%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : RNG047+2 : TPTP v9.3.1. Released v4.0.0.
% 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 : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:37:35 AM UTC 2026
% Result : Theorem 0.42s 0.36s
% Output : CNFRefutation 0.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 13
% Syntax : Number of formulae : 152 ( 83 unt; 0 typ; 0 def)
% Number of atoms : 859 ( 351 equ; 0 cnn)
% Maximal formula atoms : 9 ( 5 avg)
% Number of connectives : 1092 ( 253 ~; 174 |; 36 &; 580 @)
% ( 0 <=>; 49 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 17 usr; 6 con; 0-2 aty)
% Number of variables : 172 ( 0 ^; 169 !; 3 ?; 172 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_aDimensionOf0,type,
aDimensionOf0: $i > $i ).
thf(tp_aNaturalNumber0,type,
aNaturalNumber0: $i > $o ).
thf(tp_aScalar0,type,
aScalar0: $i > $o ).
thf(tp_aVector0,type,
aVector0: $i > $o ).
thf(tp_iLess0,type,
iLess0: $i > $i > $o ).
thf(tp_sK1_SY18,type,
sK1_SY18: $i > $i ).
thf(tp_sdtasdt0,type,
sdtasdt0: $i > $i > $i ).
thf(tp_sdtlbdtrb0,type,
sdtlbdtrb0: $i > $i > $i ).
thf(tp_sdtlseqdt0,type,
sdtlseqdt0: $i > $i > $o ).
thf(tp_sdtpldt0,type,
sdtpldt0: $i > $i > $i ).
thf(tp_smndt0,type,
smndt0: $i > $i ).
thf(tp_sz00,type,
sz00: $i ).
thf(tp_sz0z00,type,
sz0z00: $i ).
thf(tp_sziznziztdt0,type,
sziznziztdt0: $i > $i ).
thf(tp_szszuzczcdt0,type,
szszuzczcdt0: $i > $i ).
thf(tp_xs,type,
xs: $i ).
thf(tp_xt,type,
xt: $i ).
thf(1,axiom,
! [W0: $i,W1: $i] :
( ( ( aVector0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( aScalar0 @ ( sdtlbdtrb0 @ W0 @ W1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mElmSc) ).
thf(2,axiom,
! [W0: $i] :
( ( aVector0 @ W0 )
=> ( aNaturalNumber0 @ ( aDimensionOf0 @ W0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDimNat) ).
thf(3,axiom,
! [W0: $i] :
( ( aVector0 @ W0 )
=> $true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mVcSort) ).
thf(25,axiom,
! [W0: $i] :
( ( aNaturalNumber0 @ W0 )
=> ( iLess0 @ W0 @ ( szszuzczcdt0 @ W0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIH) ).
thf(26,axiom,
! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( ( iLess0 @ W0 @ W1 )
=> $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIHOrd) ).
thf(27,axiom,
! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( ( ( szszuzczcdt0 @ W0 )
= ( szszuzczcdt0 @ W1 ) )
=> ( W0 = W1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSuccEqu) ).
thf(28,axiom,
! [W0: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( W0 != sz00 ) )
=> ? [W1: $i] :
( ( aNaturalNumber0 @ W1 )
& ( W0
= ( szszuzczcdt0 @ W1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNatExtr) ).
thf(29,axiom,
! [W0: $i] :
( ( aNaturalNumber0 @ W0 )
=> ( ( aNaturalNumber0 @ ( szszuzczcdt0 @ W0 ) )
& ( ( szszuzczcdt0 @ W0 )
!= sz00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSuccNat) ).
thf(30,axiom,
aNaturalNumber0 @ sz00,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroNat) ).
thf(31,axiom,
! [W0: $i] :
( ( aNaturalNumber0 @ W0 )
=> $true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNatSort) ).
thf(32,axiom,
( ( ( aDimensionOf0 @ xs )
= ( aDimensionOf0 @ xt ) )
& ( ( aDimensionOf0 @ xt )
!= sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1329_01) ).
thf(33,axiom,
( ( aVector0 @ xs )
& ( aVector0 @ xt ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1329) ).
