%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : RNG057+2 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 05:24:02 AM UTC 2025
% Result : Theorem 1.46s 1.68s
% Output : Proof 1.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 54
% Syntax : Number of formulae : 160 ( 58 unt; 0 typ; 0 def)
% Number of atoms : 969 ( 37 equ)
% Maximal formula atoms : 31 ( 6 avg)
% Number of connectives : 1261 ( 514 ~; 471 |; 158 &)
% ( 95 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 62 ( 62 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 : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 216 ( 194 !; 0 ?; 216 :)
% Comments :
%------------------------------------------------------------------------------
tff(sdtlseqdt0_type,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(sdtasdt0_type,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(xD_type,type,
xD: $i ).
tff(xC_type,type,
xC: $i ).
tff(xH_type,type,
xH: $i ).
tff(xE_type,type,
xE: $i ).
tff(xN_type,type,
xN: $i ).
tff(xP_type,type,
xP: $i ).
tff(aScalar0_type,type,
aScalar0: $i > $o ).
tff(xB_type,type,
xB: $i ).
tff(xA_type,type,
xA: $i ).
tff(sz0z00_type,type,
sz0z00: $i ).
tff(sdtasasdt0_type,type,
sdtasasdt0: ( $i * $i ) > $i ).
tff(xq_type,type,
xq: $i ).
tff(xp_type,type,
xp: $i ).
tff(1,plain,
( ( xN = sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xC,xD)) )
<=> ( xN = sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xC,xD)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
xN = sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xC,xD)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2052) ).
tff(3,plain,
xN = sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xC,xD)),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xC,xD)) = xN,
inference(symmetry,[status(thm)],[3]) ).
tff(5,plain,
( ( sdtasdt0(xP,xP) = sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)) )
<=> ( sdtasdt0(xP,xP) = sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(6,axiom,
sdtasdt0(xP,xP) = sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2027) ).
tff(7,plain,
sdtasdt0(xP,xP) = sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)) = sdtasdt0(xP,xP),
inference(symmetry,[status(thm)],[7]) ).
tff(9,plain,
( sdtlseqdt0(sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)),sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xC,xD)))
<=> sdtlseqdt0(sdtasdt0(xP,xP),xN) ),
inference(monotonicity,[status(thm)],[8,4]) ).
tff(10,plain,
( sdtlseqdt0(sdtasdt0(xP,xP),xN)
<=> sdtlseqdt0(sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)),sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xC,xD))) ),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
( ~ sdtlseqdt0(sdtasdt0(xP,xP),xN)
<=> ~ sdtlseqdt0(sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)),sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xC,xD))) ),
inference(monotonicity,[status(thm)],[10]) ).
tff(12,plain,
( ~ sdtlseqdt0(sdtasdt0(xP,xP),xN)
<=> ~ sdtlseqdt0(sdtasdt0(xP,xP),xN) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
~ sdtlseqdt0(sdtasdt0(xP,xP),xN),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(14,plain,
~ sdtlseqdt0(sdtasdt0(xP,xP),xN),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
~ sdtlseqdt0(sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)),sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xC,xD))),
inference(modus_ponens,[status(thm)],[14,11]) ).
tff(16,plain,
( ( xH = sdtasdt0(xA,xB) )
<=> ( xH = sdtasdt0(xA,xB) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(17,axiom,
( aScalar0(xH)
& ( xH = sdtasdt0(xA,xB) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1873) ).
tff(18,plain,
xH = sdtasdt0(xA,xB),
inference(and_elim,[status(thm)],[17]) ).
tff(19,plain,
xH = sdtasdt0(xA,xB),
inference(modus_ponens,[status(thm)],[18,16]) ).
tff(20,plain,
sdtasdt0(xA,xB) = xH,
inference(symmetry,[status(thm)],[19]) ).
tff(21,plain,
sdtasdt0(sdtasdt0(xA,xB),sdtasdt0(xA,xB)) = sdtasdt0(xH,xH),
inference(monotonicity,[status(thm)],[20,20]) ).
tff(22,plain,
( aScalar0(sdtasdt0(sdtasdt0(xA,xB),sdtasdt0(xA,xB)))
<=> aScalar0(sdtasdt0(xH,xH)) ),
inference(monotonicity,[status(thm)],[21]) ).
tff(23,plain,
( aScalar0(sdtasdt0(xA,xB))
<=> aScalar0(xH) ),
inference(monotonicity,[status(thm)],[20]) ).
tff(24,plain,
( aScalar0(xH)
<=> aScalar0(sdtasdt0(xA,xB)) ),
inference(symmetry,[status(thm)],[23]) ).
tff(25,plain,
( aScalar0(xH)
<=> aScalar0(xH) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,plain,
aScalar0(xH),
inference(and_elim,[status(thm)],[17]) ).
