TSTP Solution File: NUM835+1 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : NUM835+1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n020.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 : Mon Jul 18 11:55:50 EDT 2022
% Result : Theorem 1.08s 1.26s
% Output : CNFRefutation 1.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 51
% Syntax : Number of formulae : 390 ( 228 unt; 12 typ; 0 def)
% Number of atoms : 1940 (1346 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 2945 ( 552 ~; 474 |; 38 &;1821 @)
% ( 2 <=>; 58 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 739 ( 0 ^ 709 !; 30 ?; 739 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_m,type,
m: $i > $o ).
thf(tp_sK1_Vd155,type,
sK1_Vd155: $i > $i > $i ).
thf(tp_sK2_Vd157,type,
sK2_Vd157: $i > $i > $i ).
thf(tp_sK3_Vd162,type,
sK3_Vd162: $i > $i ).
thf(tp_sK4_Vd162,type,
sK4_Vd162: $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(1,axiom,
! [Vd1: $i] :
( ( vsucc @ Vd1 )
!= v1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(restrictor(axiom(1)), holds(scope(axiom(1)), 2, 0))') ).
thf(2,axiom,
! [Vd3: $i,Vd4: $i] :
( ( ( vsucc @ Vd3 )
= ( vsucc @ Vd4 ) )
=> ( Vd3 = Vd4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(antec(axiom(3)), imp(antec(axiom(3))))') ).
thf(3,axiom,
! [Vd7: $i,Vd8: $i] :
( ( Vd7 != Vd8 )
=> ( ( vsucc @ Vd7 )
!= ( vsucc @ Vd8 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(6, 0), 0)') ).
thf(4,axiom,
! [Vd16: $i] :
( ( vsucc @ Vd16 )
!= Vd16 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(12, 0), 0)') ).
thf(5,axiom,
! [Vd24: $i] :
( ( Vd24 != v1 )
=> ( Vd24
= ( vsucc @ ( vskolem2 @ Vd24 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(20, 0), 0)') ).
thf(6,axiom,
! [Vd42: $i,Vd43: $i] :
( ( ( vplus @ Vd42 @ ( vsucc @ Vd43 ) )
= ( vsucc @ ( vplus @ Vd42 @ Vd43 ) ) )
& ( ( vplus @ Vd42 @ v1 )
= ( vsucc @ Vd42 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))') ).
thf(7,axiom,
! [Vd46: $i,Vd47: $i,Vd48: $i] :
( ( vplus @ ( vplus @ Vd46 @ Vd47 ) @ Vd48 )
= ( vplus @ Vd46 @ ( vplus @ Vd47 @ Vd48 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(33, 0), 0)') ).
thf(8,axiom,
! [Vd59: $i] :
( ( vplus @ v1 @ Vd59 )
= ( vsucc @ Vd59 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(43, 0), 0)') ).
thf(9,axiom,
! [Vd68: $i,Vd69: $i] :
( ( vplus @ ( vsucc @ Vd68 ) @ Vd69 )
= ( vsucc @ ( vplus @ Vd68 @ Vd69 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(52, 0), 0)') ).
thf(10,axiom,
! [Vd78: $i,Vd79: $i] :
( ( vplus @ Vd79 @ Vd78 )
= ( vplus @ Vd78 @ Vd79 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
thf(11,axiom,
! [Vd92: $i,Vd93: $i] :
( Vd93
!= ( vplus @ Vd92 @ Vd93 ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p','def(cond(conseq(105), 0), 1)') ).
thf(21,axiom,
! [Vd159: $i] :
( ( Vd159 = v1 )
=> ( ( ( v1 = Vd159 )
& ( vd151 = v1 ) )
| ? [Vd162: $i] :
( ( ( vplus @ v1 @ Vd162 )
= ( vplus @ Vd159 @ Vd162 ) )
& ( ( vsucc @ Vd162 )
= ( vplus @ v1 @ Vd162 ) )
& ( vd151
= ( vsucc @ Vd162 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(conseq(105), 1), 0)') ).
thf(22,axiom,
m @ v1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(109, 164, 0)') ).
thf(23,axiom,
m @ vd165,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(110, 166, 0)') ).
thf(24,axiom,
( ( vd151 = vd165 )
=> ( ( vsucc @ vd165 )
= ( vplus @ vd165 @ v1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(conseq(110), 0), 2)') ).
thf(25,axiom,
( ( vd151 = vd165 )
=> ( ( vplus @ vd165 @ v1 )
= ( vplus @ vd151 @ v1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(conseq(110), 0), 1)') ).
thf(26,axiom,
( ( vd151 = vd165 )
=> ( m @ ( vsucc @ vd165 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(conseq(110), 0), 0)') ).
thf(27,axiom,
! [Vd170: $i] :
( ( vd151
= ( vplus @ vd165 @ Vd170 ) )
=> ( ( Vd170 = v1 )
=> ( vd151
= ( vplus @ vd165 @ v1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(conseq(110), 1), 8)') ).
thf(28,axiom,
! [Vd170: $i] :
( ( vd151
= ( vplus @ vd165 @ Vd170 ) )
=> ( ( Vd170 = v1 )
=> ( ( vplus @ vd165 @ v1 )
= ( vsucc @ vd165 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(conseq(110), 1), 7)') ).
thf(29,axiom,
! [Vd170: $i] :
( ( vd151
= ( vplus @ vd165 @ Vd170 ) )
=> ( ( Vd170 = v1 )
=> ( m @ ( vsucc @ vd165 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(conseq(110), 1), 6)') ).
thf(30,axiom,
! [Vd170: $i] :
( ( vd151
= ( vplus @ vd165 @ Vd170 ) )
=> ( ( Vd170 != v1 )
=> ( Vd170
= ( vsucc @ vskolem3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(conseq(110), 1), 5)') ).
thf(31,axiom,
! [Vd170: $i] :
( ( vd151
= ( vplus @ vd165 @ Vd170 ) )
=> ( ( Vd170 != v1 )
=> ( ( vsucc @ vskolem3 )
= ( vplus @ v1 @ vskolem3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(conseq(110), 1), 4)') ).
thf(32,axiom,
! [Vd170: $i] :
( ( vd151
= ( vplus @ vd165 @ Vd170 ) )
=> ( ( Vd170 != v1 )
=> ( vd151
= ( vplus @ vd165 @ ( vplus @ v1 @ vskolem3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(conseq(110), 1), 3)') ).
thf(33,axiom,
! [Vd170: $i] :
( ( vd151
= ( vplus @ vd165 @ Vd170 ) )
=> ( ( Vd170 != v1 )
=> ( ( vplus @ vd165 @ ( vplus @ v1 @ vskolem3 ) )
= ( vplus @ ( vplus @ vd165 @ v1 ) @ vskolem3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(conseq(110), 1), 2)') ).
thf(34,axiom,
! [Vd170: $i] :
( ( vd151
= ( vplus @ vd165 @ Vd170 ) )
=> ( ( Vd170 != v1 )
=> ( ( vplus @ ( vplus @ vd165 @ v1 ) @ vskolem3 )
= ( vplus @ ( vsucc @ vd165 ) @ vskolem3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(conseq(110), 1), 1)') ).
thf(35,axiom,
! [Vd170: $i] :
( ( vd151
= ( vplus @ vd165 @ Vd170 ) )
=> ( ( Vd170 != v1 )
=> ( m @ ( vsucc @ vd165 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(conseq(110), 1), 0)') ).
thf(36,axiom,
! [Vd180: $i] :
( ( vd165
= ( vplus @ vd151 @ Vd180 ) )
=> ( ( vsucc @ vd165 )
= ( vsucc @ ( vplus @ vd151 @ Vd180 ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p','ass(cond(conseq(110), 2), 1)') ).
thf(38,axiom,
! [Vd180: $i] :
( ( vd165
= ( vplus @ vd151 @ Vd180 ) )
=> ( m @ ( vsucc @ vd165 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(conseq(110), 2), 0)') ).
thf(39,conjecture,
( ? [Vd180: $i] :
( vd165
= ( vplus @ vd151 @ Vd180 ) )
| ? [Vd170: $i] :
( vd151
= ( vplus @ vd165 @ Vd170 ) )
| ( vd151 = vd165 ) ),
file('/export/starexec/sandbox/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,
( ( ! [Vd1: $i] :
( ( vsucc @ Vd1 )
!= v1 ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(43,plain,
( ( ! [Vd3: $i,Vd4: $i] :
( ( ( vsucc @ Vd3 )
= ( vsucc @ Vd4 ) )
=> ( Vd3 = Vd4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(44,plain,
( ( ! [Vd7: $i,Vd8: $i] :
( ( Vd7 != Vd8 )
=> ( ( vsucc @ Vd7 )
!= ( vsucc @ Vd8 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(45,plain,
( ( ! [Vd16: $i] :
( ( vsucc @ Vd16 )
!= Vd16 ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(46,plain,
( ( ! [Vd24: $i] :
( ( Vd24 != v1 )
=> ( Vd24
= ( vsucc @ ( vskolem2 @ Vd24 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(47,plain,
( ( ! [Vd42: $i,Vd43: $i] :
( ( ( vplus @ Vd42 @ ( vsucc @ Vd43 ) )
= ( vsucc @ ( vplus @ Vd42 @ Vd43 ) ) )
& ( ( vplus @ Vd42 @ v1 )
= ( vsucc @ Vd42 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(48,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(49,plain,
( ( ! [Vd59: $i] :
( ( vplus @ v1 @ Vd59 )
= ( vsucc @ Vd59 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(50,plain,
( ( ! [Vd68: $i,Vd69: $i] :
( ( vplus @ ( vsucc @ Vd68 ) @ Vd69 )
= ( vsucc @ ( vplus @ Vd68 @ Vd69 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(51,plain,
( ( ! [Vd78: $i,Vd79: $i] :
( ( vplus @ Vd79 @ Vd78 )
= ( vplus @ Vd78 @ Vd79 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(52,plain,
( ( ! [Vd92: $i,Vd93: $i] :
( Vd93
!= ( vplus @ Vd92 @ Vd93 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(53,plain,
( ( ! [Vd104: $i,Vd105: $i] :
( ( Vd104 != Vd105 )
=> ! [Vd107: $i] :
( ( vplus @ Vd107 @ Vd104 )
!= ( vplus @ Vd107 @ Vd105 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(54,plain,
( ( ! [Vd127: $i,Vd128: $i] :
~ ? [Vd130: $i] :
( ( Vd127
= ( vplus @ Vd128 @ Vd130 ) )
& ( Vd127 = Vd128 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(55,plain,
( ( ! [Vd127: $i,Vd128: $i] :
~ ? [Vd133: $i] :
( ( Vd128
= ( vplus @ Vd127 @ Vd133 ) )
& ( Vd127 = Vd128 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(56,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(57,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(58,plain,
( ( ! [Vd144: $i,Vd145: $i] :
( ( Vd144 != Vd145 )
| ~ ? [Vd147: $i] :
( Vd144
= ( vplus @ Vd145 @ Vd147 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(59,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(60,plain,
( ( ! [Vd144: $i,Vd145: $i] :
( ( Vd144 != Vd145 )
| ~ ? [Vd149: $i] :
( Vd145
= ( vplus @ Vd144 @ Vd149 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(61,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(62,plain,
( ( ! [Vd159: $i] :
( ( Vd159 = v1 )
=> ( ( ( v1 = Vd159 )
& ( vd151 = v1 ) )
| ? [Vd162: $i] :
( ( ( vplus @ v1 @ Vd162 )
= ( vplus @ Vd159 @ Vd162 ) )
& ( ( vsucc @ Vd162 )
= ( vplus @ v1 @ Vd162 ) )
& ( vd151
= ( vsucc @ Vd162 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(63,plain,
( ( m @ v1 )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(64,plain,
( ( m @ vd165 )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(65,plain,
( ( ( vd151 = vd165 )
=> ( ( vsucc @ vd165 )
= ( vplus @ vd165 @ v1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(66,plain,
( ( ( vd151 = vd165 )
=> ( ( vplus @ vd165 @ v1 )
= ( vplus @ vd151 @ v1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(67,plain,
( ( ( vd151 = vd165 )
=> ( m @ ( vsucc @ vd165 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(68,plain,
( ( ! [Vd170: $i] :
( ( vd151
= ( vplus @ vd165 @ Vd170 ) )
=> ( ( Vd170 = v1 )
=> ( vd151
= ( vplus @ vd165 @ v1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(69,plain,
( ( ! [Vd170: $i] :
( ( vd151
= ( vplus @ vd165 @ Vd170 ) )
=> ( ( Vd170 = v1 )
=> ( ( vplus @ vd165 @ v1 )
= ( vsucc @ vd165 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(70,plain,
( ( ! [Vd170: $i] :
( ( vd151
= ( vplus @ vd165 @ Vd170 ) )
=> ( ( Vd170 = v1 )
=> ( m @ ( vsucc @ vd165 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(71,plain,
( ( ! [Vd170: $i] :
( ( vd151
= ( vplus @ vd165 @ Vd170 ) )
=> ( ( Vd170 != v1 )
=> ( Vd170
= ( vsucc @ vskolem3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(72,plain,
( ( ! [Vd170: $i] :
( ( vd151
= ( vplus @ vd165 @ Vd170 ) )
=> ( ( Vd170 != v1 )
=> ( ( vsucc @ vskolem3 )
= ( vplus @ v1 @ vskolem3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(73,plain,
( ( ! [Vd170: $i] :
( ( vd151
= ( vplus @ vd165 @ Vd170 ) )
=> ( ( Vd170 != v1 )
=> ( vd151
= ( vplus @ vd165 @ ( vplus @ v1 @ vskolem3 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(74,plain,
( ( ! [Vd170: $i] :
( ( vd151
= ( vplus @ vd165 @ Vd170 ) )
=> ( ( Vd170 != v1 )
=> ( ( vplus @ vd165 @ ( vplus @ v1 @ vskolem3 ) )
= ( vplus @ ( vplus @ vd165 @ v1 ) @ vskolem3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(75,plain,
( ( ! [Vd170: $i] :
( ( vd151
= ( vplus @ vd165 @ Vd170 ) )
=> ( ( Vd170 != v1 )
=> ( ( vplus @ ( vplus @ vd165 @ v1 ) @ vskolem3 )
= ( vplus @ ( vsucc @ vd165 ) @ vskolem3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(76,plain,
( ( ! [Vd170: $i] :
( ( vd151
= ( vplus @ vd165 @ Vd170 ) )
=> ( ( Vd170 != v1 )
=> ( m @ ( vsucc @ vd165 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(77,plain,
( ( ! [Vd180: $i] :
( ( vd165
= ( vplus @ vd151 @ Vd180 ) )
=> ( ( vsucc @ vd165 )
= ( vsucc @ ( vplus @ vd151 @ Vd180 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(78,plain,
( ( ! [Vd180: $i] :
( ( vd165
= ( vplus @ vd151 @ Vd180 ) )
=> ( ( vsucc @ ( vplus @ vd151 @ Vd180 ) )
= ( vplus @ vd151 @ ( vsucc @ Vd180 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(79,plain,
( ( ! [Vd180: $i] :
( ( vd165
= ( vplus @ vd151 @ Vd180 ) )
=> ( m @ ( vsucc @ vd165 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(80,plain,
( ( ~ ( ? [Vd180: $i] :
( vd165
= ( vplus @ vd151 @ Vd180 ) )
| ? [Vd170: $i] :
( vd151
= ( vplus @ vd165 @ Vd170 ) )
| ( vd151 = vd165 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[41]) ).
