%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : NUM835+2 : 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 : n001.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 10:35:20 AM UTC 2026
% Result : Theorem 0.40s 0.27s
% Output : CNFRefutation 0.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 22
% Syntax : Number of formulae : 209 ( 115 unt; 0 typ; 0 def)
% Number of atoms : 1142 ( 770 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 1710 ( 296 ~; 253 |; 3 &;1083 @)
% ( 3 <=>; 72 =>; 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 : 316 ( 0 ^; 300 !; 16 ?; 316 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_m,type,
m: $i > $o ).
thf(tp_sK1_SY39,type,
sK1_SY39: $i > $i > $i ).
thf(tp_sK2_SY40,type,
sK2_SY40: $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(3,axiom,
! [Vd42: $i,Vd43: $i] :
( ( ( vplus @ Vd42 @ ( vsucc @ Vd43 ) )
= ( vsucc @ ( vplus @ Vd42 @ Vd43 ) ) )
& ( ( vplus @ Vd42 @ v1 )
= ( vsucc @ Vd42 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))') ).
thf(4,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(5,axiom,
! [Vd59: $i] :
( ( vplus @ v1 @ Vd59 )
= ( vsucc @ Vd59 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(43, 0), 0)') ).
thf(6,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(7,axiom,
! [Vd78: $i,Vd79: $i] :
( ( vplus @ Vd79 @ Vd78 )
= ( vplus @ Vd78 @ Vd79 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
thf(8,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(9,axiom,
( ( vd151 = vd165 )
=> ( ( vsucc @ vd165 )
= ( vplus @ vd165 @ v1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(110), 0), 2)') ).
thf(10,axiom,
( ( vd151 = vd165 )
=> ( ( vplus @ vd165 @ v1 )
= ( vplus @ vd151 @ v1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(110), 0), 1)') ).
thf(11,axiom,
( ( vd151 = vd165 )
=> ( m @ ( vsucc @ vd165 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(110), 0), 0)') ).
thf(12,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(13,axiom,
! [Vd170: $i] :
( ( vd151
= ( vplus @ vd165 @ Vd170 ) )
=> ( ( Vd170 = v1 )
=> ( ( vplus @ vd165 @ v1 )
= ( vsucc @ vd165 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(110), 1), 7)') ).
thf(14,axiom,
! [Vd170: $i] :
( ( vd151
= ( vplus @ vd165 @ Vd170 ) )
=> ( ( Vd170 = v1 )
=> ( m @ ( vsucc @ vd165 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(110), 1), 6)') ).
thf(15,axiom,
! [Vd170: $i] :
( ( vd151
= ( vplus @ vd165 @ Vd170 ) )
=> ( ( Vd170 != v1 )
=> ( Vd170
= ( vsucc @ vskolem3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(110), 1), 5)') ).
thf(16,axiom,
! [Vd170: $i] :
( ( vd151
= ( vplus @ vd165 @ Vd170 ) )
=> ( ( Vd170 != v1 )
=> ( ( vsucc @ vskolem3 )
= ( vplus @ v1 @ vskolem3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(110), 1), 4)') ).
thf(17,axiom,
! [Vd170: $i] :
( ( vd151
= ( vplus @ vd165 @ Vd170 ) )
=> ( ( Vd170 != v1 )
=> ( vd151
= ( vplus @ vd165 @ ( vplus @ v1 @ vskolem3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(110), 1), 3)') ).
thf(18,axiom,
! [Vd170: $i] :
( ( vd151
= ( vplus @ vd165 @ Vd170 ) )
=> ( ( Vd170 != v1 )
=> ( ( vplus @ vd165 @ ( vplus @ v1 @ vskolem3 ) )
= ( vplus @ ( vplus @ vd165 @ v1 ) @ vskolem3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(110), 1), 2)') ).
thf(19,axiom,
! [Vd170: $i] :
( ( vd151
= ( vplus @ vd165 @ Vd170 ) )
=> ( ( Vd170 != v1 )
=> ( ( vplus @ ( vplus @ vd165 @ v1 ) @ vskolem3 )
= ( vplus @ ( vsucc @ vd165 ) @ vskolem3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(110), 1), 1)') ).
thf(20,axiom,
! [Vd170: $i] :
( ( vd151
= ( vplus @ vd165 @ Vd170 ) )
=> ( ( Vd170 != v1 )
=> ( m @ ( vsucc @ vd165 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(110), 1), 0)') ).
thf(21,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(22,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(23,axiom,
! [Vd180: $i] :
( ( vd165
= ( vplus @ vd151 @ Vd180 ) )
=> ( m @ ( vsucc @ vd165 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(110), 2), 0)') ).
thf(24,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(25,negated_conjecture,
( ( ? [Vd180: $i] :
( vd165
= ( vplus @ vd151 @ Vd180 ) )
| ? [Vd170: $i] :
( vd151
= ( vplus @ vd165 @ Vd170 ) )
| ( vd151 = vd165 ) )
= $false ),
inference(negate_conjecture,[status(cth)],[24]) ).
thf(26,plain,
( ( ? [Vd180: $i] :
( vd165
= ( vplus @ vd151 @ Vd180 ) )
| ? [Vd170: $i] :
( vd151
= ( vplus @ vd165 @ Vd170 ) )
| ( vd151 = vd165 ) )
= $false ),
inference(unfold_def,[status(thm)],[25]) ).
thf(27,plain,
( ( ! [Vd42: $i,Vd43: $i] :
( ( ( vplus @ Vd42 @ ( vsucc @ Vd43 ) )
= ( vsucc @ ( vplus @ Vd42 @ Vd43 ) ) )
& ( ( vplus @ Vd42 @ v1 )
= ( vsucc @ Vd42 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(28,plain,
( ( ! [Vd46: $i,Vd47: $i,Vd48: $i] :
( ( vplus @ ( vplus @ Vd46 @ Vd47 ) @ Vd48 )
= ( vplus @ Vd46 @ ( vplus @ Vd47 @ Vd48 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(29,plain,
( ( ! [Vd59: $i] :
( ( vplus @ v1 @ Vd59 )
= ( vsucc @ Vd59 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(30,plain,
( ( ! [Vd68: $i,Vd69: $i] :
( ( vplus @ ( vsucc @ Vd68 ) @ Vd69 )
= ( vsucc @ ( vplus @ Vd68 @ Vd69 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(31,plain,
( ( ! [Vd78: $i,Vd79: $i] :
( ( vplus @ Vd79 @ Vd78 )
= ( vplus @ Vd78 @ Vd79 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(32,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)],[8]) ).