tff(27,plain,
aScalar0(xH),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
aScalar0(sdtasdt0(xA,xB)),
inference(modus_ponens,[status(thm)],[27,24]) ).
tff(29,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(30,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)],[29]) ).
tff(31,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(32,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)],[31]) ).
tff(33,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(34,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(35,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)],[34]) ).
tff(36,axiom,
! [W0: $i,W1: $i] :
( ( aScalar0(W0)
& aScalar0(W1) )
=> aScalar0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulSc) ).
tff(37,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) ),
inference(modus_ponens,[status(thm)],[37,33]) ).
tff(39,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) ),
inference(skolemize,[status(sab)],[38]) ).
tff(40,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ),
inference(modus_ponens,[status(thm)],[39,32]) ).
tff(41,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ),
inference(modus_ponens,[status(thm)],[40,30]) ).
tff(42,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(43,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(44,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)],[43]) ).
tff(45,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)],[44,42]) ).
tff(46,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(47,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)],[46,45]) ).
tff(48,plain,
( ~ aScalar0(sdtasdt0(xA,xB))
| aScalar0(sdtasdt0(sdtasdt0(xA,xB),sdtasdt0(xA,xB))) ),
inference(unit_resolution,[status(thm)],[47,41]) ).
tff(49,plain,
aScalar0(sdtasdt0(sdtasdt0(xA,xB),sdtasdt0(xA,xB))),
inference(unit_resolution,[status(thm)],[48,28]) ).
tff(50,plain,
aScalar0(sdtasdt0(xH,xH)),
inference(modus_ponens,[status(thm)],[49,22]) ).
tff(51,plain,
^ [W0: $i] :
refl(( ( ~ aScalar0(W0)
| sdtlseqdt0(W0,W0) )
<=> ( ~ aScalar0(W0)
| sdtlseqdt0(W0,W0) ) )),
inference(bind,[status(th)],[]) ).
tff(52,plain,
( ! [W0: $i] :
( ~ aScalar0(W0)
| sdtlseqdt0(W0,W0) )
<=> ! [W0: $i] :
( ~ aScalar0(W0)
| sdtlseqdt0(W0,W0) ) ),
inference(quant_intro,[status(thm)],[51]) ).
tff(53,plain,
( ! [W0: $i] :
( ~ aScalar0(W0)
| sdtlseqdt0(W0,W0) )
<=> ! [W0: $i] :
( ~ aScalar0(W0)
| sdtlseqdt0(W0,W0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(54,plain,
^ [W0: $i] :
rewrite(( ( aScalar0(W0)
=> sdtlseqdt0(W0,W0) )
<=> ( ~ aScalar0(W0)
| sdtlseqdt0(W0,W0) ) )),
inference(bind,[status(th)],[]) ).
tff(55,plain,
( ! [W0: $i] :
( aScalar0(W0)
=> sdtlseqdt0(W0,W0) )
<=> ! [W0: $i] :
( ~ aScalar0(W0)
| sdtlseqdt0(W0,W0) ) ),
inference(quant_intro,[status(thm)],[54]) ).
tff(56,axiom,
! [W0: $i] :
( aScalar0(W0)
=> sdtlseqdt0(W0,W0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLERef) ).
tff(57,plain,
! [W0: $i] :
( ~ aScalar0(W0)
| sdtlseqdt0(W0,W0) ),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
! [W0: $i] :
( ~ aScalar0(W0)
| sdtlseqdt0(W0,W0) ),
inference(modus_ponens,[status(thm)],[57,53]) ).
tff(59,plain,
! [W0: $i] :
( ~ aScalar0(W0)
| sdtlseqdt0(W0,W0) ),
inference(skolemize,[status(sab)],[58]) ).
tff(60,plain,
! [W0: $i] :
( ~ aScalar0(W0)
| sdtlseqdt0(W0,W0) ),
inference(modus_ponens,[status(thm)],[59,52]) ).
tff(61,plain,
( ( ~ ! [W0: $i] :
( ~ aScalar0(W0)
| sdtlseqdt0(W0,W0) )
| ~ aScalar0(sdtasdt0(xH,xH))
| sdtlseqdt0(sdtasdt0(xH,xH),sdtasdt0(xH,xH)) )
<=> ( ~ ! [W0: $i] :
( ~ aScalar0(W0)
| sdtlseqdt0(W0,W0) )
| ~ aScalar0(sdtasdt0(xH,xH))
| sdtlseqdt0(sdtasdt0(xH,xH),sdtasdt0(xH,xH)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(62,plain,
( ~ ! [W0: $i] :
( ~ aScalar0(W0)
| sdtlseqdt0(W0,W0) )
| ~ aScalar0(sdtasdt0(xH,xH))
| sdtlseqdt0(sdtasdt0(xH,xH),sdtasdt0(xH,xH)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(63,plain,
( ~ ! [W0: $i] :
( ~ aScalar0(W0)
| sdtlseqdt0(W0,W0) )
| ~ aScalar0(sdtasdt0(xH,xH))
| sdtlseqdt0(sdtasdt0(xH,xH),sdtasdt0(xH,xH)) ),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
sdtlseqdt0(sdtasdt0(xH,xH),sdtasdt0(xH,xH)),
inference(unit_resolution,[status(thm)],[63,60,50]) ).
