%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : RNG078+2 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 : Sat Jun 21 05:24:07 AM UTC 2025
% Result : Theorem 18.00s 18.22s
% Output : Proof 18.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 105
% Syntax : Number of formulae : 354 ( 138 unt; 0 typ; 0 def)
% Number of atoms : 2122 ( 893 equ)
% Maximal formula atoms : 28 ( 5 avg)
% Number of connectives : 3448 (1741 ~;1361 |; 163 &)
% ( 171 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 61 ( 61 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 20 ( 20 usr; 15 con; 0-2 aty)
% Number of variables : 367 ( 346 !; 0 ?; 367 :)
% Comments :
%------------------------------------------------------------------------------
tff(sdtlseqdt0_type,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(sdtpldt0_type,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(sdtasdt0_type,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(xH_type,type,
xH: $i ).
tff(xS_type,type,
xS: $i ).
tff(xR_type,type,
xR: $i ).
tff(xD_type,type,
xD: $i ).
tff(xC_type,type,
xC: $i ).
tff(xP_type,type,
xP: $i ).
tff(xE_type,type,
xE: $i ).
tff(xG_type,type,
xG: $i ).
tff(xF_type,type,
xF: $i ).
tff(aScalar0_type,type,
aScalar0: $i > $o ).
tff(sdtasasdt0_type,type,
sdtasasdt0: ( $i * $i ) > $i ).
tff(xq_type,type,
xq: $i ).
tff(xp_type,type,
xp: $i ).
tff(xB_type,type,
xB: $i ).
tff(xA_type,type,
xA: $i ).
tff(sdtlbdtrb0_type,type,
sdtlbdtrb0: ( $i * $i ) > $i ).
tff(aDimensionOf0_type,type,
aDimensionOf0: $i > $i ).
tff(xt_type,type,
xt: $i ).
tff(xs_type,type,
xs: $i ).
tff(1,plain,
( ( xD = sdtasasdt0(xq,xq) )
<=> ( xD = sdtasasdt0(xq,xq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
( aScalar0(xD)
& ( xD = sdtasasdt0(xq,xq) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1800) ).
tff(3,plain,
xD = sdtasasdt0(xq,xq),
inference(and_elim,[status(thm)],[2]) ).
tff(4,plain,
xD = sdtasasdt0(xq,xq),
inference(modus_ponens,[status(thm)],[3,1]) ).
tff(5,plain,
sdtasasdt0(xq,xq) = xD,
inference(symmetry,[status(thm)],[4]) ).
tff(6,plain,
( ( xC = sdtasasdt0(xp,xp) )
<=> ( xC = sdtasasdt0(xp,xp) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
( aScalar0(xC)
& ( xC = sdtasasdt0(xp,xp) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1783) ).
tff(8,plain,
xC = sdtasasdt0(xp,xp),
inference(and_elim,[status(thm)],[7]) ).
tff(9,plain,
xC = sdtasasdt0(xp,xp),
inference(modus_ponens,[status(thm)],[8,6]) ).
tff(10,plain,
sdtasasdt0(xp,xp) = xC,
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
sdtasdt0(sdtasasdt0(xp,xp),sdtasasdt0(xq,xq)) = sdtasdt0(xC,xD),
inference(monotonicity,[status(thm)],[10,5]) ).
tff(12,plain,
( aScalar0(sdtasdt0(sdtasasdt0(xp,xp),sdtasasdt0(xq,xq)))
<=> aScalar0(sdtasdt0(xC,xD)) ),
inference(monotonicity,[status(thm)],[11]) ).
tff(13,plain,
( aScalar0(sdtasasdt0(xq,xq))
<=> aScalar0(xD) ),
inference(monotonicity,[status(thm)],[5]) ).
tff(14,plain,
( aScalar0(xD)
<=> aScalar0(sdtasasdt0(xq,xq)) ),
inference(symmetry,[status(thm)],[13]) ).
tff(15,plain,
( aScalar0(xD)
<=> aScalar0(xD) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,plain,
aScalar0(xD),
inference(and_elim,[status(thm)],[2]) ).
tff(17,plain,
aScalar0(xD),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
aScalar0(sdtasasdt0(xq,xq)),
inference(modus_ponens,[status(thm)],[17,14]) ).
tff(19,plain,
( aScalar0(sdtasasdt0(xp,xp))
<=> aScalar0(xC) ),
inference(monotonicity,[status(thm)],[10]) ).
tff(20,plain,
( aScalar0(xC)
<=> aScalar0(sdtasasdt0(xp,xp)) ),
inference(symmetry,[status(thm)],[19]) ).
tff(21,plain,
( aScalar0(xC)
<=> aScalar0(xC) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,plain,
aScalar0(xC),
inference(and_elim,[status(thm)],[7]) ).
tff(23,plain,
aScalar0(xC),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
aScalar0(sdtasasdt0(xp,xp)),
inference(modus_ponens,[status(thm)],[23,20]) ).
tff(25,plain,
^ [W0: $i,W1: $i] :
refl(( ( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
<=> ( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(26,plain,
( ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
<=> ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ) ),
inference(quant_intro,[status(thm)],[25]) ).
tff(27,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aScalar0(W0)
& aScalar0(W1) )
<=> ~ ( ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
( ~ ( aScalar0(W0)
& aScalar0(W1) )
<=> ~ ~ ( ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
rewrite(( ~ ~ ( ~ aScalar0(W1)
| ~ aScalar0(W0) )
<=> ( ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
( ~ ( aScalar0(W0)
& aScalar0(W1) )
<=> ( ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
( ( aScalar0(sdtasdt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) )
<=> ( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
rewrite(( ( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
<=> ( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
( ( aScalar0(sdtasdt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) )
<=> ( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(28,plain,
( ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,plain,
( ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,plain,
^ [W0: $i,W1: $i] :
rewrite(( ( ( aScalar0(W0)
& aScalar0(W1) )
=> aScalar0(sdtasdt0(W0,W1)) )
<=> ( aScalar0(sdtasdt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) ) )),
inference(bind,[status(th)],[]) ).
tff(31,plain,
( ! [W0: $i,W1: $i] :
( ( aScalar0(W0)
& aScalar0(W1) )
=> aScalar0(sdtasdt0(W0,W1)) )
<=> ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,axiom,
! [W0: $i,W1: $i] :
( ( aScalar0(W0)
& aScalar0(W1) )
=> aScalar0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulSc) ).
tff(33,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) ),
inference(modus_ponens,[status(thm)],[33,29]) ).
tff(35,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) ),
inference(skolemize,[status(sab)],[34]) ).
tff(36,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ),
inference(modus_ponens,[status(thm)],[35,28]) ).
tff(37,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ),
inference(modus_ponens,[status(thm)],[36,26]) ).
tff(38,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasasdt0(xq,xq))
| ~ aScalar0(sdtasasdt0(xp,xp))
| aScalar0(sdtasdt0(sdtasasdt0(xp,xp),sdtasasdt0(xq,xq))) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasasdt0(xq,xq))
| ~ aScalar0(sdtasasdt0(xp,xp))
| aScalar0(sdtasdt0(sdtasasdt0(xp,xp),sdtasasdt0(xq,xq))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,plain,
( ( aScalar0(sdtasdt0(sdtasasdt0(xp,xp),sdtasasdt0(xq,xq)))
| ~ aScalar0(sdtasasdt0(xq,xq))
| ~ aScalar0(sdtasasdt0(xp,xp)) )
<=> ( ~ aScalar0(sdtasasdt0(xq,xq))
| ~ aScalar0(sdtasasdt0(xp,xp))
| aScalar0(sdtasdt0(sdtasasdt0(xp,xp),sdtasasdt0(xq,xq))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(40,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtasdt0(sdtasasdt0(xp,xp),sdtasasdt0(xq,xq)))
| ~ aScalar0(sdtasasdt0(xq,xq))
| ~ aScalar0(sdtasasdt0(xp,xp)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasasdt0(xq,xq))
| ~ aScalar0(sdtasasdt0(xp,xp))
| aScalar0(sdtasdt0(sdtasasdt0(xp,xp),sdtasasdt0(xq,xq))) ) ),
inference(monotonicity,[status(thm)],[39]) ).
tff(41,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtasdt0(sdtasasdt0(xp,xp),sdtasasdt0(xq,xq)))
| ~ aScalar0(sdtasasdt0(xq,xq))
| ~ aScalar0(sdtasasdt0(xp,xp)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasasdt0(xq,xq))
| ~ aScalar0(sdtasasdt0(xp,xp))
| aScalar0(sdtasdt0(sdtasasdt0(xp,xp),sdtasasdt0(xq,xq))) ) ),
inference(transitivity,[status(thm)],[40,38]) ).
tff(42,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtasdt0(sdtasasdt0(xp,xp),sdtasasdt0(xq,xq)))
| ~ aScalar0(sdtasasdt0(xq,xq))
| ~ aScalar0(sdtasasdt0(xp,xp)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(43,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasasdt0(xq,xq))
| ~ aScalar0(sdtasasdt0(xp,xp))
| aScalar0(sdtasdt0(sdtasasdt0(xp,xp),sdtasasdt0(xq,xq))) ),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
( ~ aScalar0(sdtasasdt0(xq,xq))
| ~ aScalar0(sdtasasdt0(xp,xp))
| aScalar0(sdtasdt0(sdtasasdt0(xp,xp),sdtasasdt0(xq,xq))) ),
inference(unit_resolution,[status(thm)],[43,37]) ).
tff(45,plain,
aScalar0(sdtasdt0(sdtasasdt0(xp,xp),sdtasasdt0(xq,xq))),
inference(unit_resolution,[status(thm)],[44,24,18]) ).
tff(46,plain,
aScalar0(sdtasdt0(xC,xD)),
inference(modus_ponens,[status(thm)],[45,12]) ).
tff(47,plain,
( ( xR = sdtasdt0(xC,xG) )
<=> ( xR = sdtasdt0(xC,xG) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(48,axiom,
( aScalar0(xR)
& ( xR = sdtasdt0(xC,xG) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1892) ).
tff(49,plain,
xR = sdtasdt0(xC,xG),
inference(and_elim,[status(thm)],[48]) ).
tff(50,plain,
xR = sdtasdt0(xC,xG),
inference(modus_ponens,[status(thm)],[49,47]) ).
tff(51,plain,
sdtasdt0(xC,xG) = xR,
inference(symmetry,[status(thm)],[50]) ).
tff(52,plain,
( aScalar0(sdtasdt0(xC,xG))
<=> aScalar0(xR) ),
inference(monotonicity,[status(thm)],[51]) ).
tff(53,plain,
( aScalar0(xR)
<=> aScalar0(sdtasdt0(xC,xG)) ),
inference(symmetry,[status(thm)],[52]) ).
tff(54,plain,
( aScalar0(xR)
<=> aScalar0(xR) ),
inference(rewrite,[status(thm)],[]) ).
tff(55,plain,
aScalar0(xR),
inference(and_elim,[status(thm)],[48]) ).
tff(56,plain,
aScalar0(xR),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
aScalar0(sdtasdt0(xC,xG)),
inference(modus_ponens,[status(thm)],[56,53]) ).
tff(58,plain,
( ( xS = sdtasdt0(xF,xD) )
<=> ( xS = sdtasdt0(xF,xD) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(59,axiom,
( aScalar0(xS)
& ( xS = sdtasdt0(xF,xD) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1930) ).
tff(60,plain,
xS = sdtasdt0(xF,xD),
inference(and_elim,[status(thm)],[59]) ).
tff(61,plain,
xS = sdtasdt0(xF,xD),
inference(modus_ponens,[status(thm)],[60,58]) ).
tff(62,plain,
sdtasdt0(xF,xD) = xS,
inference(symmetry,[status(thm)],[61]) ).
