%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : NUM846+1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : 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 10:35:23 AM UTC 2026
% Result : Theorem 0.56s 0.41s
% Output : CNFRefutation 0.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 29
% Syntax : Number of formulae : 253 ( 160 unt; 0 typ; 0 def)
% Number of atoms : 1127 ( 600 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 2127 ( 388 ~; 207 |; 6 &;1493 @)
% ( 6 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 6 con; 0-2 aty)
% Number of variables : 704 ( 0 ^; 680 !; 24 ?; 704 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_geq,type,
geq: $i > $i > $o ).
thf(tp_greater,type,
greater: $i > $i > $o ).
thf(tp_leq,type,
leq: $i > $i > $o ).
thf(tp_less,type,
less: $i > $i > $o ).
thf(tp_sK1_SY124,type,
sK1_SY124: $i > $i > $i ).
thf(tp_sK2_SY116,type,
sK2_SY116: $i > $i > $i ).
thf(tp_sK3_SY125,type,
sK3_SY125: $i > $i > $i ).
thf(tp_sK4_SY127,type,
sK4_SY127: $i > $i > $i ).
thf(tp_v1,type,
v1: $i ).
thf(tp_vd436,type,
vd436: $i ).
thf(tp_vd437,type,
vd437: $i ).
thf(tp_vd439,type,
vd439: $i ).
thf(tp_vmul,type,
vmul: $i > $i > $i ).
thf(tp_vplus,type,
vplus: $i > $i > $i ).
thf(tp_vskolem2,type,
vskolem2: $i > $i ).
thf(tp_vsucc,type,
vsucc: $i > $i ).
thf(7,axiom,
! [Vd46: $i,Vd47: $i,Vd48: $i] :
( ( vplus @ ( vplus @ Vd46 @ Vd47 ) @ Vd48 )
= ( vplus @ Vd46 @ ( vplus @ Vd47 @ Vd48 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(33, 0), 0)') ).
thf(9,axiom,
! [Vd68: $i,Vd69: $i] :
( ( vplus @ ( vsucc @ Vd68 ) @ Vd69 )
= ( vsucc @ ( vplus @ Vd68 @ Vd69 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(52, 0), 0)') ).
thf(10,axiom,
! [Vd78: $i,Vd79: $i] :
( ( vplus @ Vd79 @ Vd78 )
= ( vplus @ Vd78 @ Vd79 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
thf(11,axiom,
! [Vd92: $i,Vd93: $i] :
( Vd93
!= ( vplus @ Vd92 @ Vd93 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(73, 0), 0)') ).
thf(12,axiom,
! [Vd104: $i,Vd105: $i] :
( ( Vd104 != Vd105 )
=> ! [Vd107: $i] :
( ( vplus @ Vd107 @ Vd104 )
!= ( vplus @ Vd107 @ Vd105 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(81, 0), 0)') ).
thf(13,axiom,
! [Vd120: $i,Vd121: $i] :
( ( Vd120 != Vd121 )
| ~ ? [Vd123: $i] :
( Vd120
= ( vplus @ Vd121 @ Vd123 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 3)') ).
thf(14,axiom,
! [Vd120: $i,Vd121: $i] :
( ~ ? [Vd123: $i] :
( Vd120
= ( vplus @ Vd121 @ Vd123 ) )
| ~ ? [Vd125: $i] :
( Vd121
= ( vplus @ Vd120 @ Vd125 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 2)') ).
thf(15,axiom,
! [Vd120: $i,Vd121: $i] :
( ( Vd120 != Vd121 )
| ~ ? [Vd125: $i] :
( Vd121
= ( vplus @ Vd120 @ Vd125 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 1)') ).
thf(16,axiom,
! [Vd120: $i,Vd121: $i] :
( ( Vd120 = Vd121 )
| ? [Vd123: $i] :
( Vd120
= ( vplus @ Vd121 @ Vd123 ) )
| ? [Vd125: $i] :
( Vd121
= ( vplus @ Vd120 @ Vd125 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 0)') ).
thf(17,axiom,
! [Vd193: $i,Vd194: $i] :
( ( greater @ Vd194 @ Vd193 )
<=> ? [Vd196: $i] :
( Vd194
= ( vplus @ Vd193 @ Vd196 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 11), 1)') ).
thf(18,axiom,
! [Vd198: $i,Vd199: $i] :
( ( less @ Vd199 @ Vd198 )
<=> ? [Vd201: $i] :
( Vd198
= ( vplus @ Vd199 @ Vd201 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 12), 1)') ).
thf(32,axiom,
! [Vd295: $i,Vd296: $i] : ( greater @ ( vplus @ Vd295 @ Vd296 ) @ Vd295 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(189, 0), 0)') ).
thf(33,axiom,
! [Vd301: $i,Vd302: $i,Vd303: $i] :
( ( greater @ Vd301 @ Vd302 )
=> ( greater @ ( vplus @ Vd301 @ Vd303 ) @ ( vplus @ Vd302 @ Vd303 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(193), 0), 2)') ).
thf(34,axiom,
! [Vd301: $i,Vd302: $i,Vd303: $i] :
( ( Vd301 = Vd302 )
=> ( ( vplus @ Vd301 @ Vd303 )
= ( vplus @ Vd302 @ Vd303 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(193), 0), 1)') ).
thf(35,axiom,
! [Vd301: $i,Vd302: $i,Vd303: $i] :
( ( less @ Vd301 @ Vd302 )
=> ( less @ ( vplus @ Vd301 @ Vd303 ) @ ( vplus @ Vd302 @ Vd303 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(193), 0), 0)') ).
thf(36,axiom,
! [Vd328: $i,Vd329: $i,Vd330: $i] :
( ( greater @ ( vplus @ Vd328 @ Vd330 ) @ ( vplus @ Vd329 @ Vd330 ) )
=> ( greater @ Vd328 @ Vd329 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(202), 0), 2)') ).
thf(37,axiom,
! [Vd328: $i,Vd329: $i,Vd330: $i] :
( ( ( vplus @ Vd328 @ Vd330 )
= ( vplus @ Vd329 @ Vd330 ) )
=> ( Vd328 = Vd329 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(202), 0), 1)') ).
thf(38,axiom,
! [Vd328: $i,Vd329: $i,Vd330: $i] :
( ( less @ ( vplus @ Vd328 @ Vd330 ) @ ( vplus @ Vd329 @ Vd330 ) )
=> ( less @ Vd328 @ Vd329 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(202), 0), 0)') ).
thf(39,axiom,
! [Vd337: $i,Vd338: $i,Vd340: $i,Vd341: $i] :
( ( ( greater @ Vd340 @ Vd341 )
& ( greater @ Vd337 @ Vd338 ) )
=> ( greater @ ( vplus @ Vd337 @ Vd340 ) @ ( vplus @ Vd338 @ Vd341 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(209, 0), 0)') ).
thf(41,axiom,
! [Vd362: $i,Vd363: $i,Vd365: $i,Vd366: $i] :
( ( ( geq @ Vd365 @ Vd366 )
& ( geq @ Vd362 @ Vd363 ) )
=> ( geq @ ( vplus @ Vd362 @ Vd365 ) @ ( vplus @ Vd363 @ Vd366 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(223, 0), 0)') ).
thf(46,axiom,
! [Vd400: $i] :
( ( vmul @ v1 @ Vd400 )
= Vd400 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(253, 0), 0)') ).
thf(47,axiom,
! [Vd408: $i,Vd409: $i] :
( ( vmul @ ( vsucc @ Vd408 ) @ Vd409 )
= ( vplus @ ( vmul @ Vd408 @ Vd409 ) @ Vd409 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(261, 0), 0)') ).
thf(48,axiom,
! [Vd418: $i,Vd419: $i] :
( ( vmul @ Vd418 @ Vd419 )
= ( vmul @ Vd419 @ Vd418 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(270, 0), 0)') ).
thf(50,axiom,
( ( vmul @ vd436 @ ( vsucc @ vd437 ) )
= ( vplus @ ( vmul @ vd436 @ vd437 ) @ vd436 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(284, 438, 1)') ).
thf(51,axiom,
( ( vplus @ ( vmul @ vd436 @ vd437 ) @ vd436 )
= ( vplus @ ( vmul @ vd436 @ vd437 ) @ ( vmul @ vd436 @ v1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(284, 438, 2)') ).
thf(52,axiom,
( ( vmul @ vd436 @ ( vplus @ vd437 @ vd439 ) )
= ( vplus @ ( vmul @ vd436 @ vd437 ) @ ( vmul @ vd436 @ vd439 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(285, 440, 0)') ).
thf(53,axiom,
( ( vmul @ vd436 @ ( vplus @ vd437 @ ( vsucc @ vd439 ) ) )
= ( vmul @ vd436 @ ( vsucc @ ( vplus @ vd437 @ vd439 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(286, 441, 0)') ).
