%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : RNG126+4 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:24:16 AM UTC 2025
% Result : Theorem 1.62s 1.79s
% Output : Proof 1.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 59
% Syntax : Number of formulae : 159 ( 37 unt; 0 typ; 0 def)
% Number of atoms : 1969 ( 384 equ)
% Maximal formula atoms : 48 ( 12 avg)
% Number of connectives : 3190 (1480 ~;1066 |; 426 &)
% ( 165 <=>; 53 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 100 ( 100 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 18 ( 16 usr; 1 prp; 0-4 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 564 ( 446 !; 97 ?; 564 :)
% Comments :
%------------------------------------------------------------------------------
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(xI_type,type,
xI: $i ).
tff(sdtasdt0_type,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(xu_type,type,
xu: $i ).
tff(tptp_fun_W1_22_type,type,
tptp_fun_W1_22: $i > $i ).
tff(sdtpldt1_type,type,
sdtpldt1: ( $i * $i ) > $i ).
tff(slsdtgt0_type,type,
slsdtgt0: $i > $i ).
tff(xb_type,type,
xb: $i ).
tff(xa_type,type,
xa: $i ).
tff(xc_type,type,
xc: $i ).
tff(sdtpldt0_type,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(aElement0_type,type,
aElement0: $i > $o ).
tff(aIdeal0_type,type,
aIdeal0: $i > $o ).
tff(aSet0_type,type,
aSet0: $i > $o ).
tff(doDivides0_type,type,
doDivides0: ( $i * $i ) > $o ).
tff(aDivisorOf0_type,type,
aDivisorOf0: ( $i * $i ) > $o ).
tff(aGcdOfAnd0_type,type,
aGcdOfAnd0: ( $i * $i * $i ) > $o ).
tff(sz00_type,type,
sz00: $i ).
tff(iLess0_type,type,
iLess0: ( $i * $i ) > $o ).
tff(sbrdtbr0_type,type,
sbrdtbr0: $i > $i ).
tff(1,plain,
( ( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) )
<=> ( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
( aSet0(xI)
& ! [W0: $i] :
( aElementOf0(W0,xI)
=> ( ! [W1: $i] :
( aElementOf0(W1,xI)
=> aElementOf0(sdtpldt0(W0,W1),xI) )
& ! [W1: $i] :
( aElement0(W1)
=> aElementOf0(sdtasdt0(W1,W0),xI) ) ) )
& aIdeal0(xI)
& ! [W0: $i] :
( aElementOf0(W0,slsdtgt0(xa))
<=> ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(xa,W1) = W0 ) ) )
& ! [W0: $i] :
( aElementOf0(W0,slsdtgt0(xb))
<=> ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(xb,W1) = W0 ) ) )
& ! [W0: $i] :
( aElementOf0(W0,xI)
<=> ? [W1: $i,W2: $i] :
( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& ( sdtpldt0(W1,W2) = W0 ) ) )
& ( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2174) ).
tff(3,plain,
xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)),
inference(and_elim,[status(thm)],[2]) ).
tff(4,plain,
xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)),
inference(modus_ponens,[status(thm)],[3,1]) ).
tff(5,plain,
( doDivides0(xu,xb)
<=> doDivides0(xu,xb) ),
inference(rewrite,[status(thm)],[]) ).
tff(6,axiom,
( ? [W0: $i] :
( aElement0(W0)
& ( sdtasdt0(xu,W0) = xa ) )
& doDivides0(xu,xa)
& aDivisorOf0(xu,xa)
& ? [W0: $i] :
( aElement0(W0)
& ( sdtasdt0(xu,W0) = xb ) )
& doDivides0(xu,xb)
& aDivisorOf0(xu,xb) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2373) ).
tff(7,plain,
( ? [W0: $i] :
( aElement0(W0)
& ( sdtasdt0(xu,W0) = xa ) )
& doDivides0(xu,xa)
& aDivisorOf0(xu,xa)
& ? [W0: $i] :
( aElement0(W0)
& ( sdtasdt0(xu,W0) = xb ) )
& doDivides0(xu,xb) ),
inference(and_elim,[status(thm)],[6]) ).
tff(8,plain,
doDivides0(xu,xb),
inference(and_elim,[status(thm)],[7]) ).
tff(9,plain,
doDivides0(xu,xb),
inference(modus_ponens,[status(thm)],[8,5]) ).
tff(10,plain,
( doDivides0(xu,xb)
| aDivisorOf0(xu,xb)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(xu,W1) != xb ) )
| ~ doDivides0(xu,xb) ),
inference(tautology,[status(thm)],[]) ).
tff(11,plain,
( doDivides0(xu,xb)
| aDivisorOf0(xu,xb)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(xu,W1) != xb ) ) ),
inference(unit_resolution,[status(thm)],[10,9]) ).
tff(12,plain,
( aDivisorOf0(xu,xa)
<=> aDivisorOf0(xu,xa) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,plain,
( ? [W0: $i] :
( aElement0(W0)
& ( sdtasdt0(xu,W0) = xa ) )
& doDivides0(xu,xa)
& aDivisorOf0(xu,xa)
& ? [W0: $i] :
( aElement0(W0)
& ( sdtasdt0(xu,W0) = xb ) ) ),
inference(and_elim,[status(thm)],[7]) ).
tff(14,plain,
( ? [W0: $i] :
( aElement0(W0)
& ( sdtasdt0(xu,W0) = xa ) )
& doDivides0(xu,xa)
& aDivisorOf0(xu,xa) ),
inference(and_elim,[status(thm)],[13]) ).
tff(15,plain,
aDivisorOf0(xu,xa),
inference(and_elim,[status(thm)],[14]) ).
tff(16,plain,
aDivisorOf0(xu,xa),
inference(modus_ponens,[status(thm)],[15,12]) ).
tff(17,plain,
( aDivisorOf0(xu,xa)
| ~ ( ~ aElement0(xu)
| ~ ( doDivides0(xu,xa)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(xu,W1) != xa ) ) ) )
| ~ aDivisorOf0(xu,xa) ),
inference(tautology,[status(thm)],[]) ).
tff(18,plain,
( aDivisorOf0(xu,xa)
| ~ ( ~ aElement0(xu)
| ~ ( doDivides0(xu,xa)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(xu,W1) != xa ) ) ) ) ),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
^ [W0: $i] :
trans(monotonicity(rewrite(( ~ ( aDivisorOf0(W0,xa)
| ~ ( ~ aElement0(W0)
| ~ ( doDivides0(W0,xa)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xa ) ) ) ) )
<=> ~ ( aDivisorOf0(W0,xa)
| ~ ( ~ aElement0(W0)
| ~ ( doDivides0(W0,xa)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xa ) ) ) ) ) )),
rewrite(( ~ ( aDivisorOf0(W0,xb)
| doDivides0(W0,xb)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xb ) ) )
<=> ~ ( aDivisorOf0(W0,xb)
| doDivides0(W0,xb)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xb ) ) ) )),
rewrite(( ~ ( ~ aElement0(tptp_fun_W1_22(W0))
| ( sdtasdt0(W0,tptp_fun_W1_22(W0)) != xc )
| ~ doDivides0(W0,xc) )
<=> ~ ( ~ aElement0(tptp_fun_W1_22(W0))
| ( sdtasdt0(W0,tptp_fun_W1_22(W0)) != xc )
| ~ doDivides0(W0,xc) ) )),
( ( ~ ( aDivisorOf0(W0,xa)
| ~ ( ~ aElement0(W0)
| ~ ( doDivides0(W0,xa)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xa ) ) ) ) )
| ~ ( aDivisorOf0(W0,xb)
| doDivides0(W0,xb)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xb ) ) )
| ~ ( ~ aElement0(tptp_fun_W1_22(W0))
| ( sdtasdt0(W0,tptp_fun_W1_22(W0)) != xc )
| ~ doDivides0(W0,xc) ) )
<=> ( ~ ( aDivisorOf0(W0,xa)
| ~ ( ~ aElement0(W0)
| ~ ( doDivides0(W0,xa)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xa ) ) ) ) )
| ~ ( aDivisorOf0(W0,xb)
| doDivides0(W0,xb)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xb ) ) )
| ~ ( ~ aElement0(tptp_fun_W1_22(W0))
| ( sdtasdt0(W0,tptp_fun_W1_22(W0)) != xc )
| ~ doDivides0(W0,xc) ) ) )),
rewrite(( ( ~ ( aDivisorOf0(W0,xa)
| ~ ( ~ aElement0(W0)
| ~ ( doDivides0(W0,xa)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xa ) ) ) ) )
| ~ ( aDivisorOf0(W0,xb)
| doDivides0(W0,xb)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xb ) ) )
| ~ ( ~ aElement0(tptp_fun_W1_22(W0))
| ( sdtasdt0(W0,tptp_fun_W1_22(W0)) != xc )
| ~ doDivides0(W0,xc) ) )
<=> ( ~ ( ~ aElement0(tptp_fun_W1_22(W0))
| ( sdtasdt0(W0,tptp_fun_W1_22(W0)) != xc )
| ~ doDivides0(W0,xc) )
| ~ ( aDivisorOf0(W0,xa)
| ~ ( ~ aElement0(W0)
| ~ ( doDivides0(W0,xa)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xa ) ) ) ) )
| ~ ( aDivisorOf0(W0,xb)
| doDivides0(W0,xb)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xb ) ) ) ) )),
( ( ~ ( aDivisorOf0(W0,xa)
| ~ ( ~ aElement0(W0)
| ~ ( doDivides0(W0,xa)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xa ) ) ) ) )
| ~ ( aDivisorOf0(W0,xb)
| doDivides0(W0,xb)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xb ) ) )
| ~ ( ~ aElement0(tptp_fun_W1_22(W0))
| ( sdtasdt0(W0,tptp_fun_W1_22(W0)) != xc )
| ~ doDivides0(W0,xc) ) )
<=> ( ~ ( ~ aElement0(tptp_fun_W1_22(W0))
| ( sdtasdt0(W0,tptp_fun_W1_22(W0)) != xc )
| ~ doDivides0(W0,xc) )
| ~ ( aDivisorOf0(W0,xa)
| ~ ( ~ aElement0(W0)
| ~ ( doDivides0(W0,xa)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xa ) ) ) ) )
| ~ ( aDivisorOf0(W0,xb)
| doDivides0(W0,xb)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xb ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(20,plain,
( ! [W0: $i] :
( ~ ( aDivisorOf0(W0,xa)
| ~ ( ~ aElement0(W0)
| ~ ( doDivides0(W0,xa)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xa ) ) ) ) )
| ~ ( aDivisorOf0(W0,xb)
| doDivides0(W0,xb)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xb ) ) )
| ~ ( ~ aElement0(tptp_fun_W1_22(W0))
| ( sdtasdt0(W0,tptp_fun_W1_22(W0)) != xc )
| ~ doDivides0(W0,xc) ) )
<=> ! [W0: $i] :
( ~ ( ~ aElement0(tptp_fun_W1_22(W0))
| ( sdtasdt0(W0,tptp_fun_W1_22(W0)) != xc )
| ~ doDivides0(W0,xc) )
| ~ ( aDivisorOf0(W0,xa)
| ~ ( ~ aElement0(W0)
| ~ ( doDivides0(W0,xa)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xa ) ) ) ) )
| ~ ( aDivisorOf0(W0,xb)
| doDivides0(W0,xb)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xb ) ) ) ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,plain,
^ [W0: $i] :
refl(( ( ~ ( aDivisorOf0(W0,xa)
| ~ ( ~ aElement0(W0)
| ~ ( doDivides0(W0,xa)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xa ) ) ) ) )
| ~ ( aDivisorOf0(W0,xb)
| doDivides0(W0,xb)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xb ) ) )
| ~ ( ~ aElement0(tptp_fun_W1_22(W0))
| ( sdtasdt0(W0,tptp_fun_W1_22(W0)) != xc )
| ~ doDivides0(W0,xc) ) )
<=> ( ~ ( aDivisorOf0(W0,xa)
| ~ ( ~ aElement0(W0)
| ~ ( doDivides0(W0,xa)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xa ) ) ) ) )
| ~ ( aDivisorOf0(W0,xb)
| doDivides0(W0,xb)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xb ) ) )
| ~ ( ~ aElement0(tptp_fun_W1_22(W0))
| ( sdtasdt0(W0,tptp_fun_W1_22(W0)) != xc )
| ~ doDivides0(W0,xc) ) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [W0: $i] :
( ~ ( aDivisorOf0(W0,xa)
| ~ ( ~ aElement0(W0)
| ~ ( doDivides0(W0,xa)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xa ) ) ) ) )
| ~ ( aDivisorOf0(W0,xb)
| doDivides0(W0,xb)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xb ) ) )
| ~ ( ~ aElement0(tptp_fun_W1_22(W0))
| ( sdtasdt0(W0,tptp_fun_W1_22(W0)) != xc )
| ~ doDivides0(W0,xc) ) )
<=> ! [W0: $i] :
( ~ ( aDivisorOf0(W0,xa)
| ~ ( ~ aElement0(W0)
| ~ ( doDivides0(W0,xa)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xa ) ) ) ) )
| ~ ( aDivisorOf0(W0,xb)
| doDivides0(W0,xb)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xb ) ) )
| ~ ( ~ aElement0(tptp_fun_W1_22(W0))
| ( sdtasdt0(W0,tptp_fun_W1_22(W0)) != xc )
| ~ doDivides0(W0,xc) ) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
^ [W0: $i] :
rewrite(( ( ~ ( aDivisorOf0(W0,xa)
| ~ ( ~ aElement0(W0)
| ~ ( doDivides0(W0,xa)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xa ) ) ) ) )
| ~ ( aDivisorOf0(W0,xb)
| doDivides0(W0,xb)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xb ) ) )
| ~ ( ~ aElement0(tptp_fun_W1_22(W0))
| ( sdtasdt0(W0,tptp_fun_W1_22(W0)) != xc )
| ~ doDivides0(W0,xc) ) )
<=> ( ~ ( aDivisorOf0(W0,xa)
| ~ ( ~ aElement0(W0)
| ~ ( doDivides0(W0,xa)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xa ) ) ) ) )
| ~ ( aDivisorOf0(W0,xb)
| doDivides0(W0,xb)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xb ) ) )
| ~ ( ~ aElement0(tptp_fun_W1_22(W0))
| ( sdtasdt0(W0,tptp_fun_W1_22(W0)) != xc )
| ~ doDivides0(W0,xc) ) ) )),
inference(bind,[status(th)],[]) ).