thf(81,plain,
( ( ( vd151 != vd165 )
& ! [Vd180: $i] :
( vd165
!= ( vplus @ vd151 @ Vd180 ) )
& ! [Vd170: $i] :
( vd151
!= ( vplus @ vd165 @ Vd170 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[80]) ).
thf(82,plain,
( ( ! [Vd1: $i] :
( ( vsucc @ Vd1 )
!= v1 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[42]) ).
thf(83,plain,
( ( ! [Vd3: $i,Vd4: $i] :
( ( ( vsucc @ Vd3 )
!= ( vsucc @ Vd4 ) )
| ( Vd3 = Vd4 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[43]) ).
thf(84,plain,
( ( ! [Vd7: $i,Vd8: $i] :
( ( Vd7 = Vd8 )
| ( ( vsucc @ Vd7 )
!= ( vsucc @ Vd8 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[44]) ).
thf(85,plain,
( ( ! [Vd16: $i] :
( ( vsucc @ Vd16 )
!= Vd16 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[45]) ).
thf(86,plain,
( ( ! [Vd24: $i] :
( ( Vd24 = v1 )
| ( Vd24
= ( vsucc @ ( vskolem2 @ Vd24 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[46]) ).
thf(87,plain,
( ( ! [Vd42: $i,Vd43: $i] :
( ( vplus @ Vd42 @ ( vsucc @ Vd43 ) )
= ( vsucc @ ( vplus @ Vd42 @ Vd43 ) ) )
& ! [Vd42: $i] :
( ( vplus @ Vd42 @ v1 )
= ( vsucc @ Vd42 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[47]) ).
thf(88,plain,
( ( ! [Vd92: $i,Vd93: $i] :
( Vd93
!= ( vplus @ Vd92 @ Vd93 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[52]) ).
thf(89,plain,
( ( ! [Vd104: $i,Vd105: $i] :
( ( Vd104 = Vd105 )
| ! [Vd107: $i] :
( ( vplus @ Vd107 @ Vd104 )
!= ( vplus @ Vd107 @ Vd105 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[53]) ).
thf(90,plain,
( ( ! [Vd127: $i,Vd128: $i] :
( ! [Vd130: $i] :
( Vd127
!= ( vplus @ Vd128 @ Vd130 ) )
| ( Vd127 != Vd128 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[54]) ).
thf(91,plain,
( ( ! [Vd127: $i,Vd128: $i] :
( ! [Vd133: $i] :
( Vd128
!= ( vplus @ Vd127 @ Vd133 ) )
| ( Vd127 != Vd128 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[55]) ).
thf(92,plain,
( ( ! [Vd127: $i,Vd128: $i] :
( ! [Vd137: $i] :
( Vd128
!= ( vplus @ Vd127 @ Vd137 ) )
| ! [Vd135: $i] :
( Vd127
!= ( vplus @ Vd128 @ Vd135 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[56]) ).
thf(93,plain,
( ( ! [Vd127: $i,Vd128: $i] :
( ! [Vd142: $i] :
( Vd128
!= ( vplus @ Vd127 @ Vd142 ) )
| ! [Vd140: $i] :
( Vd127
!= ( vplus @ Vd128 @ Vd140 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[57]) ).
thf(94,plain,
( ( ! [Vd144: $i,Vd145: $i] :
( ( Vd144 != Vd145 )
| ! [Vd147: $i] :
( Vd144
!= ( vplus @ Vd145 @ Vd147 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[58]) ).
thf(95,plain,
( ( ! [Vd144: $i,Vd145: $i] :
( ! [Vd147: $i] :
( Vd144
!= ( vplus @ Vd145 @ Vd147 ) )
| ! [Vd149: $i] :
( Vd145
!= ( vplus @ Vd144 @ Vd149 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[59]) ).
thf(96,plain,
( ( ! [Vd144: $i,Vd145: $i] :
( ( Vd144 != Vd145 )
| ! [Vd149: $i] :
( Vd145
!= ( vplus @ Vd144 @ Vd149 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[60]) ).
thf(97,plain,
( ( ! [Vd151: $i,Vd152: $i] :
( ~ ( m @ Vd152 )
| ( Vd152
= ( vplus @ Vd151 @ ( sK2_Vd157 @ Vd152 @ Vd151 ) ) )
| ( Vd151 = Vd152 )
| ( Vd151
= ( vplus @ Vd152 @ ( sK1_Vd155 @ Vd152 @ Vd151 ) ) ) )
& ! [Vd151: $i,Vd152: $i] :
( ! [Vd157: $i] :
( Vd152
!= ( vplus @ Vd151 @ Vd157 ) )
| ( m @ Vd152 ) )
& ! [Vd151: $i,Vd152: $i] :
( ( Vd151 != Vd152 )
| ( m @ Vd152 ) )
& ! [Vd151: $i,Vd152: $i] :
( ! [Vd155: $i] :
( Vd151
!= ( vplus @ Vd152 @ Vd155 ) )
| ( m @ Vd152 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[61]) ).
thf(98,plain,
( ( ! [Vd159: $i] :
( ( Vd159 != v1 )
| ( v1 = Vd159 )
| ( ( ( vplus @ v1 @ ( sK4_Vd162 @ Vd159 ) )
= ( vplus @ Vd159 @ ( sK4_Vd162 @ Vd159 ) ) )
& ( ( vsucc @ ( sK4_Vd162 @ Vd159 ) )
= ( vplus @ v1 @ ( sK4_Vd162 @ Vd159 ) ) )
& ( vd151
= ( vsucc @ ( sK4_Vd162 @ Vd159 ) ) ) ) )
& ! [Vd159: $i] :
( ( Vd159 != v1 )
| ( vd151 = v1 )
| ( ( ( vplus @ v1 @ ( sK3_Vd162 @ Vd159 ) )
= ( vplus @ Vd159 @ ( sK3_Vd162 @ Vd159 ) ) )
& ( ( vsucc @ ( sK3_Vd162 @ Vd159 ) )
= ( vplus @ v1 @ ( sK3_Vd162 @ Vd159 ) ) )
& ( vd151
= ( vsucc @ ( sK3_Vd162 @ Vd159 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[62]) ).
thf(99,plain,
( ( ( vd151 != vd165 )
| ( ( vsucc @ vd165 )
= ( vplus @ vd165 @ v1 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[65]) ).
thf(100,plain,
( ( ( vd151 != vd165 )
| ( ( vplus @ vd165 @ v1 )
= ( vplus @ vd151 @ v1 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[66]) ).
thf(101,plain,
( ( ( vd151 != vd165 )
| ( m @ ( vsucc @ vd165 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[67]) ).
thf(102,plain,
( ( ! [Vd170: $i] :
( ( vd151
!= ( vplus @ vd165 @ Vd170 ) )
| ( Vd170 != v1 )
| ( vd151
= ( vplus @ vd165 @ v1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[68]) ).
thf(103,plain,
( ( ! [Vd170: $i] :
( ( vd151
!= ( vplus @ vd165 @ Vd170 ) )
| ( Vd170 != v1 )
| ( ( vplus @ vd165 @ v1 )
= ( vsucc @ vd165 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[69]) ).
thf(104,plain,
( ( ! [Vd170: $i] :
( ( vd151
!= ( vplus @ vd165 @ Vd170 ) )
| ( Vd170 != v1 )
| ( m @ ( vsucc @ vd165 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[70]) ).
thf(105,plain,
( ( ! [Vd170: $i] :
( ( vd151
!= ( vplus @ vd165 @ Vd170 ) )
| ( Vd170 = v1 )
| ( Vd170
= ( vsucc @ vskolem3 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[71]) ).
thf(106,plain,
( ( ! [Vd170: $i] :
( ( vd151
!= ( vplus @ vd165 @ Vd170 ) )
| ( Vd170 = v1 )
| ( ( vsucc @ vskolem3 )
= ( vplus @ v1 @ vskolem3 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[72]) ).
thf(107,plain,
( ( ! [Vd170: $i] :
( ( vd151
!= ( vplus @ vd165 @ Vd170 ) )
| ( Vd170 = v1 )
| ( vd151
= ( vplus @ vd165 @ ( vplus @ v1 @ vskolem3 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[73]) ).
thf(108,plain,
( ( ! [Vd170: $i] :
( ( vd151
!= ( vplus @ vd165 @ Vd170 ) )
| ( Vd170 = v1 )
| ( ( vplus @ vd165 @ ( vplus @ v1 @ vskolem3 ) )
= ( vplus @ ( vplus @ vd165 @ v1 ) @ vskolem3 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[74]) ).
thf(109,plain,
( ( ! [Vd170: $i] :
( ( vd151
!= ( vplus @ vd165 @ Vd170 ) )
| ( Vd170 = v1 )
| ( ( vplus @ ( vplus @ vd165 @ v1 ) @ vskolem3 )
= ( vplus @ ( vsucc @ vd165 ) @ vskolem3 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[75]) ).
thf(110,plain,
( ( ! [Vd170: $i] :
( ( vd151
!= ( vplus @ vd165 @ Vd170 ) )
| ( Vd170 = v1 )
| ( m @ ( vsucc @ vd165 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[76]) ).
thf(111,plain,
( ( ! [Vd180: $i] :
( ( vd165
!= ( vplus @ vd151 @ Vd180 ) )
| ( ( vsucc @ vd165 )
= ( vsucc @ ( vplus @ vd151 @ Vd180 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[77]) ).
thf(112,plain,
( ( ! [Vd180: $i] :
( ( vd165
!= ( vplus @ vd151 @ Vd180 ) )
| ( ( vsucc @ ( vplus @ vd151 @ Vd180 ) )
= ( vplus @ vd151 @ ( vsucc @ Vd180 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[78]) ).
