%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM633+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 05:21:41 AM UTC 2025
% Result : Theorem 1.40s 1.62s
% Output : Proof 1.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 41
% Syntax : Number of formulae : 113 ( 29 unt; 0 typ; 0 def)
% Number of atoms : 2565 ( 437 equ)
% Maximal formula atoms : 64 ( 22 avg)
% Number of connectives : 4569 (2238 ~;1855 |; 388 &)
% ( 69 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 9 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 121 ( 121 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 19 ( 16 usr; 1 prp; 0-6 aty)
% Number of functors : 20 ( 20 usr; 9 con; 0-2 aty)
% Number of variables : 450 ( 406 !; 31 ?; 450 :)
% Comments :
%------------------------------------------------------------------------------
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(slbdtsldtrb0_type,type,
slbdtsldtrb0: ( $i * $i ) > $i ).
tff(xK_type,type,
xK: $i ).
tff(xO_type,type,
xO: $i ).
tff(tptp_fun_W2_45_type,type,
tptp_fun_W2_45: ( $i * $i ) > $i ).
tff(szDzizrdt0_type,type,
szDzizrdt0: $i > $i ).
tff(xd_type,type,
xd: $i ).
tff(sdtlcdtrc0_type,type,
sdtlcdtrc0: ( $i * $i ) > $i ).
tff(sdtlbdtrb0_type,type,
sdtlbdtrb0: ( $i * $i ) > $i ).
tff(xe_type,type,
xe: $i ).
tff(sdtlpdtrp0_type,type,
sdtlpdtrp0: ( $i * $i ) > $i ).
tff(szDzozmdt0_type,type,
szDzozmdt0: $i > $i ).
tff(aSet0_type,type,
aSet0: $i > $o ).
tff(sbrdtbr0_type,type,
sbrdtbr0: $i > $i ).
tff(aSubsetOf0_type,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff(xc_type,type,
xc: $i ).
tff(xS_type,type,
xS: $i ).
tff(tptp_fun_W2_44_type,type,
tptp_fun_W2_44: $i > $i ).
tff(isCountable0_type,type,
isCountable0: $i > $o ).
tff(xT_type,type,
xT: $i ).
tff(szNzAzT0_type,type,
szNzAzT0: $i ).
tff(slcrc0_type,type,
slcrc0: $i ).
tff(tptp_fun_W1_43_type,type,
tptp_fun_W1_43: $i > $i ).
tff(tptp_fun_W1_0_type,type,
tptp_fun_W1_0: $i > $i ).
tff(1,plain,
( ( xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))) )
<=> ( xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
( aSet0(xO)
& aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ! [W0: $i] :
( aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
<=> ( aElementOf0(W0,szDzozmdt0(xd))
& ( sdtlpdtrp0(xd,W0) = szDzizrdt0(xd) ) ) )
& ! [W0: $i] :
( aElementOf0(W0,xO)
<=> ? [W1: $i] :
( aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ( sdtlpdtrp0(xe,W1) = W0 ) ) )
& ( xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4891) ).
tff(3,plain,
xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),
inference(and_elim,[status(thm)],[2]) ).
tff(4,plain,
xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),
inference(modus_ponens,[status(thm)],[3,1]) ).
tff(5,plain,
sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))) = xO,
inference(symmetry,[status(thm)],[4]) ).
tff(6,plain,
slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),xK) = slbdtsldtrb0(xO,xK),
inference(monotonicity,[status(thm)],[5]) ).
tff(7,plain,
slbdtsldtrb0(xO,xK) = slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),xK),
inference(symmetry,[status(thm)],[6]) ).
tff(8,plain,
( aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(xO,xK))
<=> aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),xK)) ),
inference(monotonicity,[status(thm)],[7]) ).
tff(9,plain,
( aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),xK))
<=> aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(xO,xK)) ),
inference(symmetry,[status(thm)],[8]) ).
tff(10,plain,
( aSubsetOf0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),xS)
<=> aSubsetOf0(xO,xS) ),
inference(monotonicity,[status(thm)],[5]) ).
tff(11,plain,
( aSubsetOf0(xO,xS)
<=> aSubsetOf0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),xS) ),
inference(symmetry,[status(thm)],[10]) ).
tff(12,plain,
( aSubsetOf0(xO,xS)
<=> aSubsetOf0(xO,xS) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
( ! [W0: $i] :
( aElementOf0(W0,xO)
=> aElementOf0(W0,xS) )
& aSubsetOf0(xO,xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4998) ).
tff(14,plain,
aSubsetOf0(xO,xS),
inference(and_elim,[status(thm)],[13]) ).
tff(15,plain,
aSubsetOf0(xO,xS),
inference(modus_ponens,[status(thm)],[14,12]) ).
tff(16,plain,
aSubsetOf0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),xS),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( aSubsetOf0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),xS)
| ~ ( ~ aSet0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aElementOf0(tptp_fun_W2_44(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| aElementOf0(tptp_fun_W2_44(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),xS) ) )
| ~ aSubsetOf0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),xS) ),
inference(tautology,[status(thm)],[]) ).
tff(18,plain,
( aSubsetOf0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),xS)
| ~ ( ~ aSet0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aElementOf0(tptp_fun_W2_44(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| aElementOf0(tptp_fun_W2_44(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),xS) ) ) ),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
^ [W0: $i] :
rewrite(( ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_45(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_45(W1,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,W0))
| aElementOf0(W3,W1) )
| ~ aSubsetOf0(tptp_fun_W2_45(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_45(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,xK)) ) ) )
<=> ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_45(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_45(W1,W0))
| ~ aSubsetOf0(tptp_fun_W2_45(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_45(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,W0))
| aElementOf0(W3,W1) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(20,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_45(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_45(W1,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,W0))
| aElementOf0(W3,W1) )
| ~ aSubsetOf0(tptp_fun_W2_45(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_45(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,xK)) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_45(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_45(W1,W0))
| ~ aSubsetOf0(tptp_fun_W2_45(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_45(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,W0))
| aElementOf0(W3,W1) ) ) ) ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,plain,
^ [W0: $i] :
refl(( ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_45(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_45(W1,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,W0))
| aElementOf0(W3,W1) )
| ~ aSubsetOf0(tptp_fun_W2_45(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_45(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,xK)) ) ) )
<=> ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_45(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_45(W1,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,W0))
| aElementOf0(W3,W1) )
| ~ aSubsetOf0(tptp_fun_W2_45(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_45(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,xK)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_45(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_45(W1,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,W0))
| aElementOf0(W3,W1) )
| ~ aSubsetOf0(tptp_fun_W2_45(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_45(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,xK)) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_45(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_45(W1,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,W0))
| aElementOf0(W3,W1) )
| ~ aSubsetOf0(tptp_fun_W2_45(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_45(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,xK)) ) ) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
^ [W0: $i] :
rewrite(( ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_45(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_45(W1,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,W0))
| aElementOf0(W3,W1) )
| ~ aSubsetOf0(tptp_fun_W2_45(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_45(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,xK)) ) ) )
<=> ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_45(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_45(W1,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,W0))
| aElementOf0(W3,W1) )
| ~ aSubsetOf0(tptp_fun_W2_45(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_45(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,xK)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(24,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_45(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_45(W1,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,W0))
| aElementOf0(W3,W1) )
| ~ aSubsetOf0(tptp_fun_W2_45(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_45(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,xK)) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_45(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_45(W1,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,W0))
| aElementOf0(W3,W1) )
| ~ aSubsetOf0(tptp_fun_W2_45(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_45(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,xK)) ) ) ) ),
inference(quant_intro,[status(thm)],[23]) ).
tff(25,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_45(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_45(W1,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,W0))
| aElementOf0(W3,W1) )
| ~ aSubsetOf0(tptp_fun_W2_45(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_45(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,xK)) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_45(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_45(W1,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,W0))
| aElementOf0(W3,W1) )
| ~ aSubsetOf0(tptp_fun_W2_45(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_45(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,xK)) ) ) ) ),
inference(transitivity,[status(thm)],[24,22]) ).
tff(26,plain,
^ [W0: $i] :
rewrite(( ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ( ~ aSubsetOf0(W1,xS)
& ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),xS) ) ) )
| ( aSet0(tptp_fun_W2_45(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_45(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_45(W1,W0)) = xK )
& aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,xK))
& ( sdtlpdtrp0(xc,tptp_fun_W2_45(W1,W0)) != W0 ) ) ) )
<=> ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_45(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_45(W1,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,W0))
| aElementOf0(W3,W1) )
| ~ aSubsetOf0(tptp_fun_W2_45(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_45(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,xK)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(27,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ( ~ aSubsetOf0(W1,xS)
& ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),xS) ) ) )
| ( aSet0(tptp_fun_W2_45(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_45(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_45(W1,W0)) = xK )
& aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,xK))
& ( sdtlpdtrp0(xc,tptp_fun_W2_45(W1,W0)) != W0 ) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_45(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_45(W1,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,W0))
| aElementOf0(W3,W1) )
| ~ aSubsetOf0(tptp_fun_W2_45(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_45(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,xK)) ) ) ) ),
inference(quant_intro,[status(thm)],[26]) ).
tff(28,plain,
^ [W0: $i] :
rewrite(( ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,xS)
& ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),xS) ) ) )
| ~ isCountable0(W1)
| ( aSet0(tptp_fun_W2_45(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_45(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_45(W1,W0)) = xK )
& aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,xK))
& ( sdtlpdtrp0(xc,tptp_fun_W2_45(W1,W0)) != W0 ) ) ) )
<=> ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ( ~ aSubsetOf0(W1,xS)
& ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),xS) ) ) )
| ( aSet0(tptp_fun_W2_45(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_45(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_45(W1,W0)) = xK )
& aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,xK))
& ( sdtlpdtrp0(xc,tptp_fun_W2_45(W1,W0)) != W0 ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(29,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,xS)
& ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),xS) ) ) )
| ~ isCountable0(W1)
| ( aSet0(tptp_fun_W2_45(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_45(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_45(W1,W0)) = xK )
& aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,xK))
& ( sdtlpdtrp0(xc,tptp_fun_W2_45(W1,W0)) != W0 ) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ( ~ aSubsetOf0(W1,xS)
& ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),xS) ) ) )
| ( aSet0(tptp_fun_W2_45(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_45(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_45(W1,W0)) = xK )
& aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,xK))
& ( sdtlpdtrp0(xc,tptp_fun_W2_45(W1,W0)) != W0 ) ) ) ) ),
inference(quant_intro,[status(thm)],[28]) ).
