TSTP Solution File: RNG078+2 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : RNG078+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n007.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 11:49:18 EDT 2023
% Result : Theorem 171.99s 54.96s
% Output : Refutation 171.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 93
% Syntax : Number of formulae : 333 ( 102 unt; 33 typ; 0 def)
% Number of atoms : 845 ( 391 equ; 0 cnn)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 3114 ( 291 ~; 218 |; 166 &;2326 @)
% ( 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 : 215 ( 0 ^; 213 !; 2 ?; 215 :)
% 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(sdtasdt0_type,type,
sdtasdt0: $i > $i > $i ).
thf(xE_type,type,
xE: $i ).
thf(xH_type,type,
xH: $i ).
thf(xC_type,type,
xC: $i ).
thf(xD_type,type,
xD: $i ).
thf(xG_type,type,
xG: $i ).
thf(xF_type,type,
xF: $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(xq_type,type,
xq: $i ).
thf(iLess0_type,type,
iLess0: $i > $i > $o ).
thf(sdtasasdt0_type,type,
sdtasasdt0: $i > $i > $i ).
thf(smndt0_type,type,
smndt0: $i > $i ).
thf(xP_type,type,
xP: $i ).
thf(xR_type,type,
xR: $i ).
thf(xS_type,type,
xS: $i ).
thf(xN_type,type,
xN: $i ).
thf(sk1_type,type,
sk1: $i > $i ).
thf(sk2_type,type,
sk2: $i > $i > $i ).
thf(23,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(138,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)],[23]) ).
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(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 ) ) ) ) )
& ( ( ( 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(88,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)],[87]) ).
thf(91,plain,
! [B: $i,A: $i] :
( ~ ( aVector0 @ A )
| ( ( aDimensionOf0 @ A )
= sz00 )
| ( B
!= ( sziznziztdt0 @ A ) )
| ( ( szszuzczcdt0 @ ( aDimensionOf0 @ B ) )
= ( aDimensionOf0 @ A ) ) ),
inference(cnf,[status(esa)],[88]) ).
thf(100,plain,
! [B: $i,A: $i] :
( ( ( aDimensionOf0 @ A )
= sz00 )
| ( B
!= ( sziznziztdt0 @ A ) )
| ( ( szszuzczcdt0 @ ( aDimensionOf0 @ B ) )
= ( aDimensionOf0 @ A ) )
| ~ ( aVector0 @ A ) ),
inference(lifteq,[status(thm)],[91]) ).
thf(101,plain,
! [A: $i] :
( ( ( aDimensionOf0 @ A )
= sz00 )
| ( ( szszuzczcdt0 @ ( aDimensionOf0 @ ( sziznziztdt0 @ A ) ) )
= ( aDimensionOf0 @ A ) )
| ~ ( aVector0 @ A ) ),
inference(simp,[status(thm)],[100]) ).
thf(33,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(169,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)],[33]) ).
thf(170,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)],[169]) ).
thf(48,axiom,
sdtlseqdt0 @ ( sdtasdt0 @ xE @ xE ) @ ( sdtasdt0 @ xC @ xD ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1967) ).
thf(217,plain,
sdtlseqdt0 @ ( sdtasdt0 @ xE @ xE ) @ ( sdtasdt0 @ xC @ xD ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(58,axiom,
( ( aScalar0 @ xP )
& ( xP
= ( sdtasdt0 @ xE @ xH ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1911) ).
thf(256,plain,
( ( aScalar0 @ xP )
& ( xP
= ( sdtasdt0 @ xE @ xH ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(257,plain,
( xP
= ( sdtasdt0 @ xE @ xH ) ),
inference(cnf,[status(esa)],[256]) ).
thf(259,plain,
( ( sdtasdt0 @ xE @ xH )
= xP ),
inference(lifteq,[status(thm)],[257]) ).
thf(47,axiom,
( ( aScalar0 @ xR )
& ( xR
= ( sdtasdt0 @ xC @ xG ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1892) ).
thf(213,plain,
( ( aScalar0 @ xR )
& ( xR
= ( sdtasdt0 @ xC @ xG ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(214,plain,
( xR
= ( sdtasdt0 @ xC @ xG ) ),
inference(cnf,[status(esa)],[213]) ).
thf(216,plain,
( ( sdtasdt0 @ xC @ xG )
= xR ),
inference(lifteq,[status(thm)],[214]) ).
thf(39,axiom,
( ( aScalar0 @ xS )
& ( xS
= ( sdtasdt0 @ xF @ xD ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1930) ).
thf(186,plain,
( ( aScalar0 @ xS )
& ( xS
= ( sdtasdt0 @ xF @ xD ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(187,plain,
( xS
= ( sdtasdt0 @ xF @ xD ) ),
inference(cnf,[status(esa)],[186]) ).
thf(189,plain,
( ( sdtasdt0 @ xF @ xD )
= xS ),
inference(lifteq,[status(thm)],[187]) ).
thf(1,conjecture,
sdtlseqdt0 @ ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ xE @ xE ) @ ( sdtasdt0 @ xE @ xH ) ) @ ( sdtpldt0 @ ( sdtasdt0 @ xH @ xE ) @ ( sdtasdt0 @ xH @ xH ) ) ) @ ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ xC @ xD ) @ ( sdtasdt0 @ xC @ xG ) ) @ ( sdtpldt0 @ ( sdtasdt0 @ xF @ xD ) @ ( sdtasdt0 @ xF @ xG ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ( sdtlseqdt0 @ ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ xE @ xE ) @ ( sdtasdt0 @ xE @ xH ) ) @ ( sdtpldt0 @ ( sdtasdt0 @ xH @ xE ) @ ( sdtasdt0 @ xH @ xH ) ) ) @ ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ xC @ xD ) @ ( sdtasdt0 @ xC @ xG ) ) @ ( sdtpldt0 @ ( sdtasdt0 @ xF @ xD ) @ ( sdtasdt0 @ xF @ xG ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(62,plain,
~ ( sdtlseqdt0 @ ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ xE @ xE ) @ ( sdtasdt0 @ xE @ xH ) ) @ ( sdtpldt0 @ ( sdtasdt0 @ xH @ xE ) @ ( sdtasdt0 @ xH @ xH ) ) ) @ ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ xC @ xD ) @ ( sdtasdt0 @ xC @ xG ) ) @ ( sdtpldt0 @ ( sdtasdt0 @ xF @ xD ) @ ( sdtasdt0 @ xF @ xG ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(1952,plain,
~ ( sdtlseqdt0 @ ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ xE @ xE ) @ ( sdtasdt0 @ xE @ xH ) ) @ ( sdtpldt0 @ ( sdtasdt0 @ xH @ xE ) @ ( sdtasdt0 @ xH @ xH ) ) ) @ ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ xC @ xD ) @ ( sdtasdt0 @ xC @ xG ) ) @ ( sdtpldt0 @ xS @ ( sdtasdt0 @ xF @ xG ) ) ) ),
inference(rewrite,[status(thm)],[62,189]) ).
thf(1978,plain,
( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ xE @ xE ) @ ( sdtasdt0 @ xE @ xH ) ) @ ( sdtpldt0 @ ( sdtasdt0 @ xH @ xE ) @ ( sdtasdt0 @ xH @ xH ) ) ) @ ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ xC @ xD ) @ ( sdtasdt0 @ xC @ xG ) ) @ ( sdtpldt0 @ xS @ xS ) ) )
| ( ( sdtasdt0 @ xF @ xG )
!= ( sdtasdt0 @ xF @ xD ) ) ),
inference(paramod_ordered,[status(thm)],[189,1952]) ).
thf(2053,plain,
( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ xE @ xE ) @ ( sdtasdt0 @ xE @ xH ) ) @ ( sdtpldt0 @ ( sdtasdt0 @ xH @ xE ) @ ( sdtasdt0 @ xH @ xH ) ) ) @ ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ xC @ xD ) @ ( sdtasdt0 @ xC @ xG ) ) @ ( sdtpldt0 @ xS @ xS ) ) )
| ( xF != xF )
| ( xG != xD ) ),
inference(simp,[status(thm)],[1978]) ).