tff(63,plain,
( aScalar0(sdtasdt0(xF,xD))
<=> aScalar0(xS) ),
inference(monotonicity,[status(thm)],[62]) ).
tff(64,plain,
( aScalar0(xS)
<=> aScalar0(sdtasdt0(xF,xD)) ),
inference(symmetry,[status(thm)],[63]) ).
tff(65,plain,
( aScalar0(xS)
<=> aScalar0(xS) ),
inference(rewrite,[status(thm)],[]) ).
tff(66,plain,
aScalar0(xS),
inference(and_elim,[status(thm)],[59]) ).
tff(67,plain,
aScalar0(xS),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
aScalar0(sdtasdt0(xF,xD)),
inference(modus_ponens,[status(thm)],[67,64]) ).
tff(69,plain,
( ( xG = sdtasdt0(xB,xB) )
<=> ( xG = sdtasdt0(xB,xB) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(70,axiom,
( aScalar0(xG)
& ( xG = sdtasdt0(xB,xB) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1854) ).
tff(71,plain,
xG = sdtasdt0(xB,xB),
inference(and_elim,[status(thm)],[70]) ).
tff(72,plain,
xG = sdtasdt0(xB,xB),
inference(modus_ponens,[status(thm)],[71,69]) ).
tff(73,plain,
sdtasdt0(xB,xB) = xG,
inference(symmetry,[status(thm)],[72]) ).
tff(74,plain,
( ( xF = sdtasdt0(xA,xA) )
<=> ( xF = sdtasdt0(xA,xA) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(75,axiom,
( aScalar0(xF)
& ( xF = sdtasdt0(xA,xA) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
tff(76,plain,
xF = sdtasdt0(xA,xA),
inference(and_elim,[status(thm)],[75]) ).
tff(77,plain,
xF = sdtasdt0(xA,xA),
inference(modus_ponens,[status(thm)],[76,74]) ).
tff(78,plain,
sdtasdt0(xA,xA) = xF,
inference(symmetry,[status(thm)],[77]) ).
tff(79,plain,
sdtasdt0(sdtasdt0(xA,xA),sdtasdt0(xB,xB)) = sdtasdt0(xF,xG),
inference(monotonicity,[status(thm)],[78,73]) ).
tff(80,plain,
( aScalar0(sdtasdt0(sdtasdt0(xA,xA),sdtasdt0(xB,xB)))
<=> aScalar0(sdtasdt0(xF,xG)) ),
inference(monotonicity,[status(thm)],[79]) ).
tff(81,plain,
( aScalar0(sdtasdt0(xB,xB))
<=> aScalar0(xG) ),
inference(monotonicity,[status(thm)],[73]) ).
tff(82,plain,
( aScalar0(xG)
<=> aScalar0(sdtasdt0(xB,xB)) ),
inference(symmetry,[status(thm)],[81]) ).
tff(83,plain,
( aScalar0(xG)
<=> aScalar0(xG) ),
inference(rewrite,[status(thm)],[]) ).
tff(84,plain,
aScalar0(xG),
inference(and_elim,[status(thm)],[70]) ).
tff(85,plain,
aScalar0(xG),
inference(modus_ponens,[status(thm)],[84,83]) ).
tff(86,plain,
aScalar0(sdtasdt0(xB,xB)),
inference(modus_ponens,[status(thm)],[85,82]) ).
tff(87,plain,
( aScalar0(sdtasdt0(xA,xA))
<=> aScalar0(xF) ),
inference(monotonicity,[status(thm)],[78]) ).
tff(88,plain,
( aScalar0(xF)
<=> aScalar0(sdtasdt0(xA,xA)) ),
inference(symmetry,[status(thm)],[87]) ).
tff(89,plain,
( aScalar0(xF)
<=> aScalar0(xF) ),
inference(rewrite,[status(thm)],[]) ).
tff(90,plain,
aScalar0(xF),
inference(and_elim,[status(thm)],[75]) ).
tff(91,plain,
aScalar0(xF),
inference(modus_ponens,[status(thm)],[90,89]) ).
tff(92,plain,
aScalar0(sdtasdt0(xA,xA)),
inference(modus_ponens,[status(thm)],[91,88]) ).
tff(93,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(xB,xB))
| ~ aScalar0(sdtasdt0(xA,xA))
| aScalar0(sdtasdt0(sdtasdt0(xA,xA),sdtasdt0(xB,xB))) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(xB,xB))
| ~ aScalar0(sdtasdt0(xA,xA))
| aScalar0(sdtasdt0(sdtasdt0(xA,xA),sdtasdt0(xB,xB))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(94,plain,
( ( aScalar0(sdtasdt0(sdtasdt0(xA,xA),sdtasdt0(xB,xB)))
| ~ aScalar0(sdtasdt0(xB,xB))
| ~ aScalar0(sdtasdt0(xA,xA)) )
<=> ( ~ aScalar0(sdtasdt0(xB,xB))
| ~ aScalar0(sdtasdt0(xA,xA))
| aScalar0(sdtasdt0(sdtasdt0(xA,xA),sdtasdt0(xB,xB))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(95,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtasdt0(sdtasdt0(xA,xA),sdtasdt0(xB,xB)))
| ~ aScalar0(sdtasdt0(xB,xB))
| ~ aScalar0(sdtasdt0(xA,xA)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(xB,xB))
| ~ aScalar0(sdtasdt0(xA,xA))
| aScalar0(sdtasdt0(sdtasdt0(xA,xA),sdtasdt0(xB,xB))) ) ),
inference(monotonicity,[status(thm)],[94]) ).
tff(96,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtasdt0(sdtasdt0(xA,xA),sdtasdt0(xB,xB)))
| ~ aScalar0(sdtasdt0(xB,xB))
| ~ aScalar0(sdtasdt0(xA,xA)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(xB,xB))
| ~ aScalar0(sdtasdt0(xA,xA))
| aScalar0(sdtasdt0(sdtasdt0(xA,xA),sdtasdt0(xB,xB))) ) ),
inference(transitivity,[status(thm)],[95,93]) ).
tff(97,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtasdt0(sdtasdt0(xA,xA),sdtasdt0(xB,xB)))
| ~ aScalar0(sdtasdt0(xB,xB))
| ~ aScalar0(sdtasdt0(xA,xA)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(98,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(xB,xB))
| ~ aScalar0(sdtasdt0(xA,xA))
| aScalar0(sdtasdt0(sdtasdt0(xA,xA),sdtasdt0(xB,xB))) ),
inference(modus_ponens,[status(thm)],[97,96]) ).
tff(99,plain,
( ~ aScalar0(sdtasdt0(xB,xB))
| ~ aScalar0(sdtasdt0(xA,xA))
| aScalar0(sdtasdt0(sdtasdt0(xA,xA),sdtasdt0(xB,xB))) ),
inference(unit_resolution,[status(thm)],[98,37]) ).
tff(100,plain,
aScalar0(sdtasdt0(sdtasdt0(xA,xA),sdtasdt0(xB,xB))),
inference(unit_resolution,[status(thm)],[99,92,86]) ).
tff(101,plain,
aScalar0(sdtasdt0(xF,xG)),
inference(modus_ponens,[status(thm)],[100,80]) ).
tff(102,plain,
^ [W0: $i,W1: $i] :
refl(( ( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
<=> ( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(103,plain,
( ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
<=> ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ) ),
inference(quant_intro,[status(thm)],[102]) ).
tff(104,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aScalar0(W0)
& aScalar0(W1) )
<=> ~ ( ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
( ~ ( aScalar0(W0)
& aScalar0(W1) )
<=> ~ ~ ( ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
rewrite(( ~ ~ ( ~ aScalar0(W1)
| ~ aScalar0(W0) )
<=> ( ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
( ~ ( aScalar0(W0)
& aScalar0(W1) )
<=> ( ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
( ( aScalar0(sdtpldt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) )
<=> ( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
rewrite(( ( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
<=> ( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
( ( aScalar0(sdtpldt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) )
<=> ( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(105,plain,
( ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ) ),
inference(quant_intro,[status(thm)],[104]) ).
tff(106,plain,
( ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(107,plain,
^ [W0: $i,W1: $i] :
rewrite(( ( ( aScalar0(W0)
& aScalar0(W1) )
=> aScalar0(sdtpldt0(W0,W1)) )
<=> ( aScalar0(sdtpldt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) ) )),
inference(bind,[status(th)],[]) ).
tff(108,plain,
( ! [W0: $i,W1: $i] :
( ( aScalar0(W0)
& aScalar0(W1) )
=> aScalar0(sdtpldt0(W0,W1)) )
<=> ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) ) ),
inference(quant_intro,[status(thm)],[107]) ).
tff(109,axiom,
! [W0: $i,W1: $i] :
( ( aScalar0(W0)
& aScalar0(W1) )
=> aScalar0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSumSc) ).
tff(110,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) ),
inference(modus_ponens,[status(thm)],[109,108]) ).
tff(111,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) ),
inference(modus_ponens,[status(thm)],[110,106]) ).
tff(112,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) ),
inference(skolemize,[status(sab)],[111]) ).
tff(113,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ),
inference(modus_ponens,[status(thm)],[112,105]) ).
tff(114,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ),
inference(modus_ponens,[status(thm)],[113,103]) ).
tff(115,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(xF,xD))
| ~ aScalar0(sdtasdt0(xF,xG))
| aScalar0(sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG))) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(xF,xD))
| ~ aScalar0(sdtasdt0(xF,xG))
| aScalar0(sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(116,plain,
( ( aScalar0(sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG)))
| ~ aScalar0(sdtasdt0(xF,xG))
| ~ aScalar0(sdtasdt0(xF,xD)) )
<=> ( ~ aScalar0(sdtasdt0(xF,xD))
| ~ aScalar0(sdtasdt0(xF,xG))
| aScalar0(sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(117,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG)))
| ~ aScalar0(sdtasdt0(xF,xG))
| ~ aScalar0(sdtasdt0(xF,xD)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(xF,xD))
| ~ aScalar0(sdtasdt0(xF,xG))
| aScalar0(sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG))) ) ),
inference(monotonicity,[status(thm)],[116]) ).
tff(118,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG)))
| ~ aScalar0(sdtasdt0(xF,xG))
| ~ aScalar0(sdtasdt0(xF,xD)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(xF,xD))
| ~ aScalar0(sdtasdt0(xF,xG))
| aScalar0(sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG))) ) ),
inference(transitivity,[status(thm)],[117,115]) ).
tff(119,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG)))
| ~ aScalar0(sdtasdt0(xF,xG))
| ~ aScalar0(sdtasdt0(xF,xD)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(120,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(xF,xD))
| ~ aScalar0(sdtasdt0(xF,xG))
| aScalar0(sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG))) ),
inference(modus_ponens,[status(thm)],[119,118]) ).
tff(121,plain,
( ~ aScalar0(sdtasdt0(xF,xD))
| ~ aScalar0(sdtasdt0(xF,xG))
| aScalar0(sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG))) ),
inference(unit_resolution,[status(thm)],[120,114]) ).
tff(122,plain,
aScalar0(sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG))),
inference(unit_resolution,[status(thm)],[121,101,68]) ).
tff(123,plain,
^ [W0: $i,W1: $i,W2: $i] :
refl(( ( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
<=> ( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(124,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[123]) ).
tff(125,plain,
^ [W0: $i,W1: $i,W2: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
<=> ~ ( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
( ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
<=> ~ ~ ( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
rewrite(( ~ ~ ( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
<=> ( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
( ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
<=> ( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
rewrite(( ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
& ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) )
<=> ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )),
( ( ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
| ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
& ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) )
<=> ( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) ) )),
rewrite(( ( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
<=> ( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) ) )),
( ( ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
| ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
& ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) )
<=> ( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(126,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
| ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
& ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[125]) ).
