%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM596+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:21:31 AM UTC 2025
% Result : Theorem 255.30s 255.63s
% Output : Proof 255.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 158
% Syntax : Number of formulae : 391 ( 77 unt; 0 typ; 0 def)
% Number of atoms : 5098 ( 897 equ)
% Maximal formula atoms : 72 ( 13 avg)
% Number of connectives : 10027 (5488 ~;3625 |; 330 &)
% ( 517 <=>; 67 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 8 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 168 ( 168 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 16 ( 14 usr; 1 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 6 con; 0-3 aty)
% Number of variables : 1333 (1265 !; 17 ?;1333 :)
% Comments :
%------------------------------------------------------------------------------
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(szNzAzT0_type,type,
szNzAzT0: $i ).
tff(tptp_fun_W2_1_type,type,
tptp_fun_W2_1: ( $i * $i ) > $i ).
tff(sdtlcdtrc0_type,type,
sdtlcdtrc0: ( $i * $i ) > $i ).
tff(szDzozmdt0_type,type,
szDzozmdt0: $i > $i ).
tff(sdtlpdtrp0_type,type,
sdtlpdtrp0: ( $i * $i ) > $i ).
tff(sbrdtbr0_type,type,
sbrdtbr0: $i > $i ).
tff(xT_type,type,
xT: $i ).
tff(xC_type,type,
xC: $i ).
tff(sdtlbdtrb0_type,type,
sdtlbdtrb0: ( $i * $i ) > $i ).
tff(szDzizrdt0_type,type,
szDzizrdt0: $i > $i ).
tff(xd_type,type,
xd: $i ).
tff(aSubsetOf0_type,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff(aSet0_type,type,
aSet0: $i > $o ).
tff(isFinite0_type,type,
isFinite0: $i > $o ).
tff(isCountable0_type,type,
isCountable0: $i > $o ).
tff(aFunction0_type,type,
aFunction0: $i > $o ).
tff(slbdtsldtrb0_type,type,
slbdtsldtrb0: ( $i * $i ) > $i ).
tff(xk_type,type,
xk: $i ).
tff(szszuzczcdt0_type,type,
szszuzczcdt0: $i > $i ).
tff(xN_type,type,
xN: $i ).
tff(aElement0_type,type,
aElement0: $i > $o ).
tff(tptp_fun_W3_12_type,type,
tptp_fun_W3_12: ( $i * $i * $i ) > $i ).
tff(tptp_fun_W4_13_type,type,
tptp_fun_W4_13: ( $i * $i * $i ) > $i ).
tff(tptp_fun_W3_14_type,type,
tptp_fun_W3_14: ( $i * $i * $i ) > $i ).
tff(tptp_fun_W4_15_type,type,
tptp_fun_W4_15: ( $i * $i * $i ) > $i ).
tff(1,plain,
( aSet0(xT)
<=> aSet0(xT) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
( aSet0(xT)
& isFinite0(xT) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3291) ).
tff(3,plain,
aSet0(xT),
inference(and_elim,[status(thm)],[2]) ).
tff(4,plain,
aSet0(xT),
inference(modus_ponens,[status(thm)],[3,1]) ).
tff(5,plain,
^ [W0: $i] :
rewrite(( ( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(6,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[5]) ).
tff(7,plain,
^ [W0: $i] :
refl(( ( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
^ [W0: $i] :
rewrite(( ( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(10,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) ),
inference(quant_intro,[status(thm)],[9]) ).
tff(11,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) ),
inference(transitivity,[status(thm)],[10,8]) ).
tff(12,plain,
^ [W0: $i] :
rewrite(( ( ~ aSet0(W0)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,W0)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
& ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(13,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,W0)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
& ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) ),
inference(quant_intro,[status(thm)],[12]) ).
tff(14,plain,
^ [W0: $i] :
rewrite(( ( ~ aSet0(W0)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,W0)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
& ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,W0)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
& ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(15,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,W0)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
& ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,W0)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
& ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) ),
inference(quant_intro,[status(thm)],[14]) ).
tff(16,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(17,plain,
^ [W0: $i] :
trans(monotonicity(quant_intro(proof_bind(^ [W1: $i] :
rewrite(( ( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) ) ) )
<=> ( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ))),
( ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) ) ) )
<=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) )),
( ( aSet0(W0)
=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) ) ) ) )
<=> ( aSet0(W0)
=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )),
rewrite(( ( aSet0(W0)
=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )),
( ( aSet0(W0)
=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) ) ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(18,plain,
( ! [W0: $i] :
( aSet0(W0)
=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) ),
inference(quant_intro,[status(thm)],[17]) ).
tff(19,axiom,
! [W0: $i] :
( aSet0(W0)
=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSub) ).
tff(20,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ),
inference(modus_ponens,[status(thm)],[20,16]) ).
tff(22,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,W0)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
& ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ),
inference(skolemize,[status(sab)],[21]) ).
tff(23,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,W0)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
& ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ),
inference(modus_ponens,[status(thm)],[22,15]) ).
tff(24,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ),
inference(modus_ponens,[status(thm)],[23,13]) ).
tff(25,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ),
inference(modus_ponens,[status(thm)],[24,11]) ).
tff(26,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[25,6]) ).
tff(27,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(xT)
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(xT)
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(28,plain,
( ( ~ aSet0(xT)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,xT)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) ) )
<=> ( ~ aSet0(xT)
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(xT)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,xT)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(xT)
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[28]) ).
tff(30,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(xT)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,xT)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(xT)
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[29,27]) ).
tff(31,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(xT)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,xT)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(32,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(xT)
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) ),
inference(unit_resolution,[status(thm)],[32,26,4]) ).
