%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : RNG065+2 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 05:24:03 AM UTC 2025
% Result : Theorem 2.37s 2.57s
% Output : Proof 2.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 62
% Syntax : Number of formulae : 187 ( 61 unt; 0 typ; 0 def)
% Number of atoms : 1371 ( 28 equ)
% Maximal formula atoms : 25 ( 7 avg)
% Number of connectives : 1887 ( 801 ~; 723 |; 206 &)
% ( 129 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 98 ( 98 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 : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 339 ( 306 !; 0 ?; 339 :)
% Comments :
%------------------------------------------------------------------------------
tff(sdtlseqdt0_type,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(sdtpldt0_type,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(xN_type,type,
xN: $i ).
tff(sdtasdt0_type,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(xP_type,type,
xP: $i ).
tff(xS_type,type,
xS: $i ).
tff(xR_type,type,
xR: $i ).
tff(aScalar0_type,type,
aScalar0: $i > $o ).
tff(xH_type,type,
xH: $i ).
tff(xE_type,type,
xE: $i ).
tff(xD_type,type,
xD: $i ).
tff(xF_type,type,
xF: $i ).
tff(xG_type,type,
xG: $i ).
tff(xC_type,type,
xC: $i ).
tff(1,plain,
( ( xN = sdtasdt0(xR,xS) )
<=> ( xN = sdtasdt0(xR,xS) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
( aScalar0(xN)
& ( xN = sdtasdt0(xR,xS) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1949) ).
tff(3,plain,
xN = sdtasdt0(xR,xS),
inference(and_elim,[status(thm)],[2]) ).
tff(4,plain,
xN = sdtasdt0(xR,xS),
inference(modus_ponens,[status(thm)],[3,1]) ).
tff(5,plain,
sdtasdt0(xR,xS) = xN,
inference(symmetry,[status(thm)],[4]) ).
tff(6,plain,
sdtpldt0(sdtasdt0(xR,xS),sdtasdt0(xR,xS)) = sdtpldt0(xN,xN),
inference(monotonicity,[status(thm)],[5,5]) ).
tff(7,plain,
( sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xR,xS),sdtasdt0(xR,xS)))
<=> sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(xN,xN)) ),
inference(monotonicity,[status(thm)],[6]) ).
tff(8,plain,
( aScalar0(sdtasdt0(xR,xS))
<=> aScalar0(xN) ),
inference(monotonicity,[status(thm)],[5]) ).
tff(9,plain,
( aScalar0(xN)
<=> aScalar0(sdtasdt0(xR,xS)) ),
inference(symmetry,[status(thm)],[8]) ).
tff(10,plain,
( aScalar0(xN)
<=> aScalar0(xN) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,plain,
aScalar0(xN),
inference(and_elim,[status(thm)],[2]) ).
tff(12,plain,
aScalar0(xN),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
aScalar0(sdtasdt0(xR,xS)),
inference(modus_ponens,[status(thm)],[12,9]) ).
tff(14,plain,
( sdtlseqdt0(sdtasdt0(xP,xP),sdtasdt0(xR,xS))
<=> sdtlseqdt0(sdtasdt0(xP,xP),xN) ),
inference(monotonicity,[status(thm)],[5]) ).
tff(15,plain,
( sdtlseqdt0(sdtasdt0(xP,xP),xN)
<=> sdtlseqdt0(sdtasdt0(xP,xP),sdtasdt0(xR,xS)) ),
inference(symmetry,[status(thm)],[14]) ).
tff(16,plain,
( sdtlseqdt0(sdtasdt0(xP,xP),xN)
<=> sdtlseqdt0(sdtasdt0(xP,xP),xN) ),
inference(rewrite,[status(thm)],[]) ).
tff(17,axiom,
sdtlseqdt0(sdtasdt0(xP,xP),xN),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2004) ).
tff(18,plain,
sdtlseqdt0(sdtasdt0(xP,xP),xN),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
sdtlseqdt0(sdtasdt0(xP,xP),sdtasdt0(xR,xS)),
inference(modus_ponens,[status(thm)],[18,15]) ).
tff(20,plain,
( ( xP = sdtasdt0(xE,xH) )
<=> ( xP = sdtasdt0(xE,xH) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,axiom,
( aScalar0(xP)
& ( xP = sdtasdt0(xE,xH) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1911) ).
tff(22,plain,
xP = sdtasdt0(xE,xH),
inference(and_elim,[status(thm)],[21]) ).
tff(23,plain,
xP = sdtasdt0(xE,xH),
inference(modus_ponens,[status(thm)],[22,20]) ).
tff(24,plain,
sdtasdt0(xE,xH) = xP,
inference(symmetry,[status(thm)],[23]) ).
tff(25,plain,
sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)) = sdtasdt0(xP,xP),
inference(monotonicity,[status(thm)],[24,24]) ).
tff(26,plain,
( aScalar0(sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)))
<=> aScalar0(sdtasdt0(xP,xP)) ),
inference(monotonicity,[status(thm)],[25]) ).
tff(27,plain,
( aScalar0(sdtasdt0(xE,xH))
<=> aScalar0(xP) ),
inference(monotonicity,[status(thm)],[24]) ).
tff(28,plain,
( aScalar0(xP)
<=> aScalar0(sdtasdt0(xE,xH)) ),
inference(symmetry,[status(thm)],[27]) ).