thf(33,plain,
( ( ( vd151 = vd165 )
=> ( ( vsucc @ vd165 )
= ( vplus @ vd165 @ v1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(34,plain,
( ( ( vd151 = vd165 )
=> ( ( vplus @ vd165 @ v1 )
= ( vplus @ vd151 @ v1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(35,plain,
( ( ( vd151 = vd165 )
=> ( m @ ( vsucc @ vd165 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(36,plain,
( ( ! [Vd170: $i] :
( ( vd151
= ( vplus @ vd165 @ Vd170 ) )
=> ( ( Vd170 = v1 )
=> ( vd151
= ( vplus @ vd165 @ v1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(37,plain,
( ( ! [Vd170: $i] :
( ( vd151
= ( vplus @ vd165 @ Vd170 ) )
=> ( ( Vd170 = v1 )
=> ( ( vplus @ vd165 @ v1 )
= ( vsucc @ vd165 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(38,plain,
( ( ! [Vd170: $i] :
( ( vd151
= ( vplus @ vd165 @ Vd170 ) )
=> ( ( Vd170 = v1 )
=> ( m @ ( vsucc @ vd165 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(39,plain,
( ( ! [Vd170: $i] :
( ( vd151
= ( vplus @ vd165 @ Vd170 ) )
=> ( ( Vd170 != v1 )
=> ( Vd170
= ( vsucc @ vskolem3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(40,plain,
( ( ! [Vd170: $i] :
( ( vd151
= ( vplus @ vd165 @ Vd170 ) )
=> ( ( Vd170 != v1 )
=> ( ( vsucc @ vskolem3 )
= ( vplus @ v1 @ vskolem3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(41,plain,
( ( ! [Vd170: $i] :
( ( vd151
= ( vplus @ vd165 @ Vd170 ) )
=> ( ( Vd170 != v1 )
=> ( vd151
= ( vplus @ vd165 @ ( vplus @ v1 @ vskolem3 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(42,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)],[18]) ).
thf(43,plain,
( ( ! [Vd170: $i] :
( ( vd151
= ( vplus @ vd165 @ Vd170 ) )
=> ( ( Vd170 != v1 )
=> ( ( vplus @ ( vplus @ vd165 @ v1 ) @ vskolem3 )
= ( vplus @ ( vsucc @ vd165 ) @ vskolem3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(44,plain,
( ( ! [Vd170: $i] :
( ( vd151
= ( vplus @ vd165 @ Vd170 ) )
=> ( ( Vd170 != v1 )
=> ( m @ ( vsucc @ vd165 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(45,plain,
( ( ! [Vd180: $i] :
( ( vd165
= ( vplus @ vd151 @ Vd180 ) )
=> ( ( vsucc @ vd165 )
= ( vsucc @ ( vplus @ vd151 @ Vd180 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(46,plain,
( ( ! [Vd180: $i] :
( ( vd165
= ( vplus @ vd151 @ Vd180 ) )
=> ( ( vsucc @ ( vplus @ vd151 @ Vd180 ) )
= ( vplus @ vd151 @ ( vsucc @ Vd180 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(47,plain,
( ( ! [Vd180: $i] :
( ( vd165
= ( vplus @ vd151 @ Vd180 ) )
=> ( m @ ( vsucc @ vd165 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(48,plain,
( ( ~ ( ? [Vd180: $i] :
( vd165
= ( vplus @ vd151 @ Vd180 ) )
| ? [Vd170: $i] :
( vd151
= ( vplus @ vd165 @ Vd170 ) )
| ( vd151 = vd165 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[26]) ).
thf(49,plain,
( ( ! [Vd180: $i] :
( ( vd165
= ( vplus @ vd151 @ Vd180 ) )
=> ( m @ ( vsucc @ vd165 ) ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(50,plain,
( ( ! [Vd180: $i] :
( ( vd165
= ( vplus @ vd151 @ Vd180 ) )
=> ( ( vsucc @ ( vplus @ vd151 @ Vd180 ) )
= ( vplus @ vd151 @ ( vsucc @ Vd180 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(51,plain,
( ( ! [Vd180: $i] :
( ( vd165
= ( vplus @ vd151 @ Vd180 ) )
=> ( ( vsucc @ vd165 )
= ( vsucc @ ( vplus @ vd151 @ Vd180 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(52,plain,
( ( ! [Vd170: $i] :
( ( vd151
= ( vplus @ vd165 @ Vd170 ) )
=> ( ( Vd170 != v1 )
=> ( m @ ( vsucc @ vd165 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(53,plain,
( ( ! [Vd170: $i] :
( ( vd151
= ( vplus @ vd165 @ Vd170 ) )
=> ( ( Vd170 != v1 )
=> ( ( vplus @ ( vplus @ vd165 @ v1 ) @ vskolem3 )
= ( vplus @ ( vsucc @ vd165 ) @ vskolem3 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(54,plain,
( ( ! [Vd170: $i] :
( ( vd151
= ( vplus @ vd165 @ Vd170 ) )
=> ( ( Vd170 != v1 )
=> ( ( vplus @ vd165 @ ( vplus @ v1 @ vskolem3 ) )
= ( vplus @ ( vplus @ vd165 @ v1 ) @ vskolem3 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(55,plain,
( ( ! [Vd170: $i] :
( ( vd151
= ( vplus @ vd165 @ Vd170 ) )
=> ( ( Vd170 != v1 )
=> ( vd151
= ( vplus @ vd165 @ ( vplus @ v1 @ vskolem3 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(56,plain,
( ( ! [Vd170: $i] :
( ( vd151
= ( vplus @ vd165 @ Vd170 ) )
=> ( ( Vd170 != v1 )
=> ( ( vsucc @ vskolem3 )
= ( vplus @ v1 @ vskolem3 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(57,plain,
( ( ! [Vd170: $i] :
( ( vd151
= ( vplus @ vd165 @ Vd170 ) )
=> ( ( Vd170 != v1 )
=> ( Vd170
= ( vsucc @ vskolem3 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(58,plain,
( ( ! [Vd170: $i] :
( ( vd151
= ( vplus @ vd165 @ Vd170 ) )
=> ( ( Vd170 = v1 )
=> ( m @ ( vsucc @ vd165 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(59,plain,
( ( ! [Vd170: $i] :
( ( vd151
= ( vplus @ vd165 @ Vd170 ) )
=> ( ( Vd170 = v1 )
=> ( ( vplus @ vd165 @ v1 )
= ( vsucc @ vd165 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(60,plain,
( ( ! [Vd170: $i] :
( ( vd151
= ( vplus @ vd165 @ Vd170 ) )
=> ( ( Vd170 = v1 )
=> ( vd151
= ( vplus @ vd165 @ v1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(61,plain,
( ( ( vd151 = vd165 )
=> ( m @ ( vsucc @ vd165 ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(62,plain,
( ( ( vd151 = vd165 )
=> ( ( vplus @ vd165 @ v1 )
= ( vplus @ vd151 @ v1 ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(63,plain,
( ( ( vd151 = vd165 )
=> ( ( vsucc @ vd165 )
= ( vplus @ vd165 @ v1 ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(64,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)],[32]) ).