tff(34,plain,
( ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) )
| ~ ( ~ ( aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))),xT)
| ~ aSet0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))),xT),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))),xT),xT) ) )
| ~ ( ~ aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| aElementOf0(W2,xT) ) ) ) ) )
<=> ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) )
| ~ ( ~ ( aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))),xT)
| ~ aSet0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))),xT),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))),xT),xT) ) )
| ~ ( ~ aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| aElementOf0(W2,xT) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,plain,
( ~ ( ~ ( ~ aSet0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))),xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))),xT),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))),xT),xT) ) )
| ~ ( ~ aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| aElementOf0(W2,xT) ) ) ) )
<=> ~ ( ~ ( aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))),xT)
| ~ aSet0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))),xT),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))),xT),xT) ) )
| ~ ( ~ aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| aElementOf0(W2,xT) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(36,plain,
( ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) )
| ~ ( ~ ( ~ aSet0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))),xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))),xT),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))),xT),xT) ) )
| ~ ( ~ aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| aElementOf0(W2,xT) ) ) ) ) )
<=> ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) )
| ~ ( ~ ( aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))),xT)
| ~ aSet0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))),xT),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))),xT),xT) ) )
| ~ ( ~ aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| aElementOf0(W2,xT) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[35]) ).
tff(37,plain,
( ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) )
| ~ ( ~ ( ~ aSet0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))),xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))),xT),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))),xT),xT) ) )
| ~ ( ~ aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| aElementOf0(W2,xT) ) ) ) ) )
<=> ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) )
| ~ ( ~ ( aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))),xT)
| ~ aSet0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))),xT),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))),xT),xT) ) )
| ~ ( ~ aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| aElementOf0(W2,xT) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[36,34]) ).
tff(38,plain,
( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) )
| ~ ( ~ ( ~ aSet0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))),xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))),xT),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))),xT),xT) ) )
| ~ ( ~ aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| aElementOf0(W2,xT) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(39,plain,
( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) )
| ~ ( ~ ( aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))),xT)
| ~ aSet0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))),xT),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))),xT),xT) ) )
| ~ ( ~ aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| aElementOf0(W2,xT) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
~ ( ~ ( aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))),xT)
| ~ aSet0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))),xT),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))),xT),xT) ) )
| ~ ( ~ aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| aElementOf0(W2,xT) ) ) ) ),
inference(unit_resolution,[status(thm)],[39,33]) ).
tff(41,plain,
( ~ ( aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))),xT)
| ~ aSet0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))),xT),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))),xT),xT) ) )
| ~ ( ~ aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| aElementOf0(W2,xT) ) ) )
| ~ aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| aElementOf0(W2,xT) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(42,plain,
( ~ aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| aElementOf0(W2,xT) ) ) ),
inference(unit_resolution,[status(thm)],[41,40]) ).
tff(43,plain,
^ [W0: $i] :
refl(( ( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) )
<=> ( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(44,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) ) ),
inference(quant_intro,[status(thm)],[43]) ).
tff(45,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(46,plain,
^ [W0: $i] :
rewrite(( ( aSet0(W0)
=> ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) )
<=> ( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(47,plain,
( ! [W0: $i] :
( aSet0(W0)
=> ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) ) ),
inference(quant_intro,[status(thm)],[46]) ).
tff(48,axiom,
! [W0: $i] :
( aSet0(W0)
=> ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardNum) ).
tff(49,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) ),
inference(modus_ponens,[status(thm)],[49,45]) ).
tff(51,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) ),
inference(skolemize,[status(sab)],[50]) ).
tff(52,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) ),
inference(modus_ponens,[status(thm)],[51,44]) ).
tff(53,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) )
| ~ aSet0(xT)
| ( aElementOf0(sbrdtbr0(xT),szNzAzT0)
<=> isFinite0(xT) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) )
| ~ aSet0(xT)
| ( aElementOf0(sbrdtbr0(xT),szNzAzT0)
<=> isFinite0(xT) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(54,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) )
| ~ aSet0(xT)
| ( aElementOf0(sbrdtbr0(xT),szNzAzT0)
<=> isFinite0(xT) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(55,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) )
| ~ aSet0(xT)
| ( aElementOf0(sbrdtbr0(xT),szNzAzT0)
<=> isFinite0(xT) ) ),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
( aElementOf0(sbrdtbr0(xT),szNzAzT0)
<=> isFinite0(xT) ),
inference(unit_resolution,[status(thm)],[55,52,4]) ).
tff(57,plain,
( isFinite0(xT)
<=> isFinite0(xT) ),
inference(rewrite,[status(thm)],[]) ).
tff(58,plain,
isFinite0(xT),
inference(and_elim,[status(thm)],[2]) ).
tff(59,plain,
isFinite0(xT),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
( ~ ( aElementOf0(sbrdtbr0(xT),szNzAzT0)
<=> isFinite0(xT) )
| aElementOf0(sbrdtbr0(xT),szNzAzT0)
| ~ isFinite0(xT) ),
inference(tautology,[status(thm)],[]) ).
tff(61,plain,
( ~ ( aElementOf0(sbrdtbr0(xT),szNzAzT0)
<=> isFinite0(xT) )
| aElementOf0(sbrdtbr0(xT),szNzAzT0) ),
inference(unit_resolution,[status(thm)],[60,59]) ).
tff(62,plain,
aElementOf0(sbrdtbr0(xT),szNzAzT0),
inference(unit_resolution,[status(thm)],[61,56]) ).
tff(63,plain,
^ [W0: $i] :
refl(( ( ~ aElementOf0(W0,szNzAzT0)
| aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,W0),szDzozmdt0(sdtlpdtrp0(xC,W0))),xT) )
<=> ( ~ aElementOf0(W0,szNzAzT0)
| aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,W0),szDzozmdt0(sdtlpdtrp0(xC,W0))),xT) ) )),
inference(bind,[status(th)],[]) ).
tff(64,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,W0),szDzozmdt0(sdtlpdtrp0(xC,W0))),xT) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,W0),szDzozmdt0(sdtlpdtrp0(xC,W0))),xT) ) ),
inference(quant_intro,[status(thm)],[63]) ).
tff(65,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,W0),szDzozmdt0(sdtlpdtrp0(xC,W0))),xT) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,W0),szDzozmdt0(sdtlpdtrp0(xC,W0))),xT) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(66,plain,
^ [W0: $i] :
rewrite(( ( aElementOf0(W0,szNzAzT0)
=> aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,W0),szDzozmdt0(sdtlpdtrp0(xC,W0))),xT) )
<=> ( ~ aElementOf0(W0,szNzAzT0)
| aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,W0),szDzozmdt0(sdtlpdtrp0(xC,W0))),xT) ) )),
inference(bind,[status(th)],[]) ).
