TSTP Solution File: RNG064+1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : RNG064+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n019.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 11:49:14 EDT 2023
% Result : Theorem 121.71s 37.17s
% Output : Refutation 121.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 97
% Syntax : Number of formulae : 287 ( 91 unt; 33 typ; 0 def)
% Number of atoms : 704 ( 282 equ; 0 cnn)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 2521 ( 225 ~; 173 |; 162 &;1852 @)
% ( 1 <=>; 108 =>; 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 : 188 ( 0 ^; 186 !; 2 ?; 188 :)
% 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(sdtpldt0_type,type,
sdtpldt0: $i > $i > $i ).
thf(xN_type,type,
xN: $i ).
thf(sdtasdt0_type,type,
sdtasdt0: $i > $i > $i ).
thf(xR_type,type,
xR: $i ).
thf(xS_type,type,
xS: $i ).
thf(xs_type,type,
xs: $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(sz0z00_type,type,
sz0z00: $i ).
thf(xq_type,type,
xq: $i ).
thf(sdtasasdt0_type,type,
sdtasasdt0: $i > $i > $i ).
thf(xE_type,type,
xE: $i ).
thf(xp_type,type,
xp: $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(xH_type,type,
xH: $i ).
thf(xF_type,type,
xF: $i ).
thf(xG_type,type,
xG: $i ).
thf(xP_type,type,
xP: $i ).
thf(sk1_type,type,
sk1: $i > $i ).
thf(sk2_type,type,
sk2: $i > $i > $i ).
thf(63,axiom,
! [A: $i,B: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B ) )
=> ( ( sdtlseqdt0 @ A @ B )
| ( sdtlseqdt0 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETot) ).
thf(269,plain,
! [A: $i,B: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B ) )
=> ( ( sdtlseqdt0 @ A @ B )
| ( sdtlseqdt0 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(47,axiom,
( ( aScalar0 @ xN )
& ( xN
= ( sdtasdt0 @ xR @ xS ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1949) ).
thf(216,plain,
( ( aScalar0 @ xN )
& ( xN
= ( sdtasdt0 @ xR @ xS ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(217,plain,
( xN
= ( sdtasdt0 @ xR @ xS ) ),
inference(cnf,[status(esa)],[216]) ).
thf(219,plain,
( ( sdtasdt0 @ xR @ xS )
= xN ),
inference(lifteq,[status(thm)],[217]) ).
thf(1,conjecture,
sdtlseqdt0 @ ( sdtpldt0 @ xN @ xN ) @ ( sdtpldt0 @ ( sdtasdt0 @ xR @ xR ) @ ( sdtasdt0 @ xS @ xS ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ( sdtlseqdt0 @ ( sdtpldt0 @ xN @ xN ) @ ( sdtpldt0 @ ( sdtasdt0 @ xR @ xR ) @ ( sdtasdt0 @ xS @ xS ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(66,plain,
~ ( sdtlseqdt0 @ ( sdtpldt0 @ xN @ xN ) @ ( sdtpldt0 @ ( sdtasdt0 @ xR @ xR ) @ ( sdtasdt0 @ xS @ xS ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(1191,plain,
( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ xN @ xN ) @ ( sdtpldt0 @ xN @ ( sdtasdt0 @ xS @ xS ) ) )
| ( ( sdtasdt0 @ xR @ xS )
!= ( sdtasdt0 @ xR @ xR ) ) ),
inference(paramod_ordered,[status(thm)],[219,66]) ).
thf(1222,plain,
( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ xN @ xN ) @ ( sdtpldt0 @ xN @ ( sdtasdt0 @ xS @ xS ) ) )
| ( xR != xR )
| ( xS != xR ) ),
inference(simp,[status(thm)],[1191]) ).
thf(1243,plain,
( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ xN @ xN ) @ ( sdtpldt0 @ xN @ ( sdtasdt0 @ xS @ xS ) ) )
| ( xS != xR ) ),
inference(simp,[status(thm)],[1222]) ).
thf(38,axiom,
! [A: $i,B: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B ) )
=> ( ( ( sdtlseqdt0 @ A @ B )
& ( sdtlseqdt0 @ B @ A ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLEASm) ).
thf(188,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)],[38]) ).
thf(18,axiom,
( ( aScalar0 @ xC )
& ( xC
= ( sdtasasdt0 @ xp @ xp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1783) ).
thf(126,plain,
( ( aScalar0 @ xC )
& ( xC
= ( sdtasasdt0 @ xp @ xp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(127,plain,
( xC
= ( sdtasasdt0 @ xp @ xp ) ),
inference(cnf,[status(esa)],[126]) ).
thf(129,plain,
( ( sdtasasdt0 @ xp @ xp )
= xC ),
inference(lifteq,[status(thm)],[127]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( ( szszuzczcdt0 @ A )
= ( szszuzczcdt0 @ B ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/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)],[3]) ).
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(60,axiom,
sdtlseqdt0 @ sz0z00 @ ( sdtasdt0 @ ( sdtpldt0 @ xR @ ( smndt0 @ xS ) ) @ ( sdtpldt0 @ xR @ ( smndt0 @ xS ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2318) ).
thf(262,plain,
sdtlseqdt0 @ sz0z00 @ ( sdtasdt0 @ ( sdtpldt0 @ xR @ ( smndt0 @ xS ) ) @ ( sdtpldt0 @ xR @ ( smndt0 @ xS ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(44,axiom,
( ( sdtasdt0 @ ( sdtpldt0 @ xR @ ( smndt0 @ xS ) ) @ ( sdtpldt0 @ xR @ ( smndt0 @ xS ) ) )
= ( sdtpldt0 @ ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ xR @ xR ) @ ( sdtasdt0 @ xS @ xS ) ) @ ( smndt0 @ xN ) ) @ ( smndt0 @ xN ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2262) ).
thf(208,plain,
( ( sdtasdt0 @ ( sdtpldt0 @ xR @ ( smndt0 @ xS ) ) @ ( sdtpldt0 @ xR @ ( smndt0 @ xS ) ) )
= ( sdtpldt0 @ ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ xR @ xR ) @ ( sdtasdt0 @ xS @ xS ) ) @ ( smndt0 @ xN ) ) @ ( smndt0 @ xN ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(209,plain,
( ( sdtasdt0 @ ( sdtpldt0 @ xR @ ( smndt0 @ xS ) ) @ ( sdtpldt0 @ xR @ ( smndt0 @ xS ) ) )
= ( sdtpldt0 @ ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ xR @ xR ) @ ( sdtasdt0 @ xS @ xS ) ) @ ( smndt0 @ xN ) ) @ ( smndt0 @ xN ) ) ),
inference(lifteq,[status(thm)],[208]) ).