tff(65,plain,
( ( xE = sdtasasdt0(xp,xq) )
<=> ( xE = sdtasasdt0(xp,xq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(66,axiom,
( aScalar0(xE)
& ( xE = sdtasasdt0(xp,xq) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1820) ).
tff(67,plain,
xE = sdtasasdt0(xp,xq),
inference(and_elim,[status(thm)],[66]) ).
tff(68,plain,
xE = sdtasasdt0(xp,xq),
inference(modus_ponens,[status(thm)],[67,65]) ).
tff(69,plain,
sdtasasdt0(xp,xq) = xE,
inference(symmetry,[status(thm)],[68]) ).
tff(70,plain,
sdtasdt0(sdtasasdt0(xp,xq),sdtasasdt0(xp,xq)) = sdtasdt0(xE,xE),
inference(monotonicity,[status(thm)],[69,69]) ).
tff(71,plain,
( sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(xp,xq),sdtasasdt0(xp,xq)))
<=> sdtlseqdt0(sz0z00,sdtasdt0(xE,xE)) ),
inference(monotonicity,[status(thm)],[70]) ).
tff(72,plain,
( aScalar0(sdtasasdt0(xp,xq))
<=> aScalar0(xE) ),
inference(monotonicity,[status(thm)],[69]) ).
tff(73,plain,
( aScalar0(xE)
<=> aScalar0(sdtasasdt0(xp,xq)) ),
inference(symmetry,[status(thm)],[72]) ).
tff(74,plain,
( aScalar0(xE)
<=> aScalar0(xE) ),
inference(rewrite,[status(thm)],[]) ).
tff(75,plain,
aScalar0(xE),
inference(and_elim,[status(thm)],[66]) ).
tff(76,plain,
aScalar0(xE),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,plain,
aScalar0(sdtasasdt0(xp,xq)),
inference(modus_ponens,[status(thm)],[76,73]) ).
tff(78,plain,
^ [W0: $i] :
refl(( ( ~ aScalar0(W0)
| sdtlseqdt0(sz0z00,sdtasdt0(W0,W0)) )
<=> ( ~ aScalar0(W0)
| sdtlseqdt0(sz0z00,sdtasdt0(W0,W0)) ) )),
inference(bind,[status(th)],[]) ).
tff(79,plain,
( ! [W0: $i] :
( ~ aScalar0(W0)
| sdtlseqdt0(sz0z00,sdtasdt0(W0,W0)) )
<=> ! [W0: $i] :
( ~ aScalar0(W0)
| sdtlseqdt0(sz0z00,sdtasdt0(W0,W0)) ) ),
inference(quant_intro,[status(thm)],[78]) ).
tff(80,plain,
( ! [W0: $i] :
( ~ aScalar0(W0)
| sdtlseqdt0(sz0z00,sdtasdt0(W0,W0)) )
<=> ! [W0: $i] :
( ~ aScalar0(W0)
| sdtlseqdt0(sz0z00,sdtasdt0(W0,W0)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(81,plain,
^ [W0: $i] :
rewrite(( ( aScalar0(W0)
=> sdtlseqdt0(sz0z00,sdtasdt0(W0,W0)) )
<=> ( ~ aScalar0(W0)
| sdtlseqdt0(sz0z00,sdtasdt0(W0,W0)) ) )),
inference(bind,[status(th)],[]) ).
tff(82,plain,
( ! [W0: $i] :
( aScalar0(W0)
=> sdtlseqdt0(sz0z00,sdtasdt0(W0,W0)) )
<=> ! [W0: $i] :
( ~ aScalar0(W0)
| sdtlseqdt0(sz0z00,sdtasdt0(W0,W0)) ) ),
inference(quant_intro,[status(thm)],[81]) ).
tff(83,axiom,
! [W0: $i] :
( aScalar0(W0)
=> sdtlseqdt0(sz0z00,sdtasdt0(W0,W0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSqPos) ).
tff(84,plain,
! [W0: $i] :
( ~ aScalar0(W0)
| sdtlseqdt0(sz0z00,sdtasdt0(W0,W0)) ),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
! [W0: $i] :
( ~ aScalar0(W0)
| sdtlseqdt0(sz0z00,sdtasdt0(W0,W0)) ),
inference(modus_ponens,[status(thm)],[84,80]) ).