thf(54,axiom,
( ( vmul @ vd436 @ ( vsucc @ ( vplus @ vd437 @ vd439 ) ) )
= ( vplus @ ( vmul @ vd436 @ ( vplus @ vd437 @ vd439 ) ) @ vd436 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(286, 441, 1)') ).
thf(55,conjecture,
( ( vplus @ ( vmul @ vd436 @ ( vplus @ vd437 @ vd439 ) ) @ vd436 )
= ( vplus @ ( vplus @ ( vmul @ vd436 @ vd437 ) @ ( vmul @ vd436 @ vd439 ) ) @ vd436 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(286, 441, 2)') ).
thf(56,negated_conjecture,
( ( ( vplus @ ( vmul @ vd436 @ ( vplus @ vd437 @ vd439 ) ) @ vd436 )
= ( vplus @ ( vplus @ ( vmul @ vd436 @ vd437 ) @ ( vmul @ vd436 @ vd439 ) ) @ vd436 ) )
= $false ),
inference(negate_conjecture,[status(cth)],[55]) ).
thf(57,plain,
( ( ( vplus @ ( vmul @ vd436 @ ( vplus @ vd437 @ vd439 ) ) @ vd436 )
= ( vplus @ ( vplus @ ( vmul @ vd436 @ vd437 ) @ ( vmul @ vd436 @ vd439 ) ) @ vd436 ) )
= $false ),
inference(unfold_def,[status(thm)],[56]) ).
thf(58,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(59,plain,
( ( ! [Vd68: $i,Vd69: $i] :
( ( vplus @ ( vsucc @ Vd68 ) @ Vd69 )
= ( vsucc @ ( vplus @ Vd68 @ Vd69 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(60,plain,
( ( ! [Vd78: $i,Vd79: $i] :
( ( vplus @ Vd79 @ Vd78 )
= ( vplus @ Vd78 @ Vd79 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(61,plain,
( ( ! [Vd92: $i,Vd93: $i] :
( Vd93
!= ( vplus @ Vd92 @ Vd93 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(62,plain,
( ( ! [Vd104: $i,Vd105: $i] :
( ( Vd104 != Vd105 )
=> ! [Vd107: $i] :
( ( vplus @ Vd107 @ Vd104 )
!= ( vplus @ Vd107 @ Vd105 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(63,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ( Vd120 != Vd121 )
| ~ ? [Vd123: $i] :
( Vd120
= ( vplus @ Vd121 @ Vd123 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(64,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ~ ? [Vd123: $i] :
( Vd120
= ( vplus @ Vd121 @ Vd123 ) )
| ~ ? [Vd125: $i] :
( Vd121
= ( vplus @ Vd120 @ Vd125 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(65,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ( Vd120 != Vd121 )
| ~ ? [Vd125: $i] :
( Vd121
= ( vplus @ Vd120 @ Vd125 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(66,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ( Vd120 = Vd121 )
| ? [Vd123: $i] :
( Vd120
= ( vplus @ Vd121 @ Vd123 ) )
| ? [Vd125: $i] :
( Vd121
= ( vplus @ Vd120 @ Vd125 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(67,plain,
( ( ! [Vd193: $i,Vd194: $i] :
( ( greater @ Vd194 @ Vd193 )
<=> ? [Vd196: $i] :
( Vd194
= ( vplus @ Vd193 @ Vd196 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(68,plain,
( ( ! [Vd198: $i,Vd199: $i] :
( ( less @ Vd199 @ Vd198 )
<=> ? [Vd201: $i] :
( Vd198
= ( vplus @ Vd199 @ Vd201 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(69,plain,
( ( ! [Vd295: $i,Vd296: $i] : ( greater @ ( vplus @ Vd295 @ Vd296 ) @ Vd295 ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(70,plain,
( ( ! [Vd301: $i,Vd302: $i,Vd303: $i] :
( ( greater @ Vd301 @ Vd302 )
=> ( greater @ ( vplus @ Vd301 @ Vd303 ) @ ( vplus @ Vd302 @ Vd303 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(71,plain,
( ( ! [Vd301: $i,Vd302: $i,Vd303: $i] :
( ( Vd301 = Vd302 )
=> ( ( vplus @ Vd301 @ Vd303 )
= ( vplus @ Vd302 @ Vd303 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(72,plain,
( ( ! [Vd301: $i,Vd302: $i,Vd303: $i] :
( ( less @ Vd301 @ Vd302 )
=> ( less @ ( vplus @ Vd301 @ Vd303 ) @ ( vplus @ Vd302 @ Vd303 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(73,plain,
( ( ! [Vd328: $i,Vd329: $i,Vd330: $i] :
( ( greater @ ( vplus @ Vd328 @ Vd330 ) @ ( vplus @ Vd329 @ Vd330 ) )
=> ( greater @ Vd328 @ Vd329 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(74,plain,
( ( ! [Vd328: $i,Vd329: $i,Vd330: $i] :
( ( ( vplus @ Vd328 @ Vd330 )
= ( vplus @ Vd329 @ Vd330 ) )
=> ( Vd328 = Vd329 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(75,plain,
( ( ! [Vd328: $i,Vd329: $i,Vd330: $i] :
( ( less @ ( vplus @ Vd328 @ Vd330 ) @ ( vplus @ Vd329 @ Vd330 ) )
=> ( less @ Vd328 @ Vd329 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(76,plain,
( ( ! [Vd337: $i,Vd338: $i,Vd340: $i,Vd341: $i] :
( ( ( greater @ Vd340 @ Vd341 )
& ( greater @ Vd337 @ Vd338 ) )
=> ( greater @ ( vplus @ Vd337 @ Vd340 ) @ ( vplus @ Vd338 @ Vd341 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(77,plain,
( ( ! [Vd362: $i,Vd363: $i,Vd365: $i,Vd366: $i] :
( ( ( geq @ Vd365 @ Vd366 )
& ( geq @ Vd362 @ Vd363 ) )
=> ( geq @ ( vplus @ Vd362 @ Vd365 ) @ ( vplus @ Vd363 @ Vd366 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(78,plain,
( ( ! [Vd400: $i] :
( ( vmul @ v1 @ Vd400 )
= Vd400 ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(79,plain,
( ( ! [Vd408: $i,Vd409: $i] :
( ( vmul @ ( vsucc @ Vd408 ) @ Vd409 )
= ( vplus @ ( vmul @ Vd408 @ Vd409 ) @ Vd409 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(80,plain,
( ( ! [Vd418: $i,Vd419: $i] :
( ( vmul @ Vd418 @ Vd419 )
= ( vmul @ Vd419 @ Vd418 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(81,plain,
( ( ( vmul @ vd436 @ ( vsucc @ vd437 ) )
= ( vplus @ ( vmul @ vd436 @ vd437 ) @ vd436 ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(82,plain,
( ( ( vplus @ ( vmul @ vd436 @ vd437 ) @ vd436 )
= ( vplus @ ( vmul @ vd436 @ vd437 ) @ ( vmul @ vd436 @ v1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(83,plain,
( ( ( vmul @ vd436 @ ( vplus @ vd437 @ vd439 ) )
= ( vplus @ ( vmul @ vd436 @ vd437 ) @ ( vmul @ vd436 @ vd439 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(84,plain,
( ( ( vmul @ vd436 @ ( vplus @ vd437 @ ( vsucc @ vd439 ) ) )
= ( vmul @ vd436 @ ( vsucc @ ( vplus @ vd437 @ vd439 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(85,plain,
( ( ( vmul @ vd436 @ ( vsucc @ ( vplus @ vd437 @ vd439 ) ) )
= ( vplus @ ( vmul @ vd436 @ ( vplus @ vd437 @ vd439 ) ) @ vd436 ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(86,plain,
( ( ( vplus @ ( vmul @ vd436 @ ( vplus @ vd437 @ vd439 ) ) @ vd436 )
!= ( vplus @ ( vplus @ ( vmul @ vd436 @ vd437 ) @ ( vmul @ vd436 @ vd439 ) ) @ vd436 ) )
= $true ),
inference(polarity_switch,[status(thm)],[57]) ).
thf(87,plain,
( ( ( vmul @ vd436 @ ( vsucc @ ( vplus @ vd437 @ vd439 ) ) )
= ( vplus @ ( vmul @ vd436 @ ( vplus @ vd437 @ vd439 ) ) @ vd436 ) )
= $true ),
inference(copy,[status(thm)],[85]) ).