tff(127,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
| ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
& ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
| ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
& ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(128,plain,
^ [W0: $i,W1: $i,W2: $i] :
trans(monotonicity(rewrite(( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
<=> ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) ) )),
trans(monotonicity(rewrite(( ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) )
<=> ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) ) )),
( ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
& ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) )
<=> ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
& ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) )),
rewrite(( ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
& ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) )
<=> ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
& ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) )),
( ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
& ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) )
<=> ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
& ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) )),
( ( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
=> ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
& ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) )
<=> ( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
=> ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
& ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) ) )),
rewrite(( ( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
=> ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
& ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) )
<=> ( ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
| ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
& ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) ) )),
( ( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
=> ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
& ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) )
<=> ( ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
| ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
& ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(129,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
=> ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
& ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
| ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
& ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[128]) ).
tff(130,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
=> ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
& ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mArith) ).
tff(131,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
| ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
& ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) ),
inference(modus_ponens,[status(thm)],[130,129]) ).
tff(132,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
| ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
& ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) ),
inference(modus_ponens,[status(thm)],[131,127]) ).
tff(133,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
| ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
& ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) ),
inference(skolemize,[status(sab)],[132]) ).
tff(134,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) ),
inference(modus_ponens,[status(thm)],[133,126]) ).
tff(135,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) ),
inference(modus_ponens,[status(thm)],[134,124]) ).
tff(136,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtasdt0(xC,xG))
| ~ aScalar0(sdtasdt0(xC,xD))
| ~ aScalar0(sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG))) != sdtpldt0(sdtasdt0(xC,xD),sdtpldt0(sdtasdt0(xC,xG),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG)))) )
| ( sdtpldt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)) != sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xC,xD)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG))) != sdtasdt0(sdtasdt0(xC,xD),sdtasdt0(sdtasdt0(xC,xG),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG)))) )
| ( sdtasdt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)) != sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xC,xD)) ) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtasdt0(xC,xG))
| ~ aScalar0(sdtasdt0(xC,xD))
| ~ aScalar0(sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG))) != sdtpldt0(sdtasdt0(xC,xD),sdtpldt0(sdtasdt0(xC,xG),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG)))) )
| ( sdtpldt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)) != sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xC,xD)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG))) != sdtasdt0(sdtasdt0(xC,xD),sdtasdt0(sdtasdt0(xC,xG),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG)))) )
| ( sdtasdt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)) != sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xC,xD)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(137,plain,
( ( ~ aScalar0(sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG)))
| ~ aScalar0(sdtasdt0(xC,xG))
| ~ aScalar0(sdtasdt0(xC,xD))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG))) != sdtpldt0(sdtasdt0(xC,xD),sdtpldt0(sdtasdt0(xC,xG),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG)))) )
| ( sdtpldt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)) != sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xC,xD)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG))) != sdtasdt0(sdtasdt0(xC,xD),sdtasdt0(sdtasdt0(xC,xG),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG)))) )
| ( sdtasdt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)) != sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xC,xD)) ) ) )
<=> ( ~ aScalar0(sdtasdt0(xC,xG))
| ~ aScalar0(sdtasdt0(xC,xD))
| ~ aScalar0(sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG))) != sdtpldt0(sdtasdt0(xC,xD),sdtpldt0(sdtasdt0(xC,xG),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG)))) )
| ( sdtpldt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)) != sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xC,xD)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG))) != sdtasdt0(sdtasdt0(xC,xD),sdtasdt0(sdtasdt0(xC,xG),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG)))) )
| ( sdtasdt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)) != sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xC,xD)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(138,plain,
( ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG))) != sdtpldt0(sdtasdt0(xC,xD),sdtpldt0(sdtasdt0(xC,xG),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG)))) )
| ( sdtpldt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)) != sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xC,xD)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG))) != sdtasdt0(sdtasdt0(xC,xD),sdtasdt0(sdtasdt0(xC,xG),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG)))) )
| ( sdtasdt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)) != sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xC,xD)) ) )
<=> ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG))) != sdtpldt0(sdtasdt0(xC,xD),sdtpldt0(sdtasdt0(xC,xG),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG)))) )
| ( sdtpldt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)) != sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xC,xD)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG))) != sdtasdt0(sdtasdt0(xC,xD),sdtasdt0(sdtasdt0(xC,xG),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG)))) )
| ( sdtasdt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)) != sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xC,xD)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(139,plain,
( ( ~ aScalar0(sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG)))
| ~ aScalar0(sdtasdt0(xC,xG))
| ~ aScalar0(sdtasdt0(xC,xD))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG))) != sdtpldt0(sdtasdt0(xC,xD),sdtpldt0(sdtasdt0(xC,xG),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG)))) )
| ( sdtpldt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)) != sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xC,xD)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG))) != sdtasdt0(sdtasdt0(xC,xD),sdtasdt0(sdtasdt0(xC,xG),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG)))) )
| ( sdtasdt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)) != sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xC,xD)) ) ) )
<=> ( ~ aScalar0(sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG)))
| ~ aScalar0(sdtasdt0(xC,xG))
| ~ aScalar0(sdtasdt0(xC,xD))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG))) != sdtpldt0(sdtasdt0(xC,xD),sdtpldt0(sdtasdt0(xC,xG),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG)))) )
| ( sdtpldt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)) != sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xC,xD)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG))) != sdtasdt0(sdtasdt0(xC,xD),sdtasdt0(sdtasdt0(xC,xG),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG)))) )
| ( sdtasdt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)) != sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xC,xD)) ) ) ) ),
inference(monotonicity,[status(thm)],[138]) ).
tff(140,plain,
( ( ~ aScalar0(sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG)))
| ~ aScalar0(sdtasdt0(xC,xG))
| ~ aScalar0(sdtasdt0(xC,xD))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG))) != sdtpldt0(sdtasdt0(xC,xD),sdtpldt0(sdtasdt0(xC,xG),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG)))) )
| ( sdtpldt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)) != sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xC,xD)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG))) != sdtasdt0(sdtasdt0(xC,xD),sdtasdt0(sdtasdt0(xC,xG),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG)))) )
| ( sdtasdt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)) != sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xC,xD)) ) ) )
<=> ( ~ aScalar0(sdtasdt0(xC,xG))
| ~ aScalar0(sdtasdt0(xC,xD))
| ~ aScalar0(sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG))) != sdtpldt0(sdtasdt0(xC,xD),sdtpldt0(sdtasdt0(xC,xG),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG)))) )
| ( sdtpldt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)) != sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xC,xD)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG))) != sdtasdt0(sdtasdt0(xC,xD),sdtasdt0(sdtasdt0(xC,xG),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG)))) )
| ( sdtasdt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)) != sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xC,xD)) ) ) ) ),
inference(transitivity,[status(thm)],[139,137]) ).
tff(141,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG)))
| ~ aScalar0(sdtasdt0(xC,xG))
| ~ aScalar0(sdtasdt0(xC,xD))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG))) != sdtpldt0(sdtasdt0(xC,xD),sdtpldt0(sdtasdt0(xC,xG),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG)))) )
| ( sdtpldt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)) != sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xC,xD)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG))) != sdtasdt0(sdtasdt0(xC,xD),sdtasdt0(sdtasdt0(xC,xG),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG)))) )
| ( sdtasdt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)) != sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xC,xD)) ) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtasdt0(xC,xG))
| ~ aScalar0(sdtasdt0(xC,xD))
| ~ aScalar0(sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG))) != sdtpldt0(sdtasdt0(xC,xD),sdtpldt0(sdtasdt0(xC,xG),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG)))) )
| ( sdtpldt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)) != sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xC,xD)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG))) != sdtasdt0(sdtasdt0(xC,xD),sdtasdt0(sdtasdt0(xC,xG),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG)))) )
| ( sdtasdt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)) != sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xC,xD)) ) ) ) ),
inference(monotonicity,[status(thm)],[140]) ).
tff(142,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG)))
| ~ aScalar0(sdtasdt0(xC,xG))
| ~ aScalar0(sdtasdt0(xC,xD))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG))) != sdtpldt0(sdtasdt0(xC,xD),sdtpldt0(sdtasdt0(xC,xG),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG)))) )
| ( sdtpldt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)) != sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xC,xD)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG))) != sdtasdt0(sdtasdt0(xC,xD),sdtasdt0(sdtasdt0(xC,xG),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG)))) )
| ( sdtasdt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)) != sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xC,xD)) ) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtasdt0(xC,xG))
| ~ aScalar0(sdtasdt0(xC,xD))
| ~ aScalar0(sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG))) != sdtpldt0(sdtasdt0(xC,xD),sdtpldt0(sdtasdt0(xC,xG),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG)))) )
| ( sdtpldt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)) != sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xC,xD)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG))) != sdtasdt0(sdtasdt0(xC,xD),sdtasdt0(sdtasdt0(xC,xG),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG)))) )
| ( sdtasdt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)) != sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xC,xD)) ) ) ) ),
inference(transitivity,[status(thm)],[141,136]) ).
tff(143,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG)))
| ~ aScalar0(sdtasdt0(xC,xG))
| ~ aScalar0(sdtasdt0(xC,xD))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG))) != sdtpldt0(sdtasdt0(xC,xD),sdtpldt0(sdtasdt0(xC,xG),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG)))) )
| ( sdtpldt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)) != sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xC,xD)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG))) != sdtasdt0(sdtasdt0(xC,xD),sdtasdt0(sdtasdt0(xC,xG),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG)))) )
| ( sdtasdt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)) != sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xC,xD)) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(144,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtasdt0(xC,xG))
| ~ aScalar0(sdtasdt0(xC,xD))
| ~ aScalar0(sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG))) != sdtpldt0(sdtasdt0(xC,xD),sdtpldt0(sdtasdt0(xC,xG),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG)))) )
| ( sdtpldt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)) != sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xC,xD)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG))) != sdtasdt0(sdtasdt0(xC,xD),sdtasdt0(sdtasdt0(xC,xG),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG)))) )
| ( sdtasdt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)) != sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xC,xD)) ) ) ),
inference(modus_ponens,[status(thm)],[143,142]) ).
tff(145,plain,
( ~ aScalar0(sdtasdt0(xC,xG))
| ~ aScalar0(sdtasdt0(xC,xD))
| ~ aScalar0(sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG))) != sdtpldt0(sdtasdt0(xC,xD),sdtpldt0(sdtasdt0(xC,xG),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG)))) )
| ( sdtpldt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)) != sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xC,xD)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG))) != sdtasdt0(sdtasdt0(xC,xD),sdtasdt0(sdtasdt0(xC,xG),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG)))) )
| ( sdtasdt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)) != sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xC,xD)) ) ) ),
inference(unit_resolution,[status(thm)],[144,135]) ).
tff(146,plain,
~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG))) != sdtpldt0(sdtasdt0(xC,xD),sdtpldt0(sdtasdt0(xC,xG),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG)))) )
| ( sdtpldt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)) != sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xC,xD)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG))) != sdtasdt0(sdtasdt0(xC,xD),sdtasdt0(sdtasdt0(xC,xG),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG)))) )
| ( sdtasdt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)) != sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xC,xD)) ) ),
inference(unit_resolution,[status(thm)],[145,122,57,46]) ).
tff(147,plain,
( ( sdtpldt0(sdtpldt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG))) != sdtpldt0(sdtasdt0(xC,xD),sdtpldt0(sdtasdt0(xC,xG),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG)))) )
| ( sdtpldt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)) != sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xC,xD)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG))) != sdtasdt0(sdtasdt0(xC,xD),sdtasdt0(sdtasdt0(xC,xG),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG)))) )
| ( sdtasdt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)) != sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xC,xD)) )
| ( sdtpldt0(sdtpldt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG))) = sdtpldt0(sdtasdt0(xC,xD),sdtpldt0(sdtasdt0(xC,xG),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG)))) ) ),
inference(tautology,[status(thm)],[]) ).