tff(67,plain,
( ! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,W0),szDzozmdt0(sdtlpdtrp0(xC,W0))),xT) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,W0),szDzozmdt0(sdtlpdtrp0(xC,W0))),xT) ) ),
inference(quant_intro,[status(thm)],[66]) ).
tff(68,axiom,
! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,W0),szDzozmdt0(sdtlpdtrp0(xC,W0))),xT) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4182) ).
tff(69,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,W0),szDzozmdt0(sdtlpdtrp0(xC,W0))),xT) ),
inference(modus_ponens,[status(thm)],[68,67]) ).
tff(70,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,W0),szDzozmdt0(sdtlpdtrp0(xC,W0))),xT) ),
inference(modus_ponens,[status(thm)],[69,65]) ).
tff(71,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,W0),szDzozmdt0(sdtlpdtrp0(xC,W0))),xT) ),
inference(skolemize,[status(sab)],[70]) ).
tff(72,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,W0),szDzozmdt0(sdtlpdtrp0(xC,W0))),xT) ),
inference(modus_ponens,[status(thm)],[71,64]) ).
tff(73,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,W0),szDzozmdt0(sdtlpdtrp0(xC,W0))),xT) )
| ~ aElementOf0(sbrdtbr0(xT),szNzAzT0)
| aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))),xT) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,W0),szDzozmdt0(sdtlpdtrp0(xC,W0))),xT) )
| ~ aElementOf0(sbrdtbr0(xT),szNzAzT0)
| aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))),xT) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(74,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,W0),szDzozmdt0(sdtlpdtrp0(xC,W0))),xT) )
| ~ aElementOf0(sbrdtbr0(xT),szNzAzT0)
| aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))),xT) ),
inference(quant_inst,[status(thm)],[]) ).
tff(75,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,W0),szDzozmdt0(sdtlpdtrp0(xC,W0))),xT) )
| ~ aElementOf0(sbrdtbr0(xT),szNzAzT0)
| aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))),xT) ),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))),xT),
inference(unit_resolution,[status(thm)],[75,72,62]) ).
tff(77,plain,
( ~ ( ~ aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| aElementOf0(W2,xT) ) ) )
| ~ aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| aElementOf0(W2,xT) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(78,plain,
( ~ ( ~ aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| aElementOf0(W2,xT) ) ) )
| ~ ( ~ aSet0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| aElementOf0(W2,xT) ) ) ),
inference(unit_resolution,[status(thm)],[77,76]) ).
tff(79,plain,
~ ( ~ aSet0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| aElementOf0(W2,xT) ) ),
inference(unit_resolution,[status(thm)],[78,42]) ).
tff(80,plain,
( ~ aSet0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| aElementOf0(W2,xT) )
| aSet0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))) ),
inference(tautology,[status(thm)],[]) ).
tff(81,plain,
aSet0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),
inference(unit_resolution,[status(thm)],[80,79]) ).
tff(82,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),W1)
| aElementOf0(tptp_fun_W2_1(W1,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))) ) )
| ~ ( ~ aSubsetOf0(W1,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),W1)
| aElementOf0(tptp_fun_W2_1(W1,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))) ) )
| ~ ( ~ aSubsetOf0(W1,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(83,plain,
( ( ~ aSet0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),W1)
| aElementOf0(tptp_fun_W2_1(W1,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))) ) )
| ~ ( ~ aSubsetOf0(W1,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))) ) ) ) ) )
<=> ( ~ aSet0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),W1)
| aElementOf0(tptp_fun_W2_1(W1,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))) ) )
| ~ ( ~ aSubsetOf0(W1,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(84,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),W1)
| aElementOf0(tptp_fun_W2_1(W1,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))) ) )
| ~ ( ~ aSubsetOf0(W1,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),W1)
| aElementOf0(tptp_fun_W2_1(W1,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))) ) )
| ~ ( ~ aSubsetOf0(W1,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[83]) ).
tff(85,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),W1)
| aElementOf0(tptp_fun_W2_1(W1,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))) ) )
| ~ ( ~ aSubsetOf0(W1,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),W1)
| aElementOf0(tptp_fun_W2_1(W1,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))) ) )
| ~ ( ~ aSubsetOf0(W1,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[84,82]) ).
tff(86,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),W1)
| aElementOf0(tptp_fun_W2_1(W1,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))) ) )
| ~ ( ~ aSubsetOf0(W1,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(87,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),W1)
| aElementOf0(tptp_fun_W2_1(W1,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))) ) )
| ~ ( ~ aSubsetOf0(W1,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[86,85]) ).
tff(88,plain,
! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),W1)
| aElementOf0(tptp_fun_W2_1(W1,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))) ) )
| ~ ( ~ aSubsetOf0(W1,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))) ) ) ) ),
inference(unit_resolution,[status(thm)],[87,26,81]) ).
tff(89,plain,
( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),W1)
| aElementOf0(tptp_fun_W2_1(W1,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))) ) )
| ~ ( ~ aSubsetOf0(W1,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))) ) ) ) )
| ~ ( ~ ( ~ aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aElementOf0(tptp_fun_W2_1(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))) ) )
| ~ ( ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ ( ~ aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aElementOf0(W2,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(90,plain,
~ ( ~ ( ~ aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aElementOf0(tptp_fun_W2_1(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))) ) )
| ~ ( ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ ( ~ aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aElementOf0(W2,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))) ) ) ) ),
inference(unit_resolution,[status(thm)],[89,88]) ).
tff(91,plain,
( ~ ( ~ aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aElementOf0(tptp_fun_W2_1(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))) ) )
| ~ ( ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ ( ~ aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aElementOf0(W2,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))) ) ) )
| ~ aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aElementOf0(tptp_fun_W2_1(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))) ) ),
inference(tautology,[status(thm)],[]) ).
tff(92,plain,
( ~ aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aElementOf0(tptp_fun_W2_1(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))) ) ),
inference(unit_resolution,[status(thm)],[91,90]) ).
