%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : RNG050+1 : 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 : n006.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 0.09s 0.26s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 10
% Syntax : Number of formulae : 117 ( 50 unt; 0 typ; 0 def)
% Number of atoms : 968 ( 327 equ; 0 cnn)
% Maximal formula atoms : 6 ( 8 avg)
% Number of connectives : 1386 ( 349 ~; 294 |; 27 &; 678 @)
% ( 0 <=>; 38 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 5 con; 0-2 aty)
% Number of variables : 202 ( 0 ^; 202 !; 0 ?; 202 :)
% 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_sdtasasdt0,type,
sdtasasdt0: $i > $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(2,axiom,
! [W0: $i,W1: $i] :
( ( ( aVector0 @ W0 )
& ( aVector0 @ W1 ) )
=> ( ( ( ( aDimensionOf0 @ W0 )
= ( aDimensionOf0 @ W1 ) )
& ( ( aDimensionOf0 @ W1 )
= sz00 ) )
=> ( ( sdtasasdt0 @ W0 @ W1 )
= sz0z00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSPZ) ).
thf(11,axiom,
! [W0: $i,W1: $i] :
( ( ( aScalar0 @ W0 )
& ( aScalar0 @ W1 ) )
=> ( ( sdtlseqdt0 @ W0 @ W1 )
| ( sdtlseqdt0 @ W1 @ W0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETot) ).
thf(14,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( ( aScalar0 @ W0 )
& ( aScalar0 @ W1 )
& ( aScalar0 @ W2 ) )
=> ( ( ( sdtlseqdt0 @ W0 @ W1 )
& ( sdtlseqdt0 @ W1 @ W2 ) )
=> ( sdtlseqdt0 @ W0 @ W2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETrn) ).
thf(15,axiom,
! [W0: $i,W1: $i] :
( ( ( aScalar0 @ W0 )
& ( aScalar0 @ W1 ) )
=> ( ( ( sdtlseqdt0 @ W0 @ W1 )
& ( sdtlseqdt0 @ W1 @ W0 ) )
=> ( W0 = W1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLEASm) ).
thf(16,axiom,
! [W0: $i] :
( ( aScalar0 @ W0 )
=> ( sdtlseqdt0 @ W0 @ W0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLERef) ).
thf(17,axiom,
! [W0: $i,W1: $i] :
( ( ( aScalar0 @ W0 )
& ( aScalar0 @ W1 ) )
=> ( ( sdtlseqdt0 @ W0 @ W1 )
=> $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLess) ).
thf(27,axiom,
aScalar0 @ sz0z00,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSZeroSc) ).
thf(34,axiom,
aNaturalNumber0 @ sz00,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroNat) ).
thf(37,axiom,
aVector0 @ xs,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1542) ).
thf(38,conjecture,
( ( ( ( aDimensionOf0 @ xs )
!= sz00 )
=> ( sdtlseqdt0 @ sz0z00 @ ( sdtasasdt0 @ xs @ xs ) ) )
=> ( sdtlseqdt0 @ sz0z00 @ ( sdtasasdt0 @ xs @ xs ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
thf(39,negated_conjecture,
( ( ( ( ( aDimensionOf0 @ xs )
!= sz00 )
=> ( sdtlseqdt0 @ sz0z00 @ ( sdtasasdt0 @ xs @ xs ) ) )
=> ( sdtlseqdt0 @ sz0z00 @ ( sdtasasdt0 @ xs @ xs ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[38]) ).
thf(40,plain,
( ( ( ( ( aDimensionOf0 @ xs )
!= sz00 )
=> ( sdtlseqdt0 @ sz0z00 @ ( sdtasasdt0 @ xs @ xs ) ) )
=> ( sdtlseqdt0 @ sz0z00 @ ( sdtasasdt0 @ xs @ xs ) ) )
= $false ),
inference(unfold_def,[status(thm)],[39]) ).
thf(41,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aVector0 @ W0 )
& ( aVector0 @ W1 ) )
=> ( ( ( ( aDimensionOf0 @ W0 )
= ( aDimensionOf0 @ W1 ) )
& ( ( aDimensionOf0 @ W1 )
= sz00 ) )
=> ( ( sdtasasdt0 @ W0 @ W1 )
= sz0z00 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(42,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aScalar0 @ W0 )
& ( aScalar0 @ W1 ) )
=> ( ( sdtlseqdt0 @ W0 @ W1 )
| ( sdtlseqdt0 @ W1 @ W0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(43,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ( ( aScalar0 @ W0 )
& ( aScalar0 @ W1 )
& ( aScalar0 @ W2 ) )
=> ( ( ( sdtlseqdt0 @ W0 @ W1 )
& ( sdtlseqdt0 @ W1 @ W2 ) )
=> ( sdtlseqdt0 @ W0 @ W2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(44,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aScalar0 @ W0 )
& ( aScalar0 @ W1 ) )
=> ( ( ( sdtlseqdt0 @ W0 @ W1 )
& ( sdtlseqdt0 @ W1 @ W0 ) )
=> ( W0 = W1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(45,plain,
( ( ! [W0: $i] :
( ( aScalar0 @ W0 )
=> ( sdtlseqdt0 @ W0 @ W0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(46,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aScalar0 @ W0 )
& ( aScalar0 @ W1 ) )
=> ( ( sdtlseqdt0 @ W0 @ W1 )
=> $true ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(47,plain,
( ( aScalar0 @ sz0z00 )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(48,plain,
( ( aNaturalNumber0 @ sz00 )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(49,plain,
( ( aVector0 @ xs )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(50,plain,
( ( ( ( aDimensionOf0 @ xs )
!= sz00 )
=> ( sdtlseqdt0 @ sz0z00 @ ( sdtasasdt0 @ xs @ xs ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[40]) ).
