ ( ( SY34 = SV4 )
| ( in @ SY34 @ SV8 )
| ! [SX3: $o] : SX3 )
| ~ ( ( SY34 = SV4 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
| ~ ~ ( ~ ! [SY37: $o] :
( ~ SY37
| ( in @ SY34 @ SV8 )
| SY37 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(31,plain,
( ( ~ ( in @ sK1_SY0 @ omega ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[26]) ).
thf(32,plain,
( ( ~ ~ ( ~ ( in @ sK2_SY16 @ omega )
| ~ ~ ( ( ( setadjoin @ sK1_SY0 @ sK1_SY0 )
!= ( setadjoin @ sK2_SY16 @ sK2_SY16 ) )
| ~ ( ( sK1_SY0 != sK2_SY16 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[26]) ).
thf(33,plain,
! [SV5: $i,SV1: $i] :
( ( ( ~ ( in @ SV1 @ SV5 ) )
= $true )
| ( ( ~ ( in @ SV5 @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[27]) ).
thf(34,plain,
! [SV7: $i,SV3: $i] :
( ( ( ( SV3 != SV7 ) )
= $true )
| ( ( ~ ( ~ ! [SY30: $i,SY31: $i] :
( ( SY30 != SY31 )
| ~ ( in @ SY30 @ SV3 )
| ( in @ SY31 @ SV7 ) )
| ~ ! [SY32: $i,SY33: $i] :
( ( SY32 != SY33 )
| ~ ( in @ SY33 @ SV7 )
| ( in @ SY32 @ SV3 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[29]) ).
thf(35,plain,
! [SV8: $i,SV4: $i,SV9: $i] :
( ( ~ ( in @ SV9 @ ( setadjoin @ SV4 @ SV8 ) )
| ~ ( ~ ~ ( ~ ( ( SV9 = SV4 )
| ( in @ SV9 @ SV8 )
| ! [SX3: $o] : SX3 )
| ~ ( ( SV9 = SV4 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
| ~ ~ ( ~ ! [SY41: $o] :
( ~ SY41
| ( in @ SV9 @ SV8 )
| SY41 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(36,plain,
( ( in @ sK1_SY0 @ omega )
= $true ),
inference(extcnf_not_neg,[status(thm)],[31]) ).
thf(37,plain,
( ( ~ ( ~ ( in @ sK2_SY16 @ omega )
| ~ ~ ( ( ( setadjoin @ sK1_SY0 @ sK1_SY0 )
!= ( setadjoin @ sK2_SY16 @ sK2_SY16 ) )
| ~ ( ( sK1_SY0 != sK2_SY16 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[32]) ).
thf(38,plain,
! [SV5: $i,SV1: $i] :
( ( ( in @ SV1 @ SV5 )
= $false )
| ( ( ~ ( in @ SV5 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(39,plain,
! [SV7: $i,SV3: $i] :
( ( ( SV3 = SV7 )
= $false )
| ( ( ~ ( ~ ! [SY30: $i,SY31: $i] :
( ( SY30 != SY31 )
| ~ ( in @ SY30 @ SV3 )
| ( in @ SY31 @ SV7 ) )
| ~ ! [SY32: $i,SY33: $i] :
( ( SY32 != SY33 )
| ~ ( in @ SY33 @ SV7 )
| ( in @ SY32 @ SV3 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(40,plain,
! [SV8: $i,SV4: $i,SV9: $i] :
( ( ( ~ ( in @ SV9 @ ( setadjoin @ SV4 @ SV8 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( ( SV9 = SV4 )
| ( in @ SV9 @ SV8 )
| ! [SX3: $o] : SX3 )
| ~ ( ( SV9 = SV4 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
| ~ ~ ( ~ ! [SY41: $o] :
( ~ SY41
| ( in @ SV9 @ SV8 )
| SY41 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[35]) ).
