%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : RNG073+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 05:24:05 AM UTC 2025
% Result : Theorem 2.74s 2.91s
% Output : Proof 2.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 55
% Syntax : Number of formulae : 151 ( 50 unt; 0 typ; 0 def)
% Number of atoms : 1087 ( 178 equ)
% Maximal formula atoms : 24 ( 7 avg)
% Number of connectives : 1467 ( 625 ~; 548 |; 154 &)
% ( 109 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 94 ( 94 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 : 224 ( 200 !; 0 ?; 224 :)
% Comments :
%------------------------------------------------------------------------------
tff(sdtasdt0_type,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(sdtpldt0_type,type,
sdtpldt0: ( $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(xD_type,type,
xD: $i ).
tff(xF_type,type,
xF: $i ).
tff(xG_type,type,
xG: $i ).
tff(xC_type,type,
xC: $i ).
tff(xH_type,type,
xH: $i ).
tff(xE_type,type,
xE: $i ).
tff(sdtlseqdt0_type,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(sz0z00_type,type,
sz0z00: $i ).
tff(1,plain,
( ( xS = sdtasdt0(xF,xD) )
<=> ( xS = sdtasdt0(xF,xD) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
( aScalar0(xS)
& ( xS = sdtasdt0(xF,xD) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1930) ).
tff(3,plain,
xS = sdtasdt0(xF,xD),
inference(and_elim,[status(thm)],[2]) ).
tff(4,plain,
xS = sdtasdt0(xF,xD),
inference(modus_ponens,[status(thm)],[3,1]) ).
tff(5,plain,
sdtasdt0(xF,xD) = xS,
inference(symmetry,[status(thm)],[4]) ).
tff(6,plain,
( ( xR = sdtasdt0(xC,xG) )
<=> ( xR = sdtasdt0(xC,xG) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
( aScalar0(xR)
& ( xR = sdtasdt0(xC,xG) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1892) ).
tff(8,plain,
xR = sdtasdt0(xC,xG),
inference(and_elim,[status(thm)],[7]) ).
tff(9,plain,
xR = sdtasdt0(xC,xG),
inference(modus_ponens,[status(thm)],[8,6]) ).
tff(10,plain,
sdtasdt0(xC,xG) = xR,
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)) = sdtpldt0(xR,xS),
inference(monotonicity,[status(thm)],[10,5]) ).
tff(12,plain,
( aScalar0(sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)))
<=> aScalar0(sdtpldt0(xR,xS)) ),
inference(monotonicity,[status(thm)],[11]) ).
tff(13,plain,
( aScalar0(sdtasdt0(xF,xD))
<=> aScalar0(xS) ),
inference(monotonicity,[status(thm)],[5]) ).
tff(14,plain,
( aScalar0(xS)
<=> aScalar0(sdtasdt0(xF,xD)) ),
inference(symmetry,[status(thm)],[13]) ).
tff(15,plain,
( aScalar0(xS)
<=> aScalar0(xS) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,plain,
aScalar0(xS),
inference(and_elim,[status(thm)],[2]) ).
tff(17,plain,
aScalar0(xS),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
aScalar0(sdtasdt0(xF,xD)),
inference(modus_ponens,[status(thm)],[17,14]) ).
tff(19,plain,
( aScalar0(sdtasdt0(xC,xG))
<=> aScalar0(xR) ),
inference(monotonicity,[status(thm)],[10]) ).
tff(20,plain,
( aScalar0(xR)
<=> aScalar0(sdtasdt0(xC,xG)) ),
inference(symmetry,[status(thm)],[19]) ).
tff(21,plain,
( aScalar0(xR)
<=> aScalar0(xR) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,plain,
aScalar0(xR),
inference(and_elim,[status(thm)],[7]) ).
tff(23,plain,
aScalar0(xR),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
aScalar0(sdtasdt0(xC,xG)),
inference(modus_ponens,[status(thm)],[23,20]) ).
tff(25,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(26,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)],[25]) ).
tff(27,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aScalar0(W0)
& aScalar0(W1) )
<=> ~ ( ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
( ~ ( aScalar0(W0)
& aScalar0(W1) )
<=> ~ ~ ( ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
rewrite(( ~ ~ ( ~ aScalar0(W1)
| ~ aScalar0(W0) )
<=> ( ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
( ~ ( aScalar0(W0)
& aScalar0(W1) )
<=> ( ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
( ( aScalar0(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(28,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)],[27]) ).
tff(29,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(30,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(31,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)],[30]) ).
tff(32,axiom,
! [W0: $i,W1: $i] :
( ( aScalar0(W0)
& aScalar0(W1) )
=> aScalar0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSumSc) ).
