TSTP Solution File: NUM633+3 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM633+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n018.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 : Sun Sep 18 13:11:04 EDT 2022
% Result : Theorem 3.73s 2.57s
% Output : Proof 3.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 72
% Syntax : Number of formulae : 137 ( 23 unt; 29 typ; 0 def)
% Number of atoms : 2620 ( 442 equ)
% Maximal formula atoms : 64 ( 24 avg)
% Number of connectives : 4552 (2162 ~;1806 |; 502 &)
% ( 63 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 11 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 122 ( 122 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 24 ( 17 >; 7 *; 0 +; 0 <<)
% Number of predicates : 19 ( 16 usr; 1 prp; 0-6 aty)
% Number of functors : 25 ( 25 usr; 12 con; 0-2 aty)
% Number of variables : 497 ( 428 !; 55 ?; 497 :)
% Comments :
%------------------------------------------------------------------------------
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(sdtlcdtrc0_type,type,
sdtlcdtrc0: ( $i * $i ) > $i ).
tff(sdtlbdtrb0_type,type,
sdtlbdtrb0: ( $i * $i ) > $i ).
tff(szDzizrdt0_type,type,
szDzizrdt0: $i > $i ).
tff(xd_type,type,
xd: $i ).
tff(xe_type,type,
xe: $i ).
tff(tptp_fun_W1_43_type,type,
tptp_fun_W1_43: $i > $i ).
tff(tptp_fun_W2_45_type,type,
tptp_fun_W2_45: ( $i * $i ) > $i ).
tff(aSet0_type,type,
aSet0: $i > $o ).
tff(aSubsetOf0_type,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff(szszuzczcdt0_type,type,
szszuzczcdt0: $i > $i ).
tff(xk_type,type,
xk: $i ).
tff(sbrdtbr0_type,type,
sbrdtbr0: $i > $i ).
tff(slbdtsldtrb0_type,type,
slbdtsldtrb0: ( $i * $i ) > $i ).
tff(sdtlpdtrp0_type,type,
sdtlpdtrp0: ( $i * $i ) > $i ).
tff(xc_type,type,
xc: $i ).
tff(sz00_type,type,
sz00: $i ).
tff(xN_type,type,
xN: $i ).
tff(tptp_fun_W2_44_type,type,
tptp_fun_W2_44: $i > $i ).
tff(xS_type,type,
xS: $i ).
tff(xO_type,type,
xO: $i ).
tff(isCountable0_type,type,
isCountable0: $i > $o ).
tff(xT_type,type,
xT: $i ).
tff(xK_type,type,
xK: $i ).
tff(szDzozmdt0_type,type,
szDzozmdt0: $i > $i ).
tff(szNzAzT0_type,type,
szNzAzT0: $i ).
tff(slcrc0_type,type,
slcrc0: $i ).
tff(tptp_fun_W1_0_type,type,
tptp_fun_W1_0: $i > $i ).
tff(slbdtrb0_type,type,
slbdtrb0: $i > $i ).
tff(1,plain,
( aSubsetOf0(xO,xS)
<=> aSubsetOf0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),sdtlpdtrp0(xN,sz00)) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( aSubsetOf0(xO,xS)
<=> aSubsetOf0(xO,xS) ),
inference(rewrite,[status(thm)],]) ).
tff(3,axiom,
( ! [W0: $i] :
( aElementOf0(W0,xO)
=> aElementOf0(W0,xS) )
& aSubsetOf0(xO,xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4998) ).
tff(4,plain,
aSubsetOf0(xO,xS),
inference(and_elim,[status(thm)],[3]) ).
tff(5,plain,
aSubsetOf0(xO,xS),
inference(modus_ponens,[status(thm)],[4,2]) ).
tff(6,plain,
aSubsetOf0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),sdtlpdtrp0(xN,sz00)),
inference(modus_ponens,[status(thm)],[5,1]) ).
tff(7,plain,
( aSubsetOf0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),sdtlpdtrp0(xN,sz00))
| ~ ( ~ 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)))),sdtlpdtrp0(xN,sz00)) ) )
| ~ aSubsetOf0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),sdtlpdtrp0(xN,sz00)) ),
inference(tautology,[status(thm)],]) ).
tff(8,plain,
( aSubsetOf0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),sdtlpdtrp0(xN,sz00))
| ~ ( ~ 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)))),sdtlpdtrp0(xN,sz00)) ) ) ),
inference(unit_resolution,[status(thm)],[7,6]) ).
tff(9,plain,
^ [W0: $i] :
rewrite(
( ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),sdtlpdtrp0(xN,sz00)) ) ) )
| ~ ( ( 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)) != szszuzczcdt0(xk) )
| ~ aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,szszuzczcdt0(xk))) ) ) )
<=> ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),sdtlpdtrp0(xN,sz00)) ) ) )
| ~ ( ( 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)) != szszuzczcdt0(xk) )
| ~ aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,szszuzczcdt0(xk)))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,W0))
| aElementOf0(W3,W1) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(10,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),sdtlpdtrp0(xN,sz00)) ) ) )
| ~ ( ( 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)) != szszuzczcdt0(xk) )
| ~ aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,szszuzczcdt0(xk))) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),sdtlpdtrp0(xN,sz00)) ) ) )
| ~ ( ( 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)) != szszuzczcdt0(xk) )
| ~ aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,szszuzczcdt0(xk)))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,W0))
| aElementOf0(W3,W1) ) ) ) ) ),
inference(quant_intro,[status(thm)],[9]) ).
tff(11,plain,
^ [W0: $i] :
refl(
( ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),sdtlpdtrp0(xN,sz00)) ) ) )
| ~ ( ( 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)) != szszuzczcdt0(xk) )
| ~ aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,szszuzczcdt0(xk))) ) ) )
<=> ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),sdtlpdtrp0(xN,sz00)) ) ) )
| ~ ( ( 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)) != szszuzczcdt0(xk) )
| ~ aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,szszuzczcdt0(xk))) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(12,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),sdtlpdtrp0(xN,sz00)) ) ) )
| ~ ( ( 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)) != szszuzczcdt0(xk) )
| ~ aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,szszuzczcdt0(xk))) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),sdtlpdtrp0(xN,sz00)) ) ) )
| ~ ( ( 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)) != szszuzczcdt0(xk) )
| ~ aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,szszuzczcdt0(xk))) ) ) ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
^ [W0: $i] :
rewrite(
( ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),sdtlpdtrp0(xN,sz00)) ) ) )
| ~ ( ( 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)) != szszuzczcdt0(xk) )
| ~ aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,szszuzczcdt0(xk))) ) ) )
<=> ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),sdtlpdtrp0(xN,sz00)) ) ) )
| ~ ( ( 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)) != szszuzczcdt0(xk) )
| ~ aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,szszuzczcdt0(xk))) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(14,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),sdtlpdtrp0(xN,sz00)) ) ) )
| ~ ( ( 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)) != szszuzczcdt0(xk) )
| ~ aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,szszuzczcdt0(xk))) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),sdtlpdtrp0(xN,sz00)) ) ) )
| ~ ( ( 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)) != szszuzczcdt0(xk) )
| ~ aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,szszuzczcdt0(xk))) ) ) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),sdtlpdtrp0(xN,sz00)) ) ) )
| ~ ( ( 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)) != szszuzczcdt0(xk) )
| ~ aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,szszuzczcdt0(xk))) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),sdtlpdtrp0(xN,sz00)) ) ) )
| ~ ( ( 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)) != szszuzczcdt0(xk) )
| ~ aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,szszuzczcdt0(xk))) ) ) ) ),
inference(transitivity,[status(thm)],[14,12]) ).
