TSTP Solution File: SEU527^2 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU527^2 : 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 : n025.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 12:12:36 EDT 2022
% Result : Theorem 0.18s 0.39s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 10
% Syntax : Number of formulae : 100 ( 27 unt; 7 typ; 2 def)
% Number of atoms : 686 ( 269 equ; 0 cnn)
% Maximal formula atoms : 4 ( 7 avg)
% Number of connectives : 965 ( 196 ~; 298 |; 8 &; 434 @)
% ( 0 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 7 con; 0-2 aty)
% Number of variables : 309 ( 0 ^ 309 !; 0 ?; 309 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_emptyset,type,
emptyset: $i ).
thf(tp_emptysetE,type,
emptysetE: $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_sK1_Xx,type,
sK1_Xx: $i ).
thf(tp_sK2_SY10,type,
sK2_SY10: $i ).
thf(tp_setadjoin,type,
setadjoin: $i > $i > $i ).
thf(tp_setadjoinE,type,
setadjoinE: $o ).
thf(emptysetE,definition,
( emptysetE
= ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> ! [Xphi: $o] : Xphi ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetE) ).
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/sandbox2/benchmark/theBenchmark.p',setadjoinE) ).
thf(1,conjecture,
( emptysetE
=> ( setadjoinE
=> ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uniqinunit) ).
thf(2,negated_conjecture,
( ( emptysetE
=> ( setadjoinE
=> ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> ! [Xphi: $o] : Xphi )
=> ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ! [Xphi: $o] :
( ( ( Xy = Xx )
=> Xphi )
=> ( ( ( in @ Xy @ A )
=> Xphi )
=> Xphi ) ) )
=> ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,emptysetE,setadjoinE]) ).
thf(4,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> ! [Xphi: $o] : Xphi ) )
= $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,
( ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ~ ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(8,plain,
( ( ( in @ sK1_Xx @ ( setadjoin @ sK2_SY10 @ emptyset ) )
& ( sK1_Xx != sK2_SY10 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(9,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset )
| ! [Xphi: $o] : Xphi )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(10,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(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(copy,[status(thm)],[10]) ).
thf(12,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset )
| ! [Xphi: $o] : Xphi )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(13,plain,
( ( ( in @ sK1_Xx @ ( setadjoin @ sK2_SY10 @ emptyset ) )
& ( sK1_Xx != sK2_SY10 ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(14,plain,
( ( ~ ( ~ ( in @ sK1_Xx @ ( setadjoin @ sK2_SY10 @ emptyset ) )
| ~ ( ( sK1_Xx != sK2_SY10 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13,emptysetE,setadjoinE]) ).
thf(15,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)],[11,emptysetE,setadjoinE]) ).
thf(16,plain,
( ( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true )
| ( ( ! [Xphi: $o] : Xphi )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[12]) ).
thf(17,plain,
( ( ~ ( in @ sK1_Xx @ ( setadjoin @ sK2_SY10 @ emptyset ) )
| ~ ( ( sK1_Xx != sK2_SY10 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[14]) ).
thf(18,plain,
! [SV1: $i] :
( ( ! [SY11: $i,SY12: $i] :
( ~ ( in @ SY12 @ ( setadjoin @ SV1 @ SY11 ) )
| ~ ( ~ ~ ( ~ ( ( SY12 = SV1 )
| ( in @ SY12 @ SY11 )
| ! [SX3: $o] : SX3 )
| ~ ( ( SY12 = SV1 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
| ~ ~ ( ~ ! [SX3: $o] :
( ~ SX3
| ( in @ SY12 @ SY11 )
| SX3 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(19,plain,
! [SV2: $i] :
( ( ( ~ ( in @ SV2 @ emptyset ) )
= $true )
| ( ( ! [Xphi: $o] : Xphi )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(20,plain,
( ( ~ ( in @ sK1_Xx @ ( setadjoin @ sK2_SY10 @ emptyset ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(21,plain,
( ( ~ ( ( sK1_Xx != sK2_SY10 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(22,plain,
! [SV3: $i,SV1: $i] :
( ( ! [SY17: $i] :
( ~ ( in @ SY17 @ ( setadjoin @ SV1 @ SV3 ) )
| ~ ( ~ ~ ( ~ ( ( SY17 = SV1 )
| ( in @ SY17 @ SV3 )
| ! [SX3: $o] : SX3 )
| ~ ( ( SY17 = SV1 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
| ~ ~ ( ~ ! [SY20: $o] :
( ~ SY20
| ( in @ SY17 @ SV3 )
| SY20 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(23,plain,
! [SV2: $i] :
( ( ( in @ SV2 @ emptyset )
= $false )
| ( ( ! [Xphi: $o] : Xphi )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[19]) ).