thf(51,plain,
( ( sdtlseqdt0 @ sz0z00 @ ( sdtasasdt0 @ xs @ xs ) )
= $false ),
inference(standard_cnf,[status(thm)],[40]) ).
thf(52,plain,
( ( ~ ( sdtlseqdt0 @ sz0z00 @ ( sdtasasdt0 @ xs @ xs ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[51]) ).
thf(53,plain,
( ( aVector0 @ xs )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(54,plain,
( ( aNaturalNumber0 @ sz00 )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(55,plain,
( ( aScalar0 @ sz0z00 )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(56,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aScalar0 @ W0 )
& ( aScalar0 @ W1 ) )
=> ( ( sdtlseqdt0 @ W0 @ W1 )
=> $true ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(57,plain,
( ( ! [W0: $i] :
( ( aScalar0 @ W0 )
=> ( sdtlseqdt0 @ W0 @ W0 ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(58,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aScalar0 @ W0 )
& ( aScalar0 @ W1 ) )
=> ( ( ( sdtlseqdt0 @ W0 @ W1 )
& ( sdtlseqdt0 @ W1 @ W0 ) )
=> ( W0 = W1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(59,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ( ( aScalar0 @ W0 )
& ( aScalar0 @ W1 )
& ( aScalar0 @ W2 ) )
=> ( ( ( sdtlseqdt0 @ W0 @ W1 )
& ( sdtlseqdt0 @ W1 @ W2 ) )
=> ( sdtlseqdt0 @ W0 @ W2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(60,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aScalar0 @ W0 )
& ( aScalar0 @ W1 ) )
=> ( ( sdtlseqdt0 @ W0 @ W1 )
| ( sdtlseqdt0 @ W1 @ W0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(61,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aVector0 @ W0 )
& ( aVector0 @ W1 ) )
=> ( ( ( ( aDimensionOf0 @ W0 )
= ( aDimensionOf0 @ W1 ) )
& ( ( aDimensionOf0 @ W1 )
= sz00 ) )
=> ( ( sdtasasdt0 @ W0 @ W1 )
= sz0z00 ) ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(62,plain,
( ( ( ( aDimensionOf0 @ xs )
!= sz00 )
=> ( sdtlseqdt0 @ sz0z00 @ ( sdtasasdt0 @ xs @ xs ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(63,plain,
( ( ~ ( sdtlseqdt0 @ sz0z00 @ ( sdtasasdt0 @ xs @ xs ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(64,plain,
( ( ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( sdtlseqdt0 @ SX0 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(65,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( aScalar0 @ SX0 )
| ~ ( aScalar0 @ SX1 ) )
| ~ ~ ( ~ ( sdtlseqdt0 @ SX0 @ SX1 )
| ~ ( sdtlseqdt0 @ SX1 @ SX0 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(66,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( aVector0 @ SX0 )
| ~ ( aVector0 @ SX1 ) )
| ~ ~ ( ( ( aDimensionOf0 @ SX0 )
!= ( aDimensionOf0 @ SX1 ) )
| ( ( aDimensionOf0 @ SX1 )
!= sz00 ) )
| ( ( sdtasasdt0 @ SX0 @ SX1 )
= sz0z00 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(67,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( aScalar0 @ SX0 )
| ~ ( aScalar0 @ SX1 ) )
| ~ ( sdtlseqdt0 @ SX0 @ SX1 )
| $true ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(68,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ~ ( ~ ( aScalar0 @ SX0 )
| ~ ( aScalar0 @ SX1 ) )
| ~ ( aScalar0 @ SX2 ) )
| ~ ~ ( ~ ( sdtlseqdt0 @ SX0 @ SX1 )
| ~ ( sdtlseqdt0 @ SX1 @ SX2 ) )
| ( sdtlseqdt0 @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(69,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( aScalar0 @ SX0 )
| ~ ( aScalar0 @ SX1 ) )
| ( sdtlseqdt0 @ SX0 @ SX1 )
| ( sdtlseqdt0 @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(70,plain,
( ( ~ ( ( ( aDimensionOf0 @ xs )
!= sz00 ) )
| ( sdtlseqdt0 @ sz0z00 @ ( sdtasasdt0 @ xs @ xs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(71,plain,