thf(88,plain,
( ( ( vmul @ vd436 @ ( vplus @ vd437 @ ( vsucc @ vd439 ) ) )
= ( vmul @ vd436 @ ( vsucc @ ( vplus @ vd437 @ vd439 ) ) ) )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(89,plain,
( ( ( vmul @ vd436 @ ( vplus @ vd437 @ vd439 ) )
= ( vplus @ ( vmul @ vd436 @ vd437 ) @ ( vmul @ vd436 @ vd439 ) ) )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(90,plain,
( ( ( vplus @ ( vmul @ vd436 @ vd437 ) @ vd436 )
= ( vplus @ ( vmul @ vd436 @ vd437 ) @ ( vmul @ vd436 @ v1 ) ) )
= $true ),
inference(copy,[status(thm)],[82]) ).
thf(91,plain,
( ( ( vmul @ vd436 @ ( vsucc @ vd437 ) )
= ( vplus @ ( vmul @ vd436 @ vd437 ) @ vd436 ) )
= $true ),
inference(copy,[status(thm)],[81]) ).
thf(92,plain,
( ( ! [Vd418: $i,Vd419: $i] :
( ( vmul @ Vd418 @ Vd419 )
= ( vmul @ Vd419 @ Vd418 ) ) )
= $true ),
inference(copy,[status(thm)],[80]) ).
thf(93,plain,
( ( ! [Vd408: $i,Vd409: $i] :
( ( vmul @ ( vsucc @ Vd408 ) @ Vd409 )
= ( vplus @ ( vmul @ Vd408 @ Vd409 ) @ Vd409 ) ) )
= $true ),
inference(copy,[status(thm)],[79]) ).
thf(94,plain,
( ( ! [Vd400: $i] :
( ( vmul @ v1 @ Vd400 )
= Vd400 ) )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(95,plain,
( ( ! [Vd362: $i,Vd363: $i,Vd365: $i,Vd366: $i] :
( ( ( geq @ Vd365 @ Vd366 )
& ( geq @ Vd362 @ Vd363 ) )
=> ( geq @ ( vplus @ Vd362 @ Vd365 ) @ ( vplus @ Vd363 @ Vd366 ) ) ) )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(96,plain,
( ( ! [Vd337: $i,Vd338: $i,Vd340: $i,Vd341: $i] :
( ( ( greater @ Vd340 @ Vd341 )
& ( greater @ Vd337 @ Vd338 ) )
=> ( greater @ ( vplus @ Vd337 @ Vd340 ) @ ( vplus @ Vd338 @ Vd341 ) ) ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(97,plain,
( ( ! [Vd328: $i,Vd329: $i,Vd330: $i] :
( ( less @ ( vplus @ Vd328 @ Vd330 ) @ ( vplus @ Vd329 @ Vd330 ) )
=> ( less @ Vd328 @ Vd329 ) ) )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(98,plain,
( ( ! [Vd328: $i,Vd329: $i,Vd330: $i] :
( ( ( vplus @ Vd328 @ Vd330 )
= ( vplus @ Vd329 @ Vd330 ) )
=> ( Vd328 = Vd329 ) ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(99,plain,
( ( ! [Vd328: $i,Vd329: $i,Vd330: $i] :
( ( greater @ ( vplus @ Vd328 @ Vd330 ) @ ( vplus @ Vd329 @ Vd330 ) )
=> ( greater @ Vd328 @ Vd329 ) ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(100,plain,
( ( ! [Vd301: $i,Vd302: $i,Vd303: $i] :
( ( less @ Vd301 @ Vd302 )
=> ( less @ ( vplus @ Vd301 @ Vd303 ) @ ( vplus @ Vd302 @ Vd303 ) ) ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(101,plain,
( ( ! [Vd301: $i,Vd302: $i,Vd303: $i] :
( ( Vd301 = Vd302 )
=> ( ( vplus @ Vd301 @ Vd303 )
= ( vplus @ Vd302 @ Vd303 ) ) ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(102,plain,
( ( ! [Vd301: $i,Vd302: $i,Vd303: $i] :
( ( greater @ Vd301 @ Vd302 )
=> ( greater @ ( vplus @ Vd301 @ Vd303 ) @ ( vplus @ Vd302 @ Vd303 ) ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(103,plain,
( ( ! [Vd295: $i,Vd296: $i] : ( greater @ ( vplus @ Vd295 @ Vd296 ) @ Vd295 ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(104,plain,
( ( ! [Vd198: $i,Vd199: $i] :
( ( less @ Vd199 @ Vd198 )
<=> ? [Vd201: $i] :
( Vd198
= ( vplus @ Vd199 @ Vd201 ) ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(105,plain,
( ( ! [Vd193: $i,Vd194: $i] :
( ( greater @ Vd194 @ Vd193 )
<=> ? [Vd196: $i] :
( Vd194
= ( vplus @ Vd193 @ Vd196 ) ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(106,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ( Vd120 = Vd121 )
| ? [Vd123: $i] :
( Vd120
= ( vplus @ Vd121 @ Vd123 ) )
| ? [Vd125: $i] :
( Vd121
= ( vplus @ Vd120 @ Vd125 ) ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(107,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ( Vd120 != Vd121 )
| ~ ? [Vd125: $i] :
( Vd121
= ( vplus @ Vd120 @ Vd125 ) ) ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(108,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ~ ? [Vd123: $i] :
( Vd120
= ( vplus @ Vd121 @ Vd123 ) )
| ~ ? [Vd125: $i] :
( Vd121
= ( vplus @ Vd120 @ Vd125 ) ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(109,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ( Vd120 != Vd121 )
| ~ ? [Vd123: $i] :
( Vd120
= ( vplus @ Vd121 @ Vd123 ) ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(110,plain,
( ( ! [Vd104: $i,Vd105: $i] :
( ( Vd104 != Vd105 )
=> ! [Vd107: $i] :
( ( vplus @ Vd107 @ Vd104 )
!= ( vplus @ Vd107 @ Vd105 ) ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(111,plain,
( ( ! [Vd92: $i,Vd93: $i] :
( Vd93
!= ( vplus @ Vd92 @ Vd93 ) ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(112,plain,
( ( ! [Vd78: $i,Vd79: $i] :
( ( vplus @ Vd79 @ Vd78 )
= ( vplus @ Vd78 @ Vd79 ) ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(113,plain,
( ( ! [Vd68: $i,Vd69: $i] :
( ( vplus @ ( vsucc @ Vd68 ) @ Vd69 )
= ( vsucc @ ( vplus @ Vd68 @ Vd69 ) ) ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(114,plain,
( ( ! [Vd46: $i,Vd47: $i,Vd48: $i] :
( ( vplus @ ( vplus @ Vd46 @ Vd47 ) @ Vd48 )
= ( vplus @ Vd46 @ ( vplus @ Vd47 @ Vd48 ) ) ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(115,plain,
( ( ( vplus @ ( vmul @ vd436 @ ( vplus @ vd437 @ vd439 ) ) @ vd436 )
!= ( vplus @ ( vplus @ ( vmul @ vd436 @ vd437 ) @ ( vmul @ vd436 @ vd439 ) ) @ vd436 ) )
= $true ),
inference(copy,[status(thm)],[86]) ).
thf(116,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( geq @ SX2 @ SX3 )
| ~ ( geq @ SX0 @ SX1 ) )
| ( geq @ ( vplus @ SX0 @ SX2 ) @ ( vplus @ SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(117,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( greater @ ( vplus @ SX0 @ SX2 ) @ ( vplus @ SX1 @ SX2 ) )
| ( greater @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[99]) ).
thf(118,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( less @ ( vplus @ SX0 @ SX2 ) @ ( vplus @ SX1 @ SX2 ) )
| ( less @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[97]) ).
thf(119,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ( SX0 != SX1 ) )
| ! [SX2: $i] :
( ( vplus @ SX2 @ SX0 )
!= ( vplus @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[110]) ).
thf(120,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ~ ! [SX2: $i] :
( SX1
!= ( vplus @ SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[107]) ).
thf(121,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( greater @ SX1 @ SX0 )
| ~ ! [SX2: $i] :
( SX1
!= ( vplus @ SX0 @ SX2 ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
( SX1
!= ( vplus @ SX0 @ SX2 ) )
| ( greater @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[105]) ).
thf(122,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( vplus @ SX0 @ SX2 )
!= ( vplus @ SX1 @ SX2 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(123,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( less @ SX0 @ SX1 )
| ( less @ ( vplus @ SX0 @ SX2 ) @ ( vplus @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[100]) ).
thf(124,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ~ ! [SX2: $i] :
( SX0
!= ( vplus @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[109]) ).
thf(125,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( greater @ SX2 @ SX3 )
| ~ ( greater @ SX0 @ SX1 ) )
| ( greater @ ( vplus @ SX0 @ SX2 ) @ ( vplus @ SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(126,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( SX0 != SX1 )
| ( ( vplus @ SX0 @ SX2 )
= ( vplus @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[101]) ).