tff(16,plain,
^ [W0: $i] :
rewrite(
( ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
& ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),sdtlpdtrp0(xN,sz00)) ) ) )
| ( 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)) = szszuzczcdt0(xk) )
& aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,szszuzczcdt0(xk)))
& ( sdtlpdtrp0(xc,tptp_fun_W2_45(W1,W0)) != W0 ) ) ) )
<=> ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),sdtlpdtrp0(xN,sz00)) ) ) )
| ~ ( ( 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)) != szszuzczcdt0(xk) )
| ~ aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,szszuzczcdt0(xk))) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(17,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
& ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),sdtlpdtrp0(xN,sz00)) ) ) )
| ( 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)) = szszuzczcdt0(xk) )
& aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,szszuzczcdt0(xk)))
& ( sdtlpdtrp0(xc,tptp_fun_W2_45(W1,W0)) != W0 ) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),sdtlpdtrp0(xN,sz00)) ) ) )
| ~ ( ( 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)) != szszuzczcdt0(xk) )
| ~ aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,szszuzczcdt0(xk))) ) ) ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,plain,
^ [W0: $i] :
rewrite(
( ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
& ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),sdtlpdtrp0(xN,sz00)) ) ) )
| ~ 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)) = szszuzczcdt0(xk) )
& aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,szszuzczcdt0(xk)))
& ( sdtlpdtrp0(xc,tptp_fun_W2_45(W1,W0)) != W0 ) ) ) )
<=> ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
& ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),sdtlpdtrp0(xN,sz00)) ) ) )
| ( 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)) = szszuzczcdt0(xk) )
& aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,szszuzczcdt0(xk)))
& ( sdtlpdtrp0(xc,tptp_fun_W2_45(W1,W0)) != W0 ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(19,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
& ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),sdtlpdtrp0(xN,sz00)) ) ) )
| ~ 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)) = szszuzczcdt0(xk) )
& aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,szszuzczcdt0(xk)))
& ( sdtlpdtrp0(xc,tptp_fun_W2_45(W1,W0)) != W0 ) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
& ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),sdtlpdtrp0(xN,sz00)) ) ) )
| ( 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)) = szszuzczcdt0(xk) )
& aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,szszuzczcdt0(xk)))
& ( sdtlpdtrp0(xc,tptp_fun_W2_45(W1,W0)) != W0 ) ) ) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( ( aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlpdtrp0(xN,sz00)) ) ) )
& isCountable0(W1)
& ! [W2: $i] :
( ~ ( aSet0(W2)
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) )
& aSubsetOf0(W2,W1)
& ( sbrdtbr0(W2) = szszuzczcdt0(xk) )
& aElementOf0(W2,slbdtsldtrb0(W1,szszuzczcdt0(xk))) )
| ( sdtlpdtrp0(xc,W2) = W0 ) ) ) )
<=> ~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( ( aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlpdtrp0(xN,sz00)) ) ) )
& isCountable0(W1)
& ! [W2: $i] :
( ~ ( aSet0(W2)
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) )
& aSubsetOf0(W2,W1)
& ( sbrdtbr0(W2) = szszuzczcdt0(xk) )
& aElementOf0(W2,slbdtsldtrb0(W1,szszuzczcdt0(xk))) )
| ( sdtlpdtrp0(xc,W2) = W0 ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(21,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,sdtlpdtrp0(xN,sz00))
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlpdtrp0(xN,sz00)) ) ) )
& isCountable0(W1)
& ! [W2: $i] :
( ~ ( aSet0(W2)
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) )
& aSubsetOf0(W2,W1)
& ( sbrdtbr0(W2) = szszuzczcdt0(xk) )
& aElementOf0(W2,slbdtsldtrb0(W1,szszuzczcdt0(xk))) )
| ( sdtlpdtrp0(xc,W2) = W0 ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(22,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(23,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(24,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(25,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)],[24,23]) ).
tff(26,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)],[25]) ).
tff(27,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)],[26,22]) ).
tff(28,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)],[27,22]) ).
tff(29,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)],[28,22]) ).
tff(30,plain,
~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( ( aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlpdtrp0(xN,sz00)) ) ) )
& isCountable0(W1)
& ! [W2: $i] :
( ~ ( aSet0(W2)
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) )
& aSubsetOf0(W2,W1)
& ( sbrdtbr0(W2) = szszuzczcdt0(xk) )
& aElementOf0(W2,slbdtsldtrb0(W1,szszuzczcdt0(xk))) )
| ( sdtlpdtrp0(xc,W2) = W0 ) ) ) ),
inference(modus_ponens,[status(thm)],[29,21]) ).
tff(31,plain,
~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( ( aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlpdtrp0(xN,sz00)) ) ) )
& isCountable0(W1)
& ! [W2: $i] :
( ~ ( aSet0(W2)
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) )
& aSubsetOf0(W2,W1)
& ( sbrdtbr0(W2) = szszuzczcdt0(xk) )
& aElementOf0(W2,slbdtsldtrb0(W1,szszuzczcdt0(xk))) )
| ( sdtlpdtrp0(xc,W2) = W0 ) ) ) ),
inference(modus_ponens,[status(thm)],[30,20]) ).
tff(32,plain,
~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( ( aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlpdtrp0(xN,sz00)) ) ) )
& isCountable0(W1)
& ! [W2: $i] :
( ~ ( aSet0(W2)
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) )
& aSubsetOf0(W2,W1)
& ( sbrdtbr0(W2) = szszuzczcdt0(xk) )
& aElementOf0(W2,slbdtsldtrb0(W1,szszuzczcdt0(xk))) )
| ( sdtlpdtrp0(xc,W2) = W0 ) ) ) ),
inference(modus_ponens,[status(thm)],[31,20]) ).
tff(33,plain,
~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( ( aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlpdtrp0(xN,sz00)) ) ) )
& isCountable0(W1)
& ! [W2: $i] :
( ~ ( aSet0(W2)
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) )
& aSubsetOf0(W2,W1)
& ( sbrdtbr0(W2) = szszuzczcdt0(xk) )
& aElementOf0(W2,slbdtsldtrb0(W1,szszuzczcdt0(xk))) )
| ( sdtlpdtrp0(xc,W2) = W0 ) ) ) ),
inference(modus_ponens,[status(thm)],[32,20]) ).
tff(34,plain,
~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( ( aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlpdtrp0(xN,sz00)) ) ) )
& isCountable0(W1)
& ! [W2: $i] :
( ~ ( aSet0(W2)
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) )
& aSubsetOf0(W2,W1)
& ( sbrdtbr0(W2) = szszuzczcdt0(xk) )
& aElementOf0(W2,slbdtsldtrb0(W1,szszuzczcdt0(xk))) )
| ( sdtlpdtrp0(xc,W2) = W0 ) ) ) ),
inference(modus_ponens,[status(thm)],[33,20]) ).
tff(35,plain,
~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( ( aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlpdtrp0(xN,sz00)) ) ) )
& isCountable0(W1)
& ! [W2: $i] :
( ~ ( aSet0(W2)
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) )
& aSubsetOf0(W2,W1)
& ( sbrdtbr0(W2) = szszuzczcdt0(xk) )
& aElementOf0(W2,slbdtsldtrb0(W1,szszuzczcdt0(xk))) )
| ( sdtlpdtrp0(xc,W2) = W0 ) ) ) ),
inference(modus_ponens,[status(thm)],[34,20]) ).