tff(30,plain,
( ~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( ( aSubsetOf0(W1,xS)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xS) ) ) )
& isCountable0(W1)
& ! [W2: $i] :
( ~ ( aSet0(W2)
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) )
& aSubsetOf0(W2,W1)
& ( sbrdtbr0(W2) = xK )
& aElementOf0(W2,slbdtsldtrb0(W1,xK)) )
| ( sdtlpdtrp0(xc,W2) = W0 ) ) ) )
<=> ~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( ( aSubsetOf0(W1,xS)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xS) ) ) )
& isCountable0(W1)
& ! [W2: $i] :
( ~ ( aSet0(W2)
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) )
& aSubsetOf0(W2,W1)
& ( sbrdtbr0(W2) = xK )
& aElementOf0(W2,slbdtsldtrb0(W1,xK)) )
| ( sdtlpdtrp0(xc,W2) = W0 ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(31,plain,
( ~ ( ! [W0: $i] :
( ( ( ( ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xO) ) )
| aSubsetOf0(W0,xO) )
& ( sbrdtbr0(W0) = xK ) )
| aElementOf0(W0,slbdtsldtrb0(xO,xK)) )
=> ( ~ ( ~ ? [W1: $i] : aElementOf0(W1,W0)
| ( W0 = slcrc0 ) )
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,szNzAzT0) )
& aSubsetOf0(W0,szNzAzT0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& aElementOf0(W0,szDzozmdt0(xc))
& ( sdtlpdtrp0(xc,W0) = szDzizrdt0(xd) ) ) )
=> ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( ( ( aSet0(W1)
& ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,xS) ) )
| aSubsetOf0(W1,xS) )
& isCountable0(W1)
& ! [W2: $i] :
( ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
=> aElementOf0(W3,W1) )
& aSubsetOf0(W2,W1)
& ( sbrdtbr0(W2) = xK )
& aElementOf0(W2,slbdtsldtrb0(W1,xK)) )
=> ( sdtlpdtrp0(xc,W2) = W0 ) ) ) ) )
<=> ~ ( ~ ! [W0: $i] :
( ~ ( aElementOf0(W0,slbdtsldtrb0(xO,xK))
| ( ( aSubsetOf0(W0,xO)
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xO) ) ) )
& ( sbrdtbr0(W0) = xK ) ) )
| ( ~ ( ~ ? [W1: $i] : aElementOf0(W1,W0)
| ( W0 = slcrc0 ) )
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szNzAzT0) )
& aSubsetOf0(W0,szNzAzT0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& aElementOf0(W0,szDzozmdt0(xc))
& ( sdtlpdtrp0(xc,W0) = szDzizrdt0(xd) ) ) )
| ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( ( aSubsetOf0(W1,xS)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xS) ) ) )
& isCountable0(W1)
& ! [W2: $i] :
( ~ ( aSet0(W2)
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) )
& aSubsetOf0(W2,W1)
& ( sbrdtbr0(W2) = xK )
& aElementOf0(W2,slbdtsldtrb0(W1,xK)) )
| ( sdtlpdtrp0(xc,W2) = W0 ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,axiom,
~ ( ! [W0: $i] :
( ( ( ( ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xO) ) )
| aSubsetOf0(W0,xO) )
& ( sbrdtbr0(W0) = xK ) )
| aElementOf0(W0,slbdtsldtrb0(xO,xK)) )
=> ( ~ ( ~ ? [W1: $i] : aElementOf0(W1,W0)
| ( W0 = slcrc0 ) )
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,szNzAzT0) )
& aSubsetOf0(W0,szNzAzT0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& aElementOf0(W0,szDzozmdt0(xc))
& ( sdtlpdtrp0(xc,W0) = szDzizrdt0(xd) ) ) )
=> ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( ( ( aSet0(W1)
& ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,xS) ) )
| aSubsetOf0(W1,xS) )
& isCountable0(W1)
& ! [W2: $i] :
( ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
=> aElementOf0(W3,W1) )
& aSubsetOf0(W2,W1)
& ( sbrdtbr0(W2) = xK )
& aElementOf0(W2,slbdtsldtrb0(W1,xK)) )
=> ( sdtlpdtrp0(xc,W2) = W0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(33,plain,
~ ( ~ ! [W0: $i] :
( ~ ( aElementOf0(W0,slbdtsldtrb0(xO,xK))
| ( ( aSubsetOf0(W0,xO)
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xO) ) ) )
& ( sbrdtbr0(W0) = xK ) ) )
| ( ~ ( ~ ? [W1: $i] : aElementOf0(W1,W0)
| ( W0 = slcrc0 ) )
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szNzAzT0) )
& aSubsetOf0(W0,szNzAzT0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& aElementOf0(W0,szDzozmdt0(xc))
& ( sdtlpdtrp0(xc,W0) = szDzizrdt0(xd) ) ) )
| ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( ( aSubsetOf0(W1,xS)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xS) ) ) )
& isCountable0(W1)
& ! [W2: $i] :
( ~ ( aSet0(W2)
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) )
& aSubsetOf0(W2,W1)
& ( sbrdtbr0(W2) = xK )
& aElementOf0(W2,slbdtsldtrb0(W1,xK)) )
| ( sdtlpdtrp0(xc,W2) = W0 ) ) ) ) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( ( aSubsetOf0(W1,xS)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xS) ) ) )
& isCountable0(W1)
& ! [W2: $i] :
( ~ ( aSet0(W2)
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) )
& aSubsetOf0(W2,W1)
& ( sbrdtbr0(W2) = xK )
& aElementOf0(W2,slbdtsldtrb0(W1,xK)) )
| ( sdtlpdtrp0(xc,W2) = W0 ) ) ) ),
inference(or_elim,[status(thm)],[33]) ).
tff(35,plain,
~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( ( aSubsetOf0(W1,xS)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xS) ) ) )
& isCountable0(W1)
& ! [W2: $i] :
( ~ ( aSet0(W2)
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) )
& aSubsetOf0(W2,W1)
& ( sbrdtbr0(W2) = xK )
& aElementOf0(W2,slbdtsldtrb0(W1,xK)) )
| ( sdtlpdtrp0(xc,W2) = W0 ) ) ) ),
inference(modus_ponens,[status(thm)],[34,30]) ).
tff(36,plain,
~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( ( aSubsetOf0(W1,xS)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xS) ) ) )
& isCountable0(W1)
& ! [W2: $i] :
( ~ ( aSet0(W2)
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) )
& aSubsetOf0(W2,W1)
& ( sbrdtbr0(W2) = xK )
& aElementOf0(W2,slbdtsldtrb0(W1,xK)) )
| ( sdtlpdtrp0(xc,W2) = W0 ) ) ) ),
inference(modus_ponens,[status(thm)],[35,30]) ).
tff(37,plain,
~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( ( aSubsetOf0(W1,xS)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xS) ) ) )
& isCountable0(W1)
& ! [W2: $i] :
( ~ ( aSet0(W2)
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) )
& aSubsetOf0(W2,W1)
& ( sbrdtbr0(W2) = xK )
& aElementOf0(W2,slbdtsldtrb0(W1,xK)) )
| ( sdtlpdtrp0(xc,W2) = W0 ) ) ) ),
inference(modus_ponens,[status(thm)],[36,30]) ).
tff(38,plain,
^ [W0: $i] :
nnf_neg(refl($oeq(~ aElementOf0(W0,xT),~ aElementOf0(W0,xT))),
nnf_neg(proof_bind(^ [W1: $i] :
nnf_neg(nnf_neg(refl($oeq(~ aSubsetOf0(W1,xS),~ aSubsetOf0(W1,xS))),
nnf_neg(refl($oeq(~ aSet0(W1),~ aSet0(W1))),
sk($oeq(~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xS) ),
~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),xS) ))),
$oeq(~ ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xS) ) ),
( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),xS) ) ))),
$oeq(~ ( aSubsetOf0(W1,xS)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xS) ) ) ),
( ~ aSubsetOf0(W1,xS)
& ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),xS) ) ) ))),refl($oeq(~ isCountable0(W1),~ isCountable0(W1))),
trans(sk($oeq(~ ! [W2: $i] :
( ~ ( aSet0(W2)
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) )
& aSubsetOf0(W2,W1)
& ( sbrdtbr0(W2) = xK )
& aElementOf0(W2,slbdtsldtrb0(W1,xK)) )
| ( sdtlpdtrp0(xc,W2) = W0 ) ),
~ ( ~ ( aSet0(tptp_fun_W2_45(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_45(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_45(W1,W0)) = xK )
& aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,xK)) )
| ( sdtlpdtrp0(xc,tptp_fun_W2_45(W1,W0)) = W0 ) ))),
nnf_neg(nnf_neg(monotonicity(refl($oeq(aSet0(tptp_fun_W2_45(W1,W0)),aSet0(tptp_fun_W2_45(W1,W0)))),
nnf_pos(proof_bind(^ [W3: $i] :
refl($oeq(( ~ aElementOf0(W3,tptp_fun_W2_45(W1,W0))
| aElementOf0(W3,W1) ),
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,W0))
| aElementOf0(W3,W1) )))),
$oeq(! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,W0))
| aElementOf0(W3,W1) ),
! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,W0))
| aElementOf0(W3,W1) ))),
refl($oeq(aSubsetOf0(tptp_fun_W2_45(W1,W0),W1),aSubsetOf0(tptp_fun_W2_45(W1,W0),W1))),refl($oeq(sbrdtbr0(tptp_fun_W2_45(W1,W0)) = xK,sbrdtbr0(tptp_fun_W2_45(W1,W0)) = xK)),refl($oeq(aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,xK)),aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,xK)))),
$oeq(( aSet0(tptp_fun_W2_45(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_45(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_45(W1,W0)) = xK )
& aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,xK)) ),
( aSet0(tptp_fun_W2_45(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_45(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_45(W1,W0)) = xK )
& aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,xK)) ))),
$oeq(~ ~ ( aSet0(tptp_fun_W2_45(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_45(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_45(W1,W0)) = xK )
& aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,xK)) ),
( aSet0(tptp_fun_W2_45(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_45(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_45(W1,W0)) = xK )
& aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,xK)) ))),refl($oeq(sdtlpdtrp0(xc,tptp_fun_W2_45(W1,W0)) != W0,sdtlpdtrp0(xc,tptp_fun_W2_45(W1,W0)) != W0)),
$oeq(~ ( ~ ( aSet0(tptp_fun_W2_45(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_45(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_45(W1,W0)) = xK )
& aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,xK)) )
| ( sdtlpdtrp0(xc,tptp_fun_W2_45(W1,W0)) = W0 ) ),
( aSet0(tptp_fun_W2_45(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_45(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_45(W1,W0)) = xK )
& aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,xK))
& ( sdtlpdtrp0(xc,tptp_fun_W2_45(W1,W0)) != W0 ) ))),
$oeq(~ ! [W2: $i] :
( ~ ( aSet0(W2)
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) )
& aSubsetOf0(W2,W1)
& ( sbrdtbr0(W2) = xK )
& aElementOf0(W2,slbdtsldtrb0(W1,xK)) )
| ( sdtlpdtrp0(xc,W2) = W0 ) ),
( aSet0(tptp_fun_W2_45(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_45(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_45(W1,W0)) = xK )
& aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,xK))
& ( sdtlpdtrp0(xc,tptp_fun_W2_45(W1,W0)) != W0 ) ))),
$oeq(~ ( ( aSubsetOf0(W1,xS)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xS) ) ) )
& isCountable0(W1)
& ! [W2: $i] :
( ~ ( aSet0(W2)
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) )
& aSubsetOf0(W2,W1)
& ( sbrdtbr0(W2) = xK )
& aElementOf0(W2,slbdtsldtrb0(W1,xK)) )
| ( sdtlpdtrp0(xc,W2) = W0 ) ) ),
( ( ~ aSubsetOf0(W1,xS)
& ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),xS) ) ) )
| ~ isCountable0(W1)
| ( aSet0(tptp_fun_W2_45(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_45(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_45(W1,W0)) = xK )
& aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,xK))
& ( sdtlpdtrp0(xc,tptp_fun_W2_45(W1,W0)) != W0 ) ) )))),
$oeq(~ ? [W1: $i] :
( ( aSubsetOf0(W1,xS)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xS) ) ) )
& isCountable0(W1)
& ! [W2: $i] :
( ~ ( aSet0(W2)
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) )
& aSubsetOf0(W2,W1)
& ( sbrdtbr0(W2) = xK )
& aElementOf0(W2,slbdtsldtrb0(W1,xK)) )
| ( sdtlpdtrp0(xc,W2) = W0 ) ) ),
! [W1: $i] :
( ( ~ aSubsetOf0(W1,xS)
& ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),xS) ) ) )
| ~ isCountable0(W1)
| ( aSet0(tptp_fun_W2_45(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_45(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_45(W1,W0)) = xK )
& aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,xK))
& ( sdtlpdtrp0(xc,tptp_fun_W2_45(W1,W0)) != W0 ) ) ))),
$oeq(~ ( aElementOf0(W0,xT)
& ? [W1: $i] :
( ( aSubsetOf0(W1,xS)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xS) ) ) )
& isCountable0(W1)
& ! [W2: $i] :
( ~ ( aSet0(W2)
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) )
& aSubsetOf0(W2,W1)
& ( sbrdtbr0(W2) = xK )
& aElementOf0(W2,slbdtsldtrb0(W1,xK)) )
| ( sdtlpdtrp0(xc,W2) = W0 ) ) ) ),
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,xS)
& ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),xS) ) ) )
| ~ isCountable0(W1)
| ( aSet0(tptp_fun_W2_45(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_45(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_45(W1,W0)) = xK )
& aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,xK))
& ( sdtlpdtrp0(xc,tptp_fun_W2_45(W1,W0)) != W0 ) ) ) ))),
inference(bind,[status(th)],[]) ).