thf(41,plain,
( ( ~ ( in @ sK2_SY16 @ omega )
| ~ ~ ( ( ( setadjoin @ sK1_SY0 @ sK1_SY0 )
!= ( setadjoin @ sK2_SY16 @ sK2_SY16 ) )
| ~ ( ( sK1_SY0 != sK2_SY16 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(42,plain,
! [SV1: $i,SV5: $i] :
( ( ( in @ SV5 @ SV1 )
= $false )
| ( ( in @ SV1 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(43,plain,
! [SV7: $i,SV3: $i] :
( ( ( ~ ! [SY30: $i,SY31: $i] :
( ( SY30 != SY31 )
| ~ ( in @ SY30 @ SV3 )
| ( in @ SY31 @ SV7 ) )
| ~ ! [SY32: $i,SY33: $i] :
( ( SY32 != SY33 )
| ~ ( in @ SY33 @ SV7 )
| ( in @ SY32 @ SV3 ) ) )
= $false )
| ( ( SV3 = SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(44,plain,
! [SV8: $i,SV4: $i,SV9: $i] :
( ( ( in @ SV9 @ ( setadjoin @ SV4 @ SV8 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( ( SV9 = SV4 )
| ( in @ SV9 @ SV8 )
| ! [SX3: $o] : SX3 )
| ~ ( ( SV9 = SV4 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
| ~ ~ ( ~ ! [SY41: $o] :
( ~ SY41
| ( in @ SV9 @ SV8 )
| SY41 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(45,plain,
( ( ~ ( in @ sK2_SY16 @ omega ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[41]) ).
thf(46,plain,
( ( ~ ~ ( ( ( setadjoin @ sK1_SY0 @ sK1_SY0 )
!= ( setadjoin @ sK2_SY16 @ sK2_SY16 ) )
| ~ ( ( sK1_SY0 != sK2_SY16 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[41]) ).
thf(47,plain,
! [SV7: $i,SV3: $i] :
( ( ( ~ ! [SY30: $i,SY31: $i] :
( ( SY30 != SY31 )
| ~ ( in @ SY30 @ SV3 )
| ( in @ SY31 @ SV7 ) ) )
= $false )
| ( ( SV3 = SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[43]) ).
thf(48,plain,
! [SV3: $i,SV7: $i] :
( ( ( ~ ! [SY32: $i,SY33: $i] :
( ( SY32 != SY33 )
| ~ ( in @ SY33 @ SV7 )
| ( in @ SY32 @ SV3 ) ) )
= $false )
| ( ( SV3 = SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[43]) ).
thf(49,plain,
! [SV8: $i,SV4: $i,SV9: $i] :
( ( ( ~ ~ ( ~ ( ( SV9 = SV4 )
| ( in @ SV9 @ SV8 )
| ! [SX3: $o] : SX3 )
| ~ ( ( SV9 = SV4 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
| ~ ~ ( ~ ! [SY41: $o] :
( ~ SY41
| ( in @ SV9 @ SV8 )
| SY41 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) )
= $false )
| ( ( in @ SV9 @ ( setadjoin @ SV4 @ SV8 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(50,plain,
( ( in @ sK2_SY16 @ omega )
= $true ),
inference(extcnf_not_neg,[status(thm)],[45]) ).
thf(51,plain,
( ( ~ ( ( ( setadjoin @ sK1_SY0 @ sK1_SY0 )
!= ( setadjoin @ sK2_SY16 @ sK2_SY16 ) )
| ~ ( ( sK1_SY0 != sK2_SY16 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[46]) ).
thf(52,plain,
! [SV7: $i,SV3: $i] :
( ( ( ! [SY30: $i,SY31: $i] :
( ( SY30 != SY31 )
| ~ ( in @ SY30 @ SV3 )
| ( in @ SY31 @ SV7 ) ) )
= $true )
| ( ( SV3 = SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[47]) ).
thf(53,plain,
! [SV3: $i,SV7: $i] :
( ( ( ! [SY32: $i,SY33: $i] :
( ( SY32 != SY33 )
| ~ ( in @ SY33 @ SV7 )
| ( in @ SY32 @ SV3 ) ) )
= $true )
| ( ( SV3 = SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[48]) ).
thf(54,plain,
! [SV8: $i,SV4: $i,SV9: $i] :
( ( ( ~ ~ ( ~ ( ( SV9 = SV4 )
| ( in @ SV9 @ SV8 )
| ! [SX3: $o] : SX3 )
| ~ ( ( SV9 = SV4 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
= $false )
| ( ( in @ SV9 @ ( setadjoin @ SV4 @ SV8 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[49]) ).
thf(55,plain,
! [SV4: $i,SV8: $i,SV9: $i] :
( ( ( ~ ~ ( ~ ! [SY41: $o] :
( ~ SY41
| ( in @ SV9 @ SV8 )
| SY41 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) )
= $false )
| ( ( in @ SV9 @ ( setadjoin @ SV4 @ SV8 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[49]) ).