thf(2778,plain,
sdtlseqdt0 @ sz0z00 @ ( sdtpldt0 @ ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ xR @ xR ) @ ( sdtasdt0 @ xS @ xS ) ) @ ( smndt0 @ xN ) ) @ ( smndt0 @ xN ) ),
inference(rewrite,[status(thm)],[262,209]) ).
thf(54,axiom,
! [A: $i] :
( ( aVector0 @ A )
=> ( sdtlseqdt0 @ sz0z00 @ ( sdtasasdt0 @ A @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mScSqPos) ).
thf(234,plain,
! [A: $i] :
( ( aVector0 @ A )
=> ( sdtlseqdt0 @ sz0z00 @ ( sdtasasdt0 @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( ( aVector0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( aScalar0 @ ( sdtlbdtrb0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mElmSc) ).
thf(88,plain,
! [A: $i,B: $i] :
( ( ( aVector0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( aScalar0 @ ( sdtlbdtrb0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(64,axiom,
( ( aScalar0 @ xG )
& ( xG
= ( sdtasdt0 @ xB @ xB ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1854) ).
thf(271,plain,
( ( aScalar0 @ xG )
& ( xG
= ( sdtasdt0 @ xB @ xB ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(272,plain,
( xG
= ( sdtasdt0 @ xB @ xB ) ),
inference(cnf,[status(esa)],[271]) ).
thf(274,plain,
( ( sdtasdt0 @ xB @ xB )
= xG ),
inference(lifteq,[status(thm)],[272]) ).
thf(1614,plain,
( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ xN @ xN ) @ ( sdtpldt0 @ xG @ ( sdtasdt0 @ xS @ xS ) ) )
| ( ( sdtasdt0 @ xB @ xB )
!= ( sdtasdt0 @ xR @ xR ) ) ),
inference(paramod_ordered,[status(thm)],[274,66]) ).
thf(1666,plain,
( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ xN @ xN ) @ ( sdtpldt0 @ xG @ ( sdtasdt0 @ xS @ xS ) ) )
| ( xB != xR )
| ( xB != xR ) ),
inference(simp,[status(thm)],[1614]) ).
thf(1686,plain,
( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ xN @ xN ) @ ( sdtpldt0 @ xG @ ( sdtasdt0 @ xS @ xS ) ) )
| ( xB != xR ) ),
inference(simp,[status(thm)],[1666]) ).
thf(23,axiom,
( ( aScalar0 @ xD )
& ( xD
= ( sdtasasdt0 @ xq @ xq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1800) ).
thf(140,plain,
( ( aScalar0 @ xD )
& ( xD
= ( sdtasasdt0 @ xq @ xq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(142,plain,
aScalar0 @ xD,
inference(cnf,[status(esa)],[140]) ).
thf(28,axiom,
! [A: $i] :
( ( aScalar0 @ A )
=> $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mScSort) ).
thf(153,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(13,axiom,
( ( aVector0 @ xq )
& ( xq
= ( sziznziztdt0 @ xt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1726) ).
thf(110,plain,
( ( aVector0 @ xq )
& ( xq
= ( sziznziztdt0 @ xt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(17,axiom,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNatSort) ).
thf(125,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(50,axiom,
( ( aScalar0 @ xR )
& ( xR
= ( sdtasdt0 @ xC @ xG ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1892) ).
thf(226,plain,
( ( aScalar0 @ xR )
& ( xR
= ( sdtasdt0 @ xC @ xG ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(228,plain,
aScalar0 @ xR,
inference(cnf,[status(esa)],[226]) ).
thf(29,axiom,
aNaturalNumber0 @ sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroNat) ).
thf(154,plain,
aNaturalNumber0 @ sz00,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(14,axiom,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( aNaturalNumber0 @ ( szszuzczcdt0 @ A ) )
& ( ( szszuzczcdt0 @ A )
!= sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSuccNat) ).
thf(114,plain,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( aNaturalNumber0 @ ( szszuzczcdt0 @ A ) )
& ( ( szszuzczcdt0 @ A )
!= sz00 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(116,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( ( szszuzczcdt0 @ A )
!= sz00 ) ),
inference(cnf,[status(esa)],[114]) ).
thf(117,plain,
! [A: $i] :
( ( ( szszuzczcdt0 @ A )
!= sz00 )
| ~ ( aNaturalNumber0 @ A ) ),
inference(lifteq,[status(thm)],[116]) ).
thf(288,plain,
! [A: $i] :
( ( ( szszuzczcdt0 @ A )
!= sz00 )
| ( ( aNaturalNumber0 @ sz00 )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[154,117]) ).
thf(289,plain,
( ( szszuzczcdt0 @ sz00 )
!= sz00 ),
inference(pattern_uni,[status(thm)],[288:[bind(A,$thf( sz00 ))]]) ).
thf(48,axiom,
( ( aScalar0 @ xF )
& ( xF
= ( sdtasdt0 @ xA @ xA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
thf(220,plain,
( ( aScalar0 @ xF )
& ( xF
= ( sdtasdt0 @ xA @ xA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(221,plain,
( xF
= ( sdtasdt0 @ xA @ xA ) ),
inference(cnf,[status(esa)],[220]) ).
thf(223,plain,
( ( sdtasdt0 @ xA @ xA )
= xF ),
inference(lifteq,[status(thm)],[221]) ).
thf(1190,plain,
( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ xN @ xN ) @ ( sdtpldt0 @ ( sdtasdt0 @ xR @ xR ) @ xN ) )
| ( ( sdtasdt0 @ xS @ xS )
!= ( sdtasdt0 @ xR @ xS ) ) ),
inference(paramod_ordered,[status(thm)],[219,66]) ).
thf(1220,plain,
( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ xN @ xN ) @ ( sdtpldt0 @ ( sdtasdt0 @ xR @ xR ) @ xN ) )
| ( xS != xR )
| ( xS != xS ) ),
inference(simp,[status(thm)],[1190]) ).
thf(1241,plain,
( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ xN @ xN ) @ ( sdtpldt0 @ ( sdtasdt0 @ xR @ xR ) @ xN ) )
| ( xS != xR ) ),
inference(simp,[status(thm)],[1220]) ).
thf(1353,plain,
( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ xN @ xN ) @ ( sdtpldt0 @ xF @ xN ) )
| ( xS != xR )
| ( ( sdtasdt0 @ xA @ xA )
!= ( sdtasdt0 @ xR @ xR ) ) ),
inference(paramod_ordered,[status(thm)],[223,1241]) ).