tff(86,plain,
! [W0: $i] :
( ~ aScalar0(W0)
| sdtlseqdt0(sz0z00,sdtasdt0(W0,W0)) ),
inference(skolemize,[status(sab)],[85]) ).
tff(87,plain,
! [W0: $i] :
( ~ aScalar0(W0)
| sdtlseqdt0(sz0z00,sdtasdt0(W0,W0)) ),
inference(modus_ponens,[status(thm)],[86,79]) ).
tff(88,plain,
( ( ~ ! [W0: $i] :
( ~ aScalar0(W0)
| sdtlseqdt0(sz0z00,sdtasdt0(W0,W0)) )
| ~ aScalar0(sdtasasdt0(xp,xq))
| sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(xp,xq),sdtasasdt0(xp,xq))) )
<=> ( ~ ! [W0: $i] :
( ~ aScalar0(W0)
| sdtlseqdt0(sz0z00,sdtasdt0(W0,W0)) )
| ~ aScalar0(sdtasasdt0(xp,xq))
| sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(xp,xq),sdtasasdt0(xp,xq))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(89,plain,
( ~ ! [W0: $i] :
( ~ aScalar0(W0)
| sdtlseqdt0(sz0z00,sdtasdt0(W0,W0)) )
| ~ aScalar0(sdtasasdt0(xp,xq))
| sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(xp,xq),sdtasasdt0(xp,xq))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(90,plain,
( ~ ! [W0: $i] :
( ~ aScalar0(W0)
| sdtlseqdt0(sz0z00,sdtasdt0(W0,W0)) )
| ~ aScalar0(sdtasasdt0(xp,xq))
| sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(xp,xq),sdtasasdt0(xp,xq))) ),
inference(modus_ponens,[status(thm)],[89,88]) ).
tff(91,plain,
( ~ aScalar0(sdtasasdt0(xp,xq))
| sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(xp,xq),sdtasasdt0(xp,xq))) ),
inference(unit_resolution,[status(thm)],[90,87]) ).
tff(92,plain,
sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(xp,xq),sdtasasdt0(xp,xq))),
inference(unit_resolution,[status(thm)],[91,77]) ).
tff(93,plain,
sdtlseqdt0(sz0z00,sdtasdt0(xE,xE)),
inference(modus_ponens,[status(thm)],[92,71]) ).
tff(94,plain,
( ( xD = sdtasasdt0(xq,xq) )
<=> ( xD = sdtasasdt0(xq,xq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(95,axiom,
( aScalar0(xD)
& ( xD = sdtasasdt0(xq,xq) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1800) ).
tff(96,plain,
xD = sdtasasdt0(xq,xq),
inference(and_elim,[status(thm)],[95]) ).
tff(97,plain,
xD = sdtasasdt0(xq,xq),
inference(modus_ponens,[status(thm)],[96,94]) ).
tff(98,plain,
sdtasasdt0(xq,xq) = xD,
inference(symmetry,[status(thm)],[97]) ).
tff(99,plain,
( ( xC = sdtasasdt0(xp,xp) )
<=> ( xC = sdtasasdt0(xp,xp) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(100,axiom,
( aScalar0(xC)
& ( xC = sdtasasdt0(xp,xp) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1783) ).
tff(101,plain,
xC = sdtasasdt0(xp,xp),
inference(and_elim,[status(thm)],[100]) ).
tff(102,plain,
xC = sdtasasdt0(xp,xp),
inference(modus_ponens,[status(thm)],[101,99]) ).
tff(103,plain,
sdtasasdt0(xp,xp) = xC,
inference(symmetry,[status(thm)],[102]) ).
tff(104,plain,
sdtasdt0(sdtasasdt0(xp,xp),sdtasasdt0(xq,xq)) = sdtasdt0(xC,xD),
inference(monotonicity,[status(thm)],[103,98]) ).
tff(105,plain,
( aScalar0(sdtasdt0(sdtasasdt0(xp,xp),sdtasasdt0(xq,xq)))
<=> aScalar0(sdtasdt0(xC,xD)) ),
inference(monotonicity,[status(thm)],[104]) ).
tff(106,plain,
( aScalar0(sdtasasdt0(xq,xq))
<=> aScalar0(xD) ),
inference(monotonicity,[status(thm)],[98]) ).
tff(107,plain,
( aScalar0(xD)
<=> aScalar0(sdtasasdt0(xq,xq)) ),
inference(symmetry,[status(thm)],[106]) ).
tff(108,plain,
( aScalar0(xD)
<=> aScalar0(xD) ),
inference(rewrite,[status(thm)],[]) ).