thf(56,plain,
( ( ( ( setadjoin @ sK1_SY0 @ sK1_SY0 )
!= ( setadjoin @ sK2_SY16 @ sK2_SY16 ) )
| ~ ( ( sK1_SY0 != sK2_SY16 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(57,plain,
! [SV7: $i,SV3: $i,SV10: $i] :
( ( ( ! [SY43: $i] :
( ( SV10 != SY43 )
| ~ ( in @ SV10 @ SV3 )
| ( in @ SY43 @ SV7 ) ) )
= $true )
| ( ( SV3 = SV7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(58,plain,
! [SV3: $i,SV7: $i,SV11: $i] :
( ( ( ! [SY44: $i] :
( ( SV11 != SY44 )
| ~ ( in @ SY44 @ SV7 )
| ( in @ SV11 @ SV3 ) ) )
= $true )
| ( ( SV3 = SV7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(59,plain,
! [SV8: $i,SV4: $i,SV9: $i] :
( ( ( ~ ( ~ ( ( SV9 = SV4 )
| ( in @ SV9 @ SV8 )
| ! [SX3: $o] : SX3 )
| ~ ( ( SV9 = SV4 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
= $true )
| ( ( in @ SV9 @ ( setadjoin @ SV4 @ SV8 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[54]) ).
thf(60,plain,
! [SV4: $i,SV8: $i,SV9: $i] :
( ( ( ~ ( ~ ! [SY41: $o] :
( ~ SY41
| ( in @ SV9 @ SV8 )
| SY41 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) )
= $true )
| ( ( in @ SV9 @ ( setadjoin @ SV4 @ SV8 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[55]) ).
thf(61,plain,
( ( ( ( setadjoin @ sK1_SY0 @ sK1_SY0 )
!= ( setadjoin @ sK2_SY16 @ sK2_SY16 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[56]) ).
thf(62,plain,
( ( ~ ( ( sK1_SY0 != sK2_SY16 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[56]) ).
thf(63,plain,
! [SV7: $i,SV3: $i,SV12: $i,SV10: $i] :
( ( ( ( SV10 != SV12 )
| ~ ( in @ SV10 @ SV3 )
| ( in @ SV12 @ SV7 ) )
= $true )
| ( ( SV3 = SV7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(64,plain,
! [SV3: $i,SV7: $i,SV13: $i,SV11: $i] :
( ( ( ( SV11 != SV13 )
| ~ ( in @ SV13 @ SV7 )
| ( in @ SV11 @ SV3 ) )
= $true )
| ( ( SV3 = SV7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(65,plain,
! [SV8: $i,SV4: $i,SV9: $i] :
( ( ( ~ ( ( SV9 = SV4 )
| ( in @ SV9 @ SV8 )
| ! [SX3: $o] : SX3 )
| ~ ( ( SV9 = SV4 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
= $false )
| ( ( in @ SV9 @ ( setadjoin @ SV4 @ SV8 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(66,plain,
! [SV4: $i,SV8: $i,SV9: $i] :
( ( ( ~ ! [SY41: $o] :
( ~ SY41
| ( in @ SV9 @ SV8 )
| SY41 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) )
= $false )
| ( ( in @ SV9 @ ( setadjoin @ SV4 @ SV8 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(67,plain,
( ( ( setadjoin @ sK1_SY0 @ sK1_SY0 )
= ( setadjoin @ sK2_SY16 @ sK2_SY16 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[61]) ).
thf(68,plain,
( ( ( sK1_SY0 != sK2_SY16 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[62]) ).
thf(69,plain,
! [SV7: $i,SV3: $i,SV12: $i,SV10: $i] :
( ( ( ( SV10 != SV12 ) )
= $true )
| ( ( ~ ( in @ SV10 @ SV3 )
| ( in @ SV12 @ SV7 ) )
= $true )
| ( ( SV3 = SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[63]) ).
thf(70,plain,
! [SV3: $i,SV7: $i,SV13: $i,SV11: $i] :
( ( ( ( SV11 != SV13 ) )
= $true )
| ( ( ~ ( in @ SV13 @ SV7 )
| ( in @ SV11 @ SV3 ) )
= $true )
| ( ( SV3 = SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[64]) ).