tff(33,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) ),
inference(modus_ponens,[status(thm)],[33,29]) ).
tff(35,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) ),
inference(skolemize,[status(sab)],[34]) ).
tff(36,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ),
inference(modus_ponens,[status(thm)],[35,28]) ).
tff(37,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ),
inference(modus_ponens,[status(thm)],[36,26]) ).
tff(38,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(39,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(40,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)],[39]) ).
tff(41,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)],[40,38]) ).
tff(42,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(43,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)],[42,41]) ).
tff(44,plain,
( ~ aScalar0(sdtasdt0(xF,xD))
| ~ aScalar0(sdtasdt0(xC,xG))
| aScalar0(sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD))) ),
inference(unit_resolution,[status(thm)],[43,37]) ).
tff(45,plain,
aScalar0(sdtpldt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD))),
inference(unit_resolution,[status(thm)],[44,24,18]) ).
tff(46,plain,
aScalar0(sdtpldt0(xR,xS)),
inference(modus_ponens,[status(thm)],[45,12]) ).
tff(47,plain,
( ( xP = sdtasdt0(xE,xH) )
<=> ( xP = sdtasdt0(xE,xH) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(48,axiom,
( aScalar0(xP)
& ( xP = sdtasdt0(xE,xH) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1911) ).
tff(49,plain,
xP = sdtasdt0(xE,xH),
inference(and_elim,[status(thm)],[48]) ).
tff(50,plain,
xP = sdtasdt0(xE,xH),
inference(modus_ponens,[status(thm)],[49,47]) ).
tff(51,plain,
sdtasdt0(xE,xH) = xP,
inference(symmetry,[status(thm)],[50]) ).
tff(52,plain,
sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)) = sdtpldt0(xP,xP),
inference(monotonicity,[status(thm)],[51,51]) ).
tff(53,plain,
( aScalar0(sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)))
<=> aScalar0(sdtpldt0(xP,xP)) ),
inference(monotonicity,[status(thm)],[52]) ).
tff(54,plain,
( aScalar0(sdtasdt0(xE,xH))
<=> aScalar0(xP) ),
inference(monotonicity,[status(thm)],[51]) ).
tff(55,plain,
( aScalar0(xP)
<=> aScalar0(sdtasdt0(xE,xH)) ),
inference(symmetry,[status(thm)],[54]) ).
tff(56,plain,
( aScalar0(xP)
<=> aScalar0(xP) ),
inference(rewrite,[status(thm)],[]) ).
tff(57,plain,
aScalar0(xP),
inference(and_elim,[status(thm)],[48]) ).
tff(58,plain,
aScalar0(xP),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
aScalar0(sdtasdt0(xE,xH)),
inference(modus_ponens,[status(thm)],[58,55]) ).
tff(60,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(61,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(62,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)],[61]) ).
tff(63,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)],[62,60]) ).
tff(64,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(65,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)],[64,63]) ).
tff(66,plain,
( ~ aScalar0(sdtasdt0(xE,xH))
| aScalar0(sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH))) ),
inference(unit_resolution,[status(thm)],[65,37]) ).
tff(67,plain,
aScalar0(sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH))),
inference(unit_resolution,[status(thm)],[66,59]) ).
tff(68,plain,
aScalar0(sdtpldt0(xP,xP)),
inference(modus_ponens,[status(thm)],[67,53]) ).
tff(69,plain,
( ( sdtpldt0(xR,xS) != sdtpldt0(xP,xP) )
<=> ( sdtpldt0(xR,xS) != sdtpldt0(xP,xP) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(70,axiom,
sdtpldt0(xR,xS) != sdtpldt0(xP,xP),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(71,plain,
sdtpldt0(xR,xS) != sdtpldt0(xP,xP),
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,plain,
( sdtlseqdt0(sz0z00,sdtpldt0(xP,xP))
<=> sdtlseqdt0(sz0z00,sdtpldt0(xP,xP)) ),
inference(rewrite,[status(thm)],[]) ).
tff(73,axiom,
( sdtlseqdt0(sz0z00,sdtpldt0(xR,xS))
& sdtlseqdt0(sz0z00,sdtpldt0(xP,xP)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2628) ).
tff(74,plain,
sdtlseqdt0(sz0z00,sdtpldt0(xP,xP)),
inference(and_elim,[status(thm)],[73]) ).
tff(75,plain,
sdtlseqdt0(sz0z00,sdtpldt0(xP,xP)),
inference(modus_ponens,[status(thm)],[74,72]) ).
tff(76,plain,
( sdtlseqdt0(sz0z00,sdtpldt0(xR,xS))
<=> sdtlseqdt0(sz0z00,sdtpldt0(xR,xS)) ),
inference(rewrite,[status(thm)],[]) ).