thf(113,plain,
( ( ! [Vd180: $i] :
( vd165
!= ( vplus @ vd151 @ Vd180 ) )
| ( m @ ( vsucc @ vd165 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[79]) ).
thf(114,plain,
( ( ! [Vd180: $i] :
( vd165
!= ( vplus @ vd151 @ Vd180 ) )
| ( m @ ( vsucc @ vd165 ) ) )
= $true ),
inference(copy,[status(thm)],[113]) ).
thf(115,plain,
( ( ! [Vd180: $i] :
( ( vd165
!= ( vplus @ vd151 @ Vd180 ) )
| ( ( vsucc @ ( vplus @ vd151 @ Vd180 ) )
= ( vplus @ vd151 @ ( vsucc @ Vd180 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[112]) ).
thf(116,plain,
( ( ! [Vd180: $i] :
( ( vd165
!= ( vplus @ vd151 @ Vd180 ) )
| ( ( vsucc @ vd165 )
= ( vsucc @ ( vplus @ vd151 @ Vd180 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[111]) ).
thf(117,plain,
( ( ! [Vd170: $i] :
( ( vd151
!= ( vplus @ vd165 @ Vd170 ) )
| ( Vd170 = v1 )
| ( m @ ( vsucc @ vd165 ) ) ) )
= $true ),
inference(copy,[status(thm)],[110]) ).
thf(118,plain,
( ( ! [Vd170: $i] :
( ( vd151
!= ( vplus @ vd165 @ Vd170 ) )
| ( Vd170 = v1 )
| ( ( vplus @ ( vplus @ vd165 @ v1 ) @ vskolem3 )
= ( vplus @ ( vsucc @ vd165 ) @ vskolem3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[109]) ).
thf(119,plain,
( ( ! [Vd170: $i] :
( ( vd151
!= ( vplus @ vd165 @ Vd170 ) )
| ( Vd170 = v1 )
| ( ( vplus @ vd165 @ ( vplus @ v1 @ vskolem3 ) )
= ( vplus @ ( vplus @ vd165 @ v1 ) @ vskolem3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(120,plain,
( ( ! [Vd170: $i] :
( ( vd151
!= ( vplus @ vd165 @ Vd170 ) )
| ( Vd170 = v1 )
| ( vd151
= ( vplus @ vd165 @ ( vplus @ v1 @ vskolem3 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(121,plain,
( ( ! [Vd170: $i] :
( ( vd151
!= ( vplus @ vd165 @ Vd170 ) )
| ( Vd170 = v1 )
| ( ( vsucc @ vskolem3 )
= ( vplus @ v1 @ vskolem3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[106]) ).
thf(122,plain,
( ( ! [Vd170: $i] :
( ( vd151
!= ( vplus @ vd165 @ Vd170 ) )
| ( Vd170 = v1 )
| ( Vd170
= ( vsucc @ vskolem3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[105]) ).
thf(123,plain,
( ( ! [Vd170: $i] :
( ( vd151
!= ( vplus @ vd165 @ Vd170 ) )
| ( Vd170 != v1 )
| ( m @ ( vsucc @ vd165 ) ) ) )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(124,plain,
( ( ! [Vd170: $i] :
( ( vd151
!= ( vplus @ vd165 @ Vd170 ) )
| ( Vd170 != v1 )
| ( ( vplus @ vd165 @ v1 )
= ( vsucc @ vd165 ) ) ) )
= $true ),
inference(copy,[status(thm)],[103]) ).
thf(125,plain,
( ( ! [Vd170: $i] :
( ( vd151
!= ( vplus @ vd165 @ Vd170 ) )
| ( Vd170 != v1 )
| ( vd151
= ( vplus @ vd165 @ v1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(126,plain,
( ( ( vd151 != vd165 )
| ( m @ ( vsucc @ vd165 ) ) )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(127,plain,
( ( ( vd151 != vd165 )
| ( ( vplus @ vd165 @ v1 )
= ( vplus @ vd151 @ v1 ) ) )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(128,plain,
( ( ( vd151 != vd165 )
| ( ( vsucc @ vd165 )
= ( vplus @ vd165 @ v1 ) ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(129,plain,
( ( m @ vd165 )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(130,plain,
( ( m @ v1 )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(131,plain,
( ( ! [Vd159: $i] :
( ( Vd159 != v1 )
| ( v1 = Vd159 )
| ( ( ( vplus @ v1 @ ( sK4_Vd162 @ Vd159 ) )
= ( vplus @ Vd159 @ ( sK4_Vd162 @ Vd159 ) ) )
& ( ( vsucc @ ( sK4_Vd162 @ Vd159 ) )
= ( vplus @ v1 @ ( sK4_Vd162 @ Vd159 ) ) )
& ( vd151
= ( vsucc @ ( sK4_Vd162 @ Vd159 ) ) ) ) )
& ! [Vd159: $i] :
( ( Vd159 != v1 )
| ( vd151 = v1 )
| ( ( ( vplus @ v1 @ ( sK3_Vd162 @ Vd159 ) )
= ( vplus @ Vd159 @ ( sK3_Vd162 @ Vd159 ) ) )
& ( ( vsucc @ ( sK3_Vd162 @ Vd159 ) )
= ( vplus @ v1 @ ( sK3_Vd162 @ Vd159 ) ) )
& ( vd151
= ( vsucc @ ( sK3_Vd162 @ Vd159 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(132,plain,
( ( ! [Vd151: $i,Vd152: $i] :
( ~ ( m @ Vd152 )
| ( Vd152
= ( vplus @ Vd151 @ ( sK2_Vd157 @ Vd152 @ Vd151 ) ) )
| ( Vd151 = Vd152 )
| ( Vd151
= ( vplus @ Vd152 @ ( sK1_Vd155 @ Vd152 @ Vd151 ) ) ) )
& ! [Vd151: $i,Vd152: $i] :
( ! [Vd157: $i] :
( Vd152
!= ( vplus @ Vd151 @ Vd157 ) )
| ( m @ Vd152 ) )
& ! [Vd151: $i,Vd152: $i] :
( ( Vd151 != Vd152 )
| ( m @ Vd152 ) )
& ! [Vd151: $i,Vd152: $i] :
( ! [Vd155: $i] :
( Vd151
!= ( vplus @ Vd152 @ Vd155 ) )
| ( m @ Vd152 ) ) )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(133,plain,
( ( ! [Vd144: $i,Vd145: $i] :
( ( Vd144 != Vd145 )
| ! [Vd149: $i] :
( Vd145
!= ( vplus @ Vd144 @ Vd149 ) ) ) )
= $true ),
inference(copy,[status(thm)],[96]) ).
thf(134,plain,
( ( ! [Vd144: $i,Vd145: $i] :
( ! [Vd147: $i] :
( Vd144
!= ( vplus @ Vd145 @ Vd147 ) )
| ! [Vd149: $i] :
( Vd145
!= ( vplus @ Vd144 @ Vd149 ) ) ) )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(135,plain,
( ( ! [Vd144: $i,Vd145: $i] :
( ( Vd144 != Vd145 )
| ! [Vd147: $i] :
( Vd144
!= ( vplus @ Vd145 @ Vd147 ) ) ) )
= $true ),
inference(copy,[status(thm)],[94]) ).
thf(136,plain,
( ( ! [Vd127: $i,Vd128: $i] :
( ! [Vd142: $i] :
( Vd128
!= ( vplus @ Vd127 @ Vd142 ) )
| ! [Vd140: $i] :
( Vd127
!= ( vplus @ Vd128 @ Vd140 ) ) ) )
= $true ),
inference(copy,[status(thm)],[93]) ).
thf(137,plain,
( ( ! [Vd127: $i,Vd128: $i] :
( ! [Vd137: $i] :
( Vd128
!= ( vplus @ Vd127 @ Vd137 ) )
| ! [Vd135: $i] :
( Vd127
!= ( vplus @ Vd128 @ Vd135 ) ) ) )
= $true ),
inference(copy,[status(thm)],[92]) ).
thf(138,plain,
( ( ! [Vd127: $i,Vd128: $i] :
( ! [Vd133: $i] :
( Vd128
!= ( vplus @ Vd127 @ Vd133 ) )
| ( Vd127 != Vd128 ) ) )
= $true ),
inference(copy,[status(thm)],[91]) ).
thf(139,plain,
( ( ! [Vd127: $i,Vd128: $i] :
( ! [Vd130: $i] :
( Vd127
!= ( vplus @ Vd128 @ Vd130 ) )
| ( Vd127 != Vd128 ) ) )
= $true ),
inference(copy,[status(thm)],[90]) ).
thf(140,plain,
( ( ! [Vd104: $i,Vd105: $i] :
( ( Vd104 = Vd105 )
| ! [Vd107: $i] :
( ( vplus @ Vd107 @ Vd104 )
!= ( vplus @ Vd107 @ Vd105 ) ) ) )
= $true ),
inference(copy,[status(thm)],[89]) ).
thf(141,plain,
( ( ! [Vd92: $i,Vd93: $i] :
( Vd93
!= ( vplus @ Vd92 @ Vd93 ) ) )
= $true ),
inference(copy,[status(thm)],[88]) ).
thf(142,plain,
( ( ! [Vd78: $i,Vd79: $i] :
( ( vplus @ Vd79 @ Vd78 )
= ( vplus @ Vd78 @ Vd79 ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(143,plain,
( ( ! [Vd68: $i,Vd69: $i] :
( ( vplus @ ( vsucc @ Vd68 ) @ Vd69 )
= ( vsucc @ ( vplus @ Vd68 @ Vd69 ) ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(144,plain,
( ( ! [Vd59: $i] :
( ( vplus @ v1 @ Vd59 )
= ( vsucc @ Vd59 ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(145,plain,
( ( ! [Vd46: $i,Vd47: $i,Vd48: $i] :
( ( vplus @ ( vplus @ Vd46 @ Vd47 ) @ Vd48 )
= ( vplus @ Vd46 @ ( vplus @ Vd47 @ Vd48 ) ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(146,plain,
( ( ! [Vd42: $i,Vd43: $i] :
( ( vplus @ Vd42 @ ( vsucc @ Vd43 ) )
= ( vsucc @ ( vplus @ Vd42 @ Vd43 ) ) )
& ! [Vd42: $i] :
( ( vplus @ Vd42 @ v1 )
= ( vsucc @ Vd42 ) ) )
= $true ),
inference(copy,[status(thm)],[87]) ).
thf(147,plain,
( ( ! [Vd24: $i] :
( ( Vd24 = v1 )
| ( Vd24
= ( vsucc @ ( vskolem2 @ Vd24 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[86]) ).
thf(148,plain,
( ( ! [Vd16: $i] :
( ( vsucc @ Vd16 )
!= Vd16 ) )
= $true ),
inference(copy,[status(thm)],[85]) ).
thf(149,plain,
( ( ! [Vd7: $i,Vd8: $i] :
( ( Vd7 = Vd8 )
| ( ( vsucc @ Vd7 )
!= ( vsucc @ Vd8 ) ) ) )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(150,plain,
( ( ! [Vd3: $i,Vd4: $i] :
( ( ( vsucc @ Vd3 )
!= ( vsucc @ Vd4 ) )
| ( Vd3 = Vd4 ) ) )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(151,plain,
( ( ! [Vd1: $i] :
( ( vsucc @ Vd1 )
!= v1 ) )
= $true ),
inference(copy,[status(thm)],[82]) ).
thf(152,plain,
( ( ( vd151 != vd165 )
& ! [Vd180: $i] :
( vd165
!= ( vplus @ vd151 @ Vd180 ) )
& ! [Vd170: $i] :
( vd151
!= ( vplus @ vd165 @ Vd170 ) ) )
= $true ),
inference(copy,[status(thm)],[81]) ).
thf(153,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( m @ SX1 )
| ( SX1
= ( vplus @ SX0 @ ( sK2_Vd157 @ SX1 @ SX0 ) ) )
| ( SX0 = SX1 )
| ( SX0
= ( vplus @ SX1 @ ( sK1_Vd155 @ SX1 @ SX0 ) ) ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( SX1
!= ( vplus @ SX0 @ SX2 ) )
| ( m @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( m @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( SX0
!= ( vplus @ SX1 @ SX2 ) )
| ( m @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[132]) ).
thf(154,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( vplus @ SX0 @ ( vsucc @ SX1 ) )
= ( vsucc @ ( vplus @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ( vplus @ SX0 @ v1 )
= ( vsucc @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[146]) ).