thf(65,plain,
( ( ! [Vd78: $i,Vd79: $i] :
( ( vplus @ Vd79 @ Vd78 )
= ( vplus @ Vd78 @ Vd79 ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(66,plain,
( ( ! [Vd68: $i,Vd69: $i] :
( ( vplus @ ( vsucc @ Vd68 ) @ Vd69 )
= ( vsucc @ ( vplus @ Vd68 @ Vd69 ) ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(67,plain,
( ( ! [Vd59: $i] :
( ( vplus @ v1 @ Vd59 )
= ( vsucc @ Vd59 ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(68,plain,
( ( ! [Vd46: $i,Vd47: $i,Vd48: $i] :
( ( vplus @ ( vplus @ Vd46 @ Vd47 ) @ Vd48 )
= ( vplus @ Vd46 @ ( vplus @ Vd47 @ Vd48 ) ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(69,plain,
( ( ! [Vd42: $i,Vd43: $i] :
( ( ( vplus @ Vd42 @ ( vsucc @ Vd43 ) )
= ( vsucc @ ( vplus @ Vd42 @ Vd43 ) ) )
& ( ( vplus @ Vd42 @ v1 )
= ( vsucc @ Vd42 ) ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(70,plain,
( ( ~ ( ? [Vd180: $i] :
( vd165
= ( vplus @ vd151 @ Vd180 ) )
| ? [Vd170: $i] :
( vd151
= ( vplus @ vd165 @ Vd170 ) )
| ( vd151 = vd165 ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(71,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)],[64]) ).
thf(72,plain,
( ( ! [SX0: $i] :
( ( vd151
!= ( vplus @ vd165 @ SX0 ) )
| ~ ( ( SX0 != v1 ) )
| ( ( vplus @ ( vplus @ vd165 @ v1 ) @ vskolem3 )
= ( vplus @ ( vsucc @ vd165 ) @ vskolem3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(73,plain,
( ( ! [SX0: $i] :
( ( vd151
!= ( vplus @ vd165 @ SX0 ) )
| ( SX0 != v1 )
| ( m @ ( vsucc @ vd165 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(74,plain,
( ( ( vd151 != vd165 )
| ( m @ ( vsucc @ vd165 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(75,plain,
( ( ! [SX0: $i] :
( ( vd151
!= ( vplus @ vd165 @ SX0 ) )
| ( SX0 != v1 )
| ( ( vplus @ vd165 @ v1 )
= ( vsucc @ vd165 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(76,plain,
( ( ! [SX0: $i] :
( ( vd151
!= ( vplus @ vd165 @ SX0 ) )
| ( SX0 != v1 )
| ( vd151
= ( vplus @ vd165 @ v1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(77,plain,
( ( ! [SX0: $i] :
( ( vd151
!= ( vplus @ vd165 @ SX0 ) )
| ~ ( ( SX0 != v1 ) )
| ( vd151
= ( vplus @ vd165 @ ( vplus @ v1 @ vskolem3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(78,plain,
( ( ! [SX0: $i] :
( ( vd165
!= ( vplus @ vd151 @ SX0 ) )
| ( ( vsucc @ vd165 )
= ( vsucc @ ( vplus @ vd151 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(79,plain,
( ( ( vd151 != vd165 )
| ( ( vsucc @ vd165 )
= ( vplus @ vd165 @ v1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(80,plain,
( ( ! [SX0: $i] :
( ( vd151
!= ( vplus @ vd165 @ SX0 ) )
| ~ ( ( SX0 != v1 ) )
| ( SX0
= ( vsucc @ vskolem3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(81,plain,
( ( ~ ( ~ ! [SX0: $i] :
( vd165
!= ( vplus @ vd151 @ SX0 ) )
| ~ ! [SX0: $i] :
( vd151
!= ( vplus @ vd165 @ SX0 ) )
| ( vd151 = vd165 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(82,plain,
( ( ! [SX0: $i] :
( ( vd151
!= ( vplus @ vd165 @ SX0 ) )
| ~ ( ( SX0 != v1 ) )
| ( ( vplus @ vd165 @ ( vplus @ v1 @ vskolem3 ) )
= ( vplus @ ( vplus @ vd165 @ v1 ) @ vskolem3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(83,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ( ( vplus @ SX0 @ ( vsucc @ SX1 ) )
!= ( vsucc @ ( vplus @ SX0 @ SX1 ) ) )
| ( ( vplus @ SX0 @ v1 )
!= ( vsucc @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(84,plain,
( ( ! [SX0: $i] :
( ( vd151
!= ( vplus @ vd165 @ SX0 ) )
| ~ ( ( SX0 != v1 ) )
| ( ( vsucc @ vskolem3 )
= ( vplus @ v1 @ vskolem3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(85,plain,
( ( ( vd151 != vd165 )
| ( ( vplus @ vd165 @ v1 )
= ( vplus @ vd151 @ v1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(86,plain,
( ( ! [SX0: $i] :
( ( vd151
!= ( vplus @ vd165 @ SX0 ) )
| ~ ( ( SX0 != v1 ) )
| ( m @ ( vsucc @ vd165 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(87,plain,
( ( ! [SX0: $i] :
( ( vd165
!= ( vplus @ vd151 @ SX0 ) )
| ( m @ ( vsucc @ vd165 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(88,plain,
( ( ! [SX0: $i] :
( ( vd165
!= ( vplus @ vd151 @ SX0 ) )
| ( ( vsucc @ ( vplus @ vd151 @ SX0 ) )
= ( vplus @ vd151 @ ( vsucc @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(89,plain,
! [SV1: $i] :
( ( ! [SY28: $i] :
( ( vplus @ SY28 @ SV1 )
= ( vplus @ SV1 @ SY28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(90,plain,
! [SV2: $i] :
( ( ! [SY29: $i] :
( ( vplus @ ( vsucc @ SV2 ) @ SY29 )
= ( vsucc @ ( vplus @ SV2 @ SY29 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(91,plain,
! [SV3: $i] :
( ( ( vplus @ v1 @ SV3 )
= ( vsucc @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(92,plain,
! [SV4: $i] :
( ( ! [SY30: $i,SY31: $i] :
( ( vplus @ ( vplus @ SV4 @ SY30 ) @ SY31 )
= ( vplus @ SV4 @ ( vplus @ SY30 @ SY31 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(93,plain,
! [SV5: $i] :
( ( ! [SY32: $i] :
~ ( ~ ( ~ ( m @ SY32 )
| ( SV5 = SY32 )
| ~ ! [SY33: $i] :
( SV5
!= ( vplus @ SY32 @ SY33 ) )
| ~ ! [SY34: $i] :
( SY32
!= ( vplus @ SV5 @ SY34 ) ) )
| ~ ( ~ ( ( SV5 = SY32 )
| ~ ! [SY35: $i] :
( SV5
!= ( vplus @ SY32 @ SY35 ) )
| ~ ! [SY36: $i] :
( SY32
!= ( vplus @ SV5 @ SY36 ) ) )
| ( m @ SY32 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(94,plain,
! [SV6: $i] :
( ( ( vd151
!= ( vplus @ vd165 @ SV6 ) )
| ~ ( ( SV6 != v1 ) )
| ( ( vplus @ ( vplus @ vd165 @ v1 ) @ vskolem3 )
= ( vplus @ ( vsucc @ vd165 ) @ vskolem3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(95,plain,
! [SV7: $i] :
( ( ( vd151
!= ( vplus @ vd165 @ SV7 ) )
| ( SV7 != v1 )
| ( m @ ( vsucc @ vd165 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(96,plain,
( ( ( vd151 != vd165 )
= $true )
| ( ( m @ ( vsucc @ vd165 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[74]) ).