thf(2063,plain,
( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ xE @ xE ) @ ( sdtasdt0 @ xE @ xH ) ) @ ( sdtpldt0 @ ( sdtasdt0 @ xH @ xE ) @ ( sdtasdt0 @ xH @ xH ) ) ) @ ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ xC @ xD ) @ ( sdtasdt0 @ xC @ xG ) ) @ ( sdtpldt0 @ xS @ xS ) ) )
| ( xG != xD ) ),
inference(simp,[status(thm)],[2053]) ).
thf(2260,plain,
( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ xE @ xE ) @ ( sdtasdt0 @ xE @ xH ) ) @ ( sdtpldt0 @ ( sdtasdt0 @ xH @ xE ) @ ( sdtasdt0 @ xH @ xH ) ) ) @ ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ xC @ xD ) @ xR ) @ ( sdtpldt0 @ xS @ xS ) ) )
| ( xG != xD ) ),
inference(rewrite,[status(thm)],[2063,216]) ).
thf(2532,plain,
( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ xE @ xE ) @ ( sdtasdt0 @ xE @ xH ) ) @ ( sdtpldt0 @ ( sdtasdt0 @ xH @ xE ) @ ( sdtasdt0 @ xH @ xH ) ) ) @ ( sdtpldt0 @ ( sdtpldt0 @ xR @ xR ) @ ( sdtpldt0 @ xS @ xS ) ) )
| ( xG != xD )
| ( ( sdtasdt0 @ xC @ xG )
!= ( sdtasdt0 @ xC @ xD ) ) ),
inference(paramod_ordered,[status(thm)],[216,2260]) ).
thf(2572,plain,
( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ xE @ xE ) @ ( sdtasdt0 @ xE @ xH ) ) @ ( sdtpldt0 @ ( sdtasdt0 @ xH @ xE ) @ ( sdtasdt0 @ xH @ xH ) ) ) @ ( sdtpldt0 @ ( sdtpldt0 @ xR @ xR ) @ ( sdtpldt0 @ xS @ xS ) ) )
| ( xG != xD )
| ( xC != xC )
| ( xG != xD ) ),
inference(simp,[status(thm)],[2532]) ).
thf(2577,plain,
( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ xE @ xE ) @ ( sdtasdt0 @ xE @ xH ) ) @ ( sdtpldt0 @ ( sdtasdt0 @ xH @ xE ) @ ( sdtasdt0 @ xH @ xH ) ) ) @ ( sdtpldt0 @ ( sdtpldt0 @ xR @ xR ) @ ( sdtpldt0 @ xS @ xS ) ) )
| ( xG != xD ) ),
inference(simp,[status(thm)],[2572]) ).
thf(2821,plain,
( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ xE @ xE ) @ xP ) @ ( sdtpldt0 @ ( sdtasdt0 @ xH @ xE ) @ ( sdtasdt0 @ xH @ xH ) ) ) @ ( sdtpldt0 @ ( sdtpldt0 @ xR @ xR ) @ ( sdtpldt0 @ xS @ xS ) ) )
| ( xG != xD ) ),
inference(rewrite,[status(thm)],[2577,259]) ).
thf(2837,plain,
( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ xE @ xE ) @ xP ) @ ( sdtpldt0 @ xP @ ( sdtasdt0 @ xH @ xH ) ) ) @ ( sdtpldt0 @ ( sdtpldt0 @ xR @ xR ) @ ( sdtpldt0 @ xS @ xS ) ) )
| ( xG != xD )
| ( ( sdtasdt0 @ xH @ xE )
!= ( sdtasdt0 @ xE @ xH ) ) ),
inference(paramod_ordered,[status(thm)],[259,2821]) ).
thf(2887,plain,
( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ xE @ xE ) @ xP ) @ ( sdtpldt0 @ xP @ ( sdtasdt0 @ xH @ xH ) ) ) @ ( sdtpldt0 @ ( sdtpldt0 @ xR @ xR ) @ ( sdtpldt0 @ xS @ xS ) ) )
| ( xG != xD )
| ( xH != xE )
| ( xH != xE ) ),
inference(simp,[status(thm)],[2837]) ).
thf(2908,plain,
( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ xE @ xE ) @ xP ) @ ( sdtpldt0 @ xP @ ( sdtasdt0 @ xH @ xH ) ) ) @ ( sdtpldt0 @ ( sdtpldt0 @ xR @ xR ) @ ( sdtpldt0 @ xS @ xS ) ) )
| ( xG != xD )
| ( xH != xE ) ),
inference(simp,[status(thm)],[2887]) ).
thf(14,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(113,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)],[14]) ).
thf(116,plain,
( ( szszuzczcdt0 @ ( aDimensionOf0 @ xq ) )
= ( aDimensionOf0 @ xt ) ),
inference(cnf,[status(esa)],[113]) ).
thf(120,plain,
( ( szszuzczcdt0 @ ( aDimensionOf0 @ xq ) )
= ( aDimensionOf0 @ xt ) ),
inference(lifteq,[status(thm)],[116]) ).
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(247,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(8,axiom,
( ( aScalar0 @ xA )
& ( xA
= ( sdtlbdtrb0 @ xs @ ( aDimensionOf0 @ xs ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1746) ).
thf(80,plain,
( ( aScalar0 @ xA )
& ( xA
= ( sdtlbdtrb0 @ xs @ ( aDimensionOf0 @ xs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(81,plain,
( xA
= ( sdtlbdtrb0 @ xs @ ( aDimensionOf0 @ xs ) ) ),
inference(cnf,[status(esa)],[80]) ).
thf(83,plain,
( ( sdtlbdtrb0 @ xs @ ( aDimensionOf0 @ xs ) )
= xA ),
inference(lifteq,[status(thm)],[81]) ).
thf(16,axiom,
( ( aDimensionOf0 @ xs )
= ( aDimensionOf0 @ xt ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1678_01) ).
thf(122,plain,
( ( aDimensionOf0 @ xs )
= ( aDimensionOf0 @ xt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(123,plain,
( ( aDimensionOf0 @ xs )
= ( aDimensionOf0 @ xt ) ),
inference(lifteq,[status(thm)],[122]) ).
thf(2580,plain,
( ( sdtlbdtrb0 @ xs @ ( aDimensionOf0 @ xt ) )
= xA ),
inference(rewrite,[status(thm)],[83,123]) ).
thf(26,axiom,
aNaturalNumber0 @ sz00,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroNat) ).
thf(146,plain,
aNaturalNumber0 @ sz00,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(5,axiom,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( aNaturalNumber0 @ ( szszuzczcdt0 @ A ) )
& ( ( szszuzczcdt0 @ A )
!= sz00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSuccNat) ).
thf(71,plain,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( aNaturalNumber0 @ ( szszuzczcdt0 @ A ) )
& ( ( szszuzczcdt0 @ A )
!= sz00 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(72,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( aNaturalNumber0 @ ( szszuzczcdt0 @ A ) ) ),
inference(cnf,[status(esa)],[71]) ).
thf(1635,plain,
! [A: $i] :
( ( aNaturalNumber0 @ ( szszuzczcdt0 @ A ) )
| ( ( aNaturalNumber0 @ sz00 )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[146,72]) ).
thf(1636,plain,
aNaturalNumber0 @ ( szszuzczcdt0 @ sz00 ),
inference(pattern_uni,[status(thm)],[1635:[bind(A,$thf( sz00 ))]]) ).