thf(155,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( SX0 != v1 )
| ( v1 = SX0 )
| ~ ( ~ ~ ( ( ( vplus @ v1 @ ( sK4_Vd162 @ SX0 ) )
!= ( vplus @ SX0 @ ( sK4_Vd162 @ SX0 ) ) )
| ( ( vsucc @ ( sK4_Vd162 @ SX0 ) )
!= ( vplus @ v1 @ ( sK4_Vd162 @ SX0 ) ) ) )
| ( vd151
!= ( vsucc @ ( sK4_Vd162 @ SX0 ) ) ) ) )
| ~ ! [SX0: $i] :
( ( SX0 != v1 )
| ( vd151 = v1 )
| ~ ( ~ ~ ( ( ( vplus @ v1 @ ( sK3_Vd162 @ SX0 ) )
!= ( vplus @ SX0 @ ( sK3_Vd162 @ SX0 ) ) )
| ( ( vsucc @ ( sK3_Vd162 @ SX0 ) )
!= ( vplus @ v1 @ ( sK3_Vd162 @ SX0 ) ) ) )
| ( vd151
!= ( vsucc @ ( sK3_Vd162 @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[131]) ).
thf(156,plain,
( ( ~ ( ~ ( ( vd151 != vd165 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( vd165
!= ( vplus @ vd151 @ SX0 ) )
| ~ ! [SX0: $i] :
( vd151
!= ( vplus @ vd165 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[152]) ).
thf(157,plain,
( ( ( ! [Vd180: $i] :
( vd165
!= ( vplus @ vd151 @ Vd180 ) ) )
= $true )
| ( ( m @ ( vsucc @ vd165 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[114]) ).
thf(158,plain,
! [SV1: $i] :
( ( ( vd165
!= ( vplus @ vd151 @ SV1 ) )
| ( ( vsucc @ ( vplus @ vd151 @ SV1 ) )
= ( vplus @ vd151 @ ( vsucc @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(159,plain,
! [SV2: $i] :
( ( ( vd165
!= ( vplus @ vd151 @ SV2 ) )
| ( ( vsucc @ vd165 )
= ( vsucc @ ( vplus @ vd151 @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(160,plain,
! [SV3: $i] :
( ( ( vd151
!= ( vplus @ vd165 @ SV3 ) )
| ( SV3 = v1 )
| ( m @ ( vsucc @ vd165 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(161,plain,
! [SV4: $i] :
( ( ( vd151
!= ( vplus @ vd165 @ SV4 ) )
| ( SV4 = v1 )
| ( ( vplus @ ( vplus @ vd165 @ v1 ) @ vskolem3 )
= ( vplus @ ( vsucc @ vd165 ) @ vskolem3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(162,plain,
! [SV5: $i] :
( ( ( vd151
!= ( vplus @ vd165 @ SV5 ) )
| ( SV5 = v1 )
| ( ( vplus @ vd165 @ ( vplus @ v1 @ vskolem3 ) )
= ( vplus @ ( vplus @ vd165 @ v1 ) @ vskolem3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(163,plain,
! [SV6: $i] :
( ( ( vd151
!= ( vplus @ vd165 @ SV6 ) )
| ( SV6 = v1 )
| ( vd151
= ( vplus @ vd165 @ ( vplus @ v1 @ vskolem3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(164,plain,
! [SV7: $i] :
( ( ( vd151
!= ( vplus @ vd165 @ SV7 ) )
| ( SV7 = v1 )
| ( ( vsucc @ vskolem3 )
= ( vplus @ v1 @ vskolem3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(165,plain,
! [SV8: $i] :
( ( ( vd151
!= ( vplus @ vd165 @ SV8 ) )
| ( SV8 = v1 )
| ( SV8
= ( vsucc @ vskolem3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(166,plain,
! [SV9: $i] :
( ( ( vd151
!= ( vplus @ vd165 @ SV9 ) )
| ( SV9 != v1 )
| ( m @ ( vsucc @ vd165 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(167,plain,
! [SV10: $i] :
( ( ( vd151
!= ( vplus @ vd165 @ SV10 ) )
| ( SV10 != v1 )
| ( ( vplus @ vd165 @ v1 )
= ( vsucc @ vd165 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(168,plain,
! [SV11: $i] :
( ( ( vd151
!= ( vplus @ vd165 @ SV11 ) )
| ( SV11 != v1 )
| ( vd151
= ( vplus @ vd165 @ v1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(169,plain,
( ( ( ( vd151 != vd165 ) )
= $true )
| ( ( m @ ( vsucc @ vd165 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[126]) ).
thf(170,plain,
( ( ( ( vd151 != vd165 ) )
= $true )
| ( ( ( vplus @ vd165 @ v1 )
= ( vplus @ vd151 @ v1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[127]) ).
thf(171,plain,
( ( ( ( vd151 != vd165 ) )
= $true )
| ( ( ( vsucc @ vd165 )
= ( vplus @ vd165 @ v1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[128]) ).
thf(172,plain,
! [SV12: $i] :
( ( ! [SY66: $i] :
( ( SV12 != SY66 )
| ! [SY67: $i] :
( SY66
!= ( vplus @ SV12 @ SY67 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(173,plain,
! [SV13: $i] :
( ( ! [SY68: $i] :
( ! [SY69: $i] :
( SV13
!= ( vplus @ SY68 @ SY69 ) )
| ! [SY70: $i] :
( SY68
!= ( vplus @ SV13 @ SY70 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(174,plain,
! [SV14: $i] :
( ( ! [SY71: $i] :
( ( SV14 != SY71 )
| ! [SY72: $i] :
( SV14
!= ( vplus @ SY71 @ SY72 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(175,plain,
! [SV15: $i] :
( ( ! [SY73: $i] :
( ! [SY74: $i] :
( SY73
!= ( vplus @ SV15 @ SY74 ) )
| ! [SY75: $i] :
( SV15
!= ( vplus @ SY73 @ SY75 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(176,plain,
! [SV16: $i] :
( ( ! [SY76: $i] :
( ! [SY77: $i] :
( SY76
!= ( vplus @ SV16 @ SY77 ) )
| ! [SY78: $i] :
( SV16
!= ( vplus @ SY76 @ SY78 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(177,plain,
! [SV17: $i] :
( ( ! [SY79: $i] :
( ! [SY80: $i] :
( SY79
!= ( vplus @ SV17 @ SY80 ) )
| ( SV17 != SY79 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(178,plain,
! [SV18: $i] :
( ( ! [SY81: $i] :
( ! [SY82: $i] :
( SV18
!= ( vplus @ SY81 @ SY82 ) )
| ( SV18 != SY81 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(179,plain,
! [SV19: $i] :
( ( ! [SY83: $i] :
( ( SV19 = SY83 )
| ! [SY84: $i] :
( ( vplus @ SY84 @ SV19 )
!= ( vplus @ SY84 @ SY83 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(180,plain,
! [SV20: $i] :
( ( ! [SY85: $i] :
( SY85
!= ( vplus @ SV20 @ SY85 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(181,plain,
! [SV21: $i] :
( ( ! [SY86: $i] :
( ( vplus @ SY86 @ SV21 )
= ( vplus @ SV21 @ SY86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(182,plain,
! [SV22: $i] :
( ( ! [SY87: $i] :
( ( vplus @ ( vsucc @ SV22 ) @ SY87 )
= ( vsucc @ ( vplus @ SV22 @ SY87 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(183,plain,
! [SV23: $i] :
( ( ( vplus @ v1 @ SV23 )
= ( vsucc @ SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(184,plain,
! [SV24: $i] :
( ( ! [SY88: $i,SY89: $i] :
( ( vplus @ ( vplus @ SV24 @ SY88 ) @ SY89 )
= ( vplus @ SV24 @ ( vplus @ SY88 @ SY89 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(185,plain,
! [SV25: $i] :
( ( ( SV25 = v1 )
| ( SV25
= ( vsucc @ ( vskolem2 @ SV25 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(186,plain,
! [SV26: $i] :
( ( ( ( vsucc @ SV26 )
!= SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(187,plain,
! [SV27: $i] :
( ( ! [SY90: $i] :
( ( SV27 = SY90 )
| ( ( vsucc @ SV27 )
!= ( vsucc @ SY90 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(188,plain,
! [SV28: $i] :
( ( ! [SY91: $i] :
( ( ( vsucc @ SV28 )
!= ( vsucc @ SY91 ) )
| ( SV28 = SY91 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(189,plain,
! [SV29: $i] :
( ( ( ( vsucc @ SV29 )
!= v1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(190,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( m @ SX1 )
| ( SX1
= ( vplus @ SX0 @ ( sK2_Vd157 @ SX1 @ SX0 ) ) )
| ( SX0 = SX1 )
| ( SX0
= ( vplus @ SX1 @ ( sK1_Vd155 @ SX1 @ SX0 ) ) ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( SX1
!= ( vplus @ SX0 @ SX2 ) )
| ( m @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( m @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( SX0
!= ( vplus @ SX1 @ SX2 ) )
| ( m @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(191,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( vplus @ SX0 @ ( vsucc @ SX1 ) )
= ( vsucc @ ( vplus @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ( vplus @ SX0 @ v1 )
= ( vsucc @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[154]) ).
thf(192,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != v1 )
| ( v1 = SX0 )
| ~ ( ~ ~ ( ( ( vplus @ v1 @ ( sK4_Vd162 @ SX0 ) )
!= ( vplus @ SX0 @ ( sK4_Vd162 @ SX0 ) ) )
| ( ( vsucc @ ( sK4_Vd162 @ SX0 ) )
!= ( vplus @ v1 @ ( sK4_Vd162 @ SX0 ) ) ) )
| ( vd151
!= ( vsucc @ ( sK4_Vd162 @ SX0 ) ) ) ) )
| ~ ! [SX0: $i] :
( ( SX0 != v1 )
| ( vd151 = v1 )
| ~ ( ~ ~ ( ( ( vplus @ v1 @ ( sK3_Vd162 @ SX0 ) )
!= ( vplus @ SX0 @ ( sK3_Vd162 @ SX0 ) ) )
| ( ( vsucc @ ( sK3_Vd162 @ SX0 ) )
!= ( vplus @ v1 @ ( sK3_Vd162 @ SX0 ) ) ) )
| ( vd151
!= ( vsucc @ ( sK3_Vd162 @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(193,plain,
( ( ~ ( ( vd151 != vd165 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( vd165
!= ( vplus @ vd151 @ SX0 ) )
| ~ ! [SX0: $i] :
( vd151
!= ( vplus @ vd165 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(194,plain,
! [SV30: $i] :
( ( ( ( vd165
!= ( vplus @ vd151 @ SV30 ) ) )
= $true )
| ( ( m @ ( vsucc @ vd165 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(195,plain,
! [SV1: $i] :
( ( ( ( vd165
!= ( vplus @ vd151 @ SV1 ) ) )
= $true )
| ( ( ( vsucc @ ( vplus @ vd151 @ SV1 ) )
= ( vplus @ vd151 @ ( vsucc @ SV1 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[158]) ).
thf(196,plain,
! [SV2: $i] :
( ( ( ( vd165
!= ( vplus @ vd151 @ SV2 ) ) )
= $true )
| ( ( ( vsucc @ vd165 )
= ( vsucc @ ( vplus @ vd151 @ SV2 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[159]) ).
thf(197,plain,
! [SV3: $i] :
( ( ( ( vd151
!= ( vplus @ vd165 @ SV3 ) ) )
= $true )
| ( ( ( SV3 = v1 )
| ( m @ ( vsucc @ vd165 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[160]) ).
thf(198,plain,
! [SV4: $i] :
( ( ( ( vd151
!= ( vplus @ vd165 @ SV4 ) ) )
= $true )
| ( ( ( SV4 = v1 )
| ( ( vplus @ ( vplus @ vd165 @ v1 ) @ vskolem3 )
= ( vplus @ ( vsucc @ vd165 ) @ vskolem3 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[161]) ).
thf(199,plain,
! [SV5: $i] :
( ( ( ( vd151
!= ( vplus @ vd165 @ SV5 ) ) )
= $true )
| ( ( ( SV5 = v1 )
| ( ( vplus @ vd165 @ ( vplus @ v1 @ vskolem3 ) )
= ( vplus @ ( vplus @ vd165 @ v1 ) @ vskolem3 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[162]) ).
thf(200,plain,
! [SV6: $i] :
( ( ( ( vd151
!= ( vplus @ vd165 @ SV6 ) ) )
= $true )
| ( ( ( SV6 = v1 )
| ( vd151
= ( vplus @ vd165 @ ( vplus @ v1 @ vskolem3 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[163]) ).
thf(201,plain,
! [SV7: $i] :
( ( ( ( vd151
!= ( vplus @ vd165 @ SV7 ) ) )
= $true )
| ( ( ( SV7 = v1 )
| ( ( vsucc @ vskolem3 )
= ( vplus @ v1 @ vskolem3 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[164]) ).