thf(1359,plain,
( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ xN @ xN ) @ ( sdtpldt0 @ xF @ xN ) )
| ( xS != xR )
| ( xA != xR )
| ( xA != xR ) ),
inference(simp,[status(thm)],[1353]) ).
thf(1362,plain,
( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ xN @ xN ) @ ( sdtpldt0 @ xF @ xN ) )
| ( xS != xR )
| ( xA != xR ) ),
inference(simp,[status(thm)],[1359]) ).
thf(6,axiom,
! [A: $i] :
( ( aVector0 @ A )
=> $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mVcSort) ).
thf(78,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(59,axiom,
! [A: $i,B: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B ) )
=> ( ( sdtlseqdt0 @ A @ B )
=> $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLess) ).
thf(261,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(31,axiom,
! [A: $i,B: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B ) )
=> ( aScalar0 @ ( sdtasdt0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulSc) ).
thf(164,plain,
! [A: $i,B: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B ) )
=> ( aScalar0 @ ( sdtasdt0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(4,axiom,
! [A: $i] :
( ( ( aNaturalNumber0 @ A )
& ( A != sz00 ) )
=> ? [B: $i] :
( ( aNaturalNumber0 @ B )
& ( A
= ( szszuzczcdt0 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNatExtr) ).
thf(70,plain,
! [A: $i] :
( ( ( aNaturalNumber0 @ A )
& ( A != sz00 ) )
=> ? [B: $i] :
( ( aNaturalNumber0 @ B )
& ( A
= ( szszuzczcdt0 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(71,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( A = sz00 )
| ( aNaturalNumber0 @ ( sk1 @ A ) ) ),
inference(cnf,[status(esa)],[70]) ).
thf(73,plain,
! [A: $i] :
( ( A = sz00 )
| ~ ( aNaturalNumber0 @ A )
| ( aNaturalNumber0 @ ( sk1 @ A ) ) ),
inference(lifteq,[status(thm)],[71]) ).
thf(320,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( aNaturalNumber0 @ ( sk1 @ A ) )
| ~ ( sdtlseqdt0 @ ( sdtpldt0 @ xN @ xN ) @ ( sdtpldt0 @ ( sdtasdt0 @ xR @ sz00 ) @ ( sdtasdt0 @ xS @ xS ) ) )
| ( A != xR ) ),
inference(paramod_ordered,[status(thm)],[73,66]) ).
thf(321,plain,
( ~ ( aNaturalNumber0 @ xR )
| ( aNaturalNumber0 @ ( sk1 @ xR ) )
| ~ ( sdtlseqdt0 @ ( sdtpldt0 @ xN @ xN ) @ ( sdtpldt0 @ ( sdtasdt0 @ xR @ sz00 ) @ ( sdtasdt0 @ xS @ xS ) ) ) ),
inference(pattern_uni,[status(thm)],[320:[bind(A,$thf( xR ))]]) ).
thf(56,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/sandbox2/benchmark/theBenchmark.p',mLEMon) ).
thf(253,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)],[56]) ).
thf(16,axiom,
( ( aScalar0 @ xE )
& ( xE
= ( sdtasasdt0 @ xp @ xq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1820) ).
thf(121,plain,
( ( aScalar0 @ xE )
& ( xE
= ( sdtasasdt0 @ xp @ xq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(36,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/sandbox2/benchmark/theBenchmark.p',mLEMonM) ).
thf(181,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)],[36]) ).
thf(182,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)],[181]) ).
thf(400,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 @ ( sdtpldt0 @ xN @ xN ) @ ( sdtpldt0 @ ( sdtasdt0 @ xR @ xR ) @ ( sdtasdt0 @ xS @ xS ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[182,66]) ).
thf(501,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 )
!= ( sdtpldt0 @ xN @ xN ) )
| ( ( sdtasdt0 @ B @ D )
!= ( sdtpldt0 @ ( sdtasdt0 @ xR @ xR ) @ ( sdtasdt0 @ xS @ xS ) ) ) ),
inference(simp,[status(thm)],[400]) ).
thf(678,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( aScalar0 @ A )
| ~ ( aScalar0 @ B )
| ~ ( aScalar0 @ C )
| ~ ( aScalar0 @ D )
| ~ ( sdtlseqdt0 @ A @ B )
| ~ ( sdtlseqdt0 @ sz0z00 @ C )
| ( ( sdtasdt0 @ A @ C )
!= ( sdtpldt0 @ xN @ xN ) )
| ( ( sdtasdt0 @ B @ D )
!= ( sdtpldt0 @ ( sdtasdt0 @ xR @ xR ) @ ( sdtasdt0 @ xS @ xS ) ) )
| ( ( sdtlseqdt0 @ C @ D )
!= ( sdtlseqdt0 @ sz0z00 @ C ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[501]) ).
thf(681,plain,
! [B: $i,A: $i] :
( ~ ( aScalar0 @ A )
| ~ ( aScalar0 @ B )
| ~ ( aScalar0 @ sz0z00 )
| ~ ( aScalar0 @ sz0z00 )
| ~ ( sdtlseqdt0 @ A @ B )
| ~ ( sdtlseqdt0 @ sz0z00 @ sz0z00 )
| ( ( sdtasdt0 @ A @ sz0z00 )
!= ( sdtpldt0 @ xN @ xN ) )
| ( ( sdtasdt0 @ B @ sz0z00 )
!= ( sdtpldt0 @ ( sdtasdt0 @ xR @ xR ) @ ( sdtasdt0 @ xS @ xS ) ) ) ),
inference(pattern_uni,[status(thm)],[678:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sz0z00 )),bind(D,$thf( sz0z00 ))]]) ).
thf(705,plain,
! [B: $i,A: $i] :
( ~ ( aScalar0 @ A )
| ~ ( aScalar0 @ B )
| ~ ( aScalar0 @ sz0z00 )
| ~ ( sdtlseqdt0 @ A @ B )
| ~ ( sdtlseqdt0 @ sz0z00 @ sz0z00 )
| ( ( sdtasdt0 @ A @ sz0z00 )
!= ( sdtpldt0 @ xN @ xN ) )
| ( ( sdtasdt0 @ B @ sz0z00 )
!= ( sdtpldt0 @ ( sdtasdt0 @ xR @ xR ) @ ( sdtasdt0 @ xS @ xS ) ) ) ),
inference(simp,[status(thm)],[681]) ).