( ( sdtlseqdt0 @ sz0z00 @ ( sdtasasdt0 @ xs @ xs ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(72,plain,
! [SV1: $i] :
( ( ~ ( aScalar0 @ SV1 )
| ( sdtlseqdt0 @ SV1 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(73,plain,
! [SV2: $i] :
( ( ! [SY12: $i] :
( ~ ~ ( ~ ( aScalar0 @ SV2 )
| ~ ( aScalar0 @ SY12 ) )
| ~ ~ ( ~ ( sdtlseqdt0 @ SV2 @ SY12 )
| ~ ( sdtlseqdt0 @ SY12 @ SV2 ) )
| ( SV2 = SY12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(74,plain,
! [SV3: $i] :
( ( ! [SY13: $i] :
( ~ ~ ( ~ ( aVector0 @ SV3 )
| ~ ( aVector0 @ SY13 ) )
| ~ ~ ( ( ( aDimensionOf0 @ SV3 )
!= ( aDimensionOf0 @ SY13 ) )
| ( ( aDimensionOf0 @ SY13 )
!= sz00 ) )
| ( ( sdtasasdt0 @ SV3 @ SY13 )
= sz0z00 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(75,plain,
! [SV4: $i] :
( ( ! [SY14: $i] :
( ~ ~ ( ~ ( aScalar0 @ SV4 )
| ~ ( aScalar0 @ SY14 ) )
| ~ ( sdtlseqdt0 @ SV4 @ SY14 )
| $true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(76,plain,
! [SV5: $i] :
( ( ! [SY15: $i,SY16: $i] :
( ~ ~ ( ~ ~ ( ~ ( aScalar0 @ SV5 )
| ~ ( aScalar0 @ SY15 ) )
| ~ ( aScalar0 @ SY16 ) )
| ~ ~ ( ~ ( sdtlseqdt0 @ SV5 @ SY15 )
| ~ ( sdtlseqdt0 @ SY15 @ SY16 ) )
| ( sdtlseqdt0 @ SV5 @ SY16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(77,plain,
! [SV6: $i] :
( ( ! [SY17: $i] :
( ~ ~ ( ~ ( aScalar0 @ SV6 )
| ~ ( aScalar0 @ SY17 ) )
| ( sdtlseqdt0 @ SV6 @ SY17 )
| ( sdtlseqdt0 @ SY17 @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(78,plain,
( ( ( ~ ( ( ( aDimensionOf0 @ xs )
!= sz00 ) ) )
= $true )
| ( ( sdtlseqdt0 @ sz0z00 @ ( sdtasasdt0 @ xs @ xs ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[70]) ).
thf(79,plain,
! [SV1: $i] :
( ( ( ~ ( aScalar0 @ SV1 ) )
= $true )
| ( ( sdtlseqdt0 @ SV1 @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[72]) ).
thf(80,plain,
! [SV7: $i,SV2: $i] :
( ( ~ ~ ( ~ ( aScalar0 @ SV2 )
| ~ ( aScalar0 @ SV7 ) )
| ~ ~ ( ~ ( sdtlseqdt0 @ SV2 @ SV7 )
| ~ ( sdtlseqdt0 @ SV7 @ SV2 ) )
| ( SV2 = SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(81,plain,
! [SV8: $i,SV3: $i] :
( ( ~ ~ ( ~ ( aVector0 @ SV3 )
| ~ ( aVector0 @ SV8 ) )
| ~ ~ ( ( ( aDimensionOf0 @ SV3 )
!= ( aDimensionOf0 @ SV8 ) )
| ( ( aDimensionOf0 @ SV8 )
!= sz00 ) )
| ( ( sdtasasdt0 @ SV3 @ SV8 )
= sz0z00 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(82,plain,
! [SV9: $i,SV4: $i] :
( ( ~ ~ ( ~ ( aScalar0 @ SV4 )
| ~ ( aScalar0 @ SV9 ) )
| ~ ( sdtlseqdt0 @ SV4 @ SV9 )
| $true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(83,plain,
! [SV10: $i,SV5: $i] :
( ( ! [SY18: $i] :
( ~ ~ ( ~ ~ ( ~ ( aScalar0 @ SV5 )
| ~ ( aScalar0 @ SV10 ) )
| ~ ( aScalar0 @ SY18 ) )
| ~ ~ ( ~ ( sdtlseqdt0 @ SV5 @ SV10 )
| ~ ( sdtlseqdt0 @ SV10 @ SY18 ) )
| ( sdtlseqdt0 @ SV5 @ SY18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(84,plain,
! [SV11: $i,SV6: $i] :
( ( ~ ~ ( ~ ( aScalar0 @ SV6 )
| ~ ( aScalar0 @ SV11 ) )
| ( sdtlseqdt0 @ SV6 @ SV11 )
| ( sdtlseqdt0 @ SV11 @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(85,plain,
( ( ( ( aDimensionOf0 @ xs )
!= sz00 )
= $false )
| ( ( sdtlseqdt0 @ sz0z00 @ ( sdtasasdt0 @ xs @ xs ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(86,plain,
! [SV1: $i] :
( ( ( aScalar0 @ SV1 )
= $false )
| ( ( sdtlseqdt0 @ SV1 @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(87,plain,
! [SV7: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ( aScalar0 @ SV2 )
| ~ ( aScalar0 @ SV7 ) ) )
= $true )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV2 @ SV7 )
| ~ ( sdtlseqdt0 @ SV7 @ SV2 ) )
| ( SV2 = SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[80]) ).