thf(97,plain,
! [SV8: $i] :
( ( ( vd151
!= ( vplus @ vd165 @ SV8 ) )
| ( SV8 != v1 )
| ( ( vplus @ vd165 @ v1 )
= ( vsucc @ vd165 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(98,plain,
! [SV9: $i] :
( ( ( vd151
!= ( vplus @ vd165 @ SV9 ) )
| ( SV9 != v1 )
| ( vd151
= ( vplus @ vd165 @ v1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(99,plain,
! [SV10: $i] :
( ( ( vd151
!= ( vplus @ vd165 @ SV10 ) )
| ~ ( ( SV10 != v1 ) )
| ( vd151
= ( vplus @ vd165 @ ( vplus @ v1 @ vskolem3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(100,plain,
! [SV11: $i] :
( ( ( vd165
!= ( vplus @ vd151 @ SV11 ) )
| ( ( vsucc @ vd165 )
= ( vsucc @ ( vplus @ vd151 @ SV11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(101,plain,
( ( ( vd151 != vd165 )
= $true )
| ( ( ( vsucc @ vd165 )
= ( vplus @ vd165 @ v1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[79]) ).
thf(102,plain,
! [SV12: $i] :
( ( ( vd151
!= ( vplus @ vd165 @ SV12 ) )
| ~ ( ( SV12 != v1 ) )
| ( SV12
= ( vsucc @ vskolem3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(103,plain,
( ( ~ ! [SX0: $i] :
( vd165
!= ( vplus @ vd151 @ SX0 ) )
| ~ ! [SX0: $i] :
( vd151
!= ( vplus @ vd165 @ SX0 ) )
| ( vd151 = vd165 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(104,plain,
! [SV13: $i] :
( ( ( vd151
!= ( vplus @ vd165 @ SV13 ) )
| ~ ( ( SV13 != v1 ) )
| ( ( vplus @ vd165 @ ( vplus @ v1 @ vskolem3 ) )
= ( vplus @ ( vplus @ vd165 @ v1 ) @ vskolem3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(105,plain,
! [SV14: $i] :
( ( ! [SY37: $i] :
~ ( ( ( vplus @ SV14 @ ( vsucc @ SY37 ) )
!= ( vsucc @ ( vplus @ SV14 @ SY37 ) ) )
| ( ( vplus @ SV14 @ v1 )
!= ( vsucc @ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(106,plain,
! [SV15: $i] :
( ( ( vd151
!= ( vplus @ vd165 @ SV15 ) )
| ~ ( ( SV15 != v1 ) )
| ( ( vsucc @ vskolem3 )
= ( vplus @ v1 @ vskolem3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(107,plain,
( ( ( vd151 != vd165 )
= $true )
| ( ( ( vplus @ vd165 @ v1 )
= ( vplus @ vd151 @ v1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[85]) ).
thf(108,plain,
! [SV16: $i] :
( ( ( vd151
!= ( vplus @ vd165 @ SV16 ) )
| ~ ( ( SV16 != v1 ) )
| ( m @ ( vsucc @ vd165 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(109,plain,
! [SV17: $i] :
( ( ( vd165
!= ( vplus @ vd151 @ SV17 ) )
| ( m @ ( vsucc @ vd165 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(110,plain,
! [SV18: $i] :
( ( ( vd165
!= ( vplus @ vd151 @ SV18 ) )
| ( ( vsucc @ ( vplus @ vd151 @ SV18 ) )
= ( vplus @ vd151 @ ( vsucc @ SV18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(111,plain,
! [SV1: $i,SV19: $i] :
( ( ( vplus @ SV19 @ SV1 )
= ( vplus @ SV1 @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(112,plain,
! [SV20: $i,SV2: $i] :
( ( ( vplus @ ( vsucc @ SV2 ) @ SV20 )
= ( vsucc @ ( vplus @ SV2 @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(113,plain,
! [SV21: $i,SV4: $i] :
( ( ! [SY38: $i] :
( ( vplus @ ( vplus @ SV4 @ SV21 ) @ SY38 )
= ( vplus @ SV4 @ ( vplus @ SV21 @ SY38 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(114,plain,
! [SV5: $i,SV22: $i] :
( ( ~ ( ~ ( ~ ( m @ SV22 )
| ( SV5 = SV22 )
| ~ ! [SY39: $i] :
( SV5
!= ( vplus @ SV22 @ SY39 ) )
| ~ ! [SY40: $i] :
( SV22
!= ( vplus @ SV5 @ SY40 ) ) )
| ~ ( ~ ( ( SV5 = SV22 )
| ~ ! [SY41: $i] :
( SV5
!= ( vplus @ SV22 @ SY41 ) )
| ~ ! [SY42: $i] :
( SV22
!= ( vplus @ SV5 @ SY42 ) ) )
| ( m @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(115,plain,
! [SV6: $i] :
( ( ( vd151
!= ( vplus @ vd165 @ SV6 ) )
= $true )
| ( ( ~ ( ( SV6 != v1 ) )
| ( ( vplus @ ( vplus @ vd165 @ v1 ) @ vskolem3 )
= ( vplus @ ( vsucc @ vd165 ) @ vskolem3 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(116,plain,
! [SV7: $i] :
( ( ( vd151
!= ( vplus @ vd165 @ SV7 ) )
= $true )
| ( ( ( SV7 != v1 )
| ( m @ ( vsucc @ vd165 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[95]) ).
thf(117,plain,
( ( ( vd151 = vd165 )
= $false )
| ( ( m @ ( vsucc @ vd165 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(118,plain,
! [SV8: $i] :
( ( ( vd151
!= ( vplus @ vd165 @ SV8 ) )
= $true )
| ( ( ( SV8 != v1 )
| ( ( vplus @ vd165 @ v1 )
= ( vsucc @ vd165 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[97]) ).
thf(119,plain,
! [SV9: $i] :
( ( ( vd151
!= ( vplus @ vd165 @ SV9 ) )
= $true )
| ( ( ( SV9 != v1 )
| ( vd151
= ( vplus @ vd165 @ v1 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[98]) ).