thf(71,plain,
! [SV8: $i,SV4: $i,SV9: $i] :
( ( ( ~ ( ( SV9 = SV4 )
| ( in @ SV9 @ SV8 )
| ! [SX3: $o] : SX3 ) )
= $false )
| ( ( in @ SV9 @ ( setadjoin @ SV4 @ SV8 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[65]) ).
thf(72,plain,
! [SV8: $i,SV4: $i,SV9: $i] :
( ( ( ~ ( ( SV9 = SV4 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
= $false )
| ( ( in @ SV9 @ ( setadjoin @ SV4 @ SV8 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[65]) ).
thf(73,plain,
! [SV4: $i,SV8: $i,SV9: $i] :
( ( ( ~ ! [SY41: $o] :
( ~ SY41
| ( in @ SV9 @ SV8 )
| SY41 ) )
= $false )
| ( ( in @ SV9 @ ( setadjoin @ SV4 @ SV8 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[66]) ).
thf(74,plain,
! [SV8: $i,SV4: $i,SV9: $i] :
( ( ( ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) )
= $false )
| ( ( in @ SV9 @ ( setadjoin @ SV4 @ SV8 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[66]) ).
thf(75,plain,
( ( sK1_SY0 = sK2_SY16 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[68]) ).
thf(76,plain,
! [SV7: $i,SV3: $i,SV12: $i,SV10: $i] :
( ( ( SV10 = SV12 )
= $false )
| ( ( ~ ( in @ SV10 @ SV3 )
| ( in @ SV12 @ SV7 ) )
= $true )
| ( ( SV3 = SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(77,plain,
! [SV3: $i,SV7: $i,SV13: $i,SV11: $i] :
( ( ( SV11 = SV13 )
= $false )
| ( ( ~ ( in @ SV13 @ SV7 )
| ( in @ SV11 @ SV3 ) )
= $true )
| ( ( SV3 = SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(78,plain,
! [SV8: $i,SV4: $i,SV9: $i] :
( ( ( ( SV9 = SV4 )
| ( in @ SV9 @ SV8 )
| ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV9 @ ( setadjoin @ SV4 @ SV8 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[71]) ).
thf(79,plain,
! [SV8: $i,SV4: $i,SV9: $i] :
( ( ( ( SV9 = SV4 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) )
= $true )
| ( ( in @ SV9 @ ( setadjoin @ SV4 @ SV8 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[72]) ).
thf(80,plain,
! [SV4: $i,SV8: $i,SV9: $i] :
( ( ( ! [SY41: $o] :
( ~ SY41
| ( in @ SV9 @ SV8 )
| SY41 ) )
= $true )
| ( ( in @ SV9 @ ( setadjoin @ SV4 @ SV8 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[73]) ).
thf(81,plain,
! [SV8: $i,SV4: $i,SV9: $i] :
( ( ( ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) )
= $true )
| ( ( in @ SV9 @ ( setadjoin @ SV4 @ SV8 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[74]) ).
thf(82,plain,
! [SV7: $i,SV12: $i,SV3: $i,SV10: $i] :
( ( ( ~ ( in @ SV10 @ SV3 ) )
= $true )
| ( ( in @ SV12 @ SV7 )
= $true )
| ( ( SV10 = SV12 )
= $false )
| ( ( SV3 = SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[76]) ).
thf(83,plain,
! [SV3: $i,SV11: $i,SV7: $i,SV13: $i] :
( ( ( ~ ( in @ SV13 @ SV7 ) )
= $true )
| ( ( in @ SV11 @ SV3 )
= $true )
| ( ( SV11 = SV13 )
= $false )
| ( ( SV3 = SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[77]) ).
thf(84,plain,
! [SV8: $i,SV4: $i,SV9: $i] :
( ( ( SV9 = SV4 )
= $true )
| ( ( ( in @ SV9 @ SV8 )
| ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV9 @ ( setadjoin @ SV4 @ SV8 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[78]) ).
thf(85,plain,
! [SV8: $i,SV4: $i,SV9: $i] :
( ( ( SV9 = SV4 )
= $true )
| ( ( ! [SX3: $o] :
( ~ SX3
| SX3 ) )
= $true )
| ( ( in @ SV9 @ ( setadjoin @ SV4 @ SV8 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[79]) ).
thf(86,plain,
! [SV4: $i,SV8: $i,SV9: $i,SV14: $o] :
( ( ( ~ SV14
| ( in @ SV9 @ SV8 )
| SV14 )
= $true )
| ( ( in @ SV9 @ ( setadjoin @ SV4 @ SV8 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[80]) ).