tff(39,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,xS)
& ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),xS) ) ) )
| ~ isCountable0(W1)
| ( aSet0(tptp_fun_W2_45(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_45(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_45(W1,W0)) = xK )
& aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,xK))
& ( sdtlpdtrp0(xc,tptp_fun_W2_45(W1,W0)) != W0 ) ) ) ),
inference(nnf-neg,[status(sab)],[37,38]) ).
tff(40,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ( ~ aSubsetOf0(W1,xS)
& ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),xS) ) ) )
| ( aSet0(tptp_fun_W2_45(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_45(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_45(W1,W0)) = xK )
& aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,xK))
& ( sdtlpdtrp0(xc,tptp_fun_W2_45(W1,W0)) != W0 ) ) ) ),
inference(modus_ponens,[status(thm)],[39,29]) ).
tff(41,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_45(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_45(W1,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,W0))
| aElementOf0(W3,W1) )
| ~ aSubsetOf0(tptp_fun_W2_45(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_45(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,xK)) ) ) ),
inference(modus_ponens,[status(thm)],[40,27]) ).
tff(42,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_45(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_45(W1,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,W0))
| aElementOf0(W3,W1) )
| ~ aSubsetOf0(tptp_fun_W2_45(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_45(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,xK)) ) ) ),
inference(modus_ponens,[status(thm)],[41,25]) ).
tff(43,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_45(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_45(W1,W0))
| ~ aSubsetOf0(tptp_fun_W2_45(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_45(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,W0))
| aElementOf0(W3,W1) ) ) ) ),
inference(modus_ponens,[status(thm)],[42,20]) ).
tff(44,plain,
( aElementOf0(szDzizrdt0(xd),xT)
<=> aElementOf0(szDzizrdt0(xd),xT) ),
inference(rewrite,[status(thm)],[]) ).
tff(45,axiom,
( aElementOf0(szDzizrdt0(xd),xT)
& aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ! [W0: $i] :
( aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
<=> ( aElementOf0(W0,szDzozmdt0(xd))
& ( sdtlpdtrp0(xd,W0) = szDzizrdt0(xd) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4854) ).
tff(46,plain,
( aElementOf0(szDzizrdt0(xd),xT)
& aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
inference(and_elim,[status(thm)],[45]) ).
tff(47,plain,
aElementOf0(szDzizrdt0(xd),xT),
inference(and_elim,[status(thm)],[46]) ).
tff(48,plain,
aElementOf0(szDzizrdt0(xd),xT),
inference(modus_ponens,[status(thm)],[47,44]) ).
tff(49,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_45(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_45(W1,W0))
| ~ aSubsetOf0(tptp_fun_W2_45(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_45(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,W0))
| aElementOf0(W3,W1) ) ) ) )
| ~ aElementOf0(szDzizrdt0(xd),xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),xS) ) ) )
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,szDzizrdt0(xd)))
| aElementOf0(W3,W1) )
| ~ aElementOf0(tptp_fun_W2_45(W1,szDzizrdt0(xd)),slbdtsldtrb0(W1,xK))
| ( sbrdtbr0(tptp_fun_W2_45(W1,szDzizrdt0(xd))) != xK )
| ~ aSubsetOf0(tptp_fun_W2_45(W1,szDzizrdt0(xd)),W1)
| ~ aSet0(tptp_fun_W2_45(W1,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_45(W1,szDzizrdt0(xd))) = szDzizrdt0(xd) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_45(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_45(W1,W0))
| ~ aSubsetOf0(tptp_fun_W2_45(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_45(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,W0))
| aElementOf0(W3,W1) ) ) ) )
| ~ aElementOf0(szDzizrdt0(xd),xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),xS) ) ) )
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,szDzizrdt0(xd)))
| aElementOf0(W3,W1) )
| ~ aElementOf0(tptp_fun_W2_45(W1,szDzizrdt0(xd)),slbdtsldtrb0(W1,xK))
| ( sbrdtbr0(tptp_fun_W2_45(W1,szDzizrdt0(xd))) != xK )
| ~ aSubsetOf0(tptp_fun_W2_45(W1,szDzizrdt0(xd)),W1)
| ~ aSet0(tptp_fun_W2_45(W1,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_45(W1,szDzizrdt0(xd))) = szDzizrdt0(xd) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(50,plain,
( ( ~ aElementOf0(szDzizrdt0(xd),xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_45(W1,szDzizrdt0(xd))) = szDzizrdt0(xd) )
| ~ aSet0(tptp_fun_W2_45(W1,szDzizrdt0(xd)))
| ~ aSubsetOf0(tptp_fun_W2_45(W1,szDzizrdt0(xd)),W1)
| ( sbrdtbr0(tptp_fun_W2_45(W1,szDzizrdt0(xd))) != xK )
| ~ aElementOf0(tptp_fun_W2_45(W1,szDzizrdt0(xd)),slbdtsldtrb0(W1,xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,szDzizrdt0(xd)))
| aElementOf0(W3,W1) ) ) ) )
<=> ( ~ aElementOf0(szDzizrdt0(xd),xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),xS) ) ) )
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,szDzizrdt0(xd)))
| aElementOf0(W3,W1) )
| ~ aElementOf0(tptp_fun_W2_45(W1,szDzizrdt0(xd)),slbdtsldtrb0(W1,xK))
| ( sbrdtbr0(tptp_fun_W2_45(W1,szDzizrdt0(xd))) != xK )
| ~ aSubsetOf0(tptp_fun_W2_45(W1,szDzizrdt0(xd)),W1)
| ~ aSet0(tptp_fun_W2_45(W1,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_45(W1,szDzizrdt0(xd))) = szDzizrdt0(xd) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(51,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_45(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_45(W1,W0))
| ~ aSubsetOf0(tptp_fun_W2_45(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_45(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,W0))
| aElementOf0(W3,W1) ) ) ) )
| ~ aElementOf0(szDzizrdt0(xd),xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_45(W1,szDzizrdt0(xd))) = szDzizrdt0(xd) )
| ~ aSet0(tptp_fun_W2_45(W1,szDzizrdt0(xd)))
| ~ aSubsetOf0(tptp_fun_W2_45(W1,szDzizrdt0(xd)),W1)
| ( sbrdtbr0(tptp_fun_W2_45(W1,szDzizrdt0(xd))) != xK )
| ~ aElementOf0(tptp_fun_W2_45(W1,szDzizrdt0(xd)),slbdtsldtrb0(W1,xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,szDzizrdt0(xd)))
| aElementOf0(W3,W1) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_45(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_45(W1,W0))
| ~ aSubsetOf0(tptp_fun_W2_45(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_45(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,W0))
| aElementOf0(W3,W1) ) ) ) )
| ~ aElementOf0(szDzizrdt0(xd),xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),xS) ) ) )
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,szDzizrdt0(xd)))
| aElementOf0(W3,W1) )
| ~ aElementOf0(tptp_fun_W2_45(W1,szDzizrdt0(xd)),slbdtsldtrb0(W1,xK))
| ( sbrdtbr0(tptp_fun_W2_45(W1,szDzizrdt0(xd))) != xK )
| ~ aSubsetOf0(tptp_fun_W2_45(W1,szDzizrdt0(xd)),W1)
| ~ aSet0(tptp_fun_W2_45(W1,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_45(W1,szDzizrdt0(xd))) = szDzizrdt0(xd) ) ) ) ) ),
inference(monotonicity,[status(thm)],[50]) ).
tff(52,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_45(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_45(W1,W0))
| ~ aSubsetOf0(tptp_fun_W2_45(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_45(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,W0))
| aElementOf0(W3,W1) ) ) ) )
| ~ aElementOf0(szDzizrdt0(xd),xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_45(W1,szDzizrdt0(xd))) = szDzizrdt0(xd) )
| ~ aSet0(tptp_fun_W2_45(W1,szDzizrdt0(xd)))
| ~ aSubsetOf0(tptp_fun_W2_45(W1,szDzizrdt0(xd)),W1)
| ( sbrdtbr0(tptp_fun_W2_45(W1,szDzizrdt0(xd))) != xK )
| ~ aElementOf0(tptp_fun_W2_45(W1,szDzizrdt0(xd)),slbdtsldtrb0(W1,xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,szDzizrdt0(xd)))
| aElementOf0(W3,W1) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_45(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_45(W1,W0))
| ~ aSubsetOf0(tptp_fun_W2_45(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_45(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,W0))
| aElementOf0(W3,W1) ) ) ) )
| ~ aElementOf0(szDzizrdt0(xd),xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),xS) ) ) )
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,szDzizrdt0(xd)))
| aElementOf0(W3,W1) )
| ~ aElementOf0(tptp_fun_W2_45(W1,szDzizrdt0(xd)),slbdtsldtrb0(W1,xK))
| ( sbrdtbr0(tptp_fun_W2_45(W1,szDzizrdt0(xd))) != xK )
| ~ aSubsetOf0(tptp_fun_W2_45(W1,szDzizrdt0(xd)),W1)
| ~ aSet0(tptp_fun_W2_45(W1,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_45(W1,szDzizrdt0(xd))) = szDzizrdt0(xd) ) ) ) ) ),
inference(transitivity,[status(thm)],[51,49]) ).