thf(34,conjecture,
( ( ( aVector0 @ ( sziznziztdt0 @ xs ) )
& ( ( szszuzczcdt0 @ ( aDimensionOf0 @ ( sziznziztdt0 @ xs ) ) )
= ( aDimensionOf0 @ xs ) )
& ! [W0: $i] :
( ( aNaturalNumber0 @ W0 )
=> ( ( sdtlbdtrb0 @ ( sziznziztdt0 @ xs ) @ W0 )
= ( sdtlbdtrb0 @ xs @ W0 ) ) ) )
=> ( ( ( aVector0 @ ( sziznziztdt0 @ xt ) )
& ( ( szszuzczcdt0 @ ( aDimensionOf0 @ ( sziznziztdt0 @ xt ) ) )
= ( aDimensionOf0 @ xt ) )
& ! [W0: $i] :
( ( aNaturalNumber0 @ W0 )
=> ( ( sdtlbdtrb0 @ ( sziznziztdt0 @ xt ) @ W0 )
= ( sdtlbdtrb0 @ xt @ W0 ) ) ) )
=> ( ( aDimensionOf0 @ ( sziznziztdt0 @ xs ) )
= ( aDimensionOf0 @ ( sziznziztdt0 @ xt ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
thf(35,negated_conjecture,
( ( ( ( aVector0 @ ( sziznziztdt0 @ xs ) )
& ( ( szszuzczcdt0 @ ( aDimensionOf0 @ ( sziznziztdt0 @ xs ) ) )
= ( aDimensionOf0 @ xs ) )
& ! [W0: $i] :
( ( aNaturalNumber0 @ W0 )
=> ( ( sdtlbdtrb0 @ ( sziznziztdt0 @ xs ) @ W0 )
= ( sdtlbdtrb0 @ xs @ W0 ) ) ) )
=> ( ( ( aVector0 @ ( sziznziztdt0 @ xt ) )
& ( ( szszuzczcdt0 @ ( aDimensionOf0 @ ( sziznziztdt0 @ xt ) ) )
= ( aDimensionOf0 @ xt ) )
& ! [W0: $i] :
( ( aNaturalNumber0 @ W0 )
=> ( ( sdtlbdtrb0 @ ( sziznziztdt0 @ xt ) @ W0 )
= ( sdtlbdtrb0 @ xt @ W0 ) ) ) )
=> ( ( aDimensionOf0 @ ( sziznziztdt0 @ xs ) )
= ( aDimensionOf0 @ ( sziznziztdt0 @ xt ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[34]) ).
thf(36,plain,
( ( ( ( aVector0 @ ( sziznziztdt0 @ xs ) )
& ( ( szszuzczcdt0 @ ( aDimensionOf0 @ ( sziznziztdt0 @ xs ) ) )
= ( aDimensionOf0 @ xs ) )
& ! [W0: $i] :
( ( aNaturalNumber0 @ W0 )
=> ( ( sdtlbdtrb0 @ ( sziznziztdt0 @ xs ) @ W0 )
= ( sdtlbdtrb0 @ xs @ W0 ) ) ) )
=> ( ( ( aVector0 @ ( sziznziztdt0 @ xt ) )
& ( ( szszuzczcdt0 @ ( aDimensionOf0 @ ( sziznziztdt0 @ xt ) ) )
= ( aDimensionOf0 @ xt ) )
& ! [W0: $i] :
( ( aNaturalNumber0 @ W0 )
=> ( ( sdtlbdtrb0 @ ( sziznziztdt0 @ xt ) @ W0 )
= ( sdtlbdtrb0 @ xt @ W0 ) ) ) )
=> ( ( aDimensionOf0 @ ( sziznziztdt0 @ xs ) )
= ( aDimensionOf0 @ ( sziznziztdt0 @ xt ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[35]) ).
thf(37,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aVector0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( aScalar0 @ ( sdtlbdtrb0 @ W0 @ W1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(38,plain,
( ( ! [W0: $i] :
( ( aVector0 @ W0 )
=> ( aNaturalNumber0 @ ( aDimensionOf0 @ W0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(39,plain,
( ( ! [W0: $i] :
( ( aVector0 @ W0 )
=> $true ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(40,plain,
( ( ! [W0: $i] :
( ( aNaturalNumber0 @ W0 )
=> ( iLess0 @ W0 @ ( szszuzczcdt0 @ W0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(41,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( ( iLess0 @ W0 @ W1 )
=> $true ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(42,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( ( ( szszuzczcdt0 @ W0 )
= ( szszuzczcdt0 @ W1 ) )
=> ( W0 = W1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(43,plain,
( ( ! [W0: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( W0 != sz00 ) )
=> ? [W1: $i] :
( ( aNaturalNumber0 @ W1 )
& ( W0
= ( szszuzczcdt0 @ W1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(44,plain,
( ( ! [W0: $i] :
( ( aNaturalNumber0 @ W0 )
=> ( ( aNaturalNumber0 @ ( szszuzczcdt0 @ W0 ) )
& ( ( szszuzczcdt0 @ W0 )
!= sz00 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(45,plain,
( ( aNaturalNumber0 @ sz00 )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(46,plain,
( ( ! [W0: $i] :
( ( aNaturalNumber0 @ W0 )
=> $true ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(47,plain,
( ( ( ( aDimensionOf0 @ xs )
= ( aDimensionOf0 @ xt ) )
& ( ( aDimensionOf0 @ xt )
!= sz00 ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(48,plain,
( ( ( aVector0 @ xs )
& ( aVector0 @ xt ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(49,plain,
( ( aVector0 @ ( sziznziztdt0 @ xs ) )
= $true ),
inference(standard_cnf,[status(thm)],[36]) ).