thf(127,plain,
( ( ! [SX0: $i,SX1: $i] :
( SX1
!= ( vplus @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[111]) ).
thf(128,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ! [SX2: $i] :
( SX0
!= ( vplus @ SX1 @ SX2 ) )
| ~ ! [SX2: $i] :
( SX1
!= ( vplus @ SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[106]) ).
thf(129,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( greater @ SX0 @ SX1 )
| ( greater @ ( vplus @ SX0 @ SX2 ) @ ( vplus @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[102]) ).
thf(130,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( less @ SX1 @ SX0 )
| ~ ! [SX2: $i] :
( SX0
!= ( vplus @ SX1 @ SX2 ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
( SX0
!= ( vplus @ SX1 @ SX2 ) )
| ( less @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[104]) ).
thf(131,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ! [SX2: $i] :
( SX0
!= ( vplus @ SX1 @ SX2 ) )
| ~ ~ ! [SX2: $i] :
( SX1
!= ( vplus @ SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[108]) ).
thf(132,plain,
! [SV1: $i] :
( ( ! [SY65: $i] :
( ( vmul @ SV1 @ SY65 )
= ( vmul @ SY65 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(133,plain,
! [SV2: $i] :
( ( ! [SY66: $i] :
( ( vmul @ ( vsucc @ SV2 ) @ SY66 )
= ( vplus @ ( vmul @ SV2 @ SY66 ) @ SY66 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(134,plain,
! [SV3: $i] :
( ( ( vmul @ v1 @ SV3 )
= SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(135,plain,
! [SV4: $i] :
( ( ! [SY67: $i] : ( greater @ ( vplus @ SV4 @ SY67 ) @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(136,plain,
! [SV5: $i] :
( ( ! [SY68: $i] :
( ( vplus @ SY68 @ SV5 )
= ( vplus @ SV5 @ SY68 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(137,plain,
! [SV6: $i] :
( ( ! [SY69: $i] :
( ( vplus @ ( vsucc @ SV6 ) @ SY69 )
= ( vsucc @ ( vplus @ SV6 @ SY69 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(138,plain,
! [SV7: $i] :
( ( ! [SY70: $i,SY71: $i] :
( ( vplus @ ( vplus @ SV7 @ SY70 ) @ SY71 )
= ( vplus @ SV7 @ ( vplus @ SY70 @ SY71 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(139,plain,
( ( ( vplus @ ( vmul @ vd436 @ ( vplus @ vd437 @ vd439 ) ) @ vd436 )
= ( vplus @ ( vplus @ ( vmul @ vd436 @ vd437 ) @ ( vmul @ vd436 @ vd439 ) ) @ vd436 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(140,plain,
! [SV8: $i] :
( ( ! [SY72: $i,SY73: $i,SY74: $i] :
( ~ ~ ( ~ ( geq @ SY73 @ SY74 )
| ~ ( geq @ SV8 @ SY72 ) )
| ( geq @ ( vplus @ SV8 @ SY73 ) @ ( vplus @ SY72 @ SY74 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(141,plain,
! [SV9: $i] :
( ( ! [SY75: $i,SY76: $i] :
( ~ ( greater @ ( vplus @ SV9 @ SY76 ) @ ( vplus @ SY75 @ SY76 ) )
| ( greater @ SV9 @ SY75 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(142,plain,
! [SV10: $i] :
( ( ! [SY77: $i,SY78: $i] :
( ~ ( less @ ( vplus @ SV10 @ SY78 ) @ ( vplus @ SY77 @ SY78 ) )
| ( less @ SV10 @ SY77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(143,plain,
! [SV11: $i] :
( ( ! [SY79: $i] :
( ~ ( ( SV11 != SY79 ) )
| ! [SY80: $i] :
( ( vplus @ SY80 @ SV11 )
!= ( vplus @ SY80 @ SY79 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(144,plain,
! [SV12: $i] :
( ( ! [SY81: $i] :
( ( SV12 != SY81 )
| ~ ~ ! [SY82: $i] :
( SY81
!= ( vplus @ SV12 @ SY82 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(145,plain,
! [SV13: $i] :
( ( ! [SY83: $i] :
~ ( ~ ( ~ ( greater @ SY83 @ SV13 )
| ~ ! [SY84: $i] :
( SY83
!= ( vplus @ SV13 @ SY84 ) ) )
| ~ ( ~ ~ ! [SY85: $i] :
( SY83
!= ( vplus @ SV13 @ SY85 ) )
| ( greater @ SY83 @ SV13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(146,plain,
! [SV14: $i] :
( ( ! [SY86: $i,SY87: $i] :
( ( ( vplus @ SV14 @ SY87 )
!= ( vplus @ SY86 @ SY87 ) )
| ( SV14 = SY86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(147,plain,
! [SV15: $i] :
( ( ! [SY88: $i,SY89: $i] :
( ~ ( less @ SV15 @ SY88 )
| ( less @ ( vplus @ SV15 @ SY89 ) @ ( vplus @ SY88 @ SY89 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(148,plain,
! [SV16: $i] :
( ( ! [SY90: $i] :
( ( SV16 != SY90 )
| ~ ~ ! [SY91: $i] :
( SV16
!= ( vplus @ SY90 @ SY91 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(149,plain,
! [SV17: $i] :
( ( ! [SY92: $i,SY93: $i,SY94: $i] :
( ~ ~ ( ~ ( greater @ SY93 @ SY94 )
| ~ ( greater @ SV17 @ SY92 ) )
| ( greater @ ( vplus @ SV17 @ SY93 ) @ ( vplus @ SY92 @ SY94 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(150,plain,
! [SV18: $i] :
( ( ! [SY95: $i,SY96: $i] :
( ( SV18 != SY95 )
| ( ( vplus @ SV18 @ SY96 )
= ( vplus @ SY95 @ SY96 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(151,plain,
! [SV19: $i] :
( ( ! [SY97: $i] :
( SY97
!= ( vplus @ SV19 @ SY97 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(152,plain,
! [SV20: $i] :
( ( ! [SY98: $i] :
( ( SV20 = SY98 )
| ~ ! [SY99: $i] :
( SV20
!= ( vplus @ SY98 @ SY99 ) )
| ~ ! [SY100: $i] :
( SY98
!= ( vplus @ SV20 @ SY100 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(153,plain,
! [SV21: $i] :
( ( ! [SY101: $i,SY102: $i] :
( ~ ( greater @ SV21 @ SY101 )
| ( greater @ ( vplus @ SV21 @ SY102 ) @ ( vplus @ SY101 @ SY102 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(154,plain,
! [SV22: $i] :
( ( ! [SY103: $i] :
~ ( ~ ( ~ ( less @ SY103 @ SV22 )
| ~ ! [SY104: $i] :
( SV22
!= ( vplus @ SY103 @ SY104 ) ) )
| ~ ( ~ ~ ! [SY105: $i] :
( SV22
!= ( vplus @ SY103 @ SY105 ) )
| ( less @ SY103 @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(155,plain,
! [SV23: $i] :
( ( ! [SY106: $i] :
( ~ ~ ! [SY107: $i] :
( SV23
!= ( vplus @ SY106 @ SY107 ) )
| ~ ~ ! [SY108: $i] :
( SY106
!= ( vplus @ SV23 @ SY108 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(156,plain,
! [SV24: $i,SV1: $i] :
( ( ( vmul @ SV1 @ SV24 )
= ( vmul @ SV24 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(157,plain,
! [SV25: $i,SV2: $i] :
( ( ( vmul @ ( vsucc @ SV2 ) @ SV25 )
= ( vplus @ ( vmul @ SV2 @ SV25 ) @ SV25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(158,plain,
! [SV26: $i,SV4: $i] :
( ( greater @ ( vplus @ SV4 @ SV26 ) @ SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(159,plain,
! [SV5: $i,SV27: $i] :
( ( ( vplus @ SV27 @ SV5 )
= ( vplus @ SV5 @ SV27 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(160,plain,
! [SV28: $i,SV6: $i] :
( ( ( vplus @ ( vsucc @ SV6 ) @ SV28 )
= ( vsucc @ ( vplus @ SV6 @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(161,plain,
! [SV29: $i,SV7: $i] :
( ( ! [SY109: $i] :
( ( vplus @ ( vplus @ SV7 @ SV29 ) @ SY109 )
= ( vplus @ SV7 @ ( vplus @ SV29 @ SY109 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(162,plain,
! [SV30: $i,SV8: $i] :