tff(24,plain,
( ! [W0: $i] :
( ~ ( aDivisorOf0(W0,xa)
| ~ ( ~ aElement0(W0)
| ~ ( doDivides0(W0,xa)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xa ) ) ) ) )
| ~ ( aDivisorOf0(W0,xb)
| doDivides0(W0,xb)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xb ) ) )
| ~ ( ~ aElement0(tptp_fun_W1_22(W0))
| ( sdtasdt0(W0,tptp_fun_W1_22(W0)) != xc )
| ~ doDivides0(W0,xc) ) )
<=> ! [W0: $i] :
( ~ ( aDivisorOf0(W0,xa)
| ~ ( ~ aElement0(W0)
| ~ ( doDivides0(W0,xa)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xa ) ) ) ) )
| ~ ( aDivisorOf0(W0,xb)
| doDivides0(W0,xb)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xb ) ) )
| ~ ( ~ aElement0(tptp_fun_W1_22(W0))
| ( sdtasdt0(W0,tptp_fun_W1_22(W0)) != xc )
| ~ doDivides0(W0,xc) ) ) ),
inference(quant_intro,[status(thm)],[23]) ).
tff(25,plain,
( ! [W0: $i] :
( ~ ( aDivisorOf0(W0,xa)
| ~ ( ~ aElement0(W0)
| ~ ( doDivides0(W0,xa)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xa ) ) ) ) )
| ~ ( aDivisorOf0(W0,xb)
| doDivides0(W0,xb)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xb ) ) )
| ~ ( ~ aElement0(tptp_fun_W1_22(W0))
| ( sdtasdt0(W0,tptp_fun_W1_22(W0)) != xc )
| ~ doDivides0(W0,xc) ) )
<=> ! [W0: $i] :
( ~ ( aDivisorOf0(W0,xa)
| ~ ( ~ aElement0(W0)
| ~ ( doDivides0(W0,xa)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xa ) ) ) ) )
| ~ ( aDivisorOf0(W0,xb)
| doDivides0(W0,xb)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xb ) ) )
| ~ ( ~ aElement0(tptp_fun_W1_22(W0))
| ( sdtasdt0(W0,tptp_fun_W1_22(W0)) != xc )
| ~ doDivides0(W0,xc) ) ) ),
inference(transitivity,[status(thm)],[24,22]) ).
tff(26,plain,
^ [W0: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( ~ aElement0(W0)
| ( ~ doDivides0(W0,xa)
& ! [W1: $i] :
~ ( aElement0(W1)
& ( sdtasdt0(W0,W1) = xa ) ) ) )
<=> ( ~ aElement0(W0)
| ~ ( doDivides0(W0,xa)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xa ) ) ) ) )),
( ( ~ aDivisorOf0(W0,xa)
& ( ~ aElement0(W0)
| ( ~ doDivides0(W0,xa)
& ! [W1: $i] :
~ ( aElement0(W1)
& ( sdtasdt0(W0,W1) = xa ) ) ) ) )
<=> ( ~ aDivisorOf0(W0,xa)
& ( ~ aElement0(W0)
| ~ ( doDivides0(W0,xa)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xa ) ) ) ) ) )),
rewrite(( ( ~ aDivisorOf0(W0,xa)
& ( ~ aElement0(W0)
| ~ ( doDivides0(W0,xa)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xa ) ) ) ) )
<=> ~ ( aDivisorOf0(W0,xa)
| ~ ( ~ aElement0(W0)
| ~ ( doDivides0(W0,xa)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xa ) ) ) ) ) )),
( ( ~ aDivisorOf0(W0,xa)
& ( ~ aElement0(W0)
| ( ~ doDivides0(W0,xa)
& ! [W1: $i] :
~ ( aElement0(W1)
& ( sdtasdt0(W0,W1) = xa ) ) ) ) )
<=> ~ ( aDivisorOf0(W0,xa)
| ~ ( ~ aElement0(W0)
| ~ ( doDivides0(W0,xa)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xa ) ) ) ) ) )),
trans(monotonicity(quant_intro(proof_bind(^ [W1: $i] :
trans(monotonicity(rewrite(( ( aElement0(W1)
& ( sdtasdt0(W0,W1) = xb ) )
<=> ~ ( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xb ) ) )),
( ~ ( aElement0(W1)
& ( sdtasdt0(W0,W1) = xb ) )
<=> ~ ~ ( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xb ) ) )),
rewrite(( ~ ~ ( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xb ) )
<=> ( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xb ) ) )),
( ~ ( aElement0(W1)
& ( sdtasdt0(W0,W1) = xb ) )
<=> ( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xb ) ) ))),
( ! [W1: $i] :
~ ( aElement0(W1)
& ( sdtasdt0(W0,W1) = xb ) )
<=> ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xb ) ) )),
( ( ~ aDivisorOf0(W0,xb)
& ~ doDivides0(W0,xb)
& ! [W1: $i] :
~ ( aElement0(W1)
& ( sdtasdt0(W0,W1) = xb ) ) )
<=> ( ~ aDivisorOf0(W0,xb)
& ~ doDivides0(W0,xb)
& ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xb ) ) ) )),
rewrite(( ( ~ aDivisorOf0(W0,xb)
& ~ doDivides0(W0,xb)
& ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xb ) ) )
<=> ~ ( aDivisorOf0(W0,xb)
| doDivides0(W0,xb)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xb ) ) ) )),
( ( ~ aDivisorOf0(W0,xb)
& ~ doDivides0(W0,xb)
& ! [W1: $i] :
~ ( aElement0(W1)
& ( sdtasdt0(W0,W1) = xb ) ) )
<=> ~ ( aDivisorOf0(W0,xb)
| doDivides0(W0,xb)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xb ) ) ) )),
rewrite(( ( aElement0(tptp_fun_W1_22(W0))
& ( sdtasdt0(W0,tptp_fun_W1_22(W0)) = xc )
& doDivides0(W0,xc) )
<=> ~ ( ~ aElement0(tptp_fun_W1_22(W0))
| ( sdtasdt0(W0,tptp_fun_W1_22(W0)) != xc )
| ~ doDivides0(W0,xc) ) )),
( ( ( ~ aDivisorOf0(W0,xa)
& ( ~ aElement0(W0)
| ( ~ doDivides0(W0,xa)
& ! [W1: $i] :
~ ( aElement0(W1)
& ( sdtasdt0(W0,W1) = xa ) ) ) ) )
| ( ~ aDivisorOf0(W0,xb)
& ~ doDivides0(W0,xb)
& ! [W1: $i] :
~ ( aElement0(W1)
& ( sdtasdt0(W0,W1) = xb ) ) )
| ( aElement0(tptp_fun_W1_22(W0))
& ( sdtasdt0(W0,tptp_fun_W1_22(W0)) = xc )
& doDivides0(W0,xc) ) )
<=> ( ~ ( aDivisorOf0(W0,xa)
| ~ ( ~ aElement0(W0)
| ~ ( doDivides0(W0,xa)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xa ) ) ) ) )
| ~ ( aDivisorOf0(W0,xb)
| doDivides0(W0,xb)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xb ) ) )
| ~ ( ~ aElement0(tptp_fun_W1_22(W0))
| ( sdtasdt0(W0,tptp_fun_W1_22(W0)) != xc )
| ~ doDivides0(W0,xc) ) ) )),
rewrite(( ( ~ ( aDivisorOf0(W0,xa)
| ~ ( ~ aElement0(W0)
| ~ ( doDivides0(W0,xa)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xa ) ) ) ) )
| ~ ( aDivisorOf0(W0,xb)
| doDivides0(W0,xb)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xb ) ) )
| ~ ( ~ aElement0(tptp_fun_W1_22(W0))
| ( sdtasdt0(W0,tptp_fun_W1_22(W0)) != xc )
| ~ doDivides0(W0,xc) ) )
<=> ( ~ ( aDivisorOf0(W0,xa)
| ~ ( ~ aElement0(W0)
| ~ ( doDivides0(W0,xa)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xa ) ) ) ) )
| ~ ( aDivisorOf0(W0,xb)
| doDivides0(W0,xb)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xb ) ) )
| ~ ( ~ aElement0(tptp_fun_W1_22(W0))
| ( sdtasdt0(W0,tptp_fun_W1_22(W0)) != xc )
| ~ doDivides0(W0,xc) ) ) )),
( ( ( ~ aDivisorOf0(W0,xa)
& ( ~ aElement0(W0)
| ( ~ doDivides0(W0,xa)
& ! [W1: $i] :
~ ( aElement0(W1)
& ( sdtasdt0(W0,W1) = xa ) ) ) ) )
| ( ~ aDivisorOf0(W0,xb)
& ~ doDivides0(W0,xb)
& ! [W1: $i] :
~ ( aElement0(W1)
& ( sdtasdt0(W0,W1) = xb ) ) )
| ( aElement0(tptp_fun_W1_22(W0))
& ( sdtasdt0(W0,tptp_fun_W1_22(W0)) = xc )
& doDivides0(W0,xc) ) )
<=> ( ~ ( aDivisorOf0(W0,xa)
| ~ ( ~ aElement0(W0)
| ~ ( doDivides0(W0,xa)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xa ) ) ) ) )
| ~ ( aDivisorOf0(W0,xb)
| doDivides0(W0,xb)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xb ) ) )
| ~ ( ~ aElement0(tptp_fun_W1_22(W0))
| ( sdtasdt0(W0,tptp_fun_W1_22(W0)) != xc )
| ~ doDivides0(W0,xc) ) ) )),
inference(bind,[status(th)],[]) ).