thf(24,plain,
( ( in @ sK1_Xx @ ( setadjoin @ sK2_SY10 @ emptyset ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[20]) ).
thf(25,plain,
( ( ( sK1_Xx != sK2_SY10 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[21]) ).
thf(26,plain,
! [SV3: $i,SV1: $i,SV4: $i] :
( ( ~ ( in @ SV4 @ ( setadjoin @ SV1 @ SV3 ) )
| ~ ( ~ ~ ( ~ ( ( SV4 = SV1 )
| ( in @ SV4 @ SV3 )
| ! [SX3: $o] : SX3 )
| ~ ( ( SV4 = SV1 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
| ~ ~ ( ~ ! [SY24: $o] :
( ~ SY24
| ( in @ SV4 @ SV3 )
| SY24 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(27,plain,
! [SV2: $i,SV5: $o] :
( ( SV5 = $true )
| ( ( in @ SV2 @ emptyset )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[23]) ).
thf(28,plain,
! [SV2: $i] :
( ( $true = $true )
| ( ( in @ SV2 @ emptyset )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[23]) ).
thf(29,plain,
! [SV2: $i] :
( ( $false = $true )
| ( ( in @ SV2 @ emptyset )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[23]) ).
thf(30,plain,
( ( sK1_Xx = sK2_SY10 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(31,plain,
! [SV3: $i,SV1: $i,SV4: $i] :
( ( ( ~ ( in @ SV4 @ ( setadjoin @ SV1 @ SV3 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( ( SV4 = SV1 )
| ( in @ SV4 @ SV3 )
| ! [SX3: $o] : SX3 )
| ~ ( ( SV4 = SV1 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
| ~ ~ ( ~ ! [SY24: $o] :
( ~ SY24
| ( in @ SV4 @ SV3 )
| SY24 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[26]) ).
thf(32,plain,
! [SV3: $i,SV1: $i,SV4: $i] :
( ( ( in @ SV4 @ ( setadjoin @ SV1 @ SV3 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( ( SV4 = SV1 )
| ( in @ SV4 @ SV3 )
| ! [SX3: $o] : SX3 )
| ~ ( ( SV4 = SV1 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
| ~ ~ ( ~ ! [SY24: $o] :
( ~ SY24
| ( in @ SV4 @ SV3 )
| SY24 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(33,plain,
! [SV3: $i,SV1: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ( ( SV4 = SV1 )
| ( in @ SV4 @ SV3 )
| ! [SX3: $o] : SX3 )
| ~ ( ( SV4 = SV1 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
| ~ ~ ( ~ ! [SY24: $o] :
( ~ SY24
| ( in @ SV4 @ SV3 )
| SY24 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) )
= $false )
| ( ( in @ SV4 @ ( setadjoin @ SV1 @ SV3 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(34,plain,
! [SV3: $i,SV1: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ( ( SV4 = SV1 )
| ( in @ SV4 @ SV3 )
| ! [SX3: $o] : SX3 )
| ~ ( ( SV4 = SV1 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
= $false )
| ( ( in @ SV4 @ ( setadjoin @ SV1 @ SV3 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[33]) ).
thf(35,plain,
! [SV1: $i,SV3: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ! [SY24: $o] :
( ~ SY24
| ( in @ SV4 @ SV3 )
| SY24 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) )
= $false )
| ( ( in @ SV4 @ ( setadjoin @ SV1 @ SV3 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[33]) ).
thf(36,plain,
! [SV3: $i,SV1: $i,SV4: $i] :
( ( ( ~ ( ~ ( ( SV4 = SV1 )
| ( in @ SV4 @ SV3 )
| ! [SX3: $o] : SX3 )
| ~ ( ( SV4 = SV1 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
= $true )
| ( ( in @ SV4 @ ( setadjoin @ SV1 @ SV3 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[34]) ).