thf(9,axiom,
aScalar0 @ sz0z00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSZeroSc) ).
thf(87,plain,
aScalar0 @ sz0z00,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(865,plain,
! [B: $i,A: $i] :
( ~ ( aScalar0 @ A )
| ~ ( aScalar0 @ B )
| ~ $true
| ~ ( sdtlseqdt0 @ A @ B )
| ~ ( sdtlseqdt0 @ sz0z00 @ sz0z00 )
| ( ( sdtasdt0 @ A @ sz0z00 )
!= ( sdtpldt0 @ xN @ xN ) )
| ( ( sdtasdt0 @ B @ sz0z00 )
!= ( sdtpldt0 @ ( sdtasdt0 @ xR @ xR ) @ ( sdtasdt0 @ xS @ xS ) ) ) ),
inference(rewrite,[status(thm)],[705,87]) ).
thf(866,plain,
! [B: $i,A: $i] :
( ~ ( aScalar0 @ A )
| ~ ( aScalar0 @ B )
| ~ ( sdtlseqdt0 @ A @ B )
| ~ ( sdtlseqdt0 @ sz0z00 @ sz0z00 )
| ( ( sdtasdt0 @ A @ sz0z00 )
!= ( sdtpldt0 @ xN @ xN ) )
| ( ( sdtasdt0 @ B @ sz0z00 )
!= ( sdtpldt0 @ ( sdtasdt0 @ xR @ xR ) @ ( sdtasdt0 @ xS @ xS ) ) ) ),
inference(simp,[status(thm)],[865]) ).
thf(20,axiom,
( ( aVector0 @ xp )
& ( xp
= ( sziznziztdt0 @ xs ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1709) ).
thf(132,plain,
( ( aVector0 @ xp )
& ( xp
= ( sziznziztdt0 @ xs ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(89,plain,
! [B: $i,A: $i] :
( ~ ( aVector0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( aScalar0 @ ( sdtlbdtrb0 @ A @ B ) ) ),
inference(cnf,[status(esa)],[88]) ).
thf(62,axiom,
( ( aScalar0 @ xP )
& ( xP
= ( sdtasdt0 @ xE @ xH ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1911) ).
thf(265,plain,
( ( aScalar0 @ xP )
& ( xP
= ( sdtasdt0 @ xE @ xH ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(72,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( A = sz00 )
| ( A
= ( szszuzczcdt0 @ ( sk1 @ A ) ) ) ),
inference(cnf,[status(esa)],[70]) ).
thf(74,plain,
! [A: $i] :
( ( A = sz00 )
| ( ( szszuzczcdt0 @ ( sk1 @ A ) )
= A )
| ~ ( aNaturalNumber0 @ A ) ),
inference(lifteq,[status(thm)],[72]) ).
thf(43,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/sandbox2/benchmark/theBenchmark.p',mLETrn) ).
thf(206,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)],[43]) ).
thf(53,axiom,
sdtlseqdt0 @ ( sdtasdt0 @ xE @ xE ) @ ( sdtasdt0 @ xC @ xD ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1967) ).
thf(233,plain,
sdtlseqdt0 @ ( sdtasdt0 @ xE @ xE ) @ ( sdtasdt0 @ xC @ xD ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(7,axiom,
( ( aScalar0 @ xB )
& ( xB
= ( sdtlbdtrb0 @ xt @ ( aDimensionOf0 @ xt ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1766) ).
thf(79,plain,
( ( aScalar0 @ xB )
& ( xB
= ( sdtlbdtrb0 @ xt @ ( aDimensionOf0 @ xt ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(80,plain,
( xB
= ( sdtlbdtrb0 @ xt @ ( aDimensionOf0 @ xt ) ) ),
inference(cnf,[status(esa)],[79]) ).
thf(82,plain,
( ( sdtlbdtrb0 @ xt @ ( aDimensionOf0 @ xt ) )
= xB ),
inference(lifteq,[status(thm)],[80]) ).
thf(19,axiom,
( ( aDimensionOf0 @ xs )
= ( aDimensionOf0 @ xt ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1678_01) ).
thf(130,plain,
( ( aDimensionOf0 @ xs )
= ( aDimensionOf0 @ xt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(131,plain,
( ( aDimensionOf0 @ xt )
= ( aDimensionOf0 @ xs ) ),
inference(lifteq,[status(thm)],[130]) ).
thf(1067,plain,
( ( sdtlbdtrb0 @ xt @ ( aDimensionOf0 @ xs ) )
= xB ),
inference(rewrite,[status(thm)],[82,131]) ).
thf(8,axiom,
( ( aScalar0 @ xA )
& ( xA
= ( sdtlbdtrb0 @ xs @ ( aDimensionOf0 @ xs ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1746) ).
thf(83,plain,
( ( aScalar0 @ xA )
& ( xA
= ( sdtlbdtrb0 @ xs @ ( aDimensionOf0 @ xs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(85,plain,
aScalar0 @ xA,
inference(cnf,[status(esa)],[83]) ).
thf(42,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/sandbox2/benchmark/theBenchmark.p',mDistr) ).
thf(201,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)],[42]) ).
thf(65,axiom,
! [A: $i] :
( ( aScalar0 @ A )
=> ( sdtlseqdt0 @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLERef) ).
thf(275,plain,
! [A: $i] :
( ( aScalar0 @ A )
=> ( sdtlseqdt0 @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( ( aVector0 @ A )
& ( aVector0 @ B ) )
=> ( ( ( ( aDimensionOf0 @ A )
= ( aDimensionOf0 @ B ) )
& ( ( aDimensionOf0 @ B )
= sz00 ) )
=> ( ( sdtasasdt0 @ A @ B )
= sz0z00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSPZ) ).
thf(137,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)],[22]) ).
thf(227,plain,
( xR
= ( sdtasdt0 @ xC @ xG ) ),
inference(cnf,[status(esa)],[226]) ).
thf(229,plain,
( ( sdtasdt0 @ xC @ xG )
= xR ),
inference(lifteq,[status(thm)],[227]) ).
thf(41,axiom,
( ( aScalar0 @ xS )
& ( xS
= ( sdtasdt0 @ xF @ xD ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1930) ).
thf(197,plain,
( ( aScalar0 @ xS )
& ( xS
= ( sdtasdt0 @ xF @ xD ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(49,axiom,
! [A: $i,B: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B ) )
=> ( aScalar0 @ ( sdtpldt0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSumSc) ).