tff(53,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_45(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_45(W1,W0))
| ~ aSubsetOf0(tptp_fun_W2_45(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_45(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,W0))
| aElementOf0(W3,W1) ) ) ) )
| ~ aElementOf0(szDzizrdt0(xd),xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_45(W1,szDzizrdt0(xd))) = szDzizrdt0(xd) )
| ~ aSet0(tptp_fun_W2_45(W1,szDzizrdt0(xd)))
| ~ aSubsetOf0(tptp_fun_W2_45(W1,szDzizrdt0(xd)),W1)
| ( sbrdtbr0(tptp_fun_W2_45(W1,szDzizrdt0(xd))) != xK )
| ~ aElementOf0(tptp_fun_W2_45(W1,szDzizrdt0(xd)),slbdtsldtrb0(W1,xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,szDzizrdt0(xd)))
| aElementOf0(W3,W1) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(54,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_45(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_45(W1,W0))
| ~ aSubsetOf0(tptp_fun_W2_45(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_45(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,W0))
| aElementOf0(W3,W1) ) ) ) )
| ~ aElementOf0(szDzizrdt0(xd),xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),xS) ) ) )
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,szDzizrdt0(xd)))
| aElementOf0(W3,W1) )
| ~ aElementOf0(tptp_fun_W2_45(W1,szDzizrdt0(xd)),slbdtsldtrb0(W1,xK))
| ( sbrdtbr0(tptp_fun_W2_45(W1,szDzizrdt0(xd))) != xK )
| ~ aSubsetOf0(tptp_fun_W2_45(W1,szDzizrdt0(xd)),W1)
| ~ aSet0(tptp_fun_W2_45(W1,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_45(W1,szDzizrdt0(xd))) = szDzizrdt0(xd) ) ) ) ),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),xS) ) ) )
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,szDzizrdt0(xd)))
| aElementOf0(W3,W1) )
| ~ aElementOf0(tptp_fun_W2_45(W1,szDzizrdt0(xd)),slbdtsldtrb0(W1,xK))
| ( sbrdtbr0(tptp_fun_W2_45(W1,szDzizrdt0(xd))) != xK )
| ~ aSubsetOf0(tptp_fun_W2_45(W1,szDzizrdt0(xd)),W1)
| ~ aSet0(tptp_fun_W2_45(W1,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_45(W1,szDzizrdt0(xd))) = szDzizrdt0(xd) ) ) ),
inference(unit_resolution,[status(thm)],[54,48,43]) ).
tff(56,plain,
( isCountable0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
<=> isCountable0(xO) ),
inference(monotonicity,[status(thm)],[5]) ).
tff(57,plain,
( isCountable0(xO)
<=> isCountable0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ),
inference(symmetry,[status(thm)],[56]) ).
tff(58,plain,
( isCountable0(xO)
<=> isCountable0(xO) ),
inference(rewrite,[status(thm)],[]) ).
tff(59,axiom,
( aSet0(xO)
& isCountable0(xO) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4908) ).
tff(60,plain,
isCountable0(xO),
inference(and_elim,[status(thm)],[59]) ).
tff(61,plain,
isCountable0(xO),
inference(modus_ponens,[status(thm)],[60,58]) ).
tff(62,plain,
isCountable0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),
inference(modus_ponens,[status(thm)],[61,57]) ).
tff(63,plain,
( ( ~ ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),xS) ) ) )
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,szDzizrdt0(xd)))
| aElementOf0(W3,W1) )
| ~ aElementOf0(tptp_fun_W2_45(W1,szDzizrdt0(xd)),slbdtsldtrb0(W1,xK))
| ( sbrdtbr0(tptp_fun_W2_45(W1,szDzizrdt0(xd))) != xK )
| ~ aSubsetOf0(tptp_fun_W2_45(W1,szDzizrdt0(xd)),W1)
| ~ aSet0(tptp_fun_W2_45(W1,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_45(W1,szDzizrdt0(xd))) = szDzizrdt0(xd) ) ) )
| ~ isCountable0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( aSubsetOf0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),xS)
| ~ ( ~ aSet0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aElementOf0(tptp_fun_W2_44(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| aElementOf0(tptp_fun_W2_44(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) = szDzizrdt0(xd) )
| ~ aSet0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ( sbrdtbr0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != xK )
| ~ aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W3,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) )
<=> ( ~ ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),xS) ) ) )
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,szDzizrdt0(xd)))
| aElementOf0(W3,W1) )
| ~ aElementOf0(tptp_fun_W2_45(W1,szDzizrdt0(xd)),slbdtsldtrb0(W1,xK))
| ( sbrdtbr0(tptp_fun_W2_45(W1,szDzizrdt0(xd))) != xK )
| ~ aSubsetOf0(tptp_fun_W2_45(W1,szDzizrdt0(xd)),W1)
| ~ aSet0(tptp_fun_W2_45(W1,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_45(W1,szDzizrdt0(xd))) = szDzizrdt0(xd) ) ) )
| ~ isCountable0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( aSubsetOf0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),xS)
| ~ ( ~ aSet0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aElementOf0(tptp_fun_W2_44(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| aElementOf0(tptp_fun_W2_44(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) = szDzizrdt0(xd) )
| ~ aSet0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ( sbrdtbr0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != xK )
| ~ aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W3,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(64,plain,
( ( ~ isCountable0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( aSubsetOf0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),xS)
| ~ ( ~ aSet0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aElementOf0(tptp_fun_W2_44(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| aElementOf0(tptp_fun_W2_44(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) = szDzizrdt0(xd) )
| ~ aSet0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ( sbrdtbr0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != xK )
| ~ aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W3,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) )
<=> ( ~ isCountable0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( aSubsetOf0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),xS)
| ~ ( ~ aSet0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aElementOf0(tptp_fun_W2_44(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| aElementOf0(tptp_fun_W2_44(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) = szDzizrdt0(xd) )
| ~ aSet0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ( sbrdtbr0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != xK )
| ~ aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W3,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(65,plain,
( ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W3,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) )
| ~ aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),xK))
| ( sbrdtbr0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != xK )
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSet0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) = szDzizrdt0(xd) ) )
<=> ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) = szDzizrdt0(xd) )
| ~ aSet0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ( sbrdtbr0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != xK )
| ~ aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W3,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(66,plain,
( ~ ( aSubsetOf0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),xS)
| ~ ( ~ aSet0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aElementOf0(tptp_fun_W2_44(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| aElementOf0(tptp_fun_W2_44(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),xS) ) ) )
<=> ~ ( aSubsetOf0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),xS)
| ~ ( ~ aSet0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aElementOf0(tptp_fun_W2_44(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| aElementOf0(tptp_fun_W2_44(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),xS) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(67,plain,
( ( ~ isCountable0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( aSubsetOf0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),xS)
| ~ ( ~ aSet0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aElementOf0(tptp_fun_W2_44(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| aElementOf0(tptp_fun_W2_44(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),xS) ) ) )
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W3,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) )
| ~ aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),xK))
| ( sbrdtbr0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != xK )
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSet0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) = szDzizrdt0(xd) ) ) )
<=> ( ~ isCountable0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( aSubsetOf0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),xS)
| ~ ( ~ aSet0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aElementOf0(tptp_fun_W2_44(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| aElementOf0(tptp_fun_W2_44(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) = szDzizrdt0(xd) )
| ~ aSet0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ( sbrdtbr0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != xK )
| ~ aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W3,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ),
inference(monotonicity,[status(thm)],[66,65]) ).
tff(68,plain,
( ( ~ isCountable0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( aSubsetOf0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),xS)
| ~ ( ~ aSet0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aElementOf0(tptp_fun_W2_44(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| aElementOf0(tptp_fun_W2_44(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),xS) ) ) )
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W3,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) )
| ~ aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),xK))
| ( sbrdtbr0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != xK )
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSet0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) = szDzizrdt0(xd) ) ) )
<=> ( ~ isCountable0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( aSubsetOf0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),xS)
| ~ ( ~ aSet0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aElementOf0(tptp_fun_W2_44(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| aElementOf0(tptp_fun_W2_44(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) = szDzizrdt0(xd) )
| ~ aSet0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ( sbrdtbr0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != xK )
| ~ aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W3,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ),
inference(transitivity,[status(thm)],[67,64]) ).
tff(69,plain,
( ( ~ ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),xS) ) ) )
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,szDzizrdt0(xd)))
| aElementOf0(W3,W1) )
| ~ aElementOf0(tptp_fun_W2_45(W1,szDzizrdt0(xd)),slbdtsldtrb0(W1,xK))
| ( sbrdtbr0(tptp_fun_W2_45(W1,szDzizrdt0(xd))) != xK )
| ~ aSubsetOf0(tptp_fun_W2_45(W1,szDzizrdt0(xd)),W1)
| ~ aSet0(tptp_fun_W2_45(W1,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_45(W1,szDzizrdt0(xd))) = szDzizrdt0(xd) ) ) )
| ~ isCountable0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( aSubsetOf0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),xS)
| ~ ( ~ aSet0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aElementOf0(tptp_fun_W2_44(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| aElementOf0(tptp_fun_W2_44(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),xS) ) ) )
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W3,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) )
| ~ aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),xK))
| ( sbrdtbr0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != xK )
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSet0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) = szDzizrdt0(xd) ) ) )
<=> ( ~ ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),xS) ) ) )
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,szDzizrdt0(xd)))
| aElementOf0(W3,W1) )
| ~ aElementOf0(tptp_fun_W2_45(W1,szDzizrdt0(xd)),slbdtsldtrb0(W1,xK))
| ( sbrdtbr0(tptp_fun_W2_45(W1,szDzizrdt0(xd))) != xK )
| ~ aSubsetOf0(tptp_fun_W2_45(W1,szDzizrdt0(xd)),W1)
| ~ aSet0(tptp_fun_W2_45(W1,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_45(W1,szDzizrdt0(xd))) = szDzizrdt0(xd) ) ) )
| ~ isCountable0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( aSubsetOf0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),xS)
| ~ ( ~ aSet0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aElementOf0(tptp_fun_W2_44(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| aElementOf0(tptp_fun_W2_44(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) = szDzizrdt0(xd) )
| ~ aSet0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ( sbrdtbr0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != xK )
| ~ aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W3,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ),
inference(monotonicity,[status(thm)],[68]) ).
tff(70,plain,
( ( ~ ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),xS) ) ) )
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,szDzizrdt0(xd)))
| aElementOf0(W3,W1) )
| ~ aElementOf0(tptp_fun_W2_45(W1,szDzizrdt0(xd)),slbdtsldtrb0(W1,xK))
| ( sbrdtbr0(tptp_fun_W2_45(W1,szDzizrdt0(xd))) != xK )
| ~ aSubsetOf0(tptp_fun_W2_45(W1,szDzizrdt0(xd)),W1)
| ~ aSet0(tptp_fun_W2_45(W1,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_45(W1,szDzizrdt0(xd))) = szDzizrdt0(xd) ) ) )
| ~ isCountable0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( aSubsetOf0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),xS)
| ~ ( ~ aSet0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aElementOf0(tptp_fun_W2_44(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| aElementOf0(tptp_fun_W2_44(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),xS) ) ) )
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W3,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) )
| ~ aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),xK))
| ( sbrdtbr0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != xK )
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSet0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) = szDzizrdt0(xd) ) ) )
<=> ( ~ ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),xS) ) ) )
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,szDzizrdt0(xd)))
| aElementOf0(W3,W1) )
| ~ aElementOf0(tptp_fun_W2_45(W1,szDzizrdt0(xd)),slbdtsldtrb0(W1,xK))
| ( sbrdtbr0(tptp_fun_W2_45(W1,szDzizrdt0(xd))) != xK )
| ~ aSubsetOf0(tptp_fun_W2_45(W1,szDzizrdt0(xd)),W1)
| ~ aSet0(tptp_fun_W2_45(W1,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_45(W1,szDzizrdt0(xd))) = szDzizrdt0(xd) ) ) )
| ~ isCountable0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( aSubsetOf0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),xS)
| ~ ( ~ aSet0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aElementOf0(tptp_fun_W2_44(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| aElementOf0(tptp_fun_W2_44(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) = szDzizrdt0(xd) )
| ~ aSet0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ( sbrdtbr0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != xK )
| ~ aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W3,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ),
inference(transitivity,[status(thm)],[69,63]) ).
