%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : RNG076+2 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:24:06 AM UTC 2025
% Result : Theorem 2.06s 2.25s
% Output : Proof 2.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 73
% Syntax : Number of formulae : 220 ( 79 unt; 0 typ; 0 def)
% Number of atoms : 1270 ( 47 equ)
% Maximal formula atoms : 28 ( 5 avg)
% Number of connectives : 1730 ( 749 ~; 696 |; 143 &)
% ( 122 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 69 ( 69 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 : 16 ( 16 usr; 13 con; 0-2 aty)
% Number of variables : 313 ( 287 !; 0 ?; 313 :)
% Comments :
%------------------------------------------------------------------------------
tff(sdtlseqdt0_type,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(sdtpldt0_type,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(sdtasdt0_type,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(xH_type,type,
xH: $i ).
tff(xS_type,type,
xS: $i ).
tff(xR_type,type,
xR: $i ).
tff(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(xD_type,type,
xD: $i ).
tff(xF_type,type,
xF: $i ).
tff(xG_type,type,
xG: $i ).
tff(xC_type,type,
xC: $i ).
tff(xE_type,type,
xE: $i ).
tff(sdtasasdt0_type,type,
sdtasasdt0: ( $i * $i ) > $i ).
tff(xq_type,type,
xq: $i ).
tff(xp_type,type,
xp: $i ).
tff(1,plain,
( ( xH = sdtasdt0(xA,xB) )
<=> ( xH = sdtasdt0(xA,xB) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
( aScalar0(xH)
& ( xH = sdtasdt0(xA,xB) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1873) ).
tff(3,plain,
xH = sdtasdt0(xA,xB),
inference(and_elim,[status(thm)],[2]) ).
tff(4,plain,
xH = sdtasdt0(xA,xB),
inference(modus_ponens,[status(thm)],[3,1]) ).
tff(5,plain,
sdtasdt0(xA,xB) = xH,
inference(symmetry,[status(thm)],[4]) ).
tff(6,plain,
sdtasdt0(sdtasdt0(xA,xB),sdtasdt0(xA,xB)) = sdtasdt0(xH,xH),
inference(monotonicity,[status(thm)],[5,5]) ).
tff(7,plain,
( aScalar0(sdtasdt0(sdtasdt0(xA,xB),sdtasdt0(xA,xB)))
<=> aScalar0(sdtasdt0(xH,xH)) ),
inference(monotonicity,[status(thm)],[6]) ).
tff(8,plain,
( aScalar0(sdtasdt0(xA,xB))
<=> aScalar0(xH) ),
inference(monotonicity,[status(thm)],[5]) ).
tff(9,plain,
( aScalar0(xH)
<=> aScalar0(sdtasdt0(xA,xB)) ),
inference(symmetry,[status(thm)],[8]) ).
tff(10,plain,
( aScalar0(xH)
<=> aScalar0(xH) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,plain,
aScalar0(xH),
inference(and_elim,[status(thm)],[2]) ).
tff(12,plain,
aScalar0(xH),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
aScalar0(sdtasdt0(xA,xB)),
inference(modus_ponens,[status(thm)],[12,9]) ).
tff(14,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(15,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)],[14]) ).
tff(16,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(17,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)],[16]) ).
tff(18,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(19,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(20,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)],[19]) ).
tff(21,axiom,
! [W0: $i,W1: $i] :
( ( aScalar0(W0)
& aScalar0(W1) )
=> aScalar0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulSc) ).
tff(22,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) ),
inference(modus_ponens,[status(thm)],[22,18]) ).
tff(24,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) ),
inference(skolemize,[status(sab)],[23]) ).
tff(25,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ),
inference(modus_ponens,[status(thm)],[24,17]) ).
tff(26,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ),
inference(modus_ponens,[status(thm)],[25,15]) ).
tff(27,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(28,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(29,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)],[28]) ).
tff(30,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)],[29,27]) ).
tff(31,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(32,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)],[31,30]) ).
tff(33,plain,
( ~ aScalar0(sdtasdt0(xA,xB))
| aScalar0(sdtasdt0(sdtasdt0(xA,xB),sdtasdt0(xA,xB))) ),
inference(unit_resolution,[status(thm)],[32,26]) ).
tff(34,plain,
aScalar0(sdtasdt0(sdtasdt0(xA,xB),sdtasdt0(xA,xB))),
inference(unit_resolution,[status(thm)],[33,13]) ).
tff(35,plain,
aScalar0(sdtasdt0(xH,xH)),
inference(modus_ponens,[status(thm)],[34,7]) ).
tff(36,plain,
^ [W0: $i] :
refl(( ( ~ aScalar0(W0)
| sdtlseqdt0(W0,W0) )
<=> ( ~ aScalar0(W0)
| sdtlseqdt0(W0,W0) ) )),
inference(bind,[status(th)],[]) ).