thf(87,plain,
! [SV4: $i,SV8: $i,SV9: $i] :
( ( ( ~ $true
| ( in @ SV9 @ SV8 )
| $true )
= $true )
| ( ( in @ SV9 @ ( setadjoin @ SV4 @ SV8 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[80]) ).
thf(88,plain,
! [SV4: $i,SV8: $i,SV9: $i] :
( ( ( ~ $false
| ( in @ SV9 @ SV8 )
| $false )
= $true )
| ( ( in @ SV9 @ ( setadjoin @ SV4 @ SV8 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[80]) ).
thf(89,plain,
! [SV8: $i,SV4: $i,SV9: $i,SV15: $o] :
( ( ( ~ SV15
| ~ SV15
| SV15 )
= $true )
| ( ( in @ SV9 @ ( setadjoin @ SV4 @ SV8 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[81]) ).
thf(90,plain,
! [SV8: $i,SV4: $i,SV9: $i] :
( ( ( ~ $true
| ~ $true
| $true )
= $true )
| ( ( in @ SV9 @ ( setadjoin @ SV4 @ SV8 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[81]) ).
thf(91,plain,
! [SV8: $i,SV4: $i,SV9: $i] :
( ( ( ~ $false
| ~ $false
| $false )
= $true )
| ( ( in @ SV9 @ ( setadjoin @ SV4 @ SV8 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[81]) ).
thf(92,plain,
! [SV7: $i,SV12: $i,SV3: $i,SV10: $i] :
( ( ( in @ SV10 @ SV3 )
= $false )
| ( ( in @ SV12 @ SV7 )
= $true )
| ( ( SV10 = SV12 )
= $false )
| ( ( SV3 = SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(93,plain,
! [SV3: $i,SV11: $i,SV7: $i,SV13: $i] :
( ( ( in @ SV13 @ SV7 )
= $false )
| ( ( in @ SV11 @ SV3 )
= $true )
| ( ( SV11 = SV13 )
= $false )
| ( ( SV3 = SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[83]) ).
thf(94,plain,
! [SV4: $i,SV8: $i,SV9: $i] :
( ( ( in @ SV9 @ SV8 )
= $true )
| ( ( ! [SX3: $o] : SX3 )
= $true )
| ( ( SV9 = SV4 )
= $true )
| ( ( in @ SV9 @ ( setadjoin @ SV4 @ SV8 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[84]) ).
thf(95,plain,
! [SV8: $i,SV4: $i,SV9: $i,SV16: $o] :
( ( ( ~ SV16
| SV16 )
= $true )
| ( ( SV9 = SV4 )
= $true )
| ( ( in @ SV9 @ ( setadjoin @ SV4 @ SV8 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[85]) ).
thf(96,plain,
! [SV8: $i,SV4: $i,SV9: $i] :
( ( ( ~ $true
| $true )
= $true )
| ( ( SV9 = SV4 )
= $true )
| ( ( in @ SV9 @ ( setadjoin @ SV4 @ SV8 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[85]) ).
thf(97,plain,
! [SV8: $i,SV4: $i,SV9: $i] :
( ( ( ~ $false
| $false )
= $true )
| ( ( SV9 = SV4 )
= $true )
| ( ( in @ SV9 @ ( setadjoin @ SV4 @ SV8 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[85]) ).
thf(98,plain,
! [SV4: $i,SV8: $i,SV9: $i,SV14: $o] :
( ( ( ~ SV14 )
= $true )
| ( ( ( in @ SV9 @ SV8 )
| SV14 )
= $true )
| ( ( in @ SV9 @ ( setadjoin @ SV4 @ SV8 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[86]) ).
thf(99,plain,
! [SV4: $i,SV8: $i,SV9: $i] :
( ( ( ~ $true )
= $true )
| ( ( ( in @ SV9 @ SV8 )
| $true )
= $true )
| ( ( in @ SV9 @ ( setadjoin @ SV4 @ SV8 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[87]) ).
thf(100,plain,
! [SV4: $i,SV8: $i,SV9: $i] :
( ( ( ~ $false )
= $true )
| ( ( ( in @ SV9 @ SV8 )
| $false )
= $true )
| ( ( in @ SV9 @ ( setadjoin @ SV4 @ SV8 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[88]) ).