tff(71,plain,
( ~ ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),xS) ) ) )
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,szDzizrdt0(xd)))
| aElementOf0(W3,W1) )
| ~ aElementOf0(tptp_fun_W2_45(W1,szDzizrdt0(xd)),slbdtsldtrb0(W1,xK))
| ( sbrdtbr0(tptp_fun_W2_45(W1,szDzizrdt0(xd))) != xK )
| ~ aSubsetOf0(tptp_fun_W2_45(W1,szDzizrdt0(xd)),W1)
| ~ aSet0(tptp_fun_W2_45(W1,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_45(W1,szDzizrdt0(xd))) = szDzizrdt0(xd) ) ) )
| ~ isCountable0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( aSubsetOf0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),xS)
| ~ ( ~ aSet0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aElementOf0(tptp_fun_W2_44(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| aElementOf0(tptp_fun_W2_44(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),xS) ) ) )
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W3,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) )
| ~ aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),xK))
| ( sbrdtbr0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != xK )
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSet0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) = szDzizrdt0(xd) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(72,plain,
( ~ ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),xS) ) ) )
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,szDzizrdt0(xd)))
| aElementOf0(W3,W1) )
| ~ aElementOf0(tptp_fun_W2_45(W1,szDzizrdt0(xd)),slbdtsldtrb0(W1,xK))
| ( sbrdtbr0(tptp_fun_W2_45(W1,szDzizrdt0(xd))) != xK )
| ~ aSubsetOf0(tptp_fun_W2_45(W1,szDzizrdt0(xd)),W1)
| ~ aSet0(tptp_fun_W2_45(W1,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_45(W1,szDzizrdt0(xd))) = szDzizrdt0(xd) ) ) )
| ~ isCountable0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( aSubsetOf0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),xS)
| ~ ( ~ aSet0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aElementOf0(tptp_fun_W2_44(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| aElementOf0(tptp_fun_W2_44(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) = szDzizrdt0(xd) )
| ~ aSet0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ( sbrdtbr0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != xK )
| ~ aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W3,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) = szDzizrdt0(xd) )
| ~ aSet0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ( sbrdtbr0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != xK )
| ~ aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W3,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ),
inference(unit_resolution,[status(thm)],[72,62,55,18]) ).
tff(74,plain,
( ( sdtlpdtrp0(xc,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) = szDzizrdt0(xd) )
| ~ aSet0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ( sbrdtbr0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != xK )
| ~ aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W3,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) )
| aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),xK)) ),
inference(tautology,[status(thm)],[]) ).
tff(75,plain,
aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),xK)),
inference(unit_resolution,[status(thm)],[74,73]) ).
tff(76,plain,
aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(xO,xK)),
inference(modus_ponens,[status(thm)],[75,9]) ).
tff(77,plain,
( ( sdtlpdtrp0(xc,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) = szDzizrdt0(xd) )
| ~ aSet0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ( sbrdtbr0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != xK )
| ~ aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W3,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) )
| ( sdtlpdtrp0(xc,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szDzizrdt0(xd) ) ),
inference(tautology,[status(thm)],[]) ).
tff(78,plain,
sdtlpdtrp0(xc,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szDzizrdt0(xd),
inference(unit_resolution,[status(thm)],[77,73]) ).
tff(79,plain,
( ( sdtlpdtrp0(xc,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szDzizrdt0(xd) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W1,szNzAzT0) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W1,xS) )
| ~ aElementOf0(tptp_fun_W1_0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))),tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szNzAzT0)
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),xS)
| ~ aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szDzozmdt0(xc))
| ( tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)) = slcrc0 )
| ( sdtlpdtrp0(xc,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) = szDzizrdt0(xd) ) ),
inference(tautology,[status(thm)],[]) ).
tff(80,plain,
( ( sdtlpdtrp0(xc,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szDzizrdt0(xd) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W1,szNzAzT0) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W1,xS) )
| ~ aElementOf0(tptp_fun_W1_0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))),tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szNzAzT0)
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),xS)
| ~ aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szDzozmdt0(xc))
| ( tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)) = slcrc0 ) ),
inference(unit_resolution,[status(thm)],[79,78]) ).
tff(81,plain,
^ [W0: $i] :
trans(monotonicity(rewrite(( ~ ( aElementOf0(W0,slbdtsldtrb0(xO,xK))
| ~ ( ( sbrdtbr0(W0) != xK )
| ~ ( aSubsetOf0(W0,xO)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),xO) ) ) ) ) )
<=> ~ ( aElementOf0(W0,slbdtsldtrb0(xO,xK))
| ~ ( ( sbrdtbr0(W0) != xK )
| ~ ( aSubsetOf0(W0,xO)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),xO) ) ) ) ) ) )),
rewrite(( ~ ( ( W0 = slcrc0 )
| ~ aElementOf0(W0,szDzozmdt0(xc))
| ~ aSubsetOf0(W0,xS)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
| ~ aSubsetOf0(W0,szNzAzT0)
| ~ aElementOf0(tptp_fun_W1_0(W0),W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szNzAzT0) )
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) ) )
<=> ~ ( ( W0 = slcrc0 )
| ~ aElementOf0(W0,szDzozmdt0(xc))
| ~ aSubsetOf0(W0,xS)
| ~ aSubsetOf0(W0,szNzAzT0)
| ~ aElementOf0(tptp_fun_W1_0(W0),W0)
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szNzAzT0) ) ) )),
( ( ~ ( aElementOf0(W0,slbdtsldtrb0(xO,xK))
| ~ ( ( sbrdtbr0(W0) != xK )
| ~ ( aSubsetOf0(W0,xO)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),xO) ) ) ) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aElementOf0(W0,szDzozmdt0(xc))
| ~ aSubsetOf0(W0,xS)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
| ~ aSubsetOf0(W0,szNzAzT0)
| ~ aElementOf0(tptp_fun_W1_0(W0),W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szNzAzT0) )
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) ) ) )
<=> ( ~ ( aElementOf0(W0,slbdtsldtrb0(xO,xK))
| ~ ( ( sbrdtbr0(W0) != xK )
| ~ ( aSubsetOf0(W0,xO)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),xO) ) ) ) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aElementOf0(W0,szDzozmdt0(xc))
| ~ aSubsetOf0(W0,xS)
| ~ aSubsetOf0(W0,szNzAzT0)
| ~ aElementOf0(tptp_fun_W1_0(W0),W0)
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szNzAzT0) ) ) ) )),
rewrite(( ( ~ ( aElementOf0(W0,slbdtsldtrb0(xO,xK))
| ~ ( ( sbrdtbr0(W0) != xK )
| ~ ( aSubsetOf0(W0,xO)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),xO) ) ) ) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aElementOf0(W0,szDzozmdt0(xc))
| ~ aSubsetOf0(W0,xS)
| ~ aSubsetOf0(W0,szNzAzT0)
| ~ aElementOf0(tptp_fun_W1_0(W0),W0)
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szNzAzT0) ) ) )
<=> ( ~ ( aElementOf0(W0,slbdtsldtrb0(xO,xK))
| ~ ( ( sbrdtbr0(W0) != xK )
| ~ ( aSubsetOf0(W0,xO)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),xO) ) ) ) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aElementOf0(W0,szDzozmdt0(xc))
| ~ aSubsetOf0(W0,xS)
| ~ aSubsetOf0(W0,szNzAzT0)
| ~ aElementOf0(tptp_fun_W1_0(W0),W0)
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szNzAzT0) ) ) ) )),
( ( ~ ( aElementOf0(W0,slbdtsldtrb0(xO,xK))
| ~ ( ( sbrdtbr0(W0) != xK )
| ~ ( aSubsetOf0(W0,xO)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),xO) ) ) ) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aElementOf0(W0,szDzozmdt0(xc))
| ~ aSubsetOf0(W0,xS)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
| ~ aSubsetOf0(W0,szNzAzT0)
| ~ aElementOf0(tptp_fun_W1_0(W0),W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szNzAzT0) )
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) ) ) )
<=> ( ~ ( aElementOf0(W0,slbdtsldtrb0(xO,xK))
| ~ ( ( sbrdtbr0(W0) != xK )
| ~ ( aSubsetOf0(W0,xO)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),xO) ) ) ) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aElementOf0(W0,szDzozmdt0(xc))
| ~ aSubsetOf0(W0,xS)
| ~ aSubsetOf0(W0,szNzAzT0)
| ~ aElementOf0(tptp_fun_W1_0(W0),W0)
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szNzAzT0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(82,plain,
( ! [W0: $i] :
( ~ ( aElementOf0(W0,slbdtsldtrb0(xO,xK))
| ~ ( ( sbrdtbr0(W0) != xK )
| ~ ( aSubsetOf0(W0,xO)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),xO) ) ) ) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aElementOf0(W0,szDzozmdt0(xc))
| ~ aSubsetOf0(W0,xS)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
| ~ aSubsetOf0(W0,szNzAzT0)
| ~ aElementOf0(tptp_fun_W1_0(W0),W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szNzAzT0) )
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) ) ) )
<=> ! [W0: $i] :
( ~ ( aElementOf0(W0,slbdtsldtrb0(xO,xK))
| ~ ( ( sbrdtbr0(W0) != xK )
| ~ ( aSubsetOf0(W0,xO)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),xO) ) ) ) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aElementOf0(W0,szDzozmdt0(xc))
| ~ aSubsetOf0(W0,xS)
| ~ aSubsetOf0(W0,szNzAzT0)
| ~ aElementOf0(tptp_fun_W1_0(W0),W0)
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szNzAzT0) ) ) ) ),
inference(quant_intro,[status(thm)],[81]) ).
tff(83,plain,
^ [W0: $i] :
refl(( ( ~ ( aElementOf0(W0,slbdtsldtrb0(xO,xK))
| ~ ( ( sbrdtbr0(W0) != xK )
| ~ ( aSubsetOf0(W0,xO)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),xO) ) ) ) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aElementOf0(W0,szDzozmdt0(xc))
| ~ aSubsetOf0(W0,xS)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
| ~ aSubsetOf0(W0,szNzAzT0)
| ~ aElementOf0(tptp_fun_W1_0(W0),W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szNzAzT0) )
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) ) ) )
<=> ( ~ ( aElementOf0(W0,slbdtsldtrb0(xO,xK))
| ~ ( ( sbrdtbr0(W0) != xK )
| ~ ( aSubsetOf0(W0,xO)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),xO) ) ) ) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aElementOf0(W0,szDzozmdt0(xc))
| ~ aSubsetOf0(W0,xS)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
| ~ aSubsetOf0(W0,szNzAzT0)
| ~ aElementOf0(tptp_fun_W1_0(W0),W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szNzAzT0) )
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(84,plain,
( ! [W0: $i] :
( ~ ( aElementOf0(W0,slbdtsldtrb0(xO,xK))
| ~ ( ( sbrdtbr0(W0) != xK )
| ~ ( aSubsetOf0(W0,xO)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),xO) ) ) ) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aElementOf0(W0,szDzozmdt0(xc))
| ~ aSubsetOf0(W0,xS)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
| ~ aSubsetOf0(W0,szNzAzT0)
| ~ aElementOf0(tptp_fun_W1_0(W0),W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szNzAzT0) )
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) ) ) )
<=> ! [W0: $i] :
( ~ ( aElementOf0(W0,slbdtsldtrb0(xO,xK))
| ~ ( ( sbrdtbr0(W0) != xK )
| ~ ( aSubsetOf0(W0,xO)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),xO) ) ) ) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aElementOf0(W0,szDzozmdt0(xc))
| ~ aSubsetOf0(W0,xS)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
| ~ aSubsetOf0(W0,szNzAzT0)
| ~ aElementOf0(tptp_fun_W1_0(W0),W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szNzAzT0) )
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) ) ) ) ),
inference(quant_intro,[status(thm)],[83]) ).
