%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : NUM850+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 : n016.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 10:35:24 AM UTC 2026
% Result : Theorem 0.49s 0.30s
% Output : CNFRefutation 0.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 23
% Syntax : Number of formulae : 237 ( 144 unt; 0 typ; 0 def)
% Number of atoms : 1091 ( 571 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 1929 ( 395 ~; 207 |; 6 &;1288 @)
% ( 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 : 18 ( 15 usr; 5 con; 0-2 aty)
% Number of variables : 708 ( 0 ^; 679 !; 29 ?; 708 :)
% 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_SY119,type,
sK1_SY119: $i > $i > $i ).
thf(tp_sK2_SY111,type,
sK2_SY111: $i > $i > $i ).
thf(tp_sK3_SY120,type,
sK3_SY120: $i > $i > $i ).
thf(tp_sK4_SY126,type,
sK4_SY126: $i > $i > $i ).
thf(tp_v1,type,
v1: $i ).
thf(tp_vd470,type,
vd470: $i ).
thf(tp_vd471,type,
vd471: $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(31,axiom,
! [Vd295: $i,Vd296: $i] : ( greater @ ( vplus @ Vd295 @ Vd296 ) @ Vd295 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(189, 0), 0)') ).
thf(32,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(33,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(34,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(35,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(36,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(37,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(38,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(40,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(48,axiom,
! [Vd432: $i,Vd433: $i,Vd434: $i] :
( ( vmul @ Vd432 @ ( vplus @ Vd433 @ Vd434 ) )
= ( vplus @ ( vmul @ Vd432 @ Vd433 ) @ ( vmul @ Vd432 @ Vd434 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(281, 0), 0)') ).
thf(50,axiom,
greater @ vd470 @ vd471,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(antec(302), 472, 0)') ).
thf(51,conjecture,
? [Vd473: $i] :
( vd470
= ( vplus @ vd471 @ Vd473 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qe(conseq_conjunct1(conseq(302)))') ).
thf(52,negated_conjecture,
( ( ? [Vd473: $i] :
( vd470
= ( vplus @ vd471 @ Vd473 ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[51]) ).
thf(53,plain,
( ( ? [Vd473: $i] :
( vd470
= ( vplus @ vd471 @ Vd473 ) ) )
= $false ),
inference(unfold_def,[status(thm)],[52]) ).
thf(54,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(55,plain,
( ( ! [Vd68: $i,Vd69: $i] :
( ( vplus @ ( vsucc @ Vd68 ) @ Vd69 )
= ( vsucc @ ( vplus @ Vd68 @ Vd69 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(56,plain,
( ( ! [Vd78: $i,Vd79: $i] :
( ( vplus @ Vd79 @ Vd78 )
= ( vplus @ Vd78 @ Vd79 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(57,plain,
( ( ! [Vd92: $i,Vd93: $i] :
( Vd93
!= ( vplus @ Vd92 @ Vd93 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(58,plain,
( ( ! [Vd104: $i,Vd105: $i] :
( ( Vd104 != Vd105 )
=> ! [Vd107: $i] :
( ( vplus @ Vd107 @ Vd104 )
!= ( vplus @ Vd107 @ Vd105 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(59,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ( Vd120 != Vd121 )
| ~ ? [Vd123: $i] :
( Vd120
= ( vplus @ Vd121 @ Vd123 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(60,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(61,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ( Vd120 != Vd121 )
| ~ ? [Vd125: $i] :
( Vd121
= ( vplus @ Vd120 @ Vd125 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(62,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(63,plain,
( ( ! [Vd193: $i,Vd194: $i] :
( ( greater @ Vd194 @ Vd193 )
<=> ? [Vd196: $i] :
( Vd194
= ( vplus @ Vd193 @ Vd196 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(64,plain,
( ( ! [Vd198: $i,Vd199: $i] :
( ( less @ Vd199 @ Vd198 )
<=> ? [Vd201: $i] :
( Vd198
= ( vplus @ Vd199 @ Vd201 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(65,plain,
( ( ! [Vd295: $i,Vd296: $i] : ( greater @ ( vplus @ Vd295 @ Vd296 ) @ Vd295 ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(66,plain,
( ( ! [Vd301: $i,Vd302: $i,Vd303: $i] :
( ( greater @ Vd301 @ Vd302 )
=> ( greater @ ( vplus @ Vd301 @ Vd303 ) @ ( vplus @ Vd302 @ Vd303 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(67,plain,
( ( ! [Vd301: $i,Vd302: $i,Vd303: $i] :
( ( Vd301 = Vd302 )
=> ( ( vplus @ Vd301 @ Vd303 )
= ( vplus @ Vd302 @ Vd303 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(68,plain,
( ( ! [Vd301: $i,Vd302: $i,Vd303: $i] :
( ( less @ Vd301 @ Vd302 )
=> ( less @ ( vplus @ Vd301 @ Vd303 ) @ ( vplus @ Vd302 @ Vd303 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(69,plain,
( ( ! [Vd328: $i,Vd329: $i,Vd330: $i] :
( ( greater @ ( vplus @ Vd328 @ Vd330 ) @ ( vplus @ Vd329 @ Vd330 ) )
=> ( greater @ Vd328 @ Vd329 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(70,plain,
( ( ! [Vd328: $i,Vd329: $i,Vd330: $i] :
( ( ( vplus @ Vd328 @ Vd330 )
= ( vplus @ Vd329 @ Vd330 ) )
=> ( Vd328 = Vd329 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(71,plain,
( ( ! [Vd328: $i,Vd329: $i,Vd330: $i] :
( ( less @ ( vplus @ Vd328 @ Vd330 ) @ ( vplus @ Vd329 @ Vd330 ) )
=> ( less @ Vd328 @ Vd329 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(72,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)],[38]) ).
thf(73,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)],[40]) ).
thf(74,plain,
( ( ! [Vd432: $i,Vd433: $i,Vd434: $i] :
( ( vmul @ Vd432 @ ( vplus @ Vd433 @ Vd434 ) )
= ( vplus @ ( vmul @ Vd432 @ Vd433 ) @ ( vmul @ Vd432 @ Vd434 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(75,plain,
( ( greater @ vd470 @ vd471 )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(76,plain,
( ( ~ ? [Vd473: $i] :
( vd470
= ( vplus @ vd471 @ Vd473 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[53]) ).
thf(77,plain,
( ( greater @ vd470 @ vd471 )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(78,plain,
( ( ! [Vd432: $i,Vd433: $i,Vd434: $i] :
( ( vmul @ Vd432 @ ( vplus @ Vd433 @ Vd434 ) )
= ( vplus @ ( vmul @ Vd432 @ Vd433 ) @ ( vmul @ Vd432 @ Vd434 ) ) ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(79,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)],[73]) ).
thf(80,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)],[72]) ).