thf(224,plain,
! [A: $i,B: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B ) )
=> ( aScalar0 @ ( sdtpldt0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(1263,plain,
( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ xN @ xN ) @ ( sdtpldt0 @ xF @ ( sdtasdt0 @ xS @ xS ) ) )
| ( ( sdtasdt0 @ xA @ xA )
!= ( sdtasdt0 @ xR @ xR ) ) ),
inference(paramod_ordered,[status(thm)],[223,66]) ).
thf(1309,plain,
( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ xN @ xN ) @ ( sdtpldt0 @ xF @ ( sdtasdt0 @ xS @ xS ) ) )
| ( xA != xR )
| ( xA != xR ) ),
inference(simp,[status(thm)],[1263]) ).
thf(1329,plain,
( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ xN @ xN ) @ ( sdtpldt0 @ xF @ ( sdtasdt0 @ xS @ xS ) ) )
| ( xA != xR ) ),
inference(simp,[status(thm)],[1309]) ).
thf(122,plain,
( xE
= ( sdtasasdt0 @ xp @ xq ) ),
inference(cnf,[status(esa)],[121]) ).
thf(124,plain,
( ( sdtasasdt0 @ xp @ xq )
= xE ),
inference(lifteq,[status(thm)],[122]) ).
thf(5,axiom,
( ( aDimensionOf0 @ xs )
!= sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1692) ).
thf(75,plain,
( ( aDimensionOf0 @ xs )
!= sz00 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(76,plain,
( ( aDimensionOf0 @ xs )
!= sz00 ),
inference(polarity_switch,[status(thm)],[75]) ).
thf(77,plain,
( ( aDimensionOf0 @ xs )
!= sz00 ),
inference(lifteq,[status(thm)],[76]) ).
thf(39,axiom,
( ( aScalar0 @ xH )
& ( xH
= ( sdtasdt0 @ xA @ xB ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1873) ).
thf(191,plain,
( ( aScalar0 @ xH )
& ( xH
= ( sdtasdt0 @ xA @ xB ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(193,plain,
aScalar0 @ xH,
inference(cnf,[status(esa)],[191]) ).
thf(134,plain,
aVector0 @ xp,
inference(cnf,[status(esa)],[132]) ).
thf(128,plain,
aScalar0 @ xC,
inference(cnf,[status(esa)],[126]) ).
thf(310,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( aNaturalNumber0 @ ( sk1 @ A ) )
| ~ ( sdtlseqdt0 @ ( sdtpldt0 @ xN @ xN ) @ ( sdtpldt0 @ ( sdtasdt0 @ xR @ xR ) @ ( sdtasdt0 @ sz00 @ xS ) ) )
| ( A != xS ) ),
inference(paramod_ordered,[status(thm)],[73,66]) ).
thf(311,plain,
( ~ ( aNaturalNumber0 @ xS )
| ( aNaturalNumber0 @ ( sk1 @ xS ) )
| ~ ( sdtlseqdt0 @ ( sdtpldt0 @ xN @ xN ) @ ( sdtpldt0 @ ( sdtasdt0 @ xR @ xR ) @ ( sdtasdt0 @ sz00 @ xS ) ) ) ),
inference(pattern_uni,[status(thm)],[310:[bind(A,$thf( xS ))]]) ).
thf(32,axiom,
( ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ ( sdtpldt0 @ xR @ ( smndt0 @ xS ) ) @ ( sdtpldt0 @ xR @ ( smndt0 @ xS ) ) ) @ xN ) @ xN )
= ( sdtpldt0 @ ( sdtasdt0 @ xR @ xR ) @ ( sdtasdt0 @ xS @ xS ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2303) ).
thf(166,plain,
( ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ ( sdtpldt0 @ xR @ ( smndt0 @ xS ) ) @ ( sdtpldt0 @ xR @ ( smndt0 @ xS ) ) ) @ xN ) @ xN )
= ( sdtpldt0 @ ( sdtasdt0 @ xR @ xR ) @ ( sdtasdt0 @ xS @ xS ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(26,axiom,
( ( aVector0 @ xs )
& ( aVector0 @ xt ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1678) ).
thf(148,plain,
( ( aVector0 @ xs )
& ( aVector0 @ xt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(149,plain,
aVector0 @ xt,
inference(cnf,[status(esa)],[148]) ).
thf(34,axiom,
( ( ( sdtasdt0 @ xR @ ( smndt0 @ xS ) )
= ( smndt0 @ xN ) )
& ( ( sdtasdt0 @ ( smndt0 @ xS ) @ xR )
= ( smndt0 @ xN ) )
& ( ( sdtasdt0 @ ( smndt0 @ xS ) @ ( smndt0 @ xS ) )
= ( sdtasdt0 @ xS @ xS ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2144) ).
thf(171,plain,
( ( ( sdtasdt0 @ xR @ ( smndt0 @ xS ) )
= ( smndt0 @ xN ) )
& ( ( sdtasdt0 @ ( smndt0 @ xS ) @ xR )
= ( smndt0 @ xN ) )
& ( ( sdtasdt0 @ ( smndt0 @ xS ) @ ( smndt0 @ xS ) )
= ( sdtasdt0 @ xS @ xS ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(173,plain,
( ( sdtasdt0 @ ( smndt0 @ xS ) @ xR )
= ( smndt0 @ xN ) ),
inference(cnf,[status(esa)],[171]) ).
thf(176,plain,
( ( sdtasdt0 @ ( smndt0 @ xS ) @ xR )
= ( smndt0 @ xN ) ),
inference(lifteq,[status(thm)],[173]) ).
thf(167,plain,
( ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ ( sdtpldt0 @ xR @ ( smndt0 @ xS ) ) @ ( sdtpldt0 @ xR @ ( smndt0 @ xS ) ) ) @ xN ) @ xN )
= ( sdtpldt0 @ ( sdtasdt0 @ xR @ xR ) @ ( sdtasdt0 @ xS @ xS ) ) ),
inference(lifteq,[status(thm)],[166]) ).
thf(2439,plain,
( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ xN @ xN ) @ ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ ( sdtpldt0 @ xR @ ( smndt0 @ xS ) ) @ ( sdtpldt0 @ xR @ ( smndt0 @ xS ) ) ) @ xN ) @ xN ) )
| ( ( sdtpldt0 @ ( sdtasdt0 @ xR @ xR ) @ ( sdtasdt0 @ xS @ xS ) )
!= ( sdtpldt0 @ ( sdtasdt0 @ xR @ xR ) @ ( sdtasdt0 @ xS @ xS ) ) ) ),
inference(paramod_ordered,[status(thm)],[167,66]) ).