tff(109,plain,
aScalar0(xD),
inference(and_elim,[status(thm)],[95]) ).
tff(110,plain,
aScalar0(xD),
inference(modus_ponens,[status(thm)],[109,108]) ).
tff(111,plain,
aScalar0(sdtasasdt0(xq,xq)),
inference(modus_ponens,[status(thm)],[110,107]) ).
tff(112,plain,
( aScalar0(sdtasasdt0(xp,xp))
<=> aScalar0(xC) ),
inference(monotonicity,[status(thm)],[103]) ).
tff(113,plain,
( aScalar0(xC)
<=> aScalar0(sdtasasdt0(xp,xp)) ),
inference(symmetry,[status(thm)],[112]) ).
tff(114,plain,
( aScalar0(xC)
<=> aScalar0(xC) ),
inference(rewrite,[status(thm)],[]) ).
tff(115,plain,
aScalar0(xC),
inference(and_elim,[status(thm)],[100]) ).
tff(116,plain,
aScalar0(xC),
inference(modus_ponens,[status(thm)],[115,114]) ).
tff(117,plain,
aScalar0(sdtasasdt0(xp,xp)),
inference(modus_ponens,[status(thm)],[116,113]) ).
tff(118,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(119,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(120,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)],[119]) ).
tff(121,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)],[120,118]) ).
tff(122,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(123,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)],[122,121]) ).
tff(124,plain,
( ~ aScalar0(sdtasasdt0(xq,xq))
| ~ aScalar0(sdtasasdt0(xp,xp))
| aScalar0(sdtasdt0(sdtasasdt0(xp,xp),sdtasasdt0(xq,xq))) ),
inference(unit_resolution,[status(thm)],[123,41]) ).
tff(125,plain,
aScalar0(sdtasdt0(sdtasasdt0(xp,xp),sdtasasdt0(xq,xq))),
inference(unit_resolution,[status(thm)],[124,117,111]) ).
tff(126,plain,
aScalar0(sdtasdt0(xC,xD)),
inference(modus_ponens,[status(thm)],[125,105]) ).
tff(127,plain,
( aScalar0(sdtasdt0(sdtasasdt0(xp,xq),sdtasasdt0(xp,xq)))
<=> aScalar0(sdtasdt0(xE,xE)) ),
inference(monotonicity,[status(thm)],[70]) ).
tff(128,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(129,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(130,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)],[129]) ).
tff(131,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)],[130,128]) ).
tff(132,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(133,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)],[132,131]) ).
tff(134,plain,
( ~ aScalar0(sdtasasdt0(xp,xq))
| aScalar0(sdtasdt0(sdtasasdt0(xp,xq),sdtasasdt0(xp,xq))) ),
inference(unit_resolution,[status(thm)],[133,41]) ).
tff(135,plain,
aScalar0(sdtasdt0(sdtasasdt0(xp,xq),sdtasasdt0(xp,xq))),
inference(unit_resolution,[status(thm)],[134,77]) ).
tff(136,plain,
aScalar0(sdtasdt0(xE,xE)),
inference(modus_ponens,[status(thm)],[135,127]) ).
tff(137,plain,
( sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD))
<=> sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)) ),
inference(rewrite,[status(thm)],[]) ).
tff(138,axiom,
sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1967) ).
tff(139,plain,
sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)),
inference(modus_ponens,[status(thm)],[138,137]) ).
tff(140,plain,
^ [W0: $i,W1: $i,W2: $i,W3: $i] :
refl(( ( sdtlseqdt0(sdtasdt0(W0,W2),sdtasdt0(W1,W3))
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(sz0z00,W2) )
<=> ( sdtlseqdt0(sdtasdt0(W0,W2),sdtasdt0(W1,W3))
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(sz0z00,W2) ) )),
inference(bind,[status(th)],[]) ).
tff(141,plain,
( ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( sdtlseqdt0(sdtasdt0(W0,W2),sdtasdt0(W1,W3))
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(sz0z00,W2) )
<=> ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( sdtlseqdt0(sdtasdt0(W0,W2),sdtasdt0(W1,W3))
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(sz0z00,W2) ) ),
inference(quant_intro,[status(thm)],[140]) ).