thf(81,plain,
( ( ! [Vd328: $i,Vd329: $i,Vd330: $i] :
( ( less @ ( vplus @ Vd328 @ Vd330 ) @ ( vplus @ Vd329 @ Vd330 ) )
=> ( less @ Vd328 @ Vd329 ) ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(82,plain,
( ( ! [Vd328: $i,Vd329: $i,Vd330: $i] :
( ( ( vplus @ Vd328 @ Vd330 )
= ( vplus @ Vd329 @ Vd330 ) )
=> ( Vd328 = Vd329 ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(83,plain,
( ( ! [Vd328: $i,Vd329: $i,Vd330: $i] :
( ( greater @ ( vplus @ Vd328 @ Vd330 ) @ ( vplus @ Vd329 @ Vd330 ) )
=> ( greater @ Vd328 @ Vd329 ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(84,plain,
( ( ! [Vd301: $i,Vd302: $i,Vd303: $i] :
( ( less @ Vd301 @ Vd302 )
=> ( less @ ( vplus @ Vd301 @ Vd303 ) @ ( vplus @ Vd302 @ Vd303 ) ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(85,plain,
( ( ! [Vd301: $i,Vd302: $i,Vd303: $i] :
( ( Vd301 = Vd302 )
=> ( ( vplus @ Vd301 @ Vd303 )
= ( vplus @ Vd302 @ Vd303 ) ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(86,plain,
( ( ! [Vd301: $i,Vd302: $i,Vd303: $i] :
( ( greater @ Vd301 @ Vd302 )
=> ( greater @ ( vplus @ Vd301 @ Vd303 ) @ ( vplus @ Vd302 @ Vd303 ) ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(87,plain,
( ( ! [Vd295: $i,Vd296: $i] : ( greater @ ( vplus @ Vd295 @ Vd296 ) @ Vd295 ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(88,plain,
( ( ! [Vd198: $i,Vd199: $i] :
( ( less @ Vd199 @ Vd198 )
<=> ? [Vd201: $i] :
( Vd198
= ( vplus @ Vd199 @ Vd201 ) ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(89,plain,
( ( ! [Vd193: $i,Vd194: $i] :
( ( greater @ Vd194 @ Vd193 )
<=> ? [Vd196: $i] :
( Vd194
= ( vplus @ Vd193 @ Vd196 ) ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(90,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ( Vd120 = Vd121 )
| ? [Vd123: $i] :
( Vd120
= ( vplus @ Vd121 @ Vd123 ) )
| ? [Vd125: $i] :
( Vd121
= ( vplus @ Vd120 @ Vd125 ) ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(91,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ( Vd120 != Vd121 )
| ~ ? [Vd125: $i] :
( Vd121
= ( vplus @ Vd120 @ Vd125 ) ) ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(92,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ~ ? [Vd123: $i] :
( Vd120
= ( vplus @ Vd121 @ Vd123 ) )
| ~ ? [Vd125: $i] :
( Vd121
= ( vplus @ Vd120 @ Vd125 ) ) ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(93,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ( Vd120 != Vd121 )
| ~ ? [Vd123: $i] :
( Vd120
= ( vplus @ Vd121 @ Vd123 ) ) ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(94,plain,
( ( ! [Vd104: $i,Vd105: $i] :
( ( Vd104 != Vd105 )
=> ! [Vd107: $i] :
( ( vplus @ Vd107 @ Vd104 )
!= ( vplus @ Vd107 @ Vd105 ) ) ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(95,plain,
( ( ! [Vd92: $i,Vd93: $i] :
( Vd93
!= ( vplus @ Vd92 @ Vd93 ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(96,plain,
( ( ! [Vd78: $i,Vd79: $i] :
( ( vplus @ Vd79 @ Vd78 )
= ( vplus @ Vd78 @ Vd79 ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(97,plain,
( ( ! [Vd68: $i,Vd69: $i] :
( ( vplus @ ( vsucc @ Vd68 ) @ Vd69 )
= ( vsucc @ ( vplus @ Vd68 @ Vd69 ) ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(98,plain,
( ( ! [Vd46: $i,Vd47: $i,Vd48: $i] :
( ( vplus @ ( vplus @ Vd46 @ Vd47 ) @ Vd48 )
= ( vplus @ Vd46 @ ( vplus @ Vd47 @ Vd48 ) ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(99,plain,
( ( ~ ? [Vd473: $i] :
( vd470
= ( vplus @ vd471 @ Vd473 ) ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(100,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( greater @ SX0 @ SX1 )
| ( greater @ ( vplus @ SX0 @ SX2 ) @ ( vplus @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[86]) ).
thf(101,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)],[88]) ).
thf(102,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( greater @ ( vplus @ SX0 @ SX2 ) @ ( vplus @ SX1 @ SX2 ) )
| ( greater @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(103,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ! [SX2: $i] :
( SX0
!= ( vplus @ SX1 @ SX2 ) )
| ~ ~ ! [SX2: $i] :
( SX1
!= ( vplus @ SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(104,plain,
( ( ! [SX0: $i,SX1: $i] :
( SX1
!= ( vplus @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(105,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ~ ! [SX2: $i] :
( SX0
!= ( vplus @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(106,plain,
( ( ~ ~ ! [SX0: $i] :
( vd470
!= ( vplus @ vd471 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[99]) ).
thf(107,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ~ ! [SX2: $i] :
( SX1
!= ( vplus @ SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(108,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( less @ SX0 @ SX1 )
| ( less @ ( vplus @ SX0 @ SX2 ) @ ( vplus @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(109,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)],[90]) ).
thf(110,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( SX0 != SX1 )
| ( ( vplus @ SX0 @ SX2 )
= ( vplus @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[85]) ).
thf(111,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ( SX0 != SX1 ) )
| ! [SX2: $i] :
( ( vplus @ SX2 @ SX0 )
!= ( vplus @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(112,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( less @ ( vplus @ SX0 @ SX2 ) @ ( vplus @ SX1 @ SX2 ) )
| ( less @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(113,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)],[79]) ).
thf(114,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)],[89]) ).
thf(115,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( vplus @ SX0 @ SX2 )
!= ( vplus @ SX1 @ SX2 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(116,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)],[80]) ).
