%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : NUM835+1 : TPTP v9.3.1. Released v4.1.0.
% 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 : n012.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 10:35:19 AM UTC 2026
% Result : Theorem 0.76s 0.29s
% Output : CNFRefutation 0.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 19
% Syntax : Number of formulae : 215 ( 131 unt; 0 typ; 0 def)
% Number of atoms : 1036 ( 712 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 1559 ( 476 ~; 224 |; 12 &; 826 @)
% ( 3 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 590 ( 0 ^; 550 !; 40 ?; 590 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_m,type,
m: $i > $o ).
thf(tp_sK1_SY75,type,
sK1_SY75: $i > $i > $i ).
thf(tp_sK2_SY76,type,
sK2_SY76: $i > $i > $i ).
thf(tp_v1,type,
v1: $i ).
thf(tp_vd151,type,
vd151: $i ).
thf(tp_vd165,type,
vd165: $i ).
thf(tp_vplus,type,
vplus: $i > $i > $i ).
thf(tp_vskolem2,type,
vskolem2: $i > $i ).
thf(tp_vskolem3,type,
vskolem3: $i ).
thf(tp_vsucc,type,
vsucc: $i > $i ).
thf(7,axiom,
! [Vd46: $i,Vd47: $i,Vd48: $i] :
( ( vplus @ ( vplus @ Vd46 @ Vd47 ) @ Vd48 )
= ( vplus @ Vd46 @ ( vplus @ Vd47 @ Vd48 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(33, 0), 0)') ).
thf(9,axiom,
! [Vd68: $i,Vd69: $i] :
( ( vplus @ ( vsucc @ Vd68 ) @ Vd69 )
= ( vsucc @ ( vplus @ Vd68 @ Vd69 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(52, 0), 0)') ).
thf(10,axiom,
! [Vd78: $i,Vd79: $i] :
( ( vplus @ Vd79 @ Vd78 )
= ( vplus @ Vd78 @ Vd79 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
thf(11,axiom,
! [Vd92: $i,Vd93: $i] :
( Vd93
!= ( vplus @ Vd92 @ Vd93 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(73, 0), 0)') ).
thf(12,axiom,
! [Vd104: $i,Vd105: $i] :
( ( Vd104 != Vd105 )
=> ! [Vd107: $i] :
( ( vplus @ Vd107 @ Vd104 )
!= ( vplus @ Vd107 @ Vd105 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(81, 0), 0)') ).
thf(13,axiom,
! [Vd127: $i,Vd128: $i] :
~ ? [Vd130: $i] :
( ( Vd127
= ( vplus @ Vd128 @ Vd130 ) )
& ( Vd127 = Vd128 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(97), 0), 3)') ).
thf(14,axiom,
! [Vd127: $i,Vd128: $i] :
~ ? [Vd133: $i] :
( ( Vd128
= ( vplus @ Vd127 @ Vd133 ) )
& ( Vd127 = Vd128 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(97), 0), 2)') ).
thf(15,axiom,
! [Vd127: $i,Vd128: $i,Vd135: $i,Vd137: $i] :
~ ( ( Vd128
= ( vplus @ Vd127 @ Vd137 ) )
& ( Vd127
= ( vplus @ Vd128 @ Vd135 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(97), 0), 1)') ).
thf(16,axiom,
! [Vd127: $i,Vd128: $i] :
~ ? [Vd140: $i,Vd142: $i] :
( ( Vd128
= ( vplus @ Vd127 @ Vd142 ) )
& ( Vd127
= ( vplus @ Vd128 @ Vd140 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(97), 0), 0)') ).
thf(17,axiom,
! [Vd144: $i,Vd145: $i] :
( ( Vd144 != Vd145 )
| ~ ? [Vd147: $i] :
( Vd144
= ( vplus @ Vd145 @ Vd147 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(104, 0), 2)') ).
thf(18,axiom,
! [Vd144: $i,Vd145: $i] :
( ~ ? [Vd147: $i] :
( Vd144
= ( vplus @ Vd145 @ Vd147 ) )
| ~ ? [Vd149: $i] :
( Vd145
= ( vplus @ Vd144 @ Vd149 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(104, 0), 1)') ).
thf(19,axiom,
! [Vd144: $i,Vd145: $i] :
( ( Vd144 != Vd145 )
| ~ ? [Vd149: $i] :
( Vd145
= ( vplus @ Vd144 @ Vd149 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(104, 0), 0)') ).
thf(20,axiom,
! [Vd151: $i,Vd152: $i] :
( ( m @ Vd152 )
<=> ( ( Vd151 = Vd152 )
| ? [Vd155: $i] :
( Vd151
= ( vplus @ Vd152 @ Vd155 ) )
| ? [Vd157: $i] :
( Vd152
= ( vplus @ Vd151 @ Vd157 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(105), 0), 1)') ).
thf(23,axiom,
m @ vd165,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(110, 166, 0)') ).
thf(25,axiom,
( ( vd151 = vd165 )
=> ( ( vplus @ vd165 @ v1 )
= ( vplus @ vd151 @ v1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(110), 0), 1)') ).
thf(27,axiom,
! [Vd170: $i] :
( ( vd151
= ( vplus @ vd165 @ Vd170 ) )
=> ( ( Vd170 = v1 )
=> ( vd151
= ( vplus @ vd165 @ v1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(110), 1), 8)') ).
thf(36,axiom,
! [Vd180: $i] :
( ( vd165
= ( vplus @ vd151 @ Vd180 ) )
=> ( ( vsucc @ vd165 )
= ( vsucc @ ( vplus @ vd151 @ Vd180 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(110), 2), 2)') ).
thf(37,axiom,
! [Vd180: $i] :
( ( vd165
= ( vplus @ vd151 @ Vd180 ) )
=> ( ( vsucc @ ( vplus @ vd151 @ Vd180 ) )
= ( vplus @ vd151 @ ( vsucc @ Vd180 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(110), 2), 1)') ).
thf(39,conjecture,
( ? [Vd180: $i] :
( vd165
= ( vplus @ vd151 @ Vd180 ) )
| ? [Vd170: $i] :
( vd151
= ( vplus @ vd165 @ Vd170 ) )
| ( vd151 = vd165 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dis(case_distinction(conseq(110)))') ).
thf(40,negated_conjecture,
( ( ? [Vd180: $i] :
( vd165
= ( vplus @ vd151 @ Vd180 ) )
| ? [Vd170: $i] :
( vd151
= ( vplus @ vd165 @ Vd170 ) )
| ( vd151 = vd165 ) )
= $false ),
inference(negate_conjecture,[status(cth)],[39]) ).
thf(41,plain,
( ( ? [Vd180: $i] :
( vd165
= ( vplus @ vd151 @ Vd180 ) )
| ? [Vd170: $i] :
( vd151
= ( vplus @ vd165 @ Vd170 ) )
| ( vd151 = vd165 ) )
= $false ),
inference(unfold_def,[status(thm)],[40]) ).