thf(50,plain,
( ( ( szszuzczcdt0 @ ( aDimensionOf0 @ ( sziznziztdt0 @ xs ) ) )
= ( aDimensionOf0 @ xs ) )
= $true ),
inference(standard_cnf,[status(thm)],[36]) ).
thf(51,plain,
( ( ! [W0: $i] :
( ( aNaturalNumber0 @ W0 )
=> ( ( sdtlbdtrb0 @ ( sziznziztdt0 @ xs ) @ W0 )
= ( sdtlbdtrb0 @ xs @ W0 ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[36]) ).
thf(52,plain,
( ( aVector0 @ ( sziznziztdt0 @ xt ) )
= $true ),
inference(standard_cnf,[status(thm)],[36]) ).
thf(53,plain,
( ( ( szszuzczcdt0 @ ( aDimensionOf0 @ ( sziznziztdt0 @ xt ) ) )
= ( aDimensionOf0 @ xt ) )
= $true ),
inference(standard_cnf,[status(thm)],[36]) ).
thf(54,plain,
( ( ! [W0: $i] :
( ( aNaturalNumber0 @ W0 )
=> ( ( sdtlbdtrb0 @ ( sziznziztdt0 @ xt ) @ W0 )
= ( sdtlbdtrb0 @ xt @ W0 ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[36]) ).
thf(55,plain,
( ( ( aDimensionOf0 @ ( sziznziztdt0 @ xs ) )
= ( aDimensionOf0 @ ( sziznziztdt0 @ xt ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[36]) ).
thf(56,plain,
( ( ( aDimensionOf0 @ ( sziznziztdt0 @ xs ) )
!= ( aDimensionOf0 @ ( sziznziztdt0 @ xt ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[55]) ).
thf(57,plain,
( ( ( aVector0 @ xs )
& ( aVector0 @ xt ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(58,plain,
( ( ( ( aDimensionOf0 @ xs )
= ( aDimensionOf0 @ xt ) )
& ( ( aDimensionOf0 @ xt )
!= sz00 ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(59,plain,
( ( ! [W0: $i] :
( ( aNaturalNumber0 @ W0 )
=> $true ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(60,plain,
( ( aNaturalNumber0 @ sz00 )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(61,plain,
( ( ! [W0: $i] :
( ( aNaturalNumber0 @ W0 )
=> ( ( aNaturalNumber0 @ ( szszuzczcdt0 @ W0 ) )
& ( ( szszuzczcdt0 @ W0 )
!= sz00 ) ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(62,plain,
( ( ! [W0: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( W0 != sz00 ) )
=> ? [W1: $i] :
( ( aNaturalNumber0 @ W1 )
& ( W0
= ( szszuzczcdt0 @ W1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(63,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( ( ( szszuzczcdt0 @ W0 )
= ( szszuzczcdt0 @ W1 ) )
=> ( W0 = W1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(64,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( ( iLess0 @ W0 @ W1 )
=> $true ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(65,plain,
( ( ! [W0: $i] :
( ( aNaturalNumber0 @ W0 )
=> ( iLess0 @ W0 @ ( szszuzczcdt0 @ W0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(66,plain,
( ( ! [W0: $i] :
( ( aVector0 @ W0 )
=> $true ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(67,plain,
( ( ! [W0: $i] :
( ( aVector0 @ W0 )
=> ( aNaturalNumber0 @ ( aDimensionOf0 @ W0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(68,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aVector0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( aScalar0 @ ( sdtlbdtrb0 @ W0 @ W1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(69,plain,
( ( ! [W0: $i] :
( ( aNaturalNumber0 @ W0 )
=> ( ( sdtlbdtrb0 @ ( sziznziztdt0 @ xt ) @ W0 )
= ( sdtlbdtrb0 @ xt @ W0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(70,plain,
( ( ( szszuzczcdt0 @ ( aDimensionOf0 @ ( sziznziztdt0 @ xt ) ) )
= ( aDimensionOf0 @ xt ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(71,plain,
( ( aVector0 @ ( sziznziztdt0 @ xt ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(72,plain,
( ( ! [W0: $i] :
( ( aNaturalNumber0 @ W0 )
=> ( ( sdtlbdtrb0 @ ( sziznziztdt0 @ xs ) @ W0 )
= ( sdtlbdtrb0 @ xs @ W0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(73,plain,
( ( ( szszuzczcdt0 @ ( aDimensionOf0 @ ( sziznziztdt0 @ xs ) ) )
= ( aDimensionOf0 @ xs ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(74,plain,
( ( aVector0 @ ( sziznziztdt0 @ xs ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(75,plain,
( ( ( aDimensionOf0 @ ( sziznziztdt0 @ xs ) )
!= ( aDimensionOf0 @ ( sziznziztdt0 @ xt ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(76,plain,
( ( ! [SX0: $i] :
( ~ ( aVector0 @ SX0 )
| $true ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(77,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( aNaturalNumber0 @ SX1 ) )
| ~ ( iLess0 @ SX0 @ SX1 )
| $true ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(78,plain,
( ( ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( ( sdtlbdtrb0 @ ( sziznziztdt0 @ xs ) @ SX0 )
= ( sdtlbdtrb0 @ xs @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(79,plain,
( ( ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( iLess0 @ SX0 @ ( szszuzczcdt0 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(80,plain,
( ( ~ ( ( ( aDimensionOf0 @ xs )
!= ( aDimensionOf0 @ xt ) )
| ~ ( ( ( aDimensionOf0 @ xt )
!= sz00 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(81,plain,
( ( ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( ~ ( aNaturalNumber0 @ ( szszuzczcdt0 @ SX0 ) )
| ~ ( ( ( szszuzczcdt0 @ SX0 )
!= sz00 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(82,plain,
( ( ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| $true ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(83,plain,
( ( ! [SX0: $i] :
( ~ ( aVector0 @ SX0 )
| ( aNaturalNumber0 @ ( aDimensionOf0 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(84,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( aNaturalNumber0 @ SX1 ) )
| ( ( szszuzczcdt0 @ SX0 )
!= ( szszuzczcdt0 @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(85,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( aVector0 @ SX0 )
| ~ ( aNaturalNumber0 @ SX1 ) )
| ( aScalar0 @ ( sdtlbdtrb0 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(86,plain,
( ( ~ ( ~ ( aVector0 @ xs )
| ~ ( aVector0 @ xt ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(87,plain,
( ( ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( ( sdtlbdtrb0 @ ( sziznziztdt0 @ xt ) @ SX0 )
= ( sdtlbdtrb0 @ xt @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(88,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( ( SX0 != sz00 ) ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( aNaturalNumber0 @ SX1 )
| ( SX0
!= ( szszuzczcdt0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(89,plain,
( ( ( aDimensionOf0 @ ( sziznziztdt0 @ xs ) )
= ( aDimensionOf0 @ ( sziznziztdt0 @ xt ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(90,plain,
! [SV1: $i] :
( ( ~ ( aVector0 @ SV1 )
| $true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(91,plain,
! [SV2: $i] :
( ( ! [SY15: $i] :
( ~ ~ ( ~ ( aNaturalNumber0 @ SV2 )
| ~ ( aNaturalNumber0 @ SY15 ) )
| ~ ( iLess0 @ SV2 @ SY15 )
| $true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(92,plain,
! [SV3: $i] :
( ( ~ ( aNaturalNumber0 @ SV3 )
| ( ( sdtlbdtrb0 @ ( sziznziztdt0 @ xs ) @ SV3 )
= ( sdtlbdtrb0 @ xs @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(93,plain,
! [SV4: $i] :
( ( ~ ( aNaturalNumber0 @ SV4 )
| ( iLess0 @ SV4 @ ( szszuzczcdt0 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(94,plain,
( ( ( ( aDimensionOf0 @ xs )
!= ( aDimensionOf0 @ xt ) )
| ~ ( ( ( aDimensionOf0 @ xt )
!= sz00 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(95,plain,
! [SV5: $i] :
( ( ~ ( aNaturalNumber0 @ SV5 )
| ~ ( ~ ( aNaturalNumber0 @ ( szszuzczcdt0 @ SV5 ) )
| ~ ( ( ( szszuzczcdt0 @ SV5 )
!= sz00 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(96,plain,
! [SV6: $i] :
( ( ~ ( aNaturalNumber0 @ SV6 )
| $true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(97,plain,
! [SV7: $i] :
( ( ~ ( aVector0 @ SV7 )
| ( aNaturalNumber0 @ ( aDimensionOf0 @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(98,plain,
! [SV8: $i] :
( ( ! [SY16: $i] :
( ~ ~ ( ~ ( aNaturalNumber0 @ SV8 )
| ~ ( aNaturalNumber0 @ SY16 ) )
| ( ( szszuzczcdt0 @ SV8 )
!= ( szszuzczcdt0 @ SY16 ) )
| ( SV8 = SY16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(99,plain,
! [SV9: $i] :
( ( ! [SY17: $i] :
( ~ ~ ( ~ ( aVector0 @ SV9 )
| ~ ( aNaturalNumber0 @ SY17 ) )
| ( aScalar0 @ ( sdtlbdtrb0 @ SV9 @ SY17 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(100,plain,
( ( ~ ( aVector0 @ xs )
| ~ ( aVector0 @ xt ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(101,plain,
! [SV10: $i] :
( ( ~ ( aNaturalNumber0 @ SV10 )
| ( ( sdtlbdtrb0 @ ( sziznziztdt0 @ xt ) @ SV10 )
= ( sdtlbdtrb0 @ xt @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(102,plain,
! [SV11: $i] :
( ( ~ ~ ( ~ ( aNaturalNumber0 @ SV11 )
| ~ ( ( SV11 != sz00 ) ) )
| ~ ! [SY18: $i] :
~ ~ ( ~ ( aNaturalNumber0 @ SY18 )
| ( SV11
!= ( szszuzczcdt0 @ SY18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(103,plain,
! [SV1: $i] :
( ( ( ~ ( aVector0 @ SV1 ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[90]) ).