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(63,plain,
! [A: $i] :
( ( ( aNaturalNumber0 @ A )
& ( A != sz00 ) )
=> ? [B: $i] :
( ( aNaturalNumber0 @ B )
& ( A
= ( szszuzczcdt0 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(64,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( A = sz00 )
| ( aNaturalNumber0 @ ( sk1 @ A ) ) ),
inference(cnf,[status(esa)],[63]) ).
thf(66,plain,
! [A: $i] :
( ( A = sz00 )
| ~ ( aNaturalNumber0 @ A )
| ( aNaturalNumber0 @ ( sk1 @ A ) ) ),
inference(lifteq,[status(thm)],[64]) ).
thf(1657,plain,
! [A: $i] :
( ( A = sz00 )
| ( aNaturalNumber0 @ ( sk1 @ A ) )
| ( ( aNaturalNumber0 @ ( szszuzczcdt0 @ sz00 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1636,66]) ).
thf(1658,plain,
( ( ( szszuzczcdt0 @ sz00 )
= sz00 )
| ( aNaturalNumber0 @ ( sk1 @ ( szszuzczcdt0 @ sz00 ) ) ) ),
inference(pattern_uni,[status(thm)],[1657:[bind(A,$thf( szszuzczcdt0 @ sz00 ))]]) ).
thf(73,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( ( szszuzczcdt0 @ A )
!= sz00 ) ),
inference(cnf,[status(esa)],[71]) ).
thf(74,plain,
! [A: $i] :
( ( ( szszuzczcdt0 @ A )
!= sz00 )
| ~ ( aNaturalNumber0 @ A ) ),
inference(lifteq,[status(thm)],[73]) ).
thf(358,plain,
! [A: $i] :
( ( ( szszuzczcdt0 @ A )
!= sz00 )
| ( ( aNaturalNumber0 @ sz00 )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[146,74]) ).
thf(359,plain,
( ( szszuzczcdt0 @ sz00 )
!= sz00 ),
inference(pattern_uni,[status(thm)],[358:[bind(A,$thf( sz00 ))]]) ).
thf(3211,plain,
aNaturalNumber0 @ ( sk1 @ ( szszuzczcdt0 @ sz00 ) ),
inference(simplifyReflect,[status(thm)],[1658,359]) ).
thf(3237,plain,
! [A: $i] :
( ( aNaturalNumber0 @ ( szszuzczcdt0 @ A ) )
| ( ( aNaturalNumber0 @ ( sk1 @ ( szszuzczcdt0 @ sz00 ) ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3211,72]) ).
thf(3238,plain,
aNaturalNumber0 @ ( szszuzczcdt0 @ ( sk1 @ ( szszuzczcdt0 @ sz00 ) ) ),
inference(pattern_uni,[status(thm)],[3237:[bind(A,$thf( sk1 @ ( szszuzczcdt0 @ sz00 ) ))]]) ).
thf(3465,plain,
! [A: $i] :
( ( aNaturalNumber0 @ ( szszuzczcdt0 @ A ) )
| ( ( aNaturalNumber0 @ ( szszuzczcdt0 @ ( sk1 @ ( szszuzczcdt0 @ sz00 ) ) ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3238,72]) ).
thf(3466,plain,
aNaturalNumber0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( sk1 @ ( szszuzczcdt0 @ sz00 ) ) ) ),
inference(pattern_uni,[status(thm)],[3465:[bind(A,$thf( szszuzczcdt0 @ ( sk1 @ ( szszuzczcdt0 @ sz00 ) ) ))]]) ).
thf(3576,plain,
! [A: $i] :
( ( aNaturalNumber0 @ ( szszuzczcdt0 @ A ) )
| ( ( aNaturalNumber0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( sk1 @ ( szszuzczcdt0 @ sz00 ) ) ) ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3466,72]) ).
thf(3577,plain,
aNaturalNumber0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( sk1 @ ( szszuzczcdt0 @ sz00 ) ) ) ) ),
inference(pattern_uni,[status(thm)],[3576:[bind(A,$thf( szszuzczcdt0 @ ( szszuzczcdt0 @ ( sk1 @ ( szszuzczcdt0 @ sz00 ) ) ) ))]]) ).
thf(38,axiom,
sdtlseqdt0 @ ( sdtpldt0 @ xP @ xP ) @ ( sdtpldt0 @ xR @ xS ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1983) ).
thf(185,plain,
sdtlseqdt0 @ ( sdtpldt0 @ xP @ xP ) @ ( sdtpldt0 @ xR @ xS ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(1666,plain,
! [A: $i] :
( ( aNaturalNumber0 @ ( szszuzczcdt0 @ A ) )
| ( ( aNaturalNumber0 @ ( szszuzczcdt0 @ sz00 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1636,72]) ).
thf(1667,plain,
aNaturalNumber0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ),
inference(pattern_uni,[status(thm)],[1666:[bind(A,$thf( szszuzczcdt0 @ sz00 ))]]) ).
thf(2693,plain,
! [A: $i] :
( ( aNaturalNumber0 @ ( szszuzczcdt0 @ A ) )
| ( ( aNaturalNumber0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1667,72]) ).
thf(2694,plain,
aNaturalNumber0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ),
inference(pattern_uni,[status(thm)],[2693:[bind(A,$thf( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ))]]) ).
thf(1621,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( ( szszuzczcdt0 @ B )
!= sz00 )
| ( ( aNaturalNumber0 @ ( szszuzczcdt0 @ A ) )
!= ( aNaturalNumber0 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[72,74]) ).
thf(1622,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( ( szszuzczcdt0 @ ( szszuzczcdt0 @ A ) )
!= sz00 ) ),
inference(pattern_uni,[status(thm)],[1621:[bind(A,$thf( C )),bind(B,$thf( szszuzczcdt0 @ C ))]]) ).
thf(1647,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( ( szszuzczcdt0 @ ( szszuzczcdt0 @ A ) )
!= sz00 ) ),
inference(simp,[status(thm)],[1622]) ).
thf(3060,plain,
! [A: $i] :
( ( ( szszuzczcdt0 @ ( szszuzczcdt0 @ A ) )
!= sz00 )
| ( ( aNaturalNumber0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2694,1647]) ).
thf(3061,plain,
( ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ) ) )
!= sz00 ),
inference(pattern_uni,[status(thm)],[3060:[bind(A,$thf( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ))]]) ).
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(105,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,
( xp
= ( sziznziztdt0 @ xs ) ),
inference(cnf,[status(esa)],[105]) ).
thf(110,plain,
( ( sziznziztdt0 @ xs )
= xp ),
inference(lifteq,[status(thm)],[106]) ).
thf(18,axiom,
( ( aDimensionOf0 @ xs )
!= sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1692) ).
thf(125,plain,
( ( aDimensionOf0 @ xs )
!= sz00 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(126,plain,
( ( aDimensionOf0 @ xs )
!= sz00 ),
inference(polarity_switch,[status(thm)],[125]) ).
thf(127,plain,
( ( aDimensionOf0 @ xs )
!= sz00 ),
inference(lifteq,[status(thm)],[126]) ).
thf(1462,plain,
( ( aDimensionOf0 @ xt )
!= sz00 ),
inference(rewrite,[status(thm)],[127,123]) ).
thf(7,axiom,
( ( aScalar0 @ xB )
& ( xB
= ( sdtlbdtrb0 @ xt @ ( aDimensionOf0 @ xt ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1766) ).
thf(76,plain,
( ( aScalar0 @ xB )
& ( xB
= ( sdtlbdtrb0 @ xt @ ( aDimensionOf0 @ xt ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(78,plain,
aScalar0 @ xB,
inference(cnf,[status(esa)],[76]) ).
thf(31,axiom,
sdtlseqdt0 @ ( sdtpldt0 @ ( sdtasdt0 @ xE @ xE ) @ ( sdtpldt0 @ ( sdtpldt0 @ xP @ xP ) @ ( sdtasdt0 @ xH @ xH ) ) ) @ ( sdtpldt0 @ ( sdtasdt0 @ xC @ xD ) @ ( sdtpldt0 @ ( sdtpldt0 @ xR @ xS ) @ ( sdtasdt0 @ xH @ xH ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2796) ).
thf(164,plain,
sdtlseqdt0 @ ( sdtpldt0 @ ( sdtasdt0 @ xE @ xE ) @ ( sdtpldt0 @ ( sdtpldt0 @ xP @ xP ) @ ( sdtasdt0 @ xH @ xH ) ) ) @ ( sdtpldt0 @ ( sdtasdt0 @ xC @ xD ) @ ( sdtpldt0 @ ( sdtpldt0 @ xR @ xS ) @ ( sdtasdt0 @ xH @ xH ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(36,axiom,
( ( aScalar0 @ xH )
& ( xH
= ( sdtasdt0 @ xA @ xB ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1873) ).
thf(179,plain,
( ( aScalar0 @ xH )
& ( xH
= ( sdtasdt0 @ xA @ xB ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(15,axiom,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> $true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNatSort) ).