thf(42,plain,
( ( ! [Vd46: $i,Vd47: $i,Vd48: $i] :
( ( vplus @ ( vplus @ Vd46 @ Vd47 ) @ Vd48 )
= ( vplus @ Vd46 @ ( vplus @ Vd47 @ Vd48 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(43,plain,
( ( ! [Vd68: $i,Vd69: $i] :
( ( vplus @ ( vsucc @ Vd68 ) @ Vd69 )
= ( vsucc @ ( vplus @ Vd68 @ Vd69 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(44,plain,
( ( ! [Vd78: $i,Vd79: $i] :
( ( vplus @ Vd79 @ Vd78 )
= ( vplus @ Vd78 @ Vd79 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(45,plain,
( ( ! [Vd92: $i,Vd93: $i] :
( Vd93
!= ( vplus @ Vd92 @ Vd93 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(46,plain,
( ( ! [Vd104: $i,Vd105: $i] :
( ( Vd104 != Vd105 )
=> ! [Vd107: $i] :
( ( vplus @ Vd107 @ Vd104 )
!= ( vplus @ Vd107 @ Vd105 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(47,plain,
( ( ! [Vd127: $i,Vd128: $i] :
~ ? [Vd130: $i] :
( ( Vd127
= ( vplus @ Vd128 @ Vd130 ) )
& ( Vd127 = Vd128 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(48,plain,
( ( ! [Vd127: $i,Vd128: $i] :
~ ? [Vd133: $i] :
( ( Vd128
= ( vplus @ Vd127 @ Vd133 ) )
& ( Vd127 = Vd128 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(49,plain,
( ( ! [Vd127: $i,Vd128: $i,Vd135: $i,Vd137: $i] :
~ ( ( Vd128
= ( vplus @ Vd127 @ Vd137 ) )
& ( Vd127
= ( vplus @ Vd128 @ Vd135 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(50,plain,
( ( ! [Vd127: $i,Vd128: $i] :
~ ? [Vd140: $i,Vd142: $i] :
( ( Vd128
= ( vplus @ Vd127 @ Vd142 ) )
& ( Vd127
= ( vplus @ Vd128 @ Vd140 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(51,plain,
( ( ! [Vd144: $i,Vd145: $i] :
( ( Vd144 != Vd145 )
| ~ ? [Vd147: $i] :
( Vd144
= ( vplus @ Vd145 @ Vd147 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(52,plain,
( ( ! [Vd144: $i,Vd145: $i] :
( ~ ? [Vd147: $i] :
( Vd144
= ( vplus @ Vd145 @ Vd147 ) )
| ~ ? [Vd149: $i] :
( Vd145
= ( vplus @ Vd144 @ Vd149 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(53,plain,
( ( ! [Vd144: $i,Vd145: $i] :
( ( Vd144 != Vd145 )
| ~ ? [Vd149: $i] :
( Vd145
= ( vplus @ Vd144 @ Vd149 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(54,plain,
( ( ! [Vd151: $i,Vd152: $i] :
( ( m @ Vd152 )
<=> ( ( Vd151 = Vd152 )
| ? [Vd155: $i] :
( Vd151
= ( vplus @ Vd152 @ Vd155 ) )
| ? [Vd157: $i] :
( Vd152
= ( vplus @ Vd151 @ Vd157 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(55,plain,
( ( m @ vd165 )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(56,plain,
( ( ( vd151 = vd165 )
=> ( ( vplus @ vd165 @ v1 )
= ( vplus @ vd151 @ v1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(57,plain,
( ( ! [Vd170: $i] :
( ( vd151
= ( vplus @ vd165 @ Vd170 ) )
=> ( ( Vd170 = v1 )
=> ( vd151
= ( vplus @ vd165 @ v1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(58,plain,
( ( ! [Vd180: $i] :
( ( vd165
= ( vplus @ vd151 @ Vd180 ) )
=> ( ( vsucc @ vd165 )
= ( vsucc @ ( vplus @ vd151 @ Vd180 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(59,plain,
( ( ! [Vd180: $i] :
( ( vd165
= ( vplus @ vd151 @ Vd180 ) )
=> ( ( vsucc @ ( vplus @ vd151 @ Vd180 ) )
= ( vplus @ vd151 @ ( vsucc @ Vd180 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(60,plain,
( ( ~ ( ? [Vd180: $i] :
( vd165
= ( vplus @ vd151 @ Vd180 ) )
| ? [Vd170: $i] :
( vd151
= ( vplus @ vd165 @ Vd170 ) )
| ( vd151 = vd165 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[41]) ).
thf(61,plain,
( ( ! [Vd180: $i] :
( ( vd165
= ( vplus @ vd151 @ Vd180 ) )
=> ( ( vsucc @ ( vplus @ vd151 @ Vd180 ) )
= ( vplus @ vd151 @ ( vsucc @ Vd180 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(62,plain,
( ( ! [Vd180: $i] :
( ( vd165
= ( vplus @ vd151 @ Vd180 ) )
=> ( ( vsucc @ vd165 )
= ( vsucc @ ( vplus @ vd151 @ Vd180 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(63,plain,
( ( ! [Vd170: $i] :
( ( vd151
= ( vplus @ vd165 @ Vd170 ) )
=> ( ( Vd170 = v1 )
=> ( vd151
= ( vplus @ vd165 @ v1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(64,plain,
( ( ( vd151 = vd165 )
=> ( ( vplus @ vd165 @ v1 )
= ( vplus @ vd151 @ v1 ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(65,plain,
( ( m @ vd165 )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(66,plain,
( ( ! [Vd151: $i,Vd152: $i] :
( ( m @ Vd152 )
<=> ( ( Vd151 = Vd152 )
| ? [Vd155: $i] :
( Vd151
= ( vplus @ Vd152 @ Vd155 ) )
| ? [Vd157: $i] :
( Vd152
= ( vplus @ Vd151 @ Vd157 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(67,plain,
( ( ! [Vd144: $i,Vd145: $i] :
( ( Vd144 != Vd145 )
| ~ ? [Vd149: $i] :
( Vd145
= ( vplus @ Vd144 @ Vd149 ) ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(68,plain,
( ( ! [Vd144: $i,Vd145: $i] :
( ~ ? [Vd147: $i] :
( Vd144
= ( vplus @ Vd145 @ Vd147 ) )
| ~ ? [Vd149: $i] :
( Vd145
= ( vplus @ Vd144 @ Vd149 ) ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(69,plain,
( ( ! [Vd144: $i,Vd145: $i] :
( ( Vd144 != Vd145 )
| ~ ? [Vd147: $i] :
( Vd144
= ( vplus @ Vd145 @ Vd147 ) ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(70,plain,
( ( ! [Vd127: $i,Vd128: $i] :
~ ? [Vd140: $i,Vd142: $i] :
( ( Vd128
= ( vplus @ Vd127 @ Vd142 ) )
& ( Vd127
= ( vplus @ Vd128 @ Vd140 ) ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(71,plain,
( ( ! [Vd127: $i,Vd128: $i,Vd135: $i,Vd137: $i] :
~ ( ( Vd128
= ( vplus @ Vd127 @ Vd137 ) )
& ( Vd127