tff(36,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,sdtlpdtrp0(xN,sz00)),~ aSubsetOf0(W1,sdtlpdtrp0(xN,sz00)))),
nnf_neg(refl($oeq(~ aSet0(W1),~ aSet0(W1))),
sk(
$oeq(
~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlpdtrp0(xN,sz00)) ),
~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),sdtlpdtrp0(xN,sz00)) ))),
$oeq(
~ ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlpdtrp0(xN,sz00)) ) ),
( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),sdtlpdtrp0(xN,sz00)) ) ))),
$oeq(
~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlpdtrp0(xN,sz00)) ) ) ),
( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
& ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),sdtlpdtrp0(xN,sz00)) ) ) ))),
refl($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) = szszuzczcdt0(xk) )
& aElementOf0(W2,slbdtsldtrb0(W1,szszuzczcdt0(xk))) )
| ( sdtlpdtrp0(xc,W2) = W0 ) ),
~ ( ~ ( aSet0(tptp_fun_W2_45(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_45(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_45(W1,W0)) = szszuzczcdt0(xk) )
& aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,szszuzczcdt0(xk))) )
| ( sdtlpdtrp0(xc,tptp_fun_W2_45(W1,W0)) = W0 ) ))),
nnf_neg(
nnf_neg(
monotonicity(refl($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($oeq(sbrdtbr0(tptp_fun_W2_45(W1,W0)) = szszuzczcdt0(xk),sbrdtbr0(tptp_fun_W2_45(W1,W0)) = szszuzczcdt0(xk))),refl($oeq(aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,szszuzczcdt0(xk))),aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,szszuzczcdt0(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)) = szszuzczcdt0(xk) )
& aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,szszuzczcdt0(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)) = szszuzczcdt0(xk) )
& aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,szszuzczcdt0(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)) = szszuzczcdt0(xk) )
& aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,szszuzczcdt0(xk))) ),
( aSet0(tptp_fun_W2_45(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_45(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_45(W1,W0)) = szszuzczcdt0(xk) )
& aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,szszuzczcdt0(xk))) ))),
refl($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)) = szszuzczcdt0(xk) )
& aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,szszuzczcdt0(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)) = szszuzczcdt0(xk) )
& aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,szszuzczcdt0(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) = szszuzczcdt0(xk) )
& aElementOf0(W2,slbdtsldtrb0(W1,szszuzczcdt0(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)) = szszuzczcdt0(xk) )
& aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,szszuzczcdt0(xk)))
& ( sdtlpdtrp0(xc,tptp_fun_W2_45(W1,W0)) != W0 ) ))),
$oeq(
~ ( ( aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlpdtrp0(xN,sz00)) ) ) )
& isCountable0(W1)
& ! [W2: $i] :
( ~ ( aSet0(W2)
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) )
& aSubsetOf0(W2,W1)
& ( sbrdtbr0(W2) = szszuzczcdt0(xk) )
& aElementOf0(W2,slbdtsldtrb0(W1,szszuzczcdt0(xk))) )
| ( sdtlpdtrp0(xc,W2) = W0 ) ) ),
( ( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
& ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),sdtlpdtrp0(xN,sz00)) ) ) )
| ~ 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)) = szszuzczcdt0(xk) )
& aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,szszuzczcdt0(xk)))
& ( sdtlpdtrp0(xc,tptp_fun_W2_45(W1,W0)) != W0 ) ) )))),
$oeq(
~ ? [W1: $i] :
( ( aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlpdtrp0(xN,sz00)) ) ) )
& isCountable0(W1)
& ! [W2: $i] :
( ~ ( aSet0(W2)
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) )
& aSubsetOf0(W2,W1)
& ( sbrdtbr0(W2) = szszuzczcdt0(xk) )
& aElementOf0(W2,slbdtsldtrb0(W1,szszuzczcdt0(xk))) )
| ( sdtlpdtrp0(xc,W2) = W0 ) ) ),
! [W1: $i] :
( ( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
& ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),sdtlpdtrp0(xN,sz00)) ) ) )
| ~ 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)) = szszuzczcdt0(xk) )
& aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,szszuzczcdt0(xk)))
& ( sdtlpdtrp0(xc,tptp_fun_W2_45(W1,W0)) != W0 ) ) ))),
$oeq(
~ ( aElementOf0(W0,xT)
& ? [W1: $i] :
( ( aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlpdtrp0(xN,sz00)) ) ) )
& isCountable0(W1)
& ! [W2: $i] :
( ~ ( aSet0(W2)
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) )
& aSubsetOf0(W2,W1)
& ( sbrdtbr0(W2) = szszuzczcdt0(xk) )
& aElementOf0(W2,slbdtsldtrb0(W1,szszuzczcdt0(xk))) )
| ( sdtlpdtrp0(xc,W2) = W0 ) ) ) ),
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
& ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),sdtlpdtrp0(xN,sz00)) ) ) )
| ~ 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)) = szszuzczcdt0(xk) )
& aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,szszuzczcdt0(xk)))
& ( sdtlpdtrp0(xc,tptp_fun_W2_45(W1,W0)) != W0 ) ) ) ))),
inference(bind,[status(th)],]) ).
tff(37,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
& ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),sdtlpdtrp0(xN,sz00)) ) ) )
| ~ 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)) = szszuzczcdt0(xk) )
& aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,szszuzczcdt0(xk)))
& ( sdtlpdtrp0(xc,tptp_fun_W2_45(W1,W0)) != W0 ) ) ) ),
inference(nnf-neg,[status(sab)],[35,36]) ).
tff(38,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
& ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),sdtlpdtrp0(xN,sz00)) ) ) )
| ( 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)) = szszuzczcdt0(xk) )
& aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,szszuzczcdt0(xk)))
& ( sdtlpdtrp0(xc,tptp_fun_W2_45(W1,W0)) != W0 ) ) ) ),
inference(modus_ponens,[status(thm)],[37,19]) ).
tff(39,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),sdtlpdtrp0(xN,sz00)) ) ) )
| ~ ( ( 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)) != szszuzczcdt0(xk) )
| ~ aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,szszuzczcdt0(xk))) ) ) ),
inference(modus_ponens,[status(thm)],[38,17]) ).
tff(40,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),sdtlpdtrp0(xN,sz00)) ) ) )
| ~ ( ( 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)) != szszuzczcdt0(xk) )
| ~ aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,szszuzczcdt0(xk))) ) ) ),
inference(modus_ponens,[status(thm)],[39,15]) ).
tff(41,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),sdtlpdtrp0(xN,sz00)) ) ) )
| ~ ( ( 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)) != szszuzczcdt0(xk) )
| ~ aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,szszuzczcdt0(xk)))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,W0))
| aElementOf0(W3,W1) ) ) ) ),
inference(modus_ponens,[status(thm)],[40,10]) ).
tff(42,plain,
( aElementOf0(szDzizrdt0(xd),xT)
<=> aElementOf0(szDzizrdt0(xd),xT) ),
inference(rewrite,[status(thm)],]) ).
tff(43,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(44,plain,
( aElementOf0(szDzizrdt0(xd),xT)
& aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
inference(and_elim,[status(thm)],[43]) ).
tff(45,plain,
aElementOf0(szDzizrdt0(xd),xT),
inference(and_elim,[status(thm)],[44]) ).
tff(46,plain,
aElementOf0(szDzizrdt0(xd),xT),
inference(modus_ponens,[status(thm)],[45,42]) ).
tff(47,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),sdtlpdtrp0(xN,sz00)) ) ) )
| ~ ( ( 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)) != szszuzczcdt0(xk) )
| ~ aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,szszuzczcdt0(xk)))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,W0))
| aElementOf0(W3,W1) ) ) ) )
| ~ aElementOf0(szDzizrdt0(xd),xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),sdtlpdtrp0(xN,sz00)) ) ) )
| ~ ( ( 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))) != szszuzczcdt0(xk) )
| ~ aElementOf0(tptp_fun_W2_45(W1,szDzizrdt0(xd)),slbdtsldtrb0(W1,szszuzczcdt0(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,sdtlpdtrp0(xN,sz00))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),sdtlpdtrp0(xN,sz00)) ) ) )
| ~ ( ( 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)) != szszuzczcdt0(xk) )
| ~ aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,szszuzczcdt0(xk)))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,W0))
| aElementOf0(W3,W1) ) ) ) )
| ~ aElementOf0(szDzizrdt0(xd),xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),sdtlpdtrp0(xN,sz00)) ) ) )
| ~ ( ( 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))) != szszuzczcdt0(xk) )
| ~ aElementOf0(tptp_fun_W2_45(W1,szDzizrdt0(xd)),slbdtsldtrb0(W1,szszuzczcdt0(xk)))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,szDzizrdt0(xd)))
| aElementOf0(W3,W1) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(48,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),sdtlpdtrp0(xN,sz00)) ) ) )
| ~ ( ( 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)) != szszuzczcdt0(xk) )
| ~ aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,szszuzczcdt0(xk)))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,W0))
| aElementOf0(W3,W1) ) ) ) )
| ~ aElementOf0(szDzizrdt0(xd),xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),sdtlpdtrp0(xN,sz00)) ) ) )
| ~ ( ( 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))) != szszuzczcdt0(xk) )
| ~ aElementOf0(tptp_fun_W2_45(W1,szDzizrdt0(xd)),slbdtsldtrb0(W1,szszuzczcdt0(xk)))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,szDzizrdt0(xd)))
| aElementOf0(W3,W1) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(49,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),sdtlpdtrp0(xN,sz00)) ) ) )
| ~ ( ( 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)) != szszuzczcdt0(xk) )
| ~ aElementOf0(tptp_fun_W2_45(W1,W0),slbdtsldtrb0(W1,szszuzczcdt0(xk)))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,W0))
| aElementOf0(W3,W1) ) ) ) )
| ~ aElementOf0(szDzizrdt0(xd),xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),sdtlpdtrp0(xN,sz00)) ) ) )
| ~ ( ( 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))) != szszuzczcdt0(xk) )
| ~ aElementOf0(tptp_fun_W2_45(W1,szDzizrdt0(xd)),slbdtsldtrb0(W1,szszuzczcdt0(xk)))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,szDzizrdt0(xd)))
| aElementOf0(W3,W1) ) ) ) ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),sdtlpdtrp0(xN,sz00)) ) ) )
| ~ ( ( 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))) != szszuzczcdt0(xk) )
| ~ aElementOf0(tptp_fun_W2_45(W1,szDzizrdt0(xd)),slbdtsldtrb0(W1,szszuzczcdt0(xk)))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,szDzizrdt0(xd)))
| aElementOf0(W3,W1) ) ) ),
inference(unit_resolution,[status(thm)],[49,46,41]) ).
tff(51,plain,
( isCountable0(xO)
<=> isCountable0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ),
inference(rewrite,[status(thm)],]) ).
