%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : NUM854+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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 10:35:25 AM UTC 2026
% Result : Theorem 7.87s 1.69s
% Output : CNFRefutation 7.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 24
% Syntax : Number of formulae : 205 ( 138 unt; 0 typ; 0 def)
% Number of atoms : 899 ( 355 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 1602 ( 200 ~; 180 |; 3 &;1180 @)
% ( 6 <=>; 33 =>; 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 : 17 ( 14 usr; 7 con; 0-2 aty)
% Number of variables : 513 ( 0 ^; 510 !; 3 ?; 513 :)
% 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_SY100,type,
sK1_SY100: $i > $i > $i ).
thf(tp_v1,type,
v1: $i ).
thf(tp_vd508,type,
vd508: $i ).
thf(tp_vd509,type,
vd509: $i ).
thf(tp_vd511,type,
vd511: $i ).
thf(tp_vd512,type,
vd512: $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(17,axiom,
! [Vd193: $i,Vd194: $i] :
( ( greater @ Vd194 @ Vd193 )
<=> ? [Vd196: $i] :
( Vd194
= ( vplus @ Vd193 @ Vd196 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 11), 1)') ).
thf(19,axiom,
! [Vd203: $i,Vd204: $i] :
( ( Vd203 != Vd204 )
| ~ ( greater @ Vd203 @ Vd204 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 3)') ).
thf(20,axiom,
! [Vd203: $i,Vd204: $i] :
( ~ ( greater @ Vd203 @ Vd204 )
| ~ ( less @ Vd203 @ Vd204 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 2)') ).
thf(22,axiom,
! [Vd203: $i,Vd204: $i] :
( ( Vd203 = Vd204 )
| ( greater @ Vd203 @ Vd204 )
| ( less @ Vd203 @ Vd204 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 0)') ).
thf(23,axiom,
! [Vd208: $i,Vd209: $i] :
( ( greater @ Vd208 @ Vd209 )
=> ( less @ Vd209 @ Vd208 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(140, 0), 0)') ).
thf(24,axiom,
! [Vd226: $i,Vd227: $i] :
( ( less @ Vd226 @ Vd227 )
=> ( greater @ Vd227 @ Vd226 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(147, 0), 0)') ).
thf(25,axiom,
! [Vd244: $i,Vd245: $i] :
( ( geq @ Vd245 @ Vd244 )
<=> ( ( greater @ Vd245 @ Vd244 )
| ( Vd245 = Vd244 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 16), 1)') ).
thf(32,axiom,
! [Vd295: $i,Vd296: $i] : ( greater @ ( vplus @ Vd295 @ Vd296 ) @ Vd295 ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p','ass(cond(goal(193), 0), 2)') ).
thf(36,axiom,
! [Vd328: $i,Vd329: $i,Vd330: $i] :
( ( greater @ ( vplus @ Vd328 @ Vd330 ) @ ( vplus @ Vd329 @ Vd330 ) )
=> ( greater @ Vd328 @ Vd329 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(202), 0), 2)') ).
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/sandbox/benchmark/theBenchmark.p','ass(cond(209, 0), 0)') ).
thf(46,axiom,
! [Vd400: $i] :
( ( vmul @ v1 @ Vd400 )
= Vd400 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(253, 0), 0)') ).
thf(48,axiom,
! [Vd418: $i,Vd419: $i] :
( ( vmul @ Vd418 @ Vd419 )
= ( vmul @ Vd419 @ Vd418 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(270, 0), 0)') ).
thf(49,axiom,
! [Vd432: $i,Vd433: $i,Vd434: $i] :
( ( vmul @ Vd432 @ ( vplus @ Vd433 @ Vd434 ) )
= ( vplus @ ( vmul @ Vd432 @ Vd433 ) @ ( vmul @ Vd432 @ Vd434 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(281, 0), 0)') ).
thf(50,axiom,
! [Vd444: $i,Vd445: $i,Vd446: $i] :
( ( vmul @ ( vmul @ Vd444 @ Vd445 ) @ Vd446 )
= ( vmul @ Vd444 @ ( vmul @ Vd445 @ Vd446 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(290, 0), 0)') ).
thf(51,axiom,
! [Vd456: $i,Vd457: $i,Vd458: $i] :
( ( greater @ Vd457 @ Vd458 )
=> ( greater @ ( vmul @ Vd457 @ Vd456 ) @ ( vmul @ Vd458 @ Vd456 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(299, 0), 2)') ).
thf(52,axiom,
! [Vd456: $i,Vd461: $i,Vd462: $i] :
( ( Vd461 = Vd462 )
=> ( ( vmul @ Vd461 @ Vd456 )
= ( vmul @ Vd462 @ Vd456 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(299, 0), 1)') ).
thf(53,axiom,
! [Vd456: $i,Vd465: $i,Vd466: $i] :
( ( less @ Vd465 @ Vd466 )
=> ( less @ ( vmul @ Vd465 @ Vd456 ) @ ( vmul @ Vd466 @ Vd456 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(299, 0), 0)') ).
thf(54,axiom,
! [Vd486: $i,Vd487: $i,Vd488: $i] :
( ( greater @ ( vmul @ Vd486 @ Vd487 ) @ ( vmul @ Vd488 @ Vd487 ) )
=> ( greater @ Vd486 @ Vd488 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(conjunct1(307), 0), 0)') ).
thf(55,axiom,
! [Vd491: $i,Vd492: $i,Vd493: $i] :
( ( ( vmul @ Vd491 @ Vd492 )
= ( vmul @ Vd493 @ Vd492 ) )
=> ( Vd491 = Vd493 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(conjunct1(conjunct2(307)), 0), 0)') ).
thf(56,axiom,
! [Vd496: $i,Vd497: $i,Vd498: $i] :
( ( less @ ( vmul @ Vd496 @ Vd497 ) @ ( vmul @ Vd498 @ Vd497 ) )
=> ( less @ Vd496 @ Vd498 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(conjunct2(conjunct2(307)), 0), 0)') ).
thf(57,axiom,
greater @ vd508 @ vd509,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conjunct1(314), 510, 0)') ).
