TSTP Solution File: RNG057+2 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : RNG057+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:49:12 EDT 2023
% Result : Theorem 231.90s 71.84s
% Output : Refutation 232.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 92
% Syntax : Number of formulae : 417 ( 113 unt; 33 typ; 0 def)
% Number of atoms : 1180 ( 478 equ; 0 cnn)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 3502 ( 491 ~; 427 |; 166 &;2305 @)
% ( 1 <=>; 112 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% Number of symbols : 36 ( 33 usr; 20 con; 0-2 aty)
% Number of variables : 272 ( 0 ^; 270 !; 2 ?; 272 :)
% Comments :
%------------------------------------------------------------------------------
thf(aVector0_type,type,
aVector0: $i > $o ).
thf(aDimensionOf0_type,type,
aDimensionOf0: $i > $i ).
thf(sz00_type,type,
sz00: $i ).
thf(sziznziztdt0_type,type,
sziznziztdt0: $i > $i ).
thf(szszuzczcdt0_type,type,
szszuzczcdt0: $i > $i ).
thf(aNaturalNumber0_type,type,
aNaturalNumber0: $i > $o ).
thf(sdtlbdtrb0_type,type,
sdtlbdtrb0: $i > $i > $i ).
thf(sdtlseqdt0_type,type,
sdtlseqdt0: $i > $i > $o ).
thf(sdtasdt0_type,type,
sdtasdt0: $i > $i > $i ).
thf(xP_type,type,
xP: $i ).
thf(xN_type,type,
xN: $i ).
thf(aScalar0_type,type,
aScalar0: $i > $o ).
thf(xB_type,type,
xB: $i ).
thf(xt_type,type,
xt: $i ).
thf(xA_type,type,
xA: $i ).
thf(xs_type,type,
xs: $i ).
thf(sz0z00_type,type,
sz0z00: $i ).
thf(xp_type,type,
xp: $i ).
thf(xE_type,type,
xE: $i ).
thf(sdtasasdt0_type,type,
sdtasasdt0: $i > $i > $i ).
thf(xq_type,type,
xq: $i ).
thf(xC_type,type,
xC: $i ).
thf(iLess0_type,type,
iLess0: $i > $i > $o ).
thf(xD_type,type,
xD: $i ).
thf(smndt0_type,type,
smndt0: $i > $i ).
thf(sdtpldt0_type,type,
sdtpldt0: $i > $i > $i ).
thf(xH_type,type,
xH: $i ).
thf(xS_type,type,
xS: $i ).
thf(xF_type,type,
xF: $i ).
thf(xR_type,type,
xR: $i ).
thf(xG_type,type,
xG: $i ).
thf(sk1_type,type,
sk1: $i > $i ).
thf(sk2_type,type,
sk2: $i > $i > $i ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( ( szszuzczcdt0 @ A )
= ( szszuzczcdt0 @ B ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSuccEqu) ).
thf(67,plain,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( ( szszuzczcdt0 @ A )
= ( szszuzczcdt0 @ B ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(68,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( ( szszuzczcdt0 @ A )
!= ( szszuzczcdt0 @ B ) )
| ( A = B ) ),
inference(cnf,[status(esa)],[67]) ).
thf(69,plain,
! [B: $i,A: $i] :
( ( ( szszuzczcdt0 @ A )
!= ( szszuzczcdt0 @ B ) )
| ( A = B )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B ) ),
inference(lifteq,[status(thm)],[68]) ).
thf(15,axiom,
( ( aVector0 @ xq )
& ( ( szszuzczcdt0 @ ( aDimensionOf0 @ xq ) )
= ( aDimensionOf0 @ xt ) )
& ! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( sdtlbdtrb0 @ xq @ A )
= ( sdtlbdtrb0 @ xt @ A ) ) )
& ( xq
= ( sziznziztdt0 @ xt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1726) ).
thf(116,plain,
( ( aVector0 @ xq )
& ( ( szszuzczcdt0 @ ( aDimensionOf0 @ xq ) )
= ( aDimensionOf0 @ xt ) )
& ! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( sdtlbdtrb0 @ xq @ A )
= ( sdtlbdtrb0 @ xt @ A ) ) )
& ( xq
= ( sziznziztdt0 @ xt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(119,plain,
( ( szszuzczcdt0 @ ( aDimensionOf0 @ xq ) )
= ( aDimensionOf0 @ xt ) ),
inference(cnf,[status(esa)],[116]) ).
thf(123,plain,
( ( szszuzczcdt0 @ ( aDimensionOf0 @ xq ) )
= ( aDimensionOf0 @ xt ) ),
inference(lifteq,[status(thm)],[119]) ).
thf(30,axiom,
aNaturalNumber0 @ sz00,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroNat) ).
thf(159,plain,
aNaturalNumber0 @ sz00,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(5,axiom,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( aNaturalNumber0 @ ( szszuzczcdt0 @ A ) )
& ( ( szszuzczcdt0 @ A )
!= sz00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSuccNat) ).
thf(70,plain,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( aNaturalNumber0 @ ( szszuzczcdt0 @ A ) )
& ( ( szszuzczcdt0 @ A )
!= sz00 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(71,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( aNaturalNumber0 @ ( szszuzczcdt0 @ A ) ) ),
inference(cnf,[status(esa)],[70]) ).
thf(1035,plain,
! [A: $i] :
( ( aNaturalNumber0 @ ( szszuzczcdt0 @ A ) )
| ( ( aNaturalNumber0 @ sz00 )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[159,71]) ).
thf(1036,plain,
aNaturalNumber0 @ ( szszuzczcdt0 @ sz00 ),
inference(pattern_uni,[status(thm)],[1035:[bind(A,$thf( sz00 ))]]) ).
thf(72,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( ( szszuzczcdt0 @ A )
!= sz00 ) ),
inference(cnf,[status(esa)],[70]) ).
thf(73,plain,
! [A: $i] :
( ( ( szszuzczcdt0 @ A )
!= sz00 )
| ~ ( aNaturalNumber0 @ A ) ),
inference(lifteq,[status(thm)],[72]) ).
thf(1069,plain,
! [A: $i] :
( ( ( szszuzczcdt0 @ A )
!= sz00 )
| ( ( aNaturalNumber0 @ ( szszuzczcdt0 @ sz00 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1036,73]) ).
thf(1070,plain,
( ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) )
!= sz00 ),
inference(pattern_uni,[status(thm)],[1069:[bind(A,$thf( szszuzczcdt0 @ sz00 ))]]) ).
thf(1661,plain,
( ( ( szszuzczcdt0 @ ( aDimensionOf0 @ xt ) )
!= sz00 )
| ( ( szszuzczcdt0 @ ( aDimensionOf0 @ xq ) )
!= ( szszuzczcdt0 @ sz00 ) ) ),
inference(paramod_ordered,[status(thm)],[123,1070]) ).
thf(1665,plain,
( ( ( szszuzczcdt0 @ ( aDimensionOf0 @ xt ) )
!= sz00 )
| ( ( aDimensionOf0 @ xq )
!= sz00 ) ),
inference(simp,[status(thm)],[1661]) ).
thf(1071,plain,
! [A: $i] :
( ( aNaturalNumber0 @ ( szszuzczcdt0 @ A ) )
| ( ( aNaturalNumber0 @ ( szszuzczcdt0 @ sz00 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1036,71]) ).
thf(1072,plain,
aNaturalNumber0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ),
inference(pattern_uni,[status(thm)],[1071:[bind(A,$thf( szszuzczcdt0 @ sz00 ))]]) ).
thf(1589,plain,
! [A: $i] :
( ( aNaturalNumber0 @ ( szszuzczcdt0 @ A ) )
| ( ( aNaturalNumber0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1072,71]) ).
thf(1590,plain,
aNaturalNumber0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ),
inference(pattern_uni,[status(thm)],[1589:[bind(A,$thf( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ))]]) ).
thf(1730,plain,
! [A: $i] :
( ( aNaturalNumber0 @ ( szszuzczcdt0 @ A ) )
| ( ( aNaturalNumber0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1590,71]) ).
thf(1731,plain,
aNaturalNumber0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ) ),
inference(pattern_uni,[status(thm)],[1730:[bind(A,$thf( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ))]]) ).
thf(1925,plain,
! [A: $i] :
( ( aNaturalNumber0 @ ( szszuzczcdt0 @ A ) )
| ( ( aNaturalNumber0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ) ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1731,71]) ).
thf(1926,plain,
aNaturalNumber0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1925:[bind(A,$thf( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ) ))]]) ).
thf(2454,plain,
! [A: $i] :
( ( aNaturalNumber0 @ ( szszuzczcdt0 @ A ) )
| ( ( aNaturalNumber0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ) ) ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1926,71]) ).
thf(2455,plain,
aNaturalNumber0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[2454:[bind(A,$thf( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ) ) ))]]) ).
thf(3420,plain,
! [A: $i] :
( ( aNaturalNumber0 @ ( szszuzczcdt0 @ A ) )
| ( ( aNaturalNumber0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ) ) ) ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2455,71]) ).
thf(3421,plain,
aNaturalNumber0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[3420:[bind(A,$thf( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ) ) ) ))]]) ).
thf(3882,plain,
! [A: $i] :
( ( aNaturalNumber0 @ ( szszuzczcdt0 @ A ) )
| ( ( aNaturalNumber0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ) ) ) ) ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3421,71]) ).
thf(3883,plain,
aNaturalNumber0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[3882:[bind(A,$thf( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ) ) ) ) ))]]) ).
thf(22,axiom,
( ( aScalar0 @ xD )
& ( xD
= ( sdtasasdt0 @ xq @ xq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1800) ).
thf(138,plain,
( ( aScalar0 @ xD )
& ( xD
= ( sdtasasdt0 @ xq @ xq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(59,axiom,
( ( aScalar0 @ xG )
& ( xG
= ( sdtasdt0 @ xB @ xB ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1854) ).
thf(261,plain,
( ( aScalar0 @ xG )
& ( xG
= ( sdtasdt0 @ xB @ xB ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(262,plain,
( xG
= ( sdtasdt0 @ xB @ xB ) ),
inference(cnf,[status(esa)],[261]) ).
thf(264,plain,
( ( sdtasdt0 @ xB @ xB )
= xG ),
inference(lifteq,[status(thm)],[262]) ).
thf(1,conjecture,
sdtlseqdt0 @ ( sdtasdt0 @ xP @ xP ) @ xN,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ( sdtlseqdt0 @ ( sdtasdt0 @ xP @ xP ) @ xN ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(61,plain,
~ ( sdtlseqdt0 @ ( sdtasdt0 @ xP @ xP ) @ xN ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(1511,plain,
( ~ ( sdtlseqdt0 @ xG @ xN )
| ( ( sdtasdt0 @ xB @ xB )
!= ( sdtasdt0 @ xP @ xP ) ) ),
inference(paramod_ordered,[status(thm)],[264,61]) ).
thf(1539,plain,
( ~ ( sdtlseqdt0 @ xG @ xN )
| ( xB != xP )
| ( xB != xP ) ),
inference(simp,[status(thm)],[1511]) ).
thf(1559,plain,
( ~ ( sdtlseqdt0 @ xG @ xN )
| ( xB != xP ) ),
inference(simp,[status(thm)],[1539]) ).
thf(1728,plain,
! [A: $i] :
( ( ( szszuzczcdt0 @ A )
!= sz00 )
| ( ( aNaturalNumber0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1590,73]) ).
thf(1729,plain,
( ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ) )
!= sz00 ),
inference(pattern_uni,[status(thm)],[1728:[bind(A,$thf( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ))]]) ).
thf(20,axiom,
( ( aDimensionOf0 @ xs )
!= sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1692) ).
thf(132,plain,
( ( aDimensionOf0 @ xs )
!= sz00 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(133,plain,
( ( aDimensionOf0 @ xs )
!= sz00 ),
inference(polarity_switch,[status(thm)],[132]) ).
thf(134,plain,
( ( aDimensionOf0 @ xs )
!= sz00 ),
inference(lifteq,[status(thm)],[133]) ).
thf(18,axiom,
( ( aDimensionOf0 @ xs )
= ( aDimensionOf0 @ xt ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1678_01) ).
thf(129,plain,
( ( aDimensionOf0 @ xs )
= ( aDimensionOf0 @ xt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(130,plain,
( ( aDimensionOf0 @ xs )
= ( aDimensionOf0 @ xt ) ),
inference(lifteq,[status(thm)],[129]) ).
thf(1083,plain,
( ( aDimensionOf0 @ xt )
!= sz00 ),
inference(rewrite,[status(thm)],[134,130]) ).
thf(1923,plain,
! [A: $i] :
( ( ( szszuzczcdt0 @ A )
!= sz00 )
| ( ( aNaturalNumber0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ) ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1731,73]) ).
thf(1924,plain,
( ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ) ) )
!= sz00 ),
inference(pattern_uni,[status(thm)],[1923:[bind(A,$thf( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ) ))]]) ).
thf(14,axiom,
( ( aScalar0 @ xE )
& ( xE
= ( sdtasasdt0 @ xp @ xq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1820) ).