tff(37,plain,
( ! [W0: $i] :
( ~ aScalar0(W0)
| sdtlseqdt0(W0,W0) )
<=> ! [W0: $i] :
( ~ aScalar0(W0)
| sdtlseqdt0(W0,W0) ) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,plain,
( ! [W0: $i] :
( ~ aScalar0(W0)
| sdtlseqdt0(W0,W0) )
<=> ! [W0: $i] :
( ~ aScalar0(W0)
| sdtlseqdt0(W0,W0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,plain,
^ [W0: $i] :
rewrite(( ( aScalar0(W0)
=> sdtlseqdt0(W0,W0) )
<=> ( ~ aScalar0(W0)
| sdtlseqdt0(W0,W0) ) )),
inference(bind,[status(th)],[]) ).
tff(40,plain,
( ! [W0: $i] :
( aScalar0(W0)
=> sdtlseqdt0(W0,W0) )
<=> ! [W0: $i] :
( ~ aScalar0(W0)
| sdtlseqdt0(W0,W0) ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,axiom,
! [W0: $i] :
( aScalar0(W0)
=> sdtlseqdt0(W0,W0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLERef) ).
tff(42,plain,
! [W0: $i] :
( ~ aScalar0(W0)
| sdtlseqdt0(W0,W0) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
! [W0: $i] :
( ~ aScalar0(W0)
| sdtlseqdt0(W0,W0) ),
inference(modus_ponens,[status(thm)],[42,38]) ).
tff(44,plain,
! [W0: $i] :
( ~ aScalar0(W0)
| sdtlseqdt0(W0,W0) ),
inference(skolemize,[status(sab)],[43]) ).
tff(45,plain,
! [W0: $i] :
( ~ aScalar0(W0)
| sdtlseqdt0(W0,W0) ),
inference(modus_ponens,[status(thm)],[44,37]) ).
tff(46,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(47,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(48,plain,
( ~ ! [W0: $i] :
( ~ aScalar0(W0)
| sdtlseqdt0(W0,W0) )
| ~ aScalar0(sdtasdt0(xH,xH))
| sdtlseqdt0(sdtasdt0(xH,xH),sdtasdt0(xH,xH)) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
sdtlseqdt0(sdtasdt0(xH,xH),sdtasdt0(xH,xH)),
inference(unit_resolution,[status(thm)],[48,45,35]) ).
tff(50,plain,
( ( xS = sdtasdt0(xF,xD) )
<=> ( xS = sdtasdt0(xF,xD) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(51,axiom,
( aScalar0(xS)
& ( xS = sdtasdt0(xF,xD) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1930) ).
tff(52,plain,
xS = sdtasdt0(xF,xD),
inference(and_elim,[status(thm)],[51]) ).
tff(53,plain,
xS = sdtasdt0(xF,xD),
inference(modus_ponens,[status(thm)],[52,50]) ).
tff(54,plain,
sdtasdt0(xF,xD) = xS,
inference(symmetry,[status(thm)],[53]) ).
tff(55,plain,
( ( xR = sdtasdt0(xC,xG) )
<=> ( xR = sdtasdt0(xC,xG) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(56,axiom,
( aScalar0(xR)
& ( xR = sdtasdt0(xC,xG) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1892) ).
tff(57,plain,
xR = sdtasdt0(xC,xG),
inference(and_elim,[status(thm)],[56]) ).
tff(58,plain,
xR = sdtasdt0(xC,xG),
inference(modus_ponens,[status(thm)],[57,55]) ).
tff(59,plain,
sdtasdt0(xC,xG) = xR,
inference(symmetry,[status(thm)],[58]) ).
tff(60,plain,
sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)) = sdtpldt0(xR,xS),
inference(monotonicity,[status(thm)],[59,54]) ).
tff(61,plain,
( aScalar0(sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)))
<=> aScalar0(sdtpldt0(xR,xS)) ),
inference(monotonicity,[status(thm)],[60]) ).
tff(62,plain,
( aScalar0(sdtasdt0(xF,xD))
<=> aScalar0(xS) ),
inference(monotonicity,[status(thm)],[54]) ).
tff(63,plain,
( aScalar0(xS)
<=> aScalar0(sdtasdt0(xF,xD)) ),
inference(symmetry,[status(thm)],[62]) ).
tff(64,plain,
( aScalar0(xS)
<=> aScalar0(xS) ),
inference(rewrite,[status(thm)],[]) ).
tff(65,plain,
aScalar0(xS),
inference(and_elim,[status(thm)],[51]) ).
tff(66,plain,
aScalar0(xS),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
aScalar0(sdtasdt0(xF,xD)),
inference(modus_ponens,[status(thm)],[66,63]) ).