tff(29,plain,
( aScalar0(xP)
<=> aScalar0(xP) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,plain,
aScalar0(xP),
inference(and_elim,[status(thm)],[21]) ).
tff(31,plain,
aScalar0(xP),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
aScalar0(sdtasdt0(xE,xH)),
inference(modus_ponens,[status(thm)],[31,28]) ).
tff(33,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(34,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)],[33]) ).
tff(35,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(36,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)],[35]) ).
tff(37,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(38,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(39,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)],[38]) ).
tff(40,axiom,
! [W0: $i,W1: $i] :
( ( aScalar0(W0)
& aScalar0(W1) )
=> aScalar0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulSc) ).
tff(41,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) ),
inference(modus_ponens,[status(thm)],[41,37]) ).
tff(43,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) ),
inference(skolemize,[status(sab)],[42]) ).
tff(44,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ),
inference(modus_ponens,[status(thm)],[43,36]) ).
tff(45,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ),
inference(modus_ponens,[status(thm)],[44,34]) ).
tff(46,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(xE,xH))
| aScalar0(sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH))) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(xE,xH))
| aScalar0(sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,plain,
( ( aScalar0(sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)))
| ~ aScalar0(sdtasdt0(xE,xH))
| ~ aScalar0(sdtasdt0(xE,xH)) )
<=> ( ~ aScalar0(sdtasdt0(xE,xH))
| aScalar0(sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(48,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)))
| ~ aScalar0(sdtasdt0(xE,xH))
| ~ aScalar0(sdtasdt0(xE,xH)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(xE,xH))
| aScalar0(sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH))) ) ),
inference(monotonicity,[status(thm)],[47]) ).
tff(49,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)))
| ~ aScalar0(sdtasdt0(xE,xH))
| ~ aScalar0(sdtasdt0(xE,xH)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(xE,xH))
| aScalar0(sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH))) ) ),
inference(transitivity,[status(thm)],[48,46]) ).
tff(50,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)))
| ~ aScalar0(sdtasdt0(xE,xH))
| ~ aScalar0(sdtasdt0(xE,xH)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(51,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(xE,xH))
| aScalar0(sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH))) ),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
( ~ aScalar0(sdtasdt0(xE,xH))
| aScalar0(sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH))) ),
inference(unit_resolution,[status(thm)],[51,45]) ).
tff(53,plain,
aScalar0(sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH))),
inference(unit_resolution,[status(thm)],[52,32]) ).
tff(54,plain,
aScalar0(sdtasdt0(xP,xP)),
inference(modus_ponens,[status(thm)],[53,26]) ).
tff(55,plain,
^ [W0: $i,W1: $i,W2: $i,W3: $i] :
refl(( ( sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3))
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(W0,W1) )
<=> ( sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3))
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(W0,W1) ) )),
inference(bind,[status(th)],[]) ).
tff(56,plain,
( ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3))
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(W0,W1) )
<=> ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3))
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(W0,W1) ) ),
inference(quant_intro,[status(thm)],[55]) ).
tff(57,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(W2,W3) )
<=> ~ ( ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(W0,W1) ) )),
( ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W2,W3) )
<=> ~ ~ ( ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(W0,W1) ) )),
rewrite(( ~ ~ ( ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(W0,W1) )
<=> ( ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(W0,W1) ) )),
( ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W2,W3) )
<=> ( ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(W0,W1) ) )),
( ( sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3))
| ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W2,W3) ) )
<=> ( sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3))
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(W0,W1) ) )),
rewrite(( ( sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3))
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(W0,W1) )
<=> ( sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3))
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(W0,W1) ) )),
( ( sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3))
| ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W2,W3) ) )
<=> ( sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3))
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(W0,W1) ) )),
inference(bind,[status(th)],[]) ).
tff(58,plain,
( ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3))
| ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W2,W3) ) )
<=> ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3))
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(W0,W1) ) ),
inference(quant_intro,[status(thm)],[57]) ).
tff(59,plain,
( ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3))
| ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W2,W3) ) )
<=> ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3))
| ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W2,W3) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(60,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) ) )),
rewrite(( ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W2,W3) )
=> sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3)) )
<=> ( ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W2,W3) )
| sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3)) ) )),
( ( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
=> ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W2,W3) )
=> sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3)) ) )
<=> ( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
=> ( ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W2,W3) )
| sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3)) ) ) )),
rewrite(( ( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
=> ( ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W2,W3) )
| sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3)) ) )
<=> ( sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3))
| ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W2,W3) ) ) )),
( ( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
=> ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W2,W3) )
=> sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3)) ) )
<=> ( sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3))
| ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W2,W3) ) ) )),
inference(bind,[status(th)],[]) ).
tff(61,plain,
( ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
=> ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W2,W3) )
=> sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3)) ) )
<=> ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3))
| ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W2,W3) ) ) ),
inference(quant_intro,[status(thm)],[60]) ).
tff(62,axiom,
! [W0: $i,W1: $i,W2: $i,W3: $i] :
( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
=> ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W2,W3) )
=> sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLEMon) ).