tff(27,plain,
( ! [W0: $i] :
( ( ~ aDivisorOf0(W0,xa)
& ( ~ aElement0(W0)
| ( ~ doDivides0(W0,xa)
& ! [W1: $i] :
~ ( aElement0(W1)
& ( sdtasdt0(W0,W1) = xa ) ) ) ) )
| ( ~ aDivisorOf0(W0,xb)
& ~ doDivides0(W0,xb)
& ! [W1: $i] :
~ ( aElement0(W1)
& ( sdtasdt0(W0,W1) = xb ) ) )
| ( aElement0(tptp_fun_W1_22(W0))
& ( sdtasdt0(W0,tptp_fun_W1_22(W0)) = xc )
& doDivides0(W0,xc) ) )
<=> ! [W0: $i] :
( ~ ( aDivisorOf0(W0,xa)
| ~ ( ~ aElement0(W0)
| ~ ( doDivides0(W0,xa)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xa ) ) ) ) )
| ~ ( aDivisorOf0(W0,xb)
| doDivides0(W0,xb)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xb ) ) )
| ~ ( ~ aElement0(tptp_fun_W1_22(W0))
| ( sdtasdt0(W0,tptp_fun_W1_22(W0)) != xc )
| ~ doDivides0(W0,xc) ) ) ),
inference(quant_intro,[status(thm)],[26]) ).
tff(28,plain,
^ [W0: $i] :
trans(monotonicity(monotonicity(monotonicity(monotonicity(rewrite(( ( ~ doDivides0(W0,xa)
& ! [W1: $i] :
~ ( aElement0(W1)
& ( sdtasdt0(W0,W1) = xa ) ) )
<=> ( ~ doDivides0(W0,xa)
& ! [W1: $i] :
~ ( aElement0(W1)
& ( sdtasdt0(W0,W1) = xa ) ) ) )),
( ( ~ aElement0(W0)
| ( ~ doDivides0(W0,xa)
& ! [W1: $i] :
~ ( aElement0(W1)
& ( sdtasdt0(W0,W1) = xa ) ) ) )
<=> ( ~ aElement0(W0)
| ( ~ doDivides0(W0,xa)
& ! [W1: $i] :
~ ( aElement0(W1)
& ( sdtasdt0(W0,W1) = xa ) ) ) ) )),
( ( ~ aDivisorOf0(W0,xa)
& ( ~ aElement0(W0)
| ( ~ doDivides0(W0,xa)
& ! [W1: $i] :
~ ( aElement0(W1)
& ( sdtasdt0(W0,W1) = xa ) ) ) ) )
<=> ( ~ aDivisorOf0(W0,xa)
& ( ~ aElement0(W0)
| ( ~ doDivides0(W0,xa)
& ! [W1: $i] :
~ ( aElement0(W1)
& ( sdtasdt0(W0,W1) = xa ) ) ) ) ) )),
rewrite(( ( ~ aDivisorOf0(W0,xb)
& ~ doDivides0(W0,xb)
& ! [W1: $i] :
~ ( aElement0(W1)
& ( sdtasdt0(W0,W1) = xb ) ) )
<=> ( ~ aDivisorOf0(W0,xb)
& ~ doDivides0(W0,xb)
& ! [W1: $i] :
~ ( aElement0(W1)
& ( sdtasdt0(W0,W1) = xb ) ) ) )),
( ( ( ~ aDivisorOf0(W0,xa)
& ( ~ aElement0(W0)
| ( ~ doDivides0(W0,xa)
& ! [W1: $i] :
~ ( aElement0(W1)
& ( sdtasdt0(W0,W1) = xa ) ) ) ) )
| ( ~ aDivisorOf0(W0,xb)
& ~ doDivides0(W0,xb)
& ! [W1: $i] :
~ ( aElement0(W1)
& ( sdtasdt0(W0,W1) = xb ) ) ) )
<=> ( ( ~ aDivisorOf0(W0,xa)
& ( ~ aElement0(W0)
| ( ~ doDivides0(W0,xa)
& ! [W1: $i] :
~ ( aElement0(W1)
& ( sdtasdt0(W0,W1) = xa ) ) ) ) )
| ( ~ aDivisorOf0(W0,xb)
& ~ doDivides0(W0,xb)
& ! [W1: $i] :
~ ( aElement0(W1)
& ( sdtasdt0(W0,W1) = xb ) ) ) ) )),
rewrite(( ( aElement0(tptp_fun_W1_22(W0))
& ( sdtasdt0(W0,tptp_fun_W1_22(W0)) = xc )
& doDivides0(W0,xc) )
<=> ( aElement0(tptp_fun_W1_22(W0))
& ( sdtasdt0(W0,tptp_fun_W1_22(W0)) = xc )
& doDivides0(W0,xc) ) )),
( ( ( ~ aDivisorOf0(W0,xa)
& ( ~ aElement0(W0)
| ( ~ doDivides0(W0,xa)
& ! [W1: $i] :
~ ( aElement0(W1)
& ( sdtasdt0(W0,W1) = xa ) ) ) ) )
| ( ~ aDivisorOf0(W0,xb)
& ~ doDivides0(W0,xb)
& ! [W1: $i] :
~ ( aElement0(W1)
& ( sdtasdt0(W0,W1) = xb ) ) )
| ( aElement0(tptp_fun_W1_22(W0))
& ( sdtasdt0(W0,tptp_fun_W1_22(W0)) = xc )
& doDivides0(W0,xc) ) )
<=> ( ( ~ aDivisorOf0(W0,xa)
& ( ~ aElement0(W0)
| ( ~ doDivides0(W0,xa)
& ! [W1: $i] :
~ ( aElement0(W1)
& ( sdtasdt0(W0,W1) = xa ) ) ) ) )
| ( ~ aDivisorOf0(W0,xb)
& ~ doDivides0(W0,xb)
& ! [W1: $i] :
~ ( aElement0(W1)
& ( sdtasdt0(W0,W1) = xb ) ) )
| ( aElement0(tptp_fun_W1_22(W0))
& ( sdtasdt0(W0,tptp_fun_W1_22(W0)) = xc )
& doDivides0(W0,xc) ) ) )),
rewrite(( ( ( ~ aDivisorOf0(W0,xa)
& ( ~ aElement0(W0)
| ( ~ doDivides0(W0,xa)
& ! [W1: $i] :
~ ( aElement0(W1)
& ( sdtasdt0(W0,W1) = xa ) ) ) ) )
| ( ~ aDivisorOf0(W0,xb)
& ~ doDivides0(W0,xb)
& ! [W1: $i] :
~ ( aElement0(W1)
& ( sdtasdt0(W0,W1) = xb ) ) )
| ( aElement0(tptp_fun_W1_22(W0))
& ( sdtasdt0(W0,tptp_fun_W1_22(W0)) = xc )
& doDivides0(W0,xc) ) )
<=> ( ( ~ aDivisorOf0(W0,xa)
& ( ~ aElement0(W0)
| ( ~ doDivides0(W0,xa)
& ! [W1: $i] :
~ ( aElement0(W1)
& ( sdtasdt0(W0,W1) = xa ) ) ) ) )
| ( ~ aDivisorOf0(W0,xb)
& ~ doDivides0(W0,xb)
& ! [W1: $i] :
~ ( aElement0(W1)
& ( sdtasdt0(W0,W1) = xb ) ) )
| ( aElement0(tptp_fun_W1_22(W0))
& ( sdtasdt0(W0,tptp_fun_W1_22(W0)) = xc )
& doDivides0(W0,xc) ) ) )),
( ( ( ~ aDivisorOf0(W0,xa)
& ( ~ aElement0(W0)
| ( ~ doDivides0(W0,xa)
& ! [W1: $i] :
~ ( aElement0(W1)
& ( sdtasdt0(W0,W1) = xa ) ) ) ) )
| ( ~ aDivisorOf0(W0,xb)
& ~ doDivides0(W0,xb)
& ! [W1: $i] :
~ ( aElement0(W1)
& ( sdtasdt0(W0,W1) = xb ) ) )
| ( aElement0(tptp_fun_W1_22(W0))
& ( sdtasdt0(W0,tptp_fun_W1_22(W0)) = xc )
& doDivides0(W0,xc) ) )
<=> ( ( ~ aDivisorOf0(W0,xa)
& ( ~ aElement0(W0)
| ( ~ doDivides0(W0,xa)
& ! [W1: $i] :
~ ( aElement0(W1)
& ( sdtasdt0(W0,W1) = xa ) ) ) ) )
| ( ~ aDivisorOf0(W0,xb)
& ~ doDivides0(W0,xb)
& ! [W1: $i] :
~ ( aElement0(W1)
& ( sdtasdt0(W0,W1) = xb ) ) )
| ( aElement0(tptp_fun_W1_22(W0))
& ( sdtasdt0(W0,tptp_fun_W1_22(W0)) = xc )
& doDivides0(W0,xc) ) ) )),
inference(bind,[status(th)],[]) ).
tff(29,plain,
( ! [W0: $i] :
( ( ~ aDivisorOf0(W0,xa)
& ( ~ aElement0(W0)
| ( ~ doDivides0(W0,xa)
& ! [W1: $i] :
~ ( aElement0(W1)
& ( sdtasdt0(W0,W1) = xa ) ) ) ) )
| ( ~ aDivisorOf0(W0,xb)
& ~ doDivides0(W0,xb)
& ! [W1: $i] :
~ ( aElement0(W1)
& ( sdtasdt0(W0,W1) = xb ) ) )
| ( aElement0(tptp_fun_W1_22(W0))
& ( sdtasdt0(W0,tptp_fun_W1_22(W0)) = xc )
& doDivides0(W0,xc) ) )
<=> ! [W0: $i] :
( ( ~ aDivisorOf0(W0,xa)
& ( ~ aElement0(W0)
| ( ~ doDivides0(W0,xa)
& ! [W1: $i] :
~ ( aElement0(W1)
& ( sdtasdt0(W0,W1) = xa ) ) ) ) )
| ( ~ aDivisorOf0(W0,xb)
& ~ doDivides0(W0,xb)
& ! [W1: $i] :
~ ( aElement0(W1)
& ( sdtasdt0(W0,W1) = xb ) ) )
| ( aElement0(tptp_fun_W1_22(W0))
& ( sdtasdt0(W0,tptp_fun_W1_22(W0)) = xc )
& doDivides0(W0,xc) ) ) ),
inference(quant_intro,[status(thm)],[28]) ).