thf(58,axiom,
greater @ vd511 @ vd512,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conjunct2(314), 513, 0)') ).
thf(59,conjecture,
greater @ ( vmul @ vd508 @ vd511 ) @ ( vmul @ vd509 @ vd511 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conjunct1(315), 514, 0)') ).
thf(60,negated_conjecture,
( ( greater @ ( vmul @ vd508 @ vd511 ) @ ( vmul @ vd509 @ vd511 ) )
= $false ),
inference(negate_conjecture,[status(cth)],[59]) ).
thf(61,plain,
( ( greater @ ( vmul @ vd508 @ vd511 ) @ ( vmul @ vd509 @ vd511 ) )
= $false ),
inference(unfold_def,[status(thm)],[60]) ).
thf(62,plain,
( ( ! [Vd193: $i,Vd194: $i] :
( ( greater @ Vd194 @ Vd193 )
<=> ? [Vd196: $i] :
( Vd194
= ( vplus @ Vd193 @ Vd196 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(63,plain,
( ( ! [Vd203: $i,Vd204: $i] :
( ( Vd203 != Vd204 )
| ~ ( greater @ Vd203 @ Vd204 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(64,plain,
( ( ! [Vd203: $i,Vd204: $i] :
( ~ ( greater @ Vd203 @ Vd204 )
| ~ ( less @ Vd203 @ Vd204 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(65,plain,
( ( ! [Vd203: $i,Vd204: $i] :
( ( Vd203 = Vd204 )
| ( greater @ Vd203 @ Vd204 )
| ( less @ Vd203 @ Vd204 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(66,plain,
( ( ! [Vd208: $i,Vd209: $i] :
( ( greater @ Vd208 @ Vd209 )
=> ( less @ Vd209 @ Vd208 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(67,plain,
( ( ! [Vd226: $i,Vd227: $i] :
( ( less @ Vd226 @ Vd227 )
=> ( greater @ Vd227 @ Vd226 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(68,plain,
( ( ! [Vd244: $i,Vd245: $i] :
( ( geq @ Vd245 @ Vd244 )
<=> ( ( greater @ Vd245 @ Vd244 )
| ( Vd245 = Vd244 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
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,
( ( ! [Vd328: $i,Vd329: $i,Vd330: $i] :
( ( greater @ ( vplus @ Vd328 @ Vd330 ) @ ( vplus @ Vd329 @ Vd330 ) )
=> ( greater @ Vd328 @ Vd329 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
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)],[39]) ).
thf(73,plain,
( ( ! [Vd400: $i] :
( ( vmul @ v1 @ Vd400 )
= Vd400 ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(74,plain,
( ( ! [Vd418: $i,Vd419: $i] :
( ( vmul @ Vd418 @ Vd419 )
= ( vmul @ Vd419 @ Vd418 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(75,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)],[49]) ).
thf(76,plain,
( ( ! [Vd444: $i,Vd445: $i,Vd446: $i] :
( ( vmul @ ( vmul @ Vd444 @ Vd445 ) @ Vd446 )
= ( vmul @ Vd444 @ ( vmul @ Vd445 @ Vd446 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(77,plain,
( ( ! [Vd456: $i,Vd457: $i,Vd458: $i] :
( ( greater @ Vd457 @ Vd458 )
=> ( greater @ ( vmul @ Vd457 @ Vd456 ) @ ( vmul @ Vd458 @ Vd456 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(78,plain,
( ( ! [Vd456: $i,Vd461: $i,Vd462: $i] :
( ( Vd461 = Vd462 )
=> ( ( vmul @ Vd461 @ Vd456 )
= ( vmul @ Vd462 @ Vd456 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(79,plain,
( ( ! [Vd456: $i,Vd465: $i,Vd466: $i] :
( ( less @ Vd465 @ Vd466 )
=> ( less @ ( vmul @ Vd465 @ Vd456 ) @ ( vmul @ Vd466 @ Vd456 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(80,plain,
( ( ! [Vd486: $i,Vd487: $i,Vd488: $i] :
( ( greater @ ( vmul @ Vd486 @ Vd487 ) @ ( vmul @ Vd488 @ Vd487 ) )
=> ( greater @ Vd486 @ Vd488 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(81,plain,
( ( ! [Vd491: $i,Vd492: $i,Vd493: $i] :
( ( ( vmul @ Vd491 @ Vd492 )
= ( vmul @ Vd493 @ Vd492 ) )
=> ( Vd491 = Vd493 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(82,plain,
( ( ! [Vd496: $i,Vd497: $i,Vd498: $i] :
( ( less @ ( vmul @ Vd496 @ Vd497 ) @ ( vmul @ Vd498 @ Vd497 ) )
=> ( less @ Vd496 @ Vd498 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(83,plain,
( ( greater @ vd508 @ vd509 )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(84,plain,
( ( greater @ vd511 @ vd512 )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(85,plain,
( ( ~ ( greater @ ( vmul @ vd508 @ vd511 ) @ ( vmul @ vd509 @ vd511 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[61]) ).
thf(86,plain,
( ( greater @ vd511 @ vd512 )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(87,plain,
( ( greater @ vd508 @ vd509 )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(88,plain,
( ( ! [Vd496: $i,Vd497: $i,Vd498: $i] :
( ( less @ ( vmul @ Vd496 @ Vd497 ) @ ( vmul @ Vd498 @ Vd497 ) )
=> ( less @ Vd496 @ Vd498 ) ) )
= $true ),
inference(copy,[status(thm)],[82]) ).
thf(89,plain,
( ( ! [Vd491: $i,Vd492: $i,Vd493: $i] :
( ( ( vmul @ Vd491 @ Vd492 )
= ( vmul @ Vd493 @ Vd492 ) )
=> ( Vd491 = Vd493 ) ) )
= $true ),
inference(copy,[status(thm)],[81]) ).
thf(90,plain,
( ( ! [Vd486: $i,Vd487: $i,Vd488: $i] :
( ( greater @ ( vmul @ Vd486 @ Vd487 ) @ ( vmul @ Vd488 @ Vd487 ) )
=> ( greater @ Vd486 @ Vd488 ) ) )
= $true ),
inference(copy,[status(thm)],[80]) ).