tff(63,plain,
! [W0: $i,W1: $i,W2: $i,W3: $i] :
( sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3))
| ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W2,W3) ) ),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
! [W0: $i,W1: $i,W2: $i,W3: $i] :
( sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3))
| ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W2,W3) ) ),
inference(modus_ponens,[status(thm)],[63,59]) ).
tff(65,plain,
! [W0: $i,W1: $i,W2: $i,W3: $i] :
( sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3))
| ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W2,W3) ) ),
inference(skolemize,[status(sab)],[64]) ).
tff(66,plain,
! [W0: $i,W1: $i,W2: $i,W3: $i] :
( sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3))
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(W0,W1) ),
inference(modus_ponens,[status(thm)],[65,58]) ).
tff(67,plain,
! [W0: $i,W1: $i,W2: $i,W3: $i] :
( sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3))
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(W0,W1) ),
inference(modus_ponens,[status(thm)],[66,56]) ).
tff(68,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3))
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(W0,W1) )
| ~ aScalar0(sdtasdt0(xR,xS))
| ~ aScalar0(sdtasdt0(xP,xP))
| ~ sdtlseqdt0(sdtasdt0(xP,xP),sdtasdt0(xR,xS))
| sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xR,xS),sdtasdt0(xR,xS))) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3))
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(W0,W1) )
| ~ aScalar0(sdtasdt0(xR,xS))
| ~ aScalar0(sdtasdt0(xP,xP))
| ~ sdtlseqdt0(sdtasdt0(xP,xP),sdtasdt0(xR,xS))
| sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xR,xS),sdtasdt0(xR,xS))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(69,plain,
( ( sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xR,xS),sdtasdt0(xR,xS)))
| ~ aScalar0(sdtasdt0(xR,xS))
| ~ aScalar0(sdtasdt0(xP,xP))
| ~ aScalar0(sdtasdt0(xR,xS))
| ~ aScalar0(sdtasdt0(xP,xP))
| ~ sdtlseqdt0(sdtasdt0(xP,xP),sdtasdt0(xR,xS))
| ~ sdtlseqdt0(sdtasdt0(xP,xP),sdtasdt0(xR,xS)) )
<=> ( ~ aScalar0(sdtasdt0(xR,xS))
| ~ aScalar0(sdtasdt0(xP,xP))
| ~ sdtlseqdt0(sdtasdt0(xP,xP),sdtasdt0(xR,xS))
| sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xR,xS),sdtasdt0(xR,xS))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(70,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3))
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(W0,W1) )
| sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xR,xS),sdtasdt0(xR,xS)))
| ~ aScalar0(sdtasdt0(xR,xS))
| ~ aScalar0(sdtasdt0(xP,xP))
| ~ aScalar0(sdtasdt0(xR,xS))
| ~ aScalar0(sdtasdt0(xP,xP))
| ~ sdtlseqdt0(sdtasdt0(xP,xP),sdtasdt0(xR,xS))
| ~ sdtlseqdt0(sdtasdt0(xP,xP),sdtasdt0(xR,xS)) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3))
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(W0,W1) )
| ~ aScalar0(sdtasdt0(xR,xS))
| ~ aScalar0(sdtasdt0(xP,xP))
| ~ sdtlseqdt0(sdtasdt0(xP,xP),sdtasdt0(xR,xS))
| sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xR,xS),sdtasdt0(xR,xS))) ) ),
inference(monotonicity,[status(thm)],[69]) ).
tff(71,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3))
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(W0,W1) )
| sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xR,xS),sdtasdt0(xR,xS)))
| ~ aScalar0(sdtasdt0(xR,xS))
| ~ aScalar0(sdtasdt0(xP,xP))
| ~ aScalar0(sdtasdt0(xR,xS))
| ~ aScalar0(sdtasdt0(xP,xP))
| ~ sdtlseqdt0(sdtasdt0(xP,xP),sdtasdt0(xR,xS))
| ~ sdtlseqdt0(sdtasdt0(xP,xP),sdtasdt0(xR,xS)) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3))
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(W0,W1) )
| ~ aScalar0(sdtasdt0(xR,xS))
| ~ aScalar0(sdtasdt0(xP,xP))
| ~ sdtlseqdt0(sdtasdt0(xP,xP),sdtasdt0(xR,xS))
| sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xR,xS),sdtasdt0(xR,xS))) ) ),
inference(transitivity,[status(thm)],[70,68]) ).
tff(72,plain,
( ~ ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3))
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(W0,W1) )
| sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xR,xS),sdtasdt0(xR,xS)))
| ~ aScalar0(sdtasdt0(xR,xS))
| ~ aScalar0(sdtasdt0(xP,xP))
| ~ aScalar0(sdtasdt0(xR,xS))
| ~ aScalar0(sdtasdt0(xP,xP))
| ~ sdtlseqdt0(sdtasdt0(xP,xP),sdtasdt0(xR,xS))
| ~ sdtlseqdt0(sdtasdt0(xP,xP),sdtasdt0(xR,xS)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(73,plain,
( ~ ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3))
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(W0,W1) )
| ~ aScalar0(sdtasdt0(xR,xS))
| ~ aScalar0(sdtasdt0(xP,xP))
| ~ sdtlseqdt0(sdtasdt0(xP,xP),sdtasdt0(xR,xS))
| sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xR,xS),sdtasdt0(xR,xS))) ),
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,plain,
( ~ aScalar0(sdtasdt0(xR,xS))
| ~ aScalar0(sdtasdt0(xP,xP))
| ~ sdtlseqdt0(sdtasdt0(xP,xP),sdtasdt0(xR,xS))
| sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xR,xS),sdtasdt0(xR,xS))) ),
inference(unit_resolution,[status(thm)],[73,67]) ).