tff(148,plain,
sdtpldt0(sdtpldt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG))) = sdtpldt0(sdtasdt0(xC,xD),sdtpldt0(sdtasdt0(xC,xG),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG)))),
inference(unit_resolution,[status(thm)],[147,146]) ).
tff(149,plain,
sdtpldt0(sdtasdt0(xC,xD),sdtpldt0(sdtasdt0(xC,xG),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG)))) = sdtpldt0(sdtpldt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG))),
inference(symmetry,[status(thm)],[148]) ).
tff(150,plain,
( ( xB = sdtlbdtrb0(xt,aDimensionOf0(xt)) )
<=> ( xB = sdtlbdtrb0(xt,aDimensionOf0(xt)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(151,axiom,
( aScalar0(xB)
& ( xB = sdtlbdtrb0(xt,aDimensionOf0(xt)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1766) ).
tff(152,plain,
xB = sdtlbdtrb0(xt,aDimensionOf0(xt)),
inference(and_elim,[status(thm)],[151]) ).
tff(153,plain,
xB = sdtlbdtrb0(xt,aDimensionOf0(xt)),
inference(modus_ponens,[status(thm)],[152,150]) ).
tff(154,plain,
sdtlbdtrb0(xt,aDimensionOf0(xt)) = xB,
inference(symmetry,[status(thm)],[153]) ).
tff(155,plain,
sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt))) = sdtasdt0(xB,xB),
inference(monotonicity,[status(thm)],[154,154]) ).
tff(156,plain,
sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt))) = xG,
inference(transitivity,[status(thm)],[155,73]) ).
tff(157,plain,
sdtasdt0(sdtasdt0(xA,xA),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) = sdtasdt0(xF,xG),
inference(monotonicity,[status(thm)],[78,156]) ).
tff(158,plain,
( aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xt)))
<=> aScalar0(xB) ),
inference(monotonicity,[status(thm)],[154]) ).
tff(159,plain,
( aScalar0(xB)
<=> aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xt))) ),
inference(symmetry,[status(thm)],[158]) ).
tff(160,plain,
( aScalar0(xB)
<=> aScalar0(xB) ),
inference(rewrite,[status(thm)],[]) ).
tff(161,plain,
aScalar0(xB),
inference(and_elim,[status(thm)],[151]) ).
tff(162,plain,
aScalar0(xB),
inference(modus_ponens,[status(thm)],[161,160]) ).
tff(163,plain,
aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xt))),
inference(modus_ponens,[status(thm)],[162,159]) ).
tff(164,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xt)))
| ~ aScalar0(sdtasdt0(xA,xA))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtasdt0(xA,xA),sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtpldt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtasdt0(xA,xA)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtasdt0(xA,xA),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtasdt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtasdt0(xA,xA)) ) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xt)))
| ~ aScalar0(sdtasdt0(xA,xA))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtasdt0(xA,xA),sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtpldt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtasdt0(xA,xA)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtasdt0(xA,xA),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtasdt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtasdt0(xA,xA)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(165,plain,
( ( ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xt)))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xt)))
| ~ aScalar0(sdtasdt0(xA,xA))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtasdt0(xA,xA),sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtpldt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtasdt0(xA,xA)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtasdt0(xA,xA),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtasdt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtasdt0(xA,xA)) ) ) )
<=> ( ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xt)))
| ~ aScalar0(sdtasdt0(xA,xA))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtasdt0(xA,xA),sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtpldt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtasdt0(xA,xA)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtasdt0(xA,xA),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtasdt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtasdt0(xA,xA)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(166,plain,
( ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtasdt0(xA,xA),sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtpldt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtasdt0(xA,xA)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtasdt0(xA,xA),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtasdt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtasdt0(xA,xA)) ) )
<=> ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtasdt0(xA,xA),sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtpldt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtasdt0(xA,xA)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtasdt0(xA,xA),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtasdt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtasdt0(xA,xA)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(167,plain,
( ( ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xt)))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xt)))
| ~ aScalar0(sdtasdt0(xA,xA))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtasdt0(xA,xA),sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtpldt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtasdt0(xA,xA)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtasdt0(xA,xA),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtasdt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtasdt0(xA,xA)) ) ) )
<=> ( ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xt)))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xt)))
| ~ aScalar0(sdtasdt0(xA,xA))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtasdt0(xA,xA),sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtpldt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtasdt0(xA,xA)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtasdt0(xA,xA),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtasdt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtasdt0(xA,xA)) ) ) ) ),
inference(monotonicity,[status(thm)],[166]) ).
tff(168,plain,
( ( ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xt)))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xt)))
| ~ aScalar0(sdtasdt0(xA,xA))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtasdt0(xA,xA),sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtpldt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtasdt0(xA,xA)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtasdt0(xA,xA),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtasdt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtasdt0(xA,xA)) ) ) )
<=> ( ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xt)))
| ~ aScalar0(sdtasdt0(xA,xA))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtasdt0(xA,xA),sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtpldt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtasdt0(xA,xA)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtasdt0(xA,xA),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtasdt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtasdt0(xA,xA)) ) ) ) ),
inference(transitivity,[status(thm)],[167,165]) ).
tff(169,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xt)))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xt)))
| ~ aScalar0(sdtasdt0(xA,xA))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtasdt0(xA,xA),sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtpldt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtasdt0(xA,xA)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtasdt0(xA,xA),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtasdt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtasdt0(xA,xA)) ) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xt)))
| ~ aScalar0(sdtasdt0(xA,xA))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtasdt0(xA,xA),sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtpldt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtasdt0(xA,xA)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtasdt0(xA,xA),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtasdt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtasdt0(xA,xA)) ) ) ) ),
inference(monotonicity,[status(thm)],[168]) ).
tff(170,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xt)))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xt)))
| ~ aScalar0(sdtasdt0(xA,xA))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtasdt0(xA,xA),sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtpldt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtasdt0(xA,xA)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtasdt0(xA,xA),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtasdt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtasdt0(xA,xA)) ) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xt)))
| ~ aScalar0(sdtasdt0(xA,xA))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtasdt0(xA,xA),sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtpldt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtasdt0(xA,xA)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtasdt0(xA,xA),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtasdt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtasdt0(xA,xA)) ) ) ) ),
inference(transitivity,[status(thm)],[169,164]) ).
tff(171,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xt)))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xt)))
| ~ aScalar0(sdtasdt0(xA,xA))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtasdt0(xA,xA),sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtpldt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtasdt0(xA,xA)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtasdt0(xA,xA),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtasdt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtasdt0(xA,xA)) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(172,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xt)))
| ~ aScalar0(sdtasdt0(xA,xA))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtasdt0(xA,xA),sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtpldt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtasdt0(xA,xA)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtasdt0(xA,xA),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtasdt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtasdt0(xA,xA)) ) ) ),
inference(modus_ponens,[status(thm)],[171,170]) ).
tff(173,plain,
( ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xt)))
| ~ aScalar0(sdtasdt0(xA,xA))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtasdt0(xA,xA),sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtpldt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtasdt0(xA,xA)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtasdt0(xA,xA),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtasdt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtasdt0(xA,xA)) ) ) ),
inference(unit_resolution,[status(thm)],[172,135]) ).
tff(174,plain,
~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtasdt0(xA,xA),sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtpldt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtasdt0(xA,xA)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtasdt0(xA,xA),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtasdt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtasdt0(xA,xA)) ) ),
inference(unit_resolution,[status(thm)],[173,92,163]) ).
tff(175,plain,
( ( sdtpldt0(sdtpldt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtasdt0(xA,xA),sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtpldt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtasdt0(xA,xA)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtasdt0(xA,xA),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtasdt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtasdt0(xA,xA)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))),sdtlbdtrb0(xt,aDimensionOf0(xt))) = sdtasdt0(sdtasdt0(xA,xA),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) ) ),
inference(tautology,[status(thm)],[]) ).
tff(176,plain,
sdtasdt0(sdtasdt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))),sdtlbdtrb0(xt,aDimensionOf0(xt))) = sdtasdt0(sdtasdt0(xA,xA),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))),
inference(unit_resolution,[status(thm)],[175,174]) ).
tff(177,plain,
( ( xA = sdtlbdtrb0(xs,aDimensionOf0(xs)) )
<=> ( xA = sdtlbdtrb0(xs,aDimensionOf0(xs)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(178,axiom,
( aScalar0(xA)
& ( xA = sdtlbdtrb0(xs,aDimensionOf0(xs)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1746) ).
tff(179,plain,
xA = sdtlbdtrb0(xs,aDimensionOf0(xs)),
inference(and_elim,[status(thm)],[178]) ).
tff(180,plain,
xA = sdtlbdtrb0(xs,aDimensionOf0(xs)),
inference(modus_ponens,[status(thm)],[179,177]) ).
tff(181,plain,
sdtlbdtrb0(xs,aDimensionOf0(xs)) = xA,
inference(symmetry,[status(thm)],[180]) ).
tff(182,plain,
sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) = sdtasdt0(xA,xA),
inference(monotonicity,[status(thm)],[181,181]) ).
tff(183,plain,
sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) = sdtasdt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))),
inference(monotonicity,[status(thm)],[182]) ).
tff(184,plain,
( aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
<=> aScalar0(xA) ),
inference(monotonicity,[status(thm)],[181]) ).
tff(185,plain,
( aScalar0(xA)
<=> aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs))) ),
inference(symmetry,[status(thm)],[184]) ).
tff(186,plain,
( aScalar0(xA)
<=> aScalar0(xA) ),
inference(rewrite,[status(thm)],[]) ).
tff(187,plain,
aScalar0(xA),
inference(and_elim,[status(thm)],[178]) ).
tff(188,plain,
aScalar0(xA),
inference(modus_ponens,[status(thm)],[187,186]) ).
tff(189,plain,
aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs))),
inference(modus_ponens,[status(thm)],[188,185]) ).
tff(190,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xt)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) ) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xt)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(191,plain,
( ( ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xt)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) ) ) )
<=> ( ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xt)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(192,plain,
( ~ ( ( sdtpldt0(sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) ) )
<=> ~ ( ( sdtpldt0(sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(193,plain,
( ( ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xt)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) ) ) )
<=> ( ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xt)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) ) ) ) ),
inference(monotonicity,[status(thm)],[192]) ).
tff(194,plain,
( ( ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xt)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) ) ) )
<=> ( ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xt)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) ) ) ) ),
inference(transitivity,[status(thm)],[193,191]) ).
tff(195,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xt)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) ) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xt)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) ) ) ) ),
inference(monotonicity,[status(thm)],[194]) ).
tff(196,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xt)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) ) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xt)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) ) ) ) ),
inference(transitivity,[status(thm)],[195,190]) ).
tff(197,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xt)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(198,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xt)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) ) ) ),
inference(modus_ponens,[status(thm)],[197,196]) ).
tff(199,plain,
~ ( ( sdtpldt0(sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) ) ),
inference(unit_resolution,[status(thm)],[198,135,189,163]) ).
tff(200,plain,
( ( sdtpldt0(sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) = sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) ) ),
inference(tautology,[status(thm)],[]) ).
tff(201,plain,
sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) = sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))),
inference(unit_resolution,[status(thm)],[200,199]) ).
tff(202,plain,
sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) = sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))),
inference(symmetry,[status(thm)],[201]) ).
tff(203,plain,
sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt))) = sdtasdt0(xA,xB),
inference(monotonicity,[status(thm)],[181,154]) ).
tff(204,plain,
sdtasdt0(xA,xB) = sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt))),
inference(symmetry,[status(thm)],[203]) ).
tff(205,plain,
sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(xA,xB)) = sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))),
inference(monotonicity,[status(thm)],[204]) ).
tff(206,plain,
( ( xH = sdtasdt0(xA,xB) )
<=> ( xH = sdtasdt0(xA,xB) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(207,axiom,
( aScalar0(xH)
& ( xH = sdtasdt0(xA,xB) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1873) ).