thf(112,plain,
( ( aScalar0 @ xE )
& ( xE
= ( sdtasasdt0 @ xp @ xq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(113,plain,
( xE
= ( sdtasasdt0 @ xp @ xq ) ),
inference(cnf,[status(esa)],[112]) ).
thf(115,plain,
( ( sdtasasdt0 @ xp @ xq )
= xE ),
inference(lifteq,[status(thm)],[113]) ).
thf(118,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( ( sdtlbdtrb0 @ xq @ A )
= ( sdtlbdtrb0 @ xt @ A ) ) ),
inference(cnf,[status(esa)],[116]) ).
thf(122,plain,
! [A: $i] :
( ( ( sdtlbdtrb0 @ xq @ A )
= ( sdtlbdtrb0 @ xt @ A ) )
| ~ ( aNaturalNumber0 @ A ) ),
inference(lifteq,[status(thm)],[118]) ).
thf(6161,plain,
! [A: $i] :
( ( ( sdtlbdtrb0 @ xq @ A )
= ( sdtlbdtrb0 @ xt @ A ) )
| ( ( aNaturalNumber0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1590,122]) ).
thf(6162,plain,
( ( sdtlbdtrb0 @ xq @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ) )
= ( sdtlbdtrb0 @ xt @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ) ) ),
inference(pattern_uni,[status(thm)],[6161:[bind(A,$thf( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ))]]) ).
thf(120,plain,
aVector0 @ xq,
inference(cnf,[status(esa)],[116]) ).
thf(42,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B )
& ( aScalar0 @ C ) )
=> ( ( ( sdtlseqdt0 @ A @ B )
& ( sdtlseqdt0 @ B @ C ) )
=> ( sdtlseqdt0 @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETrn) ).
thf(202,plain,
! [A: $i,B: $i,C: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B )
& ( aScalar0 @ C ) )
=> ( ( ( sdtlseqdt0 @ A @ B )
& ( sdtlseqdt0 @ B @ C ) )
=> ( sdtlseqdt0 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(47,axiom,
( ( sdtasdt0 @ xP @ xP )
= ( sdtasdt0 @ ( sdtasdt0 @ xH @ xH ) @ ( sdtasdt0 @ xE @ xE ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2027) ).
thf(216,plain,
( ( sdtasdt0 @ xP @ xP )
= ( sdtasdt0 @ ( sdtasdt0 @ xH @ xH ) @ ( sdtasdt0 @ xE @ xE ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(217,plain,
( ( sdtasdt0 @ ( sdtasdt0 @ xH @ xH ) @ ( sdtasdt0 @ xE @ xE ) )
= ( sdtasdt0 @ xP @ xP ) ),
inference(lifteq,[status(thm)],[216]) ).
thf(3,axiom,
! [A: $i] :
( ( ( aNaturalNumber0 @ A )
& ( A != sz00 ) )
=> ? [B: $i] :
( ( aNaturalNumber0 @ B )
& ( A
= ( szszuzczcdt0 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNatExtr) ).
thf(62,plain,
! [A: $i] :
( ( ( aNaturalNumber0 @ A )
& ( A != sz00 ) )
=> ? [B: $i] :
( ( aNaturalNumber0 @ B )
& ( A
= ( szszuzczcdt0 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(63,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( A = sz00 )
| ( aNaturalNumber0 @ ( sk1 @ A ) ) ),
inference(cnf,[status(esa)],[62]) ).
thf(65,plain,
! [A: $i] :
( ( A = sz00 )
| ~ ( aNaturalNumber0 @ A )
| ( aNaturalNumber0 @ ( sk1 @ A ) ) ),
inference(lifteq,[status(thm)],[63]) ).
thf(275,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( aNaturalNumber0 @ ( sk1 @ A ) )
| ~ ( sdtlseqdt0 @ ( sdtasdt0 @ xP @ xP ) @ sz00 )
| ( A != xN ) ),
inference(paramod_ordered,[status(thm)],[65,61]) ).
thf(276,plain,
( ~ ( aNaturalNumber0 @ xN )
| ( aNaturalNumber0 @ ( sk1 @ xN ) )
| ~ ( sdtlseqdt0 @ ( sdtasdt0 @ xP @ xP ) @ sz00 ) ),
inference(pattern_uni,[status(thm)],[275:[bind(A,$thf( xN ))]]) ).
thf(23,axiom,
! [A: $i] :
( ( aVector0 @ A )
=> ( aNaturalNumber0 @ ( aDimensionOf0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDimNat) ).
thf(142,plain,
! [A: $i] :
( ( aVector0 @ A )
=> ( aNaturalNumber0 @ ( aDimensionOf0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(13,axiom,
( ( aVector0 @ xp )
& ( ( szszuzczcdt0 @ ( aDimensionOf0 @ xp ) )
= ( aDimensionOf0 @ xs ) )
& ! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( sdtlbdtrb0 @ xp @ A )
= ( sdtlbdtrb0 @ xs @ A ) ) )
& ( xp
= ( sziznziztdt0 @ xs ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1709) ).
thf(104,plain,
( ( aVector0 @ xp )
& ( ( szszuzczcdt0 @ ( aDimensionOf0 @ xp ) )
= ( aDimensionOf0 @ xs ) )
& ! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( sdtlbdtrb0 @ xp @ A )
= ( sdtlbdtrb0 @ xs @ A ) ) )
& ( xp
= ( sziznziztdt0 @ xs ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(106,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( ( sdtlbdtrb0 @ xp @ A )
= ( sdtlbdtrb0 @ xs @ A ) ) ),
inference(cnf,[status(esa)],[104]) ).
thf(110,plain,
! [A: $i] :
( ( ( sdtlbdtrb0 @ xp @ A )
= ( sdtlbdtrb0 @ xs @ A ) )
| ~ ( aNaturalNumber0 @ A ) ),
inference(lifteq,[status(thm)],[106]) ).
thf(5673,plain,
! [A: $i] :
( ( ( sdtlbdtrb0 @ xp @ A )
= ( sdtlbdtrb0 @ xs @ A ) )
| ( ( aNaturalNumber0 @ sz00 )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[159,110]) ).
thf(5674,plain,
( ( sdtlbdtrb0 @ xp @ sz00 )
= ( sdtlbdtrb0 @ xs @ sz00 ) ),
inference(pattern_uni,[status(thm)],[5673:[bind(A,$thf( sz00 ))]]) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B ) )
=> ( ( ( sdtlseqdt0 @ sz0z00 @ A )
& ( sdtlseqdt0 @ sz0z00 @ B ) )
=> ( ( sdtlseqdt0 @ sz0z00 @ ( sdtpldt0 @ A @ B ) )
& ( sdtlseqdt0 @ sz0z00 @ ( sdtasdt0 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mPosMon) ).
thf(174,plain,
! [A: $i,B: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B ) )
=> ( ( ( sdtlseqdt0 @ sz0z00 @ A )
& ( sdtlseqdt0 @ sz0z00 @ B ) )
=> ( ( sdtlseqdt0 @ sz0z00 @ ( sdtpldt0 @ A @ B ) )
& ( sdtlseqdt0 @ sz0z00 @ ( sdtasdt0 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(271,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( aNaturalNumber0 @ ( sk1 @ A ) )
| ~ ( sdtlseqdt0 @ ( sdtasdt0 @ sz00 @ xP ) @ xN )
| ( A != xP ) ),
inference(paramod_ordered,[status(thm)],[65,61]) ).
thf(272,plain,
( ~ ( aNaturalNumber0 @ xP )
| ( aNaturalNumber0 @ ( sk1 @ xP ) )
| ~ ( sdtlseqdt0 @ ( sdtasdt0 @ sz00 @ xP ) @ xN ) ),
inference(pattern_uni,[status(thm)],[271:[bind(A,$thf( xP ))]]) ).
thf(331,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( aNaturalNumber0 @ ( sk1 @ A ) )
| ~ ( aNaturalNumber0 @ xP )
| ( aNaturalNumber0 @ ( sk1 @ xP ) )
| ~ ( sdtlseqdt0 @ ( sdtasdt0 @ sz00 @ sz00 ) @ xN )
| ( A != xP ) ),
inference(paramod_ordered,[status(thm)],[65,272]) ).
thf(332,plain,
( ~ ( aNaturalNumber0 @ xP )
| ( aNaturalNumber0 @ ( sk1 @ xP ) )
| ~ ( aNaturalNumber0 @ xP )
| ( aNaturalNumber0 @ ( sk1 @ xP ) )
| ~ ( sdtlseqdt0 @ ( sdtasdt0 @ sz00 @ sz00 ) @ xN ) ),
inference(pattern_uni,[status(thm)],[331:[bind(A,$thf( xP ))]]) ).
thf(344,plain,
( ~ ( aNaturalNumber0 @ xP )
| ( aNaturalNumber0 @ ( sk1 @ xP ) )
| ~ ( sdtlseqdt0 @ ( sdtasdt0 @ sz00 @ sz00 ) @ xN ) ),
inference(simp,[status(thm)],[332]) ).
thf(982,plain,
( ( aNaturalNumber0 @ ( sk1 @ xP ) )
| ~ ( sdtlseqdt0 @ ( sdtasdt0 @ sz00 @ sz00 ) @ xN )
| ( ( aNaturalNumber0 @ xP )
!= ( aNaturalNumber0 @ sz00 ) ) ),
inference(paramod_ordered,[status(thm)],[159,344]) ).
thf(1001,plain,
( ( aNaturalNumber0 @ ( sk1 @ xP ) )
| ~ ( sdtlseqdt0 @ ( sdtasdt0 @ sz00 @ sz00 ) @ xN )
| ( xP != sz00 ) ),
inference(simp,[status(thm)],[982]) ).
thf(49,axiom,
( ( aScalar0 @ xF )
& ( xF
= ( sdtasdt0 @ xA @ xA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
thf(222,plain,
( ( aScalar0 @ xF )
& ( xF
= ( sdtasdt0 @ xA @ xA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(223,plain,
( xF
= ( sdtasdt0 @ xA @ xA ) ),
inference(cnf,[status(esa)],[222]) ).
thf(225,plain,
( ( sdtasdt0 @ xA @ xA )
= xF ),
inference(lifteq,[status(thm)],[223]) ).
thf(1335,plain,
( ~ ( sdtlseqdt0 @ xF @ xN )
| ( ( sdtasdt0 @ xA @ xA )
!= ( sdtasdt0 @ xP @ xP ) ) ),
inference(paramod_ordered,[status(thm)],[225,61]) ).
thf(1371,plain,
( ~ ( sdtlseqdt0 @ xF @ xN )
| ( xA != xP )
| ( xA != xP ) ),
inference(simp,[status(thm)],[1335]) ).
thf(1381,plain,
( ~ ( sdtlseqdt0 @ xF @ xN )
| ( xA != xP ) ),
inference(simp,[status(thm)],[1371]) ).
thf(1390,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( aNaturalNumber0 @ ( sk1 @ A ) )
| ~ ( sdtlseqdt0 @ xF @ xN )
| ( xP != sz00 )
| ( A != xA ) ),
inference(paramod_ordered,[status(thm)],[65,1381]) ).
thf(1391,plain,
( ~ ( aNaturalNumber0 @ xA )
| ( aNaturalNumber0 @ ( sk1 @ xA ) )
| ~ ( sdtlseqdt0 @ xF @ xN )
| ( xP != sz00 ) ),
inference(pattern_uni,[status(thm)],[1390:[bind(A,$thf( xA ))]]) ).
thf(57,axiom,
( ( aScalar0 @ xP )
& ( xP
= ( sdtasdt0 @ xE @ xH ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1911) ).
thf(255,plain,
( ( aScalar0 @ xP )
& ( xP
= ( sdtasdt0 @ xE @ xH ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(256,plain,
( xP
= ( sdtasdt0 @ xE @ xH ) ),
inference(cnf,[status(esa)],[255]) ).
thf(258,plain,
( ( sdtasdt0 @ xE @ xH )
= xP ),
inference(lifteq,[status(thm)],[256]) ).
thf(1415,plain,
( ~ ( sdtlseqdt0 @ xP @ xN )
| ( ( sdtasdt0 @ xE @ xH )
!= ( sdtasdt0 @ xP @ xP ) ) ),
inference(paramod_ordered,[status(thm)],[258,61]) ).
thf(1441,plain,
( ~ ( sdtlseqdt0 @ xP @ xN )
| ( xE != xP )
| ( xH != xP ) ),
inference(simp,[status(thm)],[1415]) ).
thf(257,plain,
aScalar0 @ xP,
inference(cnf,[status(esa)],[255]) ).
thf(8,axiom,
( ( aScalar0 @ xA )
& ( xA
= ( sdtlbdtrb0 @ xs @ ( aDimensionOf0 @ xs ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1746) ).
thf(79,plain,
( ( aScalar0 @ xA )
& ( xA
= ( sdtlbdtrb0 @ xs @ ( aDimensionOf0 @ xs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(80,plain,
( xA
= ( sdtlbdtrb0 @ xs @ ( aDimensionOf0 @ xs ) ) ),
inference(cnf,[status(esa)],[79]) ).