tff(93,plain,
^ [W0: $i] :
refl(( ( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) )
<=> ( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(94,plain,
( ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) )
<=> ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) ) ),
inference(quant_intro,[status(thm)],[93]) ).
tff(95,plain,
^ [W0: $i] :
rewrite(( ( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) )
<=> ( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(96,plain,
( ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) )
<=> ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) ) ),
inference(quant_intro,[status(thm)],[95]) ).
tff(97,plain,
( ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) )
<=> ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) ) ),
inference(transitivity,[status(thm)],[96,94]) ).
tff(98,plain,
^ [W0: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aSet0(W0)
& isFinite0(W0) )
<=> ~ ( ~ aSet0(W0)
| ~ isFinite0(W0) ) )),
( ~ ( aSet0(W0)
& isFinite0(W0) )
<=> ~ ~ ( ~ aSet0(W0)
| ~ isFinite0(W0) ) )),
rewrite(( ~ ~ ( ~ aSet0(W0)
| ~ isFinite0(W0) )
<=> ( ~ aSet0(W0)
| ~ isFinite0(W0) ) )),
( ~ ( aSet0(W0)
& isFinite0(W0) )
<=> ( ~ aSet0(W0)
| ~ isFinite0(W0) ) )),
( ( ~ ( aSet0(W0)
& isFinite0(W0) )
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) )
<=> ( ~ aSet0(W0)
| ~ isFinite0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) ) )),
rewrite(( ( ~ aSet0(W0)
| ~ isFinite0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) )
<=> ( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) ) )),
( ( ~ ( aSet0(W0)
& isFinite0(W0) )
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) )
<=> ( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(99,plain,
( ! [W0: $i] :
( ~ ( aSet0(W0)
& isFinite0(W0) )
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) )
<=> ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) ) ),
inference(quant_intro,[status(thm)],[98]) ).
tff(100,plain,
( ! [W0: $i] :
( ~ ( aSet0(W0)
& isFinite0(W0) )
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) )
<=> ! [W0: $i] :
( ~ ( aSet0(W0)
& isFinite0(W0) )
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(101,plain,
^ [W0: $i] :
trans(monotonicity(quant_intro(proof_bind(^ [W1: $i] :
rewrite(( ( aSubsetOf0(W1,W0)
=> isFinite0(W1) )
<=> ( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) ))),
( ! [W1: $i] :
( aSubsetOf0(W1,W0)
=> isFinite0(W1) )
<=> ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) )),
( ( ( aSet0(W0)
& isFinite0(W0) )
=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
=> isFinite0(W1) ) )
<=> ( ( aSet0(W0)
& isFinite0(W0) )
=> ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) ) )),
rewrite(( ( ( aSet0(W0)
& isFinite0(W0) )
=> ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) )
<=> ( ~ ( aSet0(W0)
& isFinite0(W0) )
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) ) )),
( ( ( aSet0(W0)
& isFinite0(W0) )
=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
=> isFinite0(W1) ) )
<=> ( ~ ( aSet0(W0)
& isFinite0(W0) )
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(102,plain,
( ! [W0: $i] :
( ( aSet0(W0)
& isFinite0(W0) )
=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
=> isFinite0(W1) ) )
<=> ! [W0: $i] :
( ~ ( aSet0(W0)
& isFinite0(W0) )
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) ) ),
inference(quant_intro,[status(thm)],[101]) ).
tff(103,axiom,
! [W0: $i] :
( ( aSet0(W0)
& isFinite0(W0) )
=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
=> isFinite0(W1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubFSet) ).
tff(104,plain,
! [W0: $i] :
( ~ ( aSet0(W0)
& isFinite0(W0) )
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[103,102]) ).
tff(105,plain,
! [W0: $i] :
( ~ ( aSet0(W0)
& isFinite0(W0) )
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[104,100]) ).
tff(106,plain,
! [W0: $i] :
( ~ ( aSet0(W0)
& isFinite0(W0) )
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) ),
inference(skolemize,[status(sab)],[105]) ).
tff(107,plain,
! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[106,99]) ).
tff(108,plain,
! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[107,97]) ).
tff(109,plain,
( ( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) )
| ~ aSet0(xT)
| ~ isFinite0(xT)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,xT) ) )
<=> ( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) )
| ~ aSet0(xT)
| ~ isFinite0(xT)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,xT) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(110,plain,
( ( ~ isFinite0(xT)
| ~ aSet0(xT)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,xT) ) )
<=> ( ~ aSet0(xT)
| ~ isFinite0(xT)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,xT) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(111,plain,
( ( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) )
| ~ isFinite0(xT)
| ~ aSet0(xT)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,xT) ) )
<=> ( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) )
| ~ aSet0(xT)
| ~ isFinite0(xT)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,xT) ) ) ),
inference(monotonicity,[status(thm)],[110]) ).
tff(112,plain,
( ( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) )
| ~ isFinite0(xT)
| ~ aSet0(xT)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,xT) ) )
<=> ( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) )
| ~ aSet0(xT)
| ~ isFinite0(xT)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,xT) ) ) ),
inference(transitivity,[status(thm)],[111,109]) ).
tff(113,plain,
( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) )
| ~ isFinite0(xT)
| ~ aSet0(xT)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,xT) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(114,plain,
( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) )
| ~ aSet0(xT)
| ~ isFinite0(xT)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,xT) ) ),
inference(modus_ponens,[status(thm)],[113,112]) ).
tff(115,plain,
! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,xT) ),
inference(unit_resolution,[status(thm)],[114,108,4,59]) ).
tff(116,plain,
( ( ~ ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,xT) )
| isFinite0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))),xT) )
<=> ( ~ ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,xT) )
| isFinite0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))),xT) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(117,plain,
( ~ ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,xT) )
| isFinite0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))),xT) ),
inference(quant_inst,[status(thm)],[]) ).
tff(118,plain,
( ~ ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,xT) )
| isFinite0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))),xT) ),
inference(modus_ponens,[status(thm)],[117,116]) ).
tff(119,plain,
isFinite0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),
inference(unit_resolution,[status(thm)],[118,115,76]) ).