tff(77,plain,
sdtlseqdt0(sz0z00,sdtpldt0(xR,xS)),
inference(and_elim,[status(thm)],[73]) ).
tff(78,plain,
sdtlseqdt0(sz0z00,sdtpldt0(xR,xS)),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
^ [W0: $i,W1: $i] :
refl(( ( ( W0 = W1 )
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(sz0z00,W0)
| ~ sdtlseqdt0(sz0z00,W1)
| ( sdtasdt0(W0,W0) != sdtasdt0(W1,W1) ) )
<=> ( ( W0 = W1 )
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(sz0z00,W0)
| ~ sdtlseqdt0(sz0z00,W1)
| ( sdtasdt0(W0,W0) != sdtasdt0(W1,W1) ) ) )),
inference(bind,[status(th)],[]) ).
tff(80,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(sz0z00,W0)
| ~ sdtlseqdt0(sz0z00,W1)
| ( sdtasdt0(W0,W0) != sdtasdt0(W1,W1) ) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(sz0z00,W0)
| ~ sdtlseqdt0(sz0z00,W1)
| ( sdtasdt0(W0,W0) != sdtasdt0(W1,W1) ) ) ),
inference(quant_intro,[status(thm)],[79]) ).
tff(81,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) ) )),
trans(monotonicity(rewrite(( ( sdtlseqdt0(sz0z00,W0)
& sdtlseqdt0(sz0z00,W1)
& ( sdtasdt0(W0,W0) = sdtasdt0(W1,W1) ) )
<=> ~ ( ~ sdtlseqdt0(sz0z00,W0)
| ~ sdtlseqdt0(sz0z00,W1)
| ( sdtasdt0(W0,W0) != sdtasdt0(W1,W1) ) ) )),
( ~ ( sdtlseqdt0(sz0z00,W0)
& sdtlseqdt0(sz0z00,W1)
& ( sdtasdt0(W0,W0) = sdtasdt0(W1,W1) ) )
<=> ~ ~ ( ~ sdtlseqdt0(sz0z00,W0)
| ~ sdtlseqdt0(sz0z00,W1)
| ( sdtasdt0(W0,W0) != sdtasdt0(W1,W1) ) ) )),
rewrite(( ~ ~ ( ~ sdtlseqdt0(sz0z00,W0)
| ~ sdtlseqdt0(sz0z00,W1)
| ( sdtasdt0(W0,W0) != sdtasdt0(W1,W1) ) )
<=> ( ~ sdtlseqdt0(sz0z00,W0)
| ~ sdtlseqdt0(sz0z00,W1)
| ( sdtasdt0(W0,W0) != sdtasdt0(W1,W1) ) ) )),
( ~ ( sdtlseqdt0(sz0z00,W0)
& sdtlseqdt0(sz0z00,W1)
& ( sdtasdt0(W0,W0) = sdtasdt0(W1,W1) ) )
<=> ( ~ sdtlseqdt0(sz0z00,W0)
| ~ sdtlseqdt0(sz0z00,W1)
| ( sdtasdt0(W0,W0) != sdtasdt0(W1,W1) ) ) )),
( ( ( W0 = W1 )
| ~ ( aScalar0(W0)
& aScalar0(W1) )
| ~ ( sdtlseqdt0(sz0z00,W0)
& sdtlseqdt0(sz0z00,W1)
& ( sdtasdt0(W0,W0) = sdtasdt0(W1,W1) ) ) )
<=> ( ( W0 = W1 )
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(sz0z00,W0)
| ~ sdtlseqdt0(sz0z00,W1)
| ( sdtasdt0(W0,W0) != sdtasdt0(W1,W1) ) ) )),
rewrite(( ( ( W0 = W1 )
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(sz0z00,W0)
| ~ sdtlseqdt0(sz0z00,W1)
| ( sdtasdt0(W0,W0) != sdtasdt0(W1,W1) ) )
<=> ( ( W0 = W1 )
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(sz0z00,W0)
| ~ sdtlseqdt0(sz0z00,W1)
| ( sdtasdt0(W0,W0) != sdtasdt0(W1,W1) ) ) )),
( ( ( W0 = W1 )
| ~ ( aScalar0(W0)
& aScalar0(W1) )
| ~ ( sdtlseqdt0(sz0z00,W0)
& sdtlseqdt0(sz0z00,W1)
& ( sdtasdt0(W0,W0) = sdtasdt0(W1,W1) ) ) )
<=> ( ( W0 = W1 )
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(sz0z00,W0)
| ~ sdtlseqdt0(sz0z00,W1)
| ( sdtasdt0(W0,W0) != sdtasdt0(W1,W1) ) ) )),
inference(bind,[status(th)],[]) ).