tff(52,plain,
( isCountable0(xO)
<=> isCountable0(xO) ),
inference(rewrite,[status(thm)],]) ).
tff(53,axiom,
( aSet0(xO)
& isCountable0(xO) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4908) ).
tff(54,plain,
isCountable0(xO),
inference(and_elim,[status(thm)],[53]) ).
tff(55,plain,
isCountable0(xO),
inference(modus_ponens,[status(thm)],[54,52]) ).
tff(56,plain,
isCountable0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),
inference(modus_ponens,[status(thm)],[55,51]) ).
tff(57,plain,
( ( ~ ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),sdtlpdtrp0(xN,sz00)) ) ) )
| ~ ( ( 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))) != szszuzczcdt0(xk) )
| ~ aElementOf0(tptp_fun_W2_45(W1,szDzizrdt0(xd)),slbdtsldtrb0(W1,szszuzczcdt0(xk)))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,szDzizrdt0(xd)))
| aElementOf0(W3,W1) ) ) )
| ~ isCountable0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( aSubsetOf0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),sdtlpdtrp0(xN,sz00))
| ~ ( ~ 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)))),sdtlpdtrp0(xN,sz00)) ) ) )
| ~ ( ( 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))))
| ~ aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ( sbrdtbr0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szszuzczcdt0(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,sdtlpdtrp0(xN,sz00))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),sdtlpdtrp0(xN,sz00)) ) ) )
| ~ ( ( 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))) != szszuzczcdt0(xk) )
| ~ aElementOf0(tptp_fun_W2_45(W1,szDzizrdt0(xd)),slbdtsldtrb0(W1,szszuzczcdt0(xk)))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,szDzizrdt0(xd)))
| aElementOf0(W3,W1) ) ) )
| ~ isCountable0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( aSubsetOf0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),sdtlpdtrp0(xN,sz00))
| ~ ( ~ 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)))),sdtlpdtrp0(xN,sz00)) ) ) )
| ~ ( ( 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))))
| ~ aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ( sbrdtbr0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szszuzczcdt0(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(58,plain,
( ( ~ isCountable0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( aSubsetOf0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),sdtlpdtrp0(xN,sz00))
| ~ ( ~ 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)))),sdtlpdtrp0(xN,sz00)) ) ) )
| ~ ( ( 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))))
| ~ aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ( sbrdtbr0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szszuzczcdt0(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))),sdtlpdtrp0(xN,sz00))
| ~ ( ~ 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)))),sdtlpdtrp0(xN,sz00)) ) ) )
| ~ ( ( 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))))
| ~ aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ( sbrdtbr0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szszuzczcdt0(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(59,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))) != szszuzczcdt0(xk) )
| ~ aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(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) )
| ~ 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))))
| ~ aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ( sbrdtbr0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szszuzczcdt0(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(60,plain,
( ~ ( aSubsetOf0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),sdtlpdtrp0(xN,sz00))
| ~ ( ~ 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)))),sdtlpdtrp0(xN,sz00)) ) ) )
<=> ~ ( aSubsetOf0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),sdtlpdtrp0(xN,sz00))
| ~ ( ~ 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)))),sdtlpdtrp0(xN,sz00)) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(61,plain,
( ( ~ isCountable0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( aSubsetOf0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),sdtlpdtrp0(xN,sz00))
| ~ ( ~ 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)))),sdtlpdtrp0(xN,sz00)) ) ) )
| ~ ( ( 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))) != szszuzczcdt0(xk) )
| ~ aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(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))),sdtlpdtrp0(xN,sz00))
| ~ ( ~ 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)))),sdtlpdtrp0(xN,sz00)) ) ) )
| ~ ( ( 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))))
| ~ aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ( sbrdtbr0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szszuzczcdt0(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)],[60,59]) ).
tff(62,plain,
( ( ~ isCountable0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( aSubsetOf0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),sdtlpdtrp0(xN,sz00))
| ~ ( ~ 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)))),sdtlpdtrp0(xN,sz00)) ) ) )
| ~ ( ( 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))) != szszuzczcdt0(xk) )
| ~ aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(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))),sdtlpdtrp0(xN,sz00))
| ~ ( ~ 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)))),sdtlpdtrp0(xN,sz00)) ) ) )
| ~ ( ( 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))))
| ~ aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ( sbrdtbr0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szszuzczcdt0(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)],[61,58]) ).
tff(63,plain,
( ( ~ ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),sdtlpdtrp0(xN,sz00)) ) ) )
| ~ ( ( 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))) != szszuzczcdt0(xk) )
| ~ aElementOf0(tptp_fun_W2_45(W1,szDzizrdt0(xd)),slbdtsldtrb0(W1,szszuzczcdt0(xk)))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,szDzizrdt0(xd)))
| aElementOf0(W3,W1) ) ) )
| ~ isCountable0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( aSubsetOf0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),sdtlpdtrp0(xN,sz00))
| ~ ( ~ 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)))),sdtlpdtrp0(xN,sz00)) ) ) )
| ~ ( ( 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))) != szszuzczcdt0(xk) )
| ~ aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(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,sdtlpdtrp0(xN,sz00))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),sdtlpdtrp0(xN,sz00)) ) ) )
| ~ ( ( 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))) != szszuzczcdt0(xk) )
| ~ aElementOf0(tptp_fun_W2_45(W1,szDzizrdt0(xd)),slbdtsldtrb0(W1,szszuzczcdt0(xk)))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,szDzizrdt0(xd)))
| aElementOf0(W3,W1) ) ) )
| ~ isCountable0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( aSubsetOf0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),sdtlpdtrp0(xN,sz00))
| ~ ( ~ 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)))),sdtlpdtrp0(xN,sz00)) ) ) )
| ~ ( ( 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))))
| ~ aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ( sbrdtbr0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szszuzczcdt0(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)],[62]) ).
tff(64,plain,
( ( ~ ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),sdtlpdtrp0(xN,sz00)) ) ) )
| ~ ( ( 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))) != szszuzczcdt0(xk) )
| ~ aElementOf0(tptp_fun_W2_45(W1,szDzizrdt0(xd)),slbdtsldtrb0(W1,szszuzczcdt0(xk)))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,szDzizrdt0(xd)))
| aElementOf0(W3,W1) ) ) )
| ~ isCountable0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( aSubsetOf0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),sdtlpdtrp0(xN,sz00))
| ~ ( ~ 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)))),sdtlpdtrp0(xN,sz00)) ) ) )
| ~ ( ( 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))) != szszuzczcdt0(xk) )
| ~ aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(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,sdtlpdtrp0(xN,sz00))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),sdtlpdtrp0(xN,sz00)) ) ) )
| ~ ( ( 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))) != szszuzczcdt0(xk) )
| ~ aElementOf0(tptp_fun_W2_45(W1,szDzizrdt0(xd)),slbdtsldtrb0(W1,szszuzczcdt0(xk)))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,szDzizrdt0(xd)))
| aElementOf0(W3,W1) ) ) )
| ~ isCountable0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( aSubsetOf0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),sdtlpdtrp0(xN,sz00))
| ~ ( ~ 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)))),sdtlpdtrp0(xN,sz00)) ) ) )
| ~ ( ( 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))))
| ~ aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ( sbrdtbr0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szszuzczcdt0(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)],[63,57]) ).
tff(65,plain,
( ~ ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),sdtlpdtrp0(xN,sz00)) ) ) )
| ~ ( ( 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))) != szszuzczcdt0(xk) )
| ~ aElementOf0(tptp_fun_W2_45(W1,szDzizrdt0(xd)),slbdtsldtrb0(W1,szszuzczcdt0(xk)))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,szDzizrdt0(xd)))
| aElementOf0(W3,W1) ) ) )
| ~ isCountable0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( aSubsetOf0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),sdtlpdtrp0(xN,sz00))
| ~ ( ~ 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)))),sdtlpdtrp0(xN,sz00)) ) ) )
| ~ ( ( 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))) != szszuzczcdt0(xk) )
| ~ aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(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(quant_inst,[status(thm)],]) ).
tff(66,plain,
( ~ ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_44(W1),W1)
| aElementOf0(tptp_fun_W2_44(W1),sdtlpdtrp0(xN,sz00)) ) ) )
| ~ ( ( 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))) != szszuzczcdt0(xk) )
| ~ aElementOf0(tptp_fun_W2_45(W1,szDzizrdt0(xd)),slbdtsldtrb0(W1,szszuzczcdt0(xk)))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_45(W1,szDzizrdt0(xd)))
| aElementOf0(W3,W1) ) ) )
| ~ isCountable0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( aSubsetOf0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),sdtlpdtrp0(xN,sz00))
| ~ ( ~ 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)))),sdtlpdtrp0(xN,sz00)) ) ) )
| ~ ( ( 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))))
| ~ aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ( sbrdtbr0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szszuzczcdt0(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)],[65,64]) ).