thf(121,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(46,axiom,
! [A: $i,B: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B ) )
=> ( aScalar0 @ ( sdtpldt0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSumSc) ).
thf(211,plain,
! [A: $i,B: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B ) )
=> ( aScalar0 @ ( sdtpldt0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(56,axiom,
! [A: $i,B: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B ) )
=> ( ( sdtlseqdt0 @ A @ B )
=> $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLess) ).
thf(253,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(9,axiom,
aScalar0 @ sz0z00,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSZeroSc) ).
thf(84,plain,
aScalar0 @ sz0z00,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(2925,plain,
( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ xE @ xE ) @ xP ) @ ( sdtpldt0 @ xP @ xP ) ) @ ( sdtpldt0 @ ( sdtpldt0 @ xR @ xR ) @ ( sdtpldt0 @ xS @ xS ) ) )
| ( xG != xD )
| ( xH != xE )
| ( ( sdtasdt0 @ xH @ xH )
!= ( sdtasdt0 @ xE @ xH ) ) ),
inference(paramod_ordered,[status(thm)],[259,2908]) ).
thf(2972,plain,
( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ xE @ xE ) @ xP ) @ ( sdtpldt0 @ xP @ xP ) ) @ ( sdtpldt0 @ ( sdtpldt0 @ xR @ xR ) @ ( sdtpldt0 @ xS @ xS ) ) )
| ( xG != xD )
| ( xH != xE )
| ( xH != xE )
| ( xH != xH ) ),
inference(simp,[status(thm)],[2925]) ).
thf(2986,plain,
( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ xE @ xE ) @ xP ) @ ( sdtpldt0 @ xP @ xP ) ) @ ( sdtpldt0 @ ( sdtpldt0 @ xR @ xR ) @ ( sdtpldt0 @ xS @ xS ) ) )
| ( xG != xD )
| ( xH != xE ) ),
inference(simp,[status(thm)],[2972]) ).
thf(3250,plain,
( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ ( sdtpldt0 @ xP @ xP ) @ ( sdtpldt0 @ xP @ xP ) ) @ ( sdtpldt0 @ ( sdtpldt0 @ xR @ xR ) @ ( sdtpldt0 @ xS @ xS ) ) )
| ( xG != xD )
| ( xH != xE )
| ( ( sdtasdt0 @ xE @ xH )
!= ( sdtasdt0 @ xE @ xE ) ) ),
inference(paramod_ordered,[status(thm)],[259,2986]) ).
thf(3294,plain,
( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ ( sdtpldt0 @ xP @ xP ) @ ( sdtpldt0 @ xP @ xP ) ) @ ( sdtpldt0 @ ( sdtpldt0 @ xR @ xR ) @ ( sdtpldt0 @ xS @ xS ) ) )
| ( xG != xD )
| ( xH != xE )
| ( xE != xE )
| ( xH != xE ) ),
inference(simp,[status(thm)],[3250]) ).
thf(3300,plain,
( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ ( sdtpldt0 @ xP @ xP ) @ ( sdtpldt0 @ xP @ xP ) ) @ ( sdtpldt0 @ ( sdtpldt0 @ xR @ xR ) @ ( sdtpldt0 @ xS @ xS ) ) )
| ( xG != xD )
| ( xH != xE ) ),
inference(simp,[status(thm)],[3294]) ).
thf(27,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(147,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)],[27]) ).
thf(3067,plain,
! [A: $i] :
( ( aNaturalNumber0 @ ( szszuzczcdt0 @ A ) )
| ( ( aNaturalNumber0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2694,72]) ).
thf(3068,plain,
aNaturalNumber0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ) ),
inference(pattern_uni,[status(thm)],[3067:[bind(A,$thf( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ))]]) ).
thf(49,axiom,
( ( aScalar0 @ xE )
& ( xE
= ( sdtasasdt0 @ xp @ xq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1820) ).
thf(218,plain,
( ( aScalar0 @ xE )
& ( xE
= ( sdtasasdt0 @ xp @ xq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(219,plain,
( xE
= ( sdtasasdt0 @ xp @ xq ) ),
inference(cnf,[status(esa)],[218]) ).
thf(221,plain,
( ( sdtasasdt0 @ xp @ xq )
= xE ),
inference(lifteq,[status(thm)],[219]) ).
thf(2771,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( ( szszuzczcdt0 @ ( aDimensionOf0 @ xt ) )
!= sz00 )
| ( ( szszuzczcdt0 @ ( aDimensionOf0 @ xq ) )
!= ( szszuzczcdt0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[120,1647]) ).
thf(2772,plain,
( ~ ( aNaturalNumber0 @ ( aDimensionOf0 @ xq ) )
| ( ( szszuzczcdt0 @ ( aDimensionOf0 @ xt ) )
!= sz00 ) ),
inference(pattern_uni,[status(thm)],[2771:[bind(A,$thf( aDimensionOf0 @ xq ))]]) ).
thf(21,axiom,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( iLess0 @ A @ ( szszuzczcdt0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIH) ).
thf(133,plain,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( iLess0 @ A @ ( szszuzczcdt0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(52,axiom,
( ( aScalar0 @ xC )
& ( xC
= ( sdtasasdt0 @ xp @ xp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1783) ).
thf(241,plain,
( ( aScalar0 @ xC )
& ( xC
= ( sdtasasdt0 @ xp @ xp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(243,plain,
aScalar0 @ xC,
inference(cnf,[status(esa)],[241]) ).
thf(60,axiom,
( ( aScalar0 @ xG )
& ( xG
= ( sdtasdt0 @ xB @ xB ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1854) ).
thf(262,plain,
( ( aScalar0 @ xG )
& ( xG
= ( sdtasdt0 @ xB @ xB ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(263,plain,
( xG
= ( sdtasdt0 @ xB @ xB ) ),
inference(cnf,[status(esa)],[262]) ).
thf(265,plain,
( ( sdtasdt0 @ xB @ xB )
= xG ),
inference(lifteq,[status(thm)],[263]) ).
thf(44,axiom,
( ( aScalar0 @ xN )
& ( xN
= ( sdtasdt0 @ xR @ xS ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1949) ).
thf(203,plain,
( ( aScalar0 @ xN )
& ( xN
= ( sdtasdt0 @ xR @ xS ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(204,plain,
( xN
= ( sdtasdt0 @ xR @ xS ) ),
inference(cnf,[status(esa)],[203]) ).
thf(206,plain,
( ( sdtasdt0 @ xR @ xS )
= xN ),
inference(lifteq,[status(thm)],[204]) ).
thf(2829,plain,
( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ ( sdtpldt0 @ xG @ xP ) @ ( sdtpldt0 @ ( sdtasdt0 @ xH @ xE ) @ ( sdtasdt0 @ xH @ xH ) ) ) @ ( sdtpldt0 @ ( sdtpldt0 @ xR @ xR ) @ ( sdtpldt0 @ xS @ xS ) ) )
| ( xG != xD )
| ( ( sdtasdt0 @ xB @ xB )
!= ( sdtasdt0 @ xE @ xE ) ) ),
inference(paramod_ordered,[status(thm)],[265,2821]) ).
thf(2892,plain,
( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ ( sdtpldt0 @ xG @ xP ) @ ( sdtpldt0 @ ( sdtasdt0 @ xH @ xE ) @ ( sdtasdt0 @ xH @ xH ) ) ) @ ( sdtpldt0 @ ( sdtpldt0 @ xR @ xR ) @ ( sdtpldt0 @ xS @ xS ) ) )
| ( xG != xD )
| ( xB != xE )
| ( xB != xE ) ),
inference(simp,[status(thm)],[2829]) ).
thf(2910,plain,
( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ ( sdtpldt0 @ xG @ xP ) @ ( sdtpldt0 @ ( sdtasdt0 @ xH @ xE ) @ ( sdtasdt0 @ xH @ xH ) ) ) @ ( sdtpldt0 @ ( sdtpldt0 @ xR @ xR ) @ ( sdtpldt0 @ xS @ xS ) ) )
| ( xG != xD )
| ( xB != xE ) ),
inference(simp,[status(thm)],[2892]) ).