thf(117,plain,
! [SV1: $i] :
( ( ! [SY64: $i,SY65: $i] :
( ( vmul @ SV1 @ ( vplus @ SY64 @ SY65 ) )
= ( vplus @ ( vmul @ SV1 @ SY64 ) @ ( vmul @ SV1 @ SY65 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(118,plain,
! [SV2: $i] :
( ( ! [SY66: $i] : ( greater @ ( vplus @ SV2 @ SY66 ) @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(119,plain,
! [SV3: $i] :
( ( ! [SY67: $i] :
( ( vplus @ SY67 @ SV3 )
= ( vplus @ SV3 @ SY67 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(120,plain,
! [SV4: $i] :
( ( ! [SY68: $i] :
( ( vplus @ ( vsucc @ SV4 ) @ SY68 )
= ( vsucc @ ( vplus @ SV4 @ SY68 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(121,plain,
! [SV5: $i] :
( ( ! [SY69: $i,SY70: $i] :
( ( vplus @ ( vplus @ SV5 @ SY69 ) @ SY70 )
= ( vplus @ SV5 @ ( vplus @ SY69 @ SY70 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(122,plain,
! [SV6: $i] :
( ( ! [SY71: $i,SY72: $i] :
( ~ ( greater @ SV6 @ SY71 )
| ( greater @ ( vplus @ SV6 @ SY72 ) @ ( vplus @ SY71 @ SY72 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(123,plain,
! [SV7: $i] :
( ( ! [SY73: $i] :
~ ( ~ ( ~ ( less @ SY73 @ SV7 )
| ~ ! [SY74: $i] :
( SV7
!= ( vplus @ SY73 @ SY74 ) ) )
| ~ ( ~ ~ ! [SY75: $i] :
( SV7
!= ( vplus @ SY73 @ SY75 ) )
| ( less @ SY73 @ SV7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(124,plain,
! [SV8: $i] :
( ( ! [SY76: $i,SY77: $i] :
( ~ ( greater @ ( vplus @ SV8 @ SY77 ) @ ( vplus @ SY76 @ SY77 ) )
| ( greater @ SV8 @ SY76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(125,plain,
! [SV9: $i] :
( ( ! [SY78: $i] :
( ~ ~ ! [SY79: $i] :
( SV9
!= ( vplus @ SY78 @ SY79 ) )
| ~ ~ ! [SY80: $i] :
( SY78
!= ( vplus @ SV9 @ SY80 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(126,plain,
! [SV10: $i] :
( ( ! [SY81: $i] :
( SY81
!= ( vplus @ SV10 @ SY81 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(127,plain,
! [SV11: $i] :
( ( ! [SY82: $i] :
( ( SV11 != SY82 )
| ~ ~ ! [SY83: $i] :
( SV11
!= ( vplus @ SY82 @ SY83 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(128,plain,
( ( ~ ! [SX0: $i] :
( vd470
!= ( vplus @ vd471 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(129,plain,
! [SV12: $i] :
( ( ! [SY84: $i] :
( ( SV12 != SY84 )
| ~ ~ ! [SY85: $i] :
( SY84
!= ( vplus @ SV12 @ SY85 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(130,plain,
! [SV13: $i] :
( ( ! [SY86: $i,SY87: $i] :
( ~ ( less @ SV13 @ SY86 )
| ( less @ ( vplus @ SV13 @ SY87 ) @ ( vplus @ SY86 @ SY87 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(131,plain,
! [SV14: $i] :
( ( ! [SY88: $i] :
( ( SV14 = SY88 )
| ~ ! [SY89: $i] :
( SV14
!= ( vplus @ SY88 @ SY89 ) )
| ~ ! [SY90: $i] :
( SY88
!= ( vplus @ SV14 @ SY90 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(132,plain,
! [SV15: $i] :
( ( ! [SY91: $i,SY92: $i] :
( ( SV15 != SY91 )
| ( ( vplus @ SV15 @ SY92 )
= ( vplus @ SY91 @ SY92 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(133,plain,
! [SV16: $i] :
( ( ! [SY93: $i] :
( ~ ( ( SV16 != SY93 ) )
| ! [SY94: $i] :
( ( vplus @ SY94 @ SV16 )
!= ( vplus @ SY94 @ SY93 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(134,plain,
! [SV17: $i] :
( ( ! [SY95: $i,SY96: $i] :
( ~ ( less @ ( vplus @ SV17 @ SY96 ) @ ( vplus @ SY95 @ SY96 ) )
| ( less @ SV17 @ SY95 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(135,plain,
! [SV18: $i] :
( ( ! [SY97: $i,SY98: $i,SY99: $i] :
( ~ ~ ( ~ ( geq @ SY98 @ SY99 )
| ~ ( geq @ SV18 @ SY97 ) )
| ( geq @ ( vplus @ SV18 @ SY98 ) @ ( vplus @ SY97 @ SY99 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(136,plain,
! [SV19: $i] :
( ( ! [SY100: $i] :
~ ( ~ ( ~ ( greater @ SY100 @ SV19 )
| ~ ! [SY101: $i] :
( SY100
!= ( vplus @ SV19 @ SY101 ) ) )
| ~ ( ~ ~ ! [SY102: $i] :
( SY100
!= ( vplus @ SV19 @ SY102 ) )
| ( greater @ SY100 @ SV19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(137,plain,
! [SV20: $i] :
( ( ! [SY103: $i,SY104: $i] :
( ( ( vplus @ SV20 @ SY104 )
!= ( vplus @ SY103 @ SY104 ) )
| ( SV20 = SY103 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(138,plain,
! [SV21: $i] :
( ( ! [SY105: $i,SY106: $i,SY107: $i] :
( ~ ~ ( ~ ( greater @ SY106 @ SY107 )
| ~ ( greater @ SV21 @ SY105 ) )
| ( greater @ ( vplus @ SV21 @ SY106 ) @ ( vplus @ SY105 @ SY107 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(139,plain,
! [SV22: $i,SV1: $i] :
( ( ! [SY108: $i] :
( ( vmul @ SV1 @ ( vplus @ SV22 @ SY108 ) )
= ( vplus @ ( vmul @ SV1 @ SV22 ) @ ( vmul @ SV1 @ SY108 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(140,plain,
! [SV23: $i,SV2: $i] :
( ( greater @ ( vplus @ SV2 @ SV23 ) @ SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(141,plain,
! [SV3: $i,SV24: $i] :
( ( ( vplus @ SV24 @ SV3 )
= ( vplus @ SV3 @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(142,plain,
! [SV25: $i,SV4: $i] :
( ( ( vplus @ ( vsucc @ SV4 ) @ SV25 )
= ( vsucc @ ( vplus @ SV4 @ SV25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(143,plain,
! [SV26: $i,SV5: $i] :
( ( ! [SY109: $i] :
( ( vplus @ ( vplus @ SV5 @ SV26 ) @ SY109 )
= ( vplus @ SV5 @ ( vplus @ SV26 @ SY109 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(144,plain,
! [SV27: $i,SV6: $i] :
( ( ! [SY110: $i] :
( ~ ( greater @ SV6 @ SV27 )
| ( greater @ ( vplus @ SV6 @ SY110 ) @ ( vplus @ SV27 @ SY110 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(145,plain,
! [SV7: $i,SV28: $i] :
( ( ~ ( ~ ( ~ ( less @ SV28 @ SV7 )
| ~ ! [SY111: $i] :
( SV7
!= ( vplus @ SV28 @ SY111 ) ) )
| ~ ( ~ ~ ! [SY112: $i] :
( SV7
!= ( vplus @ SV28 @ SY112 ) )
| ( less @ SV28 @ SV7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(146,plain,
! [SV29: $i,SV8: $i] :
( ( ! [SY113: $i] :
( ~ ( greater @ ( vplus @ SV8 @ SY113 ) @ ( vplus @ SV29 @ SY113 ) )
| ( greater @ SV8 @ SV29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(147,plain,
! [SV30: $i,SV9: $i] :
( ( ~ ~ ! [SY114: $i] :
( SV9
!= ( vplus @ SV30 @ SY114 ) )
| ~ ~ ! [SY115: $i] :
( SV30
!= ( vplus @ SV9 @ SY115 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(148,plain,
! [SV10: $i,SV31: $i] :
( ( SV31
!= ( vplus @ SV10 @ SV31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(149,plain,
! [SV32: $i,SV11: $i] :
( ( ( SV11 != SV32 )
| ~ ~ ! [SY116: $i] :
( SV11
!= ( vplus @ SV32 @ SY116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(150,plain,
( ( ! [SX0: $i] :
( vd470
!= ( vplus @ vd471 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[128]) ).