thf(101,plain,
! [SV8: $i,SV4: $i,SV9: $i,SV15: $o] :
( ( ( ~ SV15 )
= $true )
| ( ( ~ SV15
| SV15 )
= $true )
| ( ( in @ SV9 @ ( setadjoin @ SV4 @ SV8 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[89]) ).
thf(102,plain,
! [SV8: $i,SV4: $i,SV9: $i] :
( ( ( ~ $true )
= $true )
| ( ( ~ $true
| $true )
= $true )
| ( ( in @ SV9 @ ( setadjoin @ SV4 @ SV8 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[90]) ).
thf(103,plain,
! [SV8: $i,SV4: $i,SV9: $i] :
( ( ( ~ $false )
= $true )
| ( ( ~ $false
| $false )
= $true )
| ( ( in @ SV9 @ ( setadjoin @ SV4 @ SV8 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[91]) ).
thf(104,plain,
! [SV4: $i,SV8: $i,SV9: $i,SV17: $o] :
( ( SV17 = $true )
| ( ( in @ SV9 @ SV8 )
= $true )
| ( ( SV9 = SV4 )
= $true )
| ( ( in @ SV9 @ ( setadjoin @ SV4 @ SV8 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[94]) ).
thf(105,plain,
! [SV4: $i,SV8: $i,SV9: $i] :
( ( $true = $true )
| ( ( in @ SV9 @ SV8 )
= $true )
| ( ( SV9 = SV4 )
= $true )
| ( ( in @ SV9 @ ( setadjoin @ SV4 @ SV8 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[94]) ).
thf(106,plain,
! [SV4: $i,SV8: $i,SV9: $i] :
( ( $false = $true )
| ( ( in @ SV9 @ SV8 )
= $true )
| ( ( SV9 = SV4 )
= $true )
| ( ( in @ SV9 @ ( setadjoin @ SV4 @ SV8 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[94]) ).
thf(107,plain,
! [SV8: $i,SV4: $i,SV9: $i,SV16: $o] :
( ( ( ~ SV16 )
= $true )
| ( SV16 = $true )
| ( ( SV9 = SV4 )
= $true )
| ( ( in @ SV9 @ ( setadjoin @ SV4 @ SV8 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[95]) ).
thf(108,plain,
! [SV8: $i,SV4: $i,SV9: $i] :
( ( ( ~ $true )
= $true )
| ( $true = $true )
| ( ( SV9 = SV4 )
= $true )
| ( ( in @ SV9 @ ( setadjoin @ SV4 @ SV8 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[96]) ).
thf(109,plain,
! [SV8: $i,SV4: $i,SV9: $i] :
( ( ( ~ $false )
= $true )
| ( $false = $true )
| ( ( SV9 = SV4 )
= $true )
| ( ( in @ SV9 @ ( setadjoin @ SV4 @ SV8 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[97]) ).
thf(110,plain,
! [SV4: $i,SV8: $i,SV9: $i,SV14: $o] :
( ( SV14 = $false )
| ( ( ( in @ SV9 @ SV8 )
| SV14 )
= $true )
| ( ( in @ SV9 @ ( setadjoin @ SV4 @ SV8 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(111,plain,
! [SV4: $i,SV8: $i,SV9: $i] :
( ( $true = $false )
| ( ( ( in @ SV9 @ SV8 )
| $true )
= $true )
| ( ( in @ SV9 @ ( setadjoin @ SV4 @ SV8 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(112,plain,
! [SV4: $i,SV8: $i,SV9: $i] :
( ( $false = $false )
| ( ( ( in @ SV9 @ SV8 )
| $false )
= $true )
| ( ( in @ SV9 @ ( setadjoin @ SV4 @ SV8 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(113,plain,
! [SV8: $i,SV4: $i,SV9: $i,SV15: $o] :
( ( SV15 = $false )
| ( ( ~ SV15
| SV15 )
= $true )
| ( ( in @ SV9 @ ( setadjoin @ SV4 @ SV8 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(114,plain,
! [SV8: $i,SV4: $i,SV9: $i] :
( ( $true = $false )
| ( ( ~ $true
| $true )
= $true )
| ( ( in @ SV9 @ ( setadjoin @ SV4 @ SV8 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(115,plain,
! [SV8: $i,SV4: $i,SV9: $i] :
( ( $false = $false )
| ( ( ~ $false
| $false )
= $true )
| ( ( in @ SV9 @ ( setadjoin @ SV4 @ SV8 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(116,plain,
! [SV8: $i,SV4: $i,SV9: $i,SV16: $o] :
( ( SV16 = $false )
| ( SV16 = $true )
| ( ( SV9 = SV4 )
= $true )
| ( ( in @ SV9 @ ( setadjoin @ SV4 @ SV8 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(117,plain,
! [SV8: $i,SV4: $i,SV9: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( SV9 = SV4 )
= $true )
| ( ( in @ SV9 @ ( setadjoin @ SV4 @ SV8 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(118,plain,
! [SV8: $i,SV4: $i,SV9: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( SV9 = SV4 )
= $true )
| ( ( in @ SV9 @ ( setadjoin @ SV4 @ SV8 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(119,plain,
! [SV4: $i,SV14: $o,SV8: $i,SV9: $i] :
( ( ( in @ SV9 @ SV8 )
= $true )
| ( SV14 = $true )
| ( SV14 = $false )
| ( ( in @ SV9 @ ( setadjoin @ SV4 @ SV8 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[110]) ).