tff(208,plain,
xH = sdtasdt0(xA,xB),
inference(and_elim,[status(thm)],[207]) ).
tff(209,plain,
xH = sdtasdt0(xA,xB),
inference(modus_ponens,[status(thm)],[208,206]) ).
tff(210,plain,
sdtasdt0(xA,xB) = xH,
inference(symmetry,[status(thm)],[209]) ).
tff(211,plain,
( aScalar0(sdtasdt0(xA,xB))
<=> aScalar0(xH) ),
inference(monotonicity,[status(thm)],[210]) ).
tff(212,plain,
( aScalar0(xH)
<=> aScalar0(sdtasdt0(xA,xB)) ),
inference(symmetry,[status(thm)],[211]) ).
tff(213,plain,
( aScalar0(xH)
<=> aScalar0(xH) ),
inference(rewrite,[status(thm)],[]) ).
tff(214,plain,
aScalar0(xH),
inference(and_elim,[status(thm)],[207]) ).
tff(215,plain,
aScalar0(xH),
inference(modus_ponens,[status(thm)],[214,213]) ).
tff(216,plain,
aScalar0(sdtasdt0(xA,xB)),
inference(modus_ponens,[status(thm)],[215,212]) ).
tff(217,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtasdt0(xA,xB))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xt)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtasdt0(xA,xB),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtpldt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(xA,xB)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtasdt0(xA,xB),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtasdt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(xA,xB)) ) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtasdt0(xA,xB))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xt)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtasdt0(xA,xB),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtpldt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(xA,xB)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtasdt0(xA,xB),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtasdt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(xA,xB)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(218,plain,
( ( ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xt)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtasdt0(xA,xB))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtasdt0(xA,xB),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtpldt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(xA,xB)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtasdt0(xA,xB),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtasdt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(xA,xB)) ) ) )
<=> ( ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtasdt0(xA,xB))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xt)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtasdt0(xA,xB),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtpldt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(xA,xB)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtasdt0(xA,xB),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtasdt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(xA,xB)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(219,plain,
( ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtasdt0(xA,xB),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtpldt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(xA,xB)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtasdt0(xA,xB),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtasdt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(xA,xB)) ) )
<=> ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtasdt0(xA,xB),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtpldt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(xA,xB)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtasdt0(xA,xB),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtasdt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(xA,xB)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(220,plain,
( ( ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xt)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtasdt0(xA,xB))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtasdt0(xA,xB),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtpldt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(xA,xB)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtasdt0(xA,xB),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtasdt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(xA,xB)) ) ) )
<=> ( ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xt)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtasdt0(xA,xB))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtasdt0(xA,xB),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtpldt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(xA,xB)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtasdt0(xA,xB),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtasdt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(xA,xB)) ) ) ) ),
inference(monotonicity,[status(thm)],[219]) ).
tff(221,plain,
( ( ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xt)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtasdt0(xA,xB))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtasdt0(xA,xB),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtpldt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(xA,xB)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtasdt0(xA,xB),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtasdt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(xA,xB)) ) ) )
<=> ( ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtasdt0(xA,xB))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xt)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtasdt0(xA,xB),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtpldt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(xA,xB)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtasdt0(xA,xB),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtasdt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(xA,xB)) ) ) ) ),
inference(transitivity,[status(thm)],[220,218]) ).
tff(222,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xt)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtasdt0(xA,xB))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtasdt0(xA,xB),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtpldt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(xA,xB)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtasdt0(xA,xB),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtasdt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(xA,xB)) ) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtasdt0(xA,xB))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xt)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtasdt0(xA,xB),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtpldt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(xA,xB)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtasdt0(xA,xB),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtasdt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(xA,xB)) ) ) ) ),
inference(monotonicity,[status(thm)],[221]) ).
tff(223,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xt)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtasdt0(xA,xB))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtasdt0(xA,xB),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtpldt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(xA,xB)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtasdt0(xA,xB),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtasdt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(xA,xB)) ) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtasdt0(xA,xB))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xt)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtasdt0(xA,xB),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtpldt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(xA,xB)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtasdt0(xA,xB),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtasdt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(xA,xB)) ) ) ) ),
inference(transitivity,[status(thm)],[222,217]) ).
tff(224,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xt)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtasdt0(xA,xB))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtasdt0(xA,xB),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtpldt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(xA,xB)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtasdt0(xA,xB),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtasdt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(xA,xB)) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(225,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtasdt0(xA,xB))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xt)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtasdt0(xA,xB),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtpldt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(xA,xB)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtasdt0(xA,xB),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtasdt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(xA,xB)) ) ) ),
inference(modus_ponens,[status(thm)],[224,223]) ).
tff(226,plain,
( ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtasdt0(xA,xB))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xt)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtasdt0(xA,xB),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtpldt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(xA,xB)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtasdt0(xA,xB),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtasdt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(xA,xB)) ) ) ),
inference(unit_resolution,[status(thm)],[225,135]) ).
tff(227,plain,
~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtasdt0(xA,xB),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtpldt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(xA,xB)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtasdt0(xA,xB),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtasdt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(xA,xB)) ) ),
inference(unit_resolution,[status(thm)],[226,216,163,189]) ).
tff(228,plain,
( ( sdtpldt0(sdtpldt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtasdt0(xA,xB),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtpldt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(xA,xB)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtasdt0(xA,xB),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtasdt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(xA,xB)) )
| ( sdtasdt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))) = sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(xA,xB)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(229,plain,
sdtasdt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))) = sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(xA,xB)),
inference(unit_resolution,[status(thm)],[228,227]) ).
tff(230,plain,
sdtasdt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))) = sdtasdt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))),
inference(transitivity,[status(thm)],[229,205,202,183]) ).
tff(231,plain,
sdtasdt0(sdtasdt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) = sdtasdt0(sdtasdt0(sdtasdt0(xA,xA),sdtlbdtrb0(xt,aDimensionOf0(xt))),sdtlbdtrb0(xt,aDimensionOf0(xt))),
inference(monotonicity,[status(thm)],[230]) ).
tff(232,plain,
( ( sdtpldt0(sdtpldt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtpldt0(sdtasdt0(xA,xB),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtpldt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(xA,xB)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) != sdtasdt0(sdtasdt0(xA,xB),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( sdtasdt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(xA,xB)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) = sdtasdt0(sdtasdt0(xA,xB),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) ) ),
inference(tautology,[status(thm)],[]) ).
tff(233,plain,
sdtasdt0(sdtasdt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))) = sdtasdt0(sdtasdt0(xA,xB),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))),
inference(unit_resolution,[status(thm)],[232,227]) ).
tff(234,plain,
sdtasdt0(sdtasdt0(xA,xB),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) = sdtasdt0(sdtasdt0(sdtasdt0(xA,xB),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xt))),
inference(symmetry,[status(thm)],[233]) ).
tff(235,plain,
xH = sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt))),
inference(transitivity,[status(thm)],[209,204]) ).
tff(236,plain,
sdtasdt0(xH,xH) = sdtasdt0(sdtasdt0(xA,xB),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))),
inference(monotonicity,[status(thm)],[209,235]) ).
tff(237,plain,
sdtasdt0(xH,xH) = sdtasdt0(xF,xG),
inference(transitivity,[status(thm)],[236,234,231,176,157]) ).
tff(238,plain,
sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xH,xH)) = sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG)),
inference(monotonicity,[status(thm)],[237]) ).
tff(239,plain,
sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG)) = sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xH,xH)),
inference(symmetry,[status(thm)],[238]) ).
tff(240,plain,
sdtpldt0(sdtasdt0(xC,xG),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG))) = sdtpldt0(sdtasdt0(xC,xG),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xH,xH))),
inference(monotonicity,[status(thm)],[239]) ).
tff(241,plain,
sdtpldt0(sdtasdt0(xC,xG),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xH,xH))) = sdtpldt0(sdtasdt0(xC,xG),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG))),
inference(symmetry,[status(thm)],[240]) ).
tff(242,plain,
sdtasdt0(sdtasdt0(xA,xB),sdtasdt0(xA,xB)) = sdtasdt0(xH,xH),
inference(monotonicity,[status(thm)],[210,210]) ).
tff(243,plain,
( aScalar0(sdtasdt0(sdtasdt0(xA,xB),sdtasdt0(xA,xB)))
<=> aScalar0(sdtasdt0(xH,xH)) ),
inference(monotonicity,[status(thm)],[242]) ).
tff(244,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(xA,xB))
| aScalar0(sdtasdt0(sdtasdt0(xA,xB),sdtasdt0(xA,xB))) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(xA,xB))
| aScalar0(sdtasdt0(sdtasdt0(xA,xB),sdtasdt0(xA,xB))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(245,plain,
( ( aScalar0(sdtasdt0(sdtasdt0(xA,xB),sdtasdt0(xA,xB)))
| ~ aScalar0(sdtasdt0(xA,xB))
| ~ aScalar0(sdtasdt0(xA,xB)) )
<=> ( ~ aScalar0(sdtasdt0(xA,xB))
| aScalar0(sdtasdt0(sdtasdt0(xA,xB),sdtasdt0(xA,xB))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(246,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtasdt0(sdtasdt0(xA,xB),sdtasdt0(xA,xB)))
| ~ aScalar0(sdtasdt0(xA,xB))
| ~ aScalar0(sdtasdt0(xA,xB)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(xA,xB))
| aScalar0(sdtasdt0(sdtasdt0(xA,xB),sdtasdt0(xA,xB))) ) ),
inference(monotonicity,[status(thm)],[245]) ).
tff(247,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtasdt0(sdtasdt0(xA,xB),sdtasdt0(xA,xB)))
| ~ aScalar0(sdtasdt0(xA,xB))
| ~ aScalar0(sdtasdt0(xA,xB)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(xA,xB))
| aScalar0(sdtasdt0(sdtasdt0(xA,xB),sdtasdt0(xA,xB))) ) ),
inference(transitivity,[status(thm)],[246,244]) ).
tff(248,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtasdt0(sdtasdt0(xA,xB),sdtasdt0(xA,xB)))
| ~ aScalar0(sdtasdt0(xA,xB))
| ~ aScalar0(sdtasdt0(xA,xB)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(249,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(xA,xB))
| aScalar0(sdtasdt0(sdtasdt0(xA,xB),sdtasdt0(xA,xB))) ),
inference(modus_ponens,[status(thm)],[248,247]) ).
tff(250,plain,
( ~ aScalar0(sdtasdt0(xA,xB))
| aScalar0(sdtasdt0(sdtasdt0(xA,xB),sdtasdt0(xA,xB))) ),
inference(unit_resolution,[status(thm)],[249,37]) ).
tff(251,plain,
aScalar0(sdtasdt0(sdtasdt0(xA,xB),sdtasdt0(xA,xB))),
inference(unit_resolution,[status(thm)],[250,216]) ).
tff(252,plain,
aScalar0(sdtasdt0(xH,xH)),
inference(modus_ponens,[status(thm)],[251,243]) ).