( ( ! [SY110: $i,SY111: $i] :
( ~ ~ ( ~ ( geq @ SY110 @ SY111 )
| ~ ( geq @ SV8 @ SV30 ) )
| ( geq @ ( vplus @ SV8 @ SY110 ) @ ( vplus @ SV30 @ SY111 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(163,plain,
! [SV31: $i,SV9: $i] :
( ( ! [SY112: $i] :
( ~ ( greater @ ( vplus @ SV9 @ SY112 ) @ ( vplus @ SV31 @ SY112 ) )
| ( greater @ SV9 @ SV31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(164,plain,
! [SV32: $i,SV10: $i] :
( ( ! [SY113: $i] :
( ~ ( less @ ( vplus @ SV10 @ SY113 ) @ ( vplus @ SV32 @ SY113 ) )
| ( less @ SV10 @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(165,plain,
! [SV33: $i,SV11: $i] :
( ( ~ ( ( SV11 != SV33 ) )
| ! [SY114: $i] :
( ( vplus @ SY114 @ SV11 )
!= ( vplus @ SY114 @ SV33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(166,plain,
! [SV34: $i,SV12: $i] :
( ( ( SV12 != SV34 )
| ~ ~ ! [SY115: $i] :
( SV34
!= ( vplus @ SV12 @ SY115 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(167,plain,
! [SV13: $i,SV35: $i] :
( ( ~ ( ~ ( ~ ( greater @ SV35 @ SV13 )
| ~ ! [SY116: $i] :
( SV35
!= ( vplus @ SV13 @ SY116 ) ) )
| ~ ( ~ ~ ! [SY117: $i] :
( SV35
!= ( vplus @ SV13 @ SY117 ) )
| ( greater @ SV35 @ SV13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(168,plain,
! [SV36: $i,SV14: $i] :
( ( ! [SY118: $i] :
( ( ( vplus @ SV14 @ SY118 )
!= ( vplus @ SV36 @ SY118 ) )
| ( SV14 = SV36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(169,plain,
! [SV37: $i,SV15: $i] :
( ( ! [SY119: $i] :
( ~ ( less @ SV15 @ SV37 )
| ( less @ ( vplus @ SV15 @ SY119 ) @ ( vplus @ SV37 @ SY119 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(170,plain,
! [SV38: $i,SV16: $i] :
( ( ( SV16 != SV38 )
| ~ ~ ! [SY120: $i] :
( SV16
!= ( vplus @ SV38 @ SY120 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(171,plain,
! [SV39: $i,SV17: $i] :
( ( ! [SY121: $i,SY122: $i] :
( ~ ~ ( ~ ( greater @ SY121 @ SY122 )
| ~ ( greater @ SV17 @ SV39 ) )
| ( greater @ ( vplus @ SV17 @ SY121 ) @ ( vplus @ SV39 @ SY122 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(172,plain,
! [SV40: $i,SV18: $i] :
( ( ! [SY123: $i] :
( ( SV18 != SV40 )
| ( ( vplus @ SV18 @ SY123 )
= ( vplus @ SV40 @ SY123 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(173,plain,
! [SV19: $i,SV41: $i] :
( ( SV41
!= ( vplus @ SV19 @ SV41 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(174,plain,
! [SV42: $i,SV20: $i] :
( ( ( SV20 = SV42 )
| ~ ! [SY124: $i] :
( SV20
!= ( vplus @ SV42 @ SY124 ) )
| ~ ! [SY125: $i] :
( SV42
!= ( vplus @ SV20 @ SY125 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(175,plain,
! [SV43: $i,SV21: $i] :
( ( ! [SY126: $i] :
( ~ ( greater @ SV21 @ SV43 )
| ( greater @ ( vplus @ SV21 @ SY126 ) @ ( vplus @ SV43 @ SY126 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(176,plain,
! [SV22: $i,SV44: $i] :
( ( ~ ( ~ ( ~ ( less @ SV44 @ SV22 )
| ~ ! [SY127: $i] :
( SV22
!= ( vplus @ SV44 @ SY127 ) ) )
| ~ ( ~ ~ ! [SY128: $i] :
( SV22
!= ( vplus @ SV44 @ SY128 ) )
| ( less @ SV44 @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(177,plain,
! [SV45: $i,SV23: $i] :
( ( ~ ~ ! [SY129: $i] :
( SV23
!= ( vplus @ SV45 @ SY129 ) )
| ~ ~ ! [SY130: $i] :
( SV45
!= ( vplus @ SV23 @ SY130 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(178,plain,
! [SV46: $i,SV29: $i,SV7: $i] :
( ( ( vplus @ ( vplus @ SV7 @ SV29 ) @ SV46 )
= ( vplus @ SV7 @ ( vplus @ SV29 @ SV46 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(179,plain,
! [SV30: $i,SV8: $i,SV47: $i] :
( ( ! [SY131: $i] :
( ~ ~ ( ~ ( geq @ SV47 @ SY131 )
| ~ ( geq @ SV8 @ SV30 ) )
| ( geq @ ( vplus @ SV8 @ SV47 ) @ ( vplus @ SV30 @ SY131 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(180,plain,
! [SV31: $i,SV48: $i,SV9: $i] :
( ( ~ ( greater @ ( vplus @ SV9 @ SV48 ) @ ( vplus @ SV31 @ SV48 ) )
| ( greater @ SV9 @ SV31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(181,plain,
! [SV32: $i,SV49: $i,SV10: $i] :
( ( ~ ( less @ ( vplus @ SV10 @ SV49 ) @ ( vplus @ SV32 @ SV49 ) )
| ( less @ SV10 @ SV32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(182,plain,
! [SV33: $i,SV11: $i] :
( ( ( ~ ( ( SV11 != SV33 ) ) )
= $true )
| ( ( ! [SY114: $i] :
( ( vplus @ SY114 @ SV11 )
!= ( vplus @ SY114 @ SV33 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[165]) ).
thf(183,plain,
! [SV34: $i,SV12: $i] :
( ( ( SV12 != SV34 )
= $true )
| ( ( ~ ~ ! [SY115: $i] :
( SV34
!= ( vplus @ SV12 @ SY115 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[166]) ).
thf(184,plain,
! [SV13: $i,SV35: $i] :
( ( ~ ( ~ ( greater @ SV35 @ SV13 )
| ~ ! [SY116: $i] :
( SV35
!= ( vplus @ SV13 @ SY116 ) ) )
| ~ ( ~ ~ ! [SY117: $i] :
( SV35
!= ( vplus @ SV13 @ SY117 ) )
| ( greater @ SV35 @ SV13 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(185,plain,
! [SV36: $i,SV50: $i,SV14: $i] :
( ( ( ( vplus @ SV14 @ SV50 )
!= ( vplus @ SV36 @ SV50 ) )
| ( SV14 = SV36 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(186,plain,
! [SV51: $i,SV37: $i,SV15: $i] :
( ( ~ ( less @ SV15 @ SV37 )
| ( less @ ( vplus @ SV15 @ SV51 ) @ ( vplus @ SV37 @ SV51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[169]) ).
thf(187,plain,
! [SV38: $i,SV16: $i] :
( ( ( SV16 != SV38 )
= $true )
| ( ( ~ ~ ! [SY120: $i] :
( SV16
!= ( vplus @ SV38 @ SY120 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[170]) ).
thf(188,plain,
! [SV39: $i,SV17: $i,SV52: $i] :
( ( ! [SY132: $i] :
( ~ ~ ( ~ ( greater @ SV52 @ SY132 )
| ~ ( greater @ SV17 @ SV39 ) )
| ( greater @ ( vplus @ SV17 @ SV52 ) @ ( vplus @ SV39 @ SY132 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(189,plain,
! [SV53: $i,SV40: $i,SV18: $i] :
( ( ( SV18 != SV40 )
| ( ( vplus @ SV18 @ SV53 )
= ( vplus @ SV40 @ SV53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(190,plain,
! [SV19: $i,SV41: $i] :
( ( SV41
= ( vplus @ SV19 @ SV41 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[173]) ).
thf(191,plain,
! [SV42: $i,SV20: $i] :
( ( ( ( SV20 = SV42 )
| ~ ! [SY124: $i] :
( SV20
!= ( vplus @ SV42 @ SY124 ) ) )
= $true )
| ( ( ~ ! [SY125: $i] :
( SV42
!= ( vplus @ SV20 @ SY125 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[174]) ).
thf(192,plain,
! [SV54: $i,SV43: $i,SV21: $i] :
( ( ~ ( greater @ SV21 @ SV43 )
| ( greater @ ( vplus @ SV21 @ SV54 ) @ ( vplus @ SV43 @ SV54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(193,plain,
! [SV22: $i,SV44: $i] :
( ( ~ ( ~ ( less @ SV44 @ SV22 )
| ~ ! [SY127: $i] :
( SV22
!= ( vplus @ SV44 @ SY127 ) ) )
| ~ ( ~ ~ ! [SY128: $i] :
( SV22
!= ( vplus @ SV44 @ SY128 ) )
| ( less @ SV44 @ SV22 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[176]) ).