tff(85,plain,
^ [W0: $i] :
rewrite(( ( ~ ( aElementOf0(W0,slbdtsldtrb0(xO,xK))
| ~ ( ( sbrdtbr0(W0) != xK )
| ~ ( aSubsetOf0(W0,xO)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),xO) ) ) ) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aElementOf0(W0,szDzozmdt0(xc))
| ~ aSubsetOf0(W0,xS)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
| ~ aSubsetOf0(W0,szNzAzT0)
| ~ aElementOf0(tptp_fun_W1_0(W0),W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szNzAzT0) )
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) ) ) )
<=> ( ~ ( aElementOf0(W0,slbdtsldtrb0(xO,xK))
| ~ ( ( sbrdtbr0(W0) != xK )
| ~ ( aSubsetOf0(W0,xO)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),xO) ) ) ) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aElementOf0(W0,szDzozmdt0(xc))
| ~ aSubsetOf0(W0,xS)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
| ~ aSubsetOf0(W0,szNzAzT0)
| ~ aElementOf0(tptp_fun_W1_0(W0),W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szNzAzT0) )
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(86,plain,
( ! [W0: $i] :
( ~ ( aElementOf0(W0,slbdtsldtrb0(xO,xK))
| ~ ( ( sbrdtbr0(W0) != xK )
| ~ ( aSubsetOf0(W0,xO)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),xO) ) ) ) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aElementOf0(W0,szDzozmdt0(xc))
| ~ aSubsetOf0(W0,xS)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
| ~ aSubsetOf0(W0,szNzAzT0)
| ~ aElementOf0(tptp_fun_W1_0(W0),W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szNzAzT0) )
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) ) ) )
<=> ! [W0: $i] :
( ~ ( aElementOf0(W0,slbdtsldtrb0(xO,xK))
| ~ ( ( sbrdtbr0(W0) != xK )
| ~ ( aSubsetOf0(W0,xO)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),xO) ) ) ) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aElementOf0(W0,szDzozmdt0(xc))
| ~ aSubsetOf0(W0,xS)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
| ~ aSubsetOf0(W0,szNzAzT0)
| ~ aElementOf0(tptp_fun_W1_0(W0),W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szNzAzT0) )
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) ) ) ) ),
inference(quant_intro,[status(thm)],[85]) ).
tff(87,plain,
( ! [W0: $i] :
( ~ ( aElementOf0(W0,slbdtsldtrb0(xO,xK))
| ~ ( ( sbrdtbr0(W0) != xK )
| ~ ( aSubsetOf0(W0,xO)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),xO) ) ) ) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aElementOf0(W0,szDzozmdt0(xc))
| ~ aSubsetOf0(W0,xS)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
| ~ aSubsetOf0(W0,szNzAzT0)
| ~ aElementOf0(tptp_fun_W1_0(W0),W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szNzAzT0) )
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) ) ) )
<=> ! [W0: $i] :
( ~ ( aElementOf0(W0,slbdtsldtrb0(xO,xK))
| ~ ( ( sbrdtbr0(W0) != xK )
| ~ ( aSubsetOf0(W0,xO)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),xO) ) ) ) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aElementOf0(W0,szDzozmdt0(xc))
| ~ aSubsetOf0(W0,xS)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
| ~ aSubsetOf0(W0,szNzAzT0)
| ~ aElementOf0(tptp_fun_W1_0(W0),W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szNzAzT0) )
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) ) ) ) ),
inference(transitivity,[status(thm)],[86,84]) ).
tff(88,plain,
^ [W0: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( ( sbrdtbr0(W0) != xK )
| ( ~ aSubsetOf0(W0,xO)
& ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),xO) ) ) ) )
<=> ( ( sbrdtbr0(W0) != xK )
| ~ ( aSubsetOf0(W0,xO)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),xO) ) ) ) ) )),
( ( ~ aElementOf0(W0,slbdtsldtrb0(xO,xK))
& ( ( sbrdtbr0(W0) != xK )
| ( ~ aSubsetOf0(W0,xO)
& ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),xO) ) ) ) ) )
<=> ( ~ aElementOf0(W0,slbdtsldtrb0(xO,xK))
& ( ( sbrdtbr0(W0) != xK )
| ~ ( aSubsetOf0(W0,xO)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),xO) ) ) ) ) ) )),
rewrite(( ( ~ aElementOf0(W0,slbdtsldtrb0(xO,xK))
& ( ( sbrdtbr0(W0) != xK )
| ~ ( aSubsetOf0(W0,xO)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),xO) ) ) ) ) )
<=> ~ ( aElementOf0(W0,slbdtsldtrb0(xO,xK))
| ~ ( ( sbrdtbr0(W0) != xK )
| ~ ( aSubsetOf0(W0,xO)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),xO) ) ) ) ) ) )),
( ( ~ aElementOf0(W0,slbdtsldtrb0(xO,xK))
& ( ( sbrdtbr0(W0) != xK )
| ( ~ aSubsetOf0(W0,xO)
& ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),xO) ) ) ) ) )
<=> ~ ( aElementOf0(W0,slbdtsldtrb0(xO,xK))
| ~ ( ( sbrdtbr0(W0) != xK )
| ~ ( aSubsetOf0(W0,xO)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),xO) ) ) ) ) ) )),
rewrite(( ( aElementOf0(tptp_fun_W1_0(W0),W0)
& ( W0 != slcrc0 )
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szNzAzT0) )
& aSubsetOf0(W0,szNzAzT0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& aElementOf0(W0,szDzozmdt0(xc))
& ( sdtlpdtrp0(xc,W0) = szDzizrdt0(xd) ) )
<=> ~ ( ( W0 = slcrc0 )
| ~ aElementOf0(W0,szDzozmdt0(xc))
| ~ aSubsetOf0(W0,xS)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
| ~ aSubsetOf0(W0,szNzAzT0)
| ~ aElementOf0(tptp_fun_W1_0(W0),W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szNzAzT0) )
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) ) ) )),
( ( ( ~ aElementOf0(W0,slbdtsldtrb0(xO,xK))
& ( ( sbrdtbr0(W0) != xK )
| ( ~ aSubsetOf0(W0,xO)
& ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),xO) ) ) ) ) )
| ( aElementOf0(tptp_fun_W1_0(W0),W0)
& ( W0 != slcrc0 )
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szNzAzT0) )
& aSubsetOf0(W0,szNzAzT0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& aElementOf0(W0,szDzozmdt0(xc))
& ( sdtlpdtrp0(xc,W0) = szDzizrdt0(xd) ) ) )
<=> ( ~ ( aElementOf0(W0,slbdtsldtrb0(xO,xK))
| ~ ( ( sbrdtbr0(W0) != xK )
| ~ ( aSubsetOf0(W0,xO)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),xO) ) ) ) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aElementOf0(W0,szDzozmdt0(xc))
| ~ aSubsetOf0(W0,xS)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
| ~ aSubsetOf0(W0,szNzAzT0)
| ~ aElementOf0(tptp_fun_W1_0(W0),W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szNzAzT0) )
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) ) ) ) )),
rewrite(( ( ~ ( aElementOf0(W0,slbdtsldtrb0(xO,xK))
| ~ ( ( sbrdtbr0(W0) != xK )
| ~ ( aSubsetOf0(W0,xO)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),xO) ) ) ) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aElementOf0(W0,szDzozmdt0(xc))
| ~ aSubsetOf0(W0,xS)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
| ~ aSubsetOf0(W0,szNzAzT0)
| ~ aElementOf0(tptp_fun_W1_0(W0),W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szNzAzT0) )
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) ) ) )
<=> ( ~ ( aElementOf0(W0,slbdtsldtrb0(xO,xK))
| ~ ( ( sbrdtbr0(W0) != xK )
| ~ ( aSubsetOf0(W0,xO)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),xO) ) ) ) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aElementOf0(W0,szDzozmdt0(xc))
| ~ aSubsetOf0(W0,xS)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
| ~ aSubsetOf0(W0,szNzAzT0)
| ~ aElementOf0(tptp_fun_W1_0(W0),W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szNzAzT0) )
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) ) ) ) )),
( ( ( ~ aElementOf0(W0,slbdtsldtrb0(xO,xK))
& ( ( sbrdtbr0(W0) != xK )
| ( ~ aSubsetOf0(W0,xO)
& ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),xO) ) ) ) ) )
| ( aElementOf0(tptp_fun_W1_0(W0),W0)
& ( W0 != slcrc0 )
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szNzAzT0) )
& aSubsetOf0(W0,szNzAzT0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& aElementOf0(W0,szDzozmdt0(xc))
& ( sdtlpdtrp0(xc,W0) = szDzizrdt0(xd) ) ) )
<=> ( ~ ( aElementOf0(W0,slbdtsldtrb0(xO,xK))
| ~ ( ( sbrdtbr0(W0) != xK )
| ~ ( aSubsetOf0(W0,xO)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),xO) ) ) ) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aElementOf0(W0,szDzozmdt0(xc))
| ~ aSubsetOf0(W0,xS)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
| ~ aSubsetOf0(W0,szNzAzT0)
| ~ aElementOf0(tptp_fun_W1_0(W0),W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szNzAzT0) )
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(89,plain,
( ! [W0: $i] :
( ( ~ aElementOf0(W0,slbdtsldtrb0(xO,xK))
& ( ( sbrdtbr0(W0) != xK )
| ( ~ aSubsetOf0(W0,xO)
& ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),xO) ) ) ) ) )
| ( aElementOf0(tptp_fun_W1_0(W0),W0)
& ( W0 != slcrc0 )
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szNzAzT0) )
& aSubsetOf0(W0,szNzAzT0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& aElementOf0(W0,szDzozmdt0(xc))
& ( sdtlpdtrp0(xc,W0) = szDzizrdt0(xd) ) ) )
<=> ! [W0: $i] :
( ~ ( aElementOf0(W0,slbdtsldtrb0(xO,xK))
| ~ ( ( sbrdtbr0(W0) != xK )
| ~ ( aSubsetOf0(W0,xO)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),xO) ) ) ) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aElementOf0(W0,szDzozmdt0(xc))
| ~ aSubsetOf0(W0,xS)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
| ~ aSubsetOf0(W0,szNzAzT0)
| ~ aElementOf0(tptp_fun_W1_0(W0),W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szNzAzT0) )
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) ) ) ) ),
inference(quant_intro,[status(thm)],[88]) ).