thf(82,plain,
( ( sdtlbdtrb0 @ xs @ ( aDimensionOf0 @ xs ) )
= xA ),
inference(lifteq,[status(thm)],[80]) ).
thf(1482,plain,
( ( sdtlbdtrb0 @ xs @ ( aDimensionOf0 @ xt ) )
= xA ),
inference(rewrite,[status(thm)],[82,130]) ).
thf(46,axiom,
( ( aScalar0 @ xN )
& ( xN
= ( sdtasdt0 @ xR @ xS ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1949) ).
thf(212,plain,
( ( aScalar0 @ xN )
& ( xN
= ( sdtasdt0 @ xR @ xS ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(213,plain,
( xN
= ( sdtasdt0 @ xR @ xS ) ),
inference(cnf,[status(esa)],[212]) ).
thf(215,plain,
( ( sdtasdt0 @ xR @ xS )
= xN ),
inference(lifteq,[status(thm)],[213]) ).
thf(1237,plain,
( ~ ( sdtlseqdt0 @ xN @ xN )
| ( ( sdtasdt0 @ xR @ xS )
!= ( sdtasdt0 @ xP @ xP ) ) ),
inference(paramod_ordered,[status(thm)],[215,61]) ).
thf(1254,plain,
( ~ ( sdtlseqdt0 @ xN @ xN )
| ( xR != xP )
| ( xS != xP ) ),
inference(simp,[status(thm)],[1237]) ).
thf(37,axiom,
! [A: $i,B: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B ) )
=> ( ( ( sdtlseqdt0 @ A @ B )
& ( sdtlseqdt0 @ B @ A ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLEASm) ).
thf(184,plain,
! [A: $i,B: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B ) )
=> ( ( ( sdtlseqdt0 @ A @ B )
& ( sdtlseqdt0 @ B @ A ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(40,axiom,
( ( aScalar0 @ xS )
& ( xS
= ( sdtasdt0 @ xF @ xD ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1930) ).
thf(193,plain,
( ( aScalar0 @ xS )
& ( xS
= ( sdtasdt0 @ xF @ xD ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(194,plain,
( xS
= ( sdtasdt0 @ xF @ xD ) ),
inference(cnf,[status(esa)],[193]) ).
thf(196,plain,
( ( sdtasdt0 @ xF @ xD )
= xS ),
inference(lifteq,[status(thm)],[194]) ).
thf(17,axiom,
( ( aScalar0 @ xC )
& ( xC
= ( sdtasasdt0 @ xp @ xp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1783) ).
thf(125,plain,
( ( aScalar0 @ xC )
& ( xC
= ( sdtasasdt0 @ xp @ xp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(38,axiom,
( ( aScalar0 @ xH )
& ( xH
= ( sdtasdt0 @ xA @ xB ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1873) ).
thf(187,plain,
( ( aScalar0 @ xH )
& ( xH
= ( sdtasdt0 @ xA @ xB ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(189,plain,
aScalar0 @ xH,
inference(cnf,[status(esa)],[187]) ).
thf(1587,plain,
! [A: $i] :
( ( ( szszuzczcdt0 @ A )
!= sz00 )
| ( ( aNaturalNumber0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1072,73]) ).
thf(1588,plain,
( ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) )
!= sz00 ),
inference(pattern_uni,[status(thm)],[1587:[bind(A,$thf( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ))]]) ).
thf(1681,plain,
( ( ( szszuzczcdt0 @ ( aDimensionOf0 @ xt ) )
!= sz00 )
| ( ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) )
!= ( szszuzczcdt0 @ ( aDimensionOf0 @ xq ) ) ) ),
inference(paramod_ordered,[status(thm)],[123,1588]) ).
thf(1704,plain,
( ( ( szszuzczcdt0 @ ( aDimensionOf0 @ xt ) )
!= sz00 )
| ( ( szszuzczcdt0 @ sz00 )
!= ( aDimensionOf0 @ xq ) ) ),
inference(simp,[status(thm)],[1681]) ).
thf(27,axiom,
! [A: $i] :
( ( aScalar0 @ A )
=> ( aScalar0 @ ( smndt0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNegSc) ).
thf(152,plain,
! [A: $i] :
( ( aScalar0 @ A )
=> ( aScalar0 @ ( smndt0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(315,plain,
! [A: $i] :
( ( ( szszuzczcdt0 @ A )
!= sz00 )
| ( ( aNaturalNumber0 @ sz00 )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[159,73]) ).
thf(316,plain,
( ( szszuzczcdt0 @ sz00 )
!= sz00 ),
inference(pattern_uni,[status(thm)],[315:[bind(A,$thf( sz00 ))]]) ).
thf(7,axiom,
( ( aScalar0 @ xB )
& ( xB
= ( sdtlbdtrb0 @ xt @ ( aDimensionOf0 @ xt ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1766) ).
thf(75,plain,
( ( aScalar0 @ xB )
& ( xB
= ( sdtlbdtrb0 @ xt @ ( aDimensionOf0 @ xt ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(76,plain,
( xB
= ( sdtlbdtrb0 @ xt @ ( aDimensionOf0 @ xt ) ) ),
inference(cnf,[status(esa)],[75]) ).
thf(78,plain,
( ( sdtlbdtrb0 @ xt @ ( aDimensionOf0 @ xt ) )
= xB ),
inference(lifteq,[status(thm)],[76]) ).
thf(36,axiom,
! [A: $i,B: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B ) )
=> ( ( ( sdtasdt0 @ A @ ( smndt0 @ B ) )
= ( smndt0 @ ( sdtasdt0 @ A @ B ) ) )
& ( ( sdtasdt0 @ ( smndt0 @ A ) @ B )
= ( smndt0 @ ( sdtasdt0 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMNeg) ).
thf(179,plain,
! [A: $i,B: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B ) )
=> ( ( ( sdtasdt0 @ A @ ( smndt0 @ B ) )
= ( smndt0 @ ( sdtasdt0 @ A @ B ) ) )
& ( ( sdtasdt0 @ ( smndt0 @ A ) @ B )
= ( smndt0 @ ( sdtasdt0 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(107,plain,
( ( szszuzczcdt0 @ ( aDimensionOf0 @ xp ) )
= ( aDimensionOf0 @ xs ) ),
inference(cnf,[status(esa)],[104]) ).
thf(111,plain,
( ( szszuzczcdt0 @ ( aDimensionOf0 @ xp ) )
= ( aDimensionOf0 @ xs ) ),
inference(lifteq,[status(thm)],[107]) ).
thf(1603,plain,
( ( szszuzczcdt0 @ ( aDimensionOf0 @ xp ) )
= ( aDimensionOf0 @ xt ) ),
inference(rewrite,[status(thm)],[111,130]) ).
thf(1626,plain,
( ( ( szszuzczcdt0 @ ( aDimensionOf0 @ xt ) )
!= sz00 )
| ( ( szszuzczcdt0 @ ( aDimensionOf0 @ xp ) )
!= ( szszuzczcdt0 @ sz00 ) ) ),
inference(paramod_ordered,[status(thm)],[1603,1070]) ).
thf(1632,plain,
( ( ( szszuzczcdt0 @ ( aDimensionOf0 @ xt ) )
!= sz00 )
| ( ( aDimensionOf0 @ xp )
!= sz00 ) ),
inference(simp,[status(thm)],[1626]) ).
thf(117,plain,
( xq
= ( sziznziztdt0 @ xt ) ),
inference(cnf,[status(esa)],[116]) ).
thf(121,plain,
( ( sziznziztdt0 @ xt )
= xq ),
inference(lifteq,[status(thm)],[117]) ).
thf(188,plain,
( xH
= ( sdtasdt0 @ xA @ xB ) ),
inference(cnf,[status(esa)],[187]) ).
thf(190,plain,
( ( sdtasdt0 @ xA @ xB )
= xH ),
inference(lifteq,[status(thm)],[188]) ).
thf(1131,plain,
( ~ ( sdtlseqdt0 @ xH @ xN )
| ( ( sdtasdt0 @ xA @ xB )
!= ( sdtasdt0 @ xP @ xP ) ) ),
inference(paramod_ordered,[status(thm)],[190,61]) ).
thf(1151,plain,
( ~ ( sdtlseqdt0 @ xH @ xN )
| ( xA != xP )
| ( xB != xP ) ),
inference(simp,[status(thm)],[1131]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( ( aVector0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( aScalar0 @ ( sdtlbdtrb0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mElmSc) ).
thf(84,plain,
! [A: $i,B: $i] :
( ( ( aVector0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( aScalar0 @ ( sdtlbdtrb0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(25,axiom,
( ( aVector0 @ xs )
& ( aVector0 @ xt ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1678) ).
thf(146,plain,
( ( aVector0 @ xs )
& ( aVector0 @ xt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(147,plain,
aVector0 @ xt,
inference(cnf,[status(esa)],[146]) ).
thf(1331,plain,
( ~ ( aNaturalNumber0 @ xN )
| ( aNaturalNumber0 @ ( sk1 @ xN ) )
| ~ ( sdtlseqdt0 @ xF @ sz00 )
| ( ( sdtasdt0 @ xA @ xA )
!= ( sdtasdt0 @ xP @ xP ) ) ),
inference(paramod_ordered,[status(thm)],[225,276]) ).
thf(1366,plain,
( ( aNaturalNumber0 @ ( sk1 @ xN ) )
| ~ ( aNaturalNumber0 @ xN )
| ~ ( sdtlseqdt0 @ xF @ sz00 )
| ( xA != xP )
| ( xA != xP ) ),
inference(simp,[status(thm)],[1331]) ).
thf(1377,plain,
( ( aNaturalNumber0 @ ( sk1 @ xN ) )
| ~ ( aNaturalNumber0 @ xN )
| ~ ( sdtlseqdt0 @ xF @ sz00 )
| ( xA != xP ) ),
inference(simp,[status(thm)],[1366]) ).
thf(1061,plain,
! [A: $i] :
( ( A = sz00 )
| ( aNaturalNumber0 @ ( sk1 @ A ) )
| ( ( aNaturalNumber0 @ ( szszuzczcdt0 @ sz00 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1036,65]) ).
thf(1062,plain,
( ( ( szszuzczcdt0 @ sz00 )
= sz00 )
| ( aNaturalNumber0 @ ( sk1 @ ( szszuzczcdt0 @ sz00 ) ) ) ),
inference(pattern_uni,[status(thm)],[1061:[bind(A,$thf( szszuzczcdt0 @ sz00 ))]]) ).
thf(2108,plain,
aNaturalNumber0 @ ( sk1 @ ( szszuzczcdt0 @ sz00 ) ),
inference(simplifyReflect,[status(thm)],[1062,316]) ).
thf(5664,plain,
! [A: $i] :
( ( ( sdtlbdtrb0 @ xp @ A )
= ( sdtlbdtrb0 @ xs @ A ) )
| ( ( aNaturalNumber0 @ ( sk1 @ ( szszuzczcdt0 @ sz00 ) ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2108,110]) ).
thf(5665,plain,
( ( sdtlbdtrb0 @ xp @ ( sk1 @ ( szszuzczcdt0 @ sz00 ) ) )
= ( sdtlbdtrb0 @ xs @ ( sk1 @ ( szszuzczcdt0 @ sz00 ) ) ) ),
inference(pattern_uni,[status(thm)],[5664:[bind(A,$thf( sk1 @ ( szszuzczcdt0 @ sz00 ) ))]]) ).
thf(60,axiom,
! [A: $i] :
( ( aScalar0 @ A )
=> ( sdtlseqdt0 @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLERef) ).
thf(265,plain,
! [A: $i] :
( ( aScalar0 @ A )
=> ( sdtlseqdt0 @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(6,axiom,
! [A: $i] :
( ( aVector0 @ A )
=> $true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mVcSort) ).
thf(74,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(5642,plain,
! [A: $i] :
( ( ( sdtlbdtrb0 @ xp @ A )
= ( sdtlbdtrb0 @ xs @ A ) )
| ( ( aNaturalNumber0 @ ( szszuzczcdt0 @ sz00 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1036,110]) ).
thf(5643,plain,
( ( sdtlbdtrb0 @ xp @ ( szszuzczcdt0 @ sz00 ) )
= ( sdtlbdtrb0 @ xs @ ( szszuzczcdt0 @ sz00 ) ) ),
inference(pattern_uni,[status(thm)],[5642:[bind(A,$thf( szszuzczcdt0 @ sz00 ))]]) ).
thf(718,plain,
( ( aNaturalNumber0 @ ( sk1 @ xN ) )
| ~ ( sdtlseqdt0 @ ( sdtasdt0 @ xP @ xP ) @ sz00 )
| ( ( aNaturalNumber0 @ xN )
!= ( aNaturalNumber0 @ sz00 ) ) ),
inference(paramod_ordered,[status(thm)],[159,276]) ).
thf(734,plain,
( ( aNaturalNumber0 @ ( sk1 @ xN ) )
| ~ ( sdtlseqdt0 @ ( sdtasdt0 @ xP @ xP ) @ sz00 )
| ( xN != sz00 ) ),
inference(simp,[status(thm)],[718]) ).