thf(91,plain,
( ( ! [Vd456: $i,Vd465: $i,Vd466: $i] :
( ( less @ Vd465 @ Vd466 )
=> ( less @ ( vmul @ Vd465 @ Vd456 ) @ ( vmul @ Vd466 @ Vd456 ) ) ) )
= $true ),
inference(copy,[status(thm)],[79]) ).
thf(92,plain,
( ( ! [Vd456: $i,Vd461: $i,Vd462: $i] :
( ( Vd461 = Vd462 )
=> ( ( vmul @ Vd461 @ Vd456 )
= ( vmul @ Vd462 @ Vd456 ) ) ) )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(93,plain,
( ( ! [Vd456: $i,Vd457: $i,Vd458: $i] :
( ( greater @ Vd457 @ Vd458 )
=> ( greater @ ( vmul @ Vd457 @ Vd456 ) @ ( vmul @ Vd458 @ Vd456 ) ) ) )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(94,plain,
( ( ! [Vd444: $i,Vd445: $i,Vd446: $i] :
( ( vmul @ ( vmul @ Vd444 @ Vd445 ) @ Vd446 )
= ( vmul @ Vd444 @ ( vmul @ Vd445 @ Vd446 ) ) ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(95,plain,
( ( ! [Vd432: $i,Vd433: $i,Vd434: $i] :
( ( vmul @ Vd432 @ ( vplus @ Vd433 @ Vd434 ) )
= ( vplus @ ( vmul @ Vd432 @ Vd433 ) @ ( vmul @ Vd432 @ Vd434 ) ) ) )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(96,plain,
( ( ! [Vd418: $i,Vd419: $i] :
( ( vmul @ Vd418 @ Vd419 )
= ( vmul @ Vd419 @ Vd418 ) ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(97,plain,
( ( ! [Vd400: $i] :
( ( vmul @ v1 @ Vd400 )
= Vd400 ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(98,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(99,plain,
( ( ! [Vd328: $i,Vd329: $i,Vd330: $i] :
( ( greater @ ( vplus @ Vd328 @ Vd330 ) @ ( vplus @ Vd329 @ Vd330 ) )
=> ( greater @ Vd328 @ Vd329 ) ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(100,plain,
( ( ! [Vd301: $i,Vd302: $i,Vd303: $i] :
( ( greater @ Vd301 @ Vd302 )
=> ( greater @ ( vplus @ Vd301 @ Vd303 ) @ ( vplus @ Vd302 @ Vd303 ) ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(101,plain,
( ( ! [Vd295: $i,Vd296: $i] : ( greater @ ( vplus @ Vd295 @ Vd296 ) @ Vd295 ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(102,plain,
( ( ! [Vd244: $i,Vd245: $i] :
( ( geq @ Vd245 @ Vd244 )
<=> ( ( greater @ Vd245 @ Vd244 )
| ( Vd245 = Vd244 ) ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(103,plain,
( ( ! [Vd226: $i,Vd227: $i] :
( ( less @ Vd226 @ Vd227 )
=> ( greater @ Vd227 @ Vd226 ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(104,plain,
( ( ! [Vd208: $i,Vd209: $i] :
( ( greater @ Vd208 @ Vd209 )
=> ( less @ Vd209 @ Vd208 ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(105,plain,
( ( ! [Vd203: $i,Vd204: $i] :
( ( Vd203 = Vd204 )
| ( greater @ Vd203 @ Vd204 )
| ( less @ Vd203 @ Vd204 ) ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(106,plain,
( ( ! [Vd203: $i,Vd204: $i] :
( ~ ( greater @ Vd203 @ Vd204 )
| ~ ( less @ Vd203 @ Vd204 ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(107,plain,
( ( ! [Vd203: $i,Vd204: $i] :
( ( Vd203 != Vd204 )
| ~ ( greater @ Vd203 @ Vd204 ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(108,plain,
( ( ! [Vd193: $i,Vd194: $i] :
( ( greater @ Vd194 @ Vd193 )
<=> ? [Vd196: $i] :
( Vd194
= ( vplus @ Vd193 @ Vd196 ) ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(109,plain,
( ( ~ ( greater @ ( vmul @ vd508 @ vd511 ) @ ( vmul @ vd509 @ vd511 ) ) )
= $true ),
inference(copy,[status(thm)],[85]) ).
thf(110,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( less @ ( vmul @ SX0 @ SX1 ) @ ( vmul @ SX2 @ SX1 ) )
| ( less @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(111,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( SX1 != SX2 )
| ( ( vmul @ SX1 @ SX0 )
= ( vmul @ SX2 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(112,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( greater @ SX1 @ SX2 )
| ( greater @ ( vmul @ SX1 @ SX0 ) @ ( vmul @ SX2 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(113,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(114,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( less @ SX1 @ SX2 )
| ( less @ ( vmul @ SX1 @ SX0 ) @ ( vmul @ SX2 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(115,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( greater @ ( vmul @ SX0 @ SX1 ) @ ( vmul @ SX2 @ SX1 ) )
| ( greater @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(116,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ( greater @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[107]) ).
thf(117,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)],[98]) ).
thf(118,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( greater @ SX0 @ SX1 )
| ( greater @ ( vplus @ SX0 @ SX2 ) @ ( vplus @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[100]) ).
thf(119,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( vmul @ SX0 @ SX1 )
!= ( vmul @ SX2 @ SX1 ) )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(120,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( geq @ SX1 @ SX0 )
| ( greater @ SX1 @ SX0 )
| ( SX1 = SX0 ) )
| ~ ( ~ ( ( greater @ SX1 @ SX0 )
| ( SX1 = SX0 ) )
| ( geq @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[102]) ).
thf(121,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( less @ SX0 @ SX1 )
| ( greater @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[103]) ).
thf(122,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( greater @ SX0 @ SX1 )
| ( less @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[104]) ).
thf(123,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)],[108]) ).