thf(88,plain,
! [SV8: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( aVector0 @ SV3 )
| ~ ( aVector0 @ SV8 ) ) )
= $true )
| ( ( ~ ~ ( ( ( aDimensionOf0 @ SV3 )
!= ( aDimensionOf0 @ SV8 ) )
| ( ( aDimensionOf0 @ SV8 )
!= sz00 ) )
| ( ( sdtasasdt0 @ SV3 @ SV8 )
= sz0z00 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[81]) ).
thf(89,plain,
! [SV9: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ( aScalar0 @ SV4 )
| ~ ( aScalar0 @ SV9 ) ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV4 @ SV9 )
| $true )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[82]) ).
thf(90,plain,
! [SV12: $i,SV10: $i,SV5: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( aScalar0 @ SV5 )
| ~ ( aScalar0 @ SV10 ) )
| ~ ( aScalar0 @ SV12 ) )
| ~ ~ ( ~ ( sdtlseqdt0 @ SV5 @ SV10 )
| ~ ( sdtlseqdt0 @ SV10 @ SV12 ) )
| ( sdtlseqdt0 @ SV5 @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(91,plain,
! [SV11: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ( aScalar0 @ SV6 )
| ~ ( aScalar0 @ SV11 ) ) )
= $true )
| ( ( ( sdtlseqdt0 @ SV6 @ SV11 )
| ( sdtlseqdt0 @ SV11 @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[84]) ).
thf(92,plain,
( ( ( ( aDimensionOf0 @ xs )
= sz00 )
= $true )
| ( ( sdtlseqdt0 @ sz0z00 @ ( sdtasasdt0 @ xs @ xs ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[85]) ).
thf(93,plain,
! [SV7: $i,SV2: $i] :
( ( ( ~ ( ~ ( aScalar0 @ SV2 )
| ~ ( aScalar0 @ SV7 ) ) )
= $false )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV2 @ SV7 )
| ~ ( sdtlseqdt0 @ SV7 @ SV2 ) )
| ( SV2 = SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[87]) ).
thf(94,plain,
! [SV8: $i,SV3: $i] :
( ( ( ~ ( ~ ( aVector0 @ SV3 )
| ~ ( aVector0 @ SV8 ) ) )
= $false )
| ( ( ~ ~ ( ( ( aDimensionOf0 @ SV3 )
!= ( aDimensionOf0 @ SV8 ) )
| ( ( aDimensionOf0 @ SV8 )
!= sz00 ) )
| ( ( sdtasasdt0 @ SV3 @ SV8 )
= sz0z00 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(95,plain,
! [SV9: $i,SV4: $i] :
( ( ( ~ ( ~ ( aScalar0 @ SV4 )
| ~ ( aScalar0 @ SV9 ) ) )
= $false )
| ( ( ~ ( sdtlseqdt0 @ SV4 @ SV9 )
| $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(96,plain,
! [SV12: $i,SV10: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( aScalar0 @ SV5 )
| ~ ( aScalar0 @ SV10 ) )
| ~ ( aScalar0 @ SV12 ) ) )
= $true )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV5 @ SV10 )
| ~ ( sdtlseqdt0 @ SV10 @ SV12 ) )
| ( sdtlseqdt0 @ SV5 @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[90]) ).
thf(97,plain,
! [SV11: $i,SV6: $i] :
( ( ( ~ ( ~ ( aScalar0 @ SV6 )
| ~ ( aScalar0 @ SV11 ) ) )
= $false )
| ( ( ( sdtlseqdt0 @ SV6 @ SV11 )
| ( sdtlseqdt0 @ SV11 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(98,plain,
! [SV7: $i,SV2: $i] :
( ( ( ~ ( aScalar0 @ SV2 )
| ~ ( aScalar0 @ SV7 ) )
= $true )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV2 @ SV7 )
| ~ ( sdtlseqdt0 @ SV7 @ SV2 ) )
| ( SV2 = SV7 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[93]) ).