tff(142,plain,
^ [W0: $i,W1: $i,W2: $i,W3: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
<=> ~ ( ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
( ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
<=> ~ ~ ( ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
rewrite(( ~ ~ ( ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
<=> ( ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
( ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
<=> ( ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
trans(monotonicity(rewrite(( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(sz0z00,W2)
& sdtlseqdt0(W2,W3) )
<=> ~ ( ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(sz0z00,W2) ) )),
( ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(sz0z00,W2)
& sdtlseqdt0(W2,W3) )
<=> ~ ~ ( ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(sz0z00,W2) ) )),
rewrite(( ~ ~ ( ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(sz0z00,W2) )
<=> ( ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(sz0z00,W2) ) )),
( ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(sz0z00,W2)
& sdtlseqdt0(W2,W3) )
<=> ( ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(sz0z00,W2) ) )),
( ( sdtlseqdt0(sdtasdt0(W0,W2),sdtasdt0(W1,W3))
| ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(sz0z00,W2)
& sdtlseqdt0(W2,W3) ) )
<=> ( sdtlseqdt0(sdtasdt0(W0,W2),sdtasdt0(W1,W3))
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(sz0z00,W2) ) )),
rewrite(( ( sdtlseqdt0(sdtasdt0(W0,W2),sdtasdt0(W1,W3))
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(sz0z00,W2) )
<=> ( sdtlseqdt0(sdtasdt0(W0,W2),sdtasdt0(W1,W3))
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(sz0z00,W2) ) )),
( ( sdtlseqdt0(sdtasdt0(W0,W2),sdtasdt0(W1,W3))
| ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(sz0z00,W2)
& sdtlseqdt0(W2,W3) ) )
<=> ( sdtlseqdt0(sdtasdt0(W0,W2),sdtasdt0(W1,W3))
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(sz0z00,W2) ) )),
inference(bind,[status(th)],[]) ).
tff(143,plain,
( ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( sdtlseqdt0(sdtasdt0(W0,W2),sdtasdt0(W1,W3))
| ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(sz0z00,W2)
& sdtlseqdt0(W2,W3) ) )
<=> ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( sdtlseqdt0(sdtasdt0(W0,W2),sdtasdt0(W1,W3))
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(sz0z00,W2) ) ),
inference(quant_intro,[status(thm)],[142]) ).
tff(144,plain,
( ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( sdtlseqdt0(sdtasdt0(W0,W2),sdtasdt0(W1,W3))
| ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(sz0z00,W2)
& sdtlseqdt0(W2,W3) ) )
<=> ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( sdtlseqdt0(sdtasdt0(W0,W2),sdtasdt0(W1,W3))
| ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(sz0z00,W2)
& sdtlseqdt0(W2,W3) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(145,plain,
^ [W0: $i,W1: $i,W2: $i,W3: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
<=> ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) ) )),
( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
<=> ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) ) )),
rewrite(( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
<=> ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) ) )),
( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
<=> ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) ) )),
trans(monotonicity(rewrite(( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(sz0z00,W2)
& sdtlseqdt0(W2,W3) )
<=> ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(sz0z00,W2)
& sdtlseqdt0(W2,W3) ) )),
( ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(sz0z00,W2)
& sdtlseqdt0(W2,W3) )
=> sdtlseqdt0(sdtasdt0(W0,W2),sdtasdt0(W1,W3)) )
<=> ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(sz0z00,W2)
& sdtlseqdt0(W2,W3) )
=> sdtlseqdt0(sdtasdt0(W0,W2),sdtasdt0(W1,W3)) ) )),
rewrite(( ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(sz0z00,W2)
& sdtlseqdt0(W2,W3) )
=> sdtlseqdt0(sdtasdt0(W0,W2),sdtasdt0(W1,W3)) )
<=> ( ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(sz0z00,W2)
& sdtlseqdt0(W2,W3) )
| sdtlseqdt0(sdtasdt0(W0,W2),sdtasdt0(W1,W3)) ) )),
( ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(sz0z00,W2)
& sdtlseqdt0(W2,W3) )
=> sdtlseqdt0(sdtasdt0(W0,W2),sdtasdt0(W1,W3)) )
<=> ( ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(sz0z00,W2)
& sdtlseqdt0(W2,W3) )
| sdtlseqdt0(sdtasdt0(W0,W2),sdtasdt0(W1,W3)) ) )),
( ( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
=> ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(sz0z00,W2)
& sdtlseqdt0(W2,W3) )
=> sdtlseqdt0(sdtasdt0(W0,W2),sdtasdt0(W1,W3)) ) )
<=> ( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
=> ( ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(sz0z00,W2)
& sdtlseqdt0(W2,W3) )
| sdtlseqdt0(sdtasdt0(W0,W2),sdtasdt0(W1,W3)) ) ) )),
rewrite(( ( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
=> ( ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(sz0z00,W2)
& sdtlseqdt0(W2,W3) )
| sdtlseqdt0(sdtasdt0(W0,W2),sdtasdt0(W1,W3)) ) )
<=> ( sdtlseqdt0(sdtasdt0(W0,W2),sdtasdt0(W1,W3))
| ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(sz0z00,W2)
& sdtlseqdt0(W2,W3) ) ) )),
( ( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
=> ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(sz0z00,W2)
& sdtlseqdt0(W2,W3) )
=> sdtlseqdt0(sdtasdt0(W0,W2),sdtasdt0(W1,W3)) ) )
<=> ( sdtlseqdt0(sdtasdt0(W0,W2),sdtasdt0(W1,W3))
| ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(sz0z00,W2)
& sdtlseqdt0(W2,W3) ) ) )),
inference(bind,[status(th)],[]) ).