tff(30,plain,
( ! [W0: $i] :
( ~ ( ( aDivisorOf0(W0,xa)
| ( aElement0(W0)
& ( doDivides0(W0,xa)
| ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(W0,W1) = xa ) ) ) ) )
& ( aDivisorOf0(W0,xb)
| doDivides0(W0,xb)
| ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(W0,W1) = xb ) ) ) )
| ( ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(W0,W1) = xc ) )
& doDivides0(W0,xc) ) )
<=> ! [W0: $i] :
( ~ ( ( aDivisorOf0(W0,xa)
| ( aElement0(W0)
& ( doDivides0(W0,xa)
| ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(W0,W1) = xa ) ) ) ) )
& ( aDivisorOf0(W0,xb)
| doDivides0(W0,xb)
| ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(W0,W1) = xb ) ) ) )
| ( ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(W0,W1) = xc ) )
& doDivides0(W0,xc) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(31,plain,
^ [W0: $i] :
trans(monotonicity(rewrite(( ( ( ( aElement0(W0)
& ( ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(W0,W1) = xa ) )
| doDivides0(W0,xa) ) )
| aDivisorOf0(W0,xa) )
& ( ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(W0,W1) = xb ) )
| doDivides0(W0,xb)
| aDivisorOf0(W0,xb) ) )
<=> ( ( aDivisorOf0(W0,xa)
| ( aElement0(W0)
& ( doDivides0(W0,xa)
| ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(W0,W1) = xa ) ) ) ) )
& ( aDivisorOf0(W0,xb)
| doDivides0(W0,xb)
| ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(W0,W1) = xb ) ) ) ) )),
rewrite(( ( ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(W0,W1) = xc ) )
& doDivides0(W0,xc) )
<=> ( ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(W0,W1) = xc ) )
& doDivides0(W0,xc) ) )),
( ( ( ( ( aElement0(W0)
& ( ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(W0,W1) = xa ) )
| doDivides0(W0,xa) ) )
| aDivisorOf0(W0,xa) )
& ( ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(W0,W1) = xb ) )
| doDivides0(W0,xb)
| aDivisorOf0(W0,xb) ) )
=> ( ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(W0,W1) = xc ) )
& doDivides0(W0,xc) ) )
<=> ( ( ( aDivisorOf0(W0,xa)
| ( aElement0(W0)
& ( doDivides0(W0,xa)
| ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(W0,W1) = xa ) ) ) ) )
& ( aDivisorOf0(W0,xb)
| doDivides0(W0,xb)
| ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(W0,W1) = xb ) ) ) )
=> ( ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(W0,W1) = xc ) )
& doDivides0(W0,xc) ) ) )),
rewrite(( ( ( ( aDivisorOf0(W0,xa)
| ( aElement0(W0)
& ( doDivides0(W0,xa)
| ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(W0,W1) = xa ) ) ) ) )
& ( aDivisorOf0(W0,xb)
| doDivides0(W0,xb)
| ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(W0,W1) = xb ) ) ) )
=> ( ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(W0,W1) = xc ) )
& doDivides0(W0,xc) ) )
<=> ( ~ ( ( aDivisorOf0(W0,xa)
| ( aElement0(W0)
& ( doDivides0(W0,xa)
| ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(W0,W1) = xa ) ) ) ) )
& ( aDivisorOf0(W0,xb)
| doDivides0(W0,xb)
| ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(W0,W1) = xb ) ) ) )
| ( ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(W0,W1) = xc ) )
& doDivides0(W0,xc) ) ) )),
( ( ( ( ( aElement0(W0)
& ( ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(W0,W1) = xa ) )
| doDivides0(W0,xa) ) )
| aDivisorOf0(W0,xa) )
& ( ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(W0,W1) = xb ) )
| doDivides0(W0,xb)
| aDivisorOf0(W0,xb) ) )
=> ( ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(W0,W1) = xc ) )
& doDivides0(W0,xc) ) )
<=> ( ~ ( ( aDivisorOf0(W0,xa)
| ( aElement0(W0)
& ( doDivides0(W0,xa)
| ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(W0,W1) = xa ) ) ) ) )
& ( aDivisorOf0(W0,xb)
| doDivides0(W0,xb)
| ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(W0,W1) = xb ) ) ) )
| ( ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(W0,W1) = xc ) )
& doDivides0(W0,xc) ) ) )),
inference(bind,[status(th)],[]) ).
tff(32,plain,
( ! [W0: $i] :
( ( ( ( aElement0(W0)
& ( ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(W0,W1) = xa ) )
| doDivides0(W0,xa) ) )
| aDivisorOf0(W0,xa) )
& ( ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(W0,W1) = xb ) )
| doDivides0(W0,xb)
| aDivisorOf0(W0,xb) ) )
=> ( ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(W0,W1) = xc ) )
& doDivides0(W0,xc) ) )
<=> ! [W0: $i] :
( ~ ( ( aDivisorOf0(W0,xa)
| ( aElement0(W0)
& ( doDivides0(W0,xa)
| ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(W0,W1) = xa ) ) ) ) )
& ( aDivisorOf0(W0,xb)
| doDivides0(W0,xb)
| ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(W0,W1) = xb ) ) ) )
| ( ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(W0,W1) = xc ) )
& doDivides0(W0,xc) ) ) ),
inference(quant_intro,[status(thm)],[31]) ).
tff(33,axiom,
( aElement0(xc)
& ? [W0: $i] :
( aElement0(W0)
& ( sdtasdt0(xc,W0) = xa ) )
& doDivides0(xc,xa)
& aDivisorOf0(xc,xa)
& aElement0(xc)
& ? [W0: $i] :
( aElement0(W0)
& ( sdtasdt0(xc,W0) = xb ) )
& doDivides0(xc,xb)
& aDivisorOf0(xc,xb)
& ! [W0: $i] :
( ( ( ( aElement0(W0)
& ( ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(W0,W1) = xa ) )
| doDivides0(W0,xa) ) )
| aDivisorOf0(W0,xa) )
& ( ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(W0,W1) = xb ) )
| doDivides0(W0,xb)
| aDivisorOf0(W0,xb) ) )
=> ( ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(W0,W1) = xc ) )
& doDivides0(W0,xc) ) )
& aGcdOfAnd0(xc,xa,xb) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2129) ).
tff(34,plain,
( aElement0(xc)
& ? [W0: $i] :
( aElement0(W0)
& ( sdtasdt0(xc,W0) = xa ) )
& doDivides0(xc,xa)
& aDivisorOf0(xc,xa)
& aElement0(xc)
& ? [W0: $i] :
( aElement0(W0)
& ( sdtasdt0(xc,W0) = xb ) )
& doDivides0(xc,xb)
& aDivisorOf0(xc,xb)
& ! [W0: $i] :
( ( ( ( aElement0(W0)
& ( ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(W0,W1) = xa ) )
| doDivides0(W0,xa) ) )
| aDivisorOf0(W0,xa) )
& ( ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(W0,W1) = xb ) )
| doDivides0(W0,xb)
| aDivisorOf0(W0,xb) ) )
=> ( ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(W0,W1) = xc ) )
& doDivides0(W0,xc) ) ) ),
inference(and_elim,[status(thm)],[33]) ).
tff(35,plain,
! [W0: $i] :
( ( ( ( aElement0(W0)
& ( ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(W0,W1) = xa ) )
| doDivides0(W0,xa) ) )
| aDivisorOf0(W0,xa) )
& ( ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(W0,W1) = xb ) )
| doDivides0(W0,xb)
| aDivisorOf0(W0,xb) ) )
=> ( ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(W0,W1) = xc ) )
& doDivides0(W0,xc) ) ),
inference(and_elim,[status(thm)],[34]) ).
tff(36,plain,
! [W0: $i] :
( ~ ( ( aDivisorOf0(W0,xa)
| ( aElement0(W0)
& ( doDivides0(W0,xa)
| ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(W0,W1) = xa ) ) ) ) )
& ( aDivisorOf0(W0,xb)
| doDivides0(W0,xb)
| ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(W0,W1) = xb ) ) ) )
| ( ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(W0,W1) = xc ) )
& doDivides0(W0,xc) ) ),
inference(modus_ponens,[status(thm)],[35,32]) ).
tff(37,plain,
! [W0: $i] :
( ~ ( ( aDivisorOf0(W0,xa)
| ( aElement0(W0)
& ( doDivides0(W0,xa)
| ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(W0,W1) = xa ) ) ) ) )
& ( aDivisorOf0(W0,xb)
| doDivides0(W0,xb)
| ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(W0,W1) = xb ) ) ) )
| ( ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(W0,W1) = xc ) )
& doDivides0(W0,xc) ) ),
inference(modus_ponens,[status(thm)],[36,30]) ).
tff(38,plain,
! [W0: $i] :
( ( ~ aDivisorOf0(W0,xa)
& ( ~ aElement0(W0)
| ( ~ doDivides0(W0,xa)
& ! [W1: $i] :
~ ( aElement0(W1)
& ( sdtasdt0(W0,W1) = xa ) ) ) ) )
| ( ~ aDivisorOf0(W0,xb)
& ~ doDivides0(W0,xb)
& ! [W1: $i] :
~ ( aElement0(W1)
& ( sdtasdt0(W0,W1) = xb ) ) )
| ( aElement0(tptp_fun_W1_22(W0))
& ( sdtasdt0(W0,tptp_fun_W1_22(W0)) = xc )
& doDivides0(W0,xc) ) ),
inference(skolemize,[status(sab)],[37]) ).
tff(39,plain,
! [W0: $i] :
( ( ~ aDivisorOf0(W0,xa)
& ( ~ aElement0(W0)
| ( ~ doDivides0(W0,xa)
& ! [W1: $i] :
~ ( aElement0(W1)
& ( sdtasdt0(W0,W1) = xa ) ) ) ) )
| ( ~ aDivisorOf0(W0,xb)
& ~ doDivides0(W0,xb)
& ! [W1: $i] :
~ ( aElement0(W1)
& ( sdtasdt0(W0,W1) = xb ) ) )
| ( aElement0(tptp_fun_W1_22(W0))
& ( sdtasdt0(W0,tptp_fun_W1_22(W0)) = xc )
& doDivides0(W0,xc) ) ),
inference(modus_ponens,[status(thm)],[38,29]) ).
tff(40,plain,
! [W0: $i] :
( ~ ( aDivisorOf0(W0,xa)
| ~ ( ~ aElement0(W0)
| ~ ( doDivides0(W0,xa)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xa ) ) ) ) )
| ~ ( aDivisorOf0(W0,xb)
| doDivides0(W0,xb)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xb ) ) )
| ~ ( ~ aElement0(tptp_fun_W1_22(W0))
| ( sdtasdt0(W0,tptp_fun_W1_22(W0)) != xc )
| ~ doDivides0(W0,xc) ) ),
inference(modus_ponens,[status(thm)],[39,27]) ).
tff(41,plain,
! [W0: $i] :
( ~ ( aDivisorOf0(W0,xa)
| ~ ( ~ aElement0(W0)
| ~ ( doDivides0(W0,xa)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xa ) ) ) ) )
| ~ ( aDivisorOf0(W0,xb)
| doDivides0(W0,xb)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xb ) ) )
| ~ ( ~ aElement0(tptp_fun_W1_22(W0))
| ( sdtasdt0(W0,tptp_fun_W1_22(W0)) != xc )
| ~ doDivides0(W0,xc) ) ),
inference(modus_ponens,[status(thm)],[40,25]) ).
tff(42,plain,
! [W0: $i] :
( ~ ( ~ aElement0(tptp_fun_W1_22(W0))
| ( sdtasdt0(W0,tptp_fun_W1_22(W0)) != xc )
| ~ doDivides0(W0,xc) )
| ~ ( aDivisorOf0(W0,xa)
| ~ ( ~ aElement0(W0)
| ~ ( doDivides0(W0,xa)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xa ) ) ) ) )
| ~ ( aDivisorOf0(W0,xb)
| doDivides0(W0,xb)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xb ) ) ) ),
inference(modus_ponens,[status(thm)],[41,20]) ).