tff(120,plain,
( ( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) )
| ~ aSet0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ isFinite0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))) ) )
<=> ( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) )
| ~ aSet0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ isFinite0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(121,plain,
( ( ~ isFinite0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ aSet0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))) ) )
<=> ( ~ aSet0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ isFinite0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(122,plain,
( ( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) )
| ~ isFinite0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ aSet0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))) ) )
<=> ( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) )
| ~ aSet0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ isFinite0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))) ) ) ),
inference(monotonicity,[status(thm)],[121]) ).
tff(123,plain,
( ( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) )
| ~ isFinite0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ aSet0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))) ) )
<=> ( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) )
| ~ aSet0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ isFinite0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))) ) ) ),
inference(transitivity,[status(thm)],[122,120]) ).
tff(124,plain,
( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) )
| ~ isFinite0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ aSet0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(125,plain,
( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) )
| ~ aSet0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ isFinite0(sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))) ) ),
inference(modus_ponens,[status(thm)],[124,123]) ).
tff(126,plain,
! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))) ),
inference(unit_resolution,[status(thm)],[125,108,81,119]) ).
tff(127,plain,
( aSet0(szNzAzT0)
<=> aSet0(szNzAzT0) ),
inference(rewrite,[status(thm)],[]) ).
tff(128,axiom,
( aSet0(szNzAzT0)
& isCountable0(szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNATSet) ).
tff(129,plain,
aSet0(szNzAzT0),
inference(and_elim,[status(thm)],[128]) ).
tff(130,plain,
aSet0(szNzAzT0),
inference(modus_ponens,[status(thm)],[129,127]) ).
tff(131,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(szNzAzT0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,szNzAzT0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,szNzAzT0),W1)
| aElementOf0(tptp_fun_W2_1(W1,szNzAzT0),szNzAzT0) ) )
| ~ ( ~ aSubsetOf0(W1,szNzAzT0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,szNzAzT0) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(szNzAzT0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,szNzAzT0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,szNzAzT0),W1)
| aElementOf0(tptp_fun_W2_1(W1,szNzAzT0),szNzAzT0) ) )
| ~ ( ~ aSubsetOf0(W1,szNzAzT0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,szNzAzT0) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(132,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(szNzAzT0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,szNzAzT0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,szNzAzT0),W1)
| aElementOf0(tptp_fun_W2_1(W1,szNzAzT0),szNzAzT0) ) )
| ~ ( ~ aSubsetOf0(W1,szNzAzT0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,szNzAzT0) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(133,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(szNzAzT0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,szNzAzT0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,szNzAzT0),W1)
| aElementOf0(tptp_fun_W2_1(W1,szNzAzT0),szNzAzT0) ) )
| ~ ( ~ aSubsetOf0(W1,szNzAzT0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,szNzAzT0) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[132,131]) ).
tff(134,plain,
! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,szNzAzT0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,szNzAzT0),W1)
| aElementOf0(tptp_fun_W2_1(W1,szNzAzT0),szNzAzT0) ) )
| ~ ( ~ aSubsetOf0(W1,szNzAzT0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,szNzAzT0) ) ) ) ),
inference(unit_resolution,[status(thm)],[133,26,130]) ).
tff(135,plain,
( ~ ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,szNzAzT0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,szNzAzT0),W1)
| aElementOf0(tptp_fun_W2_1(W1,szNzAzT0),szNzAzT0) ) )
| ~ ( ~ aSubsetOf0(W1,szNzAzT0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,szNzAzT0) ) ) ) )
| ~ ( ~ ( aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szNzAzT0)
| ~ aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlbdtrb0(xd,szDzizrdt0(xd)),szNzAzT0),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aElementOf0(tptp_fun_W2_1(sdtlbdtrb0(xd,szDzizrdt0(xd)),szNzAzT0),szNzAzT0) ) )
| ~ ( ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szNzAzT0)
| ~ ( ~ aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aElementOf0(W2,szNzAzT0) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(136,plain,
~ ( ~ ( aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szNzAzT0)
| ~ aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlbdtrb0(xd,szDzizrdt0(xd)),szNzAzT0),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aElementOf0(tptp_fun_W2_1(sdtlbdtrb0(xd,szDzizrdt0(xd)),szNzAzT0),szNzAzT0) ) )
| ~ ( ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szNzAzT0)
| ~ ( ~ aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aElementOf0(W2,szNzAzT0) ) ) ) ),
inference(unit_resolution,[status(thm)],[135,134]) ).
tff(137,plain,
( ~ ( aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szNzAzT0)
| ~ aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlbdtrb0(xd,szDzizrdt0(xd)),szNzAzT0),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aElementOf0(tptp_fun_W2_1(sdtlbdtrb0(xd,szDzizrdt0(xd)),szNzAzT0),szNzAzT0) ) )
| ~ ( ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szNzAzT0)
| ~ ( ~ aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aElementOf0(W2,szNzAzT0) ) ) )
| ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szNzAzT0)
| ~ ( ~ aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aElementOf0(W2,szNzAzT0) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(138,plain,
( ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szNzAzT0)
| ~ ( ~ aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aElementOf0(W2,szNzAzT0) ) ) ),
inference(unit_resolution,[status(thm)],[137,136]) ).
tff(139,plain,
( ( szDzozmdt0(xd) = szNzAzT0 )
<=> ( szDzozmdt0(xd) = szNzAzT0 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(140,axiom,
( aFunction0(xd)
& ( szDzozmdt0(xd) = szNzAzT0 )
& ! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> ! [W1: $i] :
( ( aSet0(W1)
& aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk)) )
=> ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4730) ).
tff(141,plain,
( aFunction0(xd)
& ( szDzozmdt0(xd) = szNzAzT0 ) ),
inference(and_elim,[status(thm)],[140]) ).
tff(142,plain,
szDzozmdt0(xd) = szNzAzT0,
inference(and_elim,[status(thm)],[141]) ).
tff(143,plain,
szDzozmdt0(xd) = szNzAzT0,
inference(modus_ponens,[status(thm)],[142,139]) ).