= ( vplus @ Vd128 @ Vd135 ) ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(72,plain,
( ( ! [Vd127: $i,Vd128: $i] :
~ ? [Vd133: $i] :
( ( Vd128
= ( vplus @ Vd127 @ Vd133 ) )
& ( Vd127 = Vd128 ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(73,plain,
( ( ! [Vd127: $i,Vd128: $i] :
~ ? [Vd130: $i] :
( ( Vd127
= ( vplus @ Vd128 @ Vd130 ) )
& ( Vd127 = Vd128 ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(74,plain,
( ( ! [Vd104: $i,Vd105: $i] :
( ( Vd104 != Vd105 )
=> ! [Vd107: $i] :
( ( vplus @ Vd107 @ Vd104 )
!= ( vplus @ Vd107 @ Vd105 ) ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(75,plain,
( ( ! [Vd92: $i,Vd93: $i] :
( Vd93
!= ( vplus @ Vd92 @ Vd93 ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(76,plain,
( ( ! [Vd78: $i,Vd79: $i] :
( ( vplus @ Vd79 @ Vd78 )
= ( vplus @ Vd78 @ Vd79 ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(77,plain,
( ( ! [Vd68: $i,Vd69: $i] :
( ( vplus @ ( vsucc @ Vd68 ) @ Vd69 )
= ( vsucc @ ( vplus @ Vd68 @ Vd69 ) ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(78,plain,
( ( ! [Vd46: $i,Vd47: $i,Vd48: $i] :
( ( vplus @ ( vplus @ Vd46 @ Vd47 ) @ Vd48 )
= ( vplus @ Vd46 @ ( vplus @ Vd47 @ Vd48 ) ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(79,plain,
( ( ~ ( ? [Vd180: $i] :
( vd165
= ( vplus @ vd151 @ Vd180 ) )
| ? [Vd170: $i] :
( vd151
= ( vplus @ vd165 @ Vd170 ) )
| ( vd151 = vd165 ) ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(80,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( m @ SX1 )
| ( SX0 = SX1 )
| ~ ! [SX2: $i] :
( SX0
!= ( vplus @ SX1 @ SX2 ) )
| ~ ! [SX2: $i] :
( SX1
!= ( vplus @ SX0 @ SX2 ) ) )
| ~ ( ~ ( ( SX0 = SX1 )
| ~ ! [SX2: $i] :
( SX0
!= ( vplus @ SX1 @ SX2 ) )
| ~ ! [SX2: $i] :
( SX1
!= ( vplus @ SX0 @ SX2 ) ) )
| ( m @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(81,plain,
( ( ( vd151 != vd165 )
| ( ( vplus @ vd165 @ v1 )
= ( vplus @ vd151 @ v1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(82,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ~ ! [SX2: $i] :
~ ~ ( ( SX1
!= ( vplus @ SX0 @ SX2 ) )
| ( SX0 != SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(83,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ~ ! [SX2: $i] :
~ ~ ( ( SX0
!= ( vplus @ SX1 @ SX2 ) )
| ( SX0 != SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(84,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ~ ( ( SX1
!= ( vplus @ SX0 @ SX3 ) )
| ( SX0
!= ( vplus @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(85,plain,
( ( ! [SX0: $i,SX1: $i] :
( SX1
!= ( vplus @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(86,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ( SX0 != SX1 ) )
| ! [SX2: $i] :
( ( vplus @ SX2 @ SX0 )
!= ( vplus @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(87,plain,
( ( ! [SX0: $i] :
( ( vd165
!= ( vplus @ vd151 @ SX0 ) )
| ( ( vsucc @ ( vplus @ vd151 @ SX0 ) )
= ( vplus @ vd151 @ ( vsucc @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(88,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ~ ! [SX2: $i] :
( SX1
!= ( vplus @ SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(89,plain,
( ( ! [SX0: $i] :
( ( vd151
!= ( vplus @ vd165 @ SX0 ) )
| ( SX0 != v1 )
| ( vd151
= ( vplus @ vd165 @ v1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(90,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ! [SX2: $i] :
( SX0
!= ( vplus @ SX1 @ SX2 ) )
| ~ ~ ! [SX2: $i] :
( SX1
!= ( vplus @ SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(91,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ~ ! [SX2: $i] :
~ ~ ! [SX3: $i] :
~ ~ ( ( SX1
!= ( vplus @ SX0 @ SX3 ) )
| ( SX0
!= ( vplus @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(92,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ~ ! [SX2: $i] :
( SX0
!= ( vplus @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(93,plain,
( ( ~ ( ~ ! [SX0: $i] :
( vd165
!= ( vplus @ vd151 @ SX0 ) )
| ~ ! [SX0: $i] :
( vd151
!= ( vplus @ vd165 @ SX0 ) )
| ( vd151 = vd165 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(94,plain,
( ( ! [SX0: $i] :
( ( vd165
!= ( vplus @ vd151 @ SX0 ) )
| ( ( vsucc @ vd165 )
= ( vsucc @ ( vplus @ vd151 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(95,plain,
! [SV1: $i] :
( ( ! [SY45: $i] :
( ( vplus @ SY45 @ SV1 )
= ( vplus @ SV1 @ SY45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(96,plain,
! [SV2: $i] :
( ( ! [SY46: $i] :
( ( vplus @ ( vsucc @ SV2 ) @ SY46 )
= ( vsucc @ ( vplus @ SV2 @ SY46 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(97,plain,
! [SV3: $i] :
( ( ! [SY47: $i,SY48: $i] :
( ( vplus @ ( vplus @ SV3 @ SY47 ) @ SY48 )
= ( vplus @ SV3 @ ( vplus @ SY47 @ SY48 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(98,plain,
! [SV4: $i] :
( ( ! [SY49: $i] :
~ ( ~ ( ~ ( m @ SY49 )
| ( SV4 = SY49 )
| ~ ! [SY50: $i] :
( SV4
!= ( vplus @ SY49 @ SY50 ) )
| ~ ! [SY51: $i] :
( SY49
!= ( vplus @ SV4 @ SY51 ) ) )
| ~ ( ~ ( ( SV4 = SY49 )
| ~ ! [SY52: $i] :
( SV4
!= ( vplus @ SY49 @ SY52 ) )
| ~ ! [SY53: $i] :
( SY49
!= ( vplus @ SV4 @ SY53 ) ) )
| ( m @ SY49 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(99,plain,
( ( ( vd151 != vd165 )
= $true )
| ( ( ( vplus @ vd165 @ v1 )
= ( vplus @ vd151 @ v1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[81]) ).