thf(2440,plain,
~ ( sdtlseqdt0 @ ( sdtpldt0 @ xN @ xN ) @ ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ ( sdtpldt0 @ xR @ ( smndt0 @ xS ) ) @ ( sdtpldt0 @ xR @ ( smndt0 @ xS ) ) ) @ xN ) @ xN ) ),
inference(pattern_uni,[status(thm)],[2439:[]]) ).
thf(3609,plain,
~ ( sdtlseqdt0 @ ( sdtpldt0 @ xN @ xN ) @ ( sdtpldt0 @ ( sdtpldt0 @ ( sdtpldt0 @ ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ xR @ xR ) @ ( sdtasdt0 @ xS @ xS ) ) @ ( smndt0 @ xN ) ) @ ( smndt0 @ xN ) ) @ xN ) @ xN ) ),
inference(rewrite,[status(thm)],[2440,209]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( ( aVector0 @ A )
& ( aVector0 @ B ) )
=> ( ( ( aDimensionOf0 @ A )
= ( aDimensionOf0 @ B ) )
=> ( aScalar0 @ ( sdtasasdt0 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mScPr) ).
thf(118,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)],[15]) ).
thf(312,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( aNaturalNumber0 @ ( sk1 @ A ) )
| ~ ( sdtlseqdt0 @ ( sdtpldt0 @ xN @ xN ) @ ( sdtpldt0 @ ( sdtasdt0 @ xR @ xR ) @ ( sdtasdt0 @ xS @ sz00 ) ) )
| ( A != xS ) ),
inference(paramod_ordered,[status(thm)],[73,66]) ).
thf(313,plain,
( ~ ( aNaturalNumber0 @ xS )
| ( aNaturalNumber0 @ ( sk1 @ xS ) )
| ~ ( sdtlseqdt0 @ ( sdtpldt0 @ xN @ xN ) @ ( sdtpldt0 @ ( sdtasdt0 @ xR @ xR ) @ ( sdtasdt0 @ xS @ sz00 ) ) ) ),
inference(pattern_uni,[status(thm)],[312:[bind(A,$thf( xS ))]]) ).
thf(24,axiom,
! [A: $i] :
( ( aVector0 @ A )
=> ( aNaturalNumber0 @ ( aDimensionOf0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDimNat) ).
thf(144,plain,
! [A: $i] :
( ( aVector0 @ A )
=> ( aNaturalNumber0 @ ( aDimensionOf0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(55,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/sandbox2/benchmark/theBenchmark.p',mScZero) ).
thf(236,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)],[55]) ).
thf(84,plain,
( xA
= ( sdtlbdtrb0 @ xs @ ( aDimensionOf0 @ xs ) ) ),
inference(cnf,[status(esa)],[83]) ).
thf(86,plain,
( ( sdtlbdtrb0 @ xs @ ( aDimensionOf0 @ xs ) )
= xA ),
inference(lifteq,[status(thm)],[84]) ).
thf(111,plain,
( xq
= ( sziznziztdt0 @ xt ) ),
inference(cnf,[status(esa)],[110]) ).
thf(113,plain,
( ( sziznziztdt0 @ xt )
= xq ),
inference(lifteq,[status(thm)],[111]) ).
thf(81,plain,
aScalar0 @ xB,
inference(cnf,[status(esa)],[79]) ).
thf(51,axiom,
sdtlseqdt0 @ ( sdtasdt0 @ xP @ xP ) @ xN,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2004) ).
thf(230,plain,
sdtlseqdt0 @ ( sdtasdt0 @ xP @ xP ) @ xN,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
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/sandbox2/benchmark/theBenchmark.p',mDefInit) ).
thf(90,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(91,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)],[90]) ).
thf(93,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)],[91]) ).
thf(97,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)],[93]) ).
thf(98,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)],[97]) ).
thf(46,axiom,
! [A: $i,B: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B ) )
=> ( ( sdtasdt0 @ ( smndt0 @ A ) @ ( smndt0 @ B ) )
= ( sdtasdt0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMDNeg) ).
thf(213,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)],[46]) ).
thf(30,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/sandbox2/benchmark/theBenchmark.p',mArith) ).
thf(155,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)],[30]) ).
thf(1621,plain,
( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ xN @ xN ) @ ( sdtpldt0 @ xF @ xG ) )
| ( xA != xR )
| ( ( sdtasdt0 @ xB @ xB )
!= ( sdtasdt0 @ xS @ xS ) ) ),
inference(paramod_ordered,[status(thm)],[274,1329]) ).
thf(1668,plain,
( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ xN @ xN ) @ ( sdtpldt0 @ xF @ xG ) )
| ( xA != xR )
| ( xB != xS )
| ( xB != xS ) ),
inference(simp,[status(thm)],[1621]) ).
thf(1688,plain,
( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ xN @ xN ) @ ( sdtpldt0 @ xF @ xG ) )
| ( xA != xR )
| ( xB != xS ) ),
inference(simp,[status(thm)],[1668]) ).
thf(133,plain,
( xp
= ( sziznziztdt0 @ xs ) ),
inference(cnf,[status(esa)],[132]) ).
thf(135,plain,
( ( sziznziztdt0 @ xs )
= xp ),
inference(lifteq,[status(thm)],[133]) ).
thf(267,plain,
aScalar0 @ xP,
inference(cnf,[status(esa)],[265]) ).
thf(57,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/sandbox2/benchmark/theBenchmark.p',m__1652) ).
thf(255,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)],[57]) ).
thf(112,plain,
aVector0 @ xq,
inference(cnf,[status(esa)],[110]) ).
thf(123,plain,
aScalar0 @ xE,
inference(cnf,[status(esa)],[121]) ).
thf(192,plain,
( xH
= ( sdtasdt0 @ xA @ xB ) ),
inference(cnf,[status(esa)],[191]) ).
thf(194,plain,
( ( sdtasdt0 @ xA @ xB )
= xH ),
inference(lifteq,[status(thm)],[192]) ).
thf(150,plain,
aVector0 @ xs,
inference(cnf,[status(esa)],[148]) ).
thf(61,axiom,
( ( sdtasdt0 @ ( sdtpldt0 @ xR @ ( smndt0 @ xS ) ) @ ( sdtpldt0 @ xR @ ( smndt0 @ xS ) ) )
= ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ xR @ xR ) @ ( smndt0 @ xN ) ) @ ( sdtpldt0 @ ( sdtasdt0 @ xS @ xS ) @ ( smndt0 @ xN ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2221) ).