thf(45,axiom,
( ( aScalar0 @ xF )
& ( xF
= ( sdtasdt0 @ xA @ xA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
thf(207,plain,
( ( aScalar0 @ xF )
& ( xF
= ( sdtasdt0 @ xA @ xA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(208,plain,
( xF
= ( sdtasdt0 @ xA @ xA ) ),
inference(cnf,[status(esa)],[207]) ).
thf(210,plain,
( ( sdtasdt0 @ xA @ xA )
= xF ),
inference(lifteq,[status(thm)],[208]) ).
thf(3288,plain,
( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ ( sdtpldt0 @ xF @ xP ) @ ( sdtpldt0 @ xP @ xP ) ) @ ( sdtpldt0 @ ( sdtpldt0 @ xR @ xR ) @ ( sdtpldt0 @ xS @ xS ) ) )
| ( xG != xD )
| ( xH != xE )
| ( ( sdtasdt0 @ xA @ xA )
!= ( sdtasdt0 @ xE @ xE ) ) ),
inference(paramod_ordered,[status(thm)],[210,2986]) ).
thf(3296,plain,
( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ ( sdtpldt0 @ xF @ xP ) @ ( sdtpldt0 @ xP @ xP ) ) @ ( sdtpldt0 @ ( sdtpldt0 @ xR @ xR ) @ ( sdtpldt0 @ xS @ xS ) ) )
| ( xG != xD )
| ( xH != xE )
| ( xA != xE )
| ( xA != xE ) ),
inference(simp,[status(thm)],[3288]) ).
thf(3301,plain,
( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ ( sdtpldt0 @ xF @ xP ) @ ( sdtpldt0 @ xP @ xP ) ) @ ( sdtpldt0 @ ( sdtpldt0 @ xR @ xR ) @ ( sdtpldt0 @ xS @ xS ) ) )
| ( xG != xD )
| ( xH != xE )
| ( xA != xE ) ),
inference(simp,[status(thm)],[3296]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( ( aVector0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( aScalar0 @ ( sdtlbdtrb0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mElmSc) ).
thf(85,plain,
! [A: $i,B: $i] :
( ( ( aVector0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( aScalar0 @ ( sdtlbdtrb0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(3458,plain,
! [A: $i] :
( ( ( szszuzczcdt0 @ ( szszuzczcdt0 @ A ) )
!= sz00 )
| ( ( aNaturalNumber0 @ ( szszuzczcdt0 @ ( sk1 @ ( szszuzczcdt0 @ sz00 ) ) ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3238,1647]) ).
thf(3459,plain,
( ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( sk1 @ ( szszuzczcdt0 @ sz00 ) ) ) ) )
!= sz00 ),
inference(pattern_uni,[status(thm)],[3458:[bind(A,$thf( szszuzczcdt0 @ ( sk1 @ ( szszuzczcdt0 @ sz00 ) ) ))]]) ).
thf(117,plain,
aVector0 @ xq,
inference(cnf,[status(esa)],[113]) ).
thf(108,plain,
( ( szszuzczcdt0 @ ( aDimensionOf0 @ xp ) )
= ( aDimensionOf0 @ xs ) ),
inference(cnf,[status(esa)],[105]) ).
thf(112,plain,
( ( szszuzczcdt0 @ ( aDimensionOf0 @ xp ) )
= ( aDimensionOf0 @ xs ) ),
inference(lifteq,[status(thm)],[108]) ).
thf(2697,plain,
( ( szszuzczcdt0 @ ( aDimensionOf0 @ xp ) )
= ( aDimensionOf0 @ xt ) ),
inference(rewrite,[status(thm)],[112,123]) ).
thf(1669,plain,
! [A: $i] :
( ( ( szszuzczcdt0 @ A )
!= sz00 )
| ( ( aNaturalNumber0 @ ( szszuzczcdt0 @ sz00 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1636,74]) ).
thf(1670,plain,
( ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) )
!= sz00 ),
inference(pattern_uni,[status(thm)],[1669:[bind(A,$thf( szszuzczcdt0 @ sz00 ))]]) ).
thf(2726,plain,
( ( ( szszuzczcdt0 @ ( aDimensionOf0 @ xt ) )
!= sz00 )
| ( ( szszuzczcdt0 @ ( aDimensionOf0 @ xp ) )
!= ( szszuzczcdt0 @ sz00 ) ) ),
inference(paramod_ordered,[status(thm)],[2697,1670]) ).
thf(2737,plain,
( ( ( szszuzczcdt0 @ ( aDimensionOf0 @ xt ) )
!= sz00 )
| ( ( aDimensionOf0 @ xp )
!= sz00 ) ),
inference(simp,[status(thm)],[2726]) ).
thf(220,plain,
aScalar0 @ xE,
inference(cnf,[status(esa)],[218]) ).
thf(59,axiom,
! [A: $i,B: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B ) )
=> ( ( sdtlseqdt0 @ A @ B )
| ( sdtlseqdt0 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETot) ).
thf(260,plain,
! [A: $i,B: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B ) )
=> ( ( sdtlseqdt0 @ A @ B )
| ( sdtlseqdt0 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
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(68,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(69,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( ( szszuzczcdt0 @ A )
!= ( szszuzczcdt0 @ B ) )
| ( A = B ) ),
inference(cnf,[status(esa)],[68]) ).
thf(70,plain,
! [B: $i,A: $i] :
( ( ( szszuzczcdt0 @ A )
!= ( szszuzczcdt0 @ B ) )
| ( A = B )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B ) ),
inference(lifteq,[status(thm)],[69]) ).
thf(3232,plain,
! [A: $i] :
( ( ( szszuzczcdt0 @ ( szszuzczcdt0 @ A ) )
!= sz00 )
| ( ( aNaturalNumber0 @ ( sk1 @ ( szszuzczcdt0 @ sz00 ) ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3211,1647]) ).
thf(3233,plain,
( ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( sk1 @ ( szszuzczcdt0 @ sz00 ) ) ) )
!= sz00 ),
inference(pattern_uni,[status(thm)],[3232:[bind(A,$thf( sk1 @ ( szszuzczcdt0 @ sz00 ) ))]]) ).
thf(22,axiom,
( ( aVector0 @ xs )
& ( aVector0 @ xt ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1678) ).
thf(135,plain,
( ( aVector0 @ xs )
& ( aVector0 @ xt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(137,plain,
aVector0 @ xs,
inference(cnf,[status(esa)],[135]) ).
thf(32,axiom,
( ( aScalar0 @ xD )
& ( xD
= ( sdtasasdt0 @ xq @ xq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1800) ).
thf(165,plain,
( ( aScalar0 @ xD )
& ( xD
= ( sdtasasdt0 @ xq @ xq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(42,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(197,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)],[42]) ).
thf(89,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)],[88]) ).
thf(96,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)],[89]) ).
thf(97,plain,
! [B: $i,A: $i] :
( ( ( aDimensionOf0 @ A )
= sz00 )
| ( ( sdtlbdtrb0 @ ( sziznziztdt0 @ A ) @ B )
= ( sdtlbdtrb0 @ A @ B ) )
| ~ ( aVector0 @ A )
| ~ ( aNaturalNumber0 @ B ) ),
inference(simp,[status(thm)],[96]) ).
thf(51,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(224,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)],[51]) ).
thf(2924,plain,
( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ ( sdtpldt0 @ xP @ xP ) @ ( sdtpldt0 @ xP @ ( sdtasdt0 @ xH @ xH ) ) ) @ ( sdtpldt0 @ ( sdtpldt0 @ xR @ xR ) @ ( sdtpldt0 @ xS @ xS ) ) )
| ( xG != xD )
| ( xH != xE )
| ( ( sdtasdt0 @ xE @ xH )
!= ( sdtasdt0 @ xE @ xE ) ) ),
inference(paramod_ordered,[status(thm)],[259,2908]) ).
thf(2983,plain,
( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ ( sdtpldt0 @ xP @ xP ) @ ( sdtpldt0 @ xP @ ( sdtasdt0 @ xH @ xH ) ) ) @ ( sdtpldt0 @ ( sdtpldt0 @ xR @ xR ) @ ( sdtpldt0 @ xS @ xS ) ) )
| ( xG != xD )
| ( xH != xE )
| ( xE != xE )
| ( xH != xE ) ),
inference(simp,[status(thm)],[2924]) ).