thf(100,plain,
! [SV5: $i] :
( ( ! [SY54: $i] :
~ ~ ! [SY55: $i] :
~ ~ ( ( SY54
!= ( vplus @ SV5 @ SY55 ) )
| ( SV5 != SY54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(101,plain,
! [SV6: $i] :
( ( ! [SY56: $i] :
~ ~ ! [SY57: $i] :
~ ~ ( ( SV6
!= ( vplus @ SY56 @ SY57 ) )
| ( SV6 != SY56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(102,plain,
! [SV7: $i] :
( ( ! [SY58: $i,SY59: $i,SY60: $i] :
~ ~ ( ( SY58
!= ( vplus @ SV7 @ SY60 ) )
| ( SV7
!= ( vplus @ SY58 @ SY59 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(103,plain,
! [SV8: $i] :
( ( ! [SY61: $i] :
( SY61
!= ( vplus @ SV8 @ SY61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(104,plain,
! [SV9: $i] :
( ( ! [SY62: $i] :
( ~ ( ( SV9 != SY62 ) )
| ! [SY63: $i] :
( ( vplus @ SY63 @ SV9 )
!= ( vplus @ SY63 @ SY62 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(105,plain,
! [SV10: $i] :
( ( ( vd165
!= ( vplus @ vd151 @ SV10 ) )
| ( ( vsucc @ ( vplus @ vd151 @ SV10 ) )
= ( vplus @ vd151 @ ( vsucc @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(106,plain,
! [SV11: $i] :
( ( ! [SY64: $i] :
( ( SV11 != SY64 )
| ~ ~ ! [SY65: $i] :
( SY64
!= ( vplus @ SV11 @ SY65 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(107,plain,
! [SV12: $i] :
( ( ( vd151
!= ( vplus @ vd165 @ SV12 ) )
| ( SV12 != v1 )
| ( vd151
= ( vplus @ vd165 @ v1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(108,plain,
! [SV13: $i] :
( ( ! [SY66: $i] :
( ~ ~ ! [SY67: $i] :
( SV13
!= ( vplus @ SY66 @ SY67 ) )
| ~ ~ ! [SY68: $i] :
( SY66
!= ( vplus @ SV13 @ SY68 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(109,plain,
! [SV14: $i] :
( ( ! [SY69: $i] :
~ ~ ! [SY70: $i] :
~ ~ ! [SY71: $i] :
~ ~ ( ( SY69
!= ( vplus @ SV14 @ SY71 ) )
| ( SV14
!= ( vplus @ SY69 @ SY70 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(110,plain,
! [SV15: $i] :
( ( ! [SY72: $i] :
( ( SV15 != SY72 )
| ~ ~ ! [SY73: $i] :
( SV15
!= ( vplus @ SY72 @ SY73 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(111,plain,
( ( ~ ! [SX0: $i] :
( vd165
!= ( vplus @ vd151 @ SX0 ) )
| ~ ! [SX0: $i] :
( vd151
!= ( vplus @ vd165 @ SX0 ) )
| ( vd151 = vd165 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(112,plain,
! [SV16: $i] :
( ( ( vd165
!= ( vplus @ vd151 @ SV16 ) )
| ( ( vsucc @ vd165 )
= ( vsucc @ ( vplus @ vd151 @ SV16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(113,plain,
! [SV1: $i,SV17: $i] :
( ( ( vplus @ SV17 @ SV1 )
= ( vplus @ SV1 @ SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(114,plain,
! [SV18: $i,SV2: $i] :
( ( ( vplus @ ( vsucc @ SV2 ) @ SV18 )
= ( vsucc @ ( vplus @ SV2 @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(115,plain,
! [SV19: $i,SV3: $i] :
( ( ! [SY74: $i] :
( ( vplus @ ( vplus @ SV3 @ SV19 ) @ SY74 )
= ( vplus @ SV3 @ ( vplus @ SV19 @ SY74 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(116,plain,
! [SV4: $i,SV20: $i] :
( ( ~ ( ~ ( ~ ( m @ SV20 )
| ( SV4 = SV20 )
| ~ ! [SY75: $i] :
( SV4
!= ( vplus @ SV20 @ SY75 ) )
| ~ ! [SY76: $i] :
( SV20
!= ( vplus @ SV4 @ SY76 ) ) )
| ~ ( ~ ( ( SV4 = SV20 )
| ~ ! [SY77: $i] :
( SV4
!= ( vplus @ SV20 @ SY77 ) )
| ~ ! [SY78: $i] :
( SV20
!= ( vplus @ SV4 @ SY78 ) ) )
| ( m @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(117,plain,
( ( ( vd151 = vd165 )
= $false )
| ( ( ( vplus @ vd165 @ v1 )
= ( vplus @ vd151 @ v1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(118,plain,
! [SV5: $i,SV21: $i] :
( ( ~ ~ ! [SY79: $i] :
~ ~ ( ( SV21
!= ( vplus @ SV5 @ SY79 ) )
| ( SV5 != SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(119,plain,
! [SV22: $i,SV6: $i] :
( ( ~ ~ ! [SY80: $i] :
~ ~ ( ( SV6
!= ( vplus @ SV22 @ SY80 ) )
| ( SV6 != SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(120,plain,
! [SV7: $i,SV23: $i] :
( ( ! [SY81: $i,SY82: $i] :
~ ~ ( ( SV23
!= ( vplus @ SV7 @ SY82 ) )
| ( SV7
!= ( vplus @ SV23 @ SY81 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(121,plain,
! [SV8: $i,SV24: $i] :
( ( SV24
!= ( vplus @ SV8 @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(122,plain,
! [SV25: $i,SV9: $i] :
( ( ~ ( ( SV9 != SV25 ) )
| ! [SY83: $i] :
( ( vplus @ SY83 @ SV9 )
!= ( vplus @ SY83 @ SV25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(123,plain,
! [SV10: $i] :
( ( ( vd165
!= ( vplus @ vd151 @ SV10 ) )
= $true )
| ( ( ( vsucc @ ( vplus @ vd151 @ SV10 ) )
= ( vplus @ vd151 @ ( vsucc @ SV10 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[105]) ).
thf(124,plain,
! [SV26: $i,SV11: $i] :
( ( ( SV11 != SV26 )
| ~ ~ ! [SY84: $i] :
( SV26
!= ( vplus @ SV11 @ SY84 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(125,plain,
! [SV12: $i] :
( ( ( vd151
!= ( vplus @ vd165 @ SV12 ) )
= $true )
| ( ( ( SV12 != v1 )
| ( vd151
= ( vplus @ vd165 @ v1 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[107]) ).
thf(126,plain,
! [SV27: $i,SV13: $i] :
( ( ~ ~ ! [SY85: $i] :
( SV13
!= ( vplus @ SV27 @ SY85 ) )
| ~ ~ ! [SY86: $i] :
( SV27
!= ( vplus @ SV13 @ SY86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(127,plain,
! [SV14: $i,SV28: $i] :
( ( ~ ~ ! [SY87: $i] :
~ ~ ! [SY88: $i] :
~ ~ ( ( SV28
!= ( vplus @ SV14 @ SY88 ) )
| ( SV14
!= ( vplus @ SV28 @ SY87 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(128,plain,
! [SV29: $i,SV15: $i] :
( ( ( SV15 != SV29 )
| ~ ~ ! [SY89: $i] :
( SV15
!= ( vplus @ SV29 @ SY89 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(129,plain,
( ( ~ ! [SX0: $i] :
( vd165
!= ( vplus @ vd151 @ SX0 ) )
| ~ ! [SX0: $i] :
( vd151
!= ( vplus @ vd165 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[111]) ).
thf(130,plain,
( ( vd151 = vd165 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[111]) ).
thf(131,plain,
! [SV16: $i] :
( ( ( vd165
!= ( vplus @ vd151 @ SV16 ) )
= $true )
| ( ( ( vsucc @ vd165 )
= ( vsucc @ ( vplus @ vd151 @ SV16 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[112]) ).