thf(48,axiom,
( ( aScalar0 @ xR )
& ( xR
= ( sdtasdt0 @ xC @ xG ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1892) ).
thf(218,plain,
( ( aScalar0 @ xR )
& ( xR
= ( sdtasdt0 @ xC @ xG ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(219,plain,
( xR
= ( sdtasdt0 @ xC @ xG ) ),
inference(cnf,[status(esa)],[218]) ).
thf(221,plain,
( ( sdtasdt0 @ xC @ xG )
= xR ),
inference(lifteq,[status(thm)],[219]) ).
thf(54,axiom,
! [A: $i,B: $i] :
( ( ( aVector0 @ A )
& ( aVector0 @ B ) )
=> ( ( ( aDimensionOf0 @ A )
= ( aDimensionOf0 @ B ) )
=> ( ( iLess0 @ ( aDimensionOf0 @ A ) @ ( aDimensionOf0 @ xs ) )
=> ( sdtlseqdt0 @ ( sdtasdt0 @ ( sdtasasdt0 @ A @ B ) @ ( sdtasasdt0 @ A @ B ) ) @ ( sdtasdt0 @ ( sdtasasdt0 @ A @ A ) @ ( sdtasasdt0 @ B @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1652) ).
thf(248,plain,
! [A: $i,B: $i] :
( ( ( aVector0 @ A )
& ( aVector0 @ B ) )
=> ( ( ( aDimensionOf0 @ A )
= ( aDimensionOf0 @ B ) )
=> ( ( iLess0 @ ( aDimensionOf0 @ A ) @ ( aDimensionOf0 @ xs ) )
=> ( sdtlseqdt0 @ ( sdtasdt0 @ ( sdtasasdt0 @ A @ B ) @ ( sdtasasdt0 @ A @ B ) ) @ ( sdtasdt0 @ ( sdtasasdt0 @ A @ A ) @ ( sdtasasdt0 @ B @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(85,plain,
! [B: $i,A: $i] :
( ~ ( aVector0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( aScalar0 @ ( sdtlbdtrb0 @ A @ B ) ) ),
inference(cnf,[status(esa)],[84]) ).
thf(220,plain,
aScalar0 @ xR,
inference(cnf,[status(esa)],[218]) ).
thf(1284,plain,
( ~ ( sdtlseqdt0 @ xR @ xN )
| ( ( sdtasdt0 @ xC @ xG )
!= ( sdtasdt0 @ xP @ xP ) ) ),
inference(paramod_ordered,[status(thm)],[221,61]) ).
thf(1311,plain,
( ~ ( sdtlseqdt0 @ xR @ xN )
| ( xC != xP )
| ( xG != xP ) ),
inference(simp,[status(thm)],[1284]) ).
thf(11,axiom,
! [A: $i] :
( ( aVector0 @ A )
=> ( ( ( aDimensionOf0 @ A )
!= sz00 )
=> ! [B: $i] :
( ( B
= ( sziznziztdt0 @ A ) )
<=> ( ( aVector0 @ B )
& ( ( szszuzczcdt0 @ ( aDimensionOf0 @ B ) )
= ( aDimensionOf0 @ A ) )
& ! [C: $i] :
( ( aNaturalNumber0 @ C )
=> ( ( sdtlbdtrb0 @ B @ C )
= ( sdtlbdtrb0 @ A @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefInit) ).
thf(86,plain,
! [A: $i] :
( ( aVector0 @ A )
=> ( ( ( aDimensionOf0 @ A )
!= sz00 )
=> ! [B: $i] :
( ( ( B
= ( sziznziztdt0 @ A ) )
=> ( ( aVector0 @ B )
& ( ( szszuzczcdt0 @ ( aDimensionOf0 @ B ) )
= ( aDimensionOf0 @ A ) )
& ! [C: $i] :
( ( aNaturalNumber0 @ C )
=> ( ( sdtlbdtrb0 @ B @ C )
= ( sdtlbdtrb0 @ A @ C ) ) ) ) )
& ( ( ( aVector0 @ B )
& ( ( szszuzczcdt0 @ ( aDimensionOf0 @ B ) )
= ( aDimensionOf0 @ A ) )
& ! [C: $i] :
( ( aNaturalNumber0 @ C )
=> ( ( sdtlbdtrb0 @ B @ C )
= ( sdtlbdtrb0 @ A @ C ) ) ) )
=> ( B
= ( sziznziztdt0 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(87,plain,
! [A: $i] :
( ( aVector0 @ A )
=> ( ( ( aDimensionOf0 @ A )
!= sz00 )
=> ( ! [B: $i] :
( ( B
= ( sziznziztdt0 @ A ) )
=> ( ( aVector0 @ B )
& ( ( szszuzczcdt0 @ ( aDimensionOf0 @ B ) )
= ( aDimensionOf0 @ A ) )
& ! [C: $i] :
( ( aNaturalNumber0 @ C )
=> ( ( sdtlbdtrb0 @ B @ C )
= ( sdtlbdtrb0 @ A @ C ) ) ) ) )
& ! [B: $i] :
( ( ( aVector0 @ B )
& ( ( szszuzczcdt0 @ ( aDimensionOf0 @ B ) )
= ( aDimensionOf0 @ A ) )
& ! [C: $i] :
( ( aNaturalNumber0 @ C )
=> ( ( sdtlbdtrb0 @ B @ C )
= ( sdtlbdtrb0 @ A @ C ) ) ) )
=> ( B
= ( sziznziztdt0 @ A ) ) ) ) ) ),
inference(miniscope,[status(thm)],[86]) ).
thf(90,plain,
! [B: $i,A: $i] :
( ~ ( aVector0 @ A )
| ( ( aDimensionOf0 @ A )
= sz00 )
| ( B
!= ( sziznziztdt0 @ A ) )
| ( ( szszuzczcdt0 @ ( aDimensionOf0 @ B ) )
= ( aDimensionOf0 @ A ) ) ),
inference(cnf,[status(esa)],[87]) ).
thf(101,plain,
! [B: $i,A: $i] :
( ( ( aDimensionOf0 @ A )
= sz00 )
| ( B
!= ( sziznziztdt0 @ A ) )
| ( ( szszuzczcdt0 @ ( aDimensionOf0 @ B ) )
= ( aDimensionOf0 @ A ) )
| ~ ( aVector0 @ A ) ),
inference(lifteq,[status(thm)],[90]) ).
thf(102,plain,
! [A: $i] :
( ( ( aDimensionOf0 @ A )
= sz00 )
| ( ( szszuzczcdt0 @ ( aDimensionOf0 @ ( sziznziztdt0 @ A ) ) )
= ( aDimensionOf0 @ A ) )
| ~ ( aVector0 @ A ) ),
inference(simp,[status(thm)],[101]) ).
thf(1386,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( aNaturalNumber0 @ ( sk1 @ A ) )
| ~ ( sdtlseqdt0 @ sz00 @ xN )
| ( xA != xP )
| ( A != xF ) ),
inference(paramod_ordered,[status(thm)],[65,1381]) ).
thf(1387,plain,
( ~ ( aNaturalNumber0 @ xF )
| ( aNaturalNumber0 @ ( sk1 @ xF ) )
| ~ ( sdtlseqdt0 @ sz00 @ xN )
| ( xA != xP ) ),
inference(pattern_uni,[status(thm)],[1386:[bind(A,$thf( xF ))]]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B )
& ( aScalar0 @ C ) )
=> ( ( ( sdtpldt0 @ ( sdtpldt0 @ A @ B ) @ C )
= ( sdtpldt0 @ A @ ( sdtpldt0 @ B @ C ) ) )
& ( ( sdtpldt0 @ A @ B )
= ( sdtpldt0 @ B @ A ) )
& ( ( sdtasdt0 @ ( sdtasdt0 @ A @ B ) @ C )
= ( sdtasdt0 @ A @ ( sdtasdt0 @ B @ C ) ) )
& ( ( sdtasdt0 @ A @ B )
= ( sdtasdt0 @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mArith) ).
thf(160,plain,
! [A: $i,B: $i,C: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B )
& ( aScalar0 @ C ) )
=> ( ( ( sdtpldt0 @ ( sdtpldt0 @ A @ B ) @ C )
= ( sdtpldt0 @ A @ ( sdtpldt0 @ B @ C ) ) )
& ( ( sdtpldt0 @ A @ B )
= ( sdtpldt0 @ B @ A ) )
& ( ( sdtasdt0 @ ( sdtasdt0 @ A @ B ) @ C )
= ( sdtasdt0 @ A @ ( sdtasdt0 @ B @ C ) ) )
& ( ( sdtasdt0 @ A @ B )
= ( sdtasdt0 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( ( aVector0 @ A )
& ( aVector0 @ B ) )
=> ( ( ( ( aDimensionOf0 @ A )
= ( aDimensionOf0 @ B ) )
& ( ( aDimensionOf0 @ B )
= sz00 ) )
=> ( ( sdtasasdt0 @ A @ B )
= sz0z00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSPZ) ).
thf(135,plain,
! [A: $i,B: $i] :
( ( ( aVector0 @ A )
& ( aVector0 @ B ) )
=> ( ( ( ( aDimensionOf0 @ A )
= ( aDimensionOf0 @ B ) )
& ( ( aDimensionOf0 @ B )
= sz00 ) )
=> ( ( sdtasasdt0 @ A @ B )
= sz0z00 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(136,plain,
! [B: $i,A: $i] :
( ~ ( aVector0 @ A )
| ~ ( aVector0 @ B )
| ( ( aDimensionOf0 @ A )
!= ( aDimensionOf0 @ B ) )
| ( ( aDimensionOf0 @ B )
!= sz00 )
| ( ( sdtasasdt0 @ A @ B )
= sz0z00 ) ),
inference(cnf,[status(esa)],[135]) ).
thf(137,plain,
! [B: $i,A: $i] :
( ( ( aDimensionOf0 @ A )
!= ( aDimensionOf0 @ B ) )
| ( ( aDimensionOf0 @ B )
!= sz00 )
| ( ( sdtasasdt0 @ A @ B )
= sz0z00 )
| ~ ( aVector0 @ A )
| ~ ( aVector0 @ B ) ),
inference(lifteq,[status(thm)],[136]) ).
thf(35,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B )
& ( aScalar0 @ C )
& ( aScalar0 @ D ) )
=> ( ( ( sdtlseqdt0 @ A @ B )
& ( sdtlseqdt0 @ sz0z00 @ C )
& ( sdtlseqdt0 @ C @ D ) )
=> ( sdtlseqdt0 @ ( sdtasdt0 @ A @ C ) @ ( sdtasdt0 @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLEMonM) ).
thf(177,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B )
& ( aScalar0 @ C )
& ( aScalar0 @ D ) )
=> ( ( ( sdtlseqdt0 @ A @ B )
& ( sdtlseqdt0 @ sz0z00 @ C )
& ( sdtlseqdt0 @ C @ D ) )
=> ( sdtlseqdt0 @ ( sdtasdt0 @ A @ C ) @ ( sdtasdt0 @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(178,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( aScalar0 @ A )
| ~ ( aScalar0 @ B )
| ~ ( aScalar0 @ C )
| ~ ( aScalar0 @ D )
| ~ ( sdtlseqdt0 @ A @ B )
| ~ ( sdtlseqdt0 @ sz0z00 @ C )
| ~ ( sdtlseqdt0 @ C @ D )
| ( sdtlseqdt0 @ ( sdtasdt0 @ A @ C ) @ ( sdtasdt0 @ B @ D ) ) ),
inference(cnf,[status(esa)],[177]) ).
thf(447,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( aScalar0 @ A )
| ~ ( aScalar0 @ B )
| ~ ( aScalar0 @ C )
| ~ ( aScalar0 @ D )
| ~ ( sdtlseqdt0 @ A @ B )
| ~ ( sdtlseqdt0 @ sz0z00 @ C )
| ~ ( sdtlseqdt0 @ C @ D )
| ( ( sdtlseqdt0 @ ( sdtasdt0 @ A @ C ) @ ( sdtasdt0 @ B @ D ) )
!= ( sdtlseqdt0 @ ( sdtasdt0 @ xP @ xP ) @ xN ) ) ),
inference(paramod_ordered,[status(thm)],[178,61]) ).
thf(491,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( aScalar0 @ A )
| ~ ( aScalar0 @ B )
| ~ ( aScalar0 @ C )
| ~ ( aScalar0 @ D )
| ~ ( sdtlseqdt0 @ A @ B )
| ~ ( sdtlseqdt0 @ sz0z00 @ C )
| ~ ( sdtlseqdt0 @ C @ D )
| ( ( sdtasdt0 @ A @ C )
!= ( sdtasdt0 @ xP @ xP ) )
| ( ( sdtasdt0 @ B @ D )
!= xN ) ),
inference(simp,[status(thm)],[447]) ).