tff(144,plain,
( aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzozmdt0(xd))
<=> aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szNzAzT0) ),
inference(monotonicity,[status(thm)],[143]) ).
tff(145,plain,
( aSubsetOf0(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT)
<=> aSubsetOf0(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT) ),
inference(rewrite,[status(thm)],[]) ).
tff(146,axiom,
aSubsetOf0(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4758) ).
tff(147,plain,
aSubsetOf0(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT),
inference(modus_ponens,[status(thm)],[146,145]) ).
tff(148,plain,
( ( ~ ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,xT) )
| isFinite0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ aSubsetOf0(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT) )
<=> ( ~ ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,xT) )
| isFinite0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ aSubsetOf0(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(149,plain,
( ~ ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,xT) )
| isFinite0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ aSubsetOf0(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT) ),
inference(quant_inst,[status(thm)],[]) ).
tff(150,plain,
( ~ ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,xT) )
| isFinite0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ aSubsetOf0(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT) ),
inference(modus_ponens,[status(thm)],[149,148]) ).
tff(151,plain,
isFinite0(sdtlcdtrc0(xd,szDzozmdt0(xd))),
inference(unit_resolution,[status(thm)],[150,147,115]) ).
tff(152,plain,
( isCountable0(szDzozmdt0(xd))
<=> isCountable0(szNzAzT0) ),
inference(monotonicity,[status(thm)],[143]) ).
tff(153,plain,
( isCountable0(szNzAzT0)
<=> isCountable0(szDzozmdt0(xd)) ),
inference(symmetry,[status(thm)],[152]) ).
tff(154,plain,
( isCountable0(szNzAzT0)
<=> isCountable0(szNzAzT0) ),
inference(rewrite,[status(thm)],[]) ).
tff(155,plain,
isCountable0(szNzAzT0),
inference(and_elim,[status(thm)],[128]) ).
tff(156,plain,
isCountable0(szNzAzT0),
inference(modus_ponens,[status(thm)],[155,154]) ).
tff(157,plain,
isCountable0(szDzozmdt0(xd)),
inference(modus_ponens,[status(thm)],[156,153]) ).
tff(158,plain,
( aFunction0(xd)
<=> aFunction0(xd) ),
inference(rewrite,[status(thm)],[]) ).
tff(159,plain,
aFunction0(xd),
inference(and_elim,[status(thm)],[141]) ).
tff(160,plain,
aFunction0(xd),
inference(modus_ponens,[status(thm)],[159,158]) ).
tff(161,plain,
^ [W0: $i] :
refl(( ( ~ aFunction0(W0)
| ~ isCountable0(szDzozmdt0(W0))
| ~ ( ~ aElement0(szDzizrdt0(W0))
| ~ isCountable0(sdtlbdtrb0(W0,szDzizrdt0(W0))) )
| ~ isFinite0(sdtlcdtrc0(W0,szDzozmdt0(W0))) )
<=> ( ~ aFunction0(W0)
| ~ isCountable0(szDzozmdt0(W0))
| ~ ( ~ aElement0(szDzizrdt0(W0))
| ~ isCountable0(sdtlbdtrb0(W0,szDzizrdt0(W0))) )
| ~ isFinite0(sdtlcdtrc0(W0,szDzozmdt0(W0))) ) )),
inference(bind,[status(th)],[]) ).
tff(162,plain,
( ! [W0: $i] :
( ~ aFunction0(W0)
| ~ isCountable0(szDzozmdt0(W0))
| ~ ( ~ aElement0(szDzizrdt0(W0))
| ~ isCountable0(sdtlbdtrb0(W0,szDzizrdt0(W0))) )
| ~ isFinite0(sdtlcdtrc0(W0,szDzozmdt0(W0))) )
<=> ! [W0: $i] :
( ~ aFunction0(W0)
| ~ isCountable0(szDzozmdt0(W0))
| ~ ( ~ aElement0(szDzizrdt0(W0))
| ~ isCountable0(sdtlbdtrb0(W0,szDzizrdt0(W0))) )
| ~ isFinite0(sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ),
inference(quant_intro,[status(thm)],[161]) ).
tff(163,plain,
^ [W0: $i] :
trans(monotonicity(rewrite(( ( aElement0(szDzizrdt0(W0))
& isCountable0(sdtlbdtrb0(W0,szDzizrdt0(W0))) )
<=> ~ ( ~ aElement0(szDzizrdt0(W0))
| ~ isCountable0(sdtlbdtrb0(W0,szDzizrdt0(W0))) ) )),
trans(monotonicity(rewrite(( ( isCountable0(szDzozmdt0(W0))
& isFinite0(sdtlcdtrc0(W0,szDzozmdt0(W0))) )
<=> ~ ( ~ isCountable0(szDzozmdt0(W0))
| ~ isFinite0(sdtlcdtrc0(W0,szDzozmdt0(W0))) ) )),
( ~ ( isCountable0(szDzozmdt0(W0))
& isFinite0(sdtlcdtrc0(W0,szDzozmdt0(W0))) )
<=> ~ ~ ( ~ isCountable0(szDzozmdt0(W0))