thf(132,plain,
! [SV30: $i,SV19: $i,SV3: $i] :
( ( ( vplus @ ( vplus @ SV3 @ SV19 ) @ SV30 )
= ( vplus @ SV3 @ ( vplus @ SV19 @ SV30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(133,plain,
! [SV4: $i,SV20: $i] :
( ( ~ ( ~ ( m @ SV20 )
| ( SV4 = SV20 )
| ~ ! [SY75: $i] :
( SV4
!= ( vplus @ SV20 @ SY75 ) )
| ~ ! [SY76: $i] :
( SV20
!= ( vplus @ SV4 @ SY76 ) ) )
| ~ ( ~ ( ( SV4 = SV20 )
| ~ ! [SY77: $i] :
( SV4
!= ( vplus @ SV20 @ SY77 ) )
| ~ ! [SY78: $i] :
( SV20
!= ( vplus @ SV4 @ SY78 ) ) )
| ( m @ SV20 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(134,plain,
! [SV5: $i,SV21: $i] :
( ( ~ ! [SY79: $i] :
~ ~ ( ( SV21
!= ( vplus @ SV5 @ SY79 ) )
| ( SV5 != SV21 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(135,plain,
! [SV22: $i,SV6: $i] :
( ( ~ ! [SY80: $i] :
~ ~ ( ( SV6
!= ( vplus @ SV22 @ SY80 ) )
| ( SV6 != SV22 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(136,plain,
! [SV31: $i,SV7: $i,SV23: $i] :
( ( ! [SY90: $i] :
~ ~ ( ( SV23
!= ( vplus @ SV7 @ SY90 ) )
| ( SV7
!= ( vplus @ SV23 @ SV31 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(137,plain,
! [SV8: $i,SV24: $i] :
( ( SV24
= ( vplus @ SV8 @ SV24 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[121]) ).
thf(138,plain,
! [SV25: $i,SV9: $i] :
( ( ( ~ ( ( SV9 != SV25 ) ) )
= $true )
| ( ( ! [SY83: $i] :
( ( vplus @ SY83 @ SV9 )
!= ( vplus @ SY83 @ SV25 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[122]) ).
thf(139,plain,
! [SV10: $i] :
( ( ( vd165
= ( vplus @ vd151 @ SV10 ) )
= $false )
| ( ( ( vsucc @ ( vplus @ vd151 @ SV10 ) )
= ( vplus @ vd151 @ ( vsucc @ SV10 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(140,plain,
! [SV26: $i,SV11: $i] :
( ( ( SV11 != SV26 )
= $true )
| ( ( ~ ~ ! [SY84: $i] :
( SV26
!= ( vplus @ SV11 @ SY84 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[124]) ).
thf(141,plain,
! [SV12: $i] :
( ( ( vd151
= ( vplus @ vd165 @ SV12 ) )
= $false )
| ( ( ( SV12 != v1 )
| ( vd151
= ( vplus @ vd165 @ v1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(142,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ~ ! [SY85: $i] :
( SV13
!= ( vplus @ SV27 @ SY85 ) ) )
= $true )
| ( ( ~ ~ ! [SY86: $i] :
( SV27
!= ( vplus @ SV13 @ SY86 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[126]) ).
thf(143,plain,
! [SV14: $i,SV28: $i] :
( ( ~ ! [SY87: $i] :
~ ~ ! [SY88: $i] :
~ ~ ( ( SV28
!= ( vplus @ SV14 @ SY88 ) )
| ( SV14
!= ( vplus @ SV28 @ SY87 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[127]) ).
thf(144,plain,
! [SV29: $i,SV15: $i] :
( ( ( SV15 != SV29 )
= $true )
| ( ( ~ ~ ! [SY89: $i] :
( SV15
!= ( vplus @ SV29 @ SY89 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[128]) ).
thf(145,plain,
( ( ~ ! [SX0: $i] :
( vd165
!= ( vplus @ vd151 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[129]) ).
thf(146,plain,
( ( ~ ! [SX0: $i] :
( vd151
!= ( vplus @ vd165 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[129]) ).
thf(147,plain,
! [SV16: $i] :
( ( ( vd165
= ( vplus @ vd151 @ SV16 ) )
= $false )
| ( ( ( vsucc @ vd165 )
= ( vsucc @ ( vplus @ vd151 @ SV16 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(148,plain,
! [SV4: $i,SV20: $i] :
( ( ~ ( ~ ( m @ SV20 )
| ( SV4 = SV20 )
| ~ ! [SY75: $i] :
( SV4
!= ( vplus @ SV20 @ SY75 ) )
| ~ ! [SY76: $i] :
( SV20
!= ( vplus @ SV4 @ SY76 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[133]) ).
thf(149,plain,
! [SV20: $i,SV4: $i] :
( ( ~ ( ~ ( ( SV4 = SV20 )
| ~ ! [SY77: $i] :
( SV4
!= ( vplus @ SV20 @ SY77 ) )
| ~ ! [SY78: $i] :
( SV20
!= ( vplus @ SV4 @ SY78 ) ) )
| ( m @ SV20 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[133]) ).
thf(150,plain,
! [SV5: $i,SV21: $i] :
( ( ! [SY79: $i] :
~ ~ ( ( SV21
!= ( vplus @ SV5 @ SY79 ) )
| ( SV5 != SV21 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[134]) ).
thf(151,plain,
! [SV22: $i,SV6: $i] :
( ( ! [SY80: $i] :
~ ~ ( ( SV6
!= ( vplus @ SV22 @ SY80 ) )
| ( SV6 != SV22 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[135]) ).
thf(152,plain,
! [SV31: $i,SV32: $i,SV7: $i,SV23: $i] :
( ( ~ ~ ( ( SV23
!= ( vplus @ SV7 @ SV32 ) )
| ( SV7
!= ( vplus @ SV23 @ SV31 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(153,plain,
! [SV25: $i,SV9: $i] :
( ( ( SV9 != SV25 )
= $false )
| ( ( ! [SY83: $i] :
( ( vplus @ SY83 @ SV9 )
!= ( vplus @ SY83 @ SV25 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(154,plain,
! [SV26: $i,SV11: $i] :
( ( ( SV11 = SV26 )
= $false )
| ( ( ~ ~ ! [SY84: $i] :
( SV26
!= ( vplus @ SV11 @ SY84 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(155,plain,
! [SV12: $i] :
( ( ( SV12 != v1 )
= $true )
| ( ( vd151
= ( vplus @ vd165 @ v1 ) )
= $true )
| ( ( vd151
= ( vplus @ vd165 @ SV12 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[141]) ).
thf(156,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ! [SY85: $i] :
( SV13
!= ( vplus @ SV27 @ SY85 ) ) )
= $false )
| ( ( ~ ~ ! [SY86: $i] :
( SV27
!= ( vplus @ SV13 @ SY86 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(157,plain,
! [SV14: $i,SV28: $i] :
( ( ! [SY87: $i] :
~ ~ ! [SY88: $i] :
~ ~ ( ( SV28
!= ( vplus @ SV14 @ SY88 ) )
| ( SV14
!= ( vplus @ SV28 @ SY87 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[143]) ).
thf(158,plain,
! [SV29: $i,SV15: $i] :
( ( ( SV15 = SV29 )
= $false )
| ( ( ~ ~ ! [SY89: $i] :
( SV15
!= ( vplus @ SV29 @ SY89 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(159,plain,
( ( ! [SX0: $i] :
( vd165
!= ( vplus @ vd151 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[145]) ).