thf(202,plain,
! [SV8: $i] :
( ( ( ( vd151
!= ( vplus @ vd165 @ SV8 ) ) )
= $true )
| ( ( ( SV8 = v1 )
| ( SV8
= ( vsucc @ vskolem3 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[165]) ).
thf(203,plain,
! [SV9: $i] :
( ( ( ( vd151
!= ( vplus @ vd165 @ SV9 ) ) )
= $true )
| ( ( ( SV9 != v1 )
| ( m @ ( vsucc @ vd165 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[166]) ).
thf(204,plain,
! [SV10: $i] :
( ( ( ( vd151
!= ( vplus @ vd165 @ SV10 ) ) )
= $true )
| ( ( ( SV10 != v1 )
| ( ( vplus @ vd165 @ v1 )
= ( vsucc @ vd165 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[167]) ).
thf(205,plain,
! [SV11: $i] :
( ( ( ( vd151
!= ( vplus @ vd165 @ SV11 ) ) )
= $true )
| ( ( ( SV11 != v1 )
| ( vd151
= ( vplus @ vd165 @ v1 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[168]) ).
thf(206,plain,
( ( ( vd151 = vd165 )
= $false )
| ( ( m @ ( vsucc @ vd165 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(207,plain,
( ( ( vd151 = vd165 )
= $false )
| ( ( ( vplus @ vd165 @ v1 )
= ( vplus @ vd151 @ v1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(208,plain,
( ( ( vd151 = vd165 )
= $false )
| ( ( ( vsucc @ vd165 )
= ( vplus @ vd165 @ v1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(209,plain,
! [SV31: $i,SV12: $i] :
( ( ( SV12 != SV31 )
| ! [SY92: $i] :
( SV31
!= ( vplus @ SV12 @ SY92 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(210,plain,
! [SV32: $i,SV13: $i] :
( ( ! [SY93: $i] :
( SV13
!= ( vplus @ SV32 @ SY93 ) )
| ! [SY94: $i] :
( SV32
!= ( vplus @ SV13 @ SY94 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(211,plain,
! [SV33: $i,SV14: $i] :
( ( ( SV14 != SV33 )
| ! [SY95: $i] :
( SV14
!= ( vplus @ SV33 @ SY95 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(212,plain,
! [SV15: $i,SV34: $i] :
( ( ! [SY96: $i] :
( SV34
!= ( vplus @ SV15 @ SY96 ) )
| ! [SY97: $i] :
( SV15
!= ( vplus @ SV34 @ SY97 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(213,plain,
! [SV16: $i,SV35: $i] :
( ( ! [SY98: $i] :
( SV35
!= ( vplus @ SV16 @ SY98 ) )
| ! [SY99: $i] :
( SV16
!= ( vplus @ SV35 @ SY99 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[176]) ).
thf(214,plain,
! [SV17: $i,SV36: $i] :
( ( ! [SY100: $i] :
( SV36
!= ( vplus @ SV17 @ SY100 ) )
| ( SV17 != SV36 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(215,plain,
! [SV37: $i,SV18: $i] :
( ( ! [SY101: $i] :
( SV18
!= ( vplus @ SV37 @ SY101 ) )
| ( SV18 != SV37 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(216,plain,
! [SV38: $i,SV19: $i] :
( ( ( SV19 = SV38 )
| ! [SY102: $i] :
( ( vplus @ SY102 @ SV19 )
!= ( vplus @ SY102 @ SV38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(217,plain,
! [SV20: $i,SV39: $i] :
( ( ( SV39
!= ( vplus @ SV20 @ SV39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(218,plain,
! [SV21: $i,SV40: $i] :
( ( ( vplus @ SV40 @ SV21 )
= ( vplus @ SV21 @ SV40 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(219,plain,
! [SV41: $i,SV22: $i] :
( ( ( vplus @ ( vsucc @ SV22 ) @ SV41 )
= ( vsucc @ ( vplus @ SV22 @ SV41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(220,plain,
! [SV42: $i,SV24: $i] :
( ( ! [SY103: $i] :
( ( vplus @ ( vplus @ SV24 @ SV42 ) @ SY103 )
= ( vplus @ SV24 @ ( vplus @ SV42 @ SY103 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[184]) ).
thf(221,plain,
! [SV25: $i] :
( ( ( SV25 = v1 )
= $true )
| ( ( SV25
= ( vsucc @ ( vskolem2 @ SV25 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[185]) ).
thf(222,plain,
! [SV26: $i] :
( ( ( vsucc @ SV26 )
= SV26 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[186]) ).
thf(223,plain,
! [SV43: $i,SV27: $i] :
( ( ( SV27 = SV43 )
| ( ( vsucc @ SV27 )
!= ( vsucc @ SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[187]) ).
thf(224,plain,
! [SV44: $i,SV28: $i] :
( ( ( ( vsucc @ SV28 )
!= ( vsucc @ SV44 ) )
| ( SV28 = SV44 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(225,plain,
! [SV29: $i] :
( ( ( vsucc @ SV29 )
= v1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[189]) ).
thf(226,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( m @ SX1 )
| ( SX1
= ( vplus @ SX0 @ ( sK2_Vd157 @ SX1 @ SX0 ) ) )
| ( SX0 = SX1 )
| ( SX0
= ( vplus @ SX1 @ ( sK1_Vd155 @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[190]) ).
thf(227,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( SX1
!= ( vplus @ SX0 @ SX2 ) )
| ( m @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( m @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( SX0
!= ( vplus @ SX1 @ SX2 ) )
| ( m @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[190]) ).
thf(228,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( vplus @ SX0 @ ( vsucc @ SX1 ) )
= ( vsucc @ ( vplus @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[191]) ).
thf(229,plain,
( ( ~ ! [SX0: $i] :
( ( vplus @ SX0 @ v1 )
= ( vsucc @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[191]) ).
thf(230,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != v1 )
| ( v1 = SX0 )
| ~ ( ~ ~ ( ( ( vplus @ v1 @ ( sK4_Vd162 @ SX0 ) )
!= ( vplus @ SX0 @ ( sK4_Vd162 @ SX0 ) ) )
| ( ( vsucc @ ( sK4_Vd162 @ SX0 ) )
!= ( vplus @ v1 @ ( sK4_Vd162 @ SX0 ) ) ) )
| ( vd151
!= ( vsucc @ ( sK4_Vd162 @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[192]) ).
thf(231,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != v1 )
| ( vd151 = v1 )
| ~ ( ~ ~ ( ( ( vplus @ v1 @ ( sK3_Vd162 @ SX0 ) )
!= ( vplus @ SX0 @ ( sK3_Vd162 @ SX0 ) ) )
| ( ( vsucc @ ( sK3_Vd162 @ SX0 ) )
!= ( vplus @ v1 @ ( sK3_Vd162 @ SX0 ) ) ) )
| ( vd151
!= ( vsucc @ ( sK3_Vd162 @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[192]) ).
thf(232,plain,
( ( ~ ( ( vd151 != vd165 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[193]) ).
thf(233,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( vd165
!= ( vplus @ vd151 @ SX0 ) )
| ~ ! [SX0: $i] :
( vd151
!= ( vplus @ vd165 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[193]) ).
thf(234,plain,
! [SV30: $i] :
( ( ( vd165
= ( vplus @ vd151 @ SV30 ) )
= $false )
| ( ( m @ ( vsucc @ vd165 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(235,plain,
! [SV1: $i] :
( ( ( vd165
= ( vplus @ vd151 @ SV1 ) )
= $false )
| ( ( ( vsucc @ ( vplus @ vd151 @ SV1 ) )
= ( vplus @ vd151 @ ( vsucc @ SV1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(236,plain,
! [SV2: $i] :
( ( ( vd165
= ( vplus @ vd151 @ SV2 ) )
= $false )
| ( ( ( vsucc @ vd165 )
= ( vsucc @ ( vplus @ vd151 @ SV2 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(237,plain,
! [SV3: $i] :
( ( ( vd151
= ( vplus @ vd165 @ SV3 ) )
= $false )
| ( ( ( SV3 = v1 )
| ( m @ ( vsucc @ vd165 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[197]) ).
thf(238,plain,
! [SV4: $i] :
( ( ( vd151
= ( vplus @ vd165 @ SV4 ) )
= $false )
| ( ( ( SV4 = v1 )
| ( ( vplus @ ( vplus @ vd165 @ v1 ) @ vskolem3 )
= ( vplus @ ( vsucc @ vd165 ) @ vskolem3 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[198]) ).
thf(239,plain,
! [SV5: $i] :
( ( ( vd151
= ( vplus @ vd165 @ SV5 ) )
= $false )
| ( ( ( SV5 = v1 )
| ( ( vplus @ vd165 @ ( vplus @ v1 @ vskolem3 ) )
= ( vplus @ ( vplus @ vd165 @ v1 ) @ vskolem3 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[199]) ).
thf(240,plain,
! [SV6: $i] :
( ( ( vd151
= ( vplus @ vd165 @ SV6 ) )
= $false )
| ( ( ( SV6 = v1 )
| ( vd151
= ( vplus @ vd165 @ ( vplus @ v1 @ vskolem3 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[200]) ).
thf(241,plain,
! [SV7: $i] :
( ( ( vd151
= ( vplus @ vd165 @ SV7 ) )
= $false )
| ( ( ( SV7 = v1 )
| ( ( vsucc @ vskolem3 )
= ( vplus @ v1 @ vskolem3 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(242,plain,
! [SV8: $i] :
( ( ( vd151
= ( vplus @ vd165 @ SV8 ) )
= $false )
| ( ( ( SV8 = v1 )
| ( SV8
= ( vsucc @ vskolem3 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[202]) ).
thf(243,plain,
! [SV9: $i] :
( ( ( vd151
= ( vplus @ vd165 @ SV9 ) )
= $false )
| ( ( ( SV9 != v1 )
| ( m @ ( vsucc @ vd165 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[203]) ).
thf(244,plain,
! [SV10: $i] :
( ( ( vd151
= ( vplus @ vd165 @ SV10 ) )
= $false )
| ( ( ( SV10 != v1 )
| ( ( vplus @ vd165 @ v1 )
= ( vsucc @ vd165 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(245,plain,
! [SV11: $i] :
( ( ( vd151
= ( vplus @ vd165 @ SV11 ) )
= $false )
| ( ( ( SV11 != v1 )
| ( vd151
= ( vplus @ vd165 @ v1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[205]) ).
thf(246,plain,
! [SV31: $i,SV12: $i] :
( ( ( ( SV12 != SV31 ) )
= $true )
| ( ( ! [SY92: $i] :
( SV31
!= ( vplus @ SV12 @ SY92 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[209]) ).
thf(247,plain,
! [SV32: $i,SV13: $i] :
( ( ( ! [SY93: $i] :
( SV13
!= ( vplus @ SV32 @ SY93 ) ) )
= $true )
| ( ( ! [SY94: $i] :
( SV32
!= ( vplus @ SV13 @ SY94 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[210]) ).
thf(248,plain,
! [SV33: $i,SV14: $i] :
( ( ( ( SV14 != SV33 ) )
= $true )
| ( ( ! [SY95: $i] :
( SV14
!= ( vplus @ SV33 @ SY95 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[211]) ).
thf(249,plain,
! [SV15: $i,SV34: $i] :
( ( ( ! [SY96: $i] :
( SV34
!= ( vplus @ SV15 @ SY96 ) ) )
= $true )
| ( ( ! [SY97: $i] :
( SV15
!= ( vplus @ SV34 @ SY97 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[212]) ).
thf(250,plain,
! [SV16: $i,SV35: $i] :
( ( ( ! [SY98: $i] :
( SV35
!= ( vplus @ SV16 @ SY98 ) ) )
= $true )
| ( ( ! [SY99: $i] :
( SV16
!= ( vplus @ SV35 @ SY99 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[213]) ).
thf(251,plain,
! [SV17: $i,SV36: $i] :
( ( ( ! [SY100: $i] :
( SV36
!= ( vplus @ SV17 @ SY100 ) ) )
= $true )
| ( ( ( SV17 != SV36 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[214]) ).
thf(252,plain,
! [SV37: $i,SV18: $i] :
( ( ( ! [SY101: $i] :
( SV18
!= ( vplus @ SV37 @ SY101 ) ) )
= $true )
| ( ( ( SV18 != SV37 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[215]) ).
thf(253,plain,
! [SV38: $i,SV19: $i] :
( ( ( SV19 = SV38 )
= $true )
| ( ( ! [SY102: $i] :
( ( vplus @ SY102 @ SV19 )
!= ( vplus @ SY102 @ SV38 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[216]) ).