thf(263,plain,
( ( sdtasdt0 @ ( sdtpldt0 @ xR @ ( smndt0 @ xS ) ) @ ( sdtpldt0 @ xR @ ( smndt0 @ xS ) ) )
= ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ xR @ xR ) @ ( smndt0 @ xN ) ) @ ( sdtpldt0 @ ( sdtasdt0 @ xS @ xS ) @ ( smndt0 @ xN ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(199,plain,
aScalar0 @ xS,
inference(cnf,[status(esa)],[197]) ).
thf(174,plain,
( ( sdtasdt0 @ xR @ ( smndt0 @ xS ) )
= ( smndt0 @ xN ) ),
inference(cnf,[status(esa)],[171]) ).
thf(177,plain,
( ( sdtasdt0 @ xR @ ( smndt0 @ xS ) )
= ( smndt0 @ xN ) ),
inference(lifteq,[status(thm)],[174]) ).
thf(172,plain,
( ( sdtasdt0 @ ( smndt0 @ xS ) @ ( smndt0 @ xS ) )
= ( sdtasdt0 @ xS @ xS ) ),
inference(cnf,[status(esa)],[171]) ).
thf(175,plain,
( ( sdtasdt0 @ ( smndt0 @ xS ) @ ( smndt0 @ xS ) )
= ( sdtasdt0 @ xS @ xS ) ),
inference(lifteq,[status(thm)],[172]) ).
thf(141,plain,
( xD
= ( sdtasasdt0 @ xq @ xq ) ),
inference(cnf,[status(esa)],[140]) ).
thf(143,plain,
( ( sdtasasdt0 @ xq @ xq )
= xD ),
inference(lifteq,[status(thm)],[141]) ).
thf(52,axiom,
( ( sdtasdt0 @ ( sdtpldt0 @ xR @ ( smndt0 @ xS ) ) @ ( sdtpldt0 @ xR @ ( smndt0 @ xS ) ) )
= ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ xR @ xR ) @ ( smndt0 @ xN ) ) @ ( sdtpldt0 @ ( smndt0 @ xN ) @ ( sdtasdt0 @ xS @ xS ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2180) ).
thf(231,plain,
( ( sdtasdt0 @ ( sdtpldt0 @ xR @ ( smndt0 @ xS ) ) @ ( sdtpldt0 @ xR @ ( smndt0 @ xS ) ) )
= ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ xR @ xR ) @ ( smndt0 @ xN ) ) @ ( sdtpldt0 @ ( smndt0 @ xN ) @ ( sdtasdt0 @ xS @ xS ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(218,plain,
aScalar0 @ xN,
inference(cnf,[status(esa)],[216]) ).
thf(318,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( aNaturalNumber0 @ ( sk1 @ A ) )
| ~ ( sdtlseqdt0 @ ( sdtpldt0 @ xN @ xN ) @ ( sdtpldt0 @ ( sdtasdt0 @ sz00 @ xR ) @ ( sdtasdt0 @ xS @ xS ) ) )
| ( A != xR ) ),
inference(paramod_ordered,[status(thm)],[73,66]) ).
thf(319,plain,
( ~ ( aNaturalNumber0 @ xR )
| ( aNaturalNumber0 @ ( sk1 @ xR ) )
| ~ ( sdtlseqdt0 @ ( sdtpldt0 @ xN @ xN ) @ ( sdtpldt0 @ ( sdtasdt0 @ sz00 @ xR ) @ ( sdtasdt0 @ xS @ xS ) ) ) ),
inference(pattern_uni,[status(thm)],[318:[bind(A,$thf( xR ))]]) ).
thf(58,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/sandbox2/benchmark/theBenchmark.p',mSqrt) ).
thf(258,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)],[58]) ).
thf(1608,plain,
( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ xN @ xN ) @ ( sdtpldt0 @ xN @ xG ) )
| ( xS != xR )
| ( ( sdtasdt0 @ xB @ xB )
!= ( sdtasdt0 @ xS @ xS ) ) ),
inference(paramod_ordered,[status(thm)],[274,1243]) ).
thf(1669,plain,
( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ xN @ xN ) @ ( sdtpldt0 @ xN @ xG ) )
| ( xS != xR )
| ( xB != xS )
| ( xB != xS ) ),
inference(simp,[status(thm)],[1608]) ).
thf(1689,plain,
( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ xN @ xN ) @ ( sdtpldt0 @ xN @ xG ) )
| ( xS != xR )
| ( xB != xS ) ),
inference(simp,[status(thm)],[1669]) ).
thf(1502,plain,
( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ xN @ xN ) @ ( sdtpldt0 @ xF @ xF ) )
| ( xA != xR )
| ( ( sdtasdt0 @ xA @ xA )
!= ( sdtasdt0 @ xS @ xS ) ) ),
inference(paramod_ordered,[status(thm)],[223,1329]) ).
thf(1508,plain,
( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ xN @ xN ) @ ( sdtpldt0 @ xF @ xF ) )
| ( xA != xR )
| ( xA != xS )
| ( xA != xS ) ),
inference(simp,[status(thm)],[1502]) ).
thf(1513,plain,
( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ xN @ xN ) @ ( sdtpldt0 @ xF @ xF ) )
| ( xA != xR )
| ( xA != xS ) ),
inference(simp,[status(thm)],[1508]) ).
thf(27,axiom,
! [A: $i] :
( ( aScalar0 @ A )
=> ( aScalar0 @ ( smndt0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNegSc) ).
thf(151,plain,
! [A: $i] :
( ( aScalar0 @ A )
=> ( aScalar0 @ ( smndt0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(25,axiom,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( iLess0 @ A @ ( szszuzczcdt0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIH) ).
thf(146,plain,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( iLess0 @ A @ ( szszuzczcdt0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(37,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/sandbox2/benchmark/theBenchmark.p',mMNeg) ).
thf(183,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)],[37]) ).
thf(273,plain,
aScalar0 @ xG,
inference(cnf,[status(esa)],[271]) ).
thf(1470,plain,
( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ xN @ xN ) @ ( sdtpldt0 @ xN @ xF ) )
| ( xS != xR )
| ( ( sdtasdt0 @ xA @ xA )
!= ( sdtasdt0 @ xS @ xS ) ) ),
inference(paramod_ordered,[status(thm)],[223,1243]) ).
thf(1475,plain,
( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ xN @ xN ) @ ( sdtpldt0 @ xN @ xF ) )
| ( xS != xR )
| ( xA != xS )
| ( xA != xS ) ),
inference(simp,[status(thm)],[1470]) ).
thf(1480,plain,
( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ xN @ xN ) @ ( sdtpldt0 @ xN @ xF ) )
| ( xS != xR )
| ( xA != xS ) ),
inference(simp,[status(thm)],[1475]) ).