tff(67,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))))
| ~ aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ( sbrdtbr0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szszuzczcdt0(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)],[66,56,50,8]) ).
tff(68,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))))
| ~ aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ( sbrdtbr0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szszuzczcdt0(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))),szszuzczcdt0(xk))) ),
inference(tautology,[status(thm)],]) ).
tff(69,plain,
aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk))),
inference(unit_resolution,[status(thm)],[68,67]) ).
tff(70,plain,
( aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( sbrdtbr0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szszuzczcdt0(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)))
| ~ ( ~ 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))),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))),szszuzczcdt0(xk))) ),
inference(tautology,[status(thm)],]) ).
tff(71,plain,
( aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( sbrdtbr0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szszuzczcdt0(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)))
| ~ ( ~ 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))),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) ),
inference(unit_resolution,[status(thm)],[70,69]) ).
tff(72,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))))
| ~ aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ( sbrdtbr0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szszuzczcdt0(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(73,plain,
sdtlpdtrp0(xc,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szDzizrdt0(xd),
inference(unit_resolution,[status(thm)],[72,67]) ).
tff(74,plain,
( ( sdtlpdtrp0(xc,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szDzizrdt0(xd) )
| ~ 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)) = slbdtrb0(sz00) )
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),sdtlpdtrp0(xN,sz00))
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szDzozmdt0(xN))
| ~ 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)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W1,sdtlpdtrp0(xN,sz00)) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W1,szDzozmdt0(xN)) )
| ( sdtlpdtrp0(xc,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) = szDzizrdt0(xd) ) ),
inference(tautology,[status(thm)],]) ).
tff(75,plain,
( ( sdtlpdtrp0(xc,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szDzizrdt0(xd) )
| ~ 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)) = slbdtrb0(sz00) )
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),sdtlpdtrp0(xN,sz00))
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szDzozmdt0(xN))
| ~ 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)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W1,sdtlpdtrp0(xN,sz00)) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W1,szDzozmdt0(xN)) ) ),
inference(unit_resolution,[status(thm)],[74,73]) ).
tff(76,plain,
^ [W0: $i] :
trans(
monotonicity(
rewrite(
( ~ ( aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( sbrdtbr0(W0) != szszuzczcdt0(xk) )
| ~ ( aSubsetOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) )
<=> ~ ( aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( sbrdtbr0(W0) != szszuzczcdt0(xk) )
| ~ ( aSubsetOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) ) )),
rewrite(
( ~ ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,sdtlpdtrp0(xN,sz00))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,sdtlpdtrp0(xN,sz00)) )
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_0(W0),W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szDzozmdt0(xN)) )
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) ) )
<=> ~ ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,sdtlpdtrp0(xN,sz00))
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_0(W0),W0)
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,sdtlpdtrp0(xN,sz00)) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szDzozmdt0(xN)) ) ) )),
( ( ~ ( aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( sbrdtbr0(W0) != szszuzczcdt0(xk) )
| ~ ( aSubsetOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) )
| ~ ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,sdtlpdtrp0(xN,sz00))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,sdtlpdtrp0(xN,sz00)) )
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_0(W0),W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szDzozmdt0(xN)) )
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) ) ) )
<=> ( ~ ( aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( sbrdtbr0(W0) != szszuzczcdt0(xk) )
| ~ ( aSubsetOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) )
| ~ ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,sdtlpdtrp0(xN,sz00))
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_0(W0),W0)
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,sdtlpdtrp0(xN,sz00)) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szDzozmdt0(xN)) ) ) ) )),
rewrite(
( ( ~ ( aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( sbrdtbr0(W0) != szszuzczcdt0(xk) )
| ~ ( aSubsetOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) )
| ~ ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,sdtlpdtrp0(xN,sz00))
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_0(W0),W0)
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,sdtlpdtrp0(xN,sz00)) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szDzozmdt0(xN)) ) ) )
<=> ( ~ ( aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( sbrdtbr0(W0) != szszuzczcdt0(xk) )
| ~ ( aSubsetOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) )
| ~ ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,sdtlpdtrp0(xN,sz00))
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_0(W0),W0)
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,sdtlpdtrp0(xN,sz00)) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szDzozmdt0(xN)) ) ) ) )),
( ( ~ ( aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( sbrdtbr0(W0) != szszuzczcdt0(xk) )
| ~ ( aSubsetOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) )
| ~ ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,sdtlpdtrp0(xN,sz00))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,sdtlpdtrp0(xN,sz00)) )
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_0(W0),W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szDzozmdt0(xN)) )
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) ) ) )
<=> ( ~ ( aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( sbrdtbr0(W0) != szszuzczcdt0(xk) )
| ~ ( aSubsetOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) )
| ~ ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,sdtlpdtrp0(xN,sz00))
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_0(W0),W0)
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,sdtlpdtrp0(xN,sz00)) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szDzozmdt0(xN)) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(77,plain,
( ! [W0: $i] :
( ~ ( aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( sbrdtbr0(W0) != szszuzczcdt0(xk) )
| ~ ( aSubsetOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) )
| ~ ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,sdtlpdtrp0(xN,sz00))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,sdtlpdtrp0(xN,sz00)) )
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_0(W0),W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szDzozmdt0(xN)) )
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) ) ) )
<=> ! [W0: $i] :
( ~ ( aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( sbrdtbr0(W0) != szszuzczcdt0(xk) )
| ~ ( aSubsetOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) )
| ~ ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,sdtlpdtrp0(xN,sz00))
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_0(W0),W0)
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,sdtlpdtrp0(xN,sz00)) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szDzozmdt0(xN)) ) ) ) ),
inference(quant_intro,[status(thm)],[76]) ).
tff(78,plain,
^ [W0: $i] :
refl(
( ( ~ ( aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( sbrdtbr0(W0) != szszuzczcdt0(xk) )
| ~ ( aSubsetOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) )
| ~ ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,sdtlpdtrp0(xN,sz00))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,sdtlpdtrp0(xN,sz00)) )
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_0(W0),W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szDzozmdt0(xN)) )
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) ) ) )
<=> ( ~ ( aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( sbrdtbr0(W0) != szszuzczcdt0(xk) )
| ~ ( aSubsetOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) )
| ~ ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,sdtlpdtrp0(xN,sz00))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,sdtlpdtrp0(xN,sz00)) )
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_0(W0),W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szDzozmdt0(xN)) )
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(79,plain,
( ! [W0: $i] :
( ~ ( aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( sbrdtbr0(W0) != szszuzczcdt0(xk) )
| ~ ( aSubsetOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) )
| ~ ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,sdtlpdtrp0(xN,sz00))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,sdtlpdtrp0(xN,sz00)) )
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_0(W0),W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szDzozmdt0(xN)) )
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) ) ) )
<=> ! [W0: $i] :
( ~ ( aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( sbrdtbr0(W0) != szszuzczcdt0(xk) )
| ~ ( aSubsetOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) )
| ~ ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,sdtlpdtrp0(xN,sz00))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,sdtlpdtrp0(xN,sz00)) )
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_0(W0),W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szDzozmdt0(xN)) )
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) ) ) ) ),
inference(quant_intro,[status(thm)],[78]) ).
tff(80,plain,
^ [W0: $i] :
rewrite(
( ( ~ ( aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( sbrdtbr0(W0) != szszuzczcdt0(xk) )
| ~ ( aSubsetOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) )
| ~ ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,sdtlpdtrp0(xN,sz00))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,sdtlpdtrp0(xN,sz00)) )
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_0(W0),W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szDzozmdt0(xN)) )
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) ) ) )
<=> ( ~ ( aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( sbrdtbr0(W0) != szszuzczcdt0(xk) )
| ~ ( aSubsetOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) )
| ~ ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,sdtlpdtrp0(xN,sz00))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,sdtlpdtrp0(xN,sz00)) )
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_0(W0),W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szDzozmdt0(xN)) )
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(81,plain,
( ! [W0: $i] :
( ~ ( aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( sbrdtbr0(W0) != szszuzczcdt0(xk) )
| ~ ( aSubsetOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) )
| ~ ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,sdtlpdtrp0(xN,sz00))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,sdtlpdtrp0(xN,sz00)) )
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_0(W0),W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szDzozmdt0(xN)) )
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) ) ) )
<=> ! [W0: $i] :
( ~ ( aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( sbrdtbr0(W0) != szszuzczcdt0(xk) )
| ~ ( aSubsetOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) )
| ~ ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,sdtlpdtrp0(xN,sz00))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,sdtlpdtrp0(xN,sz00)) )
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_0(W0),W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szDzozmdt0(xN)) )
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) ) ) ) ),
inference(quant_intro,[status(thm)],[80]) ).