thf(99,plain,
! [SV8: $i,SV3: $i] :
( ( ( ~ ( aVector0 @ SV3 )
| ~ ( aVector0 @ SV8 ) )
= $true )
| ( ( ~ ~ ( ( ( aDimensionOf0 @ SV3 )
!= ( aDimensionOf0 @ SV8 ) )
| ( ( aDimensionOf0 @ SV8 )
!= sz00 ) )
| ( ( sdtasasdt0 @ SV3 @ SV8 )
= sz0z00 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[94]) ).
thf(100,plain,
! [SV9: $i,SV4: $i] :
( ( ( ~ ( aScalar0 @ SV4 )
| ~ ( aScalar0 @ SV9 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV4 @ SV9 )
| $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[95]) ).
thf(101,plain,
! [SV12: $i,SV10: $i,SV5: $i] :
( ( ( ~ ( ~ ~ ( ~ ( aScalar0 @ SV5 )
| ~ ( aScalar0 @ SV10 ) )
| ~ ( aScalar0 @ SV12 ) ) )
= $false )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV5 @ SV10 )
| ~ ( sdtlseqdt0 @ SV10 @ SV12 ) )
| ( sdtlseqdt0 @ SV5 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(102,plain,
! [SV11: $i,SV6: $i] :
( ( ( ~ ( aScalar0 @ SV6 )
| ~ ( aScalar0 @ SV11 ) )
= $true )
| ( ( ( sdtlseqdt0 @ SV6 @ SV11 )
| ( sdtlseqdt0 @ SV11 @ SV6 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[97]) ).
thf(103,plain,
! [SV7: $i,SV2: $i] :
( ( ( ~ ( aScalar0 @ SV2 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV7 ) )
= $true )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV2 @ SV7 )
| ~ ( sdtlseqdt0 @ SV7 @ SV2 ) )
| ( SV2 = SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[98]) ).
thf(104,plain,
! [SV8: $i,SV3: $i] :
( ( ( ~ ( aVector0 @ SV3 ) )
= $true )
| ( ( ~ ( aVector0 @ SV8 ) )
= $true )
| ( ( ~ ~ ( ( ( aDimensionOf0 @ SV3 )
!= ( aDimensionOf0 @ SV8 ) )
| ( ( aDimensionOf0 @ SV8 )
!= sz00 ) )
| ( ( sdtasasdt0 @ SV3 @ SV8 )
= sz0z00 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[99]) ).
thf(105,plain,
! [SV9: $i,SV4: $i] :
( ( ( ~ ( aScalar0 @ SV4 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV9 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV4 @ SV9 )
| $true )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[100]) ).
thf(106,plain,
! [SV12: $i,SV10: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ( aScalar0 @ SV5 )
| ~ ( aScalar0 @ SV10 ) )
| ~ ( aScalar0 @ SV12 ) )
= $true )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV5 @ SV10 )
| ~ ( sdtlseqdt0 @ SV10 @ SV12 ) )
| ( sdtlseqdt0 @ SV5 @ SV12 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[101]) ).
thf(107,plain,
! [SV11: $i,SV6: $i] :
( ( ( ~ ( aScalar0 @ SV6 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV11 ) )
= $true )
| ( ( ( sdtlseqdt0 @ SV6 @ SV11 )
| ( sdtlseqdt0 @ SV11 @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[102]) ).
thf(108,plain,
! [SV7: $i,SV2: $i] :
( ( ( aScalar0 @ SV2 )
= $false )
| ( ( ~ ( aScalar0 @ SV7 ) )
= $true )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV2 @ SV7 )
| ~ ( sdtlseqdt0 @ SV7 @ SV2 ) )
| ( SV2 = SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(109,plain,
! [SV8: $i,SV3: $i] :
( ( ( aVector0 @ SV3 )
= $false )
| ( ( ~ ( aVector0 @ SV8 ) )
= $true )
| ( ( ~ ~ ( ( ( aDimensionOf0 @ SV3 )
!= ( aDimensionOf0 @ SV8 ) )
| ( ( aDimensionOf0 @ SV8 )
!= sz00 ) )
| ( ( sdtasasdt0 @ SV3 @ SV8 )
= sz0z00 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[104]) ).
thf(110,plain,
! [SV9: $i,SV4: $i] :
( ( ( aScalar0 @ SV4 )
= $false )
| ( ( ~ ( aScalar0 @ SV9 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV4 @ SV9 )
| $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(111,plain,
! [SV12: $i,SV10: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ( aScalar0 @ SV5 )
| ~ ( aScalar0 @ SV10 ) ) )
= $true )
| ( ( ~ ( aScalar0 @ SV12 ) )
= $true )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV5 @ SV10 )
| ~ ( sdtlseqdt0 @ SV10 @ SV12 ) )
| ( sdtlseqdt0 @ SV5 @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[106]) ).