thf(160,plain,
( ( ! [SX0: $i] :
( vd151
!= ( vplus @ vd165 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[146]) ).
thf(161,plain,
! [SV4: $i,SV20: $i] :
( ( ~ ( m @ SV20 )
| ( SV4 = SV20 )
| ~ ! [SY75: $i] :
( SV4
!= ( vplus @ SV20 @ SY75 ) )
| ~ ! [SY76: $i] :
( SV20
!= ( vplus @ SV4 @ SY76 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[148]) ).
thf(162,plain,
! [SV20: $i,SV4: $i] :
( ( ~ ( ( SV4 = SV20 )
| ~ ! [SY77: $i] :
( SV4
!= ( vplus @ SV20 @ SY77 ) )
| ~ ! [SY78: $i] :
( SV20
!= ( vplus @ SV4 @ SY78 ) ) )
| ( m @ SV20 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[149]) ).
thf(163,plain,
! [SV33: $i,SV5: $i,SV21: $i] :
( ( ~ ~ ( ( SV21
!= ( vplus @ SV5 @ SV33 ) )
| ( SV5 != SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(164,plain,
! [SV34: $i,SV22: $i,SV6: $i] :
( ( ~ ~ ( ( SV6
!= ( vplus @ SV22 @ SV34 ) )
| ( SV6 != SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(165,plain,
! [SV31: $i,SV32: $i,SV7: $i,SV23: $i] :
( ( ~ ( ( SV23
!= ( vplus @ SV7 @ SV32 ) )
| ( SV7
!= ( vplus @ SV23 @ SV31 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(166,plain,
! [SV25: $i,SV9: $i] :
( ( ( SV9 = SV25 )
= $true )
| ( ( ! [SY83: $i] :
( ( vplus @ SY83 @ SV9 )
!= ( vplus @ SY83 @ SV25 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[153]) ).
thf(167,plain,
! [SV11: $i,SV26: $i] :
( ( ( ~ ! [SY84: $i] :
( SV26
!= ( vplus @ SV11 @ SY84 ) ) )
= $false )
| ( ( SV11 = SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[154]) ).
thf(168,plain,
! [SV12: $i] :
( ( ( SV12 = v1 )
= $false )
| ( ( vd151
= ( vplus @ vd165 @ v1 ) )
= $true )
| ( ( vd151
= ( vplus @ vd165 @ SV12 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(169,plain,
! [SV27: $i,SV13: $i] :
( ( ( ! [SY85: $i] :
( SV13
!= ( vplus @ SV27 @ SY85 ) ) )
= $true )
| ( ( ~ ~ ! [SY86: $i] :
( SV27
!= ( vplus @ SV13 @ SY86 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[156]) ).
thf(170,plain,
! [SV35: $i,SV14: $i,SV28: $i] :
( ( ~ ~ ! [SY91: $i] :
~ ~ ( ( SV28
!= ( vplus @ SV14 @ SY91 ) )
| ( SV14
!= ( vplus @ SV28 @ SV35 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(171,plain,
! [SV29: $i,SV15: $i] :
( ( ( ~ ! [SY89: $i] :
( SV15
!= ( vplus @ SV29 @ SY89 ) ) )
= $false )
| ( ( SV15 = SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[158]) ).
thf(172,plain,
! [SV36: $i] :
( ( vd165
!= ( vplus @ vd151 @ SV36 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(173,plain,
! [SV37: $i] :
( ( vd151
!= ( vplus @ vd165 @ SV37 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(174,plain,
! [SV4: $i,SV20: $i] :
( ( ( ~ ( m @ SV20 ) )
= $true )
| ( ( ( SV4 = SV20 )
| ~ ! [SY75: $i] :
( SV4
!= ( vplus @ SV20 @ SY75 ) )
| ~ ! [SY76: $i] :
( SV20
!= ( vplus @ SV4 @ SY76 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[161]) ).
thf(175,plain,
! [SV20: $i,SV4: $i] :
( ( ( ~ ( ( SV4 = SV20 )
| ~ ! [SY77: $i] :
( SV4
!= ( vplus @ SV20 @ SY77 ) )
| ~ ! [SY78: $i] :
( SV20
!= ( vplus @ SV4 @ SY78 ) ) ) )
= $true )
| ( ( m @ SV20 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[162]) ).
thf(176,plain,
! [SV33: $i,SV5: $i,SV21: $i] :
( ( ~ ( ( SV21
!= ( vplus @ SV5 @ SV33 ) )
| ( SV5 != SV21 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[163]) ).
thf(177,plain,
! [SV34: $i,SV22: $i,SV6: $i] :
( ( ~ ( ( SV6
!= ( vplus @ SV22 @ SV34 ) )
| ( SV6 != SV22 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(178,plain,
! [SV31: $i,SV32: $i,SV7: $i,SV23: $i] :
( ( ( SV23
!= ( vplus @ SV7 @ SV32 ) )
| ( SV7
!= ( vplus @ SV23 @ SV31 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[165]) ).
thf(179,plain,
! [SV25: $i,SV9: $i,SV38: $i] :
( ( ( ( vplus @ SV38 @ SV9 )
!= ( vplus @ SV38 @ SV25 ) )
= $true )
| ( ( SV9 = SV25 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(180,plain,
! [SV11: $i,SV26: $i] :
( ( ( ! [SY84: $i] :
( SV26
!= ( vplus @ SV11 @ SY84 ) ) )
= $true )
| ( ( SV11 = SV26 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[167]) ).
thf(181,plain,
! [SV39: $i,SV27: $i,SV13: $i] :
( ( ( SV13
!= ( vplus @ SV27 @ SV39 ) )
= $true )
| ( ( ~ ~ ! [SY86: $i] :
( SV27
!= ( vplus @ SV13 @ SY86 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[169]) ).
thf(182,plain,
! [SV35: $i,SV14: $i,SV28: $i] :
( ( ~ ! [SY91: $i] :
~ ~ ( ( SV28
!= ( vplus @ SV14 @ SY91 ) )
| ( SV14
!= ( vplus @ SV28 @ SV35 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(183,plain,
! [SV29: $i,SV15: $i] :
( ( ( ! [SY89: $i] :
( SV15
!= ( vplus @ SV29 @ SY89 ) ) )
= $true )
| ( ( SV15 = SV29 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[171]) ).
thf(184,plain,
! [SV36: $i] :
( ( vd165
= ( vplus @ vd151 @ SV36 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(185,plain,
! [SV37: $i] :
( ( vd151
= ( vplus @ vd165 @ SV37 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[173]) ).
thf(186,plain,
! [SV4: $i,SV20: $i] :
( ( ( m @ SV20 )
= $false )
| ( ( ( SV4 = SV20 )
| ~ ! [SY75: $i] :
( SV4
!= ( vplus @ SV20 @ SY75 ) )
| ~ ! [SY76: $i] :
( SV20
!= ( vplus @ SV4 @ SY76 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[174]) ).
thf(187,plain,
! [SV20: $i,SV4: $i] :
( ( ( ( SV4 = SV20 )
| ~ ! [SY77: $i] :
( SV4
!= ( vplus @ SV20 @ SY77 ) )
| ~ ! [SY78: $i] :
( SV20
!= ( vplus @ SV4 @ SY78 ) ) )
= $false )
| ( ( m @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[175]) ).