thf(104,plain,
! [SV12: $i,SV2: $i] :
( ( ~ ~ ( ~ ( aNaturalNumber0 @ SV2 )
| ~ ( aNaturalNumber0 @ SV12 ) )
| ~ ( iLess0 @ SV2 @ SV12 )
| $true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(105,plain,
! [SV3: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV3 ) )
= $true )
| ( ( ( sdtlbdtrb0 @ ( sziznziztdt0 @ xs ) @ SV3 )
= ( sdtlbdtrb0 @ xs @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[92]) ).
thf(106,plain,
! [SV4: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV4 ) )
= $true )
| ( ( iLess0 @ SV4 @ ( szszuzczcdt0 @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[93]) ).
thf(107,plain,
( ( ( aDimensionOf0 @ xs )
!= ( aDimensionOf0 @ xt ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[94]) ).
thf(108,plain,
( ( ~ ( ( ( aDimensionOf0 @ xt )
!= sz00 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[94]) ).
thf(109,plain,
! [SV5: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV5 ) )
= $true )
| ( ( ~ ( ~ ( aNaturalNumber0 @ ( szszuzczcdt0 @ SV5 ) )
| ~ ( ( ( szszuzczcdt0 @ SV5 )
!= sz00 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[95]) ).
thf(110,plain,
! [SV6: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV6 ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[96]) ).
thf(111,plain,
! [SV7: $i] :
( ( ( ~ ( aVector0 @ SV7 ) )
= $true )
| ( ( aNaturalNumber0 @ ( aDimensionOf0 @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[97]) ).
thf(112,plain,
! [SV13: $i,SV8: $i] :
( ( ~ ~ ( ~ ( aNaturalNumber0 @ SV8 )
| ~ ( aNaturalNumber0 @ SV13 ) )
| ( ( szszuzczcdt0 @ SV8 )
!= ( szszuzczcdt0 @ SV13 ) )
| ( SV8 = SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(113,plain,
! [SV14: $i,SV9: $i] :
( ( ~ ~ ( ~ ( aVector0 @ SV9 )
| ~ ( aNaturalNumber0 @ SV14 ) )
| ( aScalar0 @ ( sdtlbdtrb0 @ SV9 @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(114,plain,
( ( ~ ( aVector0 @ xs ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[100]) ).
thf(115,plain,
( ( ~ ( aVector0 @ xt ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[100]) ).
thf(116,plain,
! [SV10: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV10 ) )
= $true )
| ( ( ( sdtlbdtrb0 @ ( sziznziztdt0 @ xt ) @ SV10 )
= ( sdtlbdtrb0 @ xt @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[101]) ).
thf(117,plain,
! [SV11: $i] :
( ( ( ~ ~ ( ~ ( aNaturalNumber0 @ SV11 )
| ~ ( ( SV11 != sz00 ) ) ) )
= $true )
| ( ( ~ ! [SY18: $i] :
~ ~ ( ~ ( aNaturalNumber0 @ SY18 )
| ( SV11
!= ( szszuzczcdt0 @ SY18 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[102]) ).
thf(118,plain,
! [SV1: $i] :
( ( ( aVector0 @ SV1 )
= $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(119,plain,
! [SV12: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ( aNaturalNumber0 @ SV2 )
| ~ ( aNaturalNumber0 @ SV12 ) ) )
= $true )
| ( ( ~ ( iLess0 @ SV2 @ SV12 )
| $true )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[104]) ).
thf(120,plain,
! [SV3: $i] :
( ( ( aNaturalNumber0 @ SV3 )
= $false )
| ( ( ( sdtlbdtrb0 @ ( sziznziztdt0 @ xs ) @ SV3 )
= ( sdtlbdtrb0 @ xs @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(121,plain,
! [SV4: $i] :
( ( ( aNaturalNumber0 @ SV4 )
= $false )
| ( ( iLess0 @ SV4 @ ( szszuzczcdt0 @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(122,plain,
( ( ( aDimensionOf0 @ xs )
= ( aDimensionOf0 @ xt ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[107]) ).
thf(123,plain,
( ( ( aDimensionOf0 @ xt )
!= sz00 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[108]) ).
thf(124,plain,
! [SV5: $i] :
( ( ( aNaturalNumber0 @ SV5 )
= $false )
| ( ( ~ ( ~ ( aNaturalNumber0 @ ( szszuzczcdt0 @ SV5 ) )
| ~ ( ( ( szszuzczcdt0 @ SV5 )
!= sz00 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(125,plain,
! [SV6: $i] :
( ( ( aNaturalNumber0 @ SV6 )
= $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(126,plain,
! [SV7: $i] :
( ( ( aVector0 @ SV7 )
= $false )
| ( ( aNaturalNumber0 @ ( aDimensionOf0 @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(127,plain,
! [SV13: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ( aNaturalNumber0 @ SV8 )
| ~ ( aNaturalNumber0 @ SV13 ) ) )
= $true )
| ( ( ( ( szszuzczcdt0 @ SV8 )
!= ( szszuzczcdt0 @ SV13 ) )
| ( SV8 = SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[112]) ).