thf(37,plain,
! [SV1: $i,SV3: $i,SV4: $i] :
( ( ( ~ ( ~ ! [SY24: $o] :
( ~ SY24
| ( in @ SV4 @ SV3 )
| SY24 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) )
= $true )
| ( ( in @ SV4 @ ( setadjoin @ SV1 @ SV3 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[35]) ).
thf(38,plain,
! [SV3: $i,SV1: $i,SV4: $i] :
( ( ( ~ ( ( SV4 = SV1 )
| ( in @ SV4 @ SV3 )
| ! [SX3: $o] : SX3 )
| ~ ( ( SV4 = SV1 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
= $false )
| ( ( in @ SV4 @ ( setadjoin @ SV1 @ SV3 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(39,plain,
! [SV1: $i,SV3: $i,SV4: $i] :
( ( ( ~ ! [SY24: $o] :
( ~ SY24
| ( in @ SV4 @ SV3 )
| SY24 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) )
= $false )
| ( ( in @ SV4 @ ( setadjoin @ SV1 @ SV3 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(40,plain,
! [SV3: $i,SV1: $i,SV4: $i] :
( ( ( ~ ( ( SV4 = SV1 )
| ( in @ SV4 @ SV3 )
| ! [SX3: $o] : SX3 ) )
= $false )
| ( ( in @ SV4 @ ( setadjoin @ SV1 @ SV3 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[38]) ).
thf(41,plain,
! [SV3: $i,SV1: $i,SV4: $i] :
( ( ( ~ ( ( SV4 = SV1 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
= $false )
| ( ( in @ SV4 @ ( setadjoin @ SV1 @ SV3 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[38]) ).
thf(42,plain,
! [SV1: $i,SV3: $i,SV4: $i] :
( ( ( ~ ! [SY24: $o] :
( ~ SY24
| ( in @ SV4 @ SV3 )
| SY24 ) )
= $false )
| ( ( in @ SV4 @ ( setadjoin @ SV1 @ SV3 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[39]) ).
thf(43,plain,
! [SV3: $i,SV1: $i,SV4: $i] :
( ( ( ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) )
= $false )
| ( ( in @ SV4 @ ( setadjoin @ SV1 @ SV3 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[39]) ).
thf(44,plain,
! [SV3: $i,SV1: $i,SV4: $i] :
( ( ( ( SV4 = SV1 )
| ( in @ SV4 @ SV3 )
| ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV4 @ ( setadjoin @ SV1 @ SV3 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[40]) ).
thf(45,plain,
! [SV3: $i,SV1: $i,SV4: $i] :
( ( ( ( SV4 = SV1 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) )
= $true )
| ( ( in @ SV4 @ ( setadjoin @ SV1 @ SV3 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[41]) ).
thf(46,plain,
! [SV1: $i,SV3: $i,SV4: $i] :
( ( ( ! [SY24: $o] :
( ~ SY24
| ( in @ SV4 @ SV3 )
| SY24 ) )
= $true )
| ( ( in @ SV4 @ ( setadjoin @ SV1 @ SV3 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[42]) ).
thf(47,plain,
! [SV3: $i,SV1: $i,SV4: $i] :
( ( ( ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) )
= $true )
| ( ( in @ SV4 @ ( setadjoin @ SV1 @ SV3 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[43]) ).
thf(48,plain,
! [SV3: $i,SV1: $i,SV4: $i] :
( ( ( SV4 = SV1 )
= $true )
| ( ( ( in @ SV4 @ SV3 )
| ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV4 @ ( setadjoin @ SV1 @ SV3 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[44]) ).
thf(49,plain,
! [SV3: $i,SV1: $i,SV4: $i] :
( ( ( SV4 = SV1 )
= $true )
| ( ( ! [SX3: $o] :
( ~ SX3
| SX3 ) )
= $true )
| ( ( in @ SV4 @ ( setadjoin @ SV1 @ SV3 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[45]) ).