thf(2990,plain,
( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ ( sdtpldt0 @ xP @ xP ) @ ( sdtpldt0 @ xP @ ( sdtasdt0 @ xH @ xH ) ) ) @ ( sdtpldt0 @ ( sdtpldt0 @ xR @ xR ) @ ( sdtpldt0 @ xS @ xS ) ) )
| ( xG != xD )
| ( xH != xE ) ),
inference(simp,[status(thm)],[2983]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B ) )
=> ( aScalar0 @ ( sdtasdt0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulSc) ).
thf(156,plain,
! [A: $i,B: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B ) )
=> ( aScalar0 @ ( sdtasdt0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(188,plain,
aScalar0 @ xS,
inference(cnf,[status(esa)],[186]) ).
thf(24,axiom,
! [A: $i] :
( ( aScalar0 @ A )
=> ( aScalar0 @ ( smndt0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNegSc) ).
thf(141,plain,
! [A: $i] :
( ( aScalar0 @ A )
=> ( aScalar0 @ ( smndt0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( iLess0 @ A @ B )
=> $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIHOrd) ).
thf(124,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(3632,plain,
( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ ( sdtpldt0 @ xP @ xP ) @ ( sdtpldt0 @ xP @ xF ) ) @ ( sdtpldt0 @ ( sdtpldt0 @ xR @ xR ) @ ( sdtpldt0 @ xS @ xS ) ) )
| ( xG != xD )
| ( xH != xE )
| ( ( sdtasdt0 @ xA @ xA )
!= ( sdtasdt0 @ xH @ xH ) ) ),
inference(paramod_ordered,[status(thm)],[210,2990]) ).
thf(3634,plain,
( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ ( sdtpldt0 @ xP @ xP ) @ ( sdtpldt0 @ xP @ xF ) ) @ ( sdtpldt0 @ ( sdtpldt0 @ xR @ xR ) @ ( sdtpldt0 @ xS @ xS ) ) )
| ( xG != xD )
| ( xH != xE )
| ( xA != xH )
| ( xA != xH ) ),
inference(simp,[status(thm)],[3632]) ).
thf(3643,plain,
( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ ( sdtpldt0 @ xP @ xP ) @ ( sdtpldt0 @ xP @ xF ) ) @ ( sdtpldt0 @ ( sdtpldt0 @ xR @ xR ) @ ( sdtpldt0 @ xS @ xS ) ) )
| ( xG != xD )
| ( xH != xE )
| ( xA != xH ) ),
inference(simp,[status(thm)],[3634]) ).
thf(109,plain,
aVector0 @ xp,
inference(cnf,[status(esa)],[105]) ).
thf(3108,plain,
! [A: $i] :
( ( ( szszuzczcdt0 @ ( szszuzczcdt0 @ A ) )
!= sz00 )
| ( ( aNaturalNumber0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ) ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3068,1647]) ).
thf(3109,plain,
( ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ) ) ) )
!= sz00 ),
inference(pattern_uni,[status(thm)],[3108:[bind(A,$thf( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ) ))]]) ).
thf(3214,plain,
! [A: $i] :
( ( ( szszuzczcdt0 @ A )
!= sz00 )
| ( ( aNaturalNumber0 @ ( sk1 @ ( szszuzczcdt0 @ sz00 ) ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3211,74]) ).
thf(3215,plain,
( ( szszuzczcdt0 @ ( sk1 @ ( szszuzczcdt0 @ sz00 ) ) )
!= sz00 ),
inference(pattern_uni,[status(thm)],[3214:[bind(A,$thf( sk1 @ ( szszuzczcdt0 @ sz00 ) ))]]) ).
thf(19,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(128,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)],[19]) ).
thf(61,axiom,
! [A: $i] :
( ( aScalar0 @ A )
=> ( sdtlseqdt0 @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLERef) ).
thf(266,plain,
! [A: $i] :
( ( aScalar0 @ A )
=> ( sdtlseqdt0 @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(205,plain,
aScalar0 @ xN,
inference(cnf,[status(esa)],[203]) ).
thf(2883,plain,
( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ ( sdtpldt0 @ xF @ xP ) @ ( sdtpldt0 @ ( sdtasdt0 @ xH @ xE ) @ ( sdtasdt0 @ xH @ xH ) ) ) @ ( sdtpldt0 @ ( sdtpldt0 @ xR @ xR ) @ ( sdtpldt0 @ xS @ xS ) ) )
| ( xG != xD )
| ( ( sdtasdt0 @ xA @ xA )
!= ( sdtasdt0 @ xE @ xE ) ) ),
inference(paramod_ordered,[status(thm)],[210,2821]) ).
thf(2889,plain,
( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ ( sdtpldt0 @ xF @ xP ) @ ( sdtpldt0 @ ( sdtasdt0 @ xH @ xE ) @ ( sdtasdt0 @ xH @ xH ) ) ) @ ( sdtpldt0 @ ( sdtpldt0 @ xR @ xR ) @ ( sdtpldt0 @ xS @ xS ) ) )
| ( xG != xD )
| ( xA != xE )
| ( xA != xE ) ),
inference(simp,[status(thm)],[2883]) ).
thf(2909,plain,
( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ ( sdtpldt0 @ xF @ xP ) @ ( sdtpldt0 @ ( sdtasdt0 @ xH @ xE ) @ ( sdtasdt0 @ xH @ xH ) ) ) @ ( sdtpldt0 @ ( sdtpldt0 @ xR @ xR ) @ ( sdtpldt0 @ xS @ xS ) ) )
| ( xG != xD )
| ( xA != xE ) ),
inference(simp,[status(thm)],[2889]) ).
thf(242,plain,
( xC
= ( sdtasasdt0 @ xp @ xp ) ),
inference(cnf,[status(esa)],[241]) ).
thf(244,plain,
( ( sdtasasdt0 @ xp @ xp )
= xC ),
inference(lifteq,[status(thm)],[242]) ).
thf(264,plain,
aScalar0 @ xG,
inference(cnf,[status(esa)],[262]) ).
thf(30,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(161,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)],[30]) ).
thf(35,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(176,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)],[35]) ).
thf(114,plain,
( xq
= ( sziznziztdt0 @ xt ) ),
inference(cnf,[status(esa)],[113]) ).
thf(118,plain,
( ( sziznziztdt0 @ xt )
= xq ),
inference(lifteq,[status(thm)],[114]) ).
thf(2307,plain,
! [A: $i] :
( ( ( szszuzczcdt0 @ ( szszuzczcdt0 @ A ) )
!= sz00 )
| ( ( aNaturalNumber0 @ ( szszuzczcdt0 @ sz00 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1636,1647]) ).
thf(2308,plain,
( ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) )
!= sz00 ),
inference(pattern_uni,[status(thm)],[2307:[bind(A,$thf( szszuzczcdt0 @ sz00 ))]]) ).
thf(181,plain,
aScalar0 @ xH,
inference(cnf,[status(esa)],[179]) ).
thf(3567,plain,
! [A: $i] :
( ( ( szszuzczcdt0 @ ( szszuzczcdt0 @ A ) )
!= sz00 )
| ( ( aNaturalNumber0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( sk1 @ ( szszuzczcdt0 @ sz00 ) ) ) ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3466,1647]) ).
thf(3568,plain,
( ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( sk1 @ ( szszuzczcdt0 @ sz00 ) ) ) ) ) )
!= sz00 ),
inference(pattern_uni,[status(thm)],[3567:[bind(A,$thf( szszuzczcdt0 @ ( szszuzczcdt0 @ ( sk1 @ ( szszuzczcdt0 @ sz00 ) ) ) ))]]) ).
thf(86,plain,
! [B: $i,A: $i] :
( ~ ( aVector0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( aScalar0 @ ( sdtlbdtrb0 @ A @ B ) ) ),
inference(cnf,[status(esa)],[85]) ).