tff(75,plain,
sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xR,xS),sdtasdt0(xR,xS))),
inference(unit_resolution,[status(thm)],[74,54,19,13]) ).
tff(76,plain,
sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(xN,xN)),
inference(modus_ponens,[status(thm)],[75,7]) ).
tff(77,plain,
( ( xS = sdtasdt0(xF,xD) )
<=> ( xS = sdtasdt0(xF,xD) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(78,axiom,
( aScalar0(xS)
& ( xS = sdtasdt0(xF,xD) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1930) ).
tff(79,plain,
xS = sdtasdt0(xF,xD),
inference(and_elim,[status(thm)],[78]) ).
tff(80,plain,
xS = sdtasdt0(xF,xD),
inference(modus_ponens,[status(thm)],[79,77]) ).
tff(81,plain,
sdtasdt0(xF,xD) = xS,
inference(symmetry,[status(thm)],[80]) ).
tff(82,plain,
sdtasdt0(sdtasdt0(xF,xD),sdtasdt0(xF,xD)) = sdtasdt0(xS,xS),
inference(monotonicity,[status(thm)],[81,81]) ).
tff(83,plain,
( aScalar0(sdtasdt0(sdtasdt0(xF,xD),sdtasdt0(xF,xD)))
<=> aScalar0(sdtasdt0(xS,xS)) ),
inference(monotonicity,[status(thm)],[82]) ).
tff(84,plain,
( aScalar0(sdtasdt0(xF,xD))
<=> aScalar0(xS) ),
inference(monotonicity,[status(thm)],[81]) ).
tff(85,plain,
( aScalar0(xS)
<=> aScalar0(sdtasdt0(xF,xD)) ),
inference(symmetry,[status(thm)],[84]) ).
tff(86,plain,
( aScalar0(xS)
<=> aScalar0(xS) ),
inference(rewrite,[status(thm)],[]) ).
tff(87,plain,
aScalar0(xS),
inference(and_elim,[status(thm)],[78]) ).
tff(88,plain,
aScalar0(xS),
inference(modus_ponens,[status(thm)],[87,86]) ).
tff(89,plain,
aScalar0(sdtasdt0(xF,xD)),
inference(modus_ponens,[status(thm)],[88,85]) ).
tff(90,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(xF,xD))
| aScalar0(sdtasdt0(sdtasdt0(xF,xD),sdtasdt0(xF,xD))) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(xF,xD))
| aScalar0(sdtasdt0(sdtasdt0(xF,xD),sdtasdt0(xF,xD))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(91,plain,
( ( aScalar0(sdtasdt0(sdtasdt0(xF,xD),sdtasdt0(xF,xD)))
| ~ aScalar0(sdtasdt0(xF,xD))
| ~ aScalar0(sdtasdt0(xF,xD)) )
<=> ( ~ aScalar0(sdtasdt0(xF,xD))
| aScalar0(sdtasdt0(sdtasdt0(xF,xD),sdtasdt0(xF,xD))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(92,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtasdt0(sdtasdt0(xF,xD),sdtasdt0(xF,xD)))
| ~ aScalar0(sdtasdt0(xF,xD))
| ~ aScalar0(sdtasdt0(xF,xD)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(xF,xD))
| aScalar0(sdtasdt0(sdtasdt0(xF,xD),sdtasdt0(xF,xD))) ) ),
inference(monotonicity,[status(thm)],[91]) ).
tff(93,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtasdt0(sdtasdt0(xF,xD),sdtasdt0(xF,xD)))
| ~ aScalar0(sdtasdt0(xF,xD))
| ~ aScalar0(sdtasdt0(xF,xD)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(xF,xD))
| aScalar0(sdtasdt0(sdtasdt0(xF,xD),sdtasdt0(xF,xD))) ) ),
inference(transitivity,[status(thm)],[92,90]) ).
tff(94,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtasdt0(sdtasdt0(xF,xD),sdtasdt0(xF,xD)))
| ~ aScalar0(sdtasdt0(xF,xD))
| ~ aScalar0(sdtasdt0(xF,xD)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(95,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(xF,xD))
| aScalar0(sdtasdt0(sdtasdt0(xF,xD),sdtasdt0(xF,xD))) ),
inference(modus_ponens,[status(thm)],[94,93]) ).
tff(96,plain,
( ~ aScalar0(sdtasdt0(xF,xD))
| aScalar0(sdtasdt0(sdtasdt0(xF,xD),sdtasdt0(xF,xD))) ),
inference(unit_resolution,[status(thm)],[95,45]) ).
tff(97,plain,
aScalar0(sdtasdt0(sdtasdt0(xF,xD),sdtasdt0(xF,xD))),
inference(unit_resolution,[status(thm)],[96,89]) ).
tff(98,plain,
aScalar0(sdtasdt0(xS,xS)),
inference(modus_ponens,[status(thm)],[97,83]) ).