| ~ isFinite0(sdtlcdtrc0(W0,szDzozmdt0(W0))) ) )),
rewrite(( ~ ~ ( ~ isCountable0(szDzozmdt0(W0))
| ~ isFinite0(sdtlcdtrc0(W0,szDzozmdt0(W0))) )
<=> ( ~ isCountable0(szDzozmdt0(W0))
| ~ isFinite0(sdtlcdtrc0(W0,szDzozmdt0(W0))) ) )),
( ~ ( isCountable0(szDzozmdt0(W0))
& isFinite0(sdtlcdtrc0(W0,szDzozmdt0(W0))) )
<=> ( ~ isCountable0(szDzozmdt0(W0))
| ~ isFinite0(sdtlcdtrc0(W0,szDzozmdt0(W0))) ) )),
( ( ( aElement0(szDzizrdt0(W0))
& isCountable0(sdtlbdtrb0(W0,szDzizrdt0(W0))) )
| ~ aFunction0(W0)
| ~ ( isCountable0(szDzozmdt0(W0))
& isFinite0(sdtlcdtrc0(W0,szDzozmdt0(W0))) ) )
<=> ( ~ ( ~ aElement0(szDzizrdt0(W0))
| ~ isCountable0(sdtlbdtrb0(W0,szDzizrdt0(W0))) )
| ~ aFunction0(W0)
| ~ isCountable0(szDzozmdt0(W0))
| ~ isFinite0(sdtlcdtrc0(W0,szDzozmdt0(W0))) ) )),
rewrite(( ( ~ ( ~ aElement0(szDzizrdt0(W0))
| ~ isCountable0(sdtlbdtrb0(W0,szDzizrdt0(W0))) )
| ~ aFunction0(W0)
| ~ isCountable0(szDzozmdt0(W0))
| ~ isFinite0(sdtlcdtrc0(W0,szDzozmdt0(W0))) )
<=> ( ~ aFunction0(W0)
| ~ isCountable0(szDzozmdt0(W0))
| ~ ( ~ aElement0(szDzizrdt0(W0))
| ~ isCountable0(sdtlbdtrb0(W0,szDzizrdt0(W0))) )
| ~ isFinite0(sdtlcdtrc0(W0,szDzozmdt0(W0))) ) )),
( ( ( aElement0(szDzizrdt0(W0))
& isCountable0(sdtlbdtrb0(W0,szDzizrdt0(W0))) )
| ~ aFunction0(W0)
| ~ ( isCountable0(szDzozmdt0(W0))
& isFinite0(sdtlcdtrc0(W0,szDzozmdt0(W0))) ) )
<=> ( ~ aFunction0(W0)
| ~ isCountable0(szDzozmdt0(W0))
| ~ ( ~ aElement0(szDzizrdt0(W0))
| ~ isCountable0(sdtlbdtrb0(W0,szDzizrdt0(W0))) )
| ~ isFinite0(sdtlcdtrc0(W0,szDzozmdt0(W0))) ) )),
inference(bind,[status(th)],[]) ).
tff(164,plain,
( ! [W0: $i] :
( ( aElement0(szDzizrdt0(W0))
& isCountable0(sdtlbdtrb0(W0,szDzizrdt0(W0))) )
| ~ aFunction0(W0)
| ~ ( isCountable0(szDzozmdt0(W0))
& isFinite0(sdtlcdtrc0(W0,szDzozmdt0(W0))) ) )
<=> ! [W0: $i] :
( ~ aFunction0(W0)
| ~ isCountable0(szDzozmdt0(W0))
| ~ ( ~ aElement0(szDzizrdt0(W0))
| ~ isCountable0(sdtlbdtrb0(W0,szDzizrdt0(W0))) )
| ~ isFinite0(sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ),
inference(quant_intro,[status(thm)],[163]) ).
tff(165,plain,
( ! [W0: $i] :
( ( aElement0(szDzizrdt0(W0))
& isCountable0(sdtlbdtrb0(W0,szDzizrdt0(W0))) )
| ~ aFunction0(W0)
| ~ ( isCountable0(szDzozmdt0(W0))
& isFinite0(sdtlcdtrc0(W0,szDzozmdt0(W0))) ) )
<=> ! [W0: $i] :
( ( aElement0(szDzizrdt0(W0))
& isCountable0(sdtlbdtrb0(W0,szDzizrdt0(W0))) )
| ~ aFunction0(W0)
| ~ ( isCountable0(szDzozmdt0(W0))
& isFinite0(sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(166,plain,
^ [W0: $i] :
trans(monotonicity(rewrite(( ( ( isCountable0(szDzozmdt0(W0))
& isFinite0(sdtlcdtrc0(W0,szDzozmdt0(W0))) )
=> ( aElement0(szDzizrdt0(W0))
& isCountable0(sdtlbdtrb0(W0,szDzizrdt0(W0))) ) )
<=> ( ~ ( isCountable0(szDzozmdt0(W0))
& isFinite0(sdtlcdtrc0(W0,szDzozmdt0(W0))) )
| ( aElement0(szDzizrdt0(W0))
& isCountable0(sdtlbdtrb0(W0,szDzizrdt0(W0))) ) ) )),
( ( aFunction0(W0)
=> ( ( isCountable0(szDzozmdt0(W0))
& isFinite0(sdtlcdtrc0(W0,szDzozmdt0(W0))) )
=> ( aElement0(szDzizrdt0(W0))
& isCountable0(sdtlbdtrb0(W0,szDzizrdt0(W0))) ) ) )
<=> ( aFunction0(W0)
=> ( ~ ( isCountable0(szDzozmdt0(W0))
& isFinite0(sdtlcdtrc0(W0,szDzozmdt0(W0))) )
| ( aElement0(szDzizrdt0(W0))
& isCountable0(sdtlbdtrb0(W0,szDzizrdt0(W0))) ) ) ) )),
rewrite(( ( aFunction0(W0)
=> ( ~ ( isCountable0(szDzozmdt0(W0))
& isFinite0(sdtlcdtrc0(W0,szDzozmdt0(W0))) )
| ( aElement0(szDzizrdt0(W0))
& isCountable0(sdtlbdtrb0(W0,szDzizrdt0(W0))) ) ) )
<=> ( ( aElement0(szDzizrdt0(W0))
& isCountable0(sdtlbdtrb0(W0,szDzizrdt0(W0))) )
| ~ aFunction0(W0)
| ~ ( isCountable0(szDzozmdt0(W0))
& isFinite0(sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ) )),
( ( aFunction0(W0)
=> ( ( isCountable0(szDzozmdt0(W0))
& isFinite0(sdtlcdtrc0(W0,szDzozmdt0(W0))) )
=> ( aElement0(szDzizrdt0(W0))
& isCountable0(sdtlbdtrb0(W0,szDzizrdt0(W0))) ) ) )
<=> ( ( aElement0(szDzizrdt0(W0))
& isCountable0(sdtlbdtrb0(W0,szDzizrdt0(W0))) )
| ~ aFunction0(W0)
| ~ ( isCountable0(szDzozmdt0(W0))
& isFinite0(sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ) )),
inference(bind,[status(th)],[]) ).