thf(120,plain,
! [SV4: $i,SV8: $i,SV9: $i] :
( ( ( in @ SV9 @ SV8 )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV9 @ ( setadjoin @ SV4 @ SV8 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[111]) ).
thf(121,plain,
! [SV4: $i,SV8: $i,SV9: $i] :
( ( ( in @ SV9 @ SV8 )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV9 @ ( setadjoin @ SV4 @ SV8 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[112]) ).
thf(122,plain,
! [SV8: $i,SV4: $i,SV9: $i,SV15: $o] :
( ( ( ~ SV15 )
= $true )
| ( SV15 = $true )
| ( SV15 = $false )
| ( ( in @ SV9 @ ( setadjoin @ SV4 @ SV8 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[113]) ).
thf(123,plain,
! [SV8: $i,SV4: $i,SV9: $i] :
( ( ( ~ $true )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV9 @ ( setadjoin @ SV4 @ SV8 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[114]) ).
thf(124,plain,
! [SV8: $i,SV4: $i,SV9: $i] :
( ( ( ~ $false )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV9 @ ( setadjoin @ SV4 @ SV8 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[115]) ).
thf(125,plain,
! [SV8: $i,SV4: $i,SV9: $i,SV15: $o] :
( ( SV15 = $false )
| ( SV15 = $true )
| ( SV15 = $false )
| ( ( in @ SV9 @ ( setadjoin @ SV4 @ SV8 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(126,plain,
! [SV8: $i,SV4: $i,SV9: $i] :
( ( $true = $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV9 @ ( setadjoin @ SV4 @ SV8 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(127,plain,
! [SV8: $i,SV4: $i,SV9: $i] :
( ( $false = $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV9 @ ( setadjoin @ SV4 @ SV8 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(128,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[28,127,126,125,121,120,119,118,117,116,106,105,104,93,92,75,67,50,42,36]) ).
thf(129,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[128]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SEU811^2 : TPTP v8.1.0. Released v3.7.0.
% 0.03/0.14 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.35 % Computer : n010.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sun Jun 19 12:05:22 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35
% 0.13/0.35 No.of.Axioms: 0
% 0.13/0.35
% 0.13/0.35 Length.of.Defs: 897
% 0.13/0.35
% 0.13/0.35 Contains.Choice.Funs: false
% 0.13/0.36 (rf:0,axioms:0,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:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2,loop_count:0,foatp_calls:0,translation:fof_full).......
% 0.20/0.43
% 0.20/0.43 ********************************
% 0.20/0.43 * All subproblems solved! *
% 0.20/0.43 ********************************
% 0.20/0.43 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:4,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:10,ordering:none,proof_output:1,protocol_output:false,clause_count:128,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.20/0.43
% 0.20/0.43 %**** Beginning of derivation protocol ****
% 0.20/0.43 % SZS output start CNFRefutation
% See solution above
% 0.20/0.44
% 0.20/0.44 %**** End of derivation protocol ****
% 0.20/0.44 %**** no. of clauses in derivation: 129 ****
% 0.20/0.44 %**** clause counter: 128 ****
% 0.20/0.44
% 0.20/0.44 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:4,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:10,ordering:none,proof_output:1,protocol_output:false,clause_count:128,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------