thf(194,plain,
! [SV45: $i,SV23: $i] :
( ( ( ~ ~ ! [SY129: $i] :
( SV23
!= ( vplus @ SV45 @ SY129 ) ) )
= $true )
| ( ( ~ ~ ! [SY130: $i] :
( SV45
!= ( vplus @ SV23 @ SY130 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[177]) ).
thf(195,plain,
! [SV30: $i,SV8: $i,SV55: $i,SV47: $i] :
( ( ~ ~ ( ~ ( geq @ SV47 @ SV55 )
| ~ ( geq @ SV8 @ SV30 ) )
| ( geq @ ( vplus @ SV8 @ SV47 ) @ ( vplus @ SV30 @ SV55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(196,plain,
! [SV31: $i,SV48: $i,SV9: $i] :
( ( ( ~ ( greater @ ( vplus @ SV9 @ SV48 ) @ ( vplus @ SV31 @ SV48 ) ) )
= $true )
| ( ( greater @ SV9 @ SV31 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[180]) ).
thf(197,plain,
! [SV32: $i,SV49: $i,SV10: $i] :
( ( ( ~ ( less @ ( vplus @ SV10 @ SV49 ) @ ( vplus @ SV32 @ SV49 ) ) )
= $true )
| ( ( less @ SV10 @ SV32 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[181]) ).
thf(198,plain,
! [SV33: $i,SV11: $i] :
( ( ( SV11 != SV33 )
= $false )
| ( ( ! [SY114: $i] :
( ( vplus @ SY114 @ SV11 )
!= ( vplus @ SY114 @ SV33 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[182]) ).
thf(199,plain,
! [SV34: $i,SV12: $i] :
( ( ( SV12 = SV34 )
= $false )
| ( ( ~ ~ ! [SY115: $i] :
( SV34
!= ( vplus @ SV12 @ SY115 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[183]) ).
thf(200,plain,
! [SV13: $i,SV35: $i] :
( ( ~ ( ~ ( greater @ SV35 @ SV13 )
| ~ ! [SY116: $i] :
( SV35
!= ( vplus @ SV13 @ SY116 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[184]) ).
thf(201,plain,
! [SV13: $i,SV35: $i] :
( ( ~ ( ~ ~ ! [SY117: $i] :
( SV35
!= ( vplus @ SV13 @ SY117 ) )
| ( greater @ SV35 @ SV13 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[184]) ).
thf(202,plain,
! [SV36: $i,SV50: $i,SV14: $i] :
( ( ( ( vplus @ SV14 @ SV50 )
!= ( vplus @ SV36 @ SV50 ) )
= $true )
| ( ( SV14 = SV36 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[185]) ).
thf(203,plain,
! [SV51: $i,SV37: $i,SV15: $i] :
( ( ( ~ ( less @ SV15 @ SV37 ) )
= $true )
| ( ( less @ ( vplus @ SV15 @ SV51 ) @ ( vplus @ SV37 @ SV51 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[186]) ).
thf(204,plain,
! [SV38: $i,SV16: $i] :
( ( ( SV16 = SV38 )
= $false )
| ( ( ~ ~ ! [SY120: $i] :
( SV16
!= ( vplus @ SV38 @ SY120 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[187]) ).
thf(205,plain,
! [SV39: $i,SV17: $i,SV56: $i,SV52: $i] :
( ( ~ ~ ( ~ ( greater @ SV52 @ SV56 )
| ~ ( greater @ SV17 @ SV39 ) )
| ( greater @ ( vplus @ SV17 @ SV52 ) @ ( vplus @ SV39 @ SV56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(206,plain,
! [SV53: $i,SV40: $i,SV18: $i] :
( ( ( SV18 != SV40 )
= $true )
| ( ( ( vplus @ SV18 @ SV53 )
= ( vplus @ SV40 @ SV53 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[189]) ).
thf(207,plain,
! [SV42: $i,SV20: $i] :
( ( ( SV20 = SV42 )
= $true )
| ( ( ~ ! [SY124: $i] :
( SV20
!= ( vplus @ SV42 @ SY124 ) ) )
= $true )
| ( ( ~ ! [SY125: $i] :
( SV42
!= ( vplus @ SV20 @ SY125 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[191]) ).
thf(208,plain,
! [SV54: $i,SV43: $i,SV21: $i] :
( ( ( ~ ( greater @ SV21 @ SV43 ) )
= $true )
| ( ( greater @ ( vplus @ SV21 @ SV54 ) @ ( vplus @ SV43 @ SV54 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[192]) ).
thf(209,plain,
! [SV22: $i,SV44: $i] :
( ( ~ ( ~ ( less @ SV44 @ SV22 )
| ~ ! [SY127: $i] :
( SV22
!= ( vplus @ SV44 @ SY127 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[193]) ).
thf(210,plain,
! [SV44: $i,SV22: $i] :
( ( ~ ( ~ ~ ! [SY128: $i] :
( SV22
!= ( vplus @ SV44 @ SY128 ) )
| ( less @ SV44 @ SV22 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[193]) ).
thf(211,plain,
! [SV45: $i,SV23: $i] :
( ( ( ~ ! [SY129: $i] :
( SV23
!= ( vplus @ SV45 @ SY129 ) ) )
= $false )
| ( ( ~ ~ ! [SY130: $i] :
( SV45
!= ( vplus @ SV23 @ SY130 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(212,plain,
! [SV30: $i,SV8: $i,SV55: $i,SV47: $i] :
( ( ( ~ ~ ( ~ ( geq @ SV47 @ SV55 )
| ~ ( geq @ SV8 @ SV30 ) ) )
= $true )
| ( ( geq @ ( vplus @ SV8 @ SV47 ) @ ( vplus @ SV30 @ SV55 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[195]) ).
thf(213,plain,
! [SV31: $i,SV48: $i,SV9: $i] :
( ( ( greater @ ( vplus @ SV9 @ SV48 ) @ ( vplus @ SV31 @ SV48 ) )
= $false )
| ( ( greater @ SV9 @ SV31 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(214,plain,
! [SV32: $i,SV49: $i,SV10: $i] :
( ( ( less @ ( vplus @ SV10 @ SV49 ) @ ( vplus @ SV32 @ SV49 ) )
= $false )
| ( ( less @ SV10 @ SV32 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[197]) ).
thf(215,plain,
! [SV33: $i,SV11: $i] :
( ( ( SV11 = SV33 )
= $true )
| ( ( ! [SY114: $i] :
( ( vplus @ SY114 @ SV11 )
!= ( vplus @ SY114 @ SV33 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[198]) ).
thf(216,plain,
! [SV12: $i,SV34: $i] :
( ( ( ~ ! [SY115: $i] :
( SV34
!= ( vplus @ SV12 @ SY115 ) ) )
= $false )
| ( ( SV12 = SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[199]) ).
thf(217,plain,
! [SV13: $i,SV35: $i] :
( ( ~ ( greater @ SV35 @ SV13 )
| ~ ! [SY116: $i] :
( SV35
!= ( vplus @ SV13 @ SY116 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[200]) ).
thf(218,plain,
! [SV13: $i,SV35: $i] :
( ( ~ ~ ! [SY117: $i] :
( SV35
!= ( vplus @ SV13 @ SY117 ) )
| ( greater @ SV35 @ SV13 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[201]) ).
thf(219,plain,
! [SV36: $i,SV50: $i,SV14: $i] :
( ( ( ( vplus @ SV14 @ SV50 )
= ( vplus @ SV36 @ SV50 ) )
= $false )
| ( ( SV14 = SV36 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[202]) ).
thf(220,plain,
! [SV51: $i,SV37: $i,SV15: $i] :
( ( ( less @ SV15 @ SV37 )
= $false )
| ( ( less @ ( vplus @ SV15 @ SV51 ) @ ( vplus @ SV37 @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[203]) ).
thf(221,plain,
! [SV38: $i,SV16: $i] :
( ( ( ~ ! [SY120: $i] :
( SV16
!= ( vplus @ SV38 @ SY120 ) ) )
= $false )
| ( ( SV16 = SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(222,plain,
! [SV39: $i,SV17: $i,SV56: $i,SV52: $i] :
( ( ( ~ ~ ( ~ ( greater @ SV52 @ SV56 )
| ~ ( greater @ SV17 @ SV39 ) ) )
= $true )
| ( ( greater @ ( vplus @ SV17 @ SV52 ) @ ( vplus @ SV39 @ SV56 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[205]) ).
thf(223,plain,
! [SV53: $i,SV40: $i,SV18: $i] :
( ( ( SV18 = SV40 )
= $false )
| ( ( ( vplus @ SV18 @ SV53 )
= ( vplus @ SV40 @ SV53 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[206]) ).