thf(128,plain,
! [SV14: $i,SV9: $i] :
( ( ( ~ ~ ( ~ ( aVector0 @ SV9 )
| ~ ( aNaturalNumber0 @ SV14 ) ) )
= $true )
| ( ( aScalar0 @ ( sdtlbdtrb0 @ SV9 @ SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[113]) ).
thf(129,plain,
( ( aVector0 @ xs )
= $true ),
inference(extcnf_not_neg,[status(thm)],[114]) ).
thf(130,plain,
( ( aVector0 @ xt )
= $true ),
inference(extcnf_not_neg,[status(thm)],[115]) ).
thf(131,plain,
! [SV10: $i] :
( ( ( aNaturalNumber0 @ SV10 )
= $false )
| ( ( ( sdtlbdtrb0 @ ( sziznziztdt0 @ xt ) @ SV10 )
= ( sdtlbdtrb0 @ xt @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(132,plain,
! [SV11: $i] :
( ( ( ~ ( ~ ( aNaturalNumber0 @ SV11 )
| ~ ( ( SV11 != sz00 ) ) ) )
= $false )
| ( ( ~ ! [SY18: $i] :
~ ~ ( ~ ( aNaturalNumber0 @ SY18 )
| ( SV11
!= ( szszuzczcdt0 @ SY18 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(133,plain,
! [SV12: $i,SV2: $i] :
( ( ( ~ ( ~ ( aNaturalNumber0 @ SV2 )
| ~ ( aNaturalNumber0 @ SV12 ) ) )
= $false )
| ( ( ~ ( iLess0 @ SV2 @ SV12 )
| $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(134,plain,
( ( ( aDimensionOf0 @ xt )
= sz00 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(135,plain,
! [SV5: $i] :
( ( ( ~ ( aNaturalNumber0 @ ( szszuzczcdt0 @ SV5 ) )
| ~ ( ( ( szszuzczcdt0 @ SV5 )
!= sz00 ) ) )
= $false )
| ( ( aNaturalNumber0 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(136,plain,
! [SV13: $i,SV8: $i] :
( ( ( ~ ( ~ ( aNaturalNumber0 @ SV8 )
| ~ ( aNaturalNumber0 @ SV13 ) ) )
= $false )
| ( ( ( ( szszuzczcdt0 @ SV8 )
!= ( szszuzczcdt0 @ SV13 ) )
| ( SV8 = SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[127]) ).
thf(137,plain,
! [SV14: $i,SV9: $i] :
( ( ( ~ ( ~ ( aVector0 @ SV9 )
| ~ ( aNaturalNumber0 @ SV14 ) ) )
= $false )
| ( ( aScalar0 @ ( sdtlbdtrb0 @ SV9 @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(138,plain,
! [SV11: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV11 )
| ~ ( ( SV11 != sz00 ) ) )
= $true )
| ( ( ~ ! [SY18: $i] :
~ ~ ( ~ ( aNaturalNumber0 @ SY18 )
| ( SV11
!= ( szszuzczcdt0 @ SY18 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[132]) ).
thf(139,plain,
! [SV12: $i,SV2: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV2 )
| ~ ( aNaturalNumber0 @ SV12 ) )
= $true )
| ( ( ~ ( iLess0 @ SV2 @ SV12 )
| $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[133]) ).
thf(140,plain,
! [SV5: $i] :
( ( ( ~ ( aNaturalNumber0 @ ( szszuzczcdt0 @ SV5 ) ) )
= $false )
| ( ( aNaturalNumber0 @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[135]) ).
thf(141,plain,
! [SV5: $i] :
( ( ( ~ ( ( ( szszuzczcdt0 @ SV5 )
!= sz00 ) ) )
= $false )
| ( ( aNaturalNumber0 @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[135]) ).
thf(142,plain,
! [SV13: $i,SV8: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV8 )
| ~ ( aNaturalNumber0 @ SV13 ) )
= $true )
| ( ( ( ( szszuzczcdt0 @ SV8 )
!= ( szszuzczcdt0 @ SV13 ) )
| ( SV8 = SV13 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[136]) ).
thf(143,plain,
! [SV14: $i,SV9: $i] :
( ( ( ~ ( aVector0 @ SV9 )
| ~ ( aNaturalNumber0 @ SV14 ) )
= $true )
| ( ( aScalar0 @ ( sdtlbdtrb0 @ SV9 @ SV14 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[137]) ).