tff(68,plain,
( aScalar0(sdtasdt0(xC,xG))
<=> aScalar0(xR) ),
inference(monotonicity,[status(thm)],[59]) ).
tff(69,plain,
( aScalar0(xR)
<=> aScalar0(sdtasdt0(xC,xG)) ),
inference(symmetry,[status(thm)],[68]) ).
tff(70,plain,
( aScalar0(xR)
<=> aScalar0(xR) ),
inference(rewrite,[status(thm)],[]) ).
tff(71,plain,
aScalar0(xR),
inference(and_elim,[status(thm)],[56]) ).
tff(72,plain,
aScalar0(xR),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
aScalar0(sdtasdt0(xC,xG)),
inference(modus_ponens,[status(thm)],[72,69]) ).
tff(74,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(75,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)],[74]) ).
tff(76,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(77,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)],[76]) ).
tff(78,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(79,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(80,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)],[79]) ).
tff(81,axiom,
! [W0: $i,W1: $i] :
( ( aScalar0(W0)
& aScalar0(W1) )
=> aScalar0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSumSc) ).
tff(82,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) ),
inference(modus_ponens,[status(thm)],[81,80]) ).
tff(83,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) ),
inference(modus_ponens,[status(thm)],[82,78]) ).
tff(84,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) ),
inference(skolemize,[status(sab)],[83]) ).
tff(85,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ),
inference(modus_ponens,[status(thm)],[84,77]) ).
tff(86,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ),
inference(modus_ponens,[status(thm)],[85,75]) ).
tff(87,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(xF,xD))
| ~ aScalar0(sdtasdt0(xC,xG))
| aScalar0(sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD))) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(xF,xD))
| ~ aScalar0(sdtasdt0(xC,xG))
| aScalar0(sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(88,plain,
( ( aScalar0(sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)))
| ~ aScalar0(sdtasdt0(xF,xD))
| ~ aScalar0(sdtasdt0(xC,xG)) )
<=> ( ~ aScalar0(sdtasdt0(xF,xD))
| ~ aScalar0(sdtasdt0(xC,xG))
| aScalar0(sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(89,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)))
| ~ aScalar0(sdtasdt0(xF,xD))
| ~ aScalar0(sdtasdt0(xC,xG)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(xF,xD))
| ~ aScalar0(sdtasdt0(xC,xG))
| aScalar0(sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD))) ) ),
inference(monotonicity,[status(thm)],[88]) ).
tff(90,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)))
| ~ aScalar0(sdtasdt0(xF,xD))
| ~ aScalar0(sdtasdt0(xC,xG)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(xF,xD))
| ~ aScalar0(sdtasdt0(xC,xG))
| aScalar0(sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD))) ) ),
inference(transitivity,[status(thm)],[89,87]) ).
tff(91,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)))
| ~ aScalar0(sdtasdt0(xF,xD))
| ~ aScalar0(sdtasdt0(xC,xG)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(92,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(xF,xD))
| ~ aScalar0(sdtasdt0(xC,xG))
| aScalar0(sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD))) ),
inference(modus_ponens,[status(thm)],[91,90]) ).
tff(93,plain,
( ~ aScalar0(sdtasdt0(xF,xD))
| ~ aScalar0(sdtasdt0(xC,xG))
| aScalar0(sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD))) ),
inference(unit_resolution,[status(thm)],[92,86]) ).
tff(94,plain,
aScalar0(sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD))),
inference(unit_resolution,[status(thm)],[93,73,67]) ).
tff(95,plain,
aScalar0(sdtpldt0(xR,xS)),
inference(modus_ponens,[status(thm)],[94,61]) ).
tff(96,plain,
( ( xP = sdtasdt0(xE,xH) )
<=> ( xP = sdtasdt0(xE,xH) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(97,axiom,
( aScalar0(xP)
& ( xP = sdtasdt0(xE,xH) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1911) ).
tff(98,plain,
xP = sdtasdt0(xE,xH),
inference(and_elim,[status(thm)],[97]) ).
tff(99,plain,
xP = sdtasdt0(xE,xH),
inference(modus_ponens,[status(thm)],[98,96]) ).
tff(100,plain,
sdtasdt0(xE,xH) = xP,
inference(symmetry,[status(thm)],[99]) ).
tff(101,plain,
sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)) = sdtpldt0(xP,xP),
inference(monotonicity,[status(thm)],[100,100]) ).
tff(102,plain,
( aScalar0(sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)))
<=> aScalar0(sdtpldt0(xP,xP)) ),
inference(monotonicity,[status(thm)],[101]) ).
tff(103,plain,
( aScalar0(sdtasdt0(xE,xH))
<=> aScalar0(xP) ),
inference(monotonicity,[status(thm)],[100]) ).