thf(224,plain,
! [SV42: $i,SV20: $i] :
( ( ( ! [SY124: $i] :
( SV20
!= ( vplus @ SV42 @ SY124 ) ) )
= $false )
| ( ( SV20 = SV42 )
= $true )
| ( ( ~ ! [SY125: $i] :
( SV42
!= ( vplus @ SV20 @ SY125 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[207]) ).
thf(225,plain,
! [SV54: $i,SV43: $i,SV21: $i] :
( ( ( greater @ SV21 @ SV43 )
= $false )
| ( ( greater @ ( vplus @ SV21 @ SV54 ) @ ( vplus @ SV43 @ SV54 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[208]) ).
thf(226,plain,
! [SV22: $i,SV44: $i] :
( ( ~ ( less @ SV44 @ SV22 )
| ~ ! [SY127: $i] :
( SV22
!= ( vplus @ SV44 @ SY127 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[209]) ).
thf(227,plain,
! [SV44: $i,SV22: $i] :
( ( ~ ~ ! [SY128: $i] :
( SV22
!= ( vplus @ SV44 @ SY128 ) )
| ( less @ SV44 @ SV22 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[210]) ).
thf(228,plain,
! [SV45: $i,SV23: $i] :
( ( ( ! [SY129: $i] :
( SV23
!= ( vplus @ SV45 @ SY129 ) ) )
= $true )
| ( ( ~ ~ ! [SY130: $i] :
( SV45
!= ( vplus @ SV23 @ SY130 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[211]) ).
thf(229,plain,
! [SV30: $i,SV8: $i,SV55: $i,SV47: $i] :
( ( ( ~ ( ~ ( geq @ SV47 @ SV55 )
| ~ ( geq @ SV8 @ SV30 ) ) )
= $false )
| ( ( geq @ ( vplus @ SV8 @ SV47 ) @ ( vplus @ SV30 @ SV55 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[212]) ).
thf(230,plain,
! [SV33: $i,SV11: $i,SV57: $i] :
( ( ( ( vplus @ SV57 @ SV11 )
!= ( vplus @ SV57 @ SV33 ) )
= $true )
| ( ( SV11 = SV33 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[215]) ).
thf(231,plain,
! [SV12: $i,SV34: $i] :
( ( ( ! [SY115: $i] :
( SV34
!= ( vplus @ SV12 @ SY115 ) ) )
= $true )
| ( ( SV12 = SV34 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[216]) ).
thf(232,plain,
! [SV13: $i,SV35: $i] :
( ( ( ~ ( greater @ SV35 @ SV13 ) )
= $true )
| ( ( ~ ! [SY116: $i] :
( SV35
!= ( vplus @ SV13 @ SY116 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[217]) ).
thf(233,plain,
! [SV13: $i,SV35: $i] :
( ( ( ~ ~ ! [SY117: $i] :
( SV35
!= ( vplus @ SV13 @ SY117 ) ) )
= $true )
| ( ( greater @ SV35 @ SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[218]) ).
thf(234,plain,
! [SV38: $i,SV16: $i] :
( ( ( ! [SY120: $i] :
( SV16
!= ( vplus @ SV38 @ SY120 ) ) )
= $true )
| ( ( SV16 = SV38 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[221]) ).
thf(235,plain,
! [SV39: $i,SV17: $i,SV56: $i,SV52: $i] :
( ( ( ~ ( ~ ( greater @ SV52 @ SV56 )
| ~ ( greater @ SV17 @ SV39 ) ) )
= $false )
| ( ( greater @ ( vplus @ SV17 @ SV52 ) @ ( vplus @ SV39 @ SV56 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[222]) ).
thf(236,plain,
! [SV42: $i,SV20: $i] :
( ( ( SV20
!= ( vplus @ SV42 @ ( sK1_SY124 @ SV42 @ SV20 ) ) )
= $false )
| ( ( SV20 = SV42 )
= $true )
| ( ( ~ ! [SY125: $i] :
( SV42
!= ( vplus @ SV20 @ SY125 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[224]) ).
thf(237,plain,
! [SV22: $i,SV44: $i] :
( ( ( ~ ( less @ SV44 @ SV22 ) )
= $true )
| ( ( ~ ! [SY127: $i] :
( SV22
!= ( vplus @ SV44 @ SY127 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[226]) ).
thf(238,plain,
! [SV44: $i,SV22: $i] :
( ( ( ~ ~ ! [SY128: $i] :
( SV22
!= ( vplus @ SV44 @ SY128 ) ) )
= $true )
| ( ( less @ SV44 @ SV22 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[227]) ).
thf(239,plain,
! [SV58: $i,SV45: $i,SV23: $i] :
( ( ( SV23
!= ( vplus @ SV45 @ SV58 ) )
= $true )
| ( ( ~ ~ ! [SY130: $i] :
( SV45
!= ( vplus @ SV23 @ SY130 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[228]) ).
thf(240,plain,
! [SV30: $i,SV8: $i,SV55: $i,SV47: $i] :
( ( ( ~ ( geq @ SV47 @ SV55 )
| ~ ( geq @ SV8 @ SV30 ) )
= $true )
| ( ( geq @ ( vplus @ SV8 @ SV47 ) @ ( vplus @ SV30 @ SV55 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[229]) ).
thf(241,plain,
! [SV33: $i,SV11: $i,SV57: $i] :
( ( ( ( vplus @ SV57 @ SV11 )
= ( vplus @ SV57 @ SV33 ) )
= $false )
| ( ( SV11 = SV33 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[230]) ).
thf(242,plain,
! [SV59: $i,SV12: $i,SV34: $i] :
( ( ( SV34
!= ( vplus @ SV12 @ SV59 ) )
= $true )
| ( ( SV12 = SV34 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[231]) ).
thf(243,plain,
! [SV13: $i,SV35: $i] :
( ( ( greater @ SV35 @ SV13 )
= $false )
| ( ( ~ ! [SY116: $i] :
( SV35
!= ( vplus @ SV13 @ SY116 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[232]) ).
thf(244,plain,
! [SV13: $i,SV35: $i] :
( ( ( ~ ! [SY117: $i] :
( SV35
!= ( vplus @ SV13 @ SY117 ) ) )
= $false )
| ( ( greater @ SV35 @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[233]) ).
thf(245,plain,
! [SV60: $i,SV38: $i,SV16: $i] :
( ( ( SV16
!= ( vplus @ SV38 @ SV60 ) )
= $true )
| ( ( SV16 = SV38 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[234]) ).
thf(246,plain,
! [SV39: $i,SV17: $i,SV56: $i,SV52: $i] :
( ( ( ~ ( greater @ SV52 @ SV56 )
| ~ ( greater @ SV17 @ SV39 ) )
= $true )
| ( ( greater @ ( vplus @ SV17 @ SV52 ) @ ( vplus @ SV39 @ SV56 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[235]) ).
thf(247,plain,
! [SV42: $i,SV20: $i] :
( ( ( SV20
= ( vplus @ SV42 @ ( sK1_SY124 @ SV42 @ SV20 ) ) )
= $true )
| ( ( SV20 = SV42 )
= $true )
| ( ( ~ ! [SY125: $i] :
( SV42
!= ( vplus @ SV20 @ SY125 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[236]) ).
thf(248,plain,
! [SV22: $i,SV44: $i] :
( ( ( less @ SV44 @ SV22 )
= $false )
| ( ( ~ ! [SY127: $i] :
( SV22
!= ( vplus @ SV44 @ SY127 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[237]) ).
thf(249,plain,
! [SV44: $i,SV22: $i] :
( ( ( ~ ! [SY128: $i] :
( SV22
!= ( vplus @ SV44 @ SY128 ) ) )
= $false )
| ( ( less @ SV44 @ SV22 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[238]) ).
thf(250,plain,
! [SV58: $i,SV45: $i,SV23: $i] :
( ( ( SV23
= ( vplus @ SV45 @ SV58 ) )
= $false )
| ( ( ~ ~ ! [SY130: $i] :
( SV45
!= ( vplus @ SV23 @ SY130 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[239]) ).
thf(251,plain,
! [SV30: $i,SV8: $i,SV55: $i,SV47: $i] :
( ( ( ~ ( geq @ SV47 @ SV55 ) )
= $true )
| ( ( ~ ( geq @ SV8 @ SV30 ) )
= $true )
| ( ( geq @ ( vplus @ SV8 @ SV47 ) @ ( vplus @ SV30 @ SV55 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[240]) ).
thf(252,plain,
! [SV59: $i,SV12: $i,SV34: $i] :
( ( ( SV34
= ( vplus @ SV12 @ SV59 ) )
= $false )
| ( ( SV12 = SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[242]) ).
thf(253,plain,
! [SV13: $i,SV35: $i] :
( ( ( ! [SY116: $i] :
( SV35
!= ( vplus @ SV13 @ SY116 ) ) )
= $false )
| ( ( greater @ SV35 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[243]) ).