tff(99,plain,
( ( xR = sdtasdt0(xC,xG) )
<=> ( xR = sdtasdt0(xC,xG) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(100,axiom,
( aScalar0(xR)
& ( xR = sdtasdt0(xC,xG) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1892) ).
tff(101,plain,
xR = sdtasdt0(xC,xG),
inference(and_elim,[status(thm)],[100]) ).
tff(102,plain,
xR = sdtasdt0(xC,xG),
inference(modus_ponens,[status(thm)],[101,99]) ).
tff(103,plain,
sdtasdt0(xC,xG) = xR,
inference(symmetry,[status(thm)],[102]) ).
tff(104,plain,
sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xC,xG)) = sdtasdt0(xR,xR),
inference(monotonicity,[status(thm)],[103,103]) ).
tff(105,plain,
( aScalar0(sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xC,xG)))
<=> aScalar0(sdtasdt0(xR,xR)) ),
inference(monotonicity,[status(thm)],[104]) ).
tff(106,plain,
( aScalar0(sdtasdt0(xC,xG))
<=> aScalar0(xR) ),
inference(monotonicity,[status(thm)],[103]) ).
tff(107,plain,
( aScalar0(xR)
<=> aScalar0(sdtasdt0(xC,xG)) ),
inference(symmetry,[status(thm)],[106]) ).
tff(108,plain,
( aScalar0(xR)
<=> aScalar0(xR) ),
inference(rewrite,[status(thm)],[]) ).
tff(109,plain,
aScalar0(xR),
inference(and_elim,[status(thm)],[100]) ).
tff(110,plain,
aScalar0(xR),
inference(modus_ponens,[status(thm)],[109,108]) ).
tff(111,plain,
aScalar0(sdtasdt0(xC,xG)),
inference(modus_ponens,[status(thm)],[110,107]) ).
tff(112,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(xC,xG))
| aScalar0(sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xC,xG))) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(xC,xG))
| aScalar0(sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xC,xG))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(113,plain,
( ( aScalar0(sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xC,xG)))
| ~ aScalar0(sdtasdt0(xC,xG))
| ~ aScalar0(sdtasdt0(xC,xG)) )
<=> ( ~ aScalar0(sdtasdt0(xC,xG))
| aScalar0(sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xC,xG))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(114,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xC,xG)))
| ~ aScalar0(sdtasdt0(xC,xG))
| ~ aScalar0(sdtasdt0(xC,xG)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(xC,xG))
| aScalar0(sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xC,xG))) ) ),
inference(monotonicity,[status(thm)],[113]) ).
tff(115,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xC,xG)))
| ~ aScalar0(sdtasdt0(xC,xG))
| ~ aScalar0(sdtasdt0(xC,xG)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(xC,xG))
| aScalar0(sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xC,xG))) ) ),
inference(transitivity,[status(thm)],[114,112]) ).
tff(116,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xC,xG)))
| ~ aScalar0(sdtasdt0(xC,xG))
| ~ aScalar0(sdtasdt0(xC,xG)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(117,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(xC,xG))
| aScalar0(sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xC,xG))) ),
inference(modus_ponens,[status(thm)],[116,115]) ).
tff(118,plain,
( ~ aScalar0(sdtasdt0(xC,xG))
| aScalar0(sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xC,xG))) ),
inference(unit_resolution,[status(thm)],[117,45]) ).
tff(119,plain,
aScalar0(sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xC,xG))),
inference(unit_resolution,[status(thm)],[118,111]) ).
tff(120,plain,
aScalar0(sdtasdt0(xR,xR)),
inference(modus_ponens,[status(thm)],[119,105]) ).
tff(121,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(122,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)],[121]) ).
tff(123,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(124,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)],[123]) ).
tff(125,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(126,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(127,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)],[126]) ).
tff(128,axiom,
! [W0: $i,W1: $i] :
( ( aScalar0(W0)
& aScalar0(W1) )
=> aScalar0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSumSc) ).
tff(129,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) ),
inference(modus_ponens,[status(thm)],[128,127]) ).
tff(130,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) ),
inference(modus_ponens,[status(thm)],[129,125]) ).
tff(131,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) ),
inference(skolemize,[status(sab)],[130]) ).
tff(132,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ),
inference(modus_ponens,[status(thm)],[131,124]) ).
tff(133,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ),
inference(modus_ponens,[status(thm)],[132,122]) ).
tff(134,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(xS,xS))
| ~ aScalar0(sdtasdt0(xR,xR))
| aScalar0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS))) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(xS,xS))
| ~ aScalar0(sdtasdt0(xR,xR))
| aScalar0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(135,plain,
( ( aScalar0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)))
| ~ aScalar0(sdtasdt0(xS,xS))
| ~ aScalar0(sdtasdt0(xR,xR)) )
<=> ( ~ aScalar0(sdtasdt0(xS,xS))
| ~ aScalar0(sdtasdt0(xR,xR))
| aScalar0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(136,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)))
| ~ aScalar0(sdtasdt0(xS,xS))
| ~ aScalar0(sdtasdt0(xR,xR)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(xS,xS))
| ~ aScalar0(sdtasdt0(xR,xR))
| aScalar0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS))) ) ),
inference(monotonicity,[status(thm)],[135]) ).