tff(104,plain,
( aScalar0(xP)
<=> aScalar0(sdtasdt0(xE,xH)) ),
inference(symmetry,[status(thm)],[103]) ).
tff(105,plain,
( aScalar0(xP)
<=> aScalar0(xP) ),
inference(rewrite,[status(thm)],[]) ).
tff(106,plain,
aScalar0(xP),
inference(and_elim,[status(thm)],[97]) ).
tff(107,plain,
aScalar0(xP),
inference(modus_ponens,[status(thm)],[106,105]) ).
tff(108,plain,
aScalar0(sdtasdt0(xE,xH)),
inference(modus_ponens,[status(thm)],[107,104]) ).
tff(109,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(xE,xH))
| aScalar0(sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH))) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(xE,xH))
| aScalar0(sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(110,plain,
( ( aScalar0(sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)))
| ~ aScalar0(sdtasdt0(xE,xH))
| ~ aScalar0(sdtasdt0(xE,xH)) )
<=> ( ~ aScalar0(sdtasdt0(xE,xH))
| aScalar0(sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(111,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)))
| ~ aScalar0(sdtasdt0(xE,xH))
| ~ aScalar0(sdtasdt0(xE,xH)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(xE,xH))
| aScalar0(sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH))) ) ),
inference(monotonicity,[status(thm)],[110]) ).
tff(112,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)))
| ~ aScalar0(sdtasdt0(xE,xH))
| ~ aScalar0(sdtasdt0(xE,xH)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(xE,xH))
| aScalar0(sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH))) ) ),
inference(transitivity,[status(thm)],[111,109]) ).
tff(113,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)))
| ~ aScalar0(sdtasdt0(xE,xH))
| ~ aScalar0(sdtasdt0(xE,xH)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(114,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(xE,xH))
| aScalar0(sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH))) ),
inference(modus_ponens,[status(thm)],[113,112]) ).
tff(115,plain,
( ~ aScalar0(sdtasdt0(xE,xH))
| aScalar0(sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH))) ),
inference(unit_resolution,[status(thm)],[114,86]) ).
tff(116,plain,
aScalar0(sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH))),
inference(unit_resolution,[status(thm)],[115,108]) ).
tff(117,plain,
aScalar0(sdtpldt0(xP,xP)),
inference(modus_ponens,[status(thm)],[116,102]) ).
tff(118,plain,
( sdtlseqdt0(sdtpldt0(xP,xP),sdtpldt0(xR,xS))
<=> sdtlseqdt0(sdtpldt0(xP,xP),sdtpldt0(xR,xS)) ),
inference(rewrite,[status(thm)],[]) ).
tff(119,axiom,
sdtlseqdt0(sdtpldt0(xP,xP),sdtpldt0(xR,xS)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1983) ).
tff(120,plain,
sdtlseqdt0(sdtpldt0(xP,xP),sdtpldt0(xR,xS)),
inference(modus_ponens,[status(thm)],[119,118]) ).
tff(121,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(122,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)],[121]) ).
tff(123,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(124,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)],[123]) ).
tff(125,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(126,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(127,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)],[126]) ).
tff(128,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(129,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)],[128,127]) ).
tff(130,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)],[129,125]) ).
tff(131,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)],[130]) ).
tff(132,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)],[131,124]) ).
tff(133,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)],[132,122]) ).
tff(134,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(xH,xH))
| ~ aScalar0(sdtpldt0(xP,xP))
| ~ aScalar0(sdtpldt0(xR,xS))
| ~ sdtlseqdt0(sdtasdt0(xH,xH),sdtasdt0(xH,xH))
| sdtlseqdt0(sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)),sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH)))
| ~ sdtlseqdt0(sdtpldt0(xP,xP),sdtpldt0(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(xH,xH))
| ~ aScalar0(sdtpldt0(xP,xP))
| ~ aScalar0(sdtpldt0(xR,xS))
| ~ sdtlseqdt0(sdtasdt0(xH,xH),sdtasdt0(xH,xH))
| sdtlseqdt0(sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)),sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH)))
| ~ sdtlseqdt0(sdtpldt0(xP,xP),sdtpldt0(xR,xS)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(135,plain,
( ( sdtlseqdt0(sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)),sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH)))
| ~ aScalar0(sdtasdt0(xH,xH))
| ~ aScalar0(sdtasdt0(xH,xH))
| ~ aScalar0(sdtpldt0(xR,xS))
| ~ aScalar0(sdtpldt0(xP,xP))
| ~ sdtlseqdt0(sdtasdt0(xH,xH),sdtasdt0(xH,xH))
| ~ sdtlseqdt0(sdtpldt0(xP,xP),sdtpldt0(xR,xS)) )
<=> ( ~ aScalar0(sdtasdt0(xH,xH))
| ~ aScalar0(sdtpldt0(xP,xP))
| ~ aScalar0(sdtpldt0(xR,xS))
| ~ sdtlseqdt0(sdtasdt0(xH,xH),sdtasdt0(xH,xH))
| sdtlseqdt0(sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)),sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH)))
| ~ sdtlseqdt0(sdtpldt0(xP,xP),sdtpldt0(xR,xS)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(136,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(sdtpldt0(xP,xP),sdtasdt0(xH,xH)),sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH)))
| ~ aScalar0(sdtasdt0(xH,xH))
| ~ aScalar0(sdtasdt0(xH,xH))
| ~ aScalar0(sdtpldt0(xR,xS))
| ~ aScalar0(sdtpldt0(xP,xP))
| ~ sdtlseqdt0(sdtasdt0(xH,xH),sdtasdt0(xH,xH))
| ~ sdtlseqdt0(sdtpldt0(xP,xP),sdtpldt0(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(xH,xH))
| ~ aScalar0(sdtpldt0(xP,xP))
| ~ aScalar0(sdtpldt0(xR,xS))
| ~ sdtlseqdt0(sdtasdt0(xH,xH),sdtasdt0(xH,xH))
| sdtlseqdt0(sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)),sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH)))
| ~ sdtlseqdt0(sdtpldt0(xP,xP),sdtpldt0(xR,xS)) ) ),
inference(monotonicity,[status(thm)],[135]) ).