thf(151,plain,
! [SV33: $i,SV12: $i] :
( ( ( SV12 != SV33 )
| ~ ~ ! [SY117: $i] :
( SV33
!= ( vplus @ SV12 @ SY117 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(152,plain,
! [SV34: $i,SV13: $i] :
( ( ! [SY118: $i] :
( ~ ( less @ SV13 @ SV34 )
| ( less @ ( vplus @ SV13 @ SY118 ) @ ( vplus @ SV34 @ SY118 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(153,plain,
! [SV35: $i,SV14: $i] :
( ( ( SV14 = SV35 )
| ~ ! [SY119: $i] :
( SV14
!= ( vplus @ SV35 @ SY119 ) )
| ~ ! [SY120: $i] :
( SV35
!= ( vplus @ SV14 @ SY120 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(154,plain,
! [SV36: $i,SV15: $i] :
( ( ! [SY121: $i] :
( ( SV15 != SV36 )
| ( ( vplus @ SV15 @ SY121 )
= ( vplus @ SV36 @ SY121 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(155,plain,
! [SV37: $i,SV16: $i] :
( ( ~ ( ( SV16 != SV37 ) )
| ! [SY122: $i] :
( ( vplus @ SY122 @ SV16 )
!= ( vplus @ SY122 @ SV37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(156,plain,
! [SV38: $i,SV17: $i] :
( ( ! [SY123: $i] :
( ~ ( less @ ( vplus @ SV17 @ SY123 ) @ ( vplus @ SV38 @ SY123 ) )
| ( less @ SV17 @ SV38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(157,plain,
! [SV39: $i,SV18: $i] :
( ( ! [SY124: $i,SY125: $i] :
( ~ ~ ( ~ ( geq @ SY124 @ SY125 )
| ~ ( geq @ SV18 @ SV39 ) )
| ( geq @ ( vplus @ SV18 @ SY124 ) @ ( vplus @ SV39 @ SY125 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(158,plain,
! [SV19: $i,SV40: $i] :
( ( ~ ( ~ ( ~ ( greater @ SV40 @ SV19 )
| ~ ! [SY126: $i] :
( SV40
!= ( vplus @ SV19 @ SY126 ) ) )
| ~ ( ~ ~ ! [SY127: $i] :
( SV40
!= ( vplus @ SV19 @ SY127 ) )
| ( greater @ SV40 @ SV19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(159,plain,
! [SV41: $i,SV20: $i] :
( ( ! [SY128: $i] :
( ( ( vplus @ SV20 @ SY128 )
!= ( vplus @ SV41 @ SY128 ) )
| ( SV20 = SV41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(160,plain,
! [SV42: $i,SV21: $i] :
( ( ! [SY129: $i,SY130: $i] :
( ~ ~ ( ~ ( greater @ SY129 @ SY130 )
| ~ ( greater @ SV21 @ SV42 ) )
| ( greater @ ( vplus @ SV21 @ SY129 ) @ ( vplus @ SV42 @ SY130 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(161,plain,
! [SV43: $i,SV22: $i,SV1: $i] :
( ( ( vmul @ SV1 @ ( vplus @ SV22 @ SV43 ) )
= ( vplus @ ( vmul @ SV1 @ SV22 ) @ ( vmul @ SV1 @ SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(162,plain,
! [SV44: $i,SV26: $i,SV5: $i] :
( ( ( vplus @ ( vplus @ SV5 @ SV26 ) @ SV44 )
= ( vplus @ SV5 @ ( vplus @ SV26 @ SV44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(163,plain,
! [SV45: $i,SV27: $i,SV6: $i] :
( ( ~ ( greater @ SV6 @ SV27 )
| ( greater @ ( vplus @ SV6 @ SV45 ) @ ( vplus @ SV27 @ SV45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(164,plain,
! [SV7: $i,SV28: $i] :
( ( ~ ( ~ ( less @ SV28 @ SV7 )
| ~ ! [SY111: $i] :
( SV7
!= ( vplus @ SV28 @ SY111 ) ) )
| ~ ( ~ ~ ! [SY112: $i] :
( SV7
!= ( vplus @ SV28 @ SY112 ) )
| ( less @ SV28 @ SV7 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[145]) ).
thf(165,plain,
! [SV29: $i,SV46: $i,SV8: $i] :
( ( ~ ( greater @ ( vplus @ SV8 @ SV46 ) @ ( vplus @ SV29 @ SV46 ) )
| ( greater @ SV8 @ SV29 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(166,plain,
! [SV30: $i,SV9: $i] :
( ( ( ~ ~ ! [SY114: $i] :
( SV9
!= ( vplus @ SV30 @ SY114 ) ) )
= $true )
| ( ( ~ ~ ! [SY115: $i] :
( SV30
!= ( vplus @ SV9 @ SY115 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[147]) ).
thf(167,plain,
! [SV10: $i,SV31: $i] :
( ( SV31
= ( vplus @ SV10 @ SV31 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(168,plain,
! [SV32: $i,SV11: $i] :
( ( ( SV11 != SV32 )
= $true )
| ( ( ~ ~ ! [SY116: $i] :
( SV11
!= ( vplus @ SV32 @ SY116 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[149]) ).
thf(169,plain,
! [SV47: $i] :
( ( vd470
!= ( vplus @ vd471 @ SV47 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(170,plain,
! [SV33: $i,SV12: $i] :
( ( ( SV12 != SV33 )
= $true )
| ( ( ~ ~ ! [SY117: $i] :
( SV33
!= ( vplus @ SV12 @ SY117 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[151]) ).
thf(171,plain,
! [SV48: $i,SV34: $i,SV13: $i] :
( ( ~ ( less @ SV13 @ SV34 )
| ( less @ ( vplus @ SV13 @ SV48 ) @ ( vplus @ SV34 @ SV48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(172,plain,
! [SV35: $i,SV14: $i] :
( ( ( ( SV14 = SV35 )
| ~ ! [SY119: $i] :
( SV14
!= ( vplus @ SV35 @ SY119 ) ) )
= $true )
| ( ( ~ ! [SY120: $i] :
( SV35
!= ( vplus @ SV14 @ SY120 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[153]) ).