tff(137,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)))
| ~ aScalar0(sdtasdt0(xS,xS))
| ~ aScalar0(sdtasdt0(xR,xR)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(xS,xS))
| ~ aScalar0(sdtasdt0(xR,xR))
| aScalar0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS))) ) ),
inference(transitivity,[status(thm)],[136,134]) ).
tff(138,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)))
| ~ aScalar0(sdtasdt0(xS,xS))
| ~ aScalar0(sdtasdt0(xR,xR)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(139,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(xS,xS))
| ~ aScalar0(sdtasdt0(xR,xR))
| aScalar0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS))) ),
inference(modus_ponens,[status(thm)],[138,137]) ).
tff(140,plain,
( ~ aScalar0(sdtasdt0(xS,xS))
| ~ aScalar0(sdtasdt0(xR,xR))
| aScalar0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS))) ),
inference(unit_resolution,[status(thm)],[139,133]) ).
tff(141,plain,
aScalar0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS))),
inference(unit_resolution,[status(thm)],[140,120,98]) ).
tff(142,plain,
( aScalar0(sdtpldt0(sdtasdt0(xR,xS),sdtasdt0(xR,xS)))
<=> aScalar0(sdtpldt0(xN,xN)) ),
inference(monotonicity,[status(thm)],[6]) ).
tff(143,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(xR,xS))
| aScalar0(sdtpldt0(sdtasdt0(xR,xS),sdtasdt0(xR,xS))) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(xR,xS))
| aScalar0(sdtpldt0(sdtasdt0(xR,xS),sdtasdt0(xR,xS))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(144,plain,
( ( aScalar0(sdtpldt0(sdtasdt0(xR,xS),sdtasdt0(xR,xS)))
| ~ aScalar0(sdtasdt0(xR,xS))
| ~ aScalar0(sdtasdt0(xR,xS)) )
<=> ( ~ aScalar0(sdtasdt0(xR,xS))
| aScalar0(sdtpldt0(sdtasdt0(xR,xS),sdtasdt0(xR,xS))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(145,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtpldt0(sdtasdt0(xR,xS),sdtasdt0(xR,xS)))
| ~ aScalar0(sdtasdt0(xR,xS))
| ~ aScalar0(sdtasdt0(xR,xS)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(xR,xS))
| aScalar0(sdtpldt0(sdtasdt0(xR,xS),sdtasdt0(xR,xS))) ) ),
inference(monotonicity,[status(thm)],[144]) ).
tff(146,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtpldt0(sdtasdt0(xR,xS),sdtasdt0(xR,xS)))
| ~ aScalar0(sdtasdt0(xR,xS))
| ~ aScalar0(sdtasdt0(xR,xS)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(xR,xS))
| aScalar0(sdtpldt0(sdtasdt0(xR,xS),sdtasdt0(xR,xS))) ) ),
inference(transitivity,[status(thm)],[145,143]) ).
tff(147,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtpldt0(sdtasdt0(xR,xS),sdtasdt0(xR,xS)))
| ~ aScalar0(sdtasdt0(xR,xS))
| ~ aScalar0(sdtasdt0(xR,xS)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(148,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(xR,xS))
| aScalar0(sdtpldt0(sdtasdt0(xR,xS),sdtasdt0(xR,xS))) ),
inference(modus_ponens,[status(thm)],[147,146]) ).
tff(149,plain,
( ~ aScalar0(sdtasdt0(xR,xS))
| aScalar0(sdtpldt0(sdtasdt0(xR,xS),sdtasdt0(xR,xS))) ),
inference(unit_resolution,[status(thm)],[148,133]) ).
tff(150,plain,
aScalar0(sdtpldt0(sdtasdt0(xR,xS),sdtasdt0(xR,xS))),
inference(unit_resolution,[status(thm)],[149,13]) ).
tff(151,plain,
aScalar0(sdtpldt0(xN,xN)),
inference(modus_ponens,[status(thm)],[150,142]) ).
tff(152,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(xP,xP))
| aScalar0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP))) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(xP,xP))
| aScalar0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(153,plain,
( ( aScalar0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)))
| ~ aScalar0(sdtasdt0(xP,xP))
| ~ aScalar0(sdtasdt0(xP,xP)) )
<=> ( ~ aScalar0(sdtasdt0(xP,xP))
| aScalar0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(154,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)))
| ~ aScalar0(sdtasdt0(xP,xP))
| ~ aScalar0(sdtasdt0(xP,xP)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(xP,xP))
| aScalar0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP))) ) ),
inference(monotonicity,[status(thm)],[153]) ).
tff(155,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)))
| ~ aScalar0(sdtasdt0(xP,xP))
| ~ aScalar0(sdtasdt0(xP,xP)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(xP,xP))
| aScalar0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP))) ) ),
inference(transitivity,[status(thm)],[154,152]) ).
tff(156,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)))
| ~ aScalar0(sdtasdt0(xP,xP))
| ~ aScalar0(sdtasdt0(xP,xP)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(157,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(xP,xP))
| aScalar0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP))) ),
inference(modus_ponens,[status(thm)],[156,155]) ).
tff(158,plain,
( ~ aScalar0(sdtasdt0(xP,xP))
| aScalar0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP))) ),
inference(unit_resolution,[status(thm)],[157,133]) ).
tff(159,plain,
aScalar0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP))),
inference(unit_resolution,[status(thm)],[158,54]) ).