thf(254,plain,
! [SV20: $i,SV39: $i] :
( ( SV39
= ( vplus @ SV20 @ SV39 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[217]) ).
thf(255,plain,
! [SV45: $i,SV42: $i,SV24: $i] :
( ( ( vplus @ ( vplus @ SV24 @ SV42 ) @ SV45 )
= ( vplus @ SV24 @ ( vplus @ SV42 @ SV45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[220]) ).
thf(256,plain,
! [SV43: $i,SV27: $i] :
( ( ( SV27 = SV43 )
= $true )
| ( ( ( ( vsucc @ SV27 )
!= ( vsucc @ SV43 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[223]) ).
thf(257,plain,
! [SV44: $i,SV28: $i] :
( ( ( ( ( vsucc @ SV28 )
!= ( vsucc @ SV44 ) ) )
= $true )
| ( ( SV28 = SV44 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[224]) ).
thf(258,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( m @ SX1 )
| ( SX1
= ( vplus @ SX0 @ ( sK2_Vd157 @ SX1 @ SX0 ) ) )
| ( SX0 = SX1 )
| ( SX0
= ( vplus @ SX1 @ ( sK1_Vd155 @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[226]) ).
thf(259,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( SX1
!= ( vplus @ SX0 @ SX2 ) )
| ( m @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( m @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( SX0
!= ( vplus @ SX1 @ SX2 ) )
| ( m @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[227]) ).
thf(260,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( vplus @ SX0 @ ( vsucc @ SX1 ) )
= ( vsucc @ ( vplus @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[228]) ).
thf(261,plain,
( ( ! [SX0: $i] :
( ( vplus @ SX0 @ v1 )
= ( vsucc @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[229]) ).
thf(262,plain,
( ( ! [SX0: $i] :
( ( SX0 != v1 )
| ( v1 = SX0 )
| ~ ( ~ ~ ( ( ( vplus @ v1 @ ( sK4_Vd162 @ SX0 ) )
!= ( vplus @ SX0 @ ( sK4_Vd162 @ SX0 ) ) )
| ( ( vsucc @ ( sK4_Vd162 @ SX0 ) )
!= ( vplus @ v1 @ ( sK4_Vd162 @ SX0 ) ) ) )
| ( vd151
!= ( vsucc @ ( sK4_Vd162 @ SX0 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[230]) ).
thf(263,plain,
( ( ! [SX0: $i] :
( ( SX0 != v1 )
| ( vd151 = v1 )
| ~ ( ~ ~ ( ( ( vplus @ v1 @ ( sK3_Vd162 @ SX0 ) )
!= ( vplus @ SX0 @ ( sK3_Vd162 @ SX0 ) ) )
| ( ( vsucc @ ( sK3_Vd162 @ SX0 ) )
!= ( vplus @ v1 @ ( sK3_Vd162 @ SX0 ) ) ) )
| ( vd151
!= ( vsucc @ ( sK3_Vd162 @ SX0 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[231]) ).
thf(264,plain,
( ( ( vd151 != vd165 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[232]) ).
thf(265,plain,
( ( ~ ( ~ ! [SX0: $i] :
( vd165
!= ( vplus @ vd151 @ SX0 ) )
| ~ ! [SX0: $i] :
( vd151
!= ( vplus @ vd165 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[233]) ).
thf(266,plain,
! [SV3: $i] :
( ( ( SV3 = v1 )
= $true )
| ( ( m @ ( vsucc @ vd165 ) )
= $true )
| ( ( vd151
= ( vplus @ vd165 @ SV3 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[237]) ).
thf(267,plain,
! [SV4: $i] :
( ( ( SV4 = v1 )
= $true )
| ( ( ( vplus @ ( vplus @ vd165 @ v1 ) @ vskolem3 )
= ( vplus @ ( vsucc @ vd165 ) @ vskolem3 ) )
= $true )
| ( ( vd151
= ( vplus @ vd165 @ SV4 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[238]) ).
thf(268,plain,
! [SV5: $i] :
( ( ( SV5 = v1 )
= $true )
| ( ( ( vplus @ vd165 @ ( vplus @ v1 @ vskolem3 ) )
= ( vplus @ ( vplus @ vd165 @ v1 ) @ vskolem3 ) )
= $true )
| ( ( vd151
= ( vplus @ vd165 @ SV5 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[239]) ).
thf(269,plain,
! [SV6: $i] :
( ( ( SV6 = v1 )
= $true )
| ( ( vd151
= ( vplus @ vd165 @ ( vplus @ v1 @ vskolem3 ) ) )
= $true )
| ( ( vd151
= ( vplus @ vd165 @ SV6 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[240]) ).
thf(270,plain,
! [SV7: $i] :
( ( ( SV7 = v1 )
= $true )
| ( ( ( vsucc @ vskolem3 )
= ( vplus @ v1 @ vskolem3 ) )
= $true )
| ( ( vd151
= ( vplus @ vd165 @ SV7 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[241]) ).
thf(271,plain,
! [SV8: $i] :
( ( ( SV8 = v1 )
= $true )
| ( ( SV8
= ( vsucc @ vskolem3 ) )
= $true )
| ( ( vd151
= ( vplus @ vd165 @ SV8 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[242]) ).
thf(272,plain,
! [SV9: $i] :
( ( ( ( SV9 != v1 ) )
= $true )
| ( ( m @ ( vsucc @ vd165 ) )
= $true )
| ( ( vd151
= ( vplus @ vd165 @ SV9 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[243]) ).
thf(273,plain,
! [SV10: $i] :
( ( ( ( SV10 != v1 ) )
= $true )
| ( ( ( vplus @ vd165 @ v1 )
= ( vsucc @ vd165 ) )
= $true )
| ( ( vd151
= ( vplus @ vd165 @ SV10 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[244]) ).
thf(274,plain,
! [SV11: $i] :
( ( ( ( SV11 != v1 ) )
= $true )
| ( ( vd151
= ( vplus @ vd165 @ v1 ) )
= $true )
| ( ( vd151
= ( vplus @ vd165 @ SV11 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[245]) ).
thf(275,plain,
! [SV31: $i,SV12: $i] :
( ( ( SV12 = SV31 )
= $false )
| ( ( ! [SY92: $i] :
( SV31
!= ( vplus @ SV12 @ SY92 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[246]) ).
thf(276,plain,
! [SV46: $i,SV32: $i,SV13: $i] :
( ( ( ( SV13
!= ( vplus @ SV32 @ SV46 ) ) )
= $true )
| ( ( ! [SY94: $i] :
( SV32
!= ( vplus @ SV13 @ SY94 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[247]) ).
thf(277,plain,
! [SV33: $i,SV14: $i] :
( ( ( SV14 = SV33 )
= $false )
| ( ( ! [SY95: $i] :
( SV14
!= ( vplus @ SV33 @ SY95 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[248]) ).
thf(278,plain,
! [SV47: $i,SV15: $i,SV34: $i] :
( ( ( ( SV34
!= ( vplus @ SV15 @ SV47 ) ) )
= $true )
| ( ( ! [SY97: $i] :
( SV15
!= ( vplus @ SV34 @ SY97 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[249]) ).
thf(279,plain,
! [SV48: $i,SV16: $i,SV35: $i] :
( ( ( ( SV35
!= ( vplus @ SV16 @ SV48 ) ) )
= $true )
| ( ( ! [SY99: $i] :
( SV16
!= ( vplus @ SV35 @ SY99 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[250]) ).
thf(280,plain,
! [SV49: $i,SV17: $i,SV36: $i] :
( ( ( ( SV36
!= ( vplus @ SV17 @ SV49 ) ) )
= $true )
| ( ( ( SV17 != SV36 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[251]) ).
thf(281,plain,
! [SV50: $i,SV37: $i,SV18: $i] :
( ( ( ( SV18
!= ( vplus @ SV37 @ SV50 ) ) )
= $true )
| ( ( ( SV18 != SV37 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[252]) ).
thf(282,plain,
! [SV38: $i,SV19: $i,SV51: $i] :
( ( ( ( ( vplus @ SV51 @ SV19 )
!= ( vplus @ SV51 @ SV38 ) ) )
= $true )
| ( ( SV19 = SV38 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[253]) ).
thf(283,plain,
! [SV43: $i,SV27: $i] :
( ( ( ( vsucc @ SV27 )
= ( vsucc @ SV43 ) )
= $false )
| ( ( SV27 = SV43 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[256]) ).
thf(284,plain,
! [SV44: $i,SV28: $i] :
( ( ( ( vsucc @ SV28 )
= ( vsucc @ SV44 ) )
= $false )
| ( ( SV28 = SV44 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[257]) ).
thf(285,plain,
! [SV52: $i] :
( ( ! [SY104: $i] :
( ~ ( m @ SY104 )
| ( SY104
= ( vplus @ SV52 @ ( sK2_Vd157 @ SY104 @ SV52 ) ) )
| ( SV52 = SY104 )
| ( SV52
= ( vplus @ SY104 @ ( sK1_Vd155 @ SY104 @ SV52 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[258]) ).
thf(286,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( SX1
!= ( vplus @ SX0 @ SX2 ) )
| ( m @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( m @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( SX0
!= ( vplus @ SX1 @ SX2 ) )
| ( m @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[259]) ).
thf(287,plain,
! [SV53: $i] :
( ( ! [SY105: $i] :
( ( vplus @ SV53 @ ( vsucc @ SY105 ) )
= ( vsucc @ ( vplus @ SV53 @ SY105 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[260]) ).
thf(288,plain,
! [SV54: $i] :
( ( ( vplus @ SV54 @ v1 )
= ( vsucc @ SV54 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[261]) ).
thf(289,plain,
! [SV55: $i] :
( ( ( SV55 != v1 )
| ( v1 = SV55 )
| ~ ( ~ ~ ( ( ( vplus @ v1 @ ( sK4_Vd162 @ SV55 ) )
!= ( vplus @ SV55 @ ( sK4_Vd162 @ SV55 ) ) )
| ( ( vsucc @ ( sK4_Vd162 @ SV55 ) )
!= ( vplus @ v1 @ ( sK4_Vd162 @ SV55 ) ) ) )
| ( vd151
!= ( vsucc @ ( sK4_Vd162 @ SV55 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[262]) ).
thf(290,plain,
! [SV56: $i] :
( ( ( SV56 != v1 )
| ( vd151 = v1 )
| ~ ( ~ ~ ( ( ( vplus @ v1 @ ( sK3_Vd162 @ SV56 ) )
!= ( vplus @ SV56 @ ( sK3_Vd162 @ SV56 ) ) )
| ( ( vsucc @ ( sK3_Vd162 @ SV56 ) )
!= ( vplus @ v1 @ ( sK3_Vd162 @ SV56 ) ) ) )
| ( vd151
!= ( vsucc @ ( sK3_Vd162 @ SV56 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[263]) ).
thf(291,plain,
( ( vd151 = vd165 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[264]) ).
thf(292,plain,
( ( ~ ! [SX0: $i] :
( vd165
!= ( vplus @ vd151 @ SX0 ) )
| ~ ! [SX0: $i] :
( vd151
!= ( vplus @ vd165 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[265]) ).
thf(293,plain,
! [SV9: $i] :
( ( ( SV9 = v1 )
= $false )
| ( ( m @ ( vsucc @ vd165 ) )
= $true )
| ( ( vd151
= ( vplus @ vd165 @ SV9 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[272]) ).
thf(294,plain,
! [SV10: $i] :
( ( ( SV10 = v1 )
= $false )
| ( ( ( vplus @ vd165 @ v1 )
= ( vsucc @ vd165 ) )
= $true )
| ( ( vd151
= ( vplus @ vd165 @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[273]) ).
thf(295,plain,
! [SV11: $i] :
( ( ( SV11 = v1 )
= $false )
| ( ( vd151
= ( vplus @ vd165 @ v1 ) )
= $true )
| ( ( vd151
= ( vplus @ vd165 @ SV11 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[274]) ).
thf(296,plain,
! [SV57: $i,SV12: $i,SV31: $i] :
( ( ( ( SV31
!= ( vplus @ SV12 @ SV57 ) ) )
= $true )
| ( ( SV12 = SV31 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[275]) ).
thf(297,plain,
! [SV46: $i,SV32: $i,SV13: $i] :
( ( ( SV13
= ( vplus @ SV32 @ SV46 ) )
= $false )
| ( ( ! [SY94: $i] :
( SV32
!= ( vplus @ SV13 @ SY94 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[276]) ).