thf(173,plain,
! [SV49: $i,SV36: $i,SV15: $i] :
( ( ( SV15 != SV36 )
| ( ( vplus @ SV15 @ SV49 )
= ( vplus @ SV36 @ SV49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(174,plain,
! [SV37: $i,SV16: $i] :
( ( ( ~ ( ( SV16 != SV37 ) ) )
= $true )
| ( ( ! [SY122: $i] :
( ( vplus @ SY122 @ SV16 )
!= ( vplus @ SY122 @ SV37 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[155]) ).
thf(175,plain,
! [SV38: $i,SV50: $i,SV17: $i] :
( ( ~ ( less @ ( vplus @ SV17 @ SV50 ) @ ( vplus @ SV38 @ SV50 ) )
| ( less @ SV17 @ SV38 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(176,plain,
! [SV39: $i,SV18: $i,SV51: $i] :
( ( ! [SY131: $i] :
( ~ ~ ( ~ ( geq @ SV51 @ SY131 )
| ~ ( geq @ SV18 @ SV39 ) )
| ( geq @ ( vplus @ SV18 @ SV51 ) @ ( vplus @ SV39 @ SY131 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(177,plain,
! [SV19: $i,SV40: $i] :
( ( ~ ( ~ ( greater @ SV40 @ SV19 )
| ~ ! [SY126: $i] :
( SV40
!= ( vplus @ SV19 @ SY126 ) ) )
| ~ ( ~ ~ ! [SY127: $i] :
( SV40
!= ( vplus @ SV19 @ SY127 ) )
| ( greater @ SV40 @ SV19 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[158]) ).
thf(178,plain,
! [SV41: $i,SV52: $i,SV20: $i] :
( ( ( ( vplus @ SV20 @ SV52 )
!= ( vplus @ SV41 @ SV52 ) )
| ( SV20 = SV41 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(179,plain,
! [SV42: $i,SV21: $i,SV53: $i] :
( ( ! [SY132: $i] :
( ~ ~ ( ~ ( greater @ SV53 @ SY132 )
| ~ ( greater @ SV21 @ SV42 ) )
| ( greater @ ( vplus @ SV21 @ SV53 ) @ ( vplus @ SV42 @ SY132 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(180,plain,
! [SV45: $i,SV27: $i,SV6: $i] :
( ( ( ~ ( greater @ SV6 @ SV27 ) )
= $true )
| ( ( greater @ ( vplus @ SV6 @ SV45 ) @ ( vplus @ SV27 @ SV45 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[163]) ).
thf(181,plain,
! [SV7: $i,SV28: $i] :
( ( ~ ( ~ ( less @ SV28 @ SV7 )
| ~ ! [SY111: $i] :
( SV7
!= ( vplus @ SV28 @ SY111 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[164]) ).
thf(182,plain,
! [SV28: $i,SV7: $i] :
( ( ~ ( ~ ~ ! [SY112: $i] :
( SV7
!= ( vplus @ SV28 @ SY112 ) )
| ( less @ SV28 @ SV7 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[164]) ).
thf(183,plain,
! [SV29: $i,SV46: $i,SV8: $i] :
( ( ( ~ ( greater @ ( vplus @ SV8 @ SV46 ) @ ( vplus @ SV29 @ SV46 ) ) )
= $true )
| ( ( greater @ SV8 @ SV29 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[165]) ).
thf(184,plain,
! [SV30: $i,SV9: $i] :
( ( ( ~ ! [SY114: $i] :
( SV9
!= ( vplus @ SV30 @ SY114 ) ) )
= $false )
| ( ( ~ ~ ! [SY115: $i] :
( SV30
!= ( vplus @ SV9 @ SY115 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(185,plain,
! [SV32: $i,SV11: $i] :
( ( ( SV11 = SV32 )
= $false )
| ( ( ~ ~ ! [SY116: $i] :
( SV11
!= ( vplus @ SV32 @ SY116 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[168]) ).
thf(186,plain,
! [SV47: $i] :
( ( vd470
= ( vplus @ vd471 @ SV47 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(187,plain,
! [SV33: $i,SV12: $i] :
( ( ( SV12 = SV33 )
= $false )
| ( ( ~ ~ ! [SY117: $i] :
( SV33
!= ( vplus @ SV12 @ SY117 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(188,plain,
! [SV48: $i,SV34: $i,SV13: $i] :
( ( ( ~ ( less @ SV13 @ SV34 ) )
= $true )
| ( ( less @ ( vplus @ SV13 @ SV48 ) @ ( vplus @ SV34 @ SV48 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[171]) ).
thf(189,plain,
! [SV35: $i,SV14: $i] :
( ( ( SV14 = SV35 )
= $true )
| ( ( ~ ! [SY119: $i] :
( SV14
!= ( vplus @ SV35 @ SY119 ) ) )
= $true )
| ( ( ~ ! [SY120: $i] :
( SV35
!= ( vplus @ SV14 @ SY120 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[172]) ).
thf(190,plain,
! [SV49: $i,SV36: $i,SV15: $i] :
( ( ( SV15 != SV36 )
= $true )
| ( ( ( vplus @ SV15 @ SV49 )
= ( vplus @ SV36 @ SV49 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[173]) ).
thf(191,plain,
! [SV37: $i,SV16: $i] :
( ( ( SV16 != SV37 )
= $false )
| ( ( ! [SY122: $i] :
( ( vplus @ SY122 @ SV16 )
!= ( vplus @ SY122 @ SV37 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[174]) ).
thf(192,plain,
! [SV38: $i,SV50: $i,SV17: $i] :
( ( ( ~ ( less @ ( vplus @ SV17 @ SV50 ) @ ( vplus @ SV38 @ SV50 ) ) )
= $true )
| ( ( less @ SV17 @ SV38 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[175]) ).
thf(193,plain,
! [SV39: $i,SV18: $i,SV54: $i,SV51: $i] :
( ( ~ ~ ( ~ ( geq @ SV51 @ SV54 )
| ~ ( geq @ SV18 @ SV39 ) )
| ( geq @ ( vplus @ SV18 @ SV51 ) @ ( vplus @ SV39 @ SV54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[176]) ).
thf(194,plain,
! [SV19: $i,SV40: $i] :
( ( ~ ( ~ ( greater @ SV40 @ SV19 )
| ~ ! [SY126: $i] :
( SV40
!= ( vplus @ SV19 @ SY126 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[177]) ).
thf(195,plain,
! [SV19: $i,SV40: $i] :
( ( ~ ( ~ ~ ! [SY127: $i] :
( SV40
!= ( vplus @ SV19 @ SY127 ) )
| ( greater @ SV40 @ SV19 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[177]) ).
thf(196,plain,
! [SV41: $i,SV52: $i,SV20: $i] :
( ( ( ( vplus @ SV20 @ SV52 )
!= ( vplus @ SV41 @ SV52 ) )
= $true )
| ( ( SV20 = SV41 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[178]) ).