thf(144,plain,
! [SV11: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV11 ) )
= $true )
| ( ( ~ ( ( SV11 != sz00 ) ) )
= $true )
| ( ( ~ ! [SY18: $i] :
~ ~ ( ~ ( aNaturalNumber0 @ SY18 )
| ( SV11
!= ( szszuzczcdt0 @ SY18 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[138]) ).
thf(145,plain,
! [SV12: $i,SV2: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV2 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV12 ) )
= $true )
| ( ( ~ ( iLess0 @ SV2 @ SV12 )
| $true )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[139]) ).
thf(146,plain,
! [SV5: $i] :
( ( ( aNaturalNumber0 @ ( szszuzczcdt0 @ SV5 ) )
= $true )
| ( ( aNaturalNumber0 @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[140]) ).
thf(147,plain,
! [SV5: $i] :
( ( ( ( szszuzczcdt0 @ SV5 )
!= sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[141]) ).
thf(148,plain,
! [SV13: $i,SV8: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV8 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV13 ) )
= $true )
| ( ( ( ( szszuzczcdt0 @ SV8 )
!= ( szszuzczcdt0 @ SV13 ) )
| ( SV8 = SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[142]) ).
thf(149,plain,
! [SV14: $i,SV9: $i] :
( ( ( ~ ( aVector0 @ SV9 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV14 ) )
= $true )
| ( ( aScalar0 @ ( sdtlbdtrb0 @ SV9 @ SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[143]) ).
thf(150,plain,
! [SV11: $i] :
( ( ( aNaturalNumber0 @ SV11 )
= $false )
| ( ( ~ ( ( SV11 != sz00 ) ) )
= $true )
| ( ( ~ ! [SY18: $i] :
~ ~ ( ~ ( aNaturalNumber0 @ SY18 )
| ( SV11
!= ( szszuzczcdt0 @ SY18 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(151,plain,
! [SV12: $i,SV2: $i] :
( ( ( aNaturalNumber0 @ SV2 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV12 ) )
= $true )
| ( ( ~ ( iLess0 @ SV2 @ SV12 )
| $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[145]) ).
thf(152,plain,
! [SV5: $i] :
( ( ( ( szszuzczcdt0 @ SV5 )
= sz00 )
= $false )
| ( ( aNaturalNumber0 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(153,plain,
! [SV13: $i,SV8: $i] :
( ( ( aNaturalNumber0 @ SV8 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV13 ) )
= $true )
| ( ( ( ( szszuzczcdt0 @ SV8 )
!= ( szszuzczcdt0 @ SV13 ) )
| ( SV8 = SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(154,plain,
! [SV14: $i,SV9: $i] :
( ( ( aVector0 @ SV9 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV14 ) )
= $true )
| ( ( aScalar0 @ ( sdtlbdtrb0 @ SV9 @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(155,plain,
! [SV11: $i] :
( ( ( SV11 != sz00 )
= $false )
| ( ( aNaturalNumber0 @ SV11 )
= $false )
| ( ( ~ ! [SY18: $i] :
~ ~ ( ~ ( aNaturalNumber0 @ SY18 )
| ( SV11
!= ( szszuzczcdt0 @ SY18 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[150]) ).
thf(156,plain,
! [SV2: $i,SV12: $i] :
( ( ( aNaturalNumber0 @ SV12 )
= $false )
| ( ( aNaturalNumber0 @ SV2 )
= $false )
| ( ( ~ ( iLess0 @ SV2 @ SV12 )
| $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(157,plain,
! [SV8: $i,SV13: $i] :
( ( ( aNaturalNumber0 @ SV13 )
= $false )
| ( ( aNaturalNumber0 @ SV8 )
= $false )
| ( ( ( ( szszuzczcdt0 @ SV8 )
!= ( szszuzczcdt0 @ SV13 ) )
| ( SV8 = SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(158,plain,
! [SV9: $i,SV14: $i] :
( ( ( aNaturalNumber0 @ SV14 )
= $false )
| ( ( aVector0 @ SV9 )
= $false )
| ( ( aScalar0 @ ( sdtlbdtrb0 @ SV9 @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[154]) ).
thf(159,plain,
! [SV11: $i] :
( ( ( SV11 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV11 )
= $false )
| ( ( ~ ! [SY18: $i] :
~ ~ ( ~ ( aNaturalNumber0 @ SY18 )
| ( SV11
!= ( szszuzczcdt0 @ SY18 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[155]) ).
thf(160,plain,
! [SV12: $i,SV2: $i] :
( ( ( ~ ( iLess0 @ SV2 @ SV12 ) )
= $true )
| ( $true = $true )
| ( ( aNaturalNumber0 @ SV2 )
= $false )
| ( ( aNaturalNumber0 @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[156]) ).
thf(161,plain,
! [SV13: $i,SV8: $i] :
( ( ( ( szszuzczcdt0 @ SV8 )
!= ( szszuzczcdt0 @ SV13 ) )
= $true )
| ( ( SV8 = SV13 )
= $true )
| ( ( aNaturalNumber0 @ SV8 )
= $false )
| ( ( aNaturalNumber0 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[157]) ).