tff(253,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtasdt0(xF,xD))
| ~ aScalar0(sdtasdt0(xC,xG))
| ~ aScalar0(sdtasdt0(xH,xH))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)),sdtasdt0(xH,xH)) != sdtpldt0(sdtasdt0(xC,xG),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xH,xH))) )
| ( sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)) != sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xC,xG)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)),sdtasdt0(xH,xH)) != sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(sdtasdt0(xF,xD),sdtasdt0(xH,xH))) )
| ( sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)) != sdtasdt0(sdtasdt0(xF,xD),sdtasdt0(xC,xG)) ) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtasdt0(xF,xD))
| ~ aScalar0(sdtasdt0(xC,xG))
| ~ aScalar0(sdtasdt0(xH,xH))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)),sdtasdt0(xH,xH)) != sdtpldt0(sdtasdt0(xC,xG),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xH,xH))) )
| ( sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)) != sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xC,xG)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)),sdtasdt0(xH,xH)) != sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(sdtasdt0(xF,xD),sdtasdt0(xH,xH))) )
| ( sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)) != sdtasdt0(sdtasdt0(xF,xD),sdtasdt0(xC,xG)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(254,plain,
( ( ~ aScalar0(sdtasdt0(xH,xH))
| ~ aScalar0(sdtasdt0(xF,xD))
| ~ aScalar0(sdtasdt0(xC,xG))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)),sdtasdt0(xH,xH)) != sdtpldt0(sdtasdt0(xC,xG),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xH,xH))) )
| ( sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)) != sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xC,xG)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)),sdtasdt0(xH,xH)) != sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(sdtasdt0(xF,xD),sdtasdt0(xH,xH))) )
| ( sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)) != sdtasdt0(sdtasdt0(xF,xD),sdtasdt0(xC,xG)) ) ) )
<=> ( ~ aScalar0(sdtasdt0(xF,xD))
| ~ aScalar0(sdtasdt0(xC,xG))
| ~ aScalar0(sdtasdt0(xH,xH))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)),sdtasdt0(xH,xH)) != sdtpldt0(sdtasdt0(xC,xG),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xH,xH))) )
| ( sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)) != sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xC,xG)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)),sdtasdt0(xH,xH)) != sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(sdtasdt0(xF,xD),sdtasdt0(xH,xH))) )
| ( sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)) != sdtasdt0(sdtasdt0(xF,xD),sdtasdt0(xC,xG)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(255,plain,
( ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)),sdtasdt0(xH,xH)) != sdtpldt0(sdtasdt0(xC,xG),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xH,xH))) )
| ( sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)) != sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xC,xG)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)),sdtasdt0(xH,xH)) != sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(sdtasdt0(xF,xD),sdtasdt0(xH,xH))) )
| ( sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)) != sdtasdt0(sdtasdt0(xF,xD),sdtasdt0(xC,xG)) ) )
<=> ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)),sdtasdt0(xH,xH)) != sdtpldt0(sdtasdt0(xC,xG),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xH,xH))) )
| ( sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)) != sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xC,xG)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)),sdtasdt0(xH,xH)) != sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(sdtasdt0(xF,xD),sdtasdt0(xH,xH))) )
| ( sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)) != sdtasdt0(sdtasdt0(xF,xD),sdtasdt0(xC,xG)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(256,plain,
( ( ~ aScalar0(sdtasdt0(xH,xH))
| ~ aScalar0(sdtasdt0(xF,xD))
| ~ aScalar0(sdtasdt0(xC,xG))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)),sdtasdt0(xH,xH)) != sdtpldt0(sdtasdt0(xC,xG),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xH,xH))) )
| ( sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)) != sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xC,xG)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)),sdtasdt0(xH,xH)) != sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(sdtasdt0(xF,xD),sdtasdt0(xH,xH))) )
| ( sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)) != sdtasdt0(sdtasdt0(xF,xD),sdtasdt0(xC,xG)) ) ) )
<=> ( ~ aScalar0(sdtasdt0(xH,xH))
| ~ aScalar0(sdtasdt0(xF,xD))
| ~ aScalar0(sdtasdt0(xC,xG))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)),sdtasdt0(xH,xH)) != sdtpldt0(sdtasdt0(xC,xG),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xH,xH))) )
| ( sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)) != sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xC,xG)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)),sdtasdt0(xH,xH)) != sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(sdtasdt0(xF,xD),sdtasdt0(xH,xH))) )
| ( sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)) != sdtasdt0(sdtasdt0(xF,xD),sdtasdt0(xC,xG)) ) ) ) ),
inference(monotonicity,[status(thm)],[255]) ).
tff(257,plain,
( ( ~ aScalar0(sdtasdt0(xH,xH))
| ~ aScalar0(sdtasdt0(xF,xD))
| ~ aScalar0(sdtasdt0(xC,xG))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)),sdtasdt0(xH,xH)) != sdtpldt0(sdtasdt0(xC,xG),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xH,xH))) )
| ( sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)) != sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xC,xG)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)),sdtasdt0(xH,xH)) != sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(sdtasdt0(xF,xD),sdtasdt0(xH,xH))) )
| ( sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)) != sdtasdt0(sdtasdt0(xF,xD),sdtasdt0(xC,xG)) ) ) )
<=> ( ~ aScalar0(sdtasdt0(xF,xD))
| ~ aScalar0(sdtasdt0(xC,xG))
| ~ aScalar0(sdtasdt0(xH,xH))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)),sdtasdt0(xH,xH)) != sdtpldt0(sdtasdt0(xC,xG),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xH,xH))) )
| ( sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)) != sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xC,xG)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)),sdtasdt0(xH,xH)) != sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(sdtasdt0(xF,xD),sdtasdt0(xH,xH))) )
| ( sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)) != sdtasdt0(sdtasdt0(xF,xD),sdtasdt0(xC,xG)) ) ) ) ),
inference(transitivity,[status(thm)],[256,254]) ).
tff(258,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtasdt0(xH,xH))
| ~ aScalar0(sdtasdt0(xF,xD))
| ~ aScalar0(sdtasdt0(xC,xG))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)),sdtasdt0(xH,xH)) != sdtpldt0(sdtasdt0(xC,xG),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xH,xH))) )
| ( sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)) != sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xC,xG)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)),sdtasdt0(xH,xH)) != sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(sdtasdt0(xF,xD),sdtasdt0(xH,xH))) )
| ( sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)) != sdtasdt0(sdtasdt0(xF,xD),sdtasdt0(xC,xG)) ) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtasdt0(xF,xD))
| ~ aScalar0(sdtasdt0(xC,xG))
| ~ aScalar0(sdtasdt0(xH,xH))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)),sdtasdt0(xH,xH)) != sdtpldt0(sdtasdt0(xC,xG),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xH,xH))) )
| ( sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)) != sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xC,xG)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)),sdtasdt0(xH,xH)) != sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(sdtasdt0(xF,xD),sdtasdt0(xH,xH))) )
| ( sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)) != sdtasdt0(sdtasdt0(xF,xD),sdtasdt0(xC,xG)) ) ) ) ),
inference(monotonicity,[status(thm)],[257]) ).
tff(259,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtasdt0(xH,xH))
| ~ aScalar0(sdtasdt0(xF,xD))
| ~ aScalar0(sdtasdt0(xC,xG))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)),sdtasdt0(xH,xH)) != sdtpldt0(sdtasdt0(xC,xG),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xH,xH))) )
| ( sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)) != sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xC,xG)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)),sdtasdt0(xH,xH)) != sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(sdtasdt0(xF,xD),sdtasdt0(xH,xH))) )
| ( sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)) != sdtasdt0(sdtasdt0(xF,xD),sdtasdt0(xC,xG)) ) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtasdt0(xF,xD))
| ~ aScalar0(sdtasdt0(xC,xG))
| ~ aScalar0(sdtasdt0(xH,xH))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)),sdtasdt0(xH,xH)) != sdtpldt0(sdtasdt0(xC,xG),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xH,xH))) )
| ( sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)) != sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xC,xG)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)),sdtasdt0(xH,xH)) != sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(sdtasdt0(xF,xD),sdtasdt0(xH,xH))) )
| ( sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)) != sdtasdt0(sdtasdt0(xF,xD),sdtasdt0(xC,xG)) ) ) ) ),
inference(transitivity,[status(thm)],[258,253]) ).
tff(260,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtasdt0(xH,xH))
| ~ aScalar0(sdtasdt0(xF,xD))
| ~ aScalar0(sdtasdt0(xC,xG))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)),sdtasdt0(xH,xH)) != sdtpldt0(sdtasdt0(xC,xG),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xH,xH))) )
| ( sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)) != sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xC,xG)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)),sdtasdt0(xH,xH)) != sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(sdtasdt0(xF,xD),sdtasdt0(xH,xH))) )
| ( sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)) != sdtasdt0(sdtasdt0(xF,xD),sdtasdt0(xC,xG)) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(261,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtasdt0(xF,xD))
| ~ aScalar0(sdtasdt0(xC,xG))
| ~ aScalar0(sdtasdt0(xH,xH))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)),sdtasdt0(xH,xH)) != sdtpldt0(sdtasdt0(xC,xG),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xH,xH))) )
| ( sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)) != sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xC,xG)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)),sdtasdt0(xH,xH)) != sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(sdtasdt0(xF,xD),sdtasdt0(xH,xH))) )
| ( sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)) != sdtasdt0(sdtasdt0(xF,xD),sdtasdt0(xC,xG)) ) ) ),
inference(modus_ponens,[status(thm)],[260,259]) ).
tff(262,plain,
( ~ aScalar0(sdtasdt0(xF,xD))
| ~ aScalar0(sdtasdt0(xC,xG))
| ~ aScalar0(sdtasdt0(xH,xH))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)),sdtasdt0(xH,xH)) != sdtpldt0(sdtasdt0(xC,xG),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xH,xH))) )
| ( sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)) != sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xC,xG)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)),sdtasdt0(xH,xH)) != sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(sdtasdt0(xF,xD),sdtasdt0(xH,xH))) )
| ( sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)) != sdtasdt0(sdtasdt0(xF,xD),sdtasdt0(xC,xG)) ) ) ),
inference(unit_resolution,[status(thm)],[261,135]) ).
tff(263,plain,
~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)),sdtasdt0(xH,xH)) != sdtpldt0(sdtasdt0(xC,xG),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xH,xH))) )
| ( sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)) != sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xC,xG)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)),sdtasdt0(xH,xH)) != sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(sdtasdt0(xF,xD),sdtasdt0(xH,xH))) )
| ( sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)) != sdtasdt0(sdtasdt0(xF,xD),sdtasdt0(xC,xG)) ) ),
inference(unit_resolution,[status(thm)],[262,252,68,57]) ).
tff(264,plain,
( ( sdtpldt0(sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)),sdtasdt0(xH,xH)) != sdtpldt0(sdtasdt0(xC,xG),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xH,xH))) )
| ( sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)) != sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xC,xG)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)),sdtasdt0(xH,xH)) != sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(sdtasdt0(xF,xD),sdtasdt0(xH,xH))) )
| ( sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)) != sdtasdt0(sdtasdt0(xF,xD),sdtasdt0(xC,xG)) )
| ( sdtpldt0(sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)),sdtasdt0(xH,xH)) = sdtpldt0(sdtasdt0(xC,xG),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xH,xH))) ) ),
inference(tautology,[status(thm)],[]) ).
tff(265,plain,
sdtpldt0(sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)),sdtasdt0(xH,xH)) = sdtpldt0(sdtasdt0(xC,xG),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xH,xH))),
inference(unit_resolution,[status(thm)],[264,263]) ).
tff(266,plain,
sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)) = sdtpldt0(xR,xS),
inference(monotonicity,[status(thm)],[51,62]) ).
tff(267,plain,
sdtpldt0(sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)),sdtasdt0(xH,xH)) = sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH)),
inference(monotonicity,[status(thm)],[266]) ).
tff(268,plain,
sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH)) = sdtpldt0(sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)),sdtasdt0(xH,xH)),
inference(symmetry,[status(thm)],[267]) ).
tff(269,plain,
sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH)) = sdtpldt0(sdtasdt0(xC,xG),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG))),
inference(transitivity,[status(thm)],[268,265,241]) ).
tff(270,plain,
sdtpldt0(sdtasdt0(xC,xD),sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH))) = sdtpldt0(sdtasdt0(xC,xD),sdtpldt0(sdtasdt0(xC,xG),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG)))),
inference(monotonicity,[status(thm)],[269]) ).