thf(531,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( aScalar0 @ A )
| ~ ( aScalar0 @ B )
| ~ ( aScalar0 @ C )
| ~ ( aScalar0 @ D )
| ~ ( sdtlseqdt0 @ A @ B )
| ~ ( sdtlseqdt0 @ sz0z00 @ C )
| ~ ( sdtlseqdt0 @ C @ D )
| ( A != xP )
| ( C != xP )
| ( ( sdtasdt0 @ B @ D )
!= xN ) ),
inference(simp,[status(thm)],[491]) ).
thf(652,plain,
! [B: $i,A: $i] :
( ~ ( aScalar0 @ xP )
| ~ ( aScalar0 @ A )
| ~ ( aScalar0 @ xP )
| ~ ( aScalar0 @ B )
| ~ ( sdtlseqdt0 @ xP @ A )
| ~ ( sdtlseqdt0 @ sz0z00 @ xP )
| ~ ( sdtlseqdt0 @ xP @ B )
| ( ( sdtasdt0 @ A @ B )
!= xN ) ),
inference(simp,[status(thm)],[531]) ).
thf(824,plain,
! [B: $i,A: $i] :
( ~ ( aScalar0 @ xP )
| ~ ( aScalar0 @ A )
| ~ ( aScalar0 @ B )
| ~ ( sdtlseqdt0 @ xP @ A )
| ~ ( sdtlseqdt0 @ sz0z00 @ xP )
| ~ ( sdtlseqdt0 @ xP @ B )
| ( ( sdtasdt0 @ A @ B )
!= xN ) ),
inference(simp,[status(thm)],[652]) ).
thf(825,plain,
! [B: $i,A: $i] :
( ~ $true
| ~ ( aScalar0 @ A )
| ~ ( aScalar0 @ B )
| ~ ( sdtlseqdt0 @ xP @ A )
| ~ ( sdtlseqdt0 @ sz0z00 @ xP )
| ~ ( sdtlseqdt0 @ xP @ B )
| ( ( sdtasdt0 @ A @ B )
!= xN ) ),
inference(rewrite,[status(thm)],[824,257]) ).
thf(826,plain,
! [B: $i,A: $i] :
( ~ ( aScalar0 @ A )
| ~ ( aScalar0 @ B )
| ~ ( sdtlseqdt0 @ xP @ A )
| ~ ( sdtlseqdt0 @ sz0z00 @ xP )
| ~ ( sdtlseqdt0 @ xP @ B )
| ( ( sdtasdt0 @ A @ B )
!= xN ) ),
inference(simp,[status(thm)],[825]) ).
thf(1323,plain,
! [B: $i,A: $i] :
( ~ ( aScalar0 @ A )
| ~ ( aScalar0 @ B )
| ~ ( sdtlseqdt0 @ xP @ A )
| ~ ( sdtlseqdt0 @ sz0z00 @ xP )
| ~ ( sdtlseqdt0 @ xP @ B )
| ( xF != xN )
| ( ( sdtasdt0 @ xA @ xA )
!= ( sdtasdt0 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[225,826]) ).
thf(1324,plain,
( ~ ( aScalar0 @ xA )
| ~ ( aScalar0 @ xA )
| ~ ( sdtlseqdt0 @ xP @ xA )
| ~ ( sdtlseqdt0 @ sz0z00 @ xP )
| ~ ( sdtlseqdt0 @ xP @ xA )
| ( xF != xN ) ),
inference(pattern_uni,[status(thm)],[1323:[bind(A,$thf( xA )),bind(B,$thf( xA ))]]) ).
thf(1382,plain,
( ~ ( aScalar0 @ xA )
| ~ ( sdtlseqdt0 @ xP @ xA )
| ~ ( sdtlseqdt0 @ sz0z00 @ xP )
| ( xF != xN ) ),
inference(simp,[status(thm)],[1324]) ).
thf(81,plain,
aScalar0 @ xA,
inference(cnf,[status(esa)],[79]) ).
thf(3470,plain,
( ~ $true
| ~ ( sdtlseqdt0 @ xP @ xA )
| ~ ( sdtlseqdt0 @ sz0z00 @ xP )
| ( xF != xN ) ),
inference(rewrite,[status(thm)],[1382,81]) ).
thf(3471,plain,
( ~ ( sdtlseqdt0 @ xP @ xA )
| ~ ( sdtlseqdt0 @ sz0z00 @ xP )
| ( xF != xN ) ),
inference(simp,[status(thm)],[3470]) ).
thf(52,axiom,
! [A: $i] :
( ( aScalar0 @ A )
=> ( ( ( sdtpldt0 @ A @ sz0z00 )
= A )
& ( ( sdtpldt0 @ sz0z00 @ A )
= A )
& ( ( sdtasdt0 @ A @ sz0z00 )
= sz0z00 )
& ( ( sdtasdt0 @ sz0z00 @ A )
= sz0z00 )
& ( ( sdtpldt0 @ A @ ( smndt0 @ A ) )
= sz0z00 )
& ( ( sdtpldt0 @ ( smndt0 @ A ) @ A )
= sz0z00 )
& ( ( smndt0 @ ( smndt0 @ A ) )
= A )
& ( ( smndt0 @ sz0z00 )
= sz0z00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mScZero) ).
thf(229,plain,
! [A: $i] :
( ( aScalar0 @ A )
=> ( ( ( sdtpldt0 @ A @ sz0z00 )
= A )
& ( ( sdtpldt0 @ sz0z00 @ A )
= A )
& ( ( sdtasdt0 @ A @ sz0z00 )
= sz0z00 )
& ( ( sdtasdt0 @ sz0z00 @ A )
= sz0z00 )
& ( ( sdtpldt0 @ A @ ( smndt0 @ A ) )
= sz0z00 )
& ( ( sdtpldt0 @ ( smndt0 @ A ) @ A )
= sz0z00 )
& ( ( smndt0 @ ( smndt0 @ A ) )
= A )
& ( ( smndt0 @ sz0z00 )
= sz0z00 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(41,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B )
& ( aScalar0 @ C ) )
=> ( ( ( sdtasdt0 @ A @ ( sdtpldt0 @ B @ C ) )
= ( sdtpldt0 @ ( sdtasdt0 @ A @ B ) @ ( sdtasdt0 @ A @ C ) ) )
& ( ( sdtasdt0 @ ( sdtpldt0 @ A @ B ) @ C )
= ( sdtpldt0 @ ( sdtasdt0 @ A @ C ) @ ( sdtasdt0 @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDistr) ).
thf(197,plain,
! [A: $i,B: $i,C: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B )
& ( aScalar0 @ C ) )
=> ( ( ( sdtasdt0 @ A @ ( sdtpldt0 @ B @ C ) )
= ( sdtpldt0 @ ( sdtasdt0 @ A @ B ) @ ( sdtasdt0 @ A @ C ) ) )
& ( ( sdtasdt0 @ ( sdtpldt0 @ A @ B ) @ C )
= ( sdtpldt0 @ ( sdtasdt0 @ A @ C ) @ ( sdtasdt0 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(4946,plain,
! [A: $i] :
( ( ( szszuzczcdt0 @ A )
!= sz00 )
| ( ( aNaturalNumber0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ) ) ) ) ) ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3883,73]) ).
thf(4947,plain,
( ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ) ) ) ) ) ) )
!= sz00 ),
inference(pattern_uni,[status(thm)],[4946:[bind(A,$thf( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ) ) ) ) ) ))]]) ).
thf(224,plain,
aScalar0 @ xF,
inference(cnf,[status(esa)],[222]) ).
thf(91,plain,
! [B: $i,A: $i] :
( ~ ( aVector0 @ A )
| ( ( aDimensionOf0 @ A )
= sz00 )
| ( B
!= ( sziznziztdt0 @ A ) )
| ( aVector0 @ B ) ),
inference(cnf,[status(esa)],[87]) ).
thf(99,plain,
! [B: $i,A: $i] :
( ( ( aDimensionOf0 @ A )
= sz00 )
| ( B
!= ( sziznziztdt0 @ A ) )
| ~ ( aVector0 @ A )
| ( aVector0 @ B ) ),
inference(lifteq,[status(thm)],[91]) ).
thf(100,plain,
! [A: $i] :
( ( ( aDimensionOf0 @ A )
= sz00 )
| ~ ( aVector0 @ A )
| ( aVector0 @ ( sziznziztdt0 @ A ) ) ),
inference(simp,[status(thm)],[99]) ).
thf(4191,plain,
! [A: $i] :
( ( ( aDimensionOf0 @ A )
= sz00 )
| ( aVector0 @ ( sziznziztdt0 @ A ) )
| ( ( aVector0 @ xq )
!= ( aVector0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[120,100]) ).
thf(4192,plain,
( ( ( aDimensionOf0 @ xq )
= sz00 )
| ( aVector0 @ ( sziznziztdt0 @ xq ) ) ),
inference(pattern_uni,[status(thm)],[4191:[bind(A,$thf( xq ))]]) ).
thf(6142,plain,
! [A: $i] :
( ( ( sdtlbdtrb0 @ xq @ A )
= ( sdtlbdtrb0 @ xt @ A ) )
| ( ( aNaturalNumber0 @ ( sk1 @ ( szszuzczcdt0 @ sz00 ) ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2108,122]) ).
thf(6143,plain,
( ( sdtlbdtrb0 @ xq @ ( sk1 @ ( szszuzczcdt0 @ sz00 ) ) )
= ( sdtlbdtrb0 @ xt @ ( sk1 @ ( szszuzczcdt0 @ sz00 ) ) ) ),
inference(pattern_uni,[status(thm)],[6142:[bind(A,$thf( sk1 @ ( szszuzczcdt0 @ sz00 ) ))]]) ).
thf(829,plain,
! [B: $i,A: $i] :
( ~ ( aScalar0 @ A )
| ~ ( sdtlseqdt0 @ xP @ A )
| ~ ( sdtlseqdt0 @ sz0z00 @ xP )
| ~ ( sdtlseqdt0 @ xP @ B )
| ( ( sdtasdt0 @ A @ B )
!= xN )
| ( ( aScalar0 @ xP )
!= ( aScalar0 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[257,826]) ).
thf(830,plain,
! [A: $i] :
( ~ ( aScalar0 @ A )
| ~ ( sdtlseqdt0 @ xP @ A )
| ~ ( sdtlseqdt0 @ sz0z00 @ xP )
| ~ ( sdtlseqdt0 @ xP @ xP )
| ( ( sdtasdt0 @ A @ xP )
!= xN ) ),
inference(pattern_uni,[status(thm)],[829:[bind(A,$thf( A )),bind(B,$thf( xP ))]]) ).
thf(1782,plain,
( ( aNaturalNumber0 @ ( sk1 @ xN ) )
| ~ ( sdtlseqdt0 @ xG @ sz00 )
| ( xN != sz00 )
| ( ( sdtasdt0 @ xB @ xB )
!= ( sdtasdt0 @ xP @ xP ) ) ),
inference(paramod_ordered,[status(thm)],[264,734]) ).
thf(1786,plain,
( ( aNaturalNumber0 @ ( sk1 @ xN ) )
| ~ ( sdtlseqdt0 @ xG @ sz00 )
| ( xN != sz00 )
| ( xB != xP )
| ( xB != xP ) ),
inference(simp,[status(thm)],[1782]) ).
thf(1794,plain,
( ( aNaturalNumber0 @ ( sk1 @ xN ) )
| ~ ( sdtlseqdt0 @ xG @ sz00 )
| ( xN != sz00 )
| ( xB != xP ) ),
inference(simp,[status(thm)],[1786]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( ( aVector0 @ A )
& ( aVector0 @ B ) )
=> ( ( ( aDimensionOf0 @ A )
= ( aDimensionOf0 @ B ) )
=> ( aScalar0 @ ( sdtasasdt0 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mScPr) ).
thf(156,plain,
! [A: $i,B: $i] :
( ( ( aVector0 @ A )
& ( aVector0 @ B ) )
=> ( ( ( aDimensionOf0 @ A )
= ( aDimensionOf0 @ B ) )
=> ( aScalar0 @ ( sdtasasdt0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(1499,plain,
! [B: $i,A: $i] :
( ~ ( aScalar0 @ A )
| ~ ( aScalar0 @ B )
| ~ ( sdtlseqdt0 @ xP @ A )
| ~ ( sdtlseqdt0 @ sz0z00 @ xP )
| ~ ( sdtlseqdt0 @ xP @ B )
| ( xG != xN )
| ( ( sdtasdt0 @ xB @ xB )
!= ( sdtasdt0 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[264,826]) ).
thf(1500,plain,
( ~ ( aScalar0 @ xB )
| ~ ( aScalar0 @ xB )
| ~ ( sdtlseqdt0 @ xP @ xB )
| ~ ( sdtlseqdt0 @ sz0z00 @ xP )
| ~ ( sdtlseqdt0 @ xP @ xB )
| ( xG != xN ) ),
inference(pattern_uni,[status(thm)],[1499:[bind(A,$thf( xB )),bind(B,$thf( xB ))]]) ).