thf(124,plain,
! [SV1: $i] :
( ( ! [SY54: $i,SY55: $i] :
( ( vmul @ ( vmul @ SV1 @ SY54 ) @ SY55 )
= ( vmul @ SV1 @ ( vmul @ SY54 @ SY55 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(125,plain,
! [SV2: $i] :
( ( ! [SY56: $i,SY57: $i] :
( ( vmul @ SV2 @ ( vplus @ SY56 @ SY57 ) )
= ( vplus @ ( vmul @ SV2 @ SY56 ) @ ( vmul @ SV2 @ SY57 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(126,plain,
! [SV3: $i] :
( ( ! [SY58: $i] :
( ( vmul @ SV3 @ SY58 )
= ( vmul @ SY58 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(127,plain,
! [SV4: $i] :
( ( ( vmul @ v1 @ SV4 )
= SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(128,plain,
! [SV5: $i] :
( ( ! [SY59: $i] : ( greater @ ( vplus @ SV5 @ SY59 ) @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(129,plain,
! [SV6: $i] :
( ( ! [SY60: $i] :
( ( SV6 = SY60 )
| ( greater @ SV6 @ SY60 )
| ( less @ SV6 @ SY60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(130,plain,
! [SV7: $i] :
( ( ! [SY61: $i] :
( ~ ( greater @ SV7 @ SY61 )
| ~ ( less @ SV7 @ SY61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(131,plain,
( ( greater @ ( vmul @ vd508 @ vd511 ) @ ( vmul @ vd509 @ vd511 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(132,plain,
! [SV8: $i] :
( ( ! [SY62: $i,SY63: $i] :
( ~ ( less @ ( vmul @ SV8 @ SY62 ) @ ( vmul @ SY63 @ SY62 ) )
| ( less @ SV8 @ SY63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(133,plain,
! [SV9: $i] :
( ( ! [SY64: $i,SY65: $i] :
( ( SY64 != SY65 )
| ( ( vmul @ SY64 @ SV9 )
= ( vmul @ SY65 @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(134,plain,
! [SV10: $i] :
( ( ! [SY66: $i,SY67: $i] :
( ~ ( greater @ SY66 @ SY67 )
| ( greater @ ( vmul @ SY66 @ SV10 ) @ ( vmul @ SY67 @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(135,plain,
! [SV11: $i] :
( ( ! [SY68: $i,SY69: $i] :
( ~ ( greater @ ( vplus @ SV11 @ SY69 ) @ ( vplus @ SY68 @ SY69 ) )
| ( greater @ SV11 @ SY68 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(136,plain,
! [SV12: $i] :
( ( ! [SY70: $i,SY71: $i] :
( ~ ( less @ SY70 @ SY71 )
| ( less @ ( vmul @ SY70 @ SV12 ) @ ( vmul @ SY71 @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(137,plain,
! [SV13: $i] :
( ( ! [SY72: $i,SY73: $i] :
( ~ ( greater @ ( vmul @ SV13 @ SY72 ) @ ( vmul @ SY73 @ SY72 ) )
| ( greater @ SV13 @ SY73 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(138,plain,
! [SV14: $i] :
( ( ! [SY74: $i] :
( ( SV14 != SY74 )
| ~ ( greater @ SV14 @ SY74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(139,plain,
! [SV15: $i] :
( ( ! [SY75: $i,SY76: $i,SY77: $i] :
( ~ ~ ( ~ ( greater @ SY76 @ SY77 )
| ~ ( greater @ SV15 @ SY75 ) )
| ( greater @ ( vplus @ SV15 @ SY76 ) @ ( vplus @ SY75 @ SY77 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(140,plain,
! [SV16: $i] :
( ( ! [SY78: $i,SY79: $i] :
( ~ ( greater @ SV16 @ SY78 )
| ( greater @ ( vplus @ SV16 @ SY79 ) @ ( vplus @ SY78 @ SY79 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(141,plain,
! [SV17: $i] :
( ( ! [SY80: $i,SY81: $i] :
( ( ( vmul @ SV17 @ SY80 )
!= ( vmul @ SY81 @ SY80 ) )
| ( SV17 = SY81 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(142,plain,
! [SV18: $i] :
( ( ! [SY82: $i] :
~ ( ~ ( ~ ( geq @ SY82 @ SV18 )
| ( greater @ SY82 @ SV18 )
| ( SY82 = SV18 ) )
| ~ ( ~ ( ( greater @ SY82 @ SV18 )
| ( SY82 = SV18 ) )
| ( geq @ SY82 @ SV18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(143,plain,
! [SV19: $i] :
( ( ! [SY83: $i] :
( ~ ( less @ SV19 @ SY83 )
| ( greater @ SY83 @ SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(144,plain,
! [SV20: $i] :
( ( ! [SY84: $i] :
( ~ ( greater @ SV20 @ SY84 )
| ( less @ SY84 @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(145,plain,
! [SV21: $i] :
( ( ! [SY85: $i] :
~ ( ~ ( ~ ( greater @ SY85 @ SV21 )
| ~ ! [SY86: $i] :
( SY85
!= ( vplus @ SV21 @ SY86 ) ) )
| ~ ( ~ ~ ! [SY87: $i] :
( SY85
!= ( vplus @ SV21 @ SY87 ) )
| ( greater @ SY85 @ SV21 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(146,plain,
! [SV22: $i,SV1: $i] :
( ( ! [SY88: $i] :
( ( vmul @ ( vmul @ SV1 @ SV22 ) @ SY88 )
= ( vmul @ SV1 @ ( vmul @ SV22 @ SY88 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(147,plain,
! [SV23: $i,SV2: $i] :
( ( ! [SY89: $i] :
( ( vmul @ SV2 @ ( vplus @ SV23 @ SY89 ) )
= ( vplus @ ( vmul @ SV2 @ SV23 ) @ ( vmul @ SV2 @ SY89 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(148,plain,
! [SV24: $i,SV3: $i] :
( ( ( vmul @ SV3 @ SV24 )
= ( vmul @ SV24 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(149,plain,
! [SV25: $i,SV5: $i] :
( ( greater @ ( vplus @ SV5 @ SV25 ) @ SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(150,plain,
! [SV26: $i,SV6: $i] :
( ( ( SV6 = SV26 )
| ( greater @ SV6 @ SV26 )
| ( less @ SV6 @ SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(151,plain,
! [SV27: $i,SV7: $i] :