tff(137,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(sdtpldt0(xP,xP),sdtasdt0(xH,xH)),sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH)))
| ~ aScalar0(sdtasdt0(xH,xH))
| ~ aScalar0(sdtasdt0(xH,xH))
| ~ aScalar0(sdtpldt0(xR,xS))
| ~ aScalar0(sdtpldt0(xP,xP))
| ~ sdtlseqdt0(sdtasdt0(xH,xH),sdtasdt0(xH,xH))
| ~ sdtlseqdt0(sdtpldt0(xP,xP),sdtpldt0(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(xH,xH))
| ~ aScalar0(sdtpldt0(xP,xP))
| ~ aScalar0(sdtpldt0(xR,xS))
| ~ sdtlseqdt0(sdtasdt0(xH,xH),sdtasdt0(xH,xH))
| sdtlseqdt0(sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)),sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH)))
| ~ sdtlseqdt0(sdtpldt0(xP,xP),sdtpldt0(xR,xS)) ) ),
inference(transitivity,[status(thm)],[136,134]) ).
tff(138,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(sdtpldt0(xP,xP),sdtasdt0(xH,xH)),sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH)))
| ~ aScalar0(sdtasdt0(xH,xH))
| ~ aScalar0(sdtasdt0(xH,xH))
| ~ aScalar0(sdtpldt0(xR,xS))
| ~ aScalar0(sdtpldt0(xP,xP))
| ~ sdtlseqdt0(sdtasdt0(xH,xH),sdtasdt0(xH,xH))
| ~ sdtlseqdt0(sdtpldt0(xP,xP),sdtpldt0(xR,xS)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(139,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(xH,xH))
| ~ aScalar0(sdtpldt0(xP,xP))
| ~ aScalar0(sdtpldt0(xR,xS))
| ~ sdtlseqdt0(sdtasdt0(xH,xH),sdtasdt0(xH,xH))
| sdtlseqdt0(sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)),sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH)))
| ~ sdtlseqdt0(sdtpldt0(xP,xP),sdtpldt0(xR,xS)) ),
inference(modus_ponens,[status(thm)],[138,137]) ).
tff(140,plain,
( ~ aScalar0(sdtasdt0(xH,xH))
| ~ aScalar0(sdtpldt0(xP,xP))
| ~ aScalar0(sdtpldt0(xR,xS))
| ~ sdtlseqdt0(sdtasdt0(xH,xH),sdtasdt0(xH,xH))
| sdtlseqdt0(sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)),sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH))) ),
inference(unit_resolution,[status(thm)],[139,133,120]) ).
tff(141,plain,
sdtlseqdt0(sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)),sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH))),
inference(unit_resolution,[status(thm)],[140,117,95,49,35]) ).
tff(142,plain,
( ( xD = sdtasasdt0(xq,xq) )
<=> ( xD = sdtasasdt0(xq,xq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(143,axiom,
( aScalar0(xD)
& ( xD = sdtasasdt0(xq,xq) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1800) ).
tff(144,plain,
xD = sdtasasdt0(xq,xq),
inference(and_elim,[status(thm)],[143]) ).
tff(145,plain,
xD = sdtasasdt0(xq,xq),
inference(modus_ponens,[status(thm)],[144,142]) ).
tff(146,plain,
sdtasasdt0(xq,xq) = xD,
inference(symmetry,[status(thm)],[145]) ).