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(245,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(2884,plain,
( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ xE @ xE ) @ xP ) @ ( sdtpldt0 @ ( sdtasdt0 @ xH @ xE ) @ xF ) ) @ ( sdtpldt0 @ ( sdtpldt0 @ xR @ xR ) @ ( sdtpldt0 @ xS @ xS ) ) )
| ( xG != xD )
| ( ( sdtasdt0 @ xA @ xA )
!= ( sdtasdt0 @ xH @ xH ) ) ),
inference(paramod_ordered,[status(thm)],[210,2821]) ).
thf(2894,plain,
( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ xE @ xE ) @ xP ) @ ( sdtpldt0 @ ( sdtasdt0 @ xH @ xE ) @ xF ) ) @ ( sdtpldt0 @ ( sdtpldt0 @ xR @ xR ) @ ( sdtpldt0 @ xS @ xS ) ) )
| ( xG != xD )
| ( xA != xH )
| ( xA != xH ) ),
inference(simp,[status(thm)],[2884]) ).
thf(2911,plain,
( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ xE @ xE ) @ xP ) @ ( sdtpldt0 @ ( sdtasdt0 @ xH @ xE ) @ xF ) ) @ ( sdtpldt0 @ ( sdtpldt0 @ xR @ xR ) @ ( sdtpldt0 @ xS @ xS ) ) )
| ( xG != xD )
| ( xA != xH ) ),
inference(simp,[status(thm)],[2894]) ).
thf(92,plain,
! [B: $i,A: $i] :
( ~ ( aVector0 @ A )
| ( ( aDimensionOf0 @ A )
= sz00 )
| ( B
!= ( sziznziztdt0 @ A ) )
| ( aVector0 @ B ) ),
inference(cnf,[status(esa)],[88]) ).
thf(98,plain,
! [B: $i,A: $i] :
( ( ( aDimensionOf0 @ A )
= sz00 )
| ( B
!= ( sziznziztdt0 @ A ) )
| ~ ( aVector0 @ A )
| ( aVector0 @ B ) ),
inference(lifteq,[status(thm)],[92]) ).
thf(99,plain,
! [A: $i] :
( ( ( aDimensionOf0 @ A )
= sz00 )
| ~ ( aVector0 @ A )
| ( aVector0 @ ( sziznziztdt0 @ A ) ) ),
inference(simp,[status(thm)],[98]) ).
thf(4066,plain,
! [A: $i] :
( ( ( aDimensionOf0 @ A )
= sz00 )
| ( aVector0 @ ( sziznziztdt0 @ A ) )
| ( ( aVector0 @ xq )
!= ( aVector0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[117,99]) ).
thf(4067,plain,
( ( ( aDimensionOf0 @ xq )
= sz00 )
| ( aVector0 @ ( sziznziztdt0 @ xq ) ) ),
inference(pattern_uni,[status(thm)],[4066:[bind(A,$thf( xq ))]]) ).
thf(167,plain,
aScalar0 @ xD,
inference(cnf,[status(esa)],[165]) ).
thf(209,plain,
aScalar0 @ xF,
inference(cnf,[status(esa)],[207]) ).
thf(93,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)],[88]) ).
thf(94,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)],[93]) ).
thf(95,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)],[94]) ).
thf(3116,plain,
! [A: $i] :
( ( aNaturalNumber0 @ ( szszuzczcdt0 @ A ) )
| ( ( aNaturalNumber0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ) ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3068,72]) ).
thf(3117,plain,
aNaturalNumber0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ) ) ),
inference(pattern_uni,[status(thm)],[3116:[bind(A,$thf( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ) ))]]) ).
thf(3832,plain,
! [A: $i] :
( ( ( szszuzczcdt0 @ ( szszuzczcdt0 @ A ) )
!= sz00 )
| ( ( aNaturalNumber0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ) ) ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3117,1647]) ).
thf(3833,plain,
( ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ) ) ) ) )
!= sz00 ),
inference(pattern_uni,[status(thm)],[3832:[bind(A,$thf( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ) ) ))]]) ).
thf(65,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( A = sz00 )
| ( A
= ( szszuzczcdt0 @ ( sk1 @ A ) ) ) ),
inference(cnf,[status(esa)],[63]) ).
thf(67,plain,
! [A: $i] :
( ( A = sz00 )
| ( ( szszuzczcdt0 @ ( sk1 @ A ) )
= A )
| ~ ( aNaturalNumber0 @ A ) ),
inference(lifteq,[status(thm)],[65]) ).
thf(180,plain,
( xH
= ( sdtasdt0 @ xA @ xB ) ),
inference(cnf,[status(esa)],[179]) ).
thf(182,plain,
( ( sdtasdt0 @ xA @ xB )
= xH ),
inference(lifteq,[status(thm)],[180]) ).
thf(2699,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( ( szszuzczcdt0 @ ( aDimensionOf0 @ xt ) )
!= sz00 )
| ( ( szszuzczcdt0 @ ( aDimensionOf0 @ xp ) )
!= ( szszuzczcdt0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2697,1647]) ).
thf(2700,plain,
( ~ ( aNaturalNumber0 @ ( aDimensionOf0 @ xp ) )
| ( ( szszuzczcdt0 @ ( aDimensionOf0 @ xt ) )
!= sz00 ) ),
inference(pattern_uni,[status(thm)],[2699:[bind(A,$thf( aDimensionOf0 @ xp ))]]) ).
thf(3960,plain,
! [A: $i] :
( ( aNaturalNumber0 @ ( szszuzczcdt0 @ A ) )
| ( ( aNaturalNumber0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( sk1 @ ( szszuzczcdt0 @ sz00 ) ) ) ) ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3577,72]) ).
thf(3961,plain,
aNaturalNumber0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( sk1 @ ( szszuzczcdt0 @ sz00 ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[3960:[bind(A,$thf( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( sk1 @ ( szszuzczcdt0 @ sz00 ) ) ) ) ))]]) ).
thf(25,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(143,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)],[25]) ).
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(250,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(12,axiom,
! [A: $i] :
( ( aScalar0 @ A )
=> $true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mScSort) ).
thf(104,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(258,plain,
aScalar0 @ xP,
inference(cnf,[status(esa)],[256]) ).
thf(29,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(158,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)],[29]) ).
thf(34,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(171,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)],[34]) ).
thf(6,axiom,
! [A: $i] :
( ( aVector0 @ A )
=> $true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mVcSort) ).
thf(75,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(3592,plain,
( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ ( sdtpldt0 @ xP @ xP ) @ ( sdtpldt0 @ xP @ xG ) ) @ ( sdtpldt0 @ ( sdtpldt0 @ xR @ xR ) @ ( sdtpldt0 @ xS @ xS ) ) )
| ( xG != xD )
| ( xH != xE )
| ( ( sdtasdt0 @ xB @ xB )
!= ( sdtasdt0 @ xH @ xH ) ) ),
inference(paramod_ordered,[status(thm)],[265,2990]) ).
thf(3639,plain,
( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ ( sdtpldt0 @ xP @ xP ) @ ( sdtpldt0 @ xP @ xG ) ) @ ( sdtpldt0 @ ( sdtpldt0 @ xR @ xR ) @ ( sdtpldt0 @ xS @ xS ) ) )
| ( xG != xD )
| ( xH != xE )
| ( xB != xH )
| ( xB != xH ) ),
inference(simp,[status(thm)],[3592]) ).
thf(3645,plain,
( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ ( sdtpldt0 @ xP @ xP ) @ ( sdtpldt0 @ xP @ xG ) ) @ ( sdtpldt0 @ ( sdtpldt0 @ xR @ xR ) @ ( sdtpldt0 @ xS @ xS ) ) )
| ( xG != xD )
| ( xH != xE )
| ( xB != xH ) ),
inference(simp,[status(thm)],[3639]) ).
thf(82,plain,
aScalar0 @ xA,
inference(cnf,[status(esa)],[80]) ).
thf(40,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(190,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)],[40]) ).
thf(37,axiom,
! [A: $i] :
( ( aScalar0 @ A )
=> ( sdtlseqdt0 @ sz0z00 @ ( sdtasdt0 @ A @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSqPos) ).
thf(183,plain,
! [A: $i] :
( ( aScalar0 @ A )
=> ( sdtlseqdt0 @ sz0z00 @ ( sdtasdt0 @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(166,plain,
( xD
= ( sdtasasdt0 @ xq @ xq ) ),
inference(cnf,[status(esa)],[165]) ).