thf(120,plain,
! [SV10: $i] :
( ( ( vd151
!= ( vplus @ vd165 @ SV10 ) )
= $true )
| ( ( ~ ( ( SV10 != v1 ) )
| ( vd151
= ( vplus @ vd165 @ ( vplus @ v1 @ vskolem3 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[99]) ).
thf(121,plain,
! [SV11: $i] :
( ( ( vd165
!= ( vplus @ vd151 @ SV11 ) )
= $true )
| ( ( ( vsucc @ vd165 )
= ( vsucc @ ( vplus @ vd151 @ SV11 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[100]) ).
thf(122,plain,
( ( ( vd151 = vd165 )
= $false )
| ( ( ( vsucc @ vd165 )
= ( vplus @ vd165 @ v1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(123,plain,
! [SV12: $i] :
( ( ( vd151
!= ( vplus @ vd165 @ SV12 ) )
= $true )
| ( ( ~ ( ( SV12 != v1 ) )
| ( SV12
= ( vsucc @ vskolem3 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[102]) ).
thf(124,plain,
( ( ~ ! [SX0: $i] :
( vd165
!= ( vplus @ vd151 @ SX0 ) )
| ~ ! [SX0: $i] :
( vd151
!= ( vplus @ vd165 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[103]) ).
thf(125,plain,
( ( vd151 = vd165 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[103]) ).
thf(126,plain,
! [SV13: $i] :
( ( ( vd151
!= ( vplus @ vd165 @ SV13 ) )
= $true )
| ( ( ~ ( ( SV13 != v1 ) )
| ( ( vplus @ vd165 @ ( vplus @ v1 @ vskolem3 ) )
= ( vplus @ ( vplus @ vd165 @ v1 ) @ vskolem3 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[104]) ).
thf(127,plain,
! [SV23: $i,SV14: $i] :
( ( ~ ( ( ( vplus @ SV14 @ ( vsucc @ SV23 ) )
!= ( vsucc @ ( vplus @ SV14 @ SV23 ) ) )
| ( ( vplus @ SV14 @ v1 )
!= ( vsucc @ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(128,plain,
! [SV15: $i] :
( ( ( vd151
!= ( vplus @ vd165 @ SV15 ) )
= $true )
| ( ( ~ ( ( SV15 != v1 ) )
| ( ( vsucc @ vskolem3 )
= ( vplus @ v1 @ vskolem3 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[106]) ).
thf(129,plain,
( ( ( vd151 = vd165 )
= $false )
| ( ( ( vplus @ vd165 @ v1 )
= ( vplus @ vd151 @ v1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(130,plain,
! [SV16: $i] :
( ( ( vd151
!= ( vplus @ vd165 @ SV16 ) )
= $true )
| ( ( ~ ( ( SV16 != v1 ) )
| ( m @ ( vsucc @ vd165 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[108]) ).
thf(131,plain,
! [SV17: $i] :
( ( ( vd165
!= ( vplus @ vd151 @ SV17 ) )
= $true )
| ( ( m @ ( vsucc @ vd165 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[109]) ).
thf(132,plain,
! [SV18: $i] :
( ( ( vd165
!= ( vplus @ vd151 @ SV18 ) )
= $true )
| ( ( ( vsucc @ ( vplus @ vd151 @ SV18 ) )
= ( vplus @ vd151 @ ( vsucc @ SV18 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[110]) ).
thf(133,plain,
! [SV24: $i,SV21: $i,SV4: $i] :
( ( ( vplus @ ( vplus @ SV4 @ SV21 ) @ SV24 )
= ( vplus @ SV4 @ ( vplus @ SV21 @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(134,plain,
! [SV5: $i,SV22: $i] :
( ( ~ ( ~ ( m @ SV22 )
| ( SV5 = SV22 )
| ~ ! [SY39: $i] :
( SV5
!= ( vplus @ SV22 @ SY39 ) )
| ~ ! [SY40: $i] :
( SV22
!= ( vplus @ SV5 @ SY40 ) ) )
| ~ ( ~ ( ( SV5 = SV22 )
| ~ ! [SY41: $i] :
( SV5
!= ( vplus @ SV22 @ SY41 ) )
| ~ ! [SY42: $i] :
( SV22
!= ( vplus @ SV5 @ SY42 ) ) )
| ( m @ SV22 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[114]) ).
thf(135,plain,
! [SV6: $i] :
( ( ( vd151
= ( vplus @ vd165 @ SV6 ) )
= $false )
| ( ( ~ ( ( SV6 != v1 ) )
| ( ( vplus @ ( vplus @ vd165 @ v1 ) @ vskolem3 )
= ( vplus @ ( vsucc @ vd165 ) @ vskolem3 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(136,plain,
! [SV7: $i] :
( ( ( vd151
= ( vplus @ vd165 @ SV7 ) )
= $false )
| ( ( ( SV7 != v1 )
| ( m @ ( vsucc @ vd165 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(137,plain,
! [SV8: $i] :
( ( ( vd151
= ( vplus @ vd165 @ SV8 ) )
= $false )
| ( ( ( SV8 != v1 )
| ( ( vplus @ vd165 @ v1 )
= ( vsucc @ vd165 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(138,plain,
! [SV9: $i] :
( ( ( vd151
= ( vplus @ vd165 @ SV9 ) )
= $false )
| ( ( ( SV9 != v1 )
| ( vd151
= ( vplus @ vd165 @ v1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(139,plain,
! [SV10: $i] :
( ( ( vd151
= ( vplus @ vd165 @ SV10 ) )
= $false )
| ( ( ~ ( ( SV10 != v1 ) )
| ( vd151
= ( vplus @ vd165 @ ( vplus @ v1 @ vskolem3 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(140,plain,
! [SV11: $i] :
( ( ( vd165
= ( vplus @ vd151 @ SV11 ) )
= $false )
| ( ( ( vsucc @ vd165 )
= ( vsucc @ ( vplus @ vd151 @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[121]) ).
thf(141,plain,
! [SV12: $i] :
( ( ( vd151
= ( vplus @ vd165 @ SV12 ) )
= $false )
| ( ( ~ ( ( SV12 != v1 ) )
| ( SV12
= ( vsucc @ vskolem3 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(142,plain,
( ( ~ ! [SX0: $i] :
( vd165
!= ( vplus @ vd151 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[124]) ).
thf(143,plain,
( ( ~ ! [SX0: $i] :
( vd151
!= ( vplus @ vd165 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[124]) ).
thf(144,plain,
! [SV13: $i] :
( ( ( vd151
= ( vplus @ vd165 @ SV13 ) )
= $false )
| ( ( ~ ( ( SV13 != v1 ) )
| ( ( vplus @ vd165 @ ( vplus @ v1 @ vskolem3 ) )
= ( vplus @ ( vplus @ vd165 @ v1 ) @ vskolem3 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[126]) ).