thf(188,plain,
! [SV33: $i,SV5: $i,SV21: $i] :
( ( ( SV21
!= ( vplus @ SV5 @ SV33 ) )
| ( SV5 != SV21 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[176]) ).
thf(189,plain,
! [SV34: $i,SV22: $i,SV6: $i] :
( ( ( SV6
!= ( vplus @ SV22 @ SV34 ) )
| ( SV6 != SV22 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[177]) ).
thf(190,plain,
! [SV31: $i,SV32: $i,SV7: $i,SV23: $i] :
( ( ( SV23
!= ( vplus @ SV7 @ SV32 ) )
= $true )
| ( ( SV7
!= ( vplus @ SV23 @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[178]) ).
thf(191,plain,
! [SV25: $i,SV9: $i,SV38: $i] :
( ( ( ( vplus @ SV38 @ SV9 )
= ( vplus @ SV38 @ SV25 ) )
= $false )
| ( ( SV9 = SV25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(192,plain,
! [SV40: $i,SV11: $i,SV26: $i] :
( ( ( SV26
!= ( vplus @ SV11 @ SV40 ) )
= $true )
| ( ( SV11 = SV26 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(193,plain,
! [SV39: $i,SV27: $i,SV13: $i] :
( ( ( SV13
= ( vplus @ SV27 @ SV39 ) )
= $false )
| ( ( ~ ~ ! [SY86: $i] :
( SV27
!= ( vplus @ SV13 @ SY86 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[181]) ).
thf(194,plain,
! [SV35: $i,SV14: $i,SV28: $i] :
( ( ! [SY91: $i] :
~ ~ ( ( SV28
!= ( vplus @ SV14 @ SY91 ) )
| ( SV14
!= ( vplus @ SV28 @ SV35 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[182]) ).
thf(195,plain,
! [SV41: $i,SV29: $i,SV15: $i] :
( ( ( SV15
!= ( vplus @ SV29 @ SV41 ) )
= $true )
| ( ( SV15 = SV29 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(196,plain,
! [SV20: $i,SV4: $i] :
( ( ( ( SV4 = SV20 )
| ~ ! [SY75: $i] :
( SV4
!= ( vplus @ SV20 @ SY75 ) ) )
= $true )
| ( ( ~ ! [SY76: $i] :
( SV20
!= ( vplus @ SV4 @ SY76 ) ) )
= $true )
| ( ( m @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[186]) ).
thf(197,plain,
! [SV20: $i,SV4: $i] :
( ( ( ( SV4 = SV20 )
| ~ ! [SY77: $i] :
( SV4
!= ( vplus @ SV20 @ SY77 ) ) )
= $false )
| ( ( m @ SV20 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[187]) ).
thf(198,plain,
! [SV4: $i,SV20: $i] :
( ( ( ~ ! [SY78: $i] :
( SV20
!= ( vplus @ SV4 @ SY78 ) ) )
= $false )
| ( ( m @ SV20 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[187]) ).
thf(199,plain,
! [SV33: $i,SV5: $i,SV21: $i] :
( ( ( SV21
!= ( vplus @ SV5 @ SV33 ) )
= $true )
| ( ( SV5 != SV21 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[188]) ).
thf(200,plain,
! [SV34: $i,SV22: $i,SV6: $i] :
( ( ( SV6
!= ( vplus @ SV22 @ SV34 ) )
= $true )
| ( ( SV6 != SV22 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[189]) ).
thf(201,plain,
! [SV31: $i,SV32: $i,SV7: $i,SV23: $i] :
( ( ( SV23
= ( vplus @ SV7 @ SV32 ) )
= $false )
| ( ( SV7
!= ( vplus @ SV23 @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[190]) ).
thf(202,plain,
! [SV40: $i,SV11: $i,SV26: $i] :
( ( ( SV26
= ( vplus @ SV11 @ SV40 ) )
= $false )
| ( ( SV11 = SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(203,plain,
! [SV39: $i,SV13: $i,SV27: $i] :
( ( ( ~ ! [SY86: $i] :
( SV27
!= ( vplus @ SV13 @ SY86 ) ) )
= $false )
| ( ( SV13
= ( vplus @ SV27 @ SV39 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(204,plain,
! [SV35: $i,SV42: $i,SV14: $i,SV28: $i] :
( ( ~ ~ ( ( SV28
!= ( vplus @ SV14 @ SV42 ) )
| ( SV14
!= ( vplus @ SV28 @ SV35 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[194]) ).
thf(205,plain,
! [SV41: $i,SV29: $i,SV15: $i] :
( ( ( SV15
= ( vplus @ SV29 @ SV41 ) )
= $false )
| ( ( SV15 = SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(206,plain,
! [SV20: $i,SV4: $i] :
( ( ( SV4 = SV20 )
= $true )
| ( ( ~ ! [SY75: $i] :
( SV4
!= ( vplus @ SV20 @ SY75 ) ) )
= $true )
| ( ( ~ ! [SY76: $i] :
( SV20
!= ( vplus @ SV4 @ SY76 ) ) )
= $true )
| ( ( m @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[196]) ).
thf(207,plain,
! [SV20: $i,SV4: $i] :
( ( ( SV4 = SV20 )
= $false )
| ( ( m @ SV20 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[197]) ).
thf(208,plain,
! [SV20: $i,SV4: $i] :
( ( ( ~ ! [SY77: $i] :
( SV4
!= ( vplus @ SV20 @ SY77 ) ) )
= $false )
| ( ( m @ SV20 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[197]) ).
thf(209,plain,
! [SV4: $i,SV20: $i] :
( ( ( ! [SY78: $i] :
( SV20
!= ( vplus @ SV4 @ SY78 ) ) )
= $true )
| ( ( m @ SV20 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[198]) ).
thf(210,plain,
! [SV33: $i,SV5: $i,SV21: $i] :
( ( ( SV21
= ( vplus @ SV5 @ SV33 ) )
= $false )
| ( ( SV5 != SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[199]) ).
thf(211,plain,
! [SV34: $i,SV22: $i,SV6: $i] :
( ( ( SV6
= ( vplus @ SV22 @ SV34 ) )
= $false )
| ( ( SV6 != SV22 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[200]) ).
thf(212,plain,
! [SV32: $i,SV31: $i,SV23: $i,SV7: $i] :
( ( ( SV7
= ( vplus @ SV23 @ SV31 ) )
= $false )
| ( ( SV23
= ( vplus @ SV7 @ SV32 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(213,plain,
! [SV39: $i,SV13: $i,SV27: $i] :
( ( ( ! [SY86: $i] :
( SV27
!= ( vplus @ SV13 @ SY86 ) ) )
= $true )
| ( ( SV13
= ( vplus @ SV27 @ SV39 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[203]) ).
thf(214,plain,
! [SV35: $i,SV42: $i,SV14: $i,SV28: $i] :
( ( ~ ( ( SV28
!= ( vplus @ SV14 @ SV42 ) )
| ( SV14
!= ( vplus @ SV28 @ SV35 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(215,plain,
! [SV20: $i,SV4: $i] :
( ( ( ! [SY75: $i] :
( SV4
!= ( vplus @ SV20 @ SY75 ) ) )
= $false )
| ( ( SV4 = SV20 )
= $true )
| ( ( ~ ! [SY76: $i] :
( SV20
!= ( vplus @ SV4 @ SY76 ) ) )
= $true )
| ( ( m @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[206]) ).