tff(147,plain,
( ( xC = sdtasasdt0(xp,xp) )
<=> ( xC = sdtasasdt0(xp,xp) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(148,axiom,
( aScalar0(xC)
& ( xC = sdtasasdt0(xp,xp) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1783) ).
tff(149,plain,
xC = sdtasasdt0(xp,xp),
inference(and_elim,[status(thm)],[148]) ).
tff(150,plain,
xC = sdtasasdt0(xp,xp),
inference(modus_ponens,[status(thm)],[149,147]) ).
tff(151,plain,
sdtasasdt0(xp,xp) = xC,
inference(symmetry,[status(thm)],[150]) ).
tff(152,plain,
sdtasdt0(sdtasasdt0(xp,xp),sdtasasdt0(xq,xq)) = sdtasdt0(xC,xD),
inference(monotonicity,[status(thm)],[151,146]) ).
tff(153,plain,
( aScalar0(sdtasdt0(sdtasasdt0(xp,xp),sdtasasdt0(xq,xq)))
<=> aScalar0(sdtasdt0(xC,xD)) ),
inference(monotonicity,[status(thm)],[152]) ).
tff(154,plain,
( aScalar0(sdtasasdt0(xq,xq))
<=> aScalar0(xD) ),
inference(monotonicity,[status(thm)],[146]) ).
tff(155,plain,
( aScalar0(xD)
<=> aScalar0(sdtasasdt0(xq,xq)) ),
inference(symmetry,[status(thm)],[154]) ).
tff(156,plain,
( aScalar0(xD)
<=> aScalar0(xD) ),
inference(rewrite,[status(thm)],[]) ).
tff(157,plain,
aScalar0(xD),
inference(and_elim,[status(thm)],[143]) ).
tff(158,plain,
aScalar0(xD),
inference(modus_ponens,[status(thm)],[157,156]) ).
tff(159,plain,
aScalar0(sdtasasdt0(xq,xq)),
inference(modus_ponens,[status(thm)],[158,155]) ).
tff(160,plain,
( aScalar0(sdtasasdt0(xp,xp))
<=> aScalar0(xC) ),
inference(monotonicity,[status(thm)],[151]) ).
tff(161,plain,
( aScalar0(xC)
<=> aScalar0(sdtasasdt0(xp,xp)) ),
inference(symmetry,[status(thm)],[160]) ).
tff(162,plain,
( aScalar0(xC)
<=> aScalar0(xC) ),
inference(rewrite,[status(thm)],[]) ).
tff(163,plain,
aScalar0(xC),
inference(and_elim,[status(thm)],[148]) ).
tff(164,plain,
aScalar0(xC),
inference(modus_ponens,[status(thm)],[163,162]) ).
tff(165,plain,
aScalar0(sdtasasdt0(xp,xp)),
inference(modus_ponens,[status(thm)],[164,161]) ).
tff(166,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(167,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(168,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)],[167]) ).
tff(169,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)],[168,166]) ).
tff(170,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(171,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)],[170,169]) ).
tff(172,plain,
( ~ aScalar0(sdtasasdt0(xq,xq))
| ~ aScalar0(sdtasasdt0(xp,xp))
| aScalar0(sdtasdt0(sdtasasdt0(xp,xp),sdtasasdt0(xq,xq))) ),
inference(unit_resolution,[status(thm)],[171,26]) ).
tff(173,plain,
aScalar0(sdtasdt0(sdtasasdt0(xp,xp),sdtasasdt0(xq,xq))),
inference(unit_resolution,[status(thm)],[172,165,159]) ).
tff(174,plain,
aScalar0(sdtasdt0(xC,xD)),
inference(modus_ponens,[status(thm)],[173,153]) ).
tff(175,plain,
( ( xE = sdtasasdt0(xp,xq) )
<=> ( xE = sdtasasdt0(xp,xq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(176,axiom,
( aScalar0(xE)
& ( xE = sdtasasdt0(xp,xq) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1820) ).
tff(177,plain,
xE = sdtasasdt0(xp,xq),
inference(and_elim,[status(thm)],[176]) ).
tff(178,plain,
xE = sdtasasdt0(xp,xq),
inference(modus_ponens,[status(thm)],[177,175]) ).
tff(179,plain,
sdtasasdt0(xp,xq) = xE,
inference(symmetry,[status(thm)],[178]) ).
tff(180,plain,
sdtasdt0(sdtasasdt0(xp,xq),sdtasasdt0(xp,xq)) = sdtasdt0(xE,xE),
inference(monotonicity,[status(thm)],[179,179]) ).
tff(181,plain,
( aScalar0(sdtasdt0(sdtasasdt0(xp,xq),sdtasasdt0(xp,xq)))
<=> aScalar0(sdtasdt0(xE,xE)) ),
inference(monotonicity,[status(thm)],[180]) ).