( ( ~ ( greater @ SV7 @ SV27 )
| ~ ( less @ SV7 @ SV27 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(152,plain,
! [SV28: $i,SV8: $i] :
( ( ! [SY90: $i] :
( ~ ( less @ ( vmul @ SV8 @ SV28 ) @ ( vmul @ SY90 @ SV28 ) )
| ( less @ SV8 @ SY90 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(153,plain,
! [SV9: $i,SV29: $i] :
( ( ! [SY91: $i] :
( ( SV29 != SY91 )
| ( ( vmul @ SV29 @ SV9 )
= ( vmul @ SY91 @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(154,plain,
! [SV10: $i,SV30: $i] :
( ( ! [SY92: $i] :
( ~ ( greater @ SV30 @ SY92 )
| ( greater @ ( vmul @ SV30 @ SV10 ) @ ( vmul @ SY92 @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(155,plain,
! [SV31: $i,SV11: $i] :
( ( ! [SY93: $i] :
( ~ ( greater @ ( vplus @ SV11 @ SY93 ) @ ( vplus @ SV31 @ SY93 ) )
| ( greater @ SV11 @ SV31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(156,plain,
! [SV12: $i,SV32: $i] :
( ( ! [SY94: $i] :
( ~ ( less @ SV32 @ SY94 )
| ( less @ ( vmul @ SV32 @ SV12 ) @ ( vmul @ SY94 @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(157,plain,
! [SV33: $i,SV13: $i] :
( ( ! [SY95: $i] :
( ~ ( greater @ ( vmul @ SV13 @ SV33 ) @ ( vmul @ SY95 @ SV33 ) )
| ( greater @ SV13 @ SY95 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(158,plain,
! [SV34: $i,SV14: $i] :
( ( ( SV14 != SV34 )
| ~ ( greater @ SV14 @ SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(159,plain,
! [SV35: $i,SV15: $i] :
( ( ! [SY96: $i,SY97: $i] :
( ~ ~ ( ~ ( greater @ SY96 @ SY97 )
| ~ ( greater @ SV15 @ SV35 ) )
| ( greater @ ( vplus @ SV15 @ SY96 ) @ ( vplus @ SV35 @ SY97 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(160,plain,
! [SV36: $i,SV16: $i] :
( ( ! [SY98: $i] :
( ~ ( greater @ SV16 @ SV36 )
| ( greater @ ( vplus @ SV16 @ SY98 ) @ ( vplus @ SV36 @ SY98 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(161,plain,
! [SV37: $i,SV17: $i] :
( ( ! [SY99: $i] :
( ( ( vmul @ SV17 @ SV37 )
!= ( vmul @ SY99 @ SV37 ) )
| ( SV17 = SY99 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(162,plain,
! [SV18: $i,SV38: $i] :
( ( ~ ( ~ ( ~ ( geq @ SV38 @ SV18 )
| ( greater @ SV38 @ SV18 )
| ( SV38 = SV18 ) )
| ~ ( ~ ( ( greater @ SV38 @ SV18 )
| ( SV38 = SV18 ) )
| ( geq @ SV38 @ SV18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(163,plain,
! [SV39: $i,SV19: $i] :
( ( ~ ( less @ SV19 @ SV39 )
| ( greater @ SV39 @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(164,plain,
! [SV40: $i,SV20: $i] :
( ( ~ ( greater @ SV20 @ SV40 )
| ( less @ SV40 @ SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(165,plain,
! [SV21: $i,SV41: $i] :
( ( ~ ( ~ ( ~ ( greater @ SV41 @ SV21 )
| ~ ! [SY100: $i] :
( SV41
!= ( vplus @ SV21 @ SY100 ) ) )
| ~ ( ~ ~ ! [SY101: $i] :
( SV41
!= ( vplus @ SV21 @ SY101 ) )
| ( greater @ SV41 @ SV21 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(166,plain,
! [SV42: $i,SV22: $i,SV1: $i] :
( ( ( vmul @ ( vmul @ SV1 @ SV22 ) @ SV42 )
= ( vmul @ SV1 @ ( vmul @ SV22 @ SV42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(167,plain,
! [SV43: $i,SV23: $i,SV2: $i] :
( ( ( vmul @ SV2 @ ( vplus @ SV23 @ SV43 ) )
= ( vplus @ ( vmul @ SV2 @ SV23 ) @ ( vmul @ SV2 @ SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(168,plain,
! [SV26: $i,SV6: $i] :
( ( ( ( SV6 = SV26 )
| ( greater @ SV6 @ SV26 ) )
= $true )
| ( ( less @ SV6 @ SV26 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[150]) ).
thf(169,plain,
! [SV27: $i,SV7: $i] :
( ( ( ~ ( greater @ SV7 @ SV27 ) )
= $true )
| ( ( ~ ( less @ SV7 @ SV27 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[151]) ).
thf(170,plain,
! [SV44: $i,SV28: $i,SV8: $i] :
( ( ~ ( less @ ( vmul @ SV8 @ SV28 ) @ ( vmul @ SV44 @ SV28 ) )
| ( less @ SV8 @ SV44 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(171,plain,
! [SV9: $i,SV45: $i,SV29: $i] :
( ( ( SV29 != SV45 )
| ( ( vmul @ SV29 @ SV9 )
= ( vmul @ SV45 @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(172,plain,
! [SV10: $i,SV46: $i,SV30: $i] :
( ( ~ ( greater @ SV30 @ SV46 )
| ( greater @ ( vmul @ SV30 @ SV10 ) @ ( vmul @ SV46 @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(173,plain,
! [SV31: $i,SV47: $i,SV11: $i] :
( ( ~ ( greater @ ( vplus @ SV11 @ SV47 ) @ ( vplus @ SV31 @ SV47 ) )
| ( greater @ SV11 @ SV31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(174,plain,
! [SV12: $i,SV48: $i,SV32: $i] :
( ( ~ ( less @ SV32 @ SV48 )
| ( less @ ( vmul @ SV32 @ SV12 ) @ ( vmul @ SV48 @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(175,plain,
! [SV49: $i,SV33: $i,SV13: $i] :
( ( ~ ( greater @ ( vmul @ SV13 @ SV33 ) @ ( vmul @ SV49 @ SV33 ) )
| ( greater @ SV13 @ SV49 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(176,plain,
! [SV34: $i,SV14: $i] :
( ( ( SV14 != SV34 )
= $true )
| ( ( ~ ( greater @ SV14 @ SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[158]) ).