thf(1566,plain,
( ~ ( aScalar0 @ xB )
| ~ ( sdtlseqdt0 @ xP @ xB )
| ~ ( sdtlseqdt0 @ sz0z00 @ xP )
| ( xG != xN ) ),
inference(simp,[status(thm)],[1500]) ).
thf(77,plain,
aScalar0 @ xB,
inference(cnf,[status(esa)],[75]) ).
thf(5614,plain,
( ~ $true
| ~ ( sdtlseqdt0 @ xP @ xB )
| ~ ( sdtlseqdt0 @ sz0z00 @ xP )
| ( xG != xN ) ),
inference(rewrite,[status(thm)],[1566,77]) ).
thf(5615,plain,
( ~ ( sdtlseqdt0 @ xP @ xB )
| ~ ( sdtlseqdt0 @ sz0z00 @ xP )
| ( xG != xN ) ),
inference(simp,[status(thm)],[5614]) ).
thf(1332,plain,
( ~ ( aNaturalNumber0 @ xP )
| ( aNaturalNumber0 @ ( sk1 @ xP ) )
| ~ ( sdtlseqdt0 @ xF @ xN )
| ( ( sdtasdt0 @ xA @ xA )
!= ( sdtasdt0 @ sz00 @ sz00 ) ) ),
inference(paramod_ordered,[status(thm)],[225,344]) ).
thf(1361,plain,
( ( aNaturalNumber0 @ ( sk1 @ xP ) )
| ~ ( aNaturalNumber0 @ xP )
| ~ ( sdtlseqdt0 @ xF @ xN )
| ( xA != sz00 )
| ( xA != sz00 ) ),
inference(simp,[status(thm)],[1332]) ).
thf(1375,plain,
( ( aNaturalNumber0 @ ( sk1 @ xP ) )
| ~ ( aNaturalNumber0 @ xP )
| ~ ( sdtlseqdt0 @ xF @ xN )
| ( xA != sz00 ) ),
inference(simp,[status(thm)],[1361]) ).
thf(64,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( A = sz00 )
| ( A
= ( szszuzczcdt0 @ ( sk1 @ A ) ) ) ),
inference(cnf,[status(esa)],[62]) ).
thf(66,plain,
! [A: $i] :
( ( A = sz00 )
| ( ( szszuzczcdt0 @ ( sk1 @ A ) )
= A )
| ~ ( aNaturalNumber0 @ A ) ),
inference(lifteq,[status(thm)],[64]) ).
thf(1074,plain,
! [A: $i] :
( ( A = sz00 )
| ( ( szszuzczcdt0 @ ( sk1 @ A ) )
= A )
| ( ( aNaturalNumber0 @ ( szszuzczcdt0 @ sz00 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1036,66]) ).
thf(1075,plain,
( ( ( szszuzczcdt0 @ sz00 )
= sz00 )
| ( ( szszuzczcdt0 @ ( sk1 @ ( szszuzczcdt0 @ sz00 ) ) )
= ( szszuzczcdt0 @ sz00 ) ) ),
inference(pattern_uni,[status(thm)],[1074:[bind(A,$thf( szszuzczcdt0 @ sz00 ))]]) ).
thf(3963,plain,
( ( szszuzczcdt0 @ ( sk1 @ ( szszuzczcdt0 @ sz00 ) ) )
= ( szszuzczcdt0 @ sz00 ) ),
inference(simplifyReflect,[status(thm)],[1075,316]) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B ) )
=> ( aScalar0 @ ( sdtasdt0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulSc) ).
thf(169,plain,
! [A: $i,B: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B ) )
=> ( aScalar0 @ ( sdtasdt0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(139,plain,
( xD
= ( sdtasasdt0 @ xq @ xq ) ),
inference(cnf,[status(esa)],[138]) ).
thf(141,plain,
( ( sdtasasdt0 @ xq @ xq )
= xD ),
inference(lifteq,[status(thm)],[139]) ).
thf(4948,plain,
! [A: $i] :
( ( aNaturalNumber0 @ ( szszuzczcdt0 @ A ) )
| ( ( aNaturalNumber0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ) ) ) ) ) ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3883,71]) ).
thf(4949,plain,
aNaturalNumber0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[4948:[bind(A,$thf( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ) ) ) ) ) ))]]) ).
thf(5232,plain,
! [A: $i] :
( ( ( szszuzczcdt0 @ A )
!= sz00 )
| ( ( aNaturalNumber0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ) ) ) ) ) ) ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4949,73]) ).
thf(5233,plain,
( ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ) ) ) ) ) ) ) )
!= sz00 ),
inference(pattern_uni,[status(thm)],[5232:[bind(A,$thf( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ) ) ) ) ) ) ))]]) ).
thf(105,plain,
( xp
= ( sziznziztdt0 @ xs ) ),
inference(cnf,[status(esa)],[104]) ).
thf(109,plain,
( ( sziznziztdt0 @ xs )
= xp ),
inference(lifteq,[status(thm)],[105]) ).
thf(89,plain,
! [B: $i,A: $i] :
( ~ ( aVector0 @ A )
| ( ( aDimensionOf0 @ A )
= sz00 )
| ~ ( aVector0 @ B )
| ( ( szszuzczcdt0 @ ( aDimensionOf0 @ B ) )
!= ( aDimensionOf0 @ A ) )
| ( aNaturalNumber0 @ ( sk2 @ B @ A ) )
| ( B
= ( sziznziztdt0 @ A ) ) ),
inference(cnf,[status(esa)],[87]) ).
thf(95,plain,
! [B: $i,A: $i] :
( ( ( aDimensionOf0 @ A )
= sz00 )
| ( ( szszuzczcdt0 @ ( aDimensionOf0 @ B ) )
!= ( aDimensionOf0 @ A ) )
| ( B
= ( sziznziztdt0 @ A ) )
| ~ ( aVector0 @ A )
| ~ ( aVector0 @ B )
| ( aNaturalNumber0 @ ( sk2 @ B @ A ) ) ),
inference(lifteq,[status(thm)],[89]) ).
thf(96,plain,
! [B: $i,A: $i] :
( ( ( aDimensionOf0 @ A )
= sz00 )
| ( ( szszuzczcdt0 @ ( aDimensionOf0 @ B ) )
!= ( aDimensionOf0 @ A ) )
| ( B
= ( sziznziztdt0 @ A ) )
| ~ ( aVector0 @ A )
| ~ ( aVector0 @ B )
| ( aNaturalNumber0 @ ( sk2 @ B @ A ) ) ),
inference(simp,[status(thm)],[95]) ).
thf(16,axiom,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> $true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNatSort) ).
thf(124,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(6151,plain,
! [A: $i] :
( ( ( sdtlbdtrb0 @ xq @ A )
= ( sdtlbdtrb0 @ xt @ A ) )
| ( ( aNaturalNumber0 @ sz00 )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[159,122]) ).
thf(6152,plain,
( ( sdtlbdtrb0 @ xq @ sz00 )
= ( sdtlbdtrb0 @ xt @ sz00 ) ),
inference(pattern_uni,[status(thm)],[6151:[bind(A,$thf( sz00 ))]]) ).
thf(126,plain,
( xC
= ( sdtasasdt0 @ xp @ xp ) ),
inference(cnf,[status(esa)],[125]) ).
thf(128,plain,
( ( sdtasasdt0 @ xp @ xp )
= xC ),
inference(lifteq,[status(thm)],[126]) ).
thf(273,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( aNaturalNumber0 @ ( sk1 @ A ) )
| ~ ( sdtlseqdt0 @ ( sdtasdt0 @ xP @ sz00 ) @ xN )
| ( A != xP ) ),
inference(paramod_ordered,[status(thm)],[65,61]) ).
thf(274,plain,
( ~ ( aNaturalNumber0 @ xP )
| ( aNaturalNumber0 @ ( sk1 @ xP ) )
| ~ ( sdtlseqdt0 @ ( sdtasdt0 @ xP @ sz00 ) @ xN ) ),
inference(pattern_uni,[status(thm)],[273:[bind(A,$thf( xP ))]]) ).
thf(358,plain,
( ( aNaturalNumber0 @ ( sk1 @ xP ) )
| ~ ( sdtlseqdt0 @ ( sdtasdt0 @ xP @ sz00 ) @ xN )
| ( ( aNaturalNumber0 @ xP )
!= ( aNaturalNumber0 @ sz00 ) ) ),
inference(paramod_ordered,[status(thm)],[159,274]) ).
thf(360,plain,
( ( aNaturalNumber0 @ ( sk1 @ xP ) )
| ~ ( sdtlseqdt0 @ ( sdtasdt0 @ xP @ sz00 ) @ xN )
| ( xP != sz00 ) ),
inference(simp,[status(thm)],[358]) ).
thf(148,plain,
aVector0 @ xs,
inference(cnf,[status(esa)],[146]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( ( aVector0 @ A )
& ( aVector0 @ B ) )
=> ( ( ( ( aDimensionOf0 @ A )
= ( aDimensionOf0 @ B ) )
& ( ( aDimensionOf0 @ B )
!= sz00 ) )
=> ( ( aDimensionOf0 @ ( sziznziztdt0 @ A ) )
= ( aDimensionOf0 @ ( sziznziztdt0 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEqInit) ).
thf(149,plain,
! [A: $i,B: $i] :
( ( ( aVector0 @ A )
& ( aVector0 @ B ) )
=> ( ( ( ( aDimensionOf0 @ A )
= ( aDimensionOf0 @ B ) )
& ( ( aDimensionOf0 @ B )
!= sz00 ) )
=> ( ( aDimensionOf0 @ ( sziznziztdt0 @ A ) )
= ( aDimensionOf0 @ ( sziznziztdt0 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(39,axiom,
! [A: $i] :
( ( aScalar0 @ A )
=> ( sdtlseqdt0 @ sz0z00 @ ( sdtasdt0 @ A @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSqPos) ).
thf(191,plain,
! [A: $i] :
( ( aScalar0 @ A )
=> ( sdtlseqdt0 @ sz0z00 @ ( sdtasdt0 @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B )
& ( aScalar0 @ C )
& ( aScalar0 @ D ) )
=> ( ( sdtasdt0 @ ( sdtpldt0 @ A @ B ) @ ( sdtpldt0 @ C @ D ) )
= ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ A @ C ) @ ( sdtasdt0 @ A @ D ) ) @ ( sdtpldt0 @ ( sdtasdt0 @ B @ C ) @ ( sdtasdt0 @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDistr2) ).
thf(204,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B )
& ( aScalar0 @ C )
& ( aScalar0 @ D ) )
=> ( ( sdtasdt0 @ ( sdtpldt0 @ A @ B ) @ ( sdtpldt0 @ C @ D ) )
= ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ A @ C ) @ ( sdtasdt0 @ A @ D ) ) @ ( sdtpldt0 @ ( sdtasdt0 @ B @ C ) @ ( sdtasdt0 @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(58,axiom,
! [A: $i,B: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B ) )
=> ( ( sdtlseqdt0 @ A @ B )
| ( sdtlseqdt0 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETot) ).
thf(259,plain,
! [A: $i,B: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B ) )
=> ( ( sdtlseqdt0 @ A @ B )
| ( sdtlseqdt0 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(1781,plain,
( ( aNaturalNumber0 @ ( sk1 @ xN ) )
| ~ ( sdtlseqdt0 @ xF @ sz00 )
| ( xN != sz00 )
| ( ( sdtasdt0 @ xA @ xA )
!= ( sdtasdt0 @ xP @ xP ) ) ),
inference(paramod_ordered,[status(thm)],[225,734]) ).
thf(1790,plain,
( ( aNaturalNumber0 @ ( sk1 @ xN ) )
| ~ ( sdtlseqdt0 @ xF @ sz00 )
| ( xN != sz00 )
| ( xA != xP )
| ( xA != xP ) ),
inference(simp,[status(thm)],[1781]) ).
thf(1795,plain,
( ( aNaturalNumber0 @ ( sk1 @ xN ) )
| ~ ( sdtlseqdt0 @ xF @ sz00 )
| ( xN != sz00 )
| ( xA != xP ) ),
inference(simp,[status(thm)],[1790]) ).
thf(1695,plain,
( ( ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( aDimensionOf0 @ xt ) ) )
!= sz00 )
| ( ( szszuzczcdt0 @ ( aDimensionOf0 @ xp ) )
!= ( szszuzczcdt0 @ sz00 ) ) ),
inference(paramod_ordered,[status(thm)],[1603,1588]) ).
thf(1701,plain,
( ( ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( aDimensionOf0 @ xt ) ) )
!= sz00 )
| ( ( aDimensionOf0 @ xp )
!= sz00 ) ),
inference(simp,[status(thm)],[1695]) ).
thf(24,axiom,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( iLess0 @ A @ ( szszuzczcdt0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIH) ).
thf(144,plain,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( iLess0 @ A @ ( szszuzczcdt0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(3418,plain,
! [A: $i] :
( ( ( szszuzczcdt0 @ A )
!= sz00 )
| ( ( aNaturalNumber0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ) ) ) ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2455,73]) ).
thf(3419,plain,
( ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ) ) ) ) )
!= sz00 ),
inference(pattern_uni,[status(thm)],[3418:[bind(A,$thf( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ) ) ) ))]]) ).