thf(298,plain,
! [SV58: $i,SV33: $i,SV14: $i] :
( ( ( ( SV14
!= ( vplus @ SV33 @ SV58 ) ) )
= $true )
| ( ( SV14 = SV33 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[277]) ).
thf(299,plain,
! [SV47: $i,SV15: $i,SV34: $i] :
( ( ( SV34
= ( vplus @ SV15 @ SV47 ) )
= $false )
| ( ( ! [SY97: $i] :
( SV15
!= ( vplus @ SV34 @ SY97 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[278]) ).
thf(300,plain,
! [SV48: $i,SV16: $i,SV35: $i] :
( ( ( SV35
= ( vplus @ SV16 @ SV48 ) )
= $false )
| ( ( ! [SY99: $i] :
( SV16
!= ( vplus @ SV35 @ SY99 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[279]) ).
thf(301,plain,
! [SV49: $i,SV17: $i,SV36: $i] :
( ( ( SV36
= ( vplus @ SV17 @ SV49 ) )
= $false )
| ( ( ( SV17 != SV36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[280]) ).
thf(302,plain,
! [SV50: $i,SV37: $i,SV18: $i] :
( ( ( SV18
= ( vplus @ SV37 @ SV50 ) )
= $false )
| ( ( ( SV18 != SV37 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[281]) ).
thf(303,plain,
! [SV38: $i,SV19: $i,SV51: $i] :
( ( ( ( vplus @ SV51 @ SV19 )
= ( vplus @ SV51 @ SV38 ) )
= $false )
| ( ( SV19 = SV38 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[282]) ).
thf(304,plain,
! [SV52: $i,SV59: $i] :
( ( ~ ( m @ SV59 )
| ( SV59
= ( vplus @ SV52 @ ( sK2_Vd157 @ SV59 @ SV52 ) ) )
| ( SV52 = SV59 )
| ( SV52
= ( vplus @ SV59 @ ( sK1_Vd155 @ SV59 @ SV52 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[285]) ).
thf(305,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( SX1
!= ( vplus @ SX0 @ SX2 ) )
| ( m @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[286]) ).
thf(306,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( m @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( SX0
!= ( vplus @ SX1 @ SX2 ) )
| ( m @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[286]) ).
thf(307,plain,
! [SV60: $i,SV53: $i] :
( ( ( vplus @ SV53 @ ( vsucc @ SV60 ) )
= ( vsucc @ ( vplus @ SV53 @ SV60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[287]) ).
thf(308,plain,
! [SV55: $i] :
( ( ( ( SV55 != v1 ) )
= $true )
| ( ( ( v1 = SV55 )
| ~ ( ~ ~ ( ( ( vplus @ v1 @ ( sK4_Vd162 @ SV55 ) )
!= ( vplus @ SV55 @ ( sK4_Vd162 @ SV55 ) ) )
| ( ( vsucc @ ( sK4_Vd162 @ SV55 ) )
!= ( vplus @ v1 @ ( sK4_Vd162 @ SV55 ) ) ) )
| ( vd151
!= ( vsucc @ ( sK4_Vd162 @ SV55 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[289]) ).
thf(309,plain,
! [SV56: $i] :
( ( ( ( SV56 != v1 ) )
= $true )
| ( ( ( vd151 = v1 )
| ~ ( ~ ~ ( ( ( vplus @ v1 @ ( sK3_Vd162 @ SV56 ) )
!= ( vplus @ SV56 @ ( sK3_Vd162 @ SV56 ) ) )
| ( ( vsucc @ ( sK3_Vd162 @ SV56 ) )
!= ( vplus @ v1 @ ( sK3_Vd162 @ SV56 ) ) ) )
| ( vd151
!= ( vsucc @ ( sK3_Vd162 @ SV56 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[290]) ).
thf(310,plain,
( ( ~ ! [SX0: $i] :
( vd165
!= ( vplus @ vd151 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[292]) ).
thf(311,plain,
( ( ~ ! [SX0: $i] :
( vd151
!= ( vplus @ vd165 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[292]) ).
thf(312,plain,
! [SV57: $i,SV12: $i,SV31: $i] :
( ( ( SV31
= ( vplus @ SV12 @ SV57 ) )
= $false )
| ( ( SV12 = SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[296]) ).
thf(313,plain,
! [SV46: $i,SV61: $i,SV13: $i,SV32: $i] :
( ( ( ( SV32
!= ( vplus @ SV13 @ SV61 ) ) )
= $true )
| ( ( SV13
= ( vplus @ SV32 @ SV46 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[297]) ).
thf(314,plain,
! [SV58: $i,SV33: $i,SV14: $i] :
( ( ( SV14
= ( vplus @ SV33 @ SV58 ) )
= $false )
| ( ( SV14 = SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[298]) ).
thf(315,plain,
! [SV47: $i,SV62: $i,SV34: $i,SV15: $i] :
( ( ( ( SV15
!= ( vplus @ SV34 @ SV62 ) ) )
= $true )
| ( ( SV34
= ( vplus @ SV15 @ SV47 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[299]) ).
thf(316,plain,
! [SV48: $i,SV63: $i,SV35: $i,SV16: $i] :
( ( ( ( SV16
!= ( vplus @ SV35 @ SV63 ) ) )
= $true )
| ( ( SV35
= ( vplus @ SV16 @ SV48 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[300]) ).
thf(317,plain,
! [SV49: $i,SV36: $i,SV17: $i] :
( ( ( SV17 = SV36 )
= $false )
| ( ( SV36
= ( vplus @ SV17 @ SV49 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[301]) ).
thf(318,plain,
! [SV50: $i,SV37: $i,SV18: $i] :
( ( ( SV18 = SV37 )
= $false )
| ( ( SV18
= ( vplus @ SV37 @ SV50 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[302]) ).
thf(319,plain,
! [SV52: $i,SV59: $i] :
( ( ( ~ ( m @ SV59 ) )
= $true )
| ( ( ( SV59
= ( vplus @ SV52 @ ( sK2_Vd157 @ SV59 @ SV52 ) ) )
| ( SV52 = SV59 )
| ( SV52
= ( vplus @ SV59 @ ( sK1_Vd155 @ SV59 @ SV52 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[304]) ).
thf(320,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( SX1
!= ( vplus @ SX0 @ SX2 ) )
| ( m @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[305]) ).
thf(321,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( m @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( SX0
!= ( vplus @ SX1 @ SX2 ) )
| ( m @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[306]) ).
thf(322,plain,
! [SV55: $i] :
( ( ( SV55 = v1 )
= $false )
| ( ( ( v1 = SV55 )
| ~ ( ~ ~ ( ( ( vplus @ v1 @ ( sK4_Vd162 @ SV55 ) )
!= ( vplus @ SV55 @ ( sK4_Vd162 @ SV55 ) ) )
| ( ( vsucc @ ( sK4_Vd162 @ SV55 ) )
!= ( vplus @ v1 @ ( sK4_Vd162 @ SV55 ) ) ) )
| ( vd151
!= ( vsucc @ ( sK4_Vd162 @ SV55 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[308]) ).
thf(323,plain,
! [SV56: $i] :
( ( ( SV56 = v1 )
= $false )
| ( ( ( vd151 = v1 )
| ~ ( ~ ~ ( ( ( vplus @ v1 @ ( sK3_Vd162 @ SV56 ) )
!= ( vplus @ SV56 @ ( sK3_Vd162 @ SV56 ) ) )
| ( ( vsucc @ ( sK3_Vd162 @ SV56 ) )
!= ( vplus @ v1 @ ( sK3_Vd162 @ SV56 ) ) ) )
| ( vd151
!= ( vsucc @ ( sK3_Vd162 @ SV56 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[309]) ).
thf(324,plain,
( ( ! [SX0: $i] :
( vd165
!= ( vplus @ vd151 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[310]) ).
thf(325,plain,
( ( ! [SX0: $i] :
( vd151
!= ( vplus @ vd165 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[311]) ).
thf(326,plain,
! [SV46: $i,SV61: $i,SV13: $i,SV32: $i] :
( ( ( SV32
= ( vplus @ SV13 @ SV61 ) )
= $false )
| ( ( SV13
= ( vplus @ SV32 @ SV46 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[313]) ).
thf(327,plain,
! [SV47: $i,SV62: $i,SV34: $i,SV15: $i] :
( ( ( SV15
= ( vplus @ SV34 @ SV62 ) )
= $false )
| ( ( SV34
= ( vplus @ SV15 @ SV47 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[315]) ).
thf(328,plain,
! [SV48: $i,SV63: $i,SV35: $i,SV16: $i] :
( ( ( SV16
= ( vplus @ SV35 @ SV63 ) )
= $false )
| ( ( SV35
= ( vplus @ SV16 @ SV48 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[316]) ).
thf(329,plain,
! [SV52: $i,SV59: $i] :
( ( ( m @ SV59 )
= $false )
| ( ( ( SV59
= ( vplus @ SV52 @ ( sK2_Vd157 @ SV59 @ SV52 ) ) )
| ( SV52 = SV59 )
| ( SV52
= ( vplus @ SV59 @ ( sK1_Vd155 @ SV59 @ SV52 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[319]) ).
thf(330,plain,
! [SV64: $i] :
( ( ! [SY106: $i] :
( ! [SY107: $i] :
( SY106
!= ( vplus @ SV64 @ SY107 ) )
| ( m @ SY106 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[320]) ).
thf(331,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( m @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( SX0
!= ( vplus @ SX1 @ SX2 ) )
| ( m @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[321]) ).
thf(332,plain,
! [SV55: $i] :
( ( ( v1 = SV55 )
= $true )
| ( ( ~ ( ~ ~ ( ( ( vplus @ v1 @ ( sK4_Vd162 @ SV55 ) )
!= ( vplus @ SV55 @ ( sK4_Vd162 @ SV55 ) ) )
| ( ( vsucc @ ( sK4_Vd162 @ SV55 ) )
!= ( vplus @ v1 @ ( sK4_Vd162 @ SV55 ) ) ) )
| ( vd151
!= ( vsucc @ ( sK4_Vd162 @ SV55 ) ) ) ) )
= $true )
| ( ( SV55 = v1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[322]) ).
thf(333,plain,
! [SV56: $i] :
( ( ( vd151 = v1 )
= $true )
| ( ( ~ ( ~ ~ ( ( ( vplus @ v1 @ ( sK3_Vd162 @ SV56 ) )
!= ( vplus @ SV56 @ ( sK3_Vd162 @ SV56 ) ) )
| ( ( vsucc @ ( sK3_Vd162 @ SV56 ) )
!= ( vplus @ v1 @ ( sK3_Vd162 @ SV56 ) ) ) )
| ( vd151
!= ( vsucc @ ( sK3_Vd162 @ SV56 ) ) ) ) )
= $true )
| ( ( SV56 = v1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[323]) ).
thf(334,plain,
! [SV65: $i] :
( ( ( vd165
!= ( vplus @ vd151 @ SV65 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[324]) ).
thf(335,plain,
! [SV66: $i] :
( ( ( vd151
!= ( vplus @ vd165 @ SV66 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[325]) ).
thf(336,plain,
! [SV52: $i,SV59: $i] :
( ( ( SV59
= ( vplus @ SV52 @ ( sK2_Vd157 @ SV59 @ SV52 ) ) )
= $true )
| ( ( ( SV52 = SV59 )
| ( SV52
= ( vplus @ SV59 @ ( sK1_Vd155 @ SV59 @ SV52 ) ) ) )
= $true )
| ( ( m @ SV59 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[329]) ).
thf(337,plain,
! [SV64: $i,SV67: $i] :
( ( ! [SY108: $i] :
( SV67
!= ( vplus @ SV64 @ SY108 ) )
| ( m @ SV67 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[330]) ).
thf(338,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( m @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[331]) ).
thf(339,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( SX0
!= ( vplus @ SX1 @ SX2 ) )
| ( m @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[331]) ).
thf(340,plain,
! [SV55: $i] :
( ( ( ~ ~ ( ( ( vplus @ v1 @ ( sK4_Vd162 @ SV55 ) )
!= ( vplus @ SV55 @ ( sK4_Vd162 @ SV55 ) ) )
| ( ( vsucc @ ( sK4_Vd162 @ SV55 ) )
!= ( vplus @ v1 @ ( sK4_Vd162 @ SV55 ) ) ) )
| ( vd151
!= ( vsucc @ ( sK4_Vd162 @ SV55 ) ) ) )
= $false )
| ( ( v1 = SV55 )
= $true )
| ( ( SV55 = v1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[332]) ).