thf(177,plain,
! [SV35: $i,SV15: $i,SV50: $i] :
( ( ! [SY102: $i] :
( ~ ~ ( ~ ( greater @ SV50 @ SY102 )
| ~ ( greater @ SV15 @ SV35 ) )
| ( greater @ ( vplus @ SV15 @ SV50 ) @ ( vplus @ SV35 @ SY102 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(178,plain,
! [SV51: $i,SV36: $i,SV16: $i] :
( ( ~ ( greater @ SV16 @ SV36 )
| ( greater @ ( vplus @ SV16 @ SV51 ) @ ( vplus @ SV36 @ SV51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(179,plain,
! [SV52: $i,SV37: $i,SV17: $i] :
( ( ( ( vmul @ SV17 @ SV37 )
!= ( vmul @ SV52 @ SV37 ) )
| ( SV17 = SV52 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(180,plain,
! [SV18: $i,SV38: $i] :
( ( ~ ( ~ ( geq @ SV38 @ SV18 )
| ( greater @ SV38 @ SV18 )
| ( SV38 = SV18 ) )
| ~ ( ~ ( ( greater @ SV38 @ SV18 )
| ( SV38 = SV18 ) )
| ( geq @ SV38 @ SV18 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(181,plain,
! [SV39: $i,SV19: $i] :
( ( ( ~ ( less @ SV19 @ SV39 ) )
= $true )
| ( ( greater @ SV39 @ SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[163]) ).
thf(182,plain,
! [SV40: $i,SV20: $i] :
( ( ( ~ ( greater @ SV20 @ SV40 ) )
= $true )
| ( ( less @ SV40 @ SV20 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[164]) ).
thf(183,plain,
! [SV21: $i,SV41: $i] :
( ( ~ ( ~ ( greater @ SV41 @ SV21 )
| ~ ! [SY100: $i] :
( SV41
!= ( vplus @ SV21 @ SY100 ) ) )
| ~ ( ~ ~ ! [SY101: $i] :
( SV41
!= ( vplus @ SV21 @ SY101 ) )
| ( greater @ SV41 @ SV21 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[165]) ).
thf(184,plain,
! [SV26: $i,SV6: $i] :
( ( ( SV6 = SV26 )
= $true )
| ( ( greater @ SV6 @ SV26 )
= $true )
| ( ( less @ SV6 @ SV26 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[168]) ).
thf(185,plain,
! [SV27: $i,SV7: $i] :
( ( ( greater @ SV7 @ SV27 )
= $false )
| ( ( ~ ( less @ SV7 @ SV27 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(186,plain,
! [SV44: $i,SV28: $i,SV8: $i] :
( ( ( ~ ( less @ ( vmul @ SV8 @ SV28 ) @ ( vmul @ SV44 @ SV28 ) ) )
= $true )
| ( ( less @ SV8 @ SV44 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[170]) ).
thf(187,plain,
! [SV9: $i,SV45: $i,SV29: $i] :
( ( ( SV29 != SV45 )
= $true )
| ( ( ( vmul @ SV29 @ SV9 )
= ( vmul @ SV45 @ SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[171]) ).
thf(188,plain,
! [SV10: $i,SV46: $i,SV30: $i] :
( ( ( ~ ( greater @ SV30 @ SV46 ) )
= $true )
| ( ( greater @ ( vmul @ SV30 @ SV10 ) @ ( vmul @ SV46 @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[172]) ).
thf(189,plain,
! [SV31: $i,SV47: $i,SV11: $i] :
( ( ( ~ ( greater @ ( vplus @ SV11 @ SV47 ) @ ( vplus @ SV31 @ SV47 ) ) )
= $true )
| ( ( greater @ SV11 @ SV31 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[173]) ).
thf(190,plain,
! [SV12: $i,SV48: $i,SV32: $i] :
( ( ( ~ ( less @ SV32 @ SV48 ) )
= $true )
| ( ( less @ ( vmul @ SV32 @ SV12 ) @ ( vmul @ SV48 @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[174]) ).
thf(191,plain,
! [SV49: $i,SV33: $i,SV13: $i] :
( ( ( ~ ( greater @ ( vmul @ SV13 @ SV33 ) @ ( vmul @ SV49 @ SV33 ) ) )
= $true )
| ( ( greater @ SV13 @ SV49 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[175]) ).
thf(192,plain,
! [SV34: $i,SV14: $i] :
( ( ( SV14 = SV34 )
= $false )
| ( ( ~ ( greater @ SV14 @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[176]) ).
thf(193,plain,
! [SV35: $i,SV15: $i,SV53: $i,SV50: $i] :
( ( ~ ~ ( ~ ( greater @ SV50 @ SV53 )
| ~ ( greater @ SV15 @ SV35 ) )
| ( greater @ ( vplus @ SV15 @ SV50 ) @ ( vplus @ SV35 @ SV53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(194,plain,
! [SV51: $i,SV36: $i,SV16: $i] :
( ( ( ~ ( greater @ SV16 @ SV36 ) )
= $true )
| ( ( greater @ ( vplus @ SV16 @ SV51 ) @ ( vplus @ SV36 @ SV51 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[178]) ).
thf(195,plain,
! [SV52: $i,SV37: $i,SV17: $i] :
( ( ( ( vmul @ SV17 @ SV37 )
!= ( vmul @ SV52 @ SV37 ) )
= $true )
| ( ( SV17 = SV52 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[179]) ).
thf(196,plain,
! [SV18: $i,SV38: $i] :
( ( ~ ( ~ ( geq @ SV38 @ SV18 )
| ( greater @ SV38 @ SV18 )
| ( SV38 = SV18 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[180]) ).
thf(197,plain,
! [SV18: $i,SV38: $i] :
( ( ~ ( ~ ( ( greater @ SV38 @ SV18 )
| ( SV38 = SV18 ) )
| ( geq @ SV38 @ SV18 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[180]) ).