thf(50,plain,
! [SV1: $i,SV3: $i,SV4: $i,SV6: $o] :
( ( ( ~ SV6
| ( in @ SV4 @ SV3 )
| SV6 )
= $true )
| ( ( in @ SV4 @ ( setadjoin @ SV1 @ SV3 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[46]) ).
thf(51,plain,
! [SV1: $i,SV3: $i,SV4: $i] :
( ( ( ~ $true
| ( in @ SV4 @ SV3 )
| $true )
= $true )
| ( ( in @ SV4 @ ( setadjoin @ SV1 @ SV3 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[46]) ).
thf(52,plain,
! [SV1: $i,SV3: $i,SV4: $i] :
( ( ( ~ $false
| ( in @ SV4 @ SV3 )
| $false )
= $true )
| ( ( in @ SV4 @ ( setadjoin @ SV1 @ SV3 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[46]) ).
thf(53,plain,
! [SV3: $i,SV1: $i,SV4: $i,SV7: $o] :
( ( ( ~ SV7
| ~ SV7
| SV7 )
= $true )
| ( ( in @ SV4 @ ( setadjoin @ SV1 @ SV3 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[47]) ).
thf(54,plain,
! [SV3: $i,SV1: $i,SV4: $i] :
( ( ( ~ $true
| ~ $true
| $true )
= $true )
| ( ( in @ SV4 @ ( setadjoin @ SV1 @ SV3 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[47]) ).
thf(55,plain,
! [SV3: $i,SV1: $i,SV4: $i] :
( ( ( ~ $false
| ~ $false
| $false )
= $true )
| ( ( in @ SV4 @ ( setadjoin @ SV1 @ SV3 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[47]) ).
thf(56,plain,
! [SV1: $i,SV3: $i,SV4: $i] :
( ( ( in @ SV4 @ SV3 )
= $true )
| ( ( ! [SX3: $o] : SX3 )
= $true )
| ( ( SV4 = SV1 )
= $true )
| ( ( in @ SV4 @ ( setadjoin @ SV1 @ SV3 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[48]) ).
thf(57,plain,
! [SV3: $i,SV1: $i,SV4: $i,SV8: $o] :
( ( ( ~ SV8
| SV8 )
= $true )
| ( ( SV4 = SV1 )
= $true )
| ( ( in @ SV4 @ ( setadjoin @ SV1 @ SV3 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[49]) ).
thf(58,plain,
! [SV3: $i,SV1: $i,SV4: $i] :
( ( ( ~ $true
| $true )
= $true )
| ( ( SV4 = SV1 )
= $true )
| ( ( in @ SV4 @ ( setadjoin @ SV1 @ SV3 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[49]) ).
thf(59,plain,
! [SV3: $i,SV1: $i,SV4: $i] :
( ( ( ~ $false
| $false )
= $true )
| ( ( SV4 = SV1 )
= $true )
| ( ( in @ SV4 @ ( setadjoin @ SV1 @ SV3 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[49]) ).
thf(60,plain,
! [SV1: $i,SV3: $i,SV4: $i,SV6: $o] :
( ( ( ~ SV6 )
= $true )
| ( ( ( in @ SV4 @ SV3 )
| SV6 )
= $true )
| ( ( in @ SV4 @ ( setadjoin @ SV1 @ SV3 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[50]) ).
thf(61,plain,
! [SV1: $i,SV3: $i,SV4: $i] :
( ( ( ~ $true )
= $true )
| ( ( ( in @ SV4 @ SV3 )
| $true )
= $true )
| ( ( in @ SV4 @ ( setadjoin @ SV1 @ SV3 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[51]) ).
thf(62,plain,
! [SV1: $i,SV3: $i,SV4: $i] :
( ( ( ~ $false )
= $true )
| ( ( ( in @ SV4 @ SV3 )
| $false )
= $true )
| ( ( in @ SV4 @ ( setadjoin @ SV1 @ SV3 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[52]) ).
thf(63,plain,
! [SV3: $i,SV1: $i,SV4: $i,SV7: $o] :
( ( ( ~ SV7 )
= $true )
| ( ( ~ SV7
| SV7 )
= $true )
| ( ( in @ SV4 @ ( setadjoin @ SV1 @ SV3 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[53]) ).