tff(146,plain,
( ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
=> ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(sz0z00,W2)
& sdtlseqdt0(W2,W3) )
=> sdtlseqdt0(sdtasdt0(W0,W2),sdtasdt0(W1,W3)) ) )
<=> ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( sdtlseqdt0(sdtasdt0(W0,W2),sdtasdt0(W1,W3))
| ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(sz0z00,W2)
& sdtlseqdt0(W2,W3) ) ) ),
inference(quant_intro,[status(thm)],[145]) ).
tff(147,axiom,
! [W0: $i,W1: $i,W2: $i,W3: $i] :
( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
=> ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(sz0z00,W2)
& sdtlseqdt0(W2,W3) )
=> sdtlseqdt0(sdtasdt0(W0,W2),sdtasdt0(W1,W3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLEMonM) ).
tff(148,plain,
! [W0: $i,W1: $i,W2: $i,W3: $i] :
( sdtlseqdt0(sdtasdt0(W0,W2),sdtasdt0(W1,W3))
| ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(sz0z00,W2)
& sdtlseqdt0(W2,W3) ) ),
inference(modus_ponens,[status(thm)],[147,146]) ).
tff(149,plain,
! [W0: $i,W1: $i,W2: $i,W3: $i] :
( sdtlseqdt0(sdtasdt0(W0,W2),sdtasdt0(W1,W3))
| ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(sz0z00,W2)
& sdtlseqdt0(W2,W3) ) ),
inference(modus_ponens,[status(thm)],[148,144]) ).
tff(150,plain,
! [W0: $i,W1: $i,W2: $i,W3: $i] :
( sdtlseqdt0(sdtasdt0(W0,W2),sdtasdt0(W1,W3))
| ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(sz0z00,W2)
& sdtlseqdt0(W2,W3) ) ),
inference(skolemize,[status(sab)],[149]) ).
tff(151,plain,
! [W0: $i,W1: $i,W2: $i,W3: $i] :
( sdtlseqdt0(sdtasdt0(W0,W2),sdtasdt0(W1,W3))
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(sz0z00,W2) ),
inference(modus_ponens,[status(thm)],[150,143]) ).
tff(152,plain,
! [W0: $i,W1: $i,W2: $i,W3: $i] :
( sdtlseqdt0(sdtasdt0(W0,W2),sdtasdt0(W1,W3))
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(sz0z00,W2) ),
inference(modus_ponens,[status(thm)],[151,141]) ).
tff(153,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( sdtlseqdt0(sdtasdt0(W0,W2),sdtasdt0(W1,W3))
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(sz0z00,W2) )
| ~ aScalar0(sdtasdt0(xE,xE))
| ~ aScalar0(sdtasdt0(xH,xH))
| ~ aScalar0(sdtasdt0(xC,xD))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(xE,xE))
| ~ sdtlseqdt0(sdtasdt0(xH,xH),sdtasdt0(xH,xH))
| sdtlseqdt0(sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)),sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xC,xD)))
| ~ sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( sdtlseqdt0(sdtasdt0(W0,W2),sdtasdt0(W1,W3))
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(sz0z00,W2) )
| ~ aScalar0(sdtasdt0(xE,xE))
| ~ aScalar0(sdtasdt0(xH,xH))
| ~ aScalar0(sdtasdt0(xC,xD))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(xE,xE))
| ~ sdtlseqdt0(sdtasdt0(xH,xH),sdtasdt0(xH,xH))
| sdtlseqdt0(sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)),sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xC,xD)))
| ~ sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(154,plain,
( ( sdtlseqdt0(sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)),sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xC,xD)))
| ~ aScalar0(sdtasdt0(xC,xD))
| ~ aScalar0(sdtasdt0(xE,xE))
| ~ aScalar0(sdtasdt0(xH,xH))
| ~ aScalar0(sdtasdt0(xH,xH))
| ~ sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD))
| ~ sdtlseqdt0(sdtasdt0(xH,xH),sdtasdt0(xH,xH))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(xE,xE)) )
<=> ( ~ aScalar0(sdtasdt0(xE,xE))
| ~ aScalar0(sdtasdt0(xH,xH))
| ~ aScalar0(sdtasdt0(xC,xD))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(xE,xE))
| ~ sdtlseqdt0(sdtasdt0(xH,xH),sdtasdt0(xH,xH))
| sdtlseqdt0(sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)),sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xC,xD)))
| ~ sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(155,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( sdtlseqdt0(sdtasdt0(W0,W2),sdtasdt0(W1,W3))
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(sz0z00,W2) )
| sdtlseqdt0(sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)),sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xC,xD)))
| ~ aScalar0(sdtasdt0(xC,xD))
| ~ aScalar0(sdtasdt0(xE,xE))
| ~ aScalar0(sdtasdt0(xH,xH))
| ~ aScalar0(sdtasdt0(xH,xH))
| ~ sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD))
| ~ sdtlseqdt0(sdtasdt0(xH,xH),sdtasdt0(xH,xH))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(xE,xE)) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( sdtlseqdt0(sdtasdt0(W0,W2),sdtasdt0(W1,W3))
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(sz0z00,W2) )
| ~ aScalar0(sdtasdt0(xE,xE))
| ~ aScalar0(sdtasdt0(xH,xH))
| ~ aScalar0(sdtasdt0(xC,xD))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(xE,xE))
| ~ sdtlseqdt0(sdtasdt0(xH,xH),sdtasdt0(xH,xH))
| sdtlseqdt0(sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)),sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xC,xD)))
| ~ sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)) ) ),
inference(monotonicity,[status(thm)],[154]) ).