thf(198,plain,
! [SV39: $i,SV19: $i] :
( ( ( less @ SV19 @ SV39 )
= $false )
| ( ( greater @ SV39 @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[181]) ).
thf(199,plain,
! [SV40: $i,SV20: $i] :
( ( ( greater @ SV20 @ SV40 )
= $false )
| ( ( less @ SV40 @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[182]) ).
thf(200,plain,
! [SV21: $i,SV41: $i] :
( ( ~ ( ~ ( greater @ SV41 @ SV21 )
| ~ ! [SY100: $i] :
( SV41
!= ( vplus @ SV21 @ SY100 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[183]) ).
thf(201,plain,
! [SV21: $i,SV41: $i] :
( ( ~ ( ~ ~ ! [SY101: $i] :
( SV41
!= ( vplus @ SV21 @ SY101 ) )
| ( greater @ SV41 @ SV21 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[183]) ).
thf(202,plain,
! [SV27: $i,SV7: $i] :
( ( ( less @ SV7 @ SV27 )
= $false )
| ( ( greater @ SV7 @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[185]) ).
thf(203,plain,
! [SV44: $i,SV28: $i,SV8: $i] :
( ( ( less @ ( vmul @ SV8 @ SV28 ) @ ( vmul @ SV44 @ SV28 ) )
= $false )
| ( ( less @ SV8 @ SV44 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[186]) ).
thf(204,plain,
! [SV9: $i,SV45: $i,SV29: $i] :
( ( ( SV29 = SV45 )
= $false )
| ( ( ( vmul @ SV29 @ SV9 )
= ( vmul @ SV45 @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[187]) ).
thf(205,plain,
! [SV10: $i,SV46: $i,SV30: $i] :
( ( ( greater @ SV30 @ SV46 )
= $false )
| ( ( greater @ ( vmul @ SV30 @ SV10 ) @ ( vmul @ SV46 @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[188]) ).
thf(206,plain,
! [SV31: $i,SV47: $i,SV11: $i] :
( ( ( greater @ ( vplus @ SV11 @ SV47 ) @ ( vplus @ SV31 @ SV47 ) )
= $false )
| ( ( greater @ SV11 @ SV31 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[189]) ).
thf(207,plain,
! [SV12: $i,SV48: $i,SV32: $i] :
( ( ( less @ SV32 @ SV48 )
= $false )
| ( ( less @ ( vmul @ SV32 @ SV12 ) @ ( vmul @ SV48 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[190]) ).
thf(208,plain,
! [SV49: $i,SV33: $i,SV13: $i] :
( ( ( greater @ ( vmul @ SV13 @ SV33 ) @ ( vmul @ SV49 @ SV33 ) )
= $false )
| ( ( greater @ SV13 @ SV49 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[191]) ).
thf(209,plain,
! [SV34: $i,SV14: $i] :
( ( ( greater @ SV14 @ SV34 )
= $false )
| ( ( SV14 = SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(210,plain,
! [SV35: $i,SV15: $i,SV53: $i,SV50: $i] :
( ( ( ~ ~ ( ~ ( greater @ SV50 @ SV53 )
| ~ ( greater @ SV15 @ SV35 ) ) )
= $true )
| ( ( greater @ ( vplus @ SV15 @ SV50 ) @ ( vplus @ SV35 @ SV53 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[193]) ).
thf(211,plain,
! [SV51: $i,SV36: $i,SV16: $i] :
( ( ( greater @ SV16 @ SV36 )
= $false )
| ( ( greater @ ( vplus @ SV16 @ SV51 ) @ ( vplus @ SV36 @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(212,plain,
! [SV52: $i,SV37: $i,SV17: $i] :
( ( ( ( vmul @ SV17 @ SV37 )
= ( vmul @ SV52 @ SV37 ) )
= $false )
| ( ( SV17 = SV52 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(213,plain,
! [SV18: $i,SV38: $i] :
( ( ~ ( geq @ SV38 @ SV18 )
| ( greater @ SV38 @ SV18 )
| ( SV38 = SV18 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[196]) ).
thf(214,plain,
! [SV18: $i,SV38: $i] :
( ( ~ ( ( greater @ SV38 @ SV18 )
| ( SV38 = SV18 ) )
| ( geq @ SV38 @ SV18 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[197]) ).
thf(215,plain,
! [SV21: $i,SV41: $i] :
( ( ~ ( greater @ SV41 @ SV21 )
| ~ ! [SY100: $i] :
( SV41
!= ( vplus @ SV21 @ SY100 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[200]) ).
thf(216,plain,
! [SV21: $i,SV41: $i] :
( ( ~ ~ ! [SY101: $i] :
( SV41
!= ( vplus @ SV21 @ SY101 ) )
| ( greater @ SV41 @ SV21 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[201]) ).
thf(217,plain,
! [SV35: $i,SV15: $i,SV53: $i,SV50: $i] :
( ( ( ~ ( ~ ( greater @ SV50 @ SV53 )
| ~ ( greater @ SV15 @ SV35 ) ) )
= $false )
| ( ( greater @ ( vplus @ SV15 @ SV50 ) @ ( vplus @ SV35 @ SV53 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[210]) ).
thf(218,plain,
! [SV18: $i,SV38: $i] :
( ( ( ~ ( geq @ SV38 @ SV18 ) )
= $true )
| ( ( ( greater @ SV38 @ SV18 )
| ( SV38 = SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[213]) ).
thf(219,plain,
! [SV18: $i,SV38: $i] :
( ( ( ~ ( ( greater @ SV38 @ SV18 )
| ( SV38 = SV18 ) ) )
= $true )
| ( ( geq @ SV38 @ SV18 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[214]) ).
thf(220,plain,
! [SV21: $i,SV41: $i] :
( ( ( ~ ( greater @ SV41 @ SV21 ) )
= $true )
| ( ( ~ ! [SY100: $i] :
( SV41
!= ( vplus @ SV21 @ SY100 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[215]) ).