thf(168,plain,
( ( sdtasasdt0 @ xq @ xq )
= xD ),
inference(lifteq,[status(thm)],[166]) ).
thf(136,plain,
aVector0 @ xt,
inference(cnf,[status(esa)],[135]) ).
thf(77,plain,
( xB
= ( sdtlbdtrb0 @ xt @ ( aDimensionOf0 @ xt ) ) ),
inference(cnf,[status(esa)],[76]) ).
thf(79,plain,
( ( sdtlbdtrb0 @ xt @ ( aDimensionOf0 @ xt ) )
= xB ),
inference(lifteq,[status(thm)],[77]) ).
thf(41,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(195,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)],[41]) ).
thf(3842,plain,
! [A: $i] :
( ( aNaturalNumber0 @ ( szszuzczcdt0 @ A ) )
| ( ( aNaturalNumber0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ) ) ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3117,72]) ).
thf(3843,plain,
aNaturalNumber0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[3842:[bind(A,$thf( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ) ) ))]]) ).
thf(2798,plain,
( ( ( szszuzczcdt0 @ ( aDimensionOf0 @ xt ) )
!= sz00 )
| ( ( szszuzczcdt0 @ ( aDimensionOf0 @ xq ) )
!= ( szszuzczcdt0 @ sz00 ) ) ),
inference(paramod_ordered,[status(thm)],[120,1670]) ).
thf(2810,plain,
( ( ( szszuzczcdt0 @ ( aDimensionOf0 @ xt ) )
!= sz00 )
| ( ( aDimensionOf0 @ xq )
!= sz00 ) ),
inference(simp,[status(thm)],[2798]) ).
thf(20,axiom,
! [A: $i] :
( ( aVector0 @ A )
=> ( aNaturalNumber0 @ ( aDimensionOf0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDimNat) ).
thf(131,plain,
! [A: $i] :
( ( aVector0 @ A )
=> ( aNaturalNumber0 @ ( aDimensionOf0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(43,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(200,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)],[43]) ).
thf(57,axiom,
( ( sdtpldt0 @ ( sdtpldt0 @ xP @ xP ) @ ( sdtasdt0 @ xH @ xH ) )
= ( sdtpldt0 @ ( sdtasdt0 @ xE @ xH ) @ ( sdtpldt0 @ ( sdtasdt0 @ xH @ xE ) @ ( sdtasdt0 @ xH @ xH ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2835) ).
thf(254,plain,
( ( sdtpldt0 @ ( sdtpldt0 @ xP @ xP ) @ ( sdtasdt0 @ xH @ xH ) )
= ( sdtpldt0 @ ( sdtasdt0 @ xE @ xH ) @ ( sdtpldt0 @ ( sdtasdt0 @ xH @ xE ) @ ( sdtasdt0 @ xH @ xH ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(2671,plain,
! [A: $i] :
( ( ( szszuzczcdt0 @ ( szszuzczcdt0 @ A ) )
!= sz00 )
| ( ( aNaturalNumber0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1667,1647]) ).
thf(2672,plain,
( ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ) ) )
!= sz00 ),
inference(pattern_uni,[status(thm)],[2671:[bind(A,$thf( szszuzczcdt0 @ ( szszuzczcdt0 @ sz00 ) ))]]) ).
thf(3248,plain,
( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ ( sdtpldt0 @ xG @ xP ) @ ( sdtpldt0 @ xP @ xP ) ) @ ( sdtpldt0 @ ( sdtpldt0 @ xR @ xR ) @ ( sdtpldt0 @ xS @ xS ) ) )
| ( xG != xD )
| ( xH != xE )
| ( ( sdtasdt0 @ xB @ xB )
!= ( sdtasdt0 @ xE @ xE ) ) ),
inference(paramod_ordered,[status(thm)],[265,2986]) ).
thf(3293,plain,
( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ ( sdtpldt0 @ xG @ xP ) @ ( sdtpldt0 @ xP @ xP ) ) @ ( sdtpldt0 @ ( sdtpldt0 @ xR @ xR ) @ ( sdtpldt0 @ xS @ xS ) ) )
| ( xG != xD )
| ( xH != xE )
| ( xB != xE )
| ( xB != xE ) ),
inference(simp,[status(thm)],[3248]) ).
thf(3299,plain,
( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ ( sdtpldt0 @ xG @ xP ) @ ( sdtpldt0 @ xP @ xP ) ) @ ( sdtpldt0 @ ( sdtpldt0 @ xR @ xR ) @ ( sdtpldt0 @ xS @ xS ) ) )
| ( xG != xD )
| ( xH != xE )
| ( xB != xE ) ),
inference(simp,[status(thm)],[3293]) ).
thf(215,plain,
aScalar0 @ xR,
inference(cnf,[status(esa)],[213]) ).
thf(50,axiom,
! [A: $i] :
( ( aVector0 @ A )
=> ( sdtlseqdt0 @ sz0z00 @ ( sdtasasdt0 @ A @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mScSqPos) ).
thf(222,plain,
! [A: $i] :
( ( aVector0 @ A )
=> ( sdtlseqdt0 @ sz0z00 @ ( sdtasasdt0 @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(179483,plain,
$false,
inference(cvc4,[status(thm)],[138,101,170,217,2908,120,247,2580,3577,185,3466,3061,110,125,1462,189,78,216,164,179,121,211,253,84,3300,147,3068,221,2772,133,243,265,3211,74,206,2910,3301,85,1636,3459,117,2737,220,260,70,3233,137,165,2986,197,97,224,2990,156,2694,188,169,141,124,3643,109,256,2697,3109,3215,128,266,205,2909,105,244,264,161,176,118,259,71,2308,181,3568,86,113,3238,76,245,1667,213,66,2911,135,4067,167,241,80,209,123,63,95,1647,3833,2821,67,182,2700,359,72,1670,3117,3961,143,250,99,87,203,218,104,258,158,186,171,75,207,3645,82,146,190,183,168,262,210,136,79,195,3843,2810,131,200,68,62,254,2672,122,3299,215,222]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : RNG078+2 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n007.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % 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 20:15:24 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.93/0.89 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.25/1.05 % [INFO] Parsing done (161ms).
% 1.25/1.06 % [INFO] Running in sequential loop mode.
% 1.87/1.25 % [INFO] eprover registered as external prover.
% 1.87/1.26 % [INFO] cvc4 registered as external prover.
% 1.87/1.26 % [INFO] Scanning for conjecture ...
% 1.98/1.31 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.98/1.33 % [INFO] Found a conjecture and 59 axioms. Running axiom selection ...
% 2.30/1.39 % [INFO] Axiom selection finished. Selected 59 axioms (removed 0 axioms).
% 2.30/1.40 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.51/1.45 % [INFO] Problem is first-order (TPTP FOF).
% 2.58/1.46 % [INFO] Type checking passed.
% 2.58/1.46 % [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 ...
% 171.99/54.96 % External prover 'cvc4' found a proof!
% 171.99/54.96 % [INFO] Killing All external provers ...
% 171.99/54.96 % Time passed: 54433ms (effective reasoning time: 53898ms)
% 171.99/54.96 % 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)>
% 171.99/54.96 % Axioms used in derivation (59): mLERef, mMulSc, m__1930, mSqrt, mZeroNat, m__1766, mLess, m__1678, mSuccEqu, m__1820, mNatExtr, mArith, m__1783, mDefSPN, mMNeg, m__1854, mScSort, m__1983, mLETrn, m__1949, mDefSPZ, m__1746, mDimNat, m__1837, mLEMonM, mPosMon, mIH, m__2835, mDefInit, m__1911, mMDNeg, mLETot, m__1800, mDistr, m__1967, mEqInit, mSZeroSc, mVcSort, mLEASm, mSumSc, mScZero, mLEMon, mScPr, m__1678_01, m__2796, m__1892, mElmSc, mDistr2, mSqPos, m__1709, m__1692, m__1652, mNatSort, m__1726, mIHOrd, mNegSc, mSuccNat, mScSqPos, m__1873
% 171.99/54.96 % No. of inferences in proof: 300
% 171.99/54.96 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 54433 ms resp. 53898 ms w/o parsing
% 171.99/55.04 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 171.99/55.04 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------