tff(156,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( sdtlseqdt0(sdtasdt0(W0,W2),sdtasdt0(W1,W3))
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(sz0z00,W2) )
| sdtlseqdt0(sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)),sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xC,xD)))
| ~ aScalar0(sdtasdt0(xC,xD))
| ~ aScalar0(sdtasdt0(xE,xE))
| ~ aScalar0(sdtasdt0(xH,xH))
| ~ aScalar0(sdtasdt0(xH,xH))
| ~ sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD))
| ~ sdtlseqdt0(sdtasdt0(xH,xH),sdtasdt0(xH,xH))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(xE,xE)) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( sdtlseqdt0(sdtasdt0(W0,W2),sdtasdt0(W1,W3))
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(sz0z00,W2) )
| ~ aScalar0(sdtasdt0(xE,xE))
| ~ aScalar0(sdtasdt0(xH,xH))
| ~ aScalar0(sdtasdt0(xC,xD))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(xE,xE))
| ~ sdtlseqdt0(sdtasdt0(xH,xH),sdtasdt0(xH,xH))
| sdtlseqdt0(sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)),sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xC,xD)))
| ~ sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)) ) ),
inference(transitivity,[status(thm)],[155,153]) ).
tff(157,plain,
( ~ ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( sdtlseqdt0(sdtasdt0(W0,W2),sdtasdt0(W1,W3))
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(sz0z00,W2) )
| sdtlseqdt0(sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)),sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xC,xD)))
| ~ aScalar0(sdtasdt0(xC,xD))
| ~ aScalar0(sdtasdt0(xE,xE))
| ~ aScalar0(sdtasdt0(xH,xH))
| ~ aScalar0(sdtasdt0(xH,xH))
| ~ sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD))
| ~ sdtlseqdt0(sdtasdt0(xH,xH),sdtasdt0(xH,xH))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(xE,xE)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(158,plain,
( ~ ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( sdtlseqdt0(sdtasdt0(W0,W2),sdtasdt0(W1,W3))
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(sz0z00,W2) )
| ~ aScalar0(sdtasdt0(xE,xE))
| ~ aScalar0(sdtasdt0(xH,xH))
| ~ aScalar0(sdtasdt0(xC,xD))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(xE,xE))
| ~ sdtlseqdt0(sdtasdt0(xH,xH),sdtasdt0(xH,xH))
| sdtlseqdt0(sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)),sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xC,xD)))
| ~ sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)) ),
inference(modus_ponens,[status(thm)],[157,156]) ).
tff(159,plain,
( ~ aScalar0(sdtasdt0(xE,xE))
| ~ aScalar0(sdtasdt0(xH,xH))
| ~ aScalar0(sdtasdt0(xC,xD))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(xE,xE))
| ~ sdtlseqdt0(sdtasdt0(xH,xH),sdtasdt0(xH,xH))
| sdtlseqdt0(sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)),sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xC,xD))) ),
inference(unit_resolution,[status(thm)],[158,152,139]) ).
tff(160,plain,
$false,
inference(unit_resolution,[status(thm)],[159,136,50,126,93,64,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : RNG057+2 : TPTP v9.0.0. Released v4.0.0.
% 0.12/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n016.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 03:16:47 EDT 2025
% 0.13/0.35 % CPUTime :
% 1.46/1.68 % SZS status Theorem
% 1.46/1.68 % SZS output start Proof
% See solution above
% 1.54/1.71 % E exiting
%------------------------------------------------------------------------------