thf(221,plain,
! [SV21: $i,SV41: $i] :
( ( ( ~ ~ ! [SY101: $i] :
( SV41
!= ( vplus @ SV21 @ SY101 ) ) )
= $true )
| ( ( greater @ SV41 @ SV21 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[216]) ).
thf(222,plain,
! [SV35: $i,SV15: $i,SV53: $i,SV50: $i] :
( ( ( ~ ( greater @ SV50 @ SV53 )
| ~ ( greater @ SV15 @ SV35 ) )
= $true )
| ( ( greater @ ( vplus @ SV15 @ SV50 ) @ ( vplus @ SV35 @ SV53 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[217]) ).
thf(223,plain,
! [SV18: $i,SV38: $i] :
( ( ( geq @ SV38 @ SV18 )
= $false )
| ( ( ( greater @ SV38 @ SV18 )
| ( SV38 = SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[218]) ).
thf(224,plain,
! [SV18: $i,SV38: $i] :
( ( ( ( greater @ SV38 @ SV18 )
| ( SV38 = SV18 ) )
= $false )
| ( ( geq @ SV38 @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[219]) ).
thf(225,plain,
! [SV21: $i,SV41: $i] :
( ( ( greater @ SV41 @ SV21 )
= $false )
| ( ( ~ ! [SY100: $i] :
( SV41
!= ( vplus @ SV21 @ SY100 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[220]) ).
thf(226,plain,
! [SV21: $i,SV41: $i] :
( ( ( ~ ! [SY101: $i] :
( SV41
!= ( vplus @ SV21 @ SY101 ) ) )
= $false )
| ( ( greater @ SV41 @ SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[221]) ).
thf(227,plain,
! [SV35: $i,SV15: $i,SV53: $i,SV50: $i] :
( ( ( ~ ( greater @ SV50 @ SV53 ) )
= $true )
| ( ( ~ ( greater @ SV15 @ SV35 ) )
= $true )
| ( ( greater @ ( vplus @ SV15 @ SV50 ) @ ( vplus @ SV35 @ SV53 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[222]) ).
thf(228,plain,
! [SV18: $i,SV38: $i] :
( ( ( greater @ SV38 @ SV18 )
= $true )
| ( ( SV38 = SV18 )
= $true )
| ( ( geq @ SV38 @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[223]) ).
thf(229,plain,
! [SV18: $i,SV38: $i] :
( ( ( greater @ SV38 @ SV18 )
= $false )
| ( ( geq @ SV38 @ SV18 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[224]) ).
thf(230,plain,
! [SV18: $i,SV38: $i] :
( ( ( SV38 = SV18 )
= $false )
| ( ( geq @ SV38 @ SV18 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[224]) ).
thf(231,plain,
! [SV21: $i,SV41: $i] :
( ( ( ! [SY100: $i] :
( SV41
!= ( vplus @ SV21 @ SY100 ) ) )
= $false )
| ( ( greater @ SV41 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[225]) ).
thf(232,plain,
! [SV21: $i,SV41: $i] :
( ( ( ! [SY101: $i] :
( SV41
!= ( vplus @ SV21 @ SY101 ) ) )
= $true )
| ( ( greater @ SV41 @ SV21 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[226]) ).
thf(233,plain,
! [SV35: $i,SV15: $i,SV53: $i,SV50: $i] :
( ( ( greater @ SV50 @ SV53 )
= $false )
| ( ( ~ ( greater @ SV15 @ SV35 ) )
= $true )
| ( ( greater @ ( vplus @ SV15 @ SV50 ) @ ( vplus @ SV35 @ SV53 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[227]) ).
thf(234,plain,
! [SV21: $i,SV41: $i] :
( ( ( SV41
!= ( vplus @ SV21 @ ( sK1_SY100 @ SV21 @ SV41 ) ) )
= $false )
| ( ( greater @ SV41 @ SV21 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[231]) ).
thf(235,plain,
! [SV54: $i,SV21: $i,SV41: $i] :
( ( ( SV41
!= ( vplus @ SV21 @ SV54 ) )
= $true )
| ( ( greater @ SV41 @ SV21 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[232]) ).
thf(236,plain,
! [SV53: $i,SV50: $i,SV35: $i,SV15: $i] :
( ( ( greater @ SV15 @ SV35 )
= $false )
| ( ( greater @ SV50 @ SV53 )
= $false )
| ( ( greater @ ( vplus @ SV15 @ SV50 ) @ ( vplus @ SV35 @ SV53 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[233]) ).
thf(237,plain,
! [SV21: $i,SV41: $i] :
( ( ( SV41
= ( vplus @ SV21 @ ( sK1_SY100 @ SV21 @ SV41 ) ) )
= $true )
| ( ( greater @ SV41 @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[234]) ).
thf(238,plain,
! [SV54: $i,SV21: $i,SV41: $i] :
( ( ( SV41
= ( vplus @ SV21 @ SV54 ) )
= $false )
| ( ( greater @ SV41 @ SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[235]) ).
thf(239,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[86,238,237,236,230,229,228,212,211,209,208,207,206,205,204,203,202,199,198,184,167,166,149,148,131,127,87]) ).
thf(240,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[239]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM854+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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.21 % Computer : n007.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Tue Oct 6 13:38:45 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.87/1.69
% 7.87/1.69 No.of.Axioms: 23
% 7.87/1.69
% 7.87/1.69 Length.of.Defs: 0
% 7.87/1.69
% 7.87/1.69 Contains.Choice.Funs: false
% 7.87/1.69 ......
% 7.87/1.69
% 7.87/1.69 ********************************
% 7.87/1.69 * All subproblems solved! *
% 7.87/1.69 ********************************
% 7.87/1.69 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:23,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:239,loop_count:0,foatp_calls:1,translation:fof_full)
% 7.87/1.69
% 7.87/1.69 %**** Beginning of derivation protocol ****
% 7.87/1.69 % SZS output start CNFRefutation
% See solution above
% 7.87/1.69
% 7.87/1.69 %**** End of derivation protocol ****
% 7.87/1.69 %**** no. of clauses in derivation: 205 ****
% 7.87/1.69 %**** clause counter: 239 ****
% 7.87/1.69
% 7.87/1.69 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:23,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:239,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------