thf(197,plain,
! [SV42: $i,SV21: $i,SV55: $i,SV53: $i] :
( ( ~ ~ ( ~ ( greater @ SV53 @ SV55 )
| ~ ( greater @ SV21 @ SV42 ) )
| ( greater @ ( vplus @ SV21 @ SV53 ) @ ( vplus @ SV42 @ SV55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(198,plain,
! [SV45: $i,SV27: $i,SV6: $i] :
( ( ( greater @ SV6 @ SV27 )
= $false )
| ( ( greater @ ( vplus @ SV6 @ SV45 ) @ ( vplus @ SV27 @ SV45 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[180]) ).
thf(199,plain,
! [SV7: $i,SV28: $i] :
( ( ~ ( less @ SV28 @ SV7 )
| ~ ! [SY111: $i] :
( SV7
!= ( vplus @ SV28 @ SY111 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[181]) ).
thf(200,plain,
! [SV28: $i,SV7: $i] :
( ( ~ ~ ! [SY112: $i] :
( SV7
!= ( vplus @ SV28 @ SY112 ) )
| ( less @ SV28 @ SV7 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[182]) ).
thf(201,plain,
! [SV29: $i,SV46: $i,SV8: $i] :
( ( ( greater @ ( vplus @ SV8 @ SV46 ) @ ( vplus @ SV29 @ SV46 ) )
= $false )
| ( ( greater @ SV8 @ SV29 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[183]) ).
thf(202,plain,
! [SV30: $i,SV9: $i] :
( ( ( ! [SY114: $i] :
( SV9
!= ( vplus @ SV30 @ SY114 ) ) )
= $true )
| ( ( ~ ~ ! [SY115: $i] :
( SV30
!= ( vplus @ SV9 @ SY115 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[184]) ).
thf(203,plain,
! [SV32: $i,SV11: $i] :
( ( ( ~ ! [SY116: $i] :
( SV11
!= ( vplus @ SV32 @ SY116 ) ) )
= $false )
| ( ( SV11 = SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[185]) ).
thf(204,plain,
! [SV12: $i,SV33: $i] :
( ( ( ~ ! [SY117: $i] :
( SV33
!= ( vplus @ SV12 @ SY117 ) ) )
= $false )
| ( ( SV12 = SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[187]) ).
thf(205,plain,
! [SV48: $i,SV34: $i,SV13: $i] :
( ( ( less @ SV13 @ SV34 )
= $false )
| ( ( less @ ( vplus @ SV13 @ SV48 ) @ ( vplus @ SV34 @ SV48 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[188]) ).
thf(206,plain,
! [SV35: $i,SV14: $i] :
( ( ( ! [SY119: $i] :
( SV14
!= ( vplus @ SV35 @ SY119 ) ) )
= $false )
| ( ( SV14 = SV35 )
= $true )
| ( ( ~ ! [SY120: $i] :
( SV35
!= ( vplus @ SV14 @ SY120 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[189]) ).
thf(207,plain,
! [SV49: $i,SV36: $i,SV15: $i] :
( ( ( SV15 = SV36 )
= $false )
| ( ( ( vplus @ SV15 @ SV49 )
= ( vplus @ SV36 @ SV49 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[190]) ).
thf(208,plain,
! [SV37: $i,SV16: $i] :
( ( ( SV16 = SV37 )
= $true )
| ( ( ! [SY122: $i] :
( ( vplus @ SY122 @ SV16 )
!= ( vplus @ SY122 @ SV37 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[191]) ).
thf(209,plain,
! [SV38: $i,SV50: $i,SV17: $i] :
( ( ( less @ ( vplus @ SV17 @ SV50 ) @ ( vplus @ SV38 @ SV50 ) )
= $false )
| ( ( less @ SV17 @ SV38 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(210,plain,
! [SV39: $i,SV18: $i,SV54: $i,SV51: $i] :
( ( ( ~ ~ ( ~ ( geq @ SV51 @ SV54 )
| ~ ( geq @ SV18 @ SV39 ) ) )
= $true )
| ( ( geq @ ( vplus @ SV18 @ SV51 ) @ ( vplus @ SV39 @ SV54 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[193]) ).
thf(211,plain,
! [SV19: $i,SV40: $i] :
( ( ~ ( greater @ SV40 @ SV19 )
| ~ ! [SY126: $i] :
( SV40
!= ( vplus @ SV19 @ SY126 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[194]) ).
thf(212,plain,
! [SV19: $i,SV40: $i] :
( ( ~ ~ ! [SY127: $i] :
( SV40
!= ( vplus @ SV19 @ SY127 ) )
| ( greater @ SV40 @ SV19 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[195]) ).
thf(213,plain,
! [SV41: $i,SV52: $i,SV20: $i] :
( ( ( ( vplus @ SV20 @ SV52 )
= ( vplus @ SV41 @ SV52 ) )
= $false )
| ( ( SV20 = SV41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(214,plain,
! [SV42: $i,SV21: $i,SV55: $i,SV53: $i] :
( ( ( ~ ~ ( ~ ( greater @ SV53 @ SV55 )
| ~ ( greater @ SV21 @ SV42 ) ) )
= $true )
| ( ( greater @ ( vplus @ SV21 @ SV53 ) @ ( vplus @ SV42 @ SV55 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[197]) ).
thf(215,plain,
! [SV7: $i,SV28: $i] :
( ( ( ~ ( less @ SV28 @ SV7 ) )
= $true )
| ( ( ~ ! [SY111: $i] :
( SV7
!= ( vplus @ SV28 @ SY111 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[199]) ).
thf(216,plain,
! [SV28: $i,SV7: $i] :
( ( ( ~ ~ ! [SY112: $i] :
( SV7
!= ( vplus @ SV28 @ SY112 ) ) )
= $true )
| ( ( less @ SV28 @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[200]) ).
thf(217,plain,
! [SV56: $i,SV30: $i,SV9: $i] :
( ( ( SV9
!= ( vplus @ SV30 @ SV56 ) )
= $true )
| ( ( ~ ~ ! [SY115: $i] :
( SV30
!= ( vplus @ SV9 @ SY115 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[202]) ).
thf(218,plain,
! [SV32: $i,SV11: $i] :
( ( ( ! [SY116: $i] :
( SV11
!= ( vplus @ SV32 @ SY116 ) ) )
= $true )
| ( ( SV11 = SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[203]) ).
thf(219,plain,
! [SV12: $i,SV33: $i] :
( ( ( ! [SY117: $i] :
( SV33
!= ( vplus @ SV12 @ SY117 ) ) )
= $true )
| ( ( SV12 = SV33 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[204]) ).
thf(220,plain,
! [SV35: $i,SV14: $i] :
( ( ( SV14
!= ( vplus @ SV35 @ ( sK1_SY119 @ SV35 @ SV14 ) ) )
= $false )
| ( ( SV14 = SV35 )
= $true )
| ( ( ~ ! [SY120: $i] :
( SV35
!= ( vplus @ SV14 @ SY120 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[206]) ).
thf(221,plain,
! [SV37: $i,SV16: $i,SV57: $i] :
( ( ( ( vplus @ SV57 @ SV16 )
!= ( vplus @ SV57 @ SV37 ) )
= $true )
| ( ( SV16 = SV37 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[208]) ).