thf(64,plain,
! [SV3: $i,SV1: $i,SV4: $i] :
( ( ( ~ $true )
= $true )
| ( ( ~ $true
| $true )
= $true )
| ( ( in @ SV4 @ ( setadjoin @ SV1 @ SV3 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[54]) ).
thf(65,plain,
! [SV3: $i,SV1: $i,SV4: $i] :
( ( ( ~ $false )
= $true )
| ( ( ~ $false
| $false )
= $true )
| ( ( in @ SV4 @ ( setadjoin @ SV1 @ SV3 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[55]) ).
thf(66,plain,
! [SV1: $i,SV3: $i,SV4: $i,SV9: $o] :
( ( SV9 = $true )
| ( ( in @ SV4 @ SV3 )
= $true )
| ( ( SV4 = SV1 )
= $true )
| ( ( in @ SV4 @ ( setadjoin @ SV1 @ SV3 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[56]) ).
thf(67,plain,
! [SV1: $i,SV3: $i,SV4: $i] :
( ( $true = $true )
| ( ( in @ SV4 @ SV3 )
= $true )
| ( ( SV4 = SV1 )
= $true )
| ( ( in @ SV4 @ ( setadjoin @ SV1 @ SV3 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[56]) ).
thf(68,plain,
! [SV1: $i,SV3: $i,SV4: $i] :
( ( $false = $true )
| ( ( in @ SV4 @ SV3 )
= $true )
| ( ( SV4 = SV1 )
= $true )
| ( ( in @ SV4 @ ( setadjoin @ SV1 @ SV3 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[56]) ).
thf(69,plain,
! [SV3: $i,SV1: $i,SV4: $i,SV8: $o] :
( ( ( ~ SV8 )
= $true )
| ( SV8 = $true )
| ( ( SV4 = SV1 )
= $true )
| ( ( in @ SV4 @ ( setadjoin @ SV1 @ SV3 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[57]) ).
thf(70,plain,
! [SV3: $i,SV1: $i,SV4: $i] :
( ( ( ~ $true )
= $true )
| ( $true = $true )
| ( ( SV4 = SV1 )
= $true )
| ( ( in @ SV4 @ ( setadjoin @ SV1 @ SV3 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[58]) ).
thf(71,plain,
! [SV3: $i,SV1: $i,SV4: $i] :
( ( ( ~ $false )
= $true )
| ( $false = $true )
| ( ( SV4 = SV1 )
= $true )
| ( ( in @ SV4 @ ( setadjoin @ SV1 @ SV3 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[59]) ).
thf(72,plain,
! [SV1: $i,SV3: $i,SV4: $i,SV6: $o] :
( ( SV6 = $false )
| ( ( ( in @ SV4 @ SV3 )
| SV6 )
= $true )
| ( ( in @ SV4 @ ( setadjoin @ SV1 @ SV3 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(73,plain,
! [SV1: $i,SV3: $i,SV4: $i] :
( ( $true = $false )
| ( ( ( in @ SV4 @ SV3 )
| $true )
= $true )
| ( ( in @ SV4 @ ( setadjoin @ SV1 @ SV3 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(74,plain,
! [SV1: $i,SV3: $i,SV4: $i] :
( ( $false = $false )
| ( ( ( in @ SV4 @ SV3 )
| $false )
= $true )
| ( ( in @ SV4 @ ( setadjoin @ SV1 @ SV3 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(75,plain,
! [SV3: $i,SV1: $i,SV4: $i,SV7: $o] :
( ( SV7 = $false )
| ( ( ~ SV7
| SV7 )
= $true )
| ( ( in @ SV4 @ ( setadjoin @ SV1 @ SV3 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(76,plain,
! [SV3: $i,SV1: $i,SV4: $i] :
( ( $true = $false )
| ( ( ~ $true
| $true )
= $true )
| ( ( in @ SV4 @ ( setadjoin @ SV1 @ SV3 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(77,plain,
! [SV3: $i,SV1: $i,SV4: $i] :
( ( $false = $false )
| ( ( ~ $false
| $false )
= $true )
| ( ( in @ SV4 @ ( setadjoin @ SV1 @ SV3 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(78,plain,
! [SV3: $i,SV1: $i,SV4: $i,SV8: $o] :
( ( SV8 = $false )
| ( SV8 = $true )
| ( ( SV4 = SV1 )
= $true )
| ( ( in @ SV4 @ ( setadjoin @ SV1 @ SV3 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(79,plain,
! [SV3: $i,SV1: $i,SV4: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( SV4 = SV1 )
= $true )
| ( ( in @ SV4 @ ( setadjoin @ SV1 @ SV3 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(80,plain,
! [SV3: $i,SV1: $i,SV4: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( SV4 = SV1 )
= $true )
| ( ( in @ SV4 @ ( setadjoin @ SV1 @ SV3 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(81,plain,
! [SV1: $i,SV6: $o,SV3: $i,SV4: $i] :
( ( ( in @ SV4 @ SV3 )
= $true )
| ( SV6 = $true )
| ( SV6 = $false )
| ( ( in @ SV4 @ ( setadjoin @ SV1 @ SV3 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[72]) ).