tff(43,plain,
( ( ~ ! [W0: $i] :
( ~ ( ~ aElement0(tptp_fun_W1_22(W0))
| ( sdtasdt0(W0,tptp_fun_W1_22(W0)) != xc )
| ~ doDivides0(W0,xc) )
| ~ ( aDivisorOf0(W0,xa)
| ~ ( ~ aElement0(W0)
| ~ ( doDivides0(W0,xa)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xa ) ) ) ) )
| ~ ( aDivisorOf0(W0,xb)
| doDivides0(W0,xb)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xb ) ) ) )
| ~ ( aDivisorOf0(xu,xa)
| ~ ( ~ aElement0(xu)
| ~ ( doDivides0(xu,xa)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(xu,W1) != xa ) ) ) ) )
| ~ ( ~ doDivides0(xu,xc)
| ( sdtasdt0(xu,tptp_fun_W1_22(xu)) != xc )
| ~ aElement0(tptp_fun_W1_22(xu)) )
| ~ ( doDivides0(xu,xb)
| aDivisorOf0(xu,xb)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(xu,W1) != xb ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ ( ~ aElement0(tptp_fun_W1_22(W0))
| ( sdtasdt0(W0,tptp_fun_W1_22(W0)) != xc )
| ~ doDivides0(W0,xc) )
| ~ ( aDivisorOf0(W0,xa)
| ~ ( ~ aElement0(W0)
| ~ ( doDivides0(W0,xa)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xa ) ) ) ) )
| ~ ( aDivisorOf0(W0,xb)
| doDivides0(W0,xb)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xb ) ) ) )
| ~ ( aDivisorOf0(xu,xa)
| ~ ( ~ aElement0(xu)
| ~ ( doDivides0(xu,xa)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(xu,W1) != xa ) ) ) ) )
| ~ ( ~ doDivides0(xu,xc)
| ( sdtasdt0(xu,tptp_fun_W1_22(xu)) != xc )
| ~ aElement0(tptp_fun_W1_22(xu)) )
| ~ ( doDivides0(xu,xb)
| aDivisorOf0(xu,xb)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(xu,W1) != xb ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(44,plain,
( ( ~ ( ~ doDivides0(xu,xc)
| ( sdtasdt0(xu,tptp_fun_W1_22(xu)) != xc )
| ~ aElement0(tptp_fun_W1_22(xu)) )
| ~ ( aDivisorOf0(xu,xa)
| ~ ( ~ aElement0(xu)
| ~ ( doDivides0(xu,xa)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(xu,W1) != xa ) ) ) ) )
| ~ ( doDivides0(xu,xb)
| aDivisorOf0(xu,xb)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(xu,W1) != xb ) ) ) )
<=> ( ~ ( aDivisorOf0(xu,xa)
| ~ ( ~ aElement0(xu)
| ~ ( doDivides0(xu,xa)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(xu,W1) != xa ) ) ) ) )
| ~ ( ~ doDivides0(xu,xc)
| ( sdtasdt0(xu,tptp_fun_W1_22(xu)) != xc )
| ~ aElement0(tptp_fun_W1_22(xu)) )
| ~ ( doDivides0(xu,xb)
| aDivisorOf0(xu,xb)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(xu,W1) != xb ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(45,plain,
( ~ ( aDivisorOf0(xu,xb)
| doDivides0(xu,xb)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(xu,W1) != xb ) ) )
<=> ~ ( doDivides0(xu,xb)
| aDivisorOf0(xu,xb)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(xu,W1) != xb ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(46,plain,
( ~ ( aDivisorOf0(xu,xa)
| ~ ( ~ aElement0(xu)
| ~ ( doDivides0(xu,xa)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(xu,W1) != xa ) ) ) ) )
<=> ~ ( aDivisorOf0(xu,xa)
| ~ ( ~ aElement0(xu)
| ~ ( doDivides0(xu,xa)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(xu,W1) != xa ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,plain,
( ~ ( ~ aElement0(tptp_fun_W1_22(xu))
| ( sdtasdt0(xu,tptp_fun_W1_22(xu)) != xc )
| ~ doDivides0(xu,xc) )
<=> ~ ( ~ doDivides0(xu,xc)
| ( sdtasdt0(xu,tptp_fun_W1_22(xu)) != xc )
| ~ aElement0(tptp_fun_W1_22(xu)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(48,plain,
( ( ~ ( ~ aElement0(tptp_fun_W1_22(xu))
| ( sdtasdt0(xu,tptp_fun_W1_22(xu)) != xc )
| ~ doDivides0(xu,xc) )
| ~ ( aDivisorOf0(xu,xa)
| ~ ( ~ aElement0(xu)
| ~ ( doDivides0(xu,xa)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(xu,W1) != xa ) ) ) ) )
| ~ ( aDivisorOf0(xu,xb)
| doDivides0(xu,xb)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(xu,W1) != xb ) ) ) )
<=> ( ~ ( ~ doDivides0(xu,xc)
| ( sdtasdt0(xu,tptp_fun_W1_22(xu)) != xc )
| ~ aElement0(tptp_fun_W1_22(xu)) )
| ~ ( aDivisorOf0(xu,xa)
| ~ ( ~ aElement0(xu)
| ~ ( doDivides0(xu,xa)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(xu,W1) != xa ) ) ) ) )
| ~ ( doDivides0(xu,xb)
| aDivisorOf0(xu,xb)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(xu,W1) != xb ) ) ) ) ),
inference(monotonicity,[status(thm)],[47,46,45]) ).
tff(49,plain,
( ( ~ ( ~ aElement0(tptp_fun_W1_22(xu))
| ( sdtasdt0(xu,tptp_fun_W1_22(xu)) != xc )
| ~ doDivides0(xu,xc) )
| ~ ( aDivisorOf0(xu,xa)
| ~ ( ~ aElement0(xu)
| ~ ( doDivides0(xu,xa)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(xu,W1) != xa ) ) ) ) )
| ~ ( aDivisorOf0(xu,xb)
| doDivides0(xu,xb)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(xu,W1) != xb ) ) ) )
<=> ( ~ ( aDivisorOf0(xu,xa)
| ~ ( ~ aElement0(xu)
| ~ ( doDivides0(xu,xa)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(xu,W1) != xa ) ) ) ) )
| ~ ( ~ doDivides0(xu,xc)
| ( sdtasdt0(xu,tptp_fun_W1_22(xu)) != xc )
| ~ aElement0(tptp_fun_W1_22(xu)) )
| ~ ( doDivides0(xu,xb)
| aDivisorOf0(xu,xb)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(xu,W1) != xb ) ) ) ) ),
inference(transitivity,[status(thm)],[48,44]) ).
tff(50,plain,
( ( ~ ! [W0: $i] :
( ~ ( ~ aElement0(tptp_fun_W1_22(W0))
| ( sdtasdt0(W0,tptp_fun_W1_22(W0)) != xc )
| ~ doDivides0(W0,xc) )
| ~ ( aDivisorOf0(W0,xa)
| ~ ( ~ aElement0(W0)
| ~ ( doDivides0(W0,xa)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xa ) ) ) ) )
| ~ ( aDivisorOf0(W0,xb)
| doDivides0(W0,xb)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xb ) ) ) )
| ~ ( ~ aElement0(tptp_fun_W1_22(xu))
| ( sdtasdt0(xu,tptp_fun_W1_22(xu)) != xc )
| ~ doDivides0(xu,xc) )
| ~ ( aDivisorOf0(xu,xa)
| ~ ( ~ aElement0(xu)
| ~ ( doDivides0(xu,xa)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(xu,W1) != xa ) ) ) ) )
| ~ ( aDivisorOf0(xu,xb)
| doDivides0(xu,xb)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(xu,W1) != xb ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ ( ~ aElement0(tptp_fun_W1_22(W0))
| ( sdtasdt0(W0,tptp_fun_W1_22(W0)) != xc )
| ~ doDivides0(W0,xc) )
| ~ ( aDivisorOf0(W0,xa)
| ~ ( ~ aElement0(W0)
| ~ ( doDivides0(W0,xa)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xa ) ) ) ) )
| ~ ( aDivisorOf0(W0,xb)
| doDivides0(W0,xb)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xb ) ) ) )
| ~ ( aDivisorOf0(xu,xa)
| ~ ( ~ aElement0(xu)
| ~ ( doDivides0(xu,xa)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(xu,W1) != xa ) ) ) ) )
| ~ ( ~ doDivides0(xu,xc)
| ( sdtasdt0(xu,tptp_fun_W1_22(xu)) != xc )
| ~ aElement0(tptp_fun_W1_22(xu)) )
| ~ ( doDivides0(xu,xb)
| aDivisorOf0(xu,xb)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(xu,W1) != xb ) ) ) ) ),
inference(monotonicity,[status(thm)],[49]) ).
tff(51,plain,
( ( ~ ! [W0: $i] :
( ~ ( ~ aElement0(tptp_fun_W1_22(W0))
| ( sdtasdt0(W0,tptp_fun_W1_22(W0)) != xc )
| ~ doDivides0(W0,xc) )
| ~ ( aDivisorOf0(W0,xa)
| ~ ( ~ aElement0(W0)
| ~ ( doDivides0(W0,xa)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xa ) ) ) ) )
| ~ ( aDivisorOf0(W0,xb)
| doDivides0(W0,xb)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xb ) ) ) )
| ~ ( ~ aElement0(tptp_fun_W1_22(xu))
| ( sdtasdt0(xu,tptp_fun_W1_22(xu)) != xc )
| ~ doDivides0(xu,xc) )
| ~ ( aDivisorOf0(xu,xa)
| ~ ( ~ aElement0(xu)
| ~ ( doDivides0(xu,xa)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(xu,W1) != xa ) ) ) ) )
| ~ ( aDivisorOf0(xu,xb)
| doDivides0(xu,xb)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(xu,W1) != xb ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ ( ~ aElement0(tptp_fun_W1_22(W0))
| ( sdtasdt0(W0,tptp_fun_W1_22(W0)) != xc )
| ~ doDivides0(W0,xc) )
| ~ ( aDivisorOf0(W0,xa)
| ~ ( ~ aElement0(W0)
| ~ ( doDivides0(W0,xa)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xa ) ) ) ) )
| ~ ( aDivisorOf0(W0,xb)
| doDivides0(W0,xb)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xb ) ) ) )
| ~ ( aDivisorOf0(xu,xa)
| ~ ( ~ aElement0(xu)
| ~ ( doDivides0(xu,xa)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(xu,W1) != xa ) ) ) ) )
| ~ ( ~ doDivides0(xu,xc)
| ( sdtasdt0(xu,tptp_fun_W1_22(xu)) != xc )
| ~ aElement0(tptp_fun_W1_22(xu)) )
| ~ ( doDivides0(xu,xb)
| aDivisorOf0(xu,xb)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(xu,W1) != xb ) ) ) ) ),
inference(transitivity,[status(thm)],[50,43]) ).
tff(52,plain,
( ~ ! [W0: $i] :
( ~ ( ~ aElement0(tptp_fun_W1_22(W0))
| ( sdtasdt0(W0,tptp_fun_W1_22(W0)) != xc )
| ~ doDivides0(W0,xc) )
| ~ ( aDivisorOf0(W0,xa)
| ~ ( ~ aElement0(W0)
| ~ ( doDivides0(W0,xa)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xa ) ) ) ) )
| ~ ( aDivisorOf0(W0,xb)
| doDivides0(W0,xb)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xb ) ) ) )
| ~ ( ~ aElement0(tptp_fun_W1_22(xu))
| ( sdtasdt0(xu,tptp_fun_W1_22(xu)) != xc )
| ~ doDivides0(xu,xc) )
| ~ ( aDivisorOf0(xu,xa)
| ~ ( ~ aElement0(xu)
| ~ ( doDivides0(xu,xa)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(xu,W1) != xa ) ) ) ) )
| ~ ( aDivisorOf0(xu,xb)
| doDivides0(xu,xb)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(xu,W1) != xb ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(53,plain,
( ~ ! [W0: $i] :
( ~ ( ~ aElement0(tptp_fun_W1_22(W0))
| ( sdtasdt0(W0,tptp_fun_W1_22(W0)) != xc )
| ~ doDivides0(W0,xc) )
| ~ ( aDivisorOf0(W0,xa)
| ~ ( ~ aElement0(W0)
| ~ ( doDivides0(W0,xa)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xa ) ) ) ) )
| ~ ( aDivisorOf0(W0,xb)
| doDivides0(W0,xb)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(W0,W1) != xb ) ) ) )
| ~ ( aDivisorOf0(xu,xa)
| ~ ( ~ aElement0(xu)
| ~ ( doDivides0(xu,xa)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(xu,W1) != xa ) ) ) ) )
| ~ ( ~ doDivides0(xu,xc)
| ( sdtasdt0(xu,tptp_fun_W1_22(xu)) != xc )
| ~ aElement0(tptp_fun_W1_22(xu)) )
| ~ ( doDivides0(xu,xb)
| aDivisorOf0(xu,xb)
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ( sdtasdt0(xu,W1) != xb ) ) ) ),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
~ ( ~ doDivides0(xu,xc)
| ( sdtasdt0(xu,tptp_fun_W1_22(xu)) != xc )
| ~ aElement0(tptp_fun_W1_22(xu)) ),
inference(unit_resolution,[status(thm)],[53,42,18,11]) ).