thf(222,plain,
! [SV39: $i,SV18: $i,SV54: $i,SV51: $i] :
( ( ( ~ ( ~ ( geq @ SV51 @ SV54 )
| ~ ( geq @ SV18 @ SV39 ) ) )
= $false )
| ( ( geq @ ( vplus @ SV18 @ SV51 ) @ ( vplus @ SV39 @ SV54 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[210]) ).
thf(223,plain,
! [SV19: $i,SV40: $i] :
( ( ( ~ ( greater @ SV40 @ SV19 ) )
= $true )
| ( ( ~ ! [SY126: $i] :
( SV40
!= ( vplus @ SV19 @ SY126 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[211]) ).
thf(224,plain,
! [SV19: $i,SV40: $i] :
( ( ( ~ ~ ! [SY127: $i] :
( SV40
!= ( vplus @ SV19 @ SY127 ) ) )
= $true )
| ( ( greater @ SV40 @ SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[212]) ).
thf(225,plain,
! [SV42: $i,SV21: $i,SV55: $i,SV53: $i] :
( ( ( ~ ( ~ ( greater @ SV53 @ SV55 )
| ~ ( greater @ SV21 @ SV42 ) ) )
= $false )
| ( ( greater @ ( vplus @ SV21 @ SV53 ) @ ( vplus @ SV42 @ SV55 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[214]) ).
thf(226,plain,
! [SV7: $i,SV28: $i] :
( ( ( less @ SV28 @ SV7 )
= $false )
| ( ( ~ ! [SY111: $i] :
( SV7
!= ( vplus @ SV28 @ SY111 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[215]) ).
thf(227,plain,
! [SV28: $i,SV7: $i] :
( ( ( ~ ! [SY112: $i] :
( SV7
!= ( vplus @ SV28 @ SY112 ) ) )
= $false )
| ( ( less @ SV28 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[216]) ).
thf(228,plain,
! [SV56: $i,SV30: $i,SV9: $i] :
( ( ( SV9
= ( vplus @ SV30 @ SV56 ) )
= $false )
| ( ( ~ ~ ! [SY115: $i] :
( SV30
!= ( vplus @ SV9 @ SY115 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[217]) ).
thf(229,plain,
! [SV58: $i,SV32: $i,SV11: $i] :
( ( ( SV11
!= ( vplus @ SV32 @ SV58 ) )
= $true )
| ( ( SV11 = SV32 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[218]) ).
thf(230,plain,
! [SV59: $i,SV12: $i,SV33: $i] :
( ( ( SV33
!= ( vplus @ SV12 @ SV59 ) )
= $true )
| ( ( SV12 = SV33 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[219]) ).
thf(231,plain,
! [SV35: $i,SV14: $i] :
( ( ( SV14
= ( vplus @ SV35 @ ( sK1_SY119 @ SV35 @ SV14 ) ) )
= $true )
| ( ( SV14 = SV35 )
= $true )
| ( ( ~ ! [SY120: $i] :
( SV35
!= ( vplus @ SV14 @ SY120 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[220]) ).
thf(232,plain,
! [SV37: $i,SV16: $i,SV57: $i] :
( ( ( ( vplus @ SV57 @ SV16 )
= ( vplus @ SV57 @ SV37 ) )
= $false )
| ( ( SV16 = SV37 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[221]) ).
thf(233,plain,
! [SV39: $i,SV18: $i,SV54: $i,SV51: $i] :
( ( ( ~ ( geq @ SV51 @ SV54 )
| ~ ( geq @ SV18 @ SV39 ) )
= $true )
| ( ( geq @ ( vplus @ SV18 @ SV51 ) @ ( vplus @ SV39 @ SV54 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[222]) ).
thf(234,plain,
! [SV19: $i,SV40: $i] :
( ( ( greater @ SV40 @ SV19 )
= $false )
| ( ( ~ ! [SY126: $i] :
( SV40
!= ( vplus @ SV19 @ SY126 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[223]) ).
thf(235,plain,
! [SV19: $i,SV40: $i] :
( ( ( ~ ! [SY127: $i] :
( SV40
!= ( vplus @ SV19 @ SY127 ) ) )
= $false )
| ( ( greater @ SV40 @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[224]) ).
thf(236,plain,
! [SV42: $i,SV21: $i,SV55: $i,SV53: $i] :
( ( ( ~ ( greater @ SV53 @ SV55 )
| ~ ( greater @ SV21 @ SV42 ) )
= $true )
| ( ( greater @ ( vplus @ SV21 @ SV53 ) @ ( vplus @ SV42 @ SV55 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[225]) ).
thf(237,plain,
! [SV28: $i,SV7: $i] :
( ( ( ! [SY111: $i] :
( SV7
!= ( vplus @ SV28 @ SY111 ) ) )
= $false )
| ( ( less @ SV28 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[226]) ).
thf(238,plain,
! [SV28: $i,SV7: $i] :
( ( ( ! [SY112: $i] :
( SV7
!= ( vplus @ SV28 @ SY112 ) ) )
= $true )
| ( ( less @ SV28 @ SV7 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[227]) ).
thf(239,plain,
! [SV56: $i,SV9: $i,SV30: $i] :
( ( ( ~ ! [SY115: $i] :
( SV30
!= ( vplus @ SV9 @ SY115 ) ) )
= $false )
| ( ( SV9
= ( vplus @ SV30 @ SV56 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[228]) ).
thf(240,plain,
! [SV58: $i,SV32: $i,SV11: $i] :
( ( ( SV11
= ( vplus @ SV32 @ SV58 ) )
= $false )
| ( ( SV11 = SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[229]) ).
thf(241,plain,
! [SV59: $i,SV12: $i,SV33: $i] :
( ( ( SV33
= ( vplus @ SV12 @ SV59 ) )
= $false )
| ( ( SV12 = SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[230]) ).
thf(242,plain,
! [SV14: $i,SV35: $i] :
( ( ( ! [SY120: $i] :
( SV35
!= ( vplus @ SV14 @ SY120 ) ) )
= $false )
| ( ( SV14 = SV35 )
= $true )
| ( ( SV14
= ( vplus @ SV35 @ ( sK1_SY119 @ SV35 @ SV14 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[231]) ).
thf(243,plain,
! [SV39: $i,SV18: $i,SV54: $i,SV51: $i] :
( ( ( ~ ( geq @ SV51 @ SV54 ) )
= $true )
| ( ( ~ ( geq @ SV18 @ SV39 ) )
= $true )
| ( ( geq @ ( vplus @ SV18 @ SV51 ) @ ( vplus @ SV39 @ SV54 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[233]) ).
thf(244,plain,
! [SV19: $i,SV40: $i] :
( ( ( ! [SY126: $i] :
( SV40
!= ( vplus @ SV19 @ SY126 ) ) )
= $false )
| ( ( greater @ SV40 @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[234]) ).