thf(254,plain,
! [SV13: $i,SV35: $i] :
( ( ( ! [SY117: $i] :
( SV35
!= ( vplus @ SV13 @ SY117 ) ) )
= $true )
| ( ( greater @ SV35 @ SV13 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[244]) ).
thf(255,plain,
! [SV60: $i,SV38: $i,SV16: $i] :
( ( ( SV16
= ( vplus @ SV38 @ SV60 ) )
= $false )
| ( ( SV16 = SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[245]) ).
thf(256,plain,
! [SV39: $i,SV17: $i,SV56: $i,SV52: $i] :
( ( ( ~ ( greater @ SV52 @ SV56 ) )
= $true )
| ( ( ~ ( greater @ SV17 @ SV39 ) )
= $true )
| ( ( greater @ ( vplus @ SV17 @ SV52 ) @ ( vplus @ SV39 @ SV56 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[246]) ).
thf(257,plain,
! [SV20: $i,SV42: $i] :
( ( ( ! [SY125: $i] :
( SV42
!= ( vplus @ SV20 @ SY125 ) ) )
= $false )
| ( ( SV20 = SV42 )
= $true )
| ( ( SV20
= ( vplus @ SV42 @ ( sK1_SY124 @ SV42 @ SV20 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[247]) ).
thf(258,plain,
! [SV44: $i,SV22: $i] :
( ( ( ! [SY127: $i] :
( SV22
!= ( vplus @ SV44 @ SY127 ) ) )
= $false )
| ( ( less @ SV44 @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[248]) ).
thf(259,plain,
! [SV44: $i,SV22: $i] :
( ( ( ! [SY128: $i] :
( SV22
!= ( vplus @ SV44 @ SY128 ) ) )
= $true )
| ( ( less @ SV44 @ SV22 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[249]) ).
thf(260,plain,
! [SV58: $i,SV23: $i,SV45: $i] :
( ( ( ~ ! [SY130: $i] :
( SV45
!= ( vplus @ SV23 @ SY130 ) ) )
= $false )
| ( ( SV23
= ( vplus @ SV45 @ SV58 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[250]) ).
thf(261,plain,
! [SV30: $i,SV8: $i,SV55: $i,SV47: $i] :
( ( ( geq @ SV47 @ SV55 )
= $false )
| ( ( ~ ( geq @ SV8 @ SV30 ) )
= $true )
| ( ( geq @ ( vplus @ SV8 @ SV47 ) @ ( vplus @ SV30 @ SV55 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[251]) ).
thf(262,plain,
! [SV13: $i,SV35: $i] :
( ( ( SV35
!= ( vplus @ SV13 @ ( sK2_SY116 @ SV13 @ SV35 ) ) )
= $false )
| ( ( greater @ SV35 @ SV13 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[253]) ).
thf(263,plain,
! [SV61: $i,SV13: $i,SV35: $i] :
( ( ( SV35
!= ( vplus @ SV13 @ SV61 ) )
= $true )
| ( ( greater @ SV35 @ SV13 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[254]) ).
thf(264,plain,
! [SV39: $i,SV17: $i,SV56: $i,SV52: $i] :
( ( ( greater @ SV52 @ SV56 )
= $false )
| ( ( ~ ( greater @ SV17 @ SV39 ) )
= $true )
| ( ( greater @ ( vplus @ SV17 @ SV52 ) @ ( vplus @ SV39 @ SV56 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[256]) ).
thf(265,plain,
! [SV20: $i,SV42: $i] :
( ( ( SV42
!= ( vplus @ SV20 @ ( sK3_SY125 @ SV20 @ SV42 ) ) )
= $false )
| ( ( SV20 = SV42 )
= $true )
| ( ( SV20
= ( vplus @ SV42 @ ( sK1_SY124 @ SV42 @ SV20 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[257]) ).
thf(266,plain,
! [SV44: $i,SV22: $i] :
( ( ( SV22
!= ( vplus @ SV44 @ ( sK4_SY127 @ SV44 @ SV22 ) ) )
= $false )
| ( ( less @ SV44 @ SV22 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[258]) ).
thf(267,plain,
! [SV62: $i,SV44: $i,SV22: $i] :
( ( ( SV22
!= ( vplus @ SV44 @ SV62 ) )
= $true )
| ( ( less @ SV44 @ SV22 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[259]) ).
thf(268,plain,
! [SV58: $i,SV23: $i,SV45: $i] :
( ( ( ! [SY130: $i] :
( SV45
!= ( vplus @ SV23 @ SY130 ) ) )
= $true )
| ( ( SV23
= ( vplus @ SV45 @ SV58 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[260]) ).
thf(269,plain,
! [SV55: $i,SV47: $i,SV30: $i,SV8: $i] :
( ( ( geq @ SV8 @ SV30 )
= $false )
| ( ( geq @ SV47 @ SV55 )
= $false )
| ( ( geq @ ( vplus @ SV8 @ SV47 ) @ ( vplus @ SV30 @ SV55 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[261]) ).
thf(270,plain,
! [SV13: $i,SV35: $i] :
( ( ( SV35
= ( vplus @ SV13 @ ( sK2_SY116 @ SV13 @ SV35 ) ) )
= $true )
| ( ( greater @ SV35 @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[262]) ).
thf(271,plain,
! [SV61: $i,SV13: $i,SV35: $i] :
( ( ( SV35
= ( vplus @ SV13 @ SV61 ) )
= $false )
| ( ( greater @ SV35 @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[263]) ).
thf(272,plain,
! [SV56: $i,SV52: $i,SV39: $i,SV17: $i] :
( ( ( greater @ SV17 @ SV39 )
= $false )
| ( ( greater @ SV52 @ SV56 )
= $false )
| ( ( greater @ ( vplus @ SV17 @ SV52 ) @ ( vplus @ SV39 @ SV56 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[264]) ).
thf(273,plain,
! [SV20: $i,SV42: $i] :
( ( ( SV42
= ( vplus @ SV20 @ ( sK3_SY125 @ SV20 @ SV42 ) ) )
= $true )
| ( ( SV20 = SV42 )
= $true )
| ( ( SV20
= ( vplus @ SV42 @ ( sK1_SY124 @ SV42 @ SV20 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[265]) ).
thf(274,plain,
! [SV44: $i,SV22: $i] :
( ( ( SV22
= ( vplus @ SV44 @ ( sK4_SY127 @ SV44 @ SV22 ) ) )
= $true )
| ( ( less @ SV44 @ SV22 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[266]) ).
thf(275,plain,
! [SV62: $i,SV44: $i,SV22: $i] :
( ( ( SV22
= ( vplus @ SV44 @ SV62 ) )
= $false )
| ( ( less @ SV44 @ SV22 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[267]) ).
thf(276,plain,
! [SV58: $i,SV63: $i,SV23: $i,SV45: $i] :
( ( ( SV45
!= ( vplus @ SV23 @ SV63 ) )
= $true )
| ( ( SV23
= ( vplus @ SV45 @ SV58 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[268]) ).
thf(277,plain,
! [SV58: $i,SV63: $i,SV23: $i,SV45: $i] :
( ( ( SV45
= ( vplus @ SV23 @ SV63 ) )
= $false )
| ( ( SV23
= ( vplus @ SV45 @ SV58 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[276]) ).
thf(278,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[87,277,275,274,273,272,271,270,269,255,252,241,225,223,220,219,214,213,190,178,160,159,158,157,156,139,134,91,90,89,88]) ).
thf(279,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[278]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM846+1 : 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
% 0.07/0.19 % Computer : n001.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.20 % CPULimit : 300
% 0.07/0.20 % WCLimit : 300
% 0.07/0.20 % DateTime : Tue Oct 6 13:46:54 UTC 2026
% 0.07/0.20 % CPUTime :
% 0.07/0.20 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.56/0.41
% 0.56/0.41 No.of.Axioms: 28
% 0.56/0.41
% 0.56/0.41 Length.of.Defs: 0
% 0.56/0.41
% 0.56/0.41 Contains.Choice.Funs: false
% 0.56/0.41 ........
% 0.56/0.41
% 0.56/0.41 ********************************
% 0.56/0.41 * All subproblems solved! *
% 0.56/0.41 ********************************
% 0.56/0.41 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:28,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:278,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.56/0.41
% 0.56/0.41 %**** Beginning of derivation protocol ****
% 0.56/0.41 % SZS output start CNFRefutation
% See solution above
% 0.56/0.41
% 0.56/0.41 %**** End of derivation protocol ****
% 0.56/0.41 %**** no. of clauses in derivation: 253 ****
% 0.56/0.41 %**** clause counter: 278 ****
% 0.56/0.41
% 0.56/0.41 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:28,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:278,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------