tff(82,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ ( aScalar0(W0)
& aScalar0(W1) )
| ~ ( sdtlseqdt0(sz0z00,W0)
& sdtlseqdt0(sz0z00,W1)
& ( sdtasdt0(W0,W0) = sdtasdt0(W1,W1) ) ) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(sz0z00,W0)
| ~ sdtlseqdt0(sz0z00,W1)
| ( sdtasdt0(W0,W0) != sdtasdt0(W1,W1) ) ) ),
inference(quant_intro,[status(thm)],[81]) ).
tff(83,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ ( aScalar0(W0)
& aScalar0(W1) )
| ~ ( sdtlseqdt0(sz0z00,W0)
& sdtlseqdt0(sz0z00,W1)
& ( sdtasdt0(W0,W0) = sdtasdt0(W1,W1) ) ) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ ( aScalar0(W0)
& aScalar0(W1) )
| ~ ( sdtlseqdt0(sz0z00,W0)
& sdtlseqdt0(sz0z00,W1)
& ( sdtasdt0(W0,W0) = sdtasdt0(W1,W1) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(84,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( sdtlseqdt0(sz0z00,W0)
& sdtlseqdt0(sz0z00,W1)
& ( sdtasdt0(W0,W0) = sdtasdt0(W1,W1) ) )
<=> ( sdtlseqdt0(sz0z00,W0)
& sdtlseqdt0(sz0z00,W1)
& ( sdtasdt0(W0,W0) = sdtasdt0(W1,W1) ) ) )),
( ( ( sdtlseqdt0(sz0z00,W0)
& sdtlseqdt0(sz0z00,W1)
& ( sdtasdt0(W0,W0) = sdtasdt0(W1,W1) ) )
=> ( W0 = W1 ) )
<=> ( ( sdtlseqdt0(sz0z00,W0)
& sdtlseqdt0(sz0z00,W1)
& ( sdtasdt0(W0,W0) = sdtasdt0(W1,W1) ) )
=> ( W0 = W1 ) ) )),
rewrite(( ( ( sdtlseqdt0(sz0z00,W0)
& sdtlseqdt0(sz0z00,W1)
& ( sdtasdt0(W0,W0) = sdtasdt0(W1,W1) ) )
=> ( W0 = W1 ) )
<=> ( ~ ( sdtlseqdt0(sz0z00,W0)
& sdtlseqdt0(sz0z00,W1)
& ( sdtasdt0(W0,W0) = sdtasdt0(W1,W1) ) )
| ( W0 = W1 ) ) )),
( ( ( sdtlseqdt0(sz0z00,W0)
& sdtlseqdt0(sz0z00,W1)
& ( sdtasdt0(W0,W0) = sdtasdt0(W1,W1) ) )
=> ( W0 = W1 ) )
<=> ( ~ ( sdtlseqdt0(sz0z00,W0)
& sdtlseqdt0(sz0z00,W1)
& ( sdtasdt0(W0,W0) = sdtasdt0(W1,W1) ) )
| ( W0 = W1 ) ) )),
( ( ( aScalar0(W0)
& aScalar0(W1) )
=> ( ( sdtlseqdt0(sz0z00,W0)
& sdtlseqdt0(sz0z00,W1)
& ( sdtasdt0(W0,W0) = sdtasdt0(W1,W1) ) )
=> ( W0 = W1 ) ) )
<=> ( ( aScalar0(W0)
& aScalar0(W1) )
=> ( ~ ( sdtlseqdt0(sz0z00,W0)
& sdtlseqdt0(sz0z00,W1)
& ( sdtasdt0(W0,W0) = sdtasdt0(W1,W1) ) )
| ( W0 = W1 ) ) ) )),
rewrite(( ( ( aScalar0(W0)
& aScalar0(W1) )
=> ( ~ ( sdtlseqdt0(sz0z00,W0)
& sdtlseqdt0(sz0z00,W1)
& ( sdtasdt0(W0,W0) = sdtasdt0(W1,W1) ) )
| ( W0 = W1 ) ) )
<=> ( ( W0 = W1 )
| ~ ( aScalar0(W0)
& aScalar0(W1) )
| ~ ( sdtlseqdt0(sz0z00,W0)
& sdtlseqdt0(sz0z00,W1)
& ( sdtasdt0(W0,W0) = sdtasdt0(W1,W1) ) ) ) )),
( ( ( aScalar0(W0)
& aScalar0(W1) )
=> ( ( sdtlseqdt0(sz0z00,W0)
& sdtlseqdt0(sz0z00,W1)
& ( sdtasdt0(W0,W0) = sdtasdt0(W1,W1) ) )
=> ( W0 = W1 ) ) )
<=> ( ( W0 = W1 )
| ~ ( aScalar0(W0)
& aScalar0(W1) )
| ~ ( sdtlseqdt0(sz0z00,W0)
& sdtlseqdt0(sz0z00,W1)
& ( sdtasdt0(W0,W0) = sdtasdt0(W1,W1) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(85,plain,
( ! [W0: $i,W1: $i] :
( ( aScalar0(W0)
& aScalar0(W1) )
=> ( ( sdtlseqdt0(sz0z00,W0)
& sdtlseqdt0(sz0z00,W1)
& ( sdtasdt0(W0,W0) = sdtasdt0(W1,W1) ) )
=> ( W0 = W1 ) ) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ ( aScalar0(W0)
& aScalar0(W1) )
| ~ ( sdtlseqdt0(sz0z00,W0)
& sdtlseqdt0(sz0z00,W1)
& ( sdtasdt0(W0,W0) = sdtasdt0(W1,W1) ) ) ) ),
inference(quant_intro,[status(thm)],[84]) ).