thf(82,plain,
! [SV1: $i,SV3: $i,SV4: $i] :
( ( ( in @ SV4 @ SV3 )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV4 @ ( setadjoin @ SV1 @ SV3 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[73]) ).
thf(83,plain,
! [SV1: $i,SV3: $i,SV4: $i] :
( ( ( in @ SV4 @ SV3 )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV4 @ ( setadjoin @ SV1 @ SV3 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[74]) ).
thf(84,plain,
! [SV3: $i,SV1: $i,SV4: $i,SV7: $o] :
( ( ( ~ SV7 )
= $true )
| ( SV7 = $true )
| ( SV7 = $false )
| ( ( in @ SV4 @ ( setadjoin @ SV1 @ SV3 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[75]) ).
thf(85,plain,
! [SV3: $i,SV1: $i,SV4: $i] :
( ( ( ~ $true )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV4 @ ( setadjoin @ SV1 @ SV3 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[76]) ).
thf(86,plain,
! [SV3: $i,SV1: $i,SV4: $i] :
( ( ( ~ $false )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV4 @ ( setadjoin @ SV1 @ SV3 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[77]) ).
thf(87,plain,
! [SV3: $i,SV1: $i,SV4: $i,SV7: $o] :
( ( SV7 = $false )
| ( SV7 = $true )
| ( SV7 = $false )
| ( ( in @ SV4 @ ( setadjoin @ SV1 @ SV3 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[84]) ).
thf(88,plain,
! [SV3: $i,SV1: $i,SV4: $i] :
( ( $true = $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV4 @ ( setadjoin @ SV1 @ SV3 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[85]) ).
thf(89,plain,
! [SV3: $i,SV1: $i,SV4: $i] :
( ( $false = $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV4 @ ( setadjoin @ SV1 @ SV3 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(90,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[24,89,88,87,83,82,81,80,79,78,68,67,66,30,29,28,27]) ).
thf(91,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[90]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SEU527^2 : TPTP v8.1.0. Released v3.7.0.
% 0.03/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n025.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jun 19 18:56:44 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33
% 0.12/0.33 No.of.Axioms: 0
% 0.12/0.33
% 0.12/0.33 Length.of.Defs: 408
% 0.12/0.33
% 0.12/0.33 Contains.Choice.Funs: false
% 0.12/0.34 (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).....
% 0.18/0.39
% 0.18/0.39 ********************************
% 0.18/0.39 * All subproblems solved! *
% 0.18/0.39 ********************************
% 0.18/0.39 % SZS status Theorem for /export/starexec/sandbox2/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:10,ordering:none,proof_output:1,protocol_output:false,clause_count:90,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.18/0.39
% 0.18/0.39 %**** Beginning of derivation protocol ****
% 0.18/0.39 % SZS output start CNFRefutation
% See solution above
% 0.18/0.39
% 0.18/0.39 %**** End of derivation protocol ****
% 0.18/0.39 %**** no. of clauses in derivation: 91 ****
% 0.18/0.39 %**** clause counter: 90 ****
% 0.18/0.39
% 0.18/0.39 % SZS status Theorem for /export/starexec/sandbox2/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:10,ordering:none,proof_output:1,protocol_output:false,clause_count:90,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------