tff(82,plain,
( ! [W0: $i] :
( ~ ( aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( sbrdtbr0(W0) != szszuzczcdt0(xk) )
| ~ ( aSubsetOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) )
| ~ ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,sdtlpdtrp0(xN,sz00))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,sdtlpdtrp0(xN,sz00)) )
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_0(W0),W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szDzozmdt0(xN)) )
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) ) ) )
<=> ! [W0: $i] :
( ~ ( aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( sbrdtbr0(W0) != szszuzczcdt0(xk) )
| ~ ( aSubsetOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) )
| ~ ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,sdtlpdtrp0(xN,sz00))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,sdtlpdtrp0(xN,sz00)) )
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_0(W0),W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szDzozmdt0(xN)) )
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) ) ) ) ),
inference(transitivity,[status(thm)],[81,79]) ).
tff(83,plain,
^ [W0: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ( sbrdtbr0(W0) != szszuzczcdt0(xk) )
| ( ~ aSubsetOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
& ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) )
<=> ( ( sbrdtbr0(W0) != szszuzczcdt0(xk) )
| ~ ( aSubsetOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) )),
( ( ~ aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
& ( ( sbrdtbr0(W0) != szszuzczcdt0(xk) )
| ( ~ aSubsetOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
& ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) )
<=> ( ~ aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
& ( ( sbrdtbr0(W0) != szszuzczcdt0(xk) )
| ~ ( aSubsetOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) ) )),
rewrite(
( ( ~ aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
& ( ( sbrdtbr0(W0) != szszuzczcdt0(xk) )
| ~ ( aSubsetOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) )
<=> ~ ( aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( sbrdtbr0(W0) != szszuzczcdt0(xk) )
| ~ ( aSubsetOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) ) )),
( ( ~ aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
& ( ( sbrdtbr0(W0) != szszuzczcdt0(xk) )
| ( ~ aSubsetOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
& ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) )
<=> ~ ( aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( sbrdtbr0(W0) != szszuzczcdt0(xk) )
| ~ ( aSubsetOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) ) )),
rewrite(
( ( aElementOf0(tptp_fun_W1_0(W0),W0)
& ( W0 != slbdtrb0(sz00) )
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szDzozmdt0(xN)) )
& aSubsetOf0(W0,szDzozmdt0(xN))
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,sdtlpdtrp0(xN,sz00)) )
& aSubsetOf0(W0,sdtlpdtrp0(xN,sz00))
& aElementOf0(W0,szDzozmdt0(xc))
& ( sdtlpdtrp0(xc,W0) = szDzizrdt0(xd) ) )
<=> ~ ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,sdtlpdtrp0(xN,sz00))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,sdtlpdtrp0(xN,sz00)) )
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_0(W0),W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szDzozmdt0(xN)) )
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) ) ) )),
( ( ( ~ aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
& ( ( sbrdtbr0(W0) != szszuzczcdt0(xk) )
| ( ~ aSubsetOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
& ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) )
| ( aElementOf0(tptp_fun_W1_0(W0),W0)
& ( W0 != slbdtrb0(sz00) )
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szDzozmdt0(xN)) )
& aSubsetOf0(W0,szDzozmdt0(xN))
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,sdtlpdtrp0(xN,sz00)) )
& aSubsetOf0(W0,sdtlpdtrp0(xN,sz00))
& aElementOf0(W0,szDzozmdt0(xc))
& ( sdtlpdtrp0(xc,W0) = szDzizrdt0(xd) ) ) )
<=> ( ~ ( aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( sbrdtbr0(W0) != szszuzczcdt0(xk) )
| ~ ( aSubsetOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) )
| ~ ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,sdtlpdtrp0(xN,sz00))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,sdtlpdtrp0(xN,sz00)) )
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_0(W0),W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szDzozmdt0(xN)) )
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) ) ) ) )),
rewrite(
( ( ~ ( aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( sbrdtbr0(W0) != szszuzczcdt0(xk) )
| ~ ( aSubsetOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) )
| ~ ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,sdtlpdtrp0(xN,sz00))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,sdtlpdtrp0(xN,sz00)) )
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_0(W0),W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szDzozmdt0(xN)) )
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) ) ) )
<=> ( ~ ( aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( sbrdtbr0(W0) != szszuzczcdt0(xk) )
| ~ ( aSubsetOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) )
| ~ ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,sdtlpdtrp0(xN,sz00))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,sdtlpdtrp0(xN,sz00)) )
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_0(W0),W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szDzozmdt0(xN)) )
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) ) ) ) )),
( ( ( ~ aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
& ( ( sbrdtbr0(W0) != szszuzczcdt0(xk) )
| ( ~ aSubsetOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
& ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) )
| ( aElementOf0(tptp_fun_W1_0(W0),W0)
& ( W0 != slbdtrb0(sz00) )
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szDzozmdt0(xN)) )
& aSubsetOf0(W0,szDzozmdt0(xN))
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,sdtlpdtrp0(xN,sz00)) )
& aSubsetOf0(W0,sdtlpdtrp0(xN,sz00))
& aElementOf0(W0,szDzozmdt0(xc))
& ( sdtlpdtrp0(xc,W0) = szDzizrdt0(xd) ) ) )
<=> ( ~ ( aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( sbrdtbr0(W0) != szszuzczcdt0(xk) )
| ~ ( aSubsetOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) )
| ~ ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,sdtlpdtrp0(xN,sz00))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,sdtlpdtrp0(xN,sz00)) )
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_0(W0),W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szDzozmdt0(xN)) )
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(84,plain,
( ! [W0: $i] :
( ( ~ aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
& ( ( sbrdtbr0(W0) != szszuzczcdt0(xk) )
| ( ~ aSubsetOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
& ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) )
| ( aElementOf0(tptp_fun_W1_0(W0),W0)
& ( W0 != slbdtrb0(sz00) )
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szDzozmdt0(xN)) )
& aSubsetOf0(W0,szDzozmdt0(xN))
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,sdtlpdtrp0(xN,sz00)) )
& aSubsetOf0(W0,sdtlpdtrp0(xN,sz00))
& aElementOf0(W0,szDzozmdt0(xc))
& ( sdtlpdtrp0(xc,W0) = szDzizrdt0(xd) ) ) )
<=> ! [W0: $i] :
( ~ ( aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( sbrdtbr0(W0) != szszuzczcdt0(xk) )
| ~ ( aSubsetOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) )
| ~ ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,sdtlpdtrp0(xN,sz00))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,sdtlpdtrp0(xN,sz00)) )
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_0(W0),W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szDzozmdt0(xN)) )
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) ) ) ) ),
inference(quant_intro,[status(thm)],[83]) ).
tff(85,plain,
^ [W0: $i] :
rewrite(
( ( ( ~ aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
& ( ( ~ aSubsetOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
& ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) )
| ( sbrdtbr0(W0) != szszuzczcdt0(xk) ) ) )
| ( aElementOf0(tptp_fun_W1_0(W0),W0)
& ( W0 != slbdtrb0(sz00) )
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szDzozmdt0(xN)) )
& aSubsetOf0(W0,szDzozmdt0(xN))
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,sdtlpdtrp0(xN,sz00)) )
& aSubsetOf0(W0,sdtlpdtrp0(xN,sz00))
& aElementOf0(W0,szDzozmdt0(xc))
& ( sdtlpdtrp0(xc,W0) = szDzizrdt0(xd) ) ) )
<=> ( ( ~ aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
& ( ( sbrdtbr0(W0) != szszuzczcdt0(xk) )
| ( ~ aSubsetOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
& ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) )
| ( aElementOf0(tptp_fun_W1_0(W0),W0)
& ( W0 != slbdtrb0(sz00) )
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szDzozmdt0(xN)) )
& aSubsetOf0(W0,szDzozmdt0(xN))
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,sdtlpdtrp0(xN,sz00)) )
& aSubsetOf0(W0,sdtlpdtrp0(xN,sz00))
& aElementOf0(W0,szDzozmdt0(xc))
& ( sdtlpdtrp0(xc,W0) = szDzizrdt0(xd) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(86,plain,
( ! [W0: $i] :
( ( ~ aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
& ( ( ~ aSubsetOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
& ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) )
| ( sbrdtbr0(W0) != szszuzczcdt0(xk) ) ) )
| ( aElementOf0(tptp_fun_W1_0(W0),W0)
& ( W0 != slbdtrb0(sz00) )
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szDzozmdt0(xN)) )
& aSubsetOf0(W0,szDzozmdt0(xN))
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,sdtlpdtrp0(xN,sz00)) )
& aSubsetOf0(W0,sdtlpdtrp0(xN,sz00))
& aElementOf0(W0,szDzozmdt0(xc))
& ( sdtlpdtrp0(xc,W0) = szDzizrdt0(xd) ) ) )
<=> ! [W0: $i] :
( ( ~ aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
& ( ( sbrdtbr0(W0) != szszuzczcdt0(xk) )
| ( ~ aSubsetOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
& ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) )
| ( aElementOf0(tptp_fun_W1_0(W0),W0)
& ( W0 != slbdtrb0(sz00) )
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szDzozmdt0(xN)) )
& aSubsetOf0(W0,szDzozmdt0(xN))
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,sdtlpdtrp0(xN,sz00)) )
& aSubsetOf0(W0,sdtlpdtrp0(xN,sz00))
& aElementOf0(W0,szDzozmdt0(xc))
& ( sdtlpdtrp0(xc,W0) = szDzizrdt0(xd) ) ) ) ),
inference(quant_intro,[status(thm)],[85]) ).