tff(86,axiom,
! [W0: $i,W1: $i] :
( ( aScalar0(W0)
& aScalar0(W1) )
=> ( ( sdtlseqdt0(sz0z00,W0)
& sdtlseqdt0(sz0z00,W1)
& ( sdtasdt0(W0,W0) = sdtasdt0(W1,W1) ) )
=> ( W0 = W1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSqrt) ).
tff(87,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ ( aScalar0(W0)
& aScalar0(W1) )
| ~ ( sdtlseqdt0(sz0z00,W0)
& sdtlseqdt0(sz0z00,W1)
& ( sdtasdt0(W0,W0) = sdtasdt0(W1,W1) ) ) ),
inference(modus_ponens,[status(thm)],[86,85]) ).
tff(88,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ ( aScalar0(W0)
& aScalar0(W1) )
| ~ ( sdtlseqdt0(sz0z00,W0)
& sdtlseqdt0(sz0z00,W1)
& ( sdtasdt0(W0,W0) = sdtasdt0(W1,W1) ) ) ),
inference(modus_ponens,[status(thm)],[87,83]) ).
tff(89,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ ( aScalar0(W0)
& aScalar0(W1) )
| ~ ( sdtlseqdt0(sz0z00,W0)
& sdtlseqdt0(sz0z00,W1)
& ( sdtasdt0(W0,W0) = sdtasdt0(W1,W1) ) ) ),
inference(skolemize,[status(sab)],[88]) ).
tff(90,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(sz0z00,W0)
| ~ sdtlseqdt0(sz0z00,W1)
| ( sdtasdt0(W0,W0) != sdtasdt0(W1,W1) ) ),
inference(modus_ponens,[status(thm)],[89,82]) ).
tff(91,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(sz0z00,W0)
| ~ sdtlseqdt0(sz0z00,W1)
| ( sdtasdt0(W0,W0) != sdtasdt0(W1,W1) ) ),
inference(modus_ponens,[status(thm)],[90,80]) ).
tff(92,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(sz0z00,W0)
| ~ sdtlseqdt0(sz0z00,W1)
| ( sdtasdt0(W0,W0) != sdtasdt0(W1,W1) ) )
| ( sdtpldt0(xR,xS) = sdtpldt0(xP,xP) )
| ~ aScalar0(sdtpldt0(xP,xP))
| ~ aScalar0(sdtpldt0(xR,xS))
| ~ sdtlseqdt0(sz0z00,sdtpldt0(xP,xP))
| ~ sdtlseqdt0(sz0z00,sdtpldt0(xR,xS))
| ( sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)) != sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(sz0z00,W0)
| ~ sdtlseqdt0(sz0z00,W1)
| ( sdtasdt0(W0,W0) != sdtasdt0(W1,W1) ) )
| ( sdtpldt0(xR,xS) = sdtpldt0(xP,xP) )
| ~ aScalar0(sdtpldt0(xP,xP))
| ~ aScalar0(sdtpldt0(xR,xS))
| ~ sdtlseqdt0(sz0z00,sdtpldt0(xP,xP))
| ~ sdtlseqdt0(sz0z00,sdtpldt0(xR,xS))
| ( sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)) != sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(93,plain,
( ( ( sdtpldt0(xR,xS) = sdtpldt0(xP,xP) )
| ~ aScalar0(sdtpldt0(xP,xP))
| ~ aScalar0(sdtpldt0(xR,xS))
| ~ sdtlseqdt0(sz0z00,sdtpldt0(xR,xS))
| ~ sdtlseqdt0(sz0z00,sdtpldt0(xP,xP))
| ( sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)) != sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)) ) )
<=> ( ( sdtpldt0(xR,xS) = sdtpldt0(xP,xP) )
| ~ aScalar0(sdtpldt0(xP,xP))
| ~ aScalar0(sdtpldt0(xR,xS))
| ~ sdtlseqdt0(sz0z00,sdtpldt0(xP,xP))
| ~ sdtlseqdt0(sz0z00,sdtpldt0(xR,xS))
| ( sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)) != sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(94,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(sz0z00,W0)
| ~ sdtlseqdt0(sz0z00,W1)
| ( sdtasdt0(W0,W0) != sdtasdt0(W1,W1) ) )
| ( sdtpldt0(xR,xS) = sdtpldt0(xP,xP) )
| ~ aScalar0(sdtpldt0(xP,xP))
| ~ aScalar0(sdtpldt0(xR,xS))
| ~ sdtlseqdt0(sz0z00,sdtpldt0(xR,xS))
| ~ sdtlseqdt0(sz0z00,sdtpldt0(xP,xP))
| ( sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)) != sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(sz0z00,W0)
| ~ sdtlseqdt0(sz0z00,W1)
| ( sdtasdt0(W0,W0) != sdtasdt0(W1,W1) ) )
| ( sdtpldt0(xR,xS) = sdtpldt0(xP,xP) )
| ~ aScalar0(sdtpldt0(xP,xP))
| ~ aScalar0(sdtpldt0(xR,xS))
| ~ sdtlseqdt0(sz0z00,sdtpldt0(xP,xP))
| ~ sdtlseqdt0(sz0z00,sdtpldt0(xR,xS))
| ( sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)) != sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)) ) ) ),
inference(monotonicity,[status(thm)],[93]) ).
tff(95,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(sz0z00,W0)
| ~ sdtlseqdt0(sz0z00,W1)
| ( sdtasdt0(W0,W0) != sdtasdt0(W1,W1) ) )
| ( sdtpldt0(xR,xS) = sdtpldt0(xP,xP) )
| ~ aScalar0(sdtpldt0(xP,xP))
| ~ aScalar0(sdtpldt0(xR,xS))
| ~ sdtlseqdt0(sz0z00,sdtpldt0(xR,xS))
| ~ sdtlseqdt0(sz0z00,sdtpldt0(xP,xP))
| ( sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)) != sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(sz0z00,W0)
| ~ sdtlseqdt0(sz0z00,W1)
| ( sdtasdt0(W0,W0) != sdtasdt0(W1,W1) ) )
| ( sdtpldt0(xR,xS) = sdtpldt0(xP,xP) )
| ~ aScalar0(sdtpldt0(xP,xP))
| ~ aScalar0(sdtpldt0(xR,xS))
| ~ sdtlseqdt0(sz0z00,sdtpldt0(xP,xP))
| ~ sdtlseqdt0(sz0z00,sdtpldt0(xR,xS))
| ( sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)) != sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)) ) ) ),
inference(transitivity,[status(thm)],[94,92]) ).
tff(96,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(sz0z00,W0)
| ~ sdtlseqdt0(sz0z00,W1)
| ( sdtasdt0(W0,W0) != sdtasdt0(W1,W1) ) )
| ( sdtpldt0(xR,xS) = sdtpldt0(xP,xP) )
| ~ aScalar0(sdtpldt0(xP,xP))
| ~ aScalar0(sdtpldt0(xR,xS))
| ~ sdtlseqdt0(sz0z00,sdtpldt0(xR,xS))
| ~ sdtlseqdt0(sz0z00,sdtpldt0(xP,xP))
| ( sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)) != sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(97,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(sz0z00,W0)
| ~ sdtlseqdt0(sz0z00,W1)
| ( sdtasdt0(W0,W0) != sdtasdt0(W1,W1) ) )
| ( sdtpldt0(xR,xS) = sdtpldt0(xP,xP) )
| ~ aScalar0(sdtpldt0(xP,xP))
| ~ aScalar0(sdtpldt0(xR,xS))
| ~ sdtlseqdt0(sz0z00,sdtpldt0(xP,xP))
| ~ sdtlseqdt0(sz0z00,sdtpldt0(xR,xS))
| ( sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)) != sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)) ) ),
inference(modus_ponens,[status(thm)],[96,95]) ).
tff(98,plain,
sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)) != sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)),
inference(unit_resolution,[status(thm)],[97,91,78,75,71,68,46]) ).
tff(99,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(100,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)],[99]) ).
tff(101,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(102,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)],[101]) ).
tff(103,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(104,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(105,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)],[104]) ).
tff(106,axiom,
! [W0: $i,W1: $i] :
( ( aScalar0(W0)
& aScalar0(W1) )
=> aScalar0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulSc) ).