tff(182,plain,
( aScalar0(sdtasasdt0(xp,xq))
<=> aScalar0(xE) ),
inference(monotonicity,[status(thm)],[179]) ).
tff(183,plain,
( aScalar0(xE)
<=> aScalar0(sdtasasdt0(xp,xq)) ),
inference(symmetry,[status(thm)],[182]) ).
tff(184,plain,
( aScalar0(xE)
<=> aScalar0(xE) ),
inference(rewrite,[status(thm)],[]) ).
tff(185,plain,
aScalar0(xE),
inference(and_elim,[status(thm)],[176]) ).
tff(186,plain,
aScalar0(xE),
inference(modus_ponens,[status(thm)],[185,184]) ).
tff(187,plain,
aScalar0(sdtasasdt0(xp,xq)),
inference(modus_ponens,[status(thm)],[186,183]) ).
tff(188,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(189,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(190,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)],[189]) ).
tff(191,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)],[190,188]) ).
tff(192,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(193,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)],[192,191]) ).
tff(194,plain,
( ~ aScalar0(sdtasasdt0(xp,xq))
| aScalar0(sdtasdt0(sdtasasdt0(xp,xq),sdtasasdt0(xp,xq))) ),
inference(unit_resolution,[status(thm)],[193,26]) ).
tff(195,plain,
aScalar0(sdtasdt0(sdtasasdt0(xp,xq),sdtasasdt0(xp,xq))),
inference(unit_resolution,[status(thm)],[194,187]) ).
tff(196,plain,
aScalar0(sdtasdt0(xE,xE)),
inference(modus_ponens,[status(thm)],[195,181]) ).
tff(197,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH)))
| ~ aScalar0(sdtasdt0(xH,xH))
| ~ aScalar0(sdtpldt0(xR,xS)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH)))
| ~ aScalar0(sdtasdt0(xH,xH))
| ~ aScalar0(sdtpldt0(xR,xS)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(198,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH)))
| ~ aScalar0(sdtasdt0(xH,xH))
| ~ aScalar0(sdtpldt0(xR,xS)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(199,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH)))
| ~ aScalar0(sdtasdt0(xH,xH))
| ~ aScalar0(sdtpldt0(xR,xS)) ),
inference(modus_ponens,[status(thm)],[198,197]) ).
tff(200,plain,
( aScalar0(sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH)))
| ~ aScalar0(sdtasdt0(xH,xH))
| ~ aScalar0(sdtpldt0(xR,xS)) ),
inference(unit_resolution,[status(thm)],[199,86]) ).
tff(201,plain,
aScalar0(sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH))),
inference(unit_resolution,[status(thm)],[200,95,35]) ).
tff(202,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)))
| ~ aScalar0(sdtasdt0(xH,xH))
| ~ aScalar0(sdtpldt0(xP,xP)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)))
| ~ aScalar0(sdtasdt0(xH,xH))
| ~ aScalar0(sdtpldt0(xP,xP)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(203,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)))
| ~ aScalar0(sdtasdt0(xH,xH))
| ~ aScalar0(sdtpldt0(xP,xP)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(204,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)))
| ~ aScalar0(sdtasdt0(xH,xH))
| ~ aScalar0(sdtpldt0(xP,xP)) ),
inference(modus_ponens,[status(thm)],[203,202]) ).
tff(205,plain,
( aScalar0(sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)))
| ~ aScalar0(sdtasdt0(xH,xH))
| ~ aScalar0(sdtpldt0(xP,xP)) ),
inference(unit_resolution,[status(thm)],[204,86]) ).
tff(206,plain,
aScalar0(sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH))),
inference(unit_resolution,[status(thm)],[205,117,35]) ).
tff(207,plain,
( ~ sdtlseqdt0(sdtpldt0(sdtasdt0(xE,xE),sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH))),sdtpldt0(sdtasdt0(xC,xD),sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH))))
<=> ~ sdtlseqdt0(sdtpldt0(sdtasdt0(xE,xE),sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH))),sdtpldt0(sdtasdt0(xC,xD),sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH)))) ),
inference(rewrite,[status(thm)],[]) ).
tff(208,axiom,
~ sdtlseqdt0(sdtpldt0(sdtasdt0(xE,xE),sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH))),sdtpldt0(sdtasdt0(xC,xD),sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(209,plain,
~ sdtlseqdt0(sdtpldt0(sdtasdt0(xE,xE),sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH))),sdtpldt0(sdtasdt0(xC,xD),sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH)))),
inference(modus_ponens,[status(thm)],[208,207]) ).
tff(210,plain,
( sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD))
<=> sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)) ),
inference(rewrite,[status(thm)],[]) ).
tff(211,axiom,
sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1967) ).
tff(212,plain,
sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)),
inference(modus_ponens,[status(thm)],[211,210]) ).