thf(216,plain,
! [SV20: $i,SV4: $i] :
( ( ( ! [SY77: $i] :
( SV4
!= ( vplus @ SV20 @ SY77 ) ) )
= $true )
| ( ( m @ SV20 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[208]) ).
thf(217,plain,
! [SV43: $i,SV4: $i,SV20: $i] :
( ( ( SV20
!= ( vplus @ SV4 @ SV43 ) )
= $true )
| ( ( m @ SV20 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[209]) ).
thf(218,plain,
! [SV33: $i,SV21: $i,SV5: $i] :
( ( ( SV5 = SV21 )
= $false )
| ( ( SV21
= ( vplus @ SV5 @ SV33 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[210]) ).
thf(219,plain,
! [SV34: $i,SV22: $i,SV6: $i] :
( ( ( SV6 = SV22 )
= $false )
| ( ( SV6
= ( vplus @ SV22 @ SV34 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[211]) ).
thf(220,plain,
! [SV39: $i,SV44: $i,SV13: $i,SV27: $i] :
( ( ( SV27
!= ( vplus @ SV13 @ SV44 ) )
= $true )
| ( ( SV13
= ( vplus @ SV27 @ SV39 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[213]) ).
thf(221,plain,
! [SV35: $i,SV42: $i,SV14: $i,SV28: $i] :
( ( ( SV28
!= ( vplus @ SV14 @ SV42 ) )
| ( SV14
!= ( vplus @ SV28 @ SV35 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[214]) ).
thf(222,plain,
! [SV20: $i,SV4: $i] :
( ( ( SV4
!= ( vplus @ SV20 @ ( sK1_SY75 @ SV20 @ SV4 ) ) )
= $false )
| ( ( SV4 = SV20 )
= $true )
| ( ( ~ ! [SY76: $i] :
( SV20
!= ( vplus @ SV4 @ SY76 ) ) )
= $true )
| ( ( m @ SV20 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[215]) ).
thf(223,plain,
! [SV45: $i,SV20: $i,SV4: $i] :
( ( ( SV4
!= ( vplus @ SV20 @ SV45 ) )
= $true )
| ( ( m @ SV20 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[216]) ).
thf(224,plain,
! [SV43: $i,SV4: $i,SV20: $i] :
( ( ( SV20
= ( vplus @ SV4 @ SV43 ) )
= $false )
| ( ( m @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[217]) ).
thf(225,plain,
! [SV39: $i,SV44: $i,SV13: $i,SV27: $i] :
( ( ( SV27
= ( vplus @ SV13 @ SV44 ) )
= $false )
| ( ( SV13
= ( vplus @ SV27 @ SV39 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[220]) ).
thf(226,plain,
! [SV35: $i,SV42: $i,SV14: $i,SV28: $i] :
( ( ( SV28
!= ( vplus @ SV14 @ SV42 ) )
= $true )
| ( ( SV14
!= ( vplus @ SV28 @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[221]) ).
thf(227,plain,
! [SV20: $i,SV4: $i] :
( ( ( SV4
= ( vplus @ SV20 @ ( sK1_SY75 @ SV20 @ SV4 ) ) )
= $true )
| ( ( SV4 = SV20 )
= $true )
| ( ( ~ ! [SY76: $i] :
( SV20
!= ( vplus @ SV4 @ SY76 ) ) )
= $true )
| ( ( m @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[222]) ).
thf(228,plain,
! [SV45: $i,SV20: $i,SV4: $i] :
( ( ( SV4
= ( vplus @ SV20 @ SV45 ) )
= $false )
| ( ( m @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[223]) ).
thf(229,plain,
! [SV35: $i,SV42: $i,SV14: $i,SV28: $i] :
( ( ( SV28
= ( vplus @ SV14 @ SV42 ) )
= $false )
| ( ( SV14
!= ( vplus @ SV28 @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[226]) ).
thf(230,plain,
! [SV4: $i,SV20: $i] :
( ( ( ! [SY76: $i] :
( SV20
!= ( vplus @ SV4 @ SY76 ) ) )
= $false )
| ( ( SV4 = SV20 )
= $true )
| ( ( SV4
= ( vplus @ SV20 @ ( sK1_SY75 @ SV20 @ SV4 ) ) )
= $true )
| ( ( m @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[227]) ).
thf(231,plain,
! [SV42: $i,SV35: $i,SV28: $i,SV14: $i] :
( ( ( SV14
= ( vplus @ SV28 @ SV35 ) )
= $false )
| ( ( SV28
= ( vplus @ SV14 @ SV42 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[229]) ).
thf(232,plain,
! [SV4: $i,SV20: $i] :
( ( ( SV20
!= ( vplus @ SV4 @ ( sK2_SY76 @ SV4 @ SV20 ) ) )
= $false )
| ( ( SV4 = SV20 )
= $true )
| ( ( SV4
= ( vplus @ SV20 @ ( sK1_SY75 @ SV20 @ SV4 ) ) )
= $true )
| ( ( m @ SV20 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[230]) ).
thf(233,plain,
! [SV4: $i,SV20: $i] :
( ( ( SV20
= ( vplus @ SV4 @ ( sK2_SY76 @ SV4 @ SV20 ) ) )
= $true )
| ( ( SV4 = SV20 )
= $true )
| ( ( SV4
= ( vplus @ SV20 @ ( sK1_SY75 @ SV20 @ SV4 ) ) )
= $true )
| ( ( m @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[232]) ).
thf(234,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[65,233,231,228,225,224,219,218,212,207,205,202,191,185,184,168,147,139,137,132,130,117,114,113]) ).
thf(235,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[234]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM835+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.02 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.00/0.11 % Computer : n012.cluster.edu
% 0.00/0.11 % Model : x86_64 x86_64
% 0.00/0.11 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.11 % Memory : 8046.5625MB
% 0.00/0.11 % OS : Linux 6.8.0-71-generic
% 0.00/0.11 % CPULimit : 300
% 0.00/0.11 % WCLimit : 300
% 0.00/0.11 % DateTime : Tue Oct 6 13:40:01 UTC 2026
% 0.00/0.11 % CPUTime :
% 0.00/0.11 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.76/0.29
% 0.76/0.29 No.of.Axioms: 18
% 0.76/0.29
% 0.76/0.29 Length.of.Defs: 0
% 0.76/0.29
% 0.76/0.29 Contains.Choice.Funs: false
% 0.76/0.29 ......
% 0.76/0.29
% 0.76/0.29 ********************************
% 0.76/0.29 * All subproblems solved! *
% 0.76/0.29 ********************************
% 0.76/0.29 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:18,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:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:234,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.76/0.29
% 0.76/0.29 %**** Beginning of derivation protocol ****
% 0.76/0.29 % SZS output start CNFRefutation
% See solution above
% 0.76/0.29
% 0.76/0.29 %**** End of derivation protocol ****
% 0.76/0.29 %**** no. of clauses in derivation: 215 ****
% 0.76/0.29 %**** clause counter: 234 ****
% 0.76/0.29
% 0.76/0.29 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:18,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:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:234,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------