tff(107,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) ),
inference(modus_ponens,[status(thm)],[106,105]) ).
tff(108,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) ),
inference(modus_ponens,[status(thm)],[107,103]) ).
tff(109,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) ),
inference(skolemize,[status(sab)],[108]) ).
tff(110,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ),
inference(modus_ponens,[status(thm)],[109,102]) ).
tff(111,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ),
inference(modus_ponens,[status(thm)],[110,100]) ).
tff(112,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtpldt0(xR,xS))
| aScalar0(sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS))) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtpldt0(xR,xS))
| aScalar0(sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(113,plain,
( ( aScalar0(sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)))
| ~ aScalar0(sdtpldt0(xR,xS))
| ~ aScalar0(sdtpldt0(xR,xS)) )
<=> ( ~ aScalar0(sdtpldt0(xR,xS))
| aScalar0(sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(114,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)))
| ~ aScalar0(sdtpldt0(xR,xS))
| ~ aScalar0(sdtpldt0(xR,xS)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtpldt0(xR,xS))
| aScalar0(sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS))) ) ),
inference(monotonicity,[status(thm)],[113]) ).
tff(115,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)))
| ~ aScalar0(sdtpldt0(xR,xS))
| ~ aScalar0(sdtpldt0(xR,xS)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtpldt0(xR,xS))
| aScalar0(sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS))) ) ),
inference(transitivity,[status(thm)],[114,112]) ).
tff(116,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)))
| ~ aScalar0(sdtpldt0(xR,xS))
| ~ aScalar0(sdtpldt0(xR,xS)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(117,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtpldt0(xR,xS))
| aScalar0(sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS))) ),
inference(modus_ponens,[status(thm)],[116,115]) ).
tff(118,plain,
( ~ aScalar0(sdtpldt0(xR,xS))
| aScalar0(sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS))) ),
inference(unit_resolution,[status(thm)],[117,111]) ).
tff(119,plain,
aScalar0(sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS))),
inference(unit_resolution,[status(thm)],[118,46]) ).
tff(120,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtpldt0(xP,xP))
| aScalar0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP))) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtpldt0(xP,xP))
| aScalar0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(121,plain,
( ( aScalar0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)))
| ~ aScalar0(sdtpldt0(xP,xP))
| ~ aScalar0(sdtpldt0(xP,xP)) )
<=> ( ~ aScalar0(sdtpldt0(xP,xP))
| aScalar0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(122,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)))
| ~ aScalar0(sdtpldt0(xP,xP))
| ~ aScalar0(sdtpldt0(xP,xP)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtpldt0(xP,xP))
| aScalar0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP))) ) ),
inference(monotonicity,[status(thm)],[121]) ).
tff(123,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)))
| ~ aScalar0(sdtpldt0(xP,xP))
| ~ aScalar0(sdtpldt0(xP,xP)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtpldt0(xP,xP))
| aScalar0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP))) ) ),
inference(transitivity,[status(thm)],[122,120]) ).
tff(124,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)))
| ~ aScalar0(sdtpldt0(xP,xP))
| ~ aScalar0(sdtpldt0(xP,xP)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(125,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtpldt0(xP,xP))
| aScalar0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP))) ),
inference(modus_ponens,[status(thm)],[124,123]) ).
tff(126,plain,
( ~ aScalar0(sdtpldt0(xP,xP))
| aScalar0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP))) ),
inference(unit_resolution,[status(thm)],[125,111]) ).
tff(127,plain,
aScalar0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP))),
inference(unit_resolution,[status(thm)],[126,68]) ).
tff(128,plain,
( sdtlseqdt0(sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)),sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)))
<=> sdtlseqdt0(sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)),sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP))) ),
inference(rewrite,[status(thm)],[]) ).
tff(129,axiom,
sdtlseqdt0(sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)),sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2654) ).
tff(130,plain,
sdtlseqdt0(sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)),sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP))),
inference(modus_ponens,[status(thm)],[129,128]) ).
tff(131,plain,
( sdtlseqdt0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)),sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)))
<=> sdtlseqdt0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)),sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS))) ),
inference(rewrite,[status(thm)],[]) ).
tff(132,axiom,
sdtlseqdt0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)),sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2405) ).
tff(133,plain,
sdtlseqdt0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)),sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS))),
inference(modus_ponens,[status(thm)],[132,131]) ).
tff(134,plain,
^ [W0: $i,W1: $i] :
refl(( ( ( W0 = W1 )
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0) )
<=> ( ( W0 = W1 )
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0) ) )),
inference(bind,[status(th)],[]) ).
tff(135,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0) ) ),
inference(quant_intro,[status(thm)],[134]) ).