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/sandbox2/benchmark/theBenchmark.p',mDefSPN) ).
thf(168,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(45,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/sandbox2/benchmark/theBenchmark.p',mDistr2) ).
thf(210,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)],[45]) ).
thf(12,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/sandbox2/benchmark/theBenchmark.p',mEqInit) ).
thf(107,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)],[12]) ).
thf(1352,plain,
( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ xN @ xN ) @ ( sdtpldt0 @ xN @ xN ) )
| ( xS != xR )
| ( ( sdtasdt0 @ xR @ xS )
!= ( sdtasdt0 @ xR @ xR ) ) ),
inference(paramod_ordered,[status(thm)],[219,1241]) ).
thf(1360,plain,
( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ xN @ xN ) @ ( sdtpldt0 @ xN @ xN ) )
| ( xS != xR )
| ( xR != xR )
| ( xS != xR ) ),
inference(simp,[status(thm)],[1352]) ).
thf(1363,plain,
( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ xN @ xN ) @ ( sdtpldt0 @ xN @ xN ) )
| ( xS != xR ) ),
inference(simp,[status(thm)],[1360]) ).
thf(266,plain,
( xP
= ( sdtasdt0 @ xE @ xH ) ),
inference(cnf,[status(esa)],[265]) ).
thf(268,plain,
( ( sdtasdt0 @ xE @ xH )
= xP ),
inference(lifteq,[status(thm)],[266]) ).
thf(40,axiom,
! [A: $i] :
( ( aScalar0 @ A )
=> ( sdtlseqdt0 @ sz0z00 @ ( sdtasdt0 @ A @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSqPos) ).
thf(195,plain,
! [A: $i] :
( ( aScalar0 @ A )
=> ( sdtlseqdt0 @ sz0z00 @ ( sdtasdt0 @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( iLess0 @ A @ B )
=> $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIHOrd) ).
thf(136,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(198,plain,
( xS
= ( sdtasdt0 @ xF @ xD ) ),
inference(cnf,[status(esa)],[197]) ).
thf(200,plain,
( ( sdtasdt0 @ xF @ xD )
= xS ),
inference(lifteq,[status(thm)],[198]) ).
thf(35,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/sandbox2/benchmark/theBenchmark.p',mPosMon) ).
thf(178,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)],[35]) ).
thf(1262,plain,
( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ xN @ xN ) @ ( sdtpldt0 @ ( sdtasdt0 @ xR @ xR ) @ xF ) )
| ( ( sdtasdt0 @ xA @ xA )
!= ( sdtasdt0 @ xS @ xS ) ) ),
inference(paramod_ordered,[status(thm)],[223,66]) ).
thf(1313,plain,
( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ xN @ xN ) @ ( sdtpldt0 @ ( sdtasdt0 @ xR @ xR ) @ xF ) )
| ( xA != xS )
| ( xA != xS ) ),
inference(simp,[status(thm)],[1262]) ).
thf(1331,plain,
( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ xN @ xN ) @ ( sdtpldt0 @ ( sdtasdt0 @ xR @ xR ) @ xF ) )
| ( xA != xS ) ),
inference(simp,[status(thm)],[1313]) ).
thf(222,plain,
aScalar0 @ xF,
inference(cnf,[status(esa)],[220]) ).
thf(150461,plain,
$false,
inference(cvc4,[status(thm)],[269,1243,188,129,69,2778,234,88,1686,142,153,110,125,228,289,1362,78,261,216,164,321,253,121,866,132,89,265,74,206,233,117,220,1067,85,201,70,275,137,229,197,224,1329,124,77,193,134,73,128,1241,311,166,148,149,176,191,3609,118,313,144,236,181,86,113,219,274,81,230,98,271,208,140,213,66,155,1688,130,223,135,226,267,255,209,112,123,194,150,263,67,199,177,182,154,175,143,231,87,218,319,258,114,171,75,1689,1513,151,146,183,273,1480,168,262,210,107,1363,268,79,195,126,136,131,200,178,501,90,1331,83,222]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : RNG064+1 : TPTP v8.1.2. Released v4.0.0.
% 0.10/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n019.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 20:21:58 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.97/0.91 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.33/1.08 % [INFO] Parsing done (165ms).
% 1.33/1.09 % [INFO] Running in sequential loop mode.
% 1.79/1.28 % [INFO] eprover registered as external prover.
% 1.96/1.29 % [INFO] cvc4 registered as external prover.
% 1.96/1.29 % [INFO] Scanning for conjecture ...
% 1.96/1.34 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.96/1.37 % [INFO] Found a conjecture and 63 axioms. Running axiom selection ...
% 2.36/1.42 % [INFO] Axiom selection finished. Selected 63 axioms (removed 0 axioms).
% 2.42/1.44 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.42/1.49 % [INFO] Problem is first-order (TPTP FOF).
% 2.42/1.50 % [INFO] Type checking passed.
% 2.42/1.50 % [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 ...
% 121.71/37.16 % External prover 'cvc4' found a proof!
% 121.71/37.17 % [INFO] Killing All external provers ...
% 121.71/37.17 % Time passed: 36646ms (effective reasoning time: 36074ms)
% 121.71/37.17 % 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)>
% 121.71/37.17 % Axioms used in derivation (63): mLERef, mMulSc, mScSort, m__1930, mZeroNat, m__2318, m__1766, mLess, m__1678, mSuccEqu, m__1820, mNatExtr, mArith, m__2004, m__1783, mDefSPN, mMNeg, m__1854, m__2180, mLETrn, m__1949, mDefSPZ, m__1746, mSqrt, m__2303, mDimNat, m__1837, mLEMonM, mPosMon, m__2144, mIH, mDefInit, m__1911, m__2262, mMDNeg, mLETot, m__1800, mDistr, m__1967, mEqInit, mSZeroSc, mVcSort, mLEASm, mSumSc, mScZero, mLEMon, mScPr, m__1678_01, m__1892, mElmSc, m__2221, mDistr2, mSqPos, m__1709, m__1692, m__1652, mNatSort, m__1726, mIHOrd, mNegSc, mSuccNat, mScSqPos, m__1873
% 121.71/37.17 % No. of inferences in proof: 254
% 121.71/37.17 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 36646 ms resp. 36074 ms w/o parsing
% 121.71/37.22 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 121.71/37.22 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------