thf(112,plain,
! [SV11: $i,SV6: $i] :
( ( ( aScalar0 @ SV6 )
= $false )
| ( ( ~ ( aScalar0 @ SV11 ) )
= $true )
| ( ( ( sdtlseqdt0 @ SV6 @ SV11 )
| ( sdtlseqdt0 @ SV11 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(113,plain,
! [SV2: $i,SV7: $i] :
( ( ( aScalar0 @ SV7 )
= $false )
| ( ( aScalar0 @ SV2 )
= $false )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV2 @ SV7 )
| ~ ( sdtlseqdt0 @ SV7 @ SV2 ) )
| ( SV2 = SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(114,plain,
! [SV3: $i,SV8: $i] :
( ( ( aVector0 @ SV8 )
= $false )
| ( ( aVector0 @ SV3 )
= $false )
| ( ( ~ ~ ( ( ( aDimensionOf0 @ SV3 )
!= ( aDimensionOf0 @ SV8 ) )
| ( ( aDimensionOf0 @ SV8 )
!= sz00 ) )
| ( ( sdtasasdt0 @ SV3 @ SV8 )
= sz0z00 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(115,plain,
! [SV4: $i,SV9: $i] :
( ( ( aScalar0 @ SV9 )
= $false )
| ( ( aScalar0 @ SV4 )
= $false )
| ( ( ~ ( sdtlseqdt0 @ SV4 @ SV9 )
| $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(116,plain,
! [SV12: $i,SV10: $i,SV5: $i] :
( ( ( ~ ( ~ ( aScalar0 @ SV5 )
| ~ ( aScalar0 @ SV10 ) ) )
= $false )
| ( ( ~ ( aScalar0 @ SV12 ) )
= $true )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV5 @ SV10 )
| ~ ( sdtlseqdt0 @ SV10 @ SV12 ) )
| ( sdtlseqdt0 @ SV5 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(117,plain,
! [SV6: $i,SV11: $i] :
( ( ( aScalar0 @ SV11 )
= $false )
| ( ( aScalar0 @ SV6 )
= $false )
| ( ( ( sdtlseqdt0 @ SV6 @ SV11 )
| ( sdtlseqdt0 @ SV11 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(118,plain,
! [SV7: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV2 @ SV7 )
| ~ ( sdtlseqdt0 @ SV7 @ SV2 ) ) )
= $true )
| ( ( SV2 = SV7 )
= $true )
| ( ( aScalar0 @ SV2 )
= $false )
| ( ( aScalar0 @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[113]) ).
thf(119,plain,
! [SV8: $i,SV3: $i] :
( ( ( ~ ~ ( ( ( aDimensionOf0 @ SV3 )
!= ( aDimensionOf0 @ SV8 ) )
| ( ( aDimensionOf0 @ SV8 )
!= sz00 ) ) )
= $true )
| ( ( ( sdtasasdt0 @ SV3 @ SV8 )
= sz0z00 )
= $true )
| ( ( aVector0 @ SV3 )
= $false )
| ( ( aVector0 @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[114]) ).
thf(120,plain,
! [SV9: $i,SV4: $i] :
( ( ( ~ ( sdtlseqdt0 @ SV4 @ SV9 ) )
= $true )
| ( $true = $true )
| ( ( aScalar0 @ SV4 )
= $false )
| ( ( aScalar0 @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[115]) ).
thf(121,plain,
! [SV12: $i,SV10: $i,SV5: $i] :
( ( ( ~ ( aScalar0 @ SV5 )
| ~ ( aScalar0 @ SV10 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV12 ) )
= $true )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV5 @ SV10 )
| ~ ( sdtlseqdt0 @ SV10 @ SV12 ) )
| ( sdtlseqdt0 @ SV5 @ SV12 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[116]) ).
thf(122,plain,
! [SV11: $i,SV6: $i] :
( ( ( sdtlseqdt0 @ SV6 @ SV11 )
= $true )
| ( ( sdtlseqdt0 @ SV11 @ SV6 )
= $true )
| ( ( aScalar0 @ SV6 )
= $false )
| ( ( aScalar0 @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[117]) ).
thf(123,plain,
! [SV7: $i,SV2: $i] :
( ( ( ~ ( ~ ( sdtlseqdt0 @ SV2 @ SV7 )
| ~ ( sdtlseqdt0 @ SV7 @ SV2 ) ) )
= $false )
| ( ( SV2 = SV7 )
= $true )
| ( ( aScalar0 @ SV2 )
= $false )
| ( ( aScalar0 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(124,plain,
! [SV8: $i,SV3: $i] :
( ( ( ~ ( ( ( aDimensionOf0 @ SV3 )
!= ( aDimensionOf0 @ SV8 ) )
| ( ( aDimensionOf0 @ SV8 )
!= sz00 ) ) )
= $false )
| ( ( ( sdtasasdt0 @ SV3 @ SV8 )
= sz0z00 )
= $true )
| ( ( aVector0 @ SV3 )
= $false )
| ( ( aVector0 @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(125,plain,
! [SV9: $i,SV4: $i] :
( ( ( sdtlseqdt0 @ SV4 @ SV9 )
= $false )
| ( $true = $true )
| ( ( aScalar0 @ SV4 )
= $false )
| ( ( aScalar0 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(126,plain,
! [SV12: $i,SV10: $i,SV5: $i] :
( ( ( ~ ( aScalar0 @ SV5 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV10 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV12 ) )
= $true )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV5 @ SV10 )
| ~ ( sdtlseqdt0 @ SV10 @ SV12 ) )
| ( sdtlseqdt0 @ SV5 @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[121]) ).