thf(341,plain,
! [SV56: $i] :
( ( ( ~ ~ ( ( ( vplus @ v1 @ ( sK3_Vd162 @ SV56 ) )
!= ( vplus @ SV56 @ ( sK3_Vd162 @ SV56 ) ) )
| ( ( vsucc @ ( sK3_Vd162 @ SV56 ) )
!= ( vplus @ v1 @ ( sK3_Vd162 @ SV56 ) ) ) )
| ( vd151
!= ( vsucc @ ( sK3_Vd162 @ SV56 ) ) ) )
= $false )
| ( ( vd151 = v1 )
= $true )
| ( ( SV56 = v1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[333]) ).
thf(342,plain,
! [SV65: $i] :
( ( vd165
= ( vplus @ vd151 @ SV65 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[334]) ).
thf(343,plain,
! [SV66: $i] :
( ( vd151
= ( vplus @ vd165 @ SV66 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[335]) ).
thf(344,plain,
! [SV59: $i,SV52: $i] :
( ( ( SV52 = SV59 )
= $true )
| ( ( SV52
= ( vplus @ SV59 @ ( sK1_Vd155 @ SV59 @ SV52 ) ) )
= $true )
| ( ( SV59
= ( vplus @ SV52 @ ( sK2_Vd157 @ SV59 @ SV52 ) ) )
= $true )
| ( ( m @ SV59 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[336]) ).
thf(345,plain,
! [SV64: $i,SV67: $i] :
( ( ( ! [SY108: $i] :
( SV67
!= ( vplus @ SV64 @ SY108 ) ) )
= $true )
| ( ( m @ SV67 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[337]) ).
thf(346,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( m @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[338]) ).
thf(347,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( SX0
!= ( vplus @ SX1 @ SX2 ) )
| ( m @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[339]) ).
thf(348,plain,
! [SV55: $i] :
( ( ( ~ ~ ( ( ( vplus @ v1 @ ( sK4_Vd162 @ SV55 ) )
!= ( vplus @ SV55 @ ( sK4_Vd162 @ SV55 ) ) )
| ( ( vsucc @ ( sK4_Vd162 @ SV55 ) )
!= ( vplus @ v1 @ ( sK4_Vd162 @ SV55 ) ) ) ) )
= $false )
| ( ( v1 = SV55 )
= $true )
| ( ( SV55 = v1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[340]) ).
thf(349,plain,
! [SV55: $i] :
( ( ( ( vd151
!= ( vsucc @ ( sK4_Vd162 @ SV55 ) ) ) )
= $false )
| ( ( v1 = SV55 )
= $true )
| ( ( SV55 = v1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[340]) ).
thf(350,plain,
! [SV56: $i] :
( ( ( ~ ~ ( ( ( vplus @ v1 @ ( sK3_Vd162 @ SV56 ) )
!= ( vplus @ SV56 @ ( sK3_Vd162 @ SV56 ) ) )
| ( ( vsucc @ ( sK3_Vd162 @ SV56 ) )
!= ( vplus @ v1 @ ( sK3_Vd162 @ SV56 ) ) ) ) )
= $false )
| ( ( vd151 = v1 )
= $true )
| ( ( SV56 = v1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[341]) ).
thf(351,plain,
! [SV56: $i] :
( ( ( ( vd151
!= ( vsucc @ ( sK3_Vd162 @ SV56 ) ) ) )
= $false )
| ( ( vd151 = v1 )
= $true )
| ( ( SV56 = v1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[341]) ).
thf(352,plain,
! [SV68: $i,SV64: $i,SV67: $i] :
( ( ( ( SV67
!= ( vplus @ SV64 @ SV68 ) ) )
= $true )
| ( ( m @ SV67 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[345]) ).
thf(353,plain,
! [SV69: $i] :
( ( ! [SY109: $i] :
( ( SV69 != SY109 )
| ( m @ SY109 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[346]) ).
thf(354,plain,
! [SV70: $i] :
( ( ! [SY110: $i] :
( ! [SY111: $i] :
( SV70
!= ( vplus @ SY110 @ SY111 ) )
| ( m @ SY110 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[347]) ).
thf(355,plain,
! [SV55: $i] :
( ( ( ~ ( ( ( vplus @ v1 @ ( sK4_Vd162 @ SV55 ) )
!= ( vplus @ SV55 @ ( sK4_Vd162 @ SV55 ) ) )
| ( ( vsucc @ ( sK4_Vd162 @ SV55 ) )
!= ( vplus @ v1 @ ( sK4_Vd162 @ SV55 ) ) ) ) )
= $true )
| ( ( v1 = SV55 )
= $true )
| ( ( SV55 = v1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[348]) ).
thf(356,plain,
! [SV55: $i] :
( ( ( vd151
= ( vsucc @ ( sK4_Vd162 @ SV55 ) ) )
= $true )
| ( ( v1 = SV55 )
= $true )
| ( ( SV55 = v1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[349]) ).
thf(357,plain,
! [SV56: $i] :
( ( ( ~ ( ( ( vplus @ v1 @ ( sK3_Vd162 @ SV56 ) )
!= ( vplus @ SV56 @ ( sK3_Vd162 @ SV56 ) ) )
| ( ( vsucc @ ( sK3_Vd162 @ SV56 ) )
!= ( vplus @ v1 @ ( sK3_Vd162 @ SV56 ) ) ) ) )
= $true )
| ( ( vd151 = v1 )
= $true )
| ( ( SV56 = v1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[350]) ).
thf(358,plain,
! [SV56: $i] :
( ( ( vd151
= ( vsucc @ ( sK3_Vd162 @ SV56 ) ) )
= $true )
| ( ( vd151 = v1 )
= $true )
| ( ( SV56 = v1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[351]) ).
thf(359,plain,
! [SV68: $i,SV64: $i,SV67: $i] :
( ( ( SV67
= ( vplus @ SV64 @ SV68 ) )
= $false )
| ( ( m @ SV67 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[352]) ).
thf(360,plain,
! [SV71: $i,SV69: $i] :
( ( ( SV69 != SV71 )
| ( m @ SV71 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[353]) ).
thf(361,plain,
! [SV72: $i,SV70: $i] :
( ( ! [SY112: $i] :
( SV70
!= ( vplus @ SV72 @ SY112 ) )
| ( m @ SV72 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[354]) ).
thf(362,plain,
! [SV55: $i] :
( ( ( ( ( vplus @ v1 @ ( sK4_Vd162 @ SV55 ) )
!= ( vplus @ SV55 @ ( sK4_Vd162 @ SV55 ) ) )
| ( ( vsucc @ ( sK4_Vd162 @ SV55 ) )
!= ( vplus @ v1 @ ( sK4_Vd162 @ SV55 ) ) ) )
= $false )
| ( ( v1 = SV55 )
= $true )
| ( ( SV55 = v1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[355]) ).
thf(363,plain,
! [SV56: $i] :
( ( ( ( ( vplus @ v1 @ ( sK3_Vd162 @ SV56 ) )
!= ( vplus @ SV56 @ ( sK3_Vd162 @ SV56 ) ) )
| ( ( vsucc @ ( sK3_Vd162 @ SV56 ) )
!= ( vplus @ v1 @ ( sK3_Vd162 @ SV56 ) ) ) )
= $false )
| ( ( vd151 = v1 )
= $true )
| ( ( SV56 = v1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[357]) ).
thf(364,plain,
! [SV71: $i,SV69: $i] :
( ( ( ( SV69 != SV71 ) )
= $true )
| ( ( m @ SV71 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[360]) ).
thf(365,plain,
! [SV72: $i,SV70: $i] :
( ( ( ! [SY112: $i] :
( SV70
!= ( vplus @ SV72 @ SY112 ) ) )
= $true )
| ( ( m @ SV72 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[361]) ).
thf(366,plain,
! [SV55: $i] :
( ( ( ( ( vplus @ v1 @ ( sK4_Vd162 @ SV55 ) )
!= ( vplus @ SV55 @ ( sK4_Vd162 @ SV55 ) ) ) )
= $false )
| ( ( v1 = SV55 )
= $true )
| ( ( SV55 = v1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[362]) ).
thf(367,plain,
! [SV55: $i] :
( ( ( ( ( vsucc @ ( sK4_Vd162 @ SV55 ) )
!= ( vplus @ v1 @ ( sK4_Vd162 @ SV55 ) ) ) )
= $false )
| ( ( v1 = SV55 )
= $true )
| ( ( SV55 = v1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[362]) ).
thf(368,plain,
! [SV56: $i] :
( ( ( ( ( vplus @ v1 @ ( sK3_Vd162 @ SV56 ) )
!= ( vplus @ SV56 @ ( sK3_Vd162 @ SV56 ) ) ) )
= $false )
| ( ( vd151 = v1 )
= $true )
| ( ( SV56 = v1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[363]) ).
thf(369,plain,
! [SV56: $i] :
( ( ( ( ( vsucc @ ( sK3_Vd162 @ SV56 ) )
!= ( vplus @ v1 @ ( sK3_Vd162 @ SV56 ) ) ) )
= $false )
| ( ( vd151 = v1 )
= $true )
| ( ( SV56 = v1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[363]) ).
thf(370,plain,
! [SV71: $i,SV69: $i] :
( ( ( SV69 = SV71 )
= $false )
| ( ( m @ SV71 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[364]) ).
thf(371,plain,
! [SV73: $i,SV72: $i,SV70: $i] :
( ( ( ( SV70
!= ( vplus @ SV72 @ SV73 ) ) )
= $true )
| ( ( m @ SV72 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[365]) ).
thf(372,plain,
! [SV55: $i] :
( ( ( ( vplus @ v1 @ ( sK4_Vd162 @ SV55 ) )
= ( vplus @ SV55 @ ( sK4_Vd162 @ SV55 ) ) )
= $true )
| ( ( v1 = SV55 )
= $true )
| ( ( SV55 = v1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[366]) ).
thf(373,plain,
! [SV55: $i] :
( ( ( ( vsucc @ ( sK4_Vd162 @ SV55 ) )
= ( vplus @ v1 @ ( sK4_Vd162 @ SV55 ) ) )
= $true )
| ( ( v1 = SV55 )
= $true )
| ( ( SV55 = v1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[367]) ).
thf(374,plain,
! [SV56: $i] :
( ( ( ( vplus @ v1 @ ( sK3_Vd162 @ SV56 ) )
= ( vplus @ SV56 @ ( sK3_Vd162 @ SV56 ) ) )
= $true )
| ( ( vd151 = v1 )
= $true )
| ( ( SV56 = v1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[368]) ).
thf(375,plain,
! [SV56: $i] :
( ( ( ( vsucc @ ( sK3_Vd162 @ SV56 ) )
= ( vplus @ v1 @ ( sK3_Vd162 @ SV56 ) ) )
= $true )
| ( ( vd151 = v1 )
= $true )
| ( ( SV56 = v1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[369]) ).
thf(376,plain,
! [SV73: $i,SV72: $i,SV70: $i] :
( ( ( SV70
= ( vplus @ SV72 @ SV73 ) )
= $false )
| ( ( m @ SV72 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[371]) ).
thf(377,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[129,376,375,374,373,372,370,359,358,356,344,343,342,328,327,326,318,317,314,312,307,303,295,294,293,291,288,284,283,271,270,269,268,267,266,255,254,236,235,234,225,222,221,219,218,208,207,206,183,130]) ).
thf(378,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[377]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14 % Problem : NUM835+1 : TPTP v8.1.0. Released v4.1.0.
% 0.09/0.15 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.15/0.37 % Computer : n020.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 600
% 0.15/0.37 % DateTime : Wed Jul 6 09:56:59 EDT 2022
% 0.15/0.37 % CPUTime :
% 0.15/0.40
% 0.15/0.40 No.of.Axioms: 38
% 0.15/0.40
% 0.15/0.40 Length.of.Defs: 0
% 0.15/0.40
% 0.15/0.40 Contains.Choice.Funs: false
% 0.23/0.41 .
% 0.23/0.42 (rf:0,axioms:38,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:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:40,loop_count:0,foatp_calls:0,translation:fof_full).....................
% 1.08/1.26
% 1.08/1.26 ********************************
% 1.08/1.26 * All subproblems solved! *
% 1.08/1.26 ********************************
% 1.08/1.26 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:38,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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:377,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.13/1.31
% 1.13/1.31 %**** Beginning of derivation protocol ****
% 1.13/1.31 % SZS output start CNFRefutation
% See solution above
% 1.13/1.31
% 1.13/1.31 %**** End of derivation protocol ****
% 1.13/1.31 %**** no. of clauses in derivation: 378 ****
% 1.13/1.31 %**** clause counter: 377 ****
% 1.13/1.31
% 1.13/1.31 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:38,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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:377,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------