tff(90,plain,
^ [W0: $i] :
rewrite(( ( ( ~ aElementOf0(W0,slbdtsldtrb0(xO,xK))
& ( ( ~ aSubsetOf0(W0,xO)
& ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),xO) ) ) )
| ( sbrdtbr0(W0) != xK ) ) )
| ( aElementOf0(tptp_fun_W1_0(W0),W0)
& ( W0 != slcrc0 )
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szNzAzT0) )
& aSubsetOf0(W0,szNzAzT0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& aElementOf0(W0,szDzozmdt0(xc))
& ( sdtlpdtrp0(xc,W0) = szDzizrdt0(xd) ) ) )
<=> ( ( ~ aElementOf0(W0,slbdtsldtrb0(xO,xK))
& ( ( sbrdtbr0(W0) != xK )
| ( ~ aSubsetOf0(W0,xO)
& ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),xO) ) ) ) ) )
| ( aElementOf0(tptp_fun_W1_0(W0),W0)
& ( W0 != slcrc0 )
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szNzAzT0) )
& aSubsetOf0(W0,szNzAzT0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& aElementOf0(W0,szDzozmdt0(xc))
& ( sdtlpdtrp0(xc,W0) = szDzizrdt0(xd) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(91,plain,
( ! [W0: $i] :
( ( ~ aElementOf0(W0,slbdtsldtrb0(xO,xK))
& ( ( ~ aSubsetOf0(W0,xO)
& ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),xO) ) ) )
| ( sbrdtbr0(W0) != xK ) ) )
| ( aElementOf0(tptp_fun_W1_0(W0),W0)
& ( W0 != slcrc0 )
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szNzAzT0) )
& aSubsetOf0(W0,szNzAzT0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& aElementOf0(W0,szDzozmdt0(xc))
& ( sdtlpdtrp0(xc,W0) = szDzizrdt0(xd) ) ) )
<=> ! [W0: $i] :
( ( ~ aElementOf0(W0,slbdtsldtrb0(xO,xK))
& ( ( sbrdtbr0(W0) != xK )
| ( ~ aSubsetOf0(W0,xO)
& ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),xO) ) ) ) ) )
| ( aElementOf0(tptp_fun_W1_0(W0),W0)
& ( W0 != slcrc0 )
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szNzAzT0) )
& aSubsetOf0(W0,szNzAzT0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& aElementOf0(W0,szDzozmdt0(xc))
& ( sdtlpdtrp0(xc,W0) = szDzizrdt0(xd) ) ) ) ),
inference(quant_intro,[status(thm)],[90]) ).
tff(92,plain,
( ! [W0: $i] :
( ~ ( aElementOf0(W0,slbdtsldtrb0(xO,xK))
| ( ( aSubsetOf0(W0,xO)
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xO) ) ) )
& ( sbrdtbr0(W0) = xK ) ) )
| ( ~ ( ~ ? [W1: $i] : aElementOf0(W1,W0)
| ( W0 = slcrc0 ) )
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szNzAzT0) )
& aSubsetOf0(W0,szNzAzT0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& aElementOf0(W0,szDzozmdt0(xc))
& ( sdtlpdtrp0(xc,W0) = szDzizrdt0(xd) ) ) )
<=> ! [W0: $i] :
( ~ ( aElementOf0(W0,slbdtsldtrb0(xO,xK))
| ( ( aSubsetOf0(W0,xO)
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xO) ) ) )
& ( sbrdtbr0(W0) = xK ) ) )
| ( ~ ( ~ ? [W1: $i] : aElementOf0(W1,W0)
| ( W0 = slcrc0 ) )
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szNzAzT0) )
& aSubsetOf0(W0,szNzAzT0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& aElementOf0(W0,szDzozmdt0(xc))
& ( sdtlpdtrp0(xc,W0) = szDzizrdt0(xd) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(93,plain,
! [W0: $i] :
( ~ ( aElementOf0(W0,slbdtsldtrb0(xO,xK))
| ( ( aSubsetOf0(W0,xO)
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xO) ) ) )
& ( sbrdtbr0(W0) = xK ) ) )
| ( ~ ( ~ ? [W1: $i] : aElementOf0(W1,W0)
| ( W0 = slcrc0 ) )
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szNzAzT0) )
& aSubsetOf0(W0,szNzAzT0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& aElementOf0(W0,szDzozmdt0(xc))
& ( sdtlpdtrp0(xc,W0) = szDzizrdt0(xd) ) ) ),
inference(or_elim,[status(thm)],[33]) ).
tff(94,plain,
! [W0: $i] :
( ~ ( aElementOf0(W0,slbdtsldtrb0(xO,xK))
| ( ( aSubsetOf0(W0,xO)
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xO) ) ) )
& ( sbrdtbr0(W0) = xK ) ) )
| ( ~ ( ~ ? [W1: $i] : aElementOf0(W1,W0)
| ( W0 = slcrc0 ) )
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szNzAzT0) )
& aSubsetOf0(W0,szNzAzT0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& aElementOf0(W0,szDzozmdt0(xc))
& ( sdtlpdtrp0(xc,W0) = szDzizrdt0(xd) ) ) ),
inference(modus_ponens,[status(thm)],[93,92]) ).
tff(95,plain,
! [W0: $i] :
( ( ~ aElementOf0(W0,slbdtsldtrb0(xO,xK))
& ( ( ~ aSubsetOf0(W0,xO)
& ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),xO) ) ) )
| ( sbrdtbr0(W0) != xK ) ) )
| ( aElementOf0(tptp_fun_W1_0(W0),W0)
& ( W0 != slcrc0 )
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szNzAzT0) )
& aSubsetOf0(W0,szNzAzT0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& aElementOf0(W0,szDzozmdt0(xc))
& ( sdtlpdtrp0(xc,W0) = szDzizrdt0(xd) ) ) ),
inference(skolemize,[status(sab)],[94]) ).
tff(96,plain,
! [W0: $i] :
( ( ~ aElementOf0(W0,slbdtsldtrb0(xO,xK))
& ( ( sbrdtbr0(W0) != xK )
| ( ~ aSubsetOf0(W0,xO)
& ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),xO) ) ) ) ) )
| ( aElementOf0(tptp_fun_W1_0(W0),W0)
& ( W0 != slcrc0 )
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szNzAzT0) )
& aSubsetOf0(W0,szNzAzT0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& aElementOf0(W0,szDzozmdt0(xc))
& ( sdtlpdtrp0(xc,W0) = szDzizrdt0(xd) ) ) ),
inference(modus_ponens,[status(thm)],[95,91]) ).
tff(97,plain,
! [W0: $i] :
( ~ ( aElementOf0(W0,slbdtsldtrb0(xO,xK))
| ~ ( ( sbrdtbr0(W0) != xK )
| ~ ( aSubsetOf0(W0,xO)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),xO) ) ) ) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aElementOf0(W0,szDzozmdt0(xc))
| ~ aSubsetOf0(W0,xS)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
| ~ aSubsetOf0(W0,szNzAzT0)
| ~ aElementOf0(tptp_fun_W1_0(W0),W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szNzAzT0) )
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) ) ) ),
inference(modus_ponens,[status(thm)],[96,89]) ).
tff(98,plain,
! [W0: $i] :
( ~ ( aElementOf0(W0,slbdtsldtrb0(xO,xK))
| ~ ( ( sbrdtbr0(W0) != xK )
| ~ ( aSubsetOf0(W0,xO)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),xO) ) ) ) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aElementOf0(W0,szDzozmdt0(xc))
| ~ aSubsetOf0(W0,xS)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
| ~ aSubsetOf0(W0,szNzAzT0)
| ~ aElementOf0(tptp_fun_W1_0(W0),W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szNzAzT0) )
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) ) ) ),
inference(modus_ponens,[status(thm)],[97,87]) ).
tff(99,plain,
! [W0: $i] :
( ~ ( aElementOf0(W0,slbdtsldtrb0(xO,xK))
| ~ ( ( sbrdtbr0(W0) != xK )
| ~ ( aSubsetOf0(W0,xO)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),xO) ) ) ) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aElementOf0(W0,szDzozmdt0(xc))
| ~ aSubsetOf0(W0,xS)
| ~ aSubsetOf0(W0,szNzAzT0)
| ~ aElementOf0(tptp_fun_W1_0(W0),W0)
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szNzAzT0) ) ) ),
inference(modus_ponens,[status(thm)],[98,82]) ).
tff(100,plain,
( ( ~ ! [W0: $i] :
( ~ ( aElementOf0(W0,slbdtsldtrb0(xO,xK))
| ~ ( ( sbrdtbr0(W0) != xK )
| ~ ( aSubsetOf0(W0,xO)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),xO) ) ) ) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aElementOf0(W0,szDzozmdt0(xc))
| ~ aSubsetOf0(W0,xS)
| ~ aSubsetOf0(W0,szNzAzT0)
| ~ aElementOf0(tptp_fun_W1_0(W0),W0)
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szNzAzT0) ) ) )
| ~ ( aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(xO,xK))
| ~ ( ( sbrdtbr0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != xK )
| ~ ( ~ ( ~ aSet0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| ~ ( ~ aElementOf0(tptp_fun_W1_43(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))),tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(tptp_fun_W1_43(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))),xO) ) )
| aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),xO) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szDzizrdt0(xd) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W1,szNzAzT0) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W1,xS) )
| ~ aElementOf0(tptp_fun_W1_0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))),tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szNzAzT0)
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),xS)
| ~ aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szDzozmdt0(xc))
| ( tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)) = slcrc0 ) ) )
<=> ( ~ ! [W0: $i] :
( ~ ( aElementOf0(W0,slbdtsldtrb0(xO,xK))
| ~ ( ( sbrdtbr0(W0) != xK )
| ~ ( aSubsetOf0(W0,xO)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),xO) ) ) ) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aElementOf0(W0,szDzozmdt0(xc))
| ~ aSubsetOf0(W0,xS)
| ~ aSubsetOf0(W0,szNzAzT0)
| ~ aElementOf0(tptp_fun_W1_0(W0),W0)
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szNzAzT0) ) ) )
| ~ ( aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(xO,xK))
| ~ ( ( sbrdtbr0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != xK )
| ~ ( ~ ( ~ aSet0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| ~ ( ~ aElementOf0(tptp_fun_W1_43(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))),tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(tptp_fun_W1_43(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))),xO) ) )
| aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),xO) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szDzizrdt0(xd) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W1,szNzAzT0) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W1,xS) )
| ~ aElementOf0(tptp_fun_W1_0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))),tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szNzAzT0)
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),xS)
| ~ aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szDzozmdt0(xc))
| ( tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)) = slcrc0 ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(101,plain,
( ( ~ ( aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(xO,xK))
| ~ ( ( sbrdtbr0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != xK )
| ~ ( ~ ( ~ aSet0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| ~ ( ~ aElementOf0(tptp_fun_W1_43(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))),tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(tptp_fun_W1_43(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))),xO) ) )
| aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),xO) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szDzizrdt0(xd) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W1,szNzAzT0) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W1,xS) )
| ~ aElementOf0(tptp_fun_W1_0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))),tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szNzAzT0)
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),xS)
| ~ aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szDzozmdt0(xc))
| ( tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)) = slcrc0 ) ) )
<=> ( ~ ( aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(xO,xK))
| ~ ( ( sbrdtbr0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != xK )
| ~ ( ~ ( ~ aSet0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| ~ ( ~ aElementOf0(tptp_fun_W1_43(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))),tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(tptp_fun_W1_43(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))),xO) ) )
| aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),xO) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szDzizrdt0(xd) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W1,szNzAzT0) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W1,xS) )
| ~ aElementOf0(tptp_fun_W1_0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))),tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szNzAzT0)
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),xS)
| ~ aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szDzozmdt0(xc))
| ( tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)) = slcrc0 ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(102,plain,
( ~ ( ( tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)) = slcrc0 )
| ~ aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szDzozmdt0(xc))
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),xS)
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szNzAzT0)
| ~ aElementOf0(tptp_fun_W1_0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))),tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szDzizrdt0(xd) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W1,xS) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W1,szNzAzT0) ) )
<=> ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szDzizrdt0(xd) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W1,szNzAzT0) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W1,xS) )
| ~ aElementOf0(tptp_fun_W1_0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))),tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szNzAzT0)
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),xS)
| ~ aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szDzozmdt0(xc))
| ( tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)) = slcrc0 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(103,plain,
( ~ ( aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(xO,xK))
| ~ ( ( sbrdtbr0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != xK )
| ~ ( aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),xO)
| ~ ( ~ aSet0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| ~ ( ~ aElementOf0(tptp_fun_W1_43(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))),tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(tptp_fun_W1_43(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))),xO) ) ) ) ) )
<=> ~ ( aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(xO,xK))
| ~ ( ( sbrdtbr0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != xK )
| ~ ( ~ ( ~ aSet0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| ~ ( ~ aElementOf0(tptp_fun_W1_43(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))),tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(tptp_fun_W1_43(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))),xO) ) )
| aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),xO) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(104,plain,
( ( ~ ( aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(xO,xK))
| ~ ( ( sbrdtbr0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != xK )
| ~ ( aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),xO)
| ~ ( ~ aSet0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| ~ ( ~ aElementOf0(tptp_fun_W1_43(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))),tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(tptp_fun_W1_43(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))),xO) ) ) ) ) )
| ~ ( ( tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)) = slcrc0 )
| ~ aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szDzozmdt0(xc))
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),xS)
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szNzAzT0)
| ~ aElementOf0(tptp_fun_W1_0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))),tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szDzizrdt0(xd) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W1,xS) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W1,szNzAzT0) ) ) )
<=> ( ~ ( aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(xO,xK))
| ~ ( ( sbrdtbr0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != xK )
| ~ ( ~ ( ~ aSet0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| ~ ( ~ aElementOf0(tptp_fun_W1_43(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))),tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(tptp_fun_W1_43(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))),xO) ) )
| aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),xO) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szDzizrdt0(xd) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W1,szNzAzT0) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W1,xS) )
| ~ aElementOf0(tptp_fun_W1_0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))),tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szNzAzT0)
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),xS)
| ~ aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szDzozmdt0(xc))
| ( tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)) = slcrc0 ) ) ) ),
inference(monotonicity,[status(thm)],[103,102]) ).