thf(127,plain,
! [SV7: $i,SV2: $i] :
( ( ( ~ ( sdtlseqdt0 @ SV2 @ SV7 )
| ~ ( sdtlseqdt0 @ SV7 @ SV2 ) )
= $true )
| ( ( SV2 = SV7 )
= $true )
| ( ( aScalar0 @ SV2 )
= $false )
| ( ( aScalar0 @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[123]) ).
thf(128,plain,
! [SV8: $i,SV3: $i] :
( ( ( ( ( aDimensionOf0 @ SV3 )
!= ( aDimensionOf0 @ SV8 ) )
| ( ( aDimensionOf0 @ SV8 )
!= sz00 ) )
= $true )
| ( ( ( sdtasasdt0 @ SV3 @ SV8 )
= sz0z00 )
= $true )
| ( ( aVector0 @ SV3 )
= $false )
| ( ( aVector0 @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[124]) ).
thf(129,plain,
! [SV12: $i,SV10: $i,SV5: $i] :
( ( ( aScalar0 @ SV5 )
= $false )
| ( ( ~ ( aScalar0 @ SV10 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV12 ) )
= $true )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV5 @ SV10 )
| ~ ( sdtlseqdt0 @ SV10 @ SV12 ) )
| ( sdtlseqdt0 @ SV5 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[126]) ).
thf(130,plain,
! [SV7: $i,SV2: $i] :
( ( ( ~ ( sdtlseqdt0 @ SV2 @ SV7 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV7 @ SV2 ) )
= $true )
| ( ( SV2 = SV7 )
= $true )
| ( ( aScalar0 @ SV2 )
= $false )
| ( ( aScalar0 @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[127]) ).
thf(131,plain,
! [SV8: $i,SV3: $i] :
( ( ( ( aDimensionOf0 @ SV3 )
!= ( aDimensionOf0 @ SV8 ) )
= $true )
| ( ( ( aDimensionOf0 @ SV8 )
!= sz00 )
= $true )
| ( ( ( sdtasasdt0 @ SV3 @ SV8 )
= sz0z00 )
= $true )
| ( ( aVector0 @ SV3 )
= $false )
| ( ( aVector0 @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[128]) ).
thf(132,plain,
! [SV12: $i,SV5: $i,SV10: $i] :
( ( ( aScalar0 @ SV10 )
= $false )
| ( ( aScalar0 @ SV5 )
= $false )
| ( ( ~ ( aScalar0 @ SV12 ) )
= $true )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV5 @ SV10 )
| ~ ( sdtlseqdt0 @ SV10 @ SV12 ) )
| ( sdtlseqdt0 @ SV5 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[129]) ).
thf(133,plain,
! [SV7: $i,SV2: $i] :
( ( ( sdtlseqdt0 @ SV2 @ SV7 )
= $false )
| ( ( ~ ( sdtlseqdt0 @ SV7 @ SV2 ) )
= $true )
| ( ( SV2 = SV7 )
= $true )
| ( ( aScalar0 @ SV2 )
= $false )
| ( ( aScalar0 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[130]) ).
thf(134,plain,
! [SV8: $i,SV3: $i] :
( ( ( ( aDimensionOf0 @ SV3 )
= ( aDimensionOf0 @ SV8 ) )
= $false )
| ( ( ( aDimensionOf0 @ SV8 )
!= sz00 )
= $true )
| ( ( ( sdtasasdt0 @ SV3 @ SV8 )
= sz0z00 )
= $true )
| ( ( aVector0 @ SV3 )
= $false )
| ( ( aVector0 @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(135,plain,
! [SV10: $i,SV5: $i,SV12: $i] :
( ( ( aScalar0 @ SV12 )
= $false )
| ( ( aScalar0 @ SV5 )
= $false )
| ( ( aScalar0 @ SV10 )
= $false )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV5 @ SV10 )
| ~ ( sdtlseqdt0 @ SV10 @ SV12 ) )
| ( sdtlseqdt0 @ SV5 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(136,plain,
! [SV2: $i,SV7: $i] :
( ( ( sdtlseqdt0 @ SV7 @ SV2 )
= $false )
| ( ( sdtlseqdt0 @ SV2 @ SV7 )
= $false )
| ( ( SV2 = SV7 )
= $true )
| ( ( aScalar0 @ SV2 )
= $false )
| ( ( aScalar0 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(137,plain,
! [SV3: $i,SV8: $i] :
( ( ( ( aDimensionOf0 @ SV8 )
= sz00 )
= $false )
| ( ( ( aDimensionOf0 @ SV3 )
= ( aDimensionOf0 @ SV8 ) )
= $false )
| ( ( ( sdtasasdt0 @ SV3 @ SV8 )
= sz0z00 )
= $true )
| ( ( aVector0 @ SV3 )
= $false )
| ( ( aVector0 @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(138,plain,
! [SV12: $i,SV10: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV5 @ SV10 )
| ~ ( sdtlseqdt0 @ SV10 @ SV12 ) ) )
= $true )
| ( ( sdtlseqdt0 @ SV5 @ SV12 )
= $true )
| ( ( aScalar0 @ SV10 )
= $false )
| ( ( aScalar0 @ SV5 )
= $false )
| ( ( aScalar0 @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[135]) ).