tff(87,plain,
^ [W0: $i] :
rewrite(
( ( ~ ( 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) ) ) )
<=> ( ~ ( aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ( ( aSubsetOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) )
& ( sbrdtbr0(W0) = szszuzczcdt0(xk) ) ) )
| ( ~ ( ~ ? [W1: $i] : aElementOf0(W1,W0)
| ( W0 = slbdtrb0(sz00) ) )
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szDzozmdt0(xN)) )
& aSubsetOf0(W0,szDzozmdt0(xN))
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,sdtlpdtrp0(xN,sz00)) )
& aSubsetOf0(W0,sdtlpdtrp0(xN,sz00))
& aElementOf0(W0,szDzozmdt0(xc))
& ( sdtlpdtrp0(xc,W0) = szDzizrdt0(xd) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(88,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(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ( ( aSubsetOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) )
& ( sbrdtbr0(W0) = szszuzczcdt0(xk) ) ) )
| ( ~ ( ~ ? [W1: $i] : aElementOf0(W1,W0)
| ( W0 = slbdtrb0(sz00) ) )
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szDzozmdt0(xN)) )
& aSubsetOf0(W0,szDzozmdt0(xN))
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,sdtlpdtrp0(xN,sz00)) )
& aSubsetOf0(W0,sdtlpdtrp0(xN,sz00))
& aElementOf0(W0,szDzozmdt0(xc))
& ( sdtlpdtrp0(xc,W0) = szDzizrdt0(xd) ) ) ) ),
inference(quant_intro,[status(thm)],[87]) ).
tff(89,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(90,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)],[25]) ).
tff(91,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)],[90,89]) ).
tff(92,plain,
! [W0: $i] :
( ~ ( aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ( ( aSubsetOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) )
& ( sbrdtbr0(W0) = szszuzczcdt0(xk) ) ) )
| ( ~ ( ~ ? [W1: $i] : aElementOf0(W1,W0)
| ( W0 = slbdtrb0(sz00) ) )
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szDzozmdt0(xN)) )
& aSubsetOf0(W0,szDzozmdt0(xN))
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,sdtlpdtrp0(xN,sz00)) )
& aSubsetOf0(W0,sdtlpdtrp0(xN,sz00))
& aElementOf0(W0,szDzozmdt0(xc))
& ( sdtlpdtrp0(xc,W0) = szDzizrdt0(xd) ) ) ),
inference(modus_ponens,[status(thm)],[91,88]) ).
tff(93,plain,
! [W0: $i] :
( ( ~ aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
& ( ( ~ aSubsetOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
& ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) )
| ( sbrdtbr0(W0) != szszuzczcdt0(xk) ) ) )
| ( aElementOf0(tptp_fun_W1_0(W0),W0)
& ( W0 != slbdtrb0(sz00) )
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szDzozmdt0(xN)) )
& aSubsetOf0(W0,szDzozmdt0(xN))
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,sdtlpdtrp0(xN,sz00)) )
& aSubsetOf0(W0,sdtlpdtrp0(xN,sz00))
& aElementOf0(W0,szDzozmdt0(xc))
& ( sdtlpdtrp0(xc,W0) = szDzizrdt0(xd) ) ) ),
inference(skolemize,[status(sab)],[92]) ).
tff(94,plain,
! [W0: $i] :
( ( ~ aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
& ( ( sbrdtbr0(W0) != szszuzczcdt0(xk) )
| ( ~ aSubsetOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
& ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) )
| ( aElementOf0(tptp_fun_W1_0(W0),W0)
& ( W0 != slbdtrb0(sz00) )
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szDzozmdt0(xN)) )
& aSubsetOf0(W0,szDzozmdt0(xN))
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,sdtlpdtrp0(xN,sz00)) )
& aSubsetOf0(W0,sdtlpdtrp0(xN,sz00))
& aElementOf0(W0,szDzozmdt0(xc))
& ( sdtlpdtrp0(xc,W0) = szDzizrdt0(xd) ) ) ),
inference(modus_ponens,[status(thm)],[93,86]) ).
tff(95,plain,
! [W0: $i] :
( ~ ( aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( sbrdtbr0(W0) != szszuzczcdt0(xk) )
| ~ ( aSubsetOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) )
| ~ ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,sdtlpdtrp0(xN,sz00))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,sdtlpdtrp0(xN,sz00)) )
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_0(W0),W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szDzozmdt0(xN)) )
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) ) ) ),
inference(modus_ponens,[status(thm)],[94,84]) ).
tff(96,plain,
! [W0: $i] :
( ~ ( aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( sbrdtbr0(W0) != szszuzczcdt0(xk) )
| ~ ( aSubsetOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) )
| ~ ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,sdtlpdtrp0(xN,sz00))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,sdtlpdtrp0(xN,sz00)) )
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_0(W0),W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szDzozmdt0(xN)) )
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) ) ) ),
inference(modus_ponens,[status(thm)],[95,82]) ).
tff(97,plain,
! [W0: $i] :
( ~ ( aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( sbrdtbr0(W0) != szszuzczcdt0(xk) )
| ~ ( aSubsetOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) )
| ~ ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,sdtlpdtrp0(xN,sz00))
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_0(W0),W0)
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,sdtlpdtrp0(xN,sz00)) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szDzozmdt0(xN)) ) ) ),
inference(modus_ponens,[status(thm)],[96,77]) ).
tff(98,plain,
( ( ~ ! [W0: $i] :
( ~ ( aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( sbrdtbr0(W0) != szszuzczcdt0(xk) )
| ~ ( aSubsetOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) )
| ~ ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,sdtlpdtrp0(xN,sz00))
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_0(W0),W0)
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,sdtlpdtrp0(xN,sz00)) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szDzozmdt0(xN)) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szDzizrdt0(xd) )
| ~ 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)) = slbdtrb0(sz00) )
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),sdtlpdtrp0(xN,sz00))
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szDzozmdt0(xN))
| ~ 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)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W1,sdtlpdtrp0(xN,sz00)) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W1,szDzozmdt0(xN)) ) )
| ~ ( aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( sbrdtbr0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szszuzczcdt0(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)))
| ~ ( ~ 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))),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ ( aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( sbrdtbr0(W0) != szszuzczcdt0(xk) )
| ~ ( aSubsetOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) )
| ~ ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,sdtlpdtrp0(xN,sz00))
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_0(W0),W0)
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,sdtlpdtrp0(xN,sz00)) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szDzozmdt0(xN)) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szDzizrdt0(xd) )
| ~ 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)) = slbdtrb0(sz00) )
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),sdtlpdtrp0(xN,sz00))
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szDzozmdt0(xN))
| ~ 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)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W1,sdtlpdtrp0(xN,sz00)) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W1,szDzozmdt0(xN)) ) )
| ~ ( aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( sbrdtbr0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szszuzczcdt0(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)))
| ~ ( ~ 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))),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(99,plain,
( ( ~ ( aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( sbrdtbr0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szszuzczcdt0(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)))
| ~ ( ~ 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))),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szDzizrdt0(xd) )
| ~ 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)) = slbdtrb0(sz00) )
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),sdtlpdtrp0(xN,sz00))
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szDzozmdt0(xN))
| ~ 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)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W1,sdtlpdtrp0(xN,sz00)) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W1,szDzozmdt0(xN)) ) ) )
<=> ( ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szDzizrdt0(xd) )
| ~ 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)) = slbdtrb0(sz00) )
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),sdtlpdtrp0(xN,sz00))
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szDzozmdt0(xN))
| ~ 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)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W1,sdtlpdtrp0(xN,sz00)) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W1,szDzozmdt0(xN)) ) )
| ~ ( aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( sbrdtbr0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szszuzczcdt0(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)))
| ~ ( ~ 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))),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(100,plain,
( ~ ( ~ 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)) = slbdtrb0(sz00) )
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),sdtlpdtrp0(xN,sz00))
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szDzozmdt0(xN))
| ~ 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,sdtlpdtrp0(xN,sz00)) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W1,szDzozmdt0(xN)) ) )
<=> ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szDzizrdt0(xd) )
| ~ 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)) = slbdtrb0(sz00) )
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),sdtlpdtrp0(xN,sz00))
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szDzozmdt0(xN))
| ~ 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)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W1,sdtlpdtrp0(xN,sz00)) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W1,szDzozmdt0(xN)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(101,plain,
( ~ ( aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( sbrdtbr0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szszuzczcdt0(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)))
| ~ ( ~ 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))),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))),szszuzczcdt0(xk)))
| ~ ( ( sbrdtbr0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szszuzczcdt0(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)))
| ~ ( ~ 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))),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(102,plain,
( ( ~ ( aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( sbrdtbr0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szszuzczcdt0(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)))
| ~ ( ~ 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))),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) )
| ~ ( ~ 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)) = slbdtrb0(sz00) )
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),sdtlpdtrp0(xN,sz00))
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szDzozmdt0(xN))
| ~ 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,sdtlpdtrp0(xN,sz00)) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W1,szDzozmdt0(xN)) ) ) )
<=> ( ~ ( aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( sbrdtbr0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szszuzczcdt0(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)))
| ~ ( ~ 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))),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szDzizrdt0(xd) )
| ~ 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)) = slbdtrb0(sz00) )
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),sdtlpdtrp0(xN,sz00))
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szDzozmdt0(xN))
| ~ 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)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W1,sdtlpdtrp0(xN,sz00)) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W1,szDzozmdt0(xN)) ) ) ) ),
inference(monotonicity,[status(thm)],[101,100]) ).