thf(245,plain,
! [SV19: $i,SV40: $i] :
( ( ( ! [SY127: $i] :
( SV40
!= ( vplus @ SV19 @ SY127 ) ) )
= $true )
| ( ( greater @ SV40 @ SV19 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[235]) ).
thf(246,plain,
! [SV42: $i,SV21: $i,SV55: $i,SV53: $i] :
( ( ( ~ ( greater @ SV53 @ SV55 ) )
= $true )
| ( ( ~ ( greater @ SV21 @ SV42 ) )
= $true )
| ( ( greater @ ( vplus @ SV21 @ SV53 ) @ ( vplus @ SV42 @ SV55 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[236]) ).
thf(247,plain,
! [SV28: $i,SV7: $i] :
( ( ( SV7
!= ( vplus @ SV28 @ ( sK2_SY111 @ SV28 @ SV7 ) ) )
= $false )
| ( ( less @ SV28 @ SV7 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[237]) ).
thf(248,plain,
! [SV60: $i,SV28: $i,SV7: $i] :
( ( ( SV7
!= ( vplus @ SV28 @ SV60 ) )
= $true )
| ( ( less @ SV28 @ SV7 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[238]) ).
thf(249,plain,
! [SV56: $i,SV9: $i,SV30: $i] :
( ( ( ! [SY115: $i] :
( SV30
!= ( vplus @ SV9 @ SY115 ) ) )
= $true )
| ( ( SV9
= ( vplus @ SV30 @ SV56 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[239]) ).
thf(250,plain,
! [SV14: $i,SV35: $i] :
( ( ( SV35
!= ( vplus @ SV14 @ ( sK3_SY120 @ SV14 @ SV35 ) ) )
= $false )
| ( ( SV14 = SV35 )
= $true )
| ( ( SV14
= ( vplus @ SV35 @ ( sK1_SY119 @ SV35 @ SV14 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[242]) ).
thf(251,plain,
! [SV39: $i,SV18: $i,SV54: $i,SV51: $i] :
( ( ( geq @ SV51 @ SV54 )
= $false )
| ( ( ~ ( geq @ SV18 @ SV39 ) )
= $true )
| ( ( geq @ ( vplus @ SV18 @ SV51 ) @ ( vplus @ SV39 @ SV54 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[243]) ).
thf(252,plain,
! [SV19: $i,SV40: $i] :
( ( ( SV40
!= ( vplus @ SV19 @ ( sK4_SY126 @ SV19 @ SV40 ) ) )
= $false )
| ( ( greater @ SV40 @ SV19 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[244]) ).
thf(253,plain,
! [SV61: $i,SV19: $i,SV40: $i] :
( ( ( SV40
!= ( vplus @ SV19 @ SV61 ) )
= $true )
| ( ( greater @ SV40 @ SV19 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[245]) ).
thf(254,plain,
! [SV42: $i,SV21: $i,SV55: $i,SV53: $i] :
( ( ( greater @ SV53 @ SV55 )
= $false )
| ( ( ~ ( greater @ SV21 @ SV42 ) )
= $true )
| ( ( greater @ ( vplus @ SV21 @ SV53 ) @ ( vplus @ SV42 @ SV55 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[246]) ).
thf(255,plain,
! [SV28: $i,SV7: $i] :
( ( ( SV7
= ( vplus @ SV28 @ ( sK2_SY111 @ SV28 @ SV7 ) ) )
= $true )
| ( ( less @ SV28 @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[247]) ).
thf(256,plain,
! [SV60: $i,SV28: $i,SV7: $i] :
( ( ( SV7
= ( vplus @ SV28 @ SV60 ) )
= $false )
| ( ( less @ SV28 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[248]) ).
thf(257,plain,
! [SV56: $i,SV62: $i,SV9: $i,SV30: $i] :
( ( ( SV30
!= ( vplus @ SV9 @ SV62 ) )
= $true )
| ( ( SV9
= ( vplus @ SV30 @ SV56 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[249]) ).
thf(258,plain,
! [SV14: $i,SV35: $i] :
( ( ( SV35
= ( vplus @ SV14 @ ( sK3_SY120 @ SV14 @ SV35 ) ) )
= $true )
| ( ( SV14 = SV35 )
= $true )
| ( ( SV14
= ( vplus @ SV35 @ ( sK1_SY119 @ SV35 @ SV14 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[250]) ).
thf(259,plain,
! [SV54: $i,SV51: $i,SV39: $i,SV18: $i] :
( ( ( geq @ SV18 @ SV39 )
= $false )
| ( ( geq @ SV51 @ SV54 )
= $false )
| ( ( geq @ ( vplus @ SV18 @ SV51 ) @ ( vplus @ SV39 @ SV54 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[251]) ).
thf(260,plain,
! [SV19: $i,SV40: $i] :
( ( ( SV40
= ( vplus @ SV19 @ ( sK4_SY126 @ SV19 @ SV40 ) ) )
= $true )
| ( ( greater @ SV40 @ SV19 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[252]) ).
thf(261,plain,
! [SV61: $i,SV19: $i,SV40: $i] :
( ( ( SV40
= ( vplus @ SV19 @ SV61 ) )
= $false )
| ( ( greater @ SV40 @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[253]) ).
thf(262,plain,
! [SV55: $i,SV53: $i,SV42: $i,SV21: $i] :
( ( ( greater @ SV21 @ SV42 )
= $false )
| ( ( greater @ SV53 @ SV55 )
= $false )
| ( ( greater @ ( vplus @ SV21 @ SV53 ) @ ( vplus @ SV42 @ SV55 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[254]) ).
thf(263,plain,
! [SV56: $i,SV62: $i,SV9: $i,SV30: $i] :
( ( ( SV30
= ( vplus @ SV9 @ SV62 ) )
= $false )
| ( ( SV9
= ( vplus @ SV30 @ SV56 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[257]) ).
thf(264,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[77,263,262,261,260,259,258,256,255,241,240,232,213,209,207,205,201,198,186,167,162,161,142,141,140]) ).
thf(265,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[264]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM850+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
% 0.07/0.19 % Computer : n016.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
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Oct 6 13:47:31 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.49/0.30
% 0.49/0.30 No.of.Axioms: 22
% 0.49/0.30
% 0.49/0.30 Length.of.Defs: 0
% 0.49/0.30
% 0.49/0.30 Contains.Choice.Funs: false
% 0.49/0.30 .......
% 0.49/0.30
% 0.49/0.30 ********************************
% 0.49/0.30 * All subproblems solved! *
% 0.49/0.30 ********************************
% 0.49/0.30 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:22,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:264,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.49/0.30
% 0.49/0.30 %**** Beginning of derivation protocol ****
% 0.49/0.30 % SZS output start CNFRefutation
% See solution above
% 0.49/0.30
% 0.49/0.30 %**** End of derivation protocol ****
% 0.49/0.30 %**** no. of clauses in derivation: 237 ****
% 0.49/0.30 %**** clause counter: 264 ****
% 0.49/0.30
% 0.49/0.30 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:22,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:264,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------