tff(136,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) ) )),
trans(monotonicity(rewrite(( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
<=> ~ ( ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0) ) )),
( ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
<=> ~ ~ ( ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0) ) )),
rewrite(( ~ ~ ( ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0) )
<=> ( ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0) ) )),
( ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
<=> ( ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0) ) )),
( ( ( W0 = W1 )
| ~ ( aScalar0(W0)
& aScalar0(W1) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) ) )
<=> ( ( W0 = W1 )
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0) ) )),
rewrite(( ( ( W0 = W1 )
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0) )
<=> ( ( W0 = W1 )
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0) ) )),
( ( ( W0 = W1 )
| ~ ( aScalar0(W0)
& aScalar0(W1) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) ) )
<=> ( ( W0 = W1 )
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0) ) )),
inference(bind,[status(th)],[]) ).
tff(137,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ ( aScalar0(W0)
& aScalar0(W1) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) ) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0) ) ),
inference(quant_intro,[status(thm)],[136]) ).
tff(138,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ ( aScalar0(W0)
& aScalar0(W1) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) ) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ ( aScalar0(W0)
& aScalar0(W1) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(139,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(rewrite(( ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
=> ( W0 = W1 ) )
<=> ( ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
| ( W0 = W1 ) ) )),
( ( ( aScalar0(W0)
& aScalar0(W1) )
=> ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
=> ( W0 = W1 ) ) )
<=> ( ( aScalar0(W0)
& aScalar0(W1) )
=> ( ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
| ( W0 = W1 ) ) ) )),
rewrite(( ( ( aScalar0(W0)
& aScalar0(W1) )
=> ( ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
| ( W0 = W1 ) ) )
<=> ( ( W0 = W1 )
| ~ ( aScalar0(W0)
& aScalar0(W1) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) ) ) )),
( ( ( aScalar0(W0)
& aScalar0(W1) )
=> ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
=> ( W0 = W1 ) ) )
<=> ( ( W0 = W1 )
| ~ ( aScalar0(W0)
& aScalar0(W1) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(140,plain,
( ! [W0: $i,W1: $i] :
( ( aScalar0(W0)
& aScalar0(W1) )
=> ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
=> ( W0 = W1 ) ) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ ( aScalar0(W0)
& aScalar0(W1) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) ) ) ),
inference(quant_intro,[status(thm)],[139]) ).
tff(141,axiom,
! [W0: $i,W1: $i] :
( ( aScalar0(W0)
& aScalar0(W1) )
=> ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
=> ( W0 = W1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLEASm) ).
tff(142,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ ( aScalar0(W0)
& aScalar0(W1) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[141,140]) ).
tff(143,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ ( aScalar0(W0)
& aScalar0(W1) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[142,138]) ).
tff(144,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ ( aScalar0(W0)
& aScalar0(W1) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) ) ),
inference(skolemize,[status(sab)],[143]) ).
tff(145,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0) ),
inference(modus_ponens,[status(thm)],[144,137]) ).
tff(146,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0) ),
inference(modus_ponens,[status(thm)],[145,135]) ).
tff(147,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0) )
| ( sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)) = sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)) )
| ~ aScalar0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)))
| ~ aScalar0(sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)))
| ~ sdtlseqdt0(sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)),sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)))
| ~ sdtlseqdt0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)),sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS))) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0) )
| ( sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)) = sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)) )
| ~ aScalar0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)))
| ~ aScalar0(sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)))
| ~ sdtlseqdt0(sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)),sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)))
| ~ sdtlseqdt0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)),sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(148,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0) )
| ( sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)) = sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)) )
| ~ aScalar0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)))
| ~ aScalar0(sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)))
| ~ sdtlseqdt0(sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)),sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)))
| ~ sdtlseqdt0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)),sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(149,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0) )
| ( sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)) = sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)) )
| ~ aScalar0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)))
| ~ aScalar0(sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)))
| ~ sdtlseqdt0(sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)),sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)))
| ~ sdtlseqdt0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)),sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS))) ),
inference(modus_ponens,[status(thm)],[148,147]) ).
tff(150,plain,
( ( sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)) = sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)) )
| ~ aScalar0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)))
| ~ aScalar0(sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS))) ),
inference(unit_resolution,[status(thm)],[149,146,133,130]) ).
tff(151,plain,
$false,
inference(unit_resolution,[status(thm)],[150,127,119,98]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : RNG073+2 : TPTP v9.0.0. Released v4.0.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n010.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 03:20:26 EDT 2025
% 0.12/0.33 % CPUTime :
% 2.74/2.91 % SZS status Theorem
% 2.74/2.91 % SZS output start Proof
% See solution above
% 2.76/2.94 % E exiting
%------------------------------------------------------------------------------