tff(271,plain,
sdtpldt0(sdtasdt0(xC,xD),sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH))) = sdtpldt0(sdtpldt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG))),
inference(transitivity,[status(thm)],[270,149]) ).
tff(272,plain,
( ( sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)) = sdtpldt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))) )
<=> ( sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)) = sdtpldt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(273,axiom,
sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)) = sdtpldt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2835) ).
tff(274,plain,
sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)) = sdtpldt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))),
inference(modus_ponens,[status(thm)],[273,272]) ).
tff(275,plain,
sdtpldt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))) = sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)),
inference(symmetry,[status(thm)],[274]) ).
tff(276,plain,
sdtpldt0(sdtasdt0(xE,xE),sdtpldt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH)))) = sdtpldt0(sdtasdt0(xE,xE),sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH))),
inference(monotonicity,[status(thm)],[275]) ).
tff(277,plain,
sdtpldt0(sdtasdt0(xE,xE),sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH))) = sdtpldt0(sdtasdt0(xE,xE),sdtpldt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH)))),
inference(symmetry,[status(thm)],[276]) ).
tff(278,plain,
( sdtlseqdt0(sdtpldt0(sdtasdt0(xE,xE),sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH))),sdtpldt0(sdtasdt0(xC,xD),sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH))))
<=> sdtlseqdt0(sdtpldt0(sdtasdt0(xE,xE),sdtpldt0(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(monotonicity,[status(thm)],[277,271]) ).
tff(279,plain,
( sdtlseqdt0(sdtpldt0(sdtasdt0(xE,xE),sdtpldt0(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))))
<=> sdtlseqdt0(sdtpldt0(sdtasdt0(xE,xE),sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH))),sdtpldt0(sdtasdt0(xC,xD),sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH)))) ),
inference(symmetry,[status(thm)],[278]) ).
tff(280,plain,
( ~ sdtlseqdt0(sdtpldt0(sdtasdt0(xE,xE),sdtpldt0(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))))
<=> ~ sdtlseqdt0(sdtpldt0(sdtasdt0(xE,xE),sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH))),sdtpldt0(sdtasdt0(xC,xD),sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH)))) ),
inference(monotonicity,[status(thm)],[279]) ).
tff(281,plain,
( ( xE = sdtasasdt0(xp,xq) )
<=> ( xE = sdtasasdt0(xp,xq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(282,axiom,
( aScalar0(xE)
& ( xE = sdtasasdt0(xp,xq) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1820) ).
tff(283,plain,
xE = sdtasasdt0(xp,xq),
inference(and_elim,[status(thm)],[282]) ).
tff(284,plain,
xE = sdtasasdt0(xp,xq),
inference(modus_ponens,[status(thm)],[283,281]) ).
tff(285,plain,
sdtasasdt0(xp,xq) = xE,
inference(symmetry,[status(thm)],[284]) ).
tff(286,plain,
sdtasdt0(sdtasasdt0(xp,xq),sdtasasdt0(xp,xq)) = sdtasdt0(xE,xE),
inference(monotonicity,[status(thm)],[285,285]) ).
tff(287,plain,
( aScalar0(sdtasdt0(sdtasasdt0(xp,xq),sdtasasdt0(xp,xq)))
<=> aScalar0(sdtasdt0(xE,xE)) ),
inference(monotonicity,[status(thm)],[286]) ).
tff(288,plain,
( aScalar0(sdtasasdt0(xp,xq))
<=> aScalar0(xE) ),
inference(monotonicity,[status(thm)],[285]) ).
tff(289,plain,
( aScalar0(xE)
<=> aScalar0(sdtasasdt0(xp,xq)) ),
inference(symmetry,[status(thm)],[288]) ).
tff(290,plain,
( aScalar0(xE)
<=> aScalar0(xE) ),
inference(rewrite,[status(thm)],[]) ).
tff(291,plain,
aScalar0(xE),
inference(and_elim,[status(thm)],[282]) ).
tff(292,plain,
aScalar0(xE),
inference(modus_ponens,[status(thm)],[291,290]) ).
tff(293,plain,
aScalar0(sdtasasdt0(xp,xq)),
inference(modus_ponens,[status(thm)],[292,289]) ).
tff(294,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasasdt0(xp,xq))
| aScalar0(sdtasdt0(sdtasasdt0(xp,xq),sdtasasdt0(xp,xq))) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasasdt0(xp,xq))
| aScalar0(sdtasdt0(sdtasasdt0(xp,xq),sdtasasdt0(xp,xq))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(295,plain,
( ( aScalar0(sdtasdt0(sdtasasdt0(xp,xq),sdtasasdt0(xp,xq)))
| ~ aScalar0(sdtasasdt0(xp,xq))
| ~ aScalar0(sdtasasdt0(xp,xq)) )
<=> ( ~ aScalar0(sdtasasdt0(xp,xq))
| aScalar0(sdtasdt0(sdtasasdt0(xp,xq),sdtasasdt0(xp,xq))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(296,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtasdt0(sdtasasdt0(xp,xq),sdtasasdt0(xp,xq)))
| ~ aScalar0(sdtasasdt0(xp,xq))
| ~ aScalar0(sdtasasdt0(xp,xq)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasasdt0(xp,xq))
| aScalar0(sdtasdt0(sdtasasdt0(xp,xq),sdtasasdt0(xp,xq))) ) ),
inference(monotonicity,[status(thm)],[295]) ).
tff(297,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtasdt0(sdtasasdt0(xp,xq),sdtasasdt0(xp,xq)))
| ~ aScalar0(sdtasasdt0(xp,xq))
| ~ aScalar0(sdtasasdt0(xp,xq)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasasdt0(xp,xq))
| aScalar0(sdtasdt0(sdtasasdt0(xp,xq),sdtasasdt0(xp,xq))) ) ),
inference(transitivity,[status(thm)],[296,294]) ).
tff(298,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtasdt0(sdtasasdt0(xp,xq),sdtasasdt0(xp,xq)))
| ~ aScalar0(sdtasasdt0(xp,xq))
| ~ aScalar0(sdtasasdt0(xp,xq)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(299,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasasdt0(xp,xq))
| aScalar0(sdtasdt0(sdtasasdt0(xp,xq),sdtasasdt0(xp,xq))) ),
inference(modus_ponens,[status(thm)],[298,297]) ).
tff(300,plain,
( ~ aScalar0(sdtasasdt0(xp,xq))
| aScalar0(sdtasdt0(sdtasasdt0(xp,xq),sdtasasdt0(xp,xq))) ),
inference(unit_resolution,[status(thm)],[299,37]) ).
tff(301,plain,
aScalar0(sdtasdt0(sdtasasdt0(xp,xq),sdtasasdt0(xp,xq))),
inference(unit_resolution,[status(thm)],[300,293]) ).
tff(302,plain,
aScalar0(sdtasdt0(xE,xE)),
inference(modus_ponens,[status(thm)],[301,287]) ).
tff(303,plain,
( ( xP = sdtasdt0(xE,xH) )
<=> ( xP = sdtasdt0(xE,xH) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(304,axiom,
( aScalar0(xP)
& ( xP = sdtasdt0(xE,xH) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1911) ).
tff(305,plain,
xP = sdtasdt0(xE,xH),
inference(and_elim,[status(thm)],[304]) ).
tff(306,plain,
xP = sdtasdt0(xE,xH),
inference(modus_ponens,[status(thm)],[305,303]) ).
tff(307,plain,
sdtasdt0(xE,xH) = xP,
inference(symmetry,[status(thm)],[306]) ).
tff(308,plain,
( aScalar0(sdtasdt0(xE,xH))
<=> aScalar0(xP) ),
inference(monotonicity,[status(thm)],[307]) ).
tff(309,plain,
( aScalar0(xP)
<=> aScalar0(sdtasdt0(xE,xH)) ),
inference(symmetry,[status(thm)],[308]) ).
tff(310,plain,
( aScalar0(xP)
<=> aScalar0(xP) ),
inference(rewrite,[status(thm)],[]) ).
tff(311,plain,
aScalar0(xP),
inference(and_elim,[status(thm)],[304]) ).
tff(312,plain,
aScalar0(xP),
inference(modus_ponens,[status(thm)],[311,310]) ).
tff(313,plain,
aScalar0(sdtasdt0(xE,xH)),
inference(modus_ponens,[status(thm)],[312,309]) ).
tff(314,plain,
sdtasdt0(xH,xE) = sdtasdt0(sdtasdt0(xA,xB),sdtasasdt0(xp,xq)),
inference(monotonicity,[status(thm)],[209,284]) ).
tff(315,plain,
sdtasdt0(sdtasdt0(xA,xB),sdtasasdt0(xp,xq)) = sdtasdt0(xH,xE),
inference(symmetry,[status(thm)],[314]) ).
tff(316,plain,
( aScalar0(sdtasdt0(sdtasdt0(xA,xB),sdtasasdt0(xp,xq)))
<=> aScalar0(sdtasdt0(xH,xE)) ),
inference(monotonicity,[status(thm)],[315]) ).
tff(317,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtasdt0(sdtasdt0(xA,xB),sdtasasdt0(xp,xq)))
| ~ aScalar0(sdtasasdt0(xp,xq))
| ~ aScalar0(sdtasdt0(xA,xB)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtasdt0(sdtasdt0(xA,xB),sdtasasdt0(xp,xq)))
| ~ aScalar0(sdtasasdt0(xp,xq))
| ~ aScalar0(sdtasdt0(xA,xB)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(318,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtasdt0(sdtasdt0(xA,xB),sdtasasdt0(xp,xq)))
| ~ aScalar0(sdtasasdt0(xp,xq))
| ~ aScalar0(sdtasdt0(xA,xB)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(319,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtasdt0(sdtasdt0(xA,xB),sdtasasdt0(xp,xq)))
| ~ aScalar0(sdtasasdt0(xp,xq))
| ~ aScalar0(sdtasdt0(xA,xB)) ),
inference(modus_ponens,[status(thm)],[318,317]) ).
tff(320,plain,
( aScalar0(sdtasdt0(sdtasdt0(xA,xB),sdtasasdt0(xp,xq)))
| ~ aScalar0(sdtasasdt0(xp,xq))
| ~ aScalar0(sdtasdt0(xA,xB)) ),
inference(unit_resolution,[status(thm)],[319,37]) ).
tff(321,plain,
aScalar0(sdtasdt0(sdtasdt0(xA,xB),sdtasasdt0(xp,xq))),
inference(unit_resolution,[status(thm)],[320,293,216]) ).
tff(322,plain,
aScalar0(sdtasdt0(xH,xE)),
inference(modus_ponens,[status(thm)],[321,316]) ).
tff(323,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(xH,xH))
| aScalar0(sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH)))
| ~ aScalar0(sdtasdt0(xH,xE)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(xH,xH))
| aScalar0(sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH)))
| ~ aScalar0(sdtasdt0(xH,xE)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(324,plain,
( ( aScalar0(sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH)))
| ~ aScalar0(sdtasdt0(xH,xH))
| ~ aScalar0(sdtasdt0(xH,xE)) )
<=> ( ~ aScalar0(sdtasdt0(xH,xH))
| aScalar0(sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH)))
| ~ aScalar0(sdtasdt0(xH,xE)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(325,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH)))
| ~ aScalar0(sdtasdt0(xH,xH))
| ~ aScalar0(sdtasdt0(xH,xE)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(xH,xH))
| aScalar0(sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH)))
| ~ aScalar0(sdtasdt0(xH,xE)) ) ),
inference(monotonicity,[status(thm)],[324]) ).
tff(326,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH)))
| ~ aScalar0(sdtasdt0(xH,xH))
| ~ aScalar0(sdtasdt0(xH,xE)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(xH,xH))
| aScalar0(sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH)))
| ~ aScalar0(sdtasdt0(xH,xE)) ) ),
inference(transitivity,[status(thm)],[325,323]) ).