thf(92,plain,
! [B: $i,A: $i] :
( ~ ( aVector0 @ A )
| ( ( aDimensionOf0 @ A )
= sz00 )
| ~ ( aVector0 @ B )
| ( ( szszuzczcdt0 @ ( aDimensionOf0 @ B ) )
!= ( aDimensionOf0 @ A ) )
| ( ( sdtlbdtrb0 @ B @ ( sk2 @ B @ A ) )
!= ( sdtlbdtrb0 @ A @ ( sk2 @ B @ A ) ) )
| ( B
= ( sziznziztdt0 @ A ) ) ),
inference(cnf,[status(esa)],[87]) ).
thf(97,plain,
! [B: $i,A: $i] :
( ( ( aDimensionOf0 @ A )
= sz00 )
| ( ( szszuzczcdt0 @ ( aDimensionOf0 @ B ) )
!= ( aDimensionOf0 @ A ) )
| ( ( sdtlbdtrb0 @ B @ ( sk2 @ B @ A ) )
!= ( sdtlbdtrb0 @ A @ ( sk2 @ B @ A ) ) )
| ( B
= ( sziznziztdt0 @ A ) )
| ~ ( aVector0 @ A )
| ~ ( aVector0 @ B ) ),
inference(lifteq,[status(thm)],[92]) ).
thf(98,plain,
! [B: $i,A: $i] :
( ( ( aDimensionOf0 @ A )
= sz00 )
| ( ( szszuzczcdt0 @ ( aDimensionOf0 @ B ) )
!= ( aDimensionOf0 @ A ) )
| ( ( sdtlbdtrb0 @ B @ ( sk2 @ B @ A ) )
!= ( sdtlbdtrb0 @ A @ ( sk2 @ B @ A ) ) )
| ( B
= ( sziznziztdt0 @ A ) )
| ~ ( aVector0 @ A )
| ~ ( aVector0 @ B ) ),
inference(simp,[status(thm)],[97]) ).
thf(44,axiom,
( xN
= ( sdtasdt0 @ ( sdtasdt0 @ xH @ xH ) @ ( sdtasdt0 @ xC @ xD ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2052) ).
thf(207,plain,
( xN
= ( sdtasdt0 @ ( sdtasdt0 @ xH @ xH ) @ ( sdtasdt0 @ xC @ xD ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(208,plain,
( ( sdtasdt0 @ ( sdtasdt0 @ xH @ xH ) @ ( sdtasdt0 @ xC @ xD ) )
= xN ),
inference(lifteq,[status(thm)],[207]) ).
thf(12,axiom,
! [A: $i] :
( ( aScalar0 @ A )
=> $true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mScSort) ).
thf(103,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(55,axiom,
! [A: $i,B: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B ) )
=> ( ( ( sdtlseqdt0 @ sz0z00 @ A )
& ( sdtlseqdt0 @ sz0z00 @ B )
& ( ( sdtasdt0 @ A @ A )
= ( sdtasdt0 @ B @ B ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSqrt) ).
thf(251,plain,
! [A: $i,B: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B ) )
=> ( ( ( sdtlseqdt0 @ sz0z00 @ A )
& ( sdtlseqdt0 @ sz0z00 @ B )
& ( ( sdtasdt0 @ A @ A )
= ( sdtasdt0 @ B @ B ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(108,plain,
aVector0 @ xp,
inference(cnf,[status(esa)],[104]) ).
thf(140,plain,
aScalar0 @ xD,
inference(cnf,[status(esa)],[138]) ).
thf(1682,plain,
( ( ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( aDimensionOf0 @ xt ) ) )
!= sz00 )
| ( ( szszuzczcdt0 @ ( aDimensionOf0 @ xq ) )
!= ( szszuzczcdt0 @ sz00 ) ) ),
inference(paramod_ordered,[status(thm)],[123,1588]) ).
thf(1699,plain,
( ( ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( aDimensionOf0 @ xt ) ) )
!= sz00 )
| ( ( aDimensionOf0 @ xq )
!= sz00 ) ),
inference(simp,[status(thm)],[1682]) ).
thf(50,axiom,
sdtlseqdt0 @ ( sdtasdt0 @ xE @ xE ) @ ( sdtasdt0 @ xC @ xD ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1967) ).
thf(226,plain,
sdtlseqdt0 @ ( sdtasdt0 @ xE @ xE ) @ ( sdtasdt0 @ xC @ xD ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(3880,plain,
! [A: $i] :
( ( ( szszuzczcdt0 @ A )
!= sz00 )
| ( ( aNaturalNumber0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ) ) ) ) ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3421,73]) ).
thf(3881,plain,
( ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ) ) ) ) ) )
!= sz00 ),
inference(pattern_uni,[status(thm)],[3880:[bind(A,$thf( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ) ) ) ) ))]]) ).
thf(45,axiom,
! [A: $i,B: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B ) )
=> ( ( sdtasdt0 @ ( smndt0 @ A ) @ ( smndt0 @ B ) )
= ( sdtasdt0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMDNeg) ).
thf(209,plain,
! [A: $i,B: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B ) )
=> ( ( sdtasdt0 @ ( smndt0 @ A ) @ ( smndt0 @ B ) )
= ( sdtasdt0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(4565,plain,
( ( aVector0 @ ( sziznziztdt0 @ xq ) )
| ( ( szszuzczcdt0 @ sz00 )
= ( aDimensionOf0 @ xt ) )
| ( ( aDimensionOf0 @ xq )
!= ( aDimensionOf0 @ xq ) ) ),
inference(paramod_ordered,[status(thm)],[4192,123]) ).
thf(4566,plain,
( ( aVector0 @ ( sziznziztdt0 @ xq ) )
| ( ( szszuzczcdt0 @ sz00 )
= ( aDimensionOf0 @ xt ) ) ),
inference(pattern_uni,[status(thm)],[4565:[]]) ).
thf(6114,plain,
! [A: $i] :
( ( ( sdtlbdtrb0 @ xq @ A )
= ( sdtlbdtrb0 @ xt @ A ) )
| ( ( aNaturalNumber0 @ ( szszuzczcdt0 @ sz00 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1036,122]) ).
thf(6115,plain,
( ( sdtlbdtrb0 @ xq @ ( szszuzczcdt0 @ sz00 ) )
= ( sdtlbdtrb0 @ xt @ ( szszuzczcdt0 @ sz00 ) ) ),
inference(pattern_uni,[status(thm)],[6114:[bind(A,$thf( szszuzczcdt0 @ sz00 ))]]) ).
thf(915,plain,
! [A: $i] :
( ~ ( sdtlseqdt0 @ xP @ A )
| ~ ( sdtlseqdt0 @ sz0z00 @ xP )
| ~ ( sdtlseqdt0 @ xP @ xP )
| ( ( sdtasdt0 @ A @ xP )
!= xN )
| ( ( aScalar0 @ xP )
!= ( aScalar0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[257,830]) ).
thf(916,plain,
( ~ ( sdtlseqdt0 @ xP @ xP )
| ~ ( sdtlseqdt0 @ sz0z00 @ xP )
| ~ ( sdtlseqdt0 @ xP @ xP )
| ( ( sdtasdt0 @ xP @ xP )
!= xN ) ),
inference(pattern_uni,[status(thm)],[915:[bind(A,$thf( xP ))]]) ).
thf(968,plain,
( ~ ( sdtlseqdt0 @ xP @ xP )
| ~ ( sdtlseqdt0 @ sz0z00 @ xP )
| ( ( sdtasdt0 @ xP @ xP )
!= xN ) ),
inference(simp,[status(thm)],[916]) ).
thf(263,plain,
aScalar0 @ xG,
inference(cnf,[status(esa)],[261]) ).
thf(5683,plain,
! [A: $i] :
( ( ( sdtlbdtrb0 @ xp @ A )
= ( sdtlbdtrb0 @ xs @ A ) )
| ( ( aNaturalNumber0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1590,110]) ).
thf(5684,plain,
( ( sdtlbdtrb0 @ xp @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ) )
= ( sdtlbdtrb0 @ xs @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ) ) ),
inference(pattern_uni,[status(thm)],[5683:[bind(A,$thf( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ))]]) ).
thf(5234,plain,
! [A: $i] :
( ( aNaturalNumber0 @ ( szszuzczcdt0 @ A ) )
| ( ( aNaturalNumber0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ) ) ) ) ) ) ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4949,71]) ).
thf(5235,plain,
aNaturalNumber0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[5234:[bind(A,$thf( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ) ) ) ) ) ) ))]]) ).
thf(4239,plain,
! [A: $i] :
( ( ( aDimensionOf0 @ A )
= sz00 )
| ( aVector0 @ ( sziznziztdt0 @ A ) )
| ( ( aVector0 @ xp )
!= ( aVector0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[108,100]) ).
thf(4240,plain,
( ( ( aDimensionOf0 @ xp )
= sz00 )
| ( aVector0 @ ( sziznziztdt0 @ xp ) ) ),
inference(pattern_uni,[status(thm)],[4239:[bind(A,$thf( xp ))]]) ).
thf(127,plain,
aScalar0 @ xC,
inference(cnf,[status(esa)],[125]) ).
thf(6124,plain,
! [A: $i] :
( ( ( sdtlbdtrb0 @ xq @ A )
= ( sdtlbdtrb0 @ xt @ A ) )
| ( ( aNaturalNumber0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1072,122]) ).
thf(6125,plain,
( ( sdtlbdtrb0 @ xq @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) )
= ( sdtlbdtrb0 @ xt @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ) ),
inference(pattern_uni,[status(thm)],[6124:[bind(A,$thf( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ))]]) ).
thf(1694,plain,
( ( ( szszuzczcdt0 @ ( aDimensionOf0 @ xt ) )
!= sz00 )
| ( ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) )
!= ( szszuzczcdt0 @ ( aDimensionOf0 @ xp ) ) ) ),
inference(paramod_ordered,[status(thm)],[1603,1588]) ).
thf(1702,plain,
( ( ( szszuzczcdt0 @ ( aDimensionOf0 @ xt ) )
!= sz00 )
| ( ( szszuzczcdt0 @ sz00 )
!= ( aDimensionOf0 @ xp ) ) ),
inference(simp,[status(thm)],[1694]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B ) )
=> ( aScalar0 @ ( sdtpldt0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSumSc) ).
thf(154,plain,
! [A: $i,B: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B ) )
=> ( aScalar0 @ ( sdtpldt0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(5652,plain,
! [A: $i] :
( ( ( sdtlbdtrb0 @ xp @ A )
= ( sdtlbdtrb0 @ xs @ A ) )
| ( ( aNaturalNumber0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1072,110]) ).
thf(5653,plain,
( ( sdtlbdtrb0 @ xp @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) )
= ( sdtlbdtrb0 @ xs @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ) ),
inference(pattern_uni,[status(thm)],[5652:[bind(A,$thf( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ))]]) ).
thf(1673,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( aNaturalNumber0 @ ( sk1 @ A ) )
| ~ ( sdtlseqdt0 @ sz00 @ xN )
| ( xB != xP )
| ( A != xG ) ),
inference(paramod_ordered,[status(thm)],[65,1559]) ).
thf(1674,plain,
( ~ ( aNaturalNumber0 @ xG )
| ( aNaturalNumber0 @ ( sk1 @ xG ) )
| ~ ( sdtlseqdt0 @ sz00 @ xN )
| ( xB != xP ) ),
inference(pattern_uni,[status(thm)],[1673:[bind(A,$thf( xG ))]]) ).
thf(114,plain,
aScalar0 @ xE,
inference(cnf,[status(esa)],[112]) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ( ( aVector0 @ A )
& ( aVector0 @ B ) )
=> ( ( ( ( aDimensionOf0 @ A )
= ( aDimensionOf0 @ B ) )
& ( ( aDimensionOf0 @ B )
!= sz00 ) )
=> ( ( sdtasasdt0 @ A @ B )
= ( sdtpldt0 @ ( sdtasasdt0 @ ( sziznziztdt0 @ A ) @ ( sziznziztdt0 @ B ) ) @ ( sdtasdt0 @ ( sdtlbdtrb0 @ A @ ( aDimensionOf0 @ A ) ) @ ( sdtlbdtrb0 @ B @ ( aDimensionOf0 @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSPN) ).
thf(171,plain,
! [A: $i,B: $i] :
( ( ( aVector0 @ A )
& ( aVector0 @ B ) )
=> ( ( ( ( aDimensionOf0 @ A )
= ( aDimensionOf0 @ B ) )
& ( ( aDimensionOf0 @ B )
!= sz00 ) )
=> ( ( sdtasasdt0 @ A @ B )
= ( sdtpldt0 @ ( sdtasasdt0 @ ( sziznziztdt0 @ A ) @ ( sziznziztdt0 @ B ) ) @ ( sdtasdt0 @ ( sdtlbdtrb0 @ A @ ( aDimensionOf0 @ A ) ) @ ( sdtlbdtrb0 @ B @ ( aDimensionOf0 @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(1507,plain,
( ~ ( aNaturalNumber0 @ xN )
| ( aNaturalNumber0 @ ( sk1 @ xN ) )
| ~ ( sdtlseqdt0 @ xG @ sz00 )
| ( ( sdtasdt0 @ xB @ xB )
!= ( sdtasdt0 @ xP @ xP ) ) ),
inference(paramod_ordered,[status(thm)],[264,276]) ).