tff(55,plain,
( ~ doDivides0(xu,xc)
| ( sdtasdt0(xu,tptp_fun_W1_22(xu)) != xc )
| ~ aElement0(tptp_fun_W1_22(xu))
| ( sdtasdt0(xu,tptp_fun_W1_22(xu)) = xc ) ),
inference(tautology,[status(thm)],[]) ).
tff(56,plain,
sdtasdt0(xu,tptp_fun_W1_22(xu)) = xc,
inference(unit_resolution,[status(thm)],[55,54]) ).
tff(57,plain,
( aElement0(xa)
<=> aElement0(xa) ),
inference(rewrite,[status(thm)],[]) ).
tff(58,axiom,
( aElement0(xa)
& aElement0(xb) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2091) ).
tff(59,plain,
aElement0(xa),
inference(and_elim,[status(thm)],[58]) ).
tff(60,plain,
aElement0(xa),
inference(modus_ponens,[status(thm)],[59,57]) ).
tff(61,plain,
^ [W0: $i] :
refl(( ( ~ aElement0(W0)
| ! [W1: $i] :
~ ( ( ~ aElement0(W1)
| ~ doDivides0(W1,W0) )
<=> aDivisorOf0(W1,W0) ) )
<=> ( ~ aElement0(W0)
| ! [W1: $i] :
~ ( ( ~ aElement0(W1)
| ~ doDivides0(W1,W0) )
<=> aDivisorOf0(W1,W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(62,plain,
( ! [W0: $i] :
( ~ aElement0(W0)
| ! [W1: $i] :
~ ( ( ~ aElement0(W1)
| ~ doDivides0(W1,W0) )
<=> aDivisorOf0(W1,W0) ) )
<=> ! [W0: $i] :
( ~ aElement0(W0)
| ! [W1: $i] :
~ ( ( ~ aElement0(W1)
| ~ doDivides0(W1,W0) )
<=> aDivisorOf0(W1,W0) ) ) ),
inference(quant_intro,[status(thm)],[61]) ).
tff(63,plain,
^ [W0: $i] :
rewrite(( ( ~ aElement0(W0)
| ! [W1: $i] :
~ ( ( ~ aElement0(W1)
| ~ doDivides0(W1,W0) )
<=> aDivisorOf0(W1,W0) ) )
<=> ( ~ aElement0(W0)
| ! [W1: $i] :
~ ( ( ~ aElement0(W1)
| ~ doDivides0(W1,W0) )
<=> aDivisorOf0(W1,W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(64,plain,
( ! [W0: $i] :
( ~ aElement0(W0)
| ! [W1: $i] :
~ ( ( ~ aElement0(W1)
| ~ doDivides0(W1,W0) )
<=> aDivisorOf0(W1,W0) ) )
<=> ! [W0: $i] :
( ~ aElement0(W0)
| ! [W1: $i] :
~ ( ( ~ aElement0(W1)
| ~ doDivides0(W1,W0) )
<=> aDivisorOf0(W1,W0) ) ) ),
inference(quant_intro,[status(thm)],[63]) ).
tff(65,plain,
( ! [W0: $i] :
( ~ aElement0(W0)
| ! [W1: $i] :
~ ( ( ~ aElement0(W1)
| ~ doDivides0(W1,W0) )
<=> aDivisorOf0(W1,W0) ) )
<=> ! [W0: $i] :
( ~ aElement0(W0)
| ! [W1: $i] :
~ ( ( ~ aElement0(W1)
| ~ doDivides0(W1,W0) )
<=> aDivisorOf0(W1,W0) ) ) ),
inference(transitivity,[status(thm)],[64,62]) ).
tff(66,plain,
^ [W0: $i] :
rewrite(( ( ~ aElement0(W0)
| ! [W1: $i] :
( aDivisorOf0(W1,W0)
<=> ( aElement0(W1)
& doDivides0(W1,W0) ) ) )
<=> ( ~ aElement0(W0)
| ! [W1: $i] :
~ ( ( ~ aElement0(W1)
| ~ doDivides0(W1,W0) )
<=> aDivisorOf0(W1,W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(67,plain,
( ! [W0: $i] :
( ~ aElement0(W0)
| ! [W1: $i] :
( aDivisorOf0(W1,W0)
<=> ( aElement0(W1)
& doDivides0(W1,W0) ) ) )
<=> ! [W0: $i] :
( ~ aElement0(W0)
| ! [W1: $i] :
~ ( ( ~ aElement0(W1)
| ~ doDivides0(W1,W0) )
<=> aDivisorOf0(W1,W0) ) ) ),
inference(quant_intro,[status(thm)],[66]) ).
tff(68,plain,
( ! [W0: $i] :
( ~ aElement0(W0)
| ! [W1: $i] :
( aDivisorOf0(W1,W0)
<=> ( aElement0(W1)
& doDivides0(W1,W0) ) ) )
<=> ! [W0: $i] :
( ~ aElement0(W0)
| ! [W1: $i] :
( aDivisorOf0(W1,W0)
<=> ( aElement0(W1)
& doDivides0(W1,W0) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(69,plain,
^ [W0: $i] :
rewrite(( ( aElement0(W0)
=> ! [W1: $i] :
( aDivisorOf0(W1,W0)
<=> ( aElement0(W1)
& doDivides0(W1,W0) ) ) )
<=> ( ~ aElement0(W0)
| ! [W1: $i] :
( aDivisorOf0(W1,W0)
<=> ( aElement0(W1)
& doDivides0(W1,W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(70,plain,
( ! [W0: $i] :
( aElement0(W0)
=> ! [W1: $i] :
( aDivisorOf0(W1,W0)
<=> ( aElement0(W1)
& doDivides0(W1,W0) ) ) )
<=> ! [W0: $i] :
( ~ aElement0(W0)
| ! [W1: $i] :
( aDivisorOf0(W1,W0)
<=> ( aElement0(W1)
& doDivides0(W1,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[69]) ).
tff(71,axiom,
! [W0: $i] :
( aElement0(W0)
=> ! [W1: $i] :
( aDivisorOf0(W1,W0)
<=> ( aElement0(W1)
& doDivides0(W1,W0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDvs) ).
tff(72,plain,
! [W0: $i] :
( ~ aElement0(W0)
| ! [W1: $i] :
( aDivisorOf0(W1,W0)
<=> ( aElement0(W1)
& doDivides0(W1,W0) ) ) ),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
! [W0: $i] :
( ~ aElement0(W0)
| ! [W1: $i] :
( aDivisorOf0(W1,W0)
<=> ( aElement0(W1)
& doDivides0(W1,W0) ) ) ),
inference(modus_ponens,[status(thm)],[72,68]) ).
tff(74,plain,
! [W0: $i] :
( ~ aElement0(W0)
| ! [W1: $i] :
( aDivisorOf0(W1,W0)
<=> ( aElement0(W1)
& doDivides0(W1,W0) ) ) ),
inference(skolemize,[status(sab)],[73]) ).
tff(75,plain,
! [W0: $i] :
( ~ aElement0(W0)
| ! [W1: $i] :
~ ( ( ~ aElement0(W1)
| ~ doDivides0(W1,W0) )
<=> aDivisorOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[74,67]) ).
tff(76,plain,
! [W0: $i] :
( ~ aElement0(W0)
| ! [W1: $i] :
~ ( ( ~ aElement0(W1)
| ~ doDivides0(W1,W0) )
<=> aDivisorOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[75,65]) ).
tff(77,plain,
( ( ~ ! [W0: $i] :
( ~ aElement0(W0)
| ! [W1: $i] :
~ ( ( ~ aElement0(W1)
| ~ doDivides0(W1,W0) )
<=> aDivisorOf0(W1,W0) ) )
| ~ aElement0(xa)
| ! [W1: $i] :
~ ( ( ~ aElement0(W1)
| ~ doDivides0(W1,xa) )
<=> aDivisorOf0(W1,xa) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElement0(W0)
| ! [W1: $i] :
~ ( ( ~ aElement0(W1)
| ~ doDivides0(W1,W0) )
<=> aDivisorOf0(W1,W0) ) )
| ~ aElement0(xa)
| ! [W1: $i] :
~ ( ( ~ aElement0(W1)
| ~ doDivides0(W1,xa) )
<=> aDivisorOf0(W1,xa) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(78,plain,
( ~ ! [W0: $i] :
( ~ aElement0(W0)
| ! [W1: $i] :
~ ( ( ~ aElement0(W1)
| ~ doDivides0(W1,W0) )
<=> aDivisorOf0(W1,W0) ) )
| ~ aElement0(xa)
| ! [W1: $i] :
~ ( ( ~ aElement0(W1)
| ~ doDivides0(W1,xa) )
<=> aDivisorOf0(W1,xa) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(79,plain,
( ~ ! [W0: $i] :
( ~ aElement0(W0)
| ! [W1: $i] :
~ ( ( ~ aElement0(W1)
| ~ doDivides0(W1,W0) )
<=> aDivisorOf0(W1,W0) ) )
| ~ aElement0(xa)
| ! [W1: $i] :
~ ( ( ~ aElement0(W1)
| ~ doDivides0(W1,xa) )
<=> aDivisorOf0(W1,xa) ) ),
inference(modus_ponens,[status(thm)],[78,77]) ).
tff(80,plain,
! [W1: $i] :
~ ( ( ~ aElement0(W1)
| ~ doDivides0(W1,xa) )
<=> aDivisorOf0(W1,xa) ),
inference(unit_resolution,[status(thm)],[79,76,60]) ).
tff(81,plain,
( ~ ! [W1: $i] :
~ ( ( ~ aElement0(W1)
| ~ doDivides0(W1,xa) )
<=> aDivisorOf0(W1,xa) )
| ~ ( ( ~ aElement0(xu)
| ~ doDivides0(xu,xa) )
<=> aDivisorOf0(xu,xa) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(82,plain,
~ ( ( ~ aElement0(xu)
| ~ doDivides0(xu,xa) )
<=> aDivisorOf0(xu,xa) ),
inference(unit_resolution,[status(thm)],[81,80]) ).
tff(83,plain,
( ( ( ~ aElement0(xu)
| ~ doDivides0(xu,xa) )
<=> aDivisorOf0(xu,xa) )
| ~ ( ~ aElement0(xu)
| ~ doDivides0(xu,xa) )
| ~ aDivisorOf0(xu,xa) ),
inference(tautology,[status(thm)],[]) ).
tff(84,plain,
( ( ( ~ aElement0(xu)
| ~ doDivides0(xu,xa) )
<=> aDivisorOf0(xu,xa) )
| ~ ( ~ aElement0(xu)
| ~ doDivides0(xu,xa) ) ),
inference(unit_resolution,[status(thm)],[83,16]) ).
tff(85,plain,
~ ( ~ aElement0(xu)
| ~ doDivides0(xu,xa) ),
inference(unit_resolution,[status(thm)],[84,82]) ).
tff(86,plain,
( ~ aElement0(xu)
| ~ doDivides0(xu,xa)
| aElement0(xu) ),
inference(tautology,[status(thm)],[]) ).
tff(87,plain,
aElement0(xu),
inference(unit_resolution,[status(thm)],[86,85]) ).
tff(88,plain,
( ~ doDivides0(xu,xc)
| ( sdtasdt0(xu,tptp_fun_W1_22(xu)) != xc )
| ~ aElement0(tptp_fun_W1_22(xu))
| aElement0(tptp_fun_W1_22(xu)) ),
inference(tautology,[status(thm)],[]) ).
tff(89,plain,
aElement0(tptp_fun_W1_22(xu)),
inference(unit_resolution,[status(thm)],[88,54]) ).
tff(90,plain,
^ [W0: $i,W1: $i] :
refl(( ( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aElement0(W1)
| ~ aElement0(W0) )
<=> ( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aElement0(W1)
| ~ aElement0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(91,plain,
( ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aElement0(W1)
| ~ aElement0(W0) )
<=> ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aElement0(W1)
| ~ aElement0(W0) ) ),
inference(quant_intro,[status(thm)],[90]) ).