thf(145,plain,
! [SV23: $i,SV14: $i] :
( ( ( ( vplus @ SV14 @ ( vsucc @ SV23 ) )
!= ( vsucc @ ( vplus @ SV14 @ SV23 ) ) )
| ( ( vplus @ SV14 @ v1 )
!= ( vsucc @ SV14 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[127]) ).
thf(146,plain,
! [SV15: $i] :
( ( ( vd151
= ( vplus @ vd165 @ SV15 ) )
= $false )
| ( ( ~ ( ( SV15 != v1 ) )
| ( ( vsucc @ vskolem3 )
= ( vplus @ v1 @ vskolem3 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(147,plain,
! [SV16: $i] :
( ( ( vd151
= ( vplus @ vd165 @ SV16 ) )
= $false )
| ( ( ~ ( ( SV16 != v1 ) )
| ( m @ ( vsucc @ vd165 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[130]) ).
thf(148,plain,
! [SV17: $i] :
( ( ( vd165
= ( vplus @ vd151 @ SV17 ) )
= $false )
| ( ( m @ ( vsucc @ vd165 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(149,plain,
! [SV18: $i] :
( ( ( vd165
= ( vplus @ vd151 @ SV18 ) )
= $false )
| ( ( ( vsucc @ ( vplus @ vd151 @ SV18 ) )
= ( vplus @ vd151 @ ( vsucc @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(150,plain,
! [SV5: $i,SV22: $i] :
( ( ~ ( ~ ( m @ SV22 )
| ( SV5 = SV22 )
| ~ ! [SY39: $i] :
( SV5
!= ( vplus @ SV22 @ SY39 ) )
| ~ ! [SY40: $i] :
( SV22
!= ( vplus @ SV5 @ SY40 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[134]) ).
thf(151,plain,
! [SV22: $i,SV5: $i] :
( ( ~ ( ~ ( ( SV5 = SV22 )
| ~ ! [SY41: $i] :
( SV5
!= ( vplus @ SV22 @ SY41 ) )
| ~ ! [SY42: $i] :
( SV22
!= ( vplus @ SV5 @ SY42 ) ) )
| ( m @ SV22 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[134]) ).
thf(152,plain,
! [SV6: $i] :
( ( ( ~ ( ( SV6 != v1 ) ) )
= $true )
| ( ( ( vplus @ ( vplus @ vd165 @ v1 ) @ vskolem3 )
= ( vplus @ ( vsucc @ vd165 ) @ vskolem3 ) )
= $true )
| ( ( vd151
= ( vplus @ vd165 @ SV6 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[135]) ).
thf(153,plain,
! [SV7: $i] :
( ( ( SV7 != v1 )
= $true )
| ( ( m @ ( vsucc @ vd165 ) )
= $true )
| ( ( vd151
= ( vplus @ vd165 @ SV7 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[136]) ).
thf(154,plain,
! [SV8: $i] :
( ( ( SV8 != v1 )
= $true )
| ( ( ( vplus @ vd165 @ v1 )
= ( vsucc @ vd165 ) )
= $true )
| ( ( vd151
= ( vplus @ vd165 @ SV8 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[137]) ).
thf(155,plain,
! [SV9: $i] :
( ( ( SV9 != v1 )
= $true )
| ( ( vd151
= ( vplus @ vd165 @ v1 ) )
= $true )
| ( ( vd151
= ( vplus @ vd165 @ SV9 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[138]) ).
thf(156,plain,
! [SV10: $i] :
( ( ( ~ ( ( SV10 != v1 ) ) )
= $true )
| ( ( vd151
= ( vplus @ vd165 @ ( vplus @ v1 @ vskolem3 ) ) )
= $true )
| ( ( vd151
= ( vplus @ vd165 @ SV10 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[139]) ).
thf(157,plain,
! [SV12: $i] :
( ( ( ~ ( ( SV12 != v1 ) ) )
= $true )
| ( ( SV12
= ( vsucc @ vskolem3 ) )
= $true )
| ( ( vd151
= ( vplus @ vd165 @ SV12 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[141]) ).
thf(158,plain,
( ( ! [SX0: $i] :
( vd165
!= ( vplus @ vd151 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[142]) ).
thf(159,plain,
( ( ! [SX0: $i] :
( vd151
!= ( vplus @ vd165 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[143]) ).
thf(160,plain,
! [SV13: $i] :
( ( ( ~ ( ( SV13 != v1 ) ) )
= $true )
| ( ( ( vplus @ vd165 @ ( vplus @ v1 @ vskolem3 ) )
= ( vplus @ ( vplus @ vd165 @ v1 ) @ vskolem3 ) )
= $true )
| ( ( vd151
= ( vplus @ vd165 @ SV13 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[144]) ).
thf(161,plain,
! [SV23: $i,SV14: $i] :
( ( ( vplus @ SV14 @ ( vsucc @ SV23 ) )
!= ( vsucc @ ( vplus @ SV14 @ SV23 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[145]) ).
thf(162,plain,
! [SV14: $i] :
( ( ( vplus @ SV14 @ v1 )
!= ( vsucc @ SV14 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[145]) ).
thf(163,plain,
! [SV15: $i] :
( ( ( ~ ( ( SV15 != v1 ) ) )
= $true )
| ( ( ( vsucc @ vskolem3 )
= ( vplus @ v1 @ vskolem3 ) )
= $true )
| ( ( vd151
= ( vplus @ vd165 @ SV15 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[146]) ).
thf(164,plain,
! [SV16: $i] :
( ( ( ~ ( ( SV16 != v1 ) ) )
= $true )
| ( ( m @ ( vsucc @ vd165 ) )
= $true )
| ( ( vd151
= ( vplus @ vd165 @ SV16 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[147]) ).
thf(165,plain,
! [SV5: $i,SV22: $i] :
( ( ~ ( m @ SV22 )
| ( SV5 = SV22 )
| ~ ! [SY39: $i] :
( SV5
!= ( vplus @ SV22 @ SY39 ) )
| ~ ! [SY40: $i] :
( SV22
!= ( vplus @ SV5 @ SY40 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[150]) ).
thf(166,plain,
! [SV22: $i,SV5: $i] :
( ( ~ ( ( SV5 = SV22 )
| ~ ! [SY41: $i] :
( SV5
!= ( vplus @ SV22 @ SY41 ) )
| ~ ! [SY42: $i] :
( SV22
!= ( vplus @ SV5 @ SY42 ) ) )
| ( m @ SV22 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[151]) ).