thf(1537,plain,
( ( aNaturalNumber0 @ ( sk1 @ xN ) )
| ~ ( aNaturalNumber0 @ xN )
| ~ ( sdtlseqdt0 @ xG @ sz00 )
| ( xB != xP )
| ( xB != xP ) ),
inference(simp,[status(thm)],[1507]) ).
thf(1558,plain,
( ( aNaturalNumber0 @ ( sk1 @ xN ) )
| ~ ( aNaturalNumber0 @ xN )
| ~ ( sdtlseqdt0 @ xG @ sz00 )
| ( xB != xP ) ),
inference(simp,[status(thm)],[1537]) ).
thf(53,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B )
& ( aScalar0 @ C )
& ( aScalar0 @ D ) )
=> ( ( ( sdtlseqdt0 @ A @ B )
& ( sdtlseqdt0 @ C @ D ) )
=> ( sdtlseqdt0 @ ( sdtpldt0 @ A @ C ) @ ( sdtpldt0 @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLEMon) ).
thf(246,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B )
& ( aScalar0 @ C )
& ( aScalar0 @ D ) )
=> ( ( ( sdtlseqdt0 @ A @ B )
& ( sdtlseqdt0 @ C @ D ) )
=> ( sdtlseqdt0 @ ( sdtpldt0 @ A @ C ) @ ( sdtpldt0 @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(1192,plain,
( ~ ( sdtlseqdt0 @ xS @ xN )
| ( ( sdtasdt0 @ xF @ xD )
!= ( sdtasdt0 @ xP @ xP ) ) ),
inference(paramod_ordered,[status(thm)],[196,61]) ).
thf(1212,plain,
( ~ ( sdtlseqdt0 @ xS @ xN )
| ( xF != xP )
| ( xD != xP ) ),
inference(simp,[status(thm)],[1192]) ).
thf(2128,plain,
! [A: $i] :
( ( ( szszuzczcdt0 @ A )
!= sz00 )
| ( ( aNaturalNumber0 @ ( sk1 @ ( szszuzczcdt0 @ sz00 ) ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2108,73]) ).
thf(2129,plain,
( ( szszuzczcdt0 @ ( sk1 @ ( szszuzczcdt0 @ sz00 ) ) )
!= sz00 ),
inference(pattern_uni,[status(thm)],[2128:[bind(A,$thf( sk1 @ ( szszuzczcdt0 @ sz00 ) ))]]) ).
thf(2292,plain,
( ( ( szszuzczcdt0 @ ( sk1 @ ( aDimensionOf0 @ xt ) ) )
!= sz00 )
| ( ( szszuzczcdt0 @ ( aDimensionOf0 @ xq ) )
!= ( szszuzczcdt0 @ sz00 ) ) ),
inference(paramod_ordered,[status(thm)],[123,2129]) ).
thf(2294,plain,
( ( ( szszuzczcdt0 @ ( sk1 @ ( aDimensionOf0 @ xt ) ) )
!= sz00 )
| ( ( aDimensionOf0 @ xq )
!= sz00 ) ),
inference(simp,[status(thm)],[2292]) ).
thf(214,plain,
aScalar0 @ xN,
inference(cnf,[status(esa)],[212]) ).
thf(1677,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( aNaturalNumber0 @ ( sk1 @ A ) )
| ~ ( sdtlseqdt0 @ xG @ xN )
| ( xP != sz00 )
| ( A != xB ) ),
inference(paramod_ordered,[status(thm)],[65,1559]) ).
thf(1678,plain,
( ~ ( aNaturalNumber0 @ xB )
| ( aNaturalNumber0 @ ( sk1 @ xB ) )
| ~ ( sdtlseqdt0 @ xG @ xN )
| ( xP != sz00 ) ),
inference(pattern_uni,[status(thm)],[1677:[bind(A,$thf( xB ))]]) ).
thf(340,plain,
( ( aNaturalNumber0 @ ( sk1 @ xP ) )
| ~ ( sdtlseqdt0 @ ( sdtasdt0 @ sz00 @ xP ) @ xN )
| ( ( aNaturalNumber0 @ xP )
!= ( aNaturalNumber0 @ sz00 ) ) ),
inference(paramod_ordered,[status(thm)],[159,272]) ).
thf(341,plain,
( ( aNaturalNumber0 @ ( sk1 @ xP ) )
| ~ ( sdtlseqdt0 @ ( sdtasdt0 @ sz00 @ xP ) @ xN )
| ( xP != sz00 ) ),
inference(simp,[status(thm)],[340]) ).
thf(195,plain,
aScalar0 @ xS,
inference(cnf,[status(esa)],[193]) ).
thf(88,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( aVector0 @ A )
| ( ( aDimensionOf0 @ A )
= sz00 )
| ( B
!= ( sziznziztdt0 @ A ) )
| ~ ( aNaturalNumber0 @ C )
| ( ( sdtlbdtrb0 @ B @ C )
= ( sdtlbdtrb0 @ A @ C ) ) ),
inference(cnf,[status(esa)],[87]) ).
thf(93,plain,
! [C: $i,B: $i,A: $i] :
( ( ( aDimensionOf0 @ A )
= sz00 )
| ( B
!= ( sziznziztdt0 @ A ) )
| ( ( sdtlbdtrb0 @ B @ C )
= ( sdtlbdtrb0 @ A @ C ) )
| ~ ( aVector0 @ A )
| ~ ( aNaturalNumber0 @ C ) ),
inference(lifteq,[status(thm)],[88]) ).
thf(94,plain,
! [B: $i,A: $i] :
( ( ( aDimensionOf0 @ A )
= sz00 )
| ( ( sdtlbdtrb0 @ ( sziznziztdt0 @ A ) @ B )
= ( sdtlbdtrb0 @ A @ B ) )
| ~ ( aVector0 @ A )
| ~ ( aNaturalNumber0 @ B ) ),
inference(simp,[status(thm)],[93]) ).
thf(5635,plain,
( ~ ( sdtlseqdt0 @ xP @ xB )
| ( xG != xN )
| ( ( sdtlseqdt0 @ sz0z00 @ xP )
!= ( sdtlseqdt0 @ xP @ xB ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[5615]) ).
thf(5637,plain,
( ~ ( sdtlseqdt0 @ xP @ xB )
| ( xG != xN )
| ( sz0z00 != xP )
| ( xB != xP ) ),
inference(simp,[status(thm)],[5635]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( iLess0 @ A @ B )
=> $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIHOrd) ).
thf(131,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(3491,plain,
( ~ ( sdtlseqdt0 @ xP @ xA )
| ( xF != xN )
| ( ( sdtlseqdt0 @ sz0z00 @ xP )
!= ( sdtlseqdt0 @ xP @ xA ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[3471]) ).
thf(3494,plain,
( ~ ( sdtlseqdt0 @ xP @ xA )
| ( xF != xN )
| ( sz0z00 != xP )
| ( xA != xP ) ),
inference(simp,[status(thm)],[3491]) ).
thf(9,axiom,
aScalar0 @ sz0z00,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSZeroSc) ).
thf(83,plain,
aScalar0 @ sz0z00,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(1508,plain,
( ~ ( aNaturalNumber0 @ xP )
| ( aNaturalNumber0 @ ( sk1 @ xP ) )
| ~ ( sdtlseqdt0 @ xG @ xN )
| ( ( sdtasdt0 @ xB @ xB )
!= ( sdtasdt0 @ sz00 @ sz00 ) ) ),
inference(paramod_ordered,[status(thm)],[264,344]) ).
thf(1553,plain,
( ( aNaturalNumber0 @ ( sk1 @ xP ) )
| ~ ( aNaturalNumber0 @ xP )
| ~ ( sdtlseqdt0 @ xG @ xN )
| ( xB != sz00 )
| ( xB != sz00 ) ),
inference(simp,[status(thm)],[1508]) ).
thf(1565,plain,
( ( aNaturalNumber0 @ ( sk1 @ xP ) )
| ~ ( aNaturalNumber0 @ xP )
| ~ ( sdtlseqdt0 @ xG @ xN )
| ( xB != sz00 ) ),
inference(simp,[status(thm)],[1553]) ).
thf(2452,plain,
! [A: $i] :
( ( ( szszuzczcdt0 @ A )
!= sz00 )
| ( ( aNaturalNumber0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ) ) ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1926,73]) ).
thf(2453,plain,
( ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ) ) ) )
!= sz00 ),
inference(pattern_uni,[status(thm)],[2452:[bind(A,$thf( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ) ) ))]]) ).
thf(56,axiom,
! [A: $i,B: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B ) )
=> ( ( sdtlseqdt0 @ A @ B )
=> $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLess) ).
thf(254,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(51,axiom,
! [A: $i] :
( ( aVector0 @ A )
=> ( sdtlseqdt0 @ sz0z00 @ ( sdtasasdt0 @ A @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mScSqPos) ).
thf(227,plain,
! [A: $i] :
( ( aVector0 @ A )
=> ( sdtlseqdt0 @ sz0z00 @ ( sdtasasdt0 @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(6960,plain,
! [A: $i] :
( ( ( szszuzczcdt0 @ A )
!= sz00 )
| ( ( aNaturalNumber0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ) ) ) ) ) ) ) ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5235,73]) ).
thf(6961,plain,
( ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ) ) ) ) ) ) ) ) )
!= sz00 ),
inference(pattern_uni,[status(thm)],[6960:[bind(A,$thf( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ) ) ) ) ) ) ) ))]]) ).
thf(259770,plain,
$false,
inference(cvc4,[status(thm)],[69,1665,1036,3883,138,1559,1729,1083,1924,115,6162,120,202,217,276,142,5674,174,1001,1391,1441,257,1482,1254,184,110,196,125,344,189,1704,152,316,78,261,216,179,1632,121,1151,84,147,1377,61,1072,132,116,5665,265,74,5643,3421,734,221,248,85,220,1311,102,1387,160,70,137,3471,229,197,4947,224,4192,65,6143,830,1794,156,5615,1375,3963,169,141,5233,109,77,193,2455,2108,212,96,124,225,1588,129,6152,73,128,360,148,264,149,191,826,204,259,1795,1701,71,144,86,159,187,274,81,3419,1603,98,208,103,66,251,1381,108,1731,140,130,1926,1699,135,226,3881,255,209,112,4566,123,6115,968,1070,263,5684,5235,67,4240,177,127,6125,1702,154,5653,218,104,1590,1674,258,114,171,1558,75,246,207,1212,272,2294,214,1678,146,190,341,79,195,94,5637,131,62,178,3494,83,4949,1565,215,2453,491,222,100,254,227,6961,122]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : RNG057+2 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n017.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu May 18 19:49:16 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.86/0.81 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.31/0.94 % [INFO] Parsing done (137ms).
% 1.31/0.95 % [INFO] Running in sequential loop mode.
% 1.67/1.14 % [INFO] eprover registered as external prover.
% 1.67/1.14 % [INFO] cvc4 registered as external prover.
% 1.67/1.14 % [INFO] Scanning for conjecture ...
% 1.92/1.19 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.92/1.21 % [INFO] Found a conjecture and 58 axioms. Running axiom selection ...
% 2.14/1.26 % [INFO] Axiom selection finished. Selected 58 axioms (removed 0 axioms).
% 2.14/1.27 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.14/1.32 % [INFO] Problem is first-order (TPTP FOF).
% 2.14/1.33 % [INFO] Type checking passed.
% 2.45/1.33 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 231.90/71.84 % External prover 'cvc4' found a proof!
% 231.90/71.84 % [INFO] Killing All external provers ...
% 231.90/71.84 % Time passed: 71332ms (effective reasoning time: 70883ms)
% 231.90/71.84 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 231.90/71.84 % Axioms used in derivation (58): mLERef, mMulSc, mScSort, m__1930, mSqrt, mZeroNat, mIH, m__1766, mLess, m__1678, mSuccEqu, m__1820, mNatExtr, mArith, m__2052, m__1783, mDefSPN, mMNeg, m__1854, mLETrn, m__1949, mDefSPZ, m__1746, mDimNat, m__1837, mLEMonM, mPosMon, mDefInit, m__1911, mMDNeg, mLETot, m__1800, mDistr, m__1967, mEqInit, mSZeroSc, mVcSort, mLEASm, mSumSc, mScZero, mLEMon, mScPr, m__1678_01, m__1892, mElmSc, mDistr2, mSqPos, m__1709, m__2027, m__1692, m__1652, mNatSort, m__1726, mIHOrd, mNegSc, mSuccNat, mScSqPos, m__1873
% 231.90/71.84 % No. of inferences in proof: 384
% 231.90/71.84 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 71332 ms resp. 70883 ms w/o parsing
% 232.18/71.91 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 232.18/71.91 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------