tff(327,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH)))
| ~ aScalar0(sdtasdt0(xH,xH))
| ~ aScalar0(sdtasdt0(xH,xE)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(328,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(xH,xH))
| aScalar0(sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH)))
| ~ aScalar0(sdtasdt0(xH,xE)) ),
inference(modus_ponens,[status(thm)],[327,326]) ).
tff(329,plain,
( ~ aScalar0(sdtasdt0(xH,xH))
| aScalar0(sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH)))
| ~ aScalar0(sdtasdt0(xH,xE)) ),
inference(unit_resolution,[status(thm)],[328,114]) ).
tff(330,plain,
aScalar0(sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))),
inference(unit_resolution,[status(thm)],[329,252,322]) ).
tff(331,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtasdt0(xE,xE))
| ~ aScalar0(sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH)))
| ~ aScalar0(sdtasdt0(xE,xH))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))) != sdtpldt0(sdtasdt0(xE,xE),sdtpldt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH)))) )
| ( sdtpldt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)) != sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xE,xE)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))) != sdtasdt0(sdtasdt0(xE,xE),sdtasdt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH)))) )
| ( sdtasdt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)) != sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xE,xE)) ) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtasdt0(xE,xE))
| ~ aScalar0(sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH)))
| ~ aScalar0(sdtasdt0(xE,xH))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))) != sdtpldt0(sdtasdt0(xE,xE),sdtpldt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH)))) )
| ( sdtpldt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)) != sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xE,xE)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))) != sdtasdt0(sdtasdt0(xE,xE),sdtasdt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH)))) )
| ( sdtasdt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)) != sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xE,xE)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(332,plain,
( ( ~ aScalar0(sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH)))
| ~ aScalar0(sdtasdt0(xE,xH))
| ~ aScalar0(sdtasdt0(xE,xE))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))) != sdtpldt0(sdtasdt0(xE,xE),sdtpldt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH)))) )
| ( sdtpldt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)) != sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xE,xE)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))) != sdtasdt0(sdtasdt0(xE,xE),sdtasdt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH)))) )
| ( sdtasdt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)) != sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xE,xE)) ) ) )
<=> ( ~ aScalar0(sdtasdt0(xE,xE))
| ~ aScalar0(sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH)))
| ~ aScalar0(sdtasdt0(xE,xH))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))) != sdtpldt0(sdtasdt0(xE,xE),sdtpldt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH)))) )
| ( sdtpldt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)) != sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xE,xE)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))) != sdtasdt0(sdtasdt0(xE,xE),sdtasdt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH)))) )
| ( sdtasdt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)) != sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xE,xE)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(333,plain,
( ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))) != sdtpldt0(sdtasdt0(xE,xE),sdtpldt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH)))) )
| ( sdtpldt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)) != sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xE,xE)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))) != sdtasdt0(sdtasdt0(xE,xE),sdtasdt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH)))) )
| ( sdtasdt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)) != sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xE,xE)) ) )
<=> ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))) != sdtpldt0(sdtasdt0(xE,xE),sdtpldt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH)))) )
| ( sdtpldt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)) != sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xE,xE)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))) != sdtasdt0(sdtasdt0(xE,xE),sdtasdt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH)))) )
| ( sdtasdt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)) != sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xE,xE)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(334,plain,
( ( ~ aScalar0(sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH)))
| ~ aScalar0(sdtasdt0(xE,xH))
| ~ aScalar0(sdtasdt0(xE,xE))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))) != sdtpldt0(sdtasdt0(xE,xE),sdtpldt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH)))) )
| ( sdtpldt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)) != sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xE,xE)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))) != sdtasdt0(sdtasdt0(xE,xE),sdtasdt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH)))) )
| ( sdtasdt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)) != sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xE,xE)) ) ) )
<=> ( ~ aScalar0(sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH)))
| ~ aScalar0(sdtasdt0(xE,xH))
| ~ aScalar0(sdtasdt0(xE,xE))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))) != sdtpldt0(sdtasdt0(xE,xE),sdtpldt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH)))) )
| ( sdtpldt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)) != sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xE,xE)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))) != sdtasdt0(sdtasdt0(xE,xE),sdtasdt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH)))) )
| ( sdtasdt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)) != sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xE,xE)) ) ) ) ),
inference(monotonicity,[status(thm)],[333]) ).
tff(335,plain,
( ( ~ aScalar0(sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH)))
| ~ aScalar0(sdtasdt0(xE,xH))
| ~ aScalar0(sdtasdt0(xE,xE))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))) != sdtpldt0(sdtasdt0(xE,xE),sdtpldt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH)))) )
| ( sdtpldt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)) != sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xE,xE)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))) != sdtasdt0(sdtasdt0(xE,xE),sdtasdt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH)))) )
| ( sdtasdt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)) != sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xE,xE)) ) ) )
<=> ( ~ aScalar0(sdtasdt0(xE,xE))
| ~ aScalar0(sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH)))
| ~ aScalar0(sdtasdt0(xE,xH))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))) != sdtpldt0(sdtasdt0(xE,xE),sdtpldt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH)))) )
| ( sdtpldt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)) != sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xE,xE)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))) != sdtasdt0(sdtasdt0(xE,xE),sdtasdt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH)))) )
| ( sdtasdt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)) != sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xE,xE)) ) ) ) ),
inference(transitivity,[status(thm)],[334,332]) ).
tff(336,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH)))
| ~ aScalar0(sdtasdt0(xE,xH))
| ~ aScalar0(sdtasdt0(xE,xE))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))) != sdtpldt0(sdtasdt0(xE,xE),sdtpldt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH)))) )
| ( sdtpldt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)) != sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xE,xE)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))) != sdtasdt0(sdtasdt0(xE,xE),sdtasdt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH)))) )
| ( sdtasdt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)) != sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xE,xE)) ) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtasdt0(xE,xE))
| ~ aScalar0(sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH)))
| ~ aScalar0(sdtasdt0(xE,xH))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))) != sdtpldt0(sdtasdt0(xE,xE),sdtpldt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH)))) )
| ( sdtpldt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)) != sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xE,xE)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))) != sdtasdt0(sdtasdt0(xE,xE),sdtasdt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH)))) )
| ( sdtasdt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)) != sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xE,xE)) ) ) ) ),
inference(monotonicity,[status(thm)],[335]) ).
tff(337,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH)))
| ~ aScalar0(sdtasdt0(xE,xH))
| ~ aScalar0(sdtasdt0(xE,xE))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))) != sdtpldt0(sdtasdt0(xE,xE),sdtpldt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH)))) )
| ( sdtpldt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)) != sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xE,xE)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))) != sdtasdt0(sdtasdt0(xE,xE),sdtasdt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH)))) )
| ( sdtasdt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)) != sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xE,xE)) ) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtasdt0(xE,xE))
| ~ aScalar0(sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH)))
| ~ aScalar0(sdtasdt0(xE,xH))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))) != sdtpldt0(sdtasdt0(xE,xE),sdtpldt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH)))) )
| ( sdtpldt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)) != sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xE,xE)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))) != sdtasdt0(sdtasdt0(xE,xE),sdtasdt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH)))) )
| ( sdtasdt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)) != sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xE,xE)) ) ) ) ),
inference(transitivity,[status(thm)],[336,331]) ).
tff(338,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH)))
| ~ aScalar0(sdtasdt0(xE,xH))
| ~ aScalar0(sdtasdt0(xE,xE))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))) != sdtpldt0(sdtasdt0(xE,xE),sdtpldt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH)))) )
| ( sdtpldt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)) != sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xE,xE)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))) != sdtasdt0(sdtasdt0(xE,xE),sdtasdt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH)))) )
| ( sdtasdt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)) != sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xE,xE)) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(339,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtasdt0(xE,xE))
| ~ aScalar0(sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH)))
| ~ aScalar0(sdtasdt0(xE,xH))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))) != sdtpldt0(sdtasdt0(xE,xE),sdtpldt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH)))) )
| ( sdtpldt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)) != sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xE,xE)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))) != sdtasdt0(sdtasdt0(xE,xE),sdtasdt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH)))) )
| ( sdtasdt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)) != sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xE,xE)) ) ) ),
inference(modus_ponens,[status(thm)],[338,337]) ).
tff(340,plain,
( ~ aScalar0(sdtasdt0(xE,xE))
| ~ aScalar0(sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH)))
| ~ aScalar0(sdtasdt0(xE,xH))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))) != sdtpldt0(sdtasdt0(xE,xE),sdtpldt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH)))) )
| ( sdtpldt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)) != sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xE,xE)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))) != sdtasdt0(sdtasdt0(xE,xE),sdtasdt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH)))) )
| ( sdtasdt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)) != sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xE,xE)) ) ) ),
inference(unit_resolution,[status(thm)],[339,135]) ).
tff(341,plain,
~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))) != sdtpldt0(sdtasdt0(xE,xE),sdtpldt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH)))) )
| ( sdtpldt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)) != sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xE,xE)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))) != sdtasdt0(sdtasdt0(xE,xE),sdtasdt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH)))) )
| ( sdtasdt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)) != sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xE,xE)) ) ),
inference(unit_resolution,[status(thm)],[340,330,313,302]) ).
tff(342,plain,
( ( sdtpldt0(sdtpldt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))) != sdtpldt0(sdtasdt0(xE,xE),sdtpldt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH)))) )
| ( sdtpldt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)) != sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xE,xE)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))) != sdtasdt0(sdtasdt0(xE,xE),sdtasdt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH)))) )
| ( sdtasdt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)) != sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xE,xE)) )
| ( sdtpldt0(sdtpldt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))) = sdtpldt0(sdtasdt0(xE,xE),sdtpldt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH)))) ) ),
inference(tautology,[status(thm)],[]) ).
tff(343,plain,
sdtpldt0(sdtpldt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))) = sdtpldt0(sdtasdt0(xE,xE),sdtpldt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH)))),
inference(unit_resolution,[status(thm)],[342,341]) ).
tff(344,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))))
<=> sdtlseqdt0(sdtpldt0(sdtasdt0(xE,xE),sdtpldt0(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(monotonicity,[status(thm)],[343]) ).
tff(345,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))))
<=> ~ sdtlseqdt0(sdtpldt0(sdtasdt0(xE,xE),sdtpldt0(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(monotonicity,[status(thm)],[344]) ).
tff(346,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))))
<=> ~ 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(rewrite,[status(thm)],[]) ).
tff(347,axiom,
~ 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/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(348,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(modus_ponens,[status(thm)],[347,346]) ).
tff(349,plain,
~ sdtlseqdt0(sdtpldt0(sdtasdt0(xE,xE),sdtpldt0(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(modus_ponens,[status(thm)],[348,345]) ).
tff(350,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(modus_ponens,[status(thm)],[349,280]) ).
tff(351,plain,
( sdtlseqdt0(sdtpldt0(sdtasdt0(xE,xE),sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH))),sdtpldt0(sdtasdt0(xC,xD),sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH))))
<=> sdtlseqdt0(sdtpldt0(sdtasdt0(xE,xE),sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH))),sdtpldt0(sdtasdt0(xC,xD),sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH)))) ),
inference(rewrite,[status(thm)],[]) ).
tff(352,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/sandbox2/benchmark/theBenchmark.p',m__2796) ).
tff(353,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(modus_ponens,[status(thm)],[352,351]) ).
tff(354,plain,
$false,
inference(unit_resolution,[status(thm)],[353,350]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : RNG078+2 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.13/0.33 % Computer : n005.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Jun 20 03:18:50 EDT 2025
% 0.13/0.34 % CPUTime :
% 18.00/18.22 % SZS status Theorem
% 18.00/18.22 % SZS output start Proof
% See solution above
% 18.11/18.32 % E exiting
%------------------------------------------------------------------------------