thf(167,plain,
! [SV6: $i] :
( ( ( SV6 != v1 )
= $false )
| ( ( ( vplus @ ( vplus @ vd165 @ v1 ) @ vskolem3 )
= ( vplus @ ( vsucc @ vd165 ) @ vskolem3 ) )
= $true )
| ( ( vd151
= ( vplus @ vd165 @ SV6 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(168,plain,
! [SV7: $i] :
( ( ( SV7 = v1 )
= $false )
| ( ( m @ ( vsucc @ vd165 ) )
= $true )
| ( ( vd151
= ( vplus @ vd165 @ SV7 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(169,plain,
! [SV8: $i] :
( ( ( SV8 = v1 )
= $false )
| ( ( ( vplus @ vd165 @ v1 )
= ( vsucc @ vd165 ) )
= $true )
| ( ( vd151
= ( vplus @ vd165 @ SV8 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[154]) ).
thf(170,plain,
! [SV9: $i] :
( ( ( SV9 = v1 )
= $false )
| ( ( vd151
= ( vplus @ vd165 @ v1 ) )
= $true )
| ( ( vd151
= ( vplus @ vd165 @ SV9 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(171,plain,
! [SV10: $i] :
( ( ( SV10 != v1 )
= $false )
| ( ( vd151
= ( vplus @ vd165 @ ( vplus @ v1 @ vskolem3 ) ) )
= $true )
| ( ( vd151
= ( vplus @ vd165 @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(172,plain,
! [SV12: $i] :
( ( ( SV12 != v1 )
= $false )
| ( ( SV12
= ( vsucc @ vskolem3 ) )
= $true )
| ( ( vd151
= ( vplus @ vd165 @ SV12 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[157]) ).
thf(173,plain,
! [SV25: $i] :
( ( vd165
!= ( vplus @ vd151 @ SV25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(174,plain,
! [SV26: $i] :
( ( vd151
!= ( vplus @ vd165 @ SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(175,plain,
! [SV13: $i] :
( ( ( SV13 != v1 )
= $false )
| ( ( ( vplus @ vd165 @ ( vplus @ v1 @ vskolem3 ) )
= ( vplus @ ( vplus @ vd165 @ v1 ) @ vskolem3 ) )
= $true )
| ( ( vd151
= ( vplus @ vd165 @ SV13 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(176,plain,
! [SV23: $i,SV14: $i] :
( ( ( vplus @ SV14 @ ( vsucc @ SV23 ) )
= ( vsucc @ ( vplus @ SV14 @ SV23 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[161]) ).
thf(177,plain,
! [SV14: $i] :
( ( ( vplus @ SV14 @ v1 )
= ( vsucc @ SV14 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[162]) ).
thf(178,plain,
! [SV15: $i] :
( ( ( SV15 != v1 )
= $false )
| ( ( ( vsucc @ vskolem3 )
= ( vplus @ v1 @ vskolem3 ) )
= $true )
| ( ( vd151
= ( vplus @ vd165 @ SV15 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[163]) ).
thf(179,plain,
! [SV16: $i] :
( ( ( SV16 != v1 )
= $false )
| ( ( m @ ( vsucc @ vd165 ) )
= $true )
| ( ( vd151
= ( vplus @ vd165 @ SV16 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(180,plain,
! [SV5: $i,SV22: $i] :
( ( ( ~ ( m @ SV22 ) )
= $true )
| ( ( ( SV5 = SV22 )
| ~ ! [SY39: $i] :
( SV5
!= ( vplus @ SV22 @ SY39 ) )
| ~ ! [SY40: $i] :
( SV22
!= ( vplus @ SV5 @ SY40 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[165]) ).
thf(181,plain,
! [SV22: $i,SV5: $i] :
( ( ( ~ ( ( SV5 = SV22 )
| ~ ! [SY41: $i] :
( SV5
!= ( vplus @ SV22 @ SY41 ) )
| ~ ! [SY42: $i] :
( SV22
!= ( vplus @ SV5 @ SY42 ) ) ) )
= $true )
| ( ( m @ SV22 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[166]) ).
thf(182,plain,
! [SV6: $i] :
( ( ( SV6 = v1 )
= $true )
| ( ( ( vplus @ ( vplus @ vd165 @ v1 ) @ vskolem3 )
= ( vplus @ ( vsucc @ vd165 ) @ vskolem3 ) )
= $true )
| ( ( vd151
= ( vplus @ vd165 @ SV6 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[167]) ).
thf(183,plain,
! [SV10: $i] :
( ( ( SV10 = v1 )
= $true )
| ( ( vd151
= ( vplus @ vd165 @ ( vplus @ v1 @ vskolem3 ) ) )
= $true )
| ( ( vd151
= ( vplus @ vd165 @ SV10 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[171]) ).
thf(184,plain,
! [SV12: $i] :
( ( ( SV12 = v1 )
= $true )
| ( ( SV12
= ( vsucc @ vskolem3 ) )
= $true )
| ( ( vd151
= ( vplus @ vd165 @ SV12 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[172]) ).
thf(185,plain,
! [SV25: $i] :
( ( vd165
= ( vplus @ vd151 @ SV25 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[173]) ).
thf(186,plain,
! [SV26: $i] :
( ( vd151
= ( vplus @ vd165 @ SV26 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[174]) ).
thf(187,plain,
! [SV13: $i] :
( ( ( SV13 = v1 )
= $true )
| ( ( ( vplus @ vd165 @ ( vplus @ v1 @ vskolem3 ) )
= ( vplus @ ( vplus @ vd165 @ v1 ) @ vskolem3 ) )
= $true )
| ( ( vd151
= ( vplus @ vd165 @ SV13 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[175]) ).
thf(188,plain,
! [SV15: $i] :
( ( ( SV15 = v1 )
= $true )
| ( ( ( vsucc @ vskolem3 )
= ( vplus @ v1 @ vskolem3 ) )
= $true )
| ( ( vd151
= ( vplus @ vd165 @ SV15 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[178]) ).
thf(189,plain,
! [SV16: $i] :
( ( ( SV16 = v1 )
= $true )
| ( ( m @ ( vsucc @ vd165 ) )
= $true )
| ( ( vd151
= ( vplus @ vd165 @ SV16 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[179]) ).
thf(190,plain,
! [SV5: $i,SV22: $i] :
( ( ( m @ SV22 )
= $false )
| ( ( ( SV5 = SV22 )
| ~ ! [SY39: $i] :
( SV5
!= ( vplus @ SV22 @ SY39 ) )
| ~ ! [SY40: $i] :
( SV22
!= ( vplus @ SV5 @ SY40 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[180]) ).
thf(191,plain,
! [SV22: $i,SV5: $i] :
( ( ( ( SV5 = SV22 )
| ~ ! [SY41: $i] :
( SV5
!= ( vplus @ SV22 @ SY41 ) )
| ~ ! [SY42: $i] :
( SV22
!= ( vplus @ SV5 @ SY42 ) ) )
= $false )
| ( ( m @ SV22 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[181]) ).