tff(92,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aElement0(W0)
& aElement0(W1) )
<=> ~ ( ~ aElement0(W1)
| ~ aElement0(W0) ) )),
( ~ ( aElement0(W0)
& aElement0(W1) )
<=> ~ ~ ( ~ aElement0(W1)
| ~ aElement0(W0) ) )),
rewrite(( ~ ~ ( ~ aElement0(W1)
| ~ aElement0(W0) )
<=> ( ~ aElement0(W1)
| ~ aElement0(W0) ) )),
( ~ ( aElement0(W0)
& aElement0(W1) )
<=> ( ~ aElement0(W1)
| ~ aElement0(W0) ) )),
( ( ~ ( aElement0(W0)
& aElement0(W1) )
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) )
<=> ( ~ aElement0(W1)
| ~ aElement0(W0)
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) )),
rewrite(( ( ~ aElement0(W1)
| ~ aElement0(W0)
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) )
<=> ( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aElement0(W1)
| ~ aElement0(W0) ) )),
( ( ~ ( aElement0(W0)
& aElement0(W1) )
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) )
<=> ( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aElement0(W1)
| ~ aElement0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(93,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aElement0(W0)
& aElement0(W1) )
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) )
<=> ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aElement0(W1)
| ~ aElement0(W0) ) ),
inference(quant_intro,[status(thm)],[92]) ).
tff(94,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aElement0(W0)
& aElement0(W1) )
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aElement0(W0)
& aElement0(W1) )
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(95,plain,
^ [W0: $i,W1: $i] :
rewrite(( ( ( aElement0(W0)
& aElement0(W1) )
=> ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) )
<=> ( ~ ( aElement0(W0)
& aElement0(W1) )
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(96,plain,
( ! [W0: $i,W1: $i] :
( ( aElement0(W0)
& aElement0(W1) )
=> ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aElement0(W0)
& aElement0(W1) )
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) ),
inference(quant_intro,[status(thm)],[95]) ).
tff(97,axiom,
! [W0: $i,W1: $i] :
( ( aElement0(W0)
& aElement0(W1) )
=> ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
tff(98,plain,
! [W0: $i,W1: $i] :
( ~ ( aElement0(W0)
& aElement0(W1) )
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[97,96]) ).
tff(99,plain,
! [W0: $i,W1: $i] :
( ~ ( aElement0(W0)
& aElement0(W1) )
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[98,94]) ).
tff(100,plain,
! [W0: $i,W1: $i] :
( ~ ( aElement0(W0)
& aElement0(W1) )
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ),
inference(skolemize,[status(sab)],[99]) ).
tff(101,plain,
! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(modus_ponens,[status(thm)],[100,93]) ).
tff(102,plain,
! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(modus_ponens,[status(thm)],[101,91]) ).
tff(103,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ~ aElement0(xu)
| ~ aElement0(tptp_fun_W1_22(xu))
| ( sdtasdt0(tptp_fun_W1_22(xu),xu) = sdtasdt0(xu,tptp_fun_W1_22(xu)) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ~ aElement0(xu)
| ~ aElement0(tptp_fun_W1_22(xu))
| ( sdtasdt0(tptp_fun_W1_22(xu),xu) = sdtasdt0(xu,tptp_fun_W1_22(xu)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(104,plain,
( ( ( sdtasdt0(tptp_fun_W1_22(xu),xu) = sdtasdt0(xu,tptp_fun_W1_22(xu)) )
| ~ aElement0(xu)
| ~ aElement0(tptp_fun_W1_22(xu)) )
<=> ( ~ aElement0(xu)
| ~ aElement0(tptp_fun_W1_22(xu))
| ( sdtasdt0(tptp_fun_W1_22(xu),xu) = sdtasdt0(xu,tptp_fun_W1_22(xu)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(105,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ( sdtasdt0(tptp_fun_W1_22(xu),xu) = sdtasdt0(xu,tptp_fun_W1_22(xu)) )
| ~ aElement0(xu)
| ~ aElement0(tptp_fun_W1_22(xu)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ~ aElement0(xu)
| ~ aElement0(tptp_fun_W1_22(xu))
| ( sdtasdt0(tptp_fun_W1_22(xu),xu) = sdtasdt0(xu,tptp_fun_W1_22(xu)) ) ) ),
inference(monotonicity,[status(thm)],[104]) ).
tff(106,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ( sdtasdt0(tptp_fun_W1_22(xu),xu) = sdtasdt0(xu,tptp_fun_W1_22(xu)) )
| ~ aElement0(xu)
| ~ aElement0(tptp_fun_W1_22(xu)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ~ aElement0(xu)
| ~ aElement0(tptp_fun_W1_22(xu))
| ( sdtasdt0(tptp_fun_W1_22(xu),xu) = sdtasdt0(xu,tptp_fun_W1_22(xu)) ) ) ),
inference(transitivity,[status(thm)],[105,103]) ).
tff(107,plain,
( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ( sdtasdt0(tptp_fun_W1_22(xu),xu) = sdtasdt0(xu,tptp_fun_W1_22(xu)) )
| ~ aElement0(xu)
| ~ aElement0(tptp_fun_W1_22(xu)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(108,plain,
( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ~ aElement0(xu)
| ~ aElement0(tptp_fun_W1_22(xu))
| ( sdtasdt0(tptp_fun_W1_22(xu),xu) = sdtasdt0(xu,tptp_fun_W1_22(xu)) ) ),
inference(modus_ponens,[status(thm)],[107,106]) ).
tff(109,plain,
( ~ aElement0(xu)
| ( sdtasdt0(tptp_fun_W1_22(xu),xu) = sdtasdt0(xu,tptp_fun_W1_22(xu)) ) ),
inference(unit_resolution,[status(thm)],[108,102,89]) ).
tff(110,plain,
sdtasdt0(tptp_fun_W1_22(xu),xu) = sdtasdt0(xu,tptp_fun_W1_22(xu)),
inference(unit_resolution,[status(thm)],[109,87]) ).
tff(111,plain,
sdtasdt0(tptp_fun_W1_22(xu),xu) = xc,
inference(transitivity,[status(thm)],[110,56]) ).
tff(112,plain,
( aElementOf0(sdtasdt0(tptp_fun_W1_22(xu),xu),xI)
<=> aElementOf0(xc,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ),
inference(monotonicity,[status(thm)],[111,4]) ).
tff(113,plain,
( aElementOf0(xc,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
<=> aElementOf0(sdtasdt0(tptp_fun_W1_22(xu),xu),xI) ),
inference(symmetry,[status(thm)],[112]) ).
tff(114,plain,
( ~ aElementOf0(xc,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
<=> ~ aElementOf0(sdtasdt0(tptp_fun_W1_22(xu),xu),xI) ),
inference(monotonicity,[status(thm)],[113]) ).
tff(115,plain,
( ~ aElementOf0(xc,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
<=> ~ aElementOf0(xc,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ),
inference(rewrite,[status(thm)],[]) ).
tff(116,plain,
( ~ ( ! [W0: $i] :
( aElementOf0(W0,slsdtgt0(xa))
<=> ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(xa,W1) = W0 ) ) )
=> ( ! [W0: $i] :
( aElementOf0(W0,slsdtgt0(xb))
<=> ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(xb,W1) = W0 ) ) )
=> ( ? [W0: $i,W1: $i] :
( aElementOf0(W0,slsdtgt0(xa))
& aElementOf0(W1,slsdtgt0(xb))
& ( sdtpldt0(W0,W1) = xc ) )
| aElementOf0(xc,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ) )
<=> ~ ( aElementOf0(xc,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ? [W0: $i,W1: $i] :
( aElementOf0(W0,slsdtgt0(xa))
& aElementOf0(W1,slsdtgt0(xb))
& ( sdtpldt0(W0,W1) = xc ) )
| ~ ! [W0: $i] :
( aElementOf0(W0,slsdtgt0(xb))
<=> ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(xb,W1) = W0 ) ) )
| ~ ! [W0: $i] :
( aElementOf0(W0,slsdtgt0(xa))
<=> ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(xa,W1) = W0 ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(117,axiom,
~ ( ! [W0: $i] :
( aElementOf0(W0,slsdtgt0(xa))
<=> ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(xa,W1) = W0 ) ) )
=> ( ! [W0: $i] :
( aElementOf0(W0,slsdtgt0(xb))
<=> ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(xb,W1) = W0 ) ) )
=> ( ? [W0: $i,W1: $i] :
( aElementOf0(W0,slsdtgt0(xa))
& aElementOf0(W1,slsdtgt0(xb))
& ( sdtpldt0(W0,W1) = xc ) )
| aElementOf0(xc,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(118,plain,
~ ( aElementOf0(xc,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ? [W0: $i,W1: $i] :
( aElementOf0(W0,slsdtgt0(xa))
& aElementOf0(W1,slsdtgt0(xb))
& ( sdtpldt0(W0,W1) = xc ) )
| ~ ! [W0: $i] :
( aElementOf0(W0,slsdtgt0(xb))
<=> ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(xb,W1) = W0 ) ) )
| ~ ! [W0: $i] :
( aElementOf0(W0,slsdtgt0(xa))
<=> ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(xa,W1) = W0 ) ) ) ),
inference(modus_ponens,[status(thm)],[117,116]) ).
tff(119,plain,
~ aElementOf0(xc,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),
inference(or_elim,[status(thm)],[118]) ).
tff(120,plain,
~ aElementOf0(xc,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),
inference(modus_ponens,[status(thm)],[119,115]) ).
tff(121,plain,
~ aElementOf0(sdtasdt0(tptp_fun_W1_22(xu),xu),xI),
inference(modus_ponens,[status(thm)],[120,114]) ).
tff(122,plain,
( aElementOf0(xu,xI)
<=> aElementOf0(xu,xI) ),
inference(rewrite,[status(thm)],[]) ).
tff(123,axiom,
( ? [W0: $i,W1: $i] :
( aElementOf0(W0,slsdtgt0(xa))
& aElementOf0(W1,slsdtgt0(xb))
& ( sdtpldt0(W0,W1) = xu ) )
& aElementOf0(xu,xI)
& ( xu != sz00 )
& ! [W0: $i] :
( ( ( ? [W1: $i,W2: $i] :
( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& ( sdtpldt0(W1,W2) = W0 ) )
| aElementOf0(W0,xI) )
& ( W0 != sz00 ) )
=> ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2273) ).
tff(124,plain,
( ? [W0: $i,W1: $i] :
( aElementOf0(W0,slsdtgt0(xa))
& aElementOf0(W1,slsdtgt0(xb))
& ( sdtpldt0(W0,W1) = xu ) )
& aElementOf0(xu,xI)
& ( xu != sz00 ) ),
inference(and_elim,[status(thm)],[123]) ).
tff(125,plain,
( ? [W0: $i,W1: $i] :
( aElementOf0(W0,slsdtgt0(xa))
& aElementOf0(W1,slsdtgt0(xb))
& ( sdtpldt0(W0,W1) = xu ) )
& aElementOf0(xu,xI) ),
inference(and_elim,[status(thm)],[124]) ).
tff(126,plain,
aElementOf0(xu,xI),
inference(and_elim,[status(thm)],[125]) ).
tff(127,plain,
aElementOf0(xu,xI),
inference(modus_ponens,[status(thm)],[126,122]) ).
tff(128,plain,
^ [W0: $i] :
refl(( ( ~ aElementOf0(W0,xI)
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| aElementOf0(sdtpldt0(W0,W1),xI) )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,W0),xI) ) ) )
<=> ( ~ aElementOf0(W0,xI)
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| aElementOf0(sdtpldt0(W0,W1),xI) )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,W0),xI) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(129,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xI)
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| aElementOf0(sdtpldt0(W0,W1),xI) )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,W0),xI) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xI)
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| aElementOf0(sdtpldt0(W0,W1),xI) )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,W0),xI) ) ) ) ),
inference(quant_intro,[status(thm)],[128]) ).