tff(105,plain,
( ( ~ ( aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(xO,xK))
| ~ ( ( sbrdtbr0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != xK )
| ~ ( aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),xO)
| ~ ( ~ aSet0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| ~ ( ~ aElementOf0(tptp_fun_W1_43(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))),tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(tptp_fun_W1_43(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))),xO) ) ) ) ) )
| ~ ( ( tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)) = slcrc0 )
| ~ aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szDzozmdt0(xc))
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),xS)
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szNzAzT0)
| ~ aElementOf0(tptp_fun_W1_0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))),tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szDzizrdt0(xd) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W1,xS) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W1,szNzAzT0) ) ) )
<=> ( ~ ( aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(xO,xK))
| ~ ( ( sbrdtbr0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != xK )
| ~ ( ~ ( ~ aSet0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| ~ ( ~ aElementOf0(tptp_fun_W1_43(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))),tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(tptp_fun_W1_43(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))),xO) ) )
| aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),xO) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szDzizrdt0(xd) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W1,szNzAzT0) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W1,xS) )
| ~ aElementOf0(tptp_fun_W1_0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))),tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szNzAzT0)
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),xS)
| ~ aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szDzozmdt0(xc))
| ( tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)) = slcrc0 ) ) ) ),
inference(transitivity,[status(thm)],[104,101]) ).
tff(106,plain,
( ( ~ ! [W0: $i] :
( ~ ( aElementOf0(W0,slbdtsldtrb0(xO,xK))
| ~ ( ( sbrdtbr0(W0) != xK )
| ~ ( aSubsetOf0(W0,xO)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),xO) ) ) ) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aElementOf0(W0,szDzozmdt0(xc))
| ~ aSubsetOf0(W0,xS)
| ~ aSubsetOf0(W0,szNzAzT0)
| ~ aElementOf0(tptp_fun_W1_0(W0),W0)
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szNzAzT0) ) ) )
| ~ ( aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(xO,xK))
| ~ ( ( sbrdtbr0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != xK )
| ~ ( aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),xO)
| ~ ( ~ aSet0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| ~ ( ~ aElementOf0(tptp_fun_W1_43(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))),tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(tptp_fun_W1_43(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))),xO) ) ) ) ) )
| ~ ( ( tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)) = slcrc0 )
| ~ aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szDzozmdt0(xc))
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),xS)
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szNzAzT0)
| ~ aElementOf0(tptp_fun_W1_0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))),tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szDzizrdt0(xd) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W1,xS) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W1,szNzAzT0) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ ( aElementOf0(W0,slbdtsldtrb0(xO,xK))
| ~ ( ( sbrdtbr0(W0) != xK )
| ~ ( aSubsetOf0(W0,xO)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),xO) ) ) ) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aElementOf0(W0,szDzozmdt0(xc))
| ~ aSubsetOf0(W0,xS)
| ~ aSubsetOf0(W0,szNzAzT0)
| ~ aElementOf0(tptp_fun_W1_0(W0),W0)
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szNzAzT0) ) ) )
| ~ ( aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(xO,xK))
| ~ ( ( sbrdtbr0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != xK )
| ~ ( ~ ( ~ aSet0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| ~ ( ~ aElementOf0(tptp_fun_W1_43(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))),tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(tptp_fun_W1_43(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))),xO) ) )
| aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),xO) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szDzizrdt0(xd) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W1,szNzAzT0) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W1,xS) )
| ~ aElementOf0(tptp_fun_W1_0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))),tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szNzAzT0)
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),xS)
| ~ aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szDzozmdt0(xc))
| ( tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)) = slcrc0 ) ) ) ),
inference(monotonicity,[status(thm)],[105]) ).
tff(107,plain,
( ( ~ ! [W0: $i] :
( ~ ( aElementOf0(W0,slbdtsldtrb0(xO,xK))
| ~ ( ( sbrdtbr0(W0) != xK )
| ~ ( aSubsetOf0(W0,xO)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),xO) ) ) ) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aElementOf0(W0,szDzozmdt0(xc))
| ~ aSubsetOf0(W0,xS)
| ~ aSubsetOf0(W0,szNzAzT0)
| ~ aElementOf0(tptp_fun_W1_0(W0),W0)
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szNzAzT0) ) ) )
| ~ ( aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(xO,xK))
| ~ ( ( sbrdtbr0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != xK )
| ~ ( aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),xO)
| ~ ( ~ aSet0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| ~ ( ~ aElementOf0(tptp_fun_W1_43(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))),tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(tptp_fun_W1_43(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))),xO) ) ) ) ) )
| ~ ( ( tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)) = slcrc0 )
| ~ aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szDzozmdt0(xc))
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),xS)
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szNzAzT0)
| ~ aElementOf0(tptp_fun_W1_0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))),tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szDzizrdt0(xd) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W1,xS) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W1,szNzAzT0) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ ( aElementOf0(W0,slbdtsldtrb0(xO,xK))
| ~ ( ( sbrdtbr0(W0) != xK )
| ~ ( aSubsetOf0(W0,xO)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),xO) ) ) ) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aElementOf0(W0,szDzozmdt0(xc))
| ~ aSubsetOf0(W0,xS)
| ~ aSubsetOf0(W0,szNzAzT0)
| ~ aElementOf0(tptp_fun_W1_0(W0),W0)
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szNzAzT0) ) ) )
| ~ ( aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(xO,xK))
| ~ ( ( sbrdtbr0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != xK )
| ~ ( ~ ( ~ aSet0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| ~ ( ~ aElementOf0(tptp_fun_W1_43(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))),tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(tptp_fun_W1_43(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))),xO) ) )
| aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),xO) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szDzizrdt0(xd) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W1,szNzAzT0) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W1,xS) )
| ~ aElementOf0(tptp_fun_W1_0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))),tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szNzAzT0)
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),xS)
| ~ aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szDzozmdt0(xc))
| ( tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)) = slcrc0 ) ) ) ),
inference(transitivity,[status(thm)],[106,100]) ).
tff(108,plain,
( ~ ! [W0: $i] :
( ~ ( aElementOf0(W0,slbdtsldtrb0(xO,xK))
| ~ ( ( sbrdtbr0(W0) != xK )
| ~ ( aSubsetOf0(W0,xO)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),xO) ) ) ) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aElementOf0(W0,szDzozmdt0(xc))
| ~ aSubsetOf0(W0,xS)
| ~ aSubsetOf0(W0,szNzAzT0)
| ~ aElementOf0(tptp_fun_W1_0(W0),W0)
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szNzAzT0) ) ) )
| ~ ( aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(xO,xK))
| ~ ( ( sbrdtbr0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != xK )
| ~ ( aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),xO)
| ~ ( ~ aSet0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| ~ ( ~ aElementOf0(tptp_fun_W1_43(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))),tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(tptp_fun_W1_43(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))),xO) ) ) ) ) )
| ~ ( ( tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)) = slcrc0 )
| ~ aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szDzozmdt0(xc))
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),xS)
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szNzAzT0)
| ~ aElementOf0(tptp_fun_W1_0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))),tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szDzizrdt0(xd) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W1,xS) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W1,szNzAzT0) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(109,plain,
( ~ ! [W0: $i] :
( ~ ( aElementOf0(W0,slbdtsldtrb0(xO,xK))
| ~ ( ( sbrdtbr0(W0) != xK )
| ~ ( aSubsetOf0(W0,xO)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),xO) ) ) ) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aElementOf0(W0,szDzozmdt0(xc))
| ~ aSubsetOf0(W0,xS)
| ~ aSubsetOf0(W0,szNzAzT0)
| ~ aElementOf0(tptp_fun_W1_0(W0),W0)
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szNzAzT0) ) ) )
| ~ ( aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(xO,xK))
| ~ ( ( sbrdtbr0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != xK )
| ~ ( ~ ( ~ aSet0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| ~ ( ~ aElementOf0(tptp_fun_W1_43(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))),tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(tptp_fun_W1_43(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))),xO) ) )
| aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),xO) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szDzizrdt0(xd) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W1,szNzAzT0) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W1,xS) )
| ~ aElementOf0(tptp_fun_W1_0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))),tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szNzAzT0)
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),xS)
| ~ aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szDzozmdt0(xc))
| ( tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)) = slcrc0 ) ) ),
inference(modus_ponens,[status(thm)],[108,107]) ).
tff(110,plain,
~ ( aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(xO,xK))
| ~ ( ( sbrdtbr0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != xK )
| ~ ( ~ ( ~ aSet0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| ~ ( ~ aElementOf0(tptp_fun_W1_43(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))),tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(tptp_fun_W1_43(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))),xO) ) )
| aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),xO) ) ) ),
inference(unit_resolution,[status(thm)],[109,99,80]) ).
tff(111,plain,
( aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(xO,xK))
| ~ ( ( sbrdtbr0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != xK )
| ~ ( ~ ( ~ aSet0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| ~ ( ~ aElementOf0(tptp_fun_W1_43(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))),tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(tptp_fun_W1_43(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))),xO) ) )
| aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),xO) ) )
| ~ aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(xO,xK)) ),
inference(tautology,[status(thm)],[]) ).
tff(112,plain,
~ aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(xO,xK)),
inference(unit_resolution,[status(thm)],[111,110]) ).
tff(113,plain,
$false,
inference(unit_resolution,[status(thm)],[112,76]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM633+3 : TPTP v9.0.0. Released v4.0.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n005.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Fri Jun 20 01:37:20 EDT 2025
% 0.12/0.33 % CPUTime :
% 1.40/1.62 % SZS status Theorem
% 1.40/1.62 % SZS output start Proof
% See solution above
% 1.48/1.67 % E exiting
%------------------------------------------------------------------------------