tff(160,plain,
( ~ sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)))
<=> ~ sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS))) ),
inference(rewrite,[status(thm)],[]) ).
tff(161,axiom,
~ sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(162,plain,
~ sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS))),
inference(modus_ponens,[status(thm)],[161,160]) ).
tff(163,plain,
( sdtlseqdt0(sdtpldt0(xN,xN),sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)))
<=> sdtlseqdt0(sdtpldt0(xN,xN),sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS))) ),
inference(rewrite,[status(thm)],[]) ).
tff(164,axiom,
sdtlseqdt0(sdtpldt0(xN,xN),sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2348) ).
tff(165,plain,
sdtlseqdt0(sdtpldt0(xN,xN),sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS))),
inference(modus_ponens,[status(thm)],[164,163]) ).
tff(166,plain,
^ [W0: $i,W1: $i,W2: $i] :
refl(( ( sdtlseqdt0(W0,W2)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W1,W2)
| ~ sdtlseqdt0(W0,W1) )
<=> ( sdtlseqdt0(W0,W2)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W1,W2)
| ~ sdtlseqdt0(W0,W1) ) )),
inference(bind,[status(th)],[]) ).
tff(167,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( sdtlseqdt0(W0,W2)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W1,W2)
| ~ sdtlseqdt0(W0,W1) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( sdtlseqdt0(W0,W2)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W1,W2)
| ~ sdtlseqdt0(W0,W1) ) ),
inference(quant_intro,[status(thm)],[166]) ).
tff(168,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) ) )),
trans(monotonicity(rewrite(( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W2) )
<=> ~ ( ~ sdtlseqdt0(W1,W2)
| ~ sdtlseqdt0(W0,W1) ) )),
( ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W2) )
<=> ~ ~ ( ~ sdtlseqdt0(W1,W2)
| ~ sdtlseqdt0(W0,W1) ) )),
rewrite(( ~ ~ ( ~ sdtlseqdt0(W1,W2)
| ~ sdtlseqdt0(W0,W1) )
<=> ( ~ sdtlseqdt0(W1,W2)
| ~ sdtlseqdt0(W0,W1) ) )),
( ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W2) )
<=> ( ~ sdtlseqdt0(W1,W2)
| ~ sdtlseqdt0(W0,W1) ) )),
( ( sdtlseqdt0(W0,W2)
| ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W2) ) )
<=> ( sdtlseqdt0(W0,W2)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W1,W2)
| ~ sdtlseqdt0(W0,W1) ) )),
rewrite(( ( sdtlseqdt0(W0,W2)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W1,W2)
| ~ sdtlseqdt0(W0,W1) )
<=> ( sdtlseqdt0(W0,W2)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W1,W2)
| ~ sdtlseqdt0(W0,W1) ) )),
( ( sdtlseqdt0(W0,W2)
| ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W2) ) )
<=> ( sdtlseqdt0(W0,W2)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W1,W2)
| ~ sdtlseqdt0(W0,W1) ) )),
inference(bind,[status(th)],[]) ).
tff(169,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( sdtlseqdt0(W0,W2)
| ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W2) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( sdtlseqdt0(W0,W2)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W1,W2)
| ~ sdtlseqdt0(W0,W1) ) ),
inference(quant_intro,[status(thm)],[168]) ).
tff(170,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( sdtlseqdt0(W0,W2)
| ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W2) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( sdtlseqdt0(W0,W2)
| ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W2) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(171,plain,
^ [W0: $i,W1: $i,W2: $i] :
trans(monotonicity(rewrite(( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
<=> ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) ) )),
rewrite(( ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W2) )
=> sdtlseqdt0(W0,W2) )
<=> ( ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W2) )
| sdtlseqdt0(W0,W2) ) )),
( ( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
=> ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W2) )
=> sdtlseqdt0(W0,W2) ) )
<=> ( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
=> ( ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W2) )
| sdtlseqdt0(W0,W2) ) ) )),
rewrite(( ( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
=> ( ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W2) )
| sdtlseqdt0(W0,W2) ) )
<=> ( sdtlseqdt0(W0,W2)
| ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W2) ) ) )),
( ( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
=> ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W2) )
=> sdtlseqdt0(W0,W2) ) )
<=> ( sdtlseqdt0(W0,W2)
| ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W2) ) ) )),
inference(bind,[status(th)],[]) ).
tff(172,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
=> ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W2) )
=> sdtlseqdt0(W0,W2) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( sdtlseqdt0(W0,W2)
| ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W2) ) ) ),
inference(quant_intro,[status(thm)],[171]) ).
tff(173,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
=> ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W2) )
=> sdtlseqdt0(W0,W2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETrn) ).
tff(174,plain,
! [W0: $i,W1: $i,W2: $i] :
( sdtlseqdt0(W0,W2)
| ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W2) ) ),
inference(modus_ponens,[status(thm)],[173,172]) ).
tff(175,plain,
! [W0: $i,W1: $i,W2: $i] :
( sdtlseqdt0(W0,W2)
| ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W2) ) ),
inference(modus_ponens,[status(thm)],[174,170]) ).
tff(176,plain,
! [W0: $i,W1: $i,W2: $i] :
( sdtlseqdt0(W0,W2)
| ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W2) ) ),
inference(skolemize,[status(sab)],[175]) ).