tff(130,plain,
^ [W0: $i] :
rewrite(( ( ~ aElementOf0(W0,xI)
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| aElementOf0(sdtpldt0(W0,W1),xI) )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,W0),xI) ) ) )
<=> ( ~ aElementOf0(W0,xI)
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| aElementOf0(sdtpldt0(W0,W1),xI) )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,W0),xI) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(131,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xI)
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| aElementOf0(sdtpldt0(W0,W1),xI) )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,W0),xI) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xI)
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| aElementOf0(sdtpldt0(W0,W1),xI) )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,W0),xI) ) ) ) ),
inference(quant_intro,[status(thm)],[130]) ).
tff(132,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xI)
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| aElementOf0(sdtpldt0(W0,W1),xI) )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,W0),xI) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xI)
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| aElementOf0(sdtpldt0(W0,W1),xI) )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,W0),xI) ) ) ) ),
inference(transitivity,[status(thm)],[131,129]) ).
tff(133,plain,
^ [W0: $i] :
rewrite(( ( ~ aElementOf0(W0,xI)
| ( ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| aElementOf0(sdtpldt0(W0,W1),xI) )
& ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,W0),xI) ) ) )
<=> ( ~ aElementOf0(W0,xI)
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| aElementOf0(sdtpldt0(W0,W1),xI) )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,W0),xI) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(134,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xI)
| ( ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| aElementOf0(sdtpldt0(W0,W1),xI) )
& ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,W0),xI) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xI)
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| aElementOf0(sdtpldt0(W0,W1),xI) )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,W0),xI) ) ) ) ),
inference(quant_intro,[status(thm)],[133]) ).
tff(135,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xI)
| ( ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| aElementOf0(sdtpldt0(W0,W1),xI) )
& ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,W0),xI) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xI)
| ( ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| aElementOf0(sdtpldt0(W0,W1),xI) )
& ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,W0),xI) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(136,plain,
^ [W0: $i] :
trans(monotonicity(rewrite(( ( ! [W1: $i] :
( aElementOf0(W1,xI)
=> aElementOf0(sdtpldt0(W0,W1),xI) )
& ! [W1: $i] :
( aElement0(W1)
=> aElementOf0(sdtasdt0(W1,W0),xI) ) )
<=> ( ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| aElementOf0(sdtpldt0(W0,W1),xI) )
& ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,W0),xI) ) ) )),
( ( aElementOf0(W0,xI)
=> ( ! [W1: $i] :
( aElementOf0(W1,xI)
=> aElementOf0(sdtpldt0(W0,W1),xI) )
& ! [W1: $i] :
( aElement0(W1)
=> aElementOf0(sdtasdt0(W1,W0),xI) ) ) )
<=> ( aElementOf0(W0,xI)
=> ( ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| aElementOf0(sdtpldt0(W0,W1),xI) )
& ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,W0),xI) ) ) ) )),
rewrite(( ( aElementOf0(W0,xI)
=> ( ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| aElementOf0(sdtpldt0(W0,W1),xI) )
& ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,W0),xI) ) ) )
<=> ( ~ aElementOf0(W0,xI)
| ( ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| aElementOf0(sdtpldt0(W0,W1),xI) )
& ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,W0),xI) ) ) ) )),
( ( aElementOf0(W0,xI)
=> ( ! [W1: $i] :
( aElementOf0(W1,xI)
=> aElementOf0(sdtpldt0(W0,W1),xI) )
& ! [W1: $i] :
( aElement0(W1)
=> aElementOf0(sdtasdt0(W1,W0),xI) ) ) )
<=> ( ~ aElementOf0(W0,xI)
| ( ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| aElementOf0(sdtpldt0(W0,W1),xI) )
& ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,W0),xI) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(137,plain,
( ! [W0: $i] :
( aElementOf0(W0,xI)
=> ( ! [W1: $i] :
( aElementOf0(W1,xI)
=> aElementOf0(sdtpldt0(W0,W1),xI) )
& ! [W1: $i] :
( aElement0(W1)
=> aElementOf0(sdtasdt0(W1,W0),xI) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xI)
| ( ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| aElementOf0(sdtpldt0(W0,W1),xI) )
& ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,W0),xI) ) ) ) ),
inference(quant_intro,[status(thm)],[136]) ).
tff(138,plain,
( aSet0(xI)
& ! [W0: $i] :
( aElementOf0(W0,xI)
=> ( ! [W1: $i] :
( aElementOf0(W1,xI)
=> aElementOf0(sdtpldt0(W0,W1),xI) )
& ! [W1: $i] :
( aElement0(W1)
=> aElementOf0(sdtasdt0(W1,W0),xI) ) ) )
& aIdeal0(xI)
& ! [W0: $i] :
( aElementOf0(W0,slsdtgt0(xa))
<=> ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(xa,W1) = W0 ) ) )
& ! [W0: $i] :
( aElementOf0(W0,slsdtgt0(xb))
<=> ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(xb,W1) = W0 ) ) )
& ! [W0: $i] :
( aElementOf0(W0,xI)
<=> ? [W1: $i,W2: $i] :
( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& ( sdtpldt0(W1,W2) = W0 ) ) ) ),
inference(and_elim,[status(thm)],[2]) ).
tff(139,plain,
( aSet0(xI)
& ! [W0: $i] :
( aElementOf0(W0,xI)
=> ( ! [W1: $i] :
( aElementOf0(W1,xI)
=> aElementOf0(sdtpldt0(W0,W1),xI) )
& ! [W1: $i] :
( aElement0(W1)
=> aElementOf0(sdtasdt0(W1,W0),xI) ) ) )
& aIdeal0(xI)
& ! [W0: $i] :
( aElementOf0(W0,slsdtgt0(xa))
<=> ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(xa,W1) = W0 ) ) )
& ! [W0: $i] :
( aElementOf0(W0,slsdtgt0(xb))
<=> ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(xb,W1) = W0 ) ) ) ),
inference(and_elim,[status(thm)],[138]) ).
tff(140,plain,
( aSet0(xI)
& ! [W0: $i] :
( aElementOf0(W0,xI)
=> ( ! [W1: $i] :
( aElementOf0(W1,xI)
=> aElementOf0(sdtpldt0(W0,W1),xI) )
& ! [W1: $i] :
( aElement0(W1)
=> aElementOf0(sdtasdt0(W1,W0),xI) ) ) )
& aIdeal0(xI)
& ! [W0: $i] :
( aElementOf0(W0,slsdtgt0(xa))
<=> ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(xa,W1) = W0 ) ) ) ),
inference(and_elim,[status(thm)],[139]) ).
tff(141,plain,
( aSet0(xI)
& ! [W0: $i] :
( aElementOf0(W0,xI)
=> ( ! [W1: $i] :
( aElementOf0(W1,xI)
=> aElementOf0(sdtpldt0(W0,W1),xI) )
& ! [W1: $i] :
( aElement0(W1)
=> aElementOf0(sdtasdt0(W1,W0),xI) ) ) )
& aIdeal0(xI) ),
inference(and_elim,[status(thm)],[140]) ).
tff(142,plain,
( aSet0(xI)
& ! [W0: $i] :
( aElementOf0(W0,xI)
=> ( ! [W1: $i] :
( aElementOf0(W1,xI)
=> aElementOf0(sdtpldt0(W0,W1),xI) )
& ! [W1: $i] :
( aElement0(W1)
=> aElementOf0(sdtasdt0(W1,W0),xI) ) ) ) ),
inference(and_elim,[status(thm)],[141]) ).
tff(143,plain,
! [W0: $i] :
( aElementOf0(W0,xI)
=> ( ! [W1: $i] :
( aElementOf0(W1,xI)
=> aElementOf0(sdtpldt0(W0,W1),xI) )
& ! [W1: $i] :
( aElement0(W1)
=> aElementOf0(sdtasdt0(W1,W0),xI) ) ) ),
inference(and_elim,[status(thm)],[142]) ).
tff(144,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xI)
| ( ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| aElementOf0(sdtpldt0(W0,W1),xI) )
& ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,W0),xI) ) ) ),
inference(modus_ponens,[status(thm)],[143,137]) ).
tff(145,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xI)
| ( ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| aElementOf0(sdtpldt0(W0,W1),xI) )
& ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,W0),xI) ) ) ),
inference(modus_ponens,[status(thm)],[144,135]) ).
tff(146,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xI)
| ( ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| aElementOf0(sdtpldt0(W0,W1),xI) )
& ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,W0),xI) ) ) ),
inference(skolemize,[status(sab)],[145]) ).
tff(147,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xI)
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| aElementOf0(sdtpldt0(W0,W1),xI) )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,W0),xI) ) ) ),
inference(modus_ponens,[status(thm)],[146,134]) ).
tff(148,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xI)
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| aElementOf0(sdtpldt0(W0,W1),xI) )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,W0),xI) ) ) ),
inference(modus_ponens,[status(thm)],[147,132]) ).
tff(149,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xI)
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| aElementOf0(sdtpldt0(W0,W1),xI) )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,W0),xI) ) ) )
| ~ aElementOf0(xu,xI)
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| aElementOf0(sdtpldt0(xu,W1),xI) )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,xu),xI) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xI)
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| aElementOf0(sdtpldt0(W0,W1),xI) )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,W0),xI) ) ) )
| ~ aElementOf0(xu,xI)
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| aElementOf0(sdtpldt0(xu,W1),xI) )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,xu),xI) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(150,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xI)
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| aElementOf0(sdtpldt0(W0,W1),xI) )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,W0),xI) ) ) )
| ~ aElementOf0(xu,xI)
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| aElementOf0(sdtpldt0(xu,W1),xI) )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,xu),xI) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(151,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xI)
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| aElementOf0(sdtpldt0(W0,W1),xI) )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,W0),xI) ) ) )
| ~ aElementOf0(xu,xI)
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| aElementOf0(sdtpldt0(xu,W1),xI) )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,xu),xI) ) ) ),
inference(modus_ponens,[status(thm)],[150,149]) ).
tff(152,plain,
~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| aElementOf0(sdtpldt0(xu,W1),xI) )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,xu),xI) ) ),
inference(unit_resolution,[status(thm)],[151,148,127]) ).
tff(153,plain,
( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| aElementOf0(sdtpldt0(xu,W1),xI) )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,xu),xI) )
| ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,xu),xI) ) ),
inference(tautology,[status(thm)],[]) ).
tff(154,plain,
! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,xu),xI) ),
inference(unit_resolution,[status(thm)],[153,152]) ).
tff(155,plain,
( ( ~ ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,xu),xI) )
| ~ aElement0(tptp_fun_W1_22(xu))
| aElementOf0(sdtasdt0(tptp_fun_W1_22(xu),xu),xI) )
<=> ( ~ ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,xu),xI) )
| ~ aElement0(tptp_fun_W1_22(xu))
| aElementOf0(sdtasdt0(tptp_fun_W1_22(xu),xu),xI) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(156,plain,
( ~ ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,xu),xI) )
| ~ aElement0(tptp_fun_W1_22(xu))
| aElementOf0(sdtasdt0(tptp_fun_W1_22(xu),xu),xI) ),
inference(quant_inst,[status(thm)],[]) ).
tff(157,plain,
( ~ ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,xu),xI) )
| ~ aElement0(tptp_fun_W1_22(xu))
| aElementOf0(sdtasdt0(tptp_fun_W1_22(xu),xu),xI) ),
inference(modus_ponens,[status(thm)],[156,155]) ).
tff(158,plain,
aElementOf0(sdtasdt0(tptp_fun_W1_22(xu),xu),xI),
inference(unit_resolution,[status(thm)],[157,154,89]) ).
tff(159,plain,
$false,
inference(unit_resolution,[status(thm)],[158,121]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.14 % Problem : RNG126+4 : TPTP v9.0.0. Released v4.0.0.
% 0.05/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n016.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Jun 20 03:26:47 EDT 2025
% 0.14/0.36 % CPUTime :
% 1.62/1.79 % SZS status Theorem
% 1.62/1.79 % SZS output start Proof
% See solution above
% 1.67/1.82 % E exiting
%------------------------------------------------------------------------------