tff(213,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(xE,xE),sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH))),sdtpldt0(sdtasdt0(xC,xD),sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH))))
| ~ aScalar0(sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)))
| ~ aScalar0(sdtasdt0(xE,xE))
| ~ aScalar0(sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH)))
| ~ aScalar0(sdtasdt0(xC,xD))
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)),sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH)))
| ~ sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)) )
<=> ( ~ ! [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(xE,xE),sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH))),sdtpldt0(sdtasdt0(xC,xD),sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH))))
| ~ aScalar0(sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)))
| ~ aScalar0(sdtasdt0(xE,xE))
| ~ aScalar0(sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH)))
| ~ aScalar0(sdtasdt0(xC,xD))
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)),sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH)))
| ~ sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(214,plain,
( ( sdtlseqdt0(sdtpldt0(sdtasdt0(xE,xE),sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH))),sdtpldt0(sdtasdt0(xC,xD),sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH))))
| ~ aScalar0(sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH)))
| ~ aScalar0(sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)))
| ~ aScalar0(sdtasdt0(xC,xD))
| ~ aScalar0(sdtasdt0(xE,xE))
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)),sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH)))
| ~ sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)) )
<=> ( sdtlseqdt0(sdtpldt0(sdtasdt0(xE,xE),sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH))),sdtpldt0(sdtasdt0(xC,xD),sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH))))
| ~ aScalar0(sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)))
| ~ aScalar0(sdtasdt0(xE,xE))
| ~ aScalar0(sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH)))
| ~ aScalar0(sdtasdt0(xC,xD))
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)),sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH)))
| ~ sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(215,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(xE,xE),sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH))),sdtpldt0(sdtasdt0(xC,xD),sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH))))
| ~ aScalar0(sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH)))
| ~ aScalar0(sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)))
| ~ aScalar0(sdtasdt0(xC,xD))
| ~ aScalar0(sdtasdt0(xE,xE))
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)),sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH)))
| ~ sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)) )
<=> ( ~ ! [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(xE,xE),sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH))),sdtpldt0(sdtasdt0(xC,xD),sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH))))
| ~ aScalar0(sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)))
| ~ aScalar0(sdtasdt0(xE,xE))
| ~ aScalar0(sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH)))
| ~ aScalar0(sdtasdt0(xC,xD))
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)),sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH)))
| ~ sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)) ) ),
inference(monotonicity,[status(thm)],[214]) ).
tff(216,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(xE,xE),sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH))),sdtpldt0(sdtasdt0(xC,xD),sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH))))
| ~ aScalar0(sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH)))
| ~ aScalar0(sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)))
| ~ aScalar0(sdtasdt0(xC,xD))
| ~ aScalar0(sdtasdt0(xE,xE))
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)),sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH)))
| ~ sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)) )
<=> ( ~ ! [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(xE,xE),sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH))),sdtpldt0(sdtasdt0(xC,xD),sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH))))
| ~ aScalar0(sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)))
| ~ aScalar0(sdtasdt0(xE,xE))
| ~ aScalar0(sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH)))
| ~ aScalar0(sdtasdt0(xC,xD))
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)),sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH)))
| ~ sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)) ) ),
inference(transitivity,[status(thm)],[215,213]) ).
tff(217,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(xE,xE),sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH))),sdtpldt0(sdtasdt0(xC,xD),sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH))))
| ~ aScalar0(sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH)))
| ~ aScalar0(sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)))
| ~ aScalar0(sdtasdt0(xC,xD))
| ~ aScalar0(sdtasdt0(xE,xE))
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)),sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH)))
| ~ sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(218,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(xE,xE),sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH))),sdtpldt0(sdtasdt0(xC,xD),sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH))))
| ~ aScalar0(sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)))
| ~ aScalar0(sdtasdt0(xE,xE))
| ~ aScalar0(sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH)))
| ~ aScalar0(sdtasdt0(xC,xD))
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)),sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH)))
| ~ sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)) ),
inference(modus_ponens,[status(thm)],[217,216]) ).
tff(219,plain,
( ~ aScalar0(sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)))
| ~ aScalar0(sdtasdt0(xE,xE))
| ~ aScalar0(sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH)))
| ~ aScalar0(sdtasdt0(xC,xD))
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)),sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH))) ),
inference(unit_resolution,[status(thm)],[218,133,212,209]) ).
tff(220,plain,
$false,
inference(unit_resolution,[status(thm)],[219,206,201,196,174,141]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : RNG076+2 : TPTP v9.0.0. Released v4.0.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n010.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 03:20:41 EDT 2025
% 0.11/0.33 % CPUTime :
% 2.06/2.25 % SZS status Theorem
% 2.06/2.25 % SZS output start Proof
% See solution above
% 2.06/2.29 % E exiting
%------------------------------------------------------------------------------