tff(177,plain,
! [W0: $i,W1: $i,W2: $i] :
( sdtlseqdt0(W0,W2)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W1,W2)
| ~ sdtlseqdt0(W0,W1) ),
inference(modus_ponens,[status(thm)],[176,169]) ).
tff(178,plain,
! [W0: $i,W1: $i,W2: $i] :
( sdtlseqdt0(W0,W2)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W1,W2)
| ~ sdtlseqdt0(W0,W1) ),
inference(modus_ponens,[status(thm)],[177,167]) ).
tff(179,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( sdtlseqdt0(W0,W2)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W1,W2)
| ~ sdtlseqdt0(W0,W1) )
| sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)))
| ~ aScalar0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)))
| ~ aScalar0(sdtpldt0(xN,xN))
| ~ sdtlseqdt0(sdtpldt0(xN,xN),sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)))
| ~ aScalar0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)))
| ~ sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(xN,xN)) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( sdtlseqdt0(W0,W2)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W1,W2)
| ~ sdtlseqdt0(W0,W1) )
| sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)))
| ~ aScalar0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)))
| ~ aScalar0(sdtpldt0(xN,xN))
| ~ sdtlseqdt0(sdtpldt0(xN,xN),sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)))
| ~ aScalar0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)))
| ~ sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(xN,xN)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(180,plain,
( ( sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)))
| ~ aScalar0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)))
| ~ aScalar0(sdtpldt0(xN,xN))
| ~ aScalar0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)))
| ~ sdtlseqdt0(sdtpldt0(xN,xN),sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)))
| ~ sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(xN,xN)) )
<=> ( sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)))
| ~ aScalar0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)))
| ~ aScalar0(sdtpldt0(xN,xN))
| ~ sdtlseqdt0(sdtpldt0(xN,xN),sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)))
| ~ aScalar0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)))
| ~ sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(xN,xN)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(181,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( sdtlseqdt0(W0,W2)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W1,W2)
| ~ sdtlseqdt0(W0,W1) )
| sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)))
| ~ aScalar0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)))
| ~ aScalar0(sdtpldt0(xN,xN))
| ~ aScalar0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)))
| ~ sdtlseqdt0(sdtpldt0(xN,xN),sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)))
| ~ sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(xN,xN)) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( sdtlseqdt0(W0,W2)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W1,W2)
| ~ sdtlseqdt0(W0,W1) )
| sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)))
| ~ aScalar0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)))
| ~ aScalar0(sdtpldt0(xN,xN))
| ~ sdtlseqdt0(sdtpldt0(xN,xN),sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)))
| ~ aScalar0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)))
| ~ sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(xN,xN)) ) ),
inference(monotonicity,[status(thm)],[180]) ).
tff(182,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( sdtlseqdt0(W0,W2)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W1,W2)
| ~ sdtlseqdt0(W0,W1) )
| sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)))
| ~ aScalar0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)))
| ~ aScalar0(sdtpldt0(xN,xN))
| ~ aScalar0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)))
| ~ sdtlseqdt0(sdtpldt0(xN,xN),sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)))
| ~ sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(xN,xN)) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( sdtlseqdt0(W0,W2)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W1,W2)
| ~ sdtlseqdt0(W0,W1) )
| sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)))
| ~ aScalar0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)))
| ~ aScalar0(sdtpldt0(xN,xN))
| ~ sdtlseqdt0(sdtpldt0(xN,xN),sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)))
| ~ aScalar0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)))
| ~ sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(xN,xN)) ) ),
inference(transitivity,[status(thm)],[181,179]) ).
tff(183,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( sdtlseqdt0(W0,W2)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W1,W2)
| ~ sdtlseqdt0(W0,W1) )
| sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)))
| ~ aScalar0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)))
| ~ aScalar0(sdtpldt0(xN,xN))
| ~ aScalar0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)))
| ~ sdtlseqdt0(sdtpldt0(xN,xN),sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)))
| ~ sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(xN,xN)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(184,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( sdtlseqdt0(W0,W2)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W1,W2)
| ~ sdtlseqdt0(W0,W1) )
| sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)))
| ~ aScalar0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)))
| ~ aScalar0(sdtpldt0(xN,xN))
| ~ sdtlseqdt0(sdtpldt0(xN,xN),sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)))
| ~ aScalar0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)))
| ~ sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(xN,xN)) ),
inference(modus_ponens,[status(thm)],[183,182]) ).
tff(185,plain,
( ~ aScalar0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)))
| ~ aScalar0(sdtpldt0(xN,xN))
| ~ aScalar0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)))
| ~ sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(xN,xN)) ),
inference(unit_resolution,[status(thm)],[184,178,165,162]) ).
tff(186,plain,
~ sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(xN,xN)),
inference(unit_resolution,[status(thm)],[185,159,151,141]) ).
tff(187,plain,
$false,
inference(unit_resolution,[status(thm)],[186,76]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.12 % Problem : RNG065+2 : TPTP v9.0.0. Released v4.0.0.
% 0.02/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 03:17:38 EDT 2025
% 0.12/0.33 % CPUTime :
% 2.37/2.57 % SZS status Theorem
% 2.37/2.57 % SZS output start Proof
% See solution above
% 2.44/2.60 % E exiting
%------------------------------------------------------------------------------