thf(192,plain,
! [SV22: $i,SV5: $i] :
( ( ( ( SV5 = SV22 )
| ~ ! [SY39: $i] :
( SV5
!= ( vplus @ SV22 @ SY39 ) ) )
= $true )
| ( ( ~ ! [SY40: $i] :
( SV22
!= ( vplus @ SV5 @ SY40 ) ) )
= $true )
| ( ( m @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[190]) ).
thf(193,plain,
! [SV22: $i,SV5: $i] :
( ( ( ( SV5 = SV22 )
| ~ ! [SY41: $i] :
( SV5
!= ( vplus @ SV22 @ SY41 ) ) )
= $false )
| ( ( m @ SV22 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[191]) ).
thf(194,plain,
! [SV5: $i,SV22: $i] :
( ( ( ~ ! [SY42: $i] :
( SV22
!= ( vplus @ SV5 @ SY42 ) ) )
= $false )
| ( ( m @ SV22 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[191]) ).
thf(195,plain,
! [SV22: $i,SV5: $i] :
( ( ( SV5 = SV22 )
= $true )
| ( ( ~ ! [SY39: $i] :
( SV5
!= ( vplus @ SV22 @ SY39 ) ) )
= $true )
| ( ( ~ ! [SY40: $i] :
( SV22
!= ( vplus @ SV5 @ SY40 ) ) )
= $true )
| ( ( m @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[192]) ).
thf(196,plain,
! [SV22: $i,SV5: $i] :
( ( ( SV5 = SV22 )
= $false )
| ( ( m @ SV22 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[193]) ).
thf(197,plain,
! [SV22: $i,SV5: $i] :
( ( ( ~ ! [SY41: $i] :
( SV5
!= ( vplus @ SV22 @ SY41 ) ) )
= $false )
| ( ( m @ SV22 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[193]) ).
thf(198,plain,
! [SV5: $i,SV22: $i] :
( ( ( ! [SY42: $i] :
( SV22
!= ( vplus @ SV5 @ SY42 ) ) )
= $true )
| ( ( m @ SV22 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[194]) ).
thf(199,plain,
! [SV22: $i,SV5: $i] :
( ( ( ! [SY39: $i] :
( SV5
!= ( vplus @ SV22 @ SY39 ) ) )
= $false )
| ( ( SV5 = SV22 )
= $true )
| ( ( ~ ! [SY40: $i] :
( SV22
!= ( vplus @ SV5 @ SY40 ) ) )
= $true )
| ( ( m @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(200,plain,
! [SV22: $i,SV5: $i] :
( ( ( ! [SY41: $i] :
( SV5
!= ( vplus @ SV22 @ SY41 ) ) )
= $true )
| ( ( m @ SV22 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[197]) ).
thf(201,plain,
! [SV27: $i,SV5: $i,SV22: $i] :
( ( ( SV22
!= ( vplus @ SV5 @ SV27 ) )
= $true )
| ( ( m @ SV22 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(202,plain,
! [SV22: $i,SV5: $i] :
( ( ( SV5
!= ( vplus @ SV22 @ ( sK1_SY39 @ SV22 @ SV5 ) ) )
= $false )
| ( ( SV5 = SV22 )
= $true )
| ( ( ~ ! [SY40: $i] :
( SV22
!= ( vplus @ SV5 @ SY40 ) ) )
= $true )
| ( ( m @ SV22 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[199]) ).
thf(203,plain,
! [SV28: $i,SV22: $i,SV5: $i] :
( ( ( SV5
!= ( vplus @ SV22 @ SV28 ) )
= $true )
| ( ( m @ SV22 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[200]) ).
thf(204,plain,
! [SV27: $i,SV5: $i,SV22: $i] :
( ( ( SV22
= ( vplus @ SV5 @ SV27 ) )
= $false )
| ( ( m @ SV22 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(205,plain,
! [SV22: $i,SV5: $i] :
( ( ( SV5
= ( vplus @ SV22 @ ( sK1_SY39 @ SV22 @ SV5 ) ) )
= $true )
| ( ( SV5 = SV22 )
= $true )
| ( ( ~ ! [SY40: $i] :
( SV22
!= ( vplus @ SV5 @ SY40 ) ) )
= $true )
| ( ( m @ SV22 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[202]) ).
thf(206,plain,
! [SV28: $i,SV22: $i,SV5: $i] :
( ( ( SV5
= ( vplus @ SV22 @ SV28 ) )
= $false )
| ( ( m @ SV22 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[203]) ).
thf(207,plain,
! [SV5: $i,SV22: $i] :
( ( ( ! [SY40: $i] :
( SV22
!= ( vplus @ SV5 @ SY40 ) ) )
= $false )
| ( ( SV5 = SV22 )
= $true )
| ( ( SV5
= ( vplus @ SV22 @ ( sK1_SY39 @ SV22 @ SV5 ) ) )
= $true )
| ( ( m @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[205]) ).
thf(208,plain,
! [SV5: $i,SV22: $i] :
( ( ( SV22
!= ( vplus @ SV5 @ ( sK2_SY40 @ SV5 @ SV22 ) ) )
= $false )
| ( ( SV5 = SV22 )
= $true )
| ( ( SV5
= ( vplus @ SV22 @ ( sK1_SY39 @ SV22 @ SV5 ) ) )
= $true )
| ( ( m @ SV22 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[207]) ).
thf(209,plain,
! [SV5: $i,SV22: $i] :
( ( ( SV22
= ( vplus @ SV5 @ ( sK2_SY40 @ SV5 @ SV22 ) ) )
= $true )
| ( ( SV5 = SV22 )
= $true )
| ( ( SV5
= ( vplus @ SV22 @ ( sK1_SY39 @ SV22 @ SV5 ) ) )
= $true )
| ( ( m @ SV22 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[208]) ).
thf(210,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[91,209,206,204,196,189,188,187,186,185,184,183,182,177,176,170,169,168,149,148,140,133,129,125,122,117,112,111]) ).
thf(211,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[210]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM835+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.17 % Computer : n001.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Oct 6 13:46:39 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.40/0.27
% 0.40/0.27 No.of.Axioms: 21
% 0.40/0.27
% 0.40/0.27 Length.of.Defs: 0
% 0.40/0.27
% 0.40/0.27 Contains.Choice.Funs: false
% 0.40/0.27 ......
% 0.40/0.27
% 0.40/0.27 ********************************
% 0.40/0.27 * All subproblems solved! *
% 0.40/0.27 ********************************
% 0.40/0.27 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:21,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:210,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.40/0.27
% 0.40/0.27 %**** Beginning of derivation protocol ****
% 0.40/0.27 % SZS output start CNFRefutation
% See solution above
% 0.40/0.27
% 0.40/0.27 %**** End of derivation protocol ****
% 0.40/0.27 %**** no. of clauses in derivation: 209 ****
% 0.40/0.27 %**** clause counter: 210 ****
% 0.40/0.27
% 0.40/0.27 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:21,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:210,loop_count:0,foatp_calls:1,translation:fof_full)
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