tff(103,plain,
( ( ~ ( aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( sbrdtbr0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szszuzczcdt0(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)))
| ~ ( ~ 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))),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) )
| ~ ( ~ 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)) = slbdtrb0(sz00) )
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),sdtlpdtrp0(xN,sz00))
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szDzozmdt0(xN))
| ~ 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,sdtlpdtrp0(xN,sz00)) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W1,szDzozmdt0(xN)) ) ) )
<=> ( ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szDzizrdt0(xd) )
| ~ 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)) = slbdtrb0(sz00) )
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),sdtlpdtrp0(xN,sz00))
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szDzozmdt0(xN))
| ~ 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)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W1,sdtlpdtrp0(xN,sz00)) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W1,szDzozmdt0(xN)) ) )
| ~ ( aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( sbrdtbr0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szszuzczcdt0(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)))
| ~ ( ~ 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))),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[102,99]) ).
tff(104,plain,
( ( ~ ! [W0: $i] :
( ~ ( aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( sbrdtbr0(W0) != szszuzczcdt0(xk) )
| ~ ( aSubsetOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) )
| ~ ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,sdtlpdtrp0(xN,sz00))
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_0(W0),W0)
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,sdtlpdtrp0(xN,sz00)) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szDzozmdt0(xN)) ) ) )
| ~ ( aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( sbrdtbr0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szszuzczcdt0(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)))
| ~ ( ~ 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))),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) )
| ~ ( ~ 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)) = slbdtrb0(sz00) )
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),sdtlpdtrp0(xN,sz00))
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szDzozmdt0(xN))
| ~ 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,sdtlpdtrp0(xN,sz00)) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W1,szDzozmdt0(xN)) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ ( aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( sbrdtbr0(W0) != szszuzczcdt0(xk) )
| ~ ( aSubsetOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) )
| ~ ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,sdtlpdtrp0(xN,sz00))
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_0(W0),W0)
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,sdtlpdtrp0(xN,sz00)) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szDzozmdt0(xN)) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szDzizrdt0(xd) )
| ~ 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)) = slbdtrb0(sz00) )
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),sdtlpdtrp0(xN,sz00))
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szDzozmdt0(xN))
| ~ 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)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W1,sdtlpdtrp0(xN,sz00)) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W1,szDzozmdt0(xN)) ) )
| ~ ( aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( sbrdtbr0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szszuzczcdt0(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)))
| ~ ( ~ 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))),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[103]) ).
tff(105,plain,
( ( ~ ! [W0: $i] :
( ~ ( aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( sbrdtbr0(W0) != szszuzczcdt0(xk) )
| ~ ( aSubsetOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) )
| ~ ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,sdtlpdtrp0(xN,sz00))
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_0(W0),W0)
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,sdtlpdtrp0(xN,sz00)) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szDzozmdt0(xN)) ) ) )
| ~ ( aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( sbrdtbr0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szszuzczcdt0(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)))
| ~ ( ~ 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))),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) )
| ~ ( ~ 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)) = slbdtrb0(sz00) )
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),sdtlpdtrp0(xN,sz00))
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szDzozmdt0(xN))
| ~ 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,sdtlpdtrp0(xN,sz00)) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W1,szDzozmdt0(xN)) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ ( aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( sbrdtbr0(W0) != szszuzczcdt0(xk) )
| ~ ( aSubsetOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) )
| ~ ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,sdtlpdtrp0(xN,sz00))
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_0(W0),W0)
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,sdtlpdtrp0(xN,sz00)) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szDzozmdt0(xN)) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szDzizrdt0(xd) )
| ~ 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)) = slbdtrb0(sz00) )
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),sdtlpdtrp0(xN,sz00))
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szDzozmdt0(xN))
| ~ 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)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W1,sdtlpdtrp0(xN,sz00)) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W1,szDzozmdt0(xN)) ) )
| ~ ( aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( sbrdtbr0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szszuzczcdt0(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)))
| ~ ( ~ 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))),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[104,98]) ).
tff(106,plain,
( ~ ! [W0: $i] :
( ~ ( aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( sbrdtbr0(W0) != szszuzczcdt0(xk) )
| ~ ( aSubsetOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) )
| ~ ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,sdtlpdtrp0(xN,sz00))
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_0(W0),W0)
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,sdtlpdtrp0(xN,sz00)) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szDzozmdt0(xN)) ) ) )
| ~ ( aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( sbrdtbr0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szszuzczcdt0(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)))
| ~ ( ~ 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))),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) )
| ~ ( ~ 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)) = slbdtrb0(sz00) )
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),sdtlpdtrp0(xN,sz00))
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szDzozmdt0(xN))
| ~ 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,sdtlpdtrp0(xN,sz00)) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W1,szDzozmdt0(xN)) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(107,plain,
( ~ ! [W0: $i] :
( ~ ( aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( sbrdtbr0(W0) != szszuzczcdt0(xk) )
| ~ ( aSubsetOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_43(W0),W0)
| aElementOf0(tptp_fun_W1_43(W0),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) )
| ~ ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,sdtlpdtrp0(xN,sz00))
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_0(W0),W0)
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,sdtlpdtrp0(xN,sz00)) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,szDzozmdt0(xN)) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szDzizrdt0(xd) )
| ~ 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)) = slbdtrb0(sz00) )
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),sdtlpdtrp0(xN,sz00))
| ~ aSubsetOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szDzozmdt0(xN))
| ~ 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)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W1,sdtlpdtrp0(xN,sz00)) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)))
| aElementOf0(W1,szDzozmdt0(xN)) ) )
| ~ ( aElementOf0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( sbrdtbr0(tptp_fun_W2_45(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szszuzczcdt0(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)))
| ~ ( ~ 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))),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[106,105]) ).
tff(108,plain,
$false,
inference(unit_resolution,[status(thm)],[107,97,75,71]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10 % Problem : NUM633+3 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.32 % Computer : n018.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Sep 2 12:36:13 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.11/0.32 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.32 Usage: tptp [options] [-file:]file
% 0.11/0.32 -h, -? prints this message.
% 0.11/0.32 -smt2 print SMT-LIB2 benchmark.
% 0.11/0.32 -m, -model generate model.
% 0.11/0.32 -p, -proof generate proof.
% 0.11/0.32 -c, -core generate unsat core of named formulas.
% 0.11/0.32 -st, -statistics display statistics.
% 0.11/0.32 -t:timeout set timeout (in second).
% 0.11/0.32 -smt2status display status in smt2 format instead of SZS.
% 0.11/0.32 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.32 -<param>:<value> configuration parameter and value.
% 0.11/0.32 -o:<output-file> file to place output in.
% 3.73/2.57 % SZS status Theorem
% 3.73/2.57 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------