thf(162,plain,
! [SV11: $i] :
( ( ( ! [SY18: $i] :
~ ~ ( ~ ( aNaturalNumber0 @ SY18 )
| ( SV11
!= ( szszuzczcdt0 @ SY18 ) ) ) )
= $false )
| ( ( aNaturalNumber0 @ SV11 )
= $false )
| ( ( SV11 = sz00 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(163,plain,
! [SV12: $i,SV2: $i] :
( ( ( iLess0 @ SV2 @ SV12 )
= $false )
| ( $true = $true )
| ( ( aNaturalNumber0 @ SV2 )
= $false )
| ( ( aNaturalNumber0 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(164,plain,
! [SV13: $i,SV8: $i] :
( ( ( ( szszuzczcdt0 @ SV8 )
= ( szszuzczcdt0 @ SV13 ) )
= $false )
| ( ( SV8 = SV13 )
= $true )
| ( ( aNaturalNumber0 @ SV8 )
= $false )
| ( ( aNaturalNumber0 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[161]) ).
thf(165,plain,
! [SV11: $i] :
( ( ( ~ ~ ( ~ ( aNaturalNumber0 @ ( sK1_SY18 @ SV11 ) )
| ( SV11
!= ( szszuzczcdt0 @ ( sK1_SY18 @ SV11 ) ) ) ) )
= $false )
| ( ( aNaturalNumber0 @ SV11 )
= $false )
| ( ( SV11 = sz00 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[162]) ).
thf(166,plain,
! [SV11: $i] :
( ( ( ~ ( ~ ( aNaturalNumber0 @ ( sK1_SY18 @ SV11 ) )
| ( SV11
!= ( szszuzczcdt0 @ ( sK1_SY18 @ SV11 ) ) ) ) )
= $true )
| ( ( aNaturalNumber0 @ SV11 )
= $false )
| ( ( SV11 = sz00 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[165]) ).
thf(167,plain,
! [SV11: $i] :
( ( ( ~ ( aNaturalNumber0 @ ( sK1_SY18 @ SV11 ) )
| ( SV11
!= ( szszuzczcdt0 @ ( sK1_SY18 @ SV11 ) ) ) )
= $false )
| ( ( aNaturalNumber0 @ SV11 )
= $false )
| ( ( SV11 = sz00 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(168,plain,
! [SV11: $i] :
( ( ( ~ ( aNaturalNumber0 @ ( sK1_SY18 @ SV11 ) ) )
= $false )
| ( ( aNaturalNumber0 @ SV11 )
= $false )
| ( ( SV11 = sz00 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[167]) ).
thf(169,plain,
! [SV11: $i] :
( ( ( SV11
!= ( szszuzczcdt0 @ ( sK1_SY18 @ SV11 ) ) )
= $false )
| ( ( aNaturalNumber0 @ SV11 )
= $false )
| ( ( SV11 = sz00 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[167]) ).
thf(170,plain,
! [SV11: $i] :
( ( ( aNaturalNumber0 @ ( sK1_SY18 @ SV11 ) )
= $true )
| ( ( aNaturalNumber0 @ SV11 )
= $false )
| ( ( SV11 = sz00 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[168]) ).
thf(171,plain,
! [SV11: $i] :
( ( ( SV11
= ( szszuzczcdt0 @ ( sK1_SY18 @ SV11 ) ) )
= $true )
| ( ( aNaturalNumber0 @ SV11 )
= $false )
| ( ( SV11 = sz00 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[169]) ).
thf(172,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[60,171,170,164,163,158,152,146,134,131,130,129,126,125,122,121,120,118,89,74,73,71,70]) ).
thf(173,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[172]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG047+2 : TPTP v9.3.1. Released v4.0.0.
% 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
% 0.08/0.19 % Computer : n001.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Oct 6 14:17:39 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.42/0.36
% 0.42/0.36 No.of.Axioms: 12
% 0.42/0.36
% 0.42/0.36 Length.of.Defs: 0
% 0.42/0.36
% 0.42/0.36 Contains.Choice.Funs: false
% 0.42/0.36 ...
% 0.42/0.36
% 0.42/0.36 ********************************
% 0.42/0.36 * All subproblems solved! *
% 0.42/0.36 ********************************
% 0.42/0.36 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:18,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:172,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.42/0.36
% 0.42/0.36 %**** Beginning of derivation protocol ****
% 0.42/0.36 % SZS output start CNFRefutation
% See solution above
% 0.42/0.36
% 0.42/0.36 %**** End of derivation protocol ****
% 0.42/0.36 %**** no. of clauses in derivation: 152 ****
% 0.42/0.36 %**** clause counter: 172 ****
% 0.42/0.36
% 0.42/0.36 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:18,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:172,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------