thf(139,plain,
! [SV12: $i,SV10: $i,SV5: $i] :
( ( ( ~ ( ~ ( sdtlseqdt0 @ SV5 @ SV10 )
| ~ ( sdtlseqdt0 @ SV10 @ SV12 ) ) )
= $false )
| ( ( sdtlseqdt0 @ SV5 @ SV12 )
= $true )
| ( ( aScalar0 @ SV10 )
= $false )
| ( ( aScalar0 @ SV5 )
= $false )
| ( ( aScalar0 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(140,plain,
! [SV12: $i,SV10: $i,SV5: $i] :
( ( ( ~ ( sdtlseqdt0 @ SV5 @ SV10 )
| ~ ( sdtlseqdt0 @ SV10 @ SV12 ) )
= $true )
| ( ( sdtlseqdt0 @ SV5 @ SV12 )
= $true )
| ( ( aScalar0 @ SV10 )
= $false )
| ( ( aScalar0 @ SV5 )
= $false )
| ( ( aScalar0 @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[139]) ).
thf(141,plain,
! [SV12: $i,SV10: $i,SV5: $i] :
( ( ( ~ ( sdtlseqdt0 @ SV5 @ SV10 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV10 @ SV12 ) )
= $true )
| ( ( sdtlseqdt0 @ SV5 @ SV12 )
= $true )
| ( ( aScalar0 @ SV10 )
= $false )
| ( ( aScalar0 @ SV5 )
= $false )
| ( ( aScalar0 @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[140]) ).
thf(142,plain,
! [SV12: $i,SV10: $i,SV5: $i] :
( ( ( sdtlseqdt0 @ SV5 @ SV10 )
= $false )
| ( ( ~ ( sdtlseqdt0 @ SV10 @ SV12 ) )
= $true )
| ( ( sdtlseqdt0 @ SV5 @ SV12 )
= $true )
| ( ( aScalar0 @ SV10 )
= $false )
| ( ( aScalar0 @ SV5 )
= $false )
| ( ( aScalar0 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(143,plain,
! [SV5: $i,SV12: $i,SV10: $i] :
( ( ( sdtlseqdt0 @ SV10 @ SV12 )
= $false )
| ( ( sdtlseqdt0 @ SV5 @ SV10 )
= $false )
| ( ( sdtlseqdt0 @ SV5 @ SV12 )
= $true )
| ( ( aScalar0 @ SV10 )
= $false )
| ( ( aScalar0 @ SV5 )
= $false )
| ( ( aScalar0 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(144,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[53,143,137,136,125,122,92,86,71,55,54]) ).
thf(145,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[144]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG050+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.13 % Computer : n006.cluster.edu
% 0.09/0.13 % Model : x86_64 x86_64
% 0.09/0.13 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.13 % Memory : 8046.5625MB
% 0.09/0.13 % OS : Linux 6.8.0-71-generic
% 0.09/0.13 % CPULimit : 300
% 0.09/0.13 % WCLimit : 300
% 0.09/0.13 % DateTime : Tue Oct 6 14:11:07 UTC 2026
% 0.09/0.14 % CPUTime :
% 0.09/0.14 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.26
% 0.09/0.26 No.of.Axioms: 9
% 0.09/0.26
% 0.09/0.26 Length.of.Defs: 0
% 0.09/0.26
% 0.09/0.26 Contains.Choice.Funs: false
% 0.09/0.26 ...
% 0.09/0.26
% 0.09/0.26 ********************************
% 0.09/0.26 * All subproblems solved! *
% 0.09/0.26 ********************************
% 0.09/0.26 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:10,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:144,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.09/0.27
% 0.09/0.27 %**** Beginning of derivation protocol ****
% 0.09/0.27 % SZS output start CNFRefutation
% See solution above
% 0.09/0.27
% 0.09/0.27 %**** End of derivation protocol ****
% 0.09/0.27 %**** no. of clauses in derivation: 117 ****
% 0.09/0.27 %**** clause counter: 144 ****
% 0.09/0.27
% 0.09/0.27 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:10,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:144,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------