tff(167,plain,
( ! [W0: $i] :
( aFunction0(W0)
=> ( ( isCountable0(szDzozmdt0(W0))
& isFinite0(sdtlcdtrc0(W0,szDzozmdt0(W0))) )
=> ( aElement0(szDzizrdt0(W0))
& isCountable0(sdtlbdtrb0(W0,szDzizrdt0(W0))) ) ) )
<=> ! [W0: $i] :
( ( aElement0(szDzizrdt0(W0))
& isCountable0(sdtlbdtrb0(W0,szDzizrdt0(W0))) )
| ~ aFunction0(W0)
| ~ ( isCountable0(szDzozmdt0(W0))
& isFinite0(sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ) ),
inference(quant_intro,[status(thm)],[166]) ).
tff(168,axiom,
! [W0: $i] :
( aFunction0(W0)
=> ( ( isCountable0(szDzozmdt0(W0))
& isFinite0(sdtlcdtrc0(W0,szDzozmdt0(W0))) )
=> ( aElement0(szDzizrdt0(W0))
& isCountable0(sdtlbdtrb0(W0,szDzizrdt0(W0))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDirichlet) ).
tff(169,plain,
! [W0: $i] :
( ( aElement0(szDzizrdt0(W0))
& isCountable0(sdtlbdtrb0(W0,szDzizrdt0(W0))) )
| ~ aFunction0(W0)
| ~ ( isCountable0(szDzozmdt0(W0))
& isFinite0(sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ),
inference(modus_ponens,[status(thm)],[168,167]) ).
tff(170,plain,
! [W0: $i] :
( ( aElement0(szDzizrdt0(W0))
& isCountable0(sdtlbdtrb0(W0,szDzizrdt0(W0))) )
| ~ aFunction0(W0)
| ~ ( isCountable0(szDzozmdt0(W0))
& isFinite0(sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ),
inference(modus_ponens,[status(thm)],[169,165]) ).
tff(171,plain,
! [W0: $i] :
( ( aElement0(szDzizrdt0(W0))
& isCountable0(sdtlbdtrb0(W0,szDzizrdt0(W0))) )
| ~ aFunction0(W0)
| ~ ( isCountable0(szDzozmdt0(W0))
& isFinite0(sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ),
inference(skolemize,[status(sab)],[170]) ).
tff(172,plain,
! [W0: $i] :
( ~ aFunction0(W0)
| ~ isCountable0(szDzozmdt0(W0))
| ~ ( ~ aElement0(szDzizrdt0(W0))
| ~ isCountable0(sdtlbdtrb0(W0,szDzizrdt0(W0))) )
| ~ isFinite0(sdtlcdtrc0(W0,szDzozmdt0(W0))) ),
inference(modus_ponens,[status(thm)],[171,164]) ).
tff(173,plain,
! [W0: $i] :
( ~ aFunction0(W0)
| ~ isCountable0(szDzozmdt0(W0))
| ~ ( ~ aElement0(szDzizrdt0(W0))
| ~ isCountable0(sdtlbdtrb0(W0,szDzizrdt0(W0))) )
| ~ isFinite0(sdtlcdtrc0(W0,szDzozmdt0(W0))) ),
inference(modus_ponens,[status(thm)],[172,162]) ).
tff(174,plain,
( ( ~ ! [W0: $i] :
( ~ aFunction0(W0)
| ~ isCountable0(szDzozmdt0(W0))
| ~ ( ~ aElement0(szDzizrdt0(W0))
| ~ isCountable0(sdtlbdtrb0(W0,szDzizrdt0(W0))) )
| ~ isFinite0(sdtlcdtrc0(W0,szDzozmdt0(W0))) )
| ~ aFunction0(xd)
| ~ isCountable0(szDzozmdt0(xd))
| ~ ( ~ aElement0(szDzizrdt0(xd))
| ~ isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd))) )
| ~ isFinite0(sdtlcdtrc0(xd,szDzozmdt0(xd))) )
<=> ( ~ ! [W0: $i] :
( ~ aFunction0(W0)
| ~ isCountable0(szDzozmdt0(W0))
| ~ ( ~ aElement0(szDzizrdt0(W0))
| ~ isCountable0(sdtlbdtrb0(W0,szDzizrdt0(W0))) )
| ~ isFinite0(sdtlcdtrc0(W0,szDzozmdt0(W0))) )
| ~ aFunction0(xd)
| ~ isCountable0(szDzozmdt0(xd))
| ~ ( ~ aElement0(szDzizrdt0(xd))
| ~ isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd))) )
| ~ isFinite0(sdtlcdtrc0(xd,szDzozmdt0(xd))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(175,plain,
( ~ ! [W0: $i] :
( ~ aFunction0(W0)
| ~ isCountable0(szDzozmdt0(W0))
| ~ ( ~ aElement0(szDzizrdt0(W0))
| ~ isCountable0(sdtlbdtrb0(W0,szDzizrdt0(W0))) )
| ~ isFinite0(sdtlcdtrc0(W0,szDzozmdt0(W0))) )
| ~ aFunction0(xd)
| ~ isCountable0(szDzozmdt0(xd))
| ~ ( ~ aElement0(szDzizrdt0(xd))
| ~ isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd))) )
| ~ isFinite0(sdtlcdtrc0(xd,szDzozmdt0(xd))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(176,plain,
( ~ ! [W0: $i] :
( ~ aFunction0(W0)
| ~ isCountable0(szDzozmdt0(W0))
| ~ ( ~ aElement0(szDzizrdt0(W0))
| ~ isCountable0(sdtlbdtrb0(W0,szDzizrdt0(W0))) )
| ~ isFinite0(sdtlcdtrc0(W0,szDzozmdt0(W0))) )
| ~ aFunction0(xd)
| ~ isCountable0(szDzozmdt0(xd))
| ~ ( ~ aElement0(szDzizrdt0(xd))
| ~ isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd))) )
| ~ isFinite0(sdtlcdtrc0(xd,szDzozmdt0(xd))) ),
inference(modus_ponens,[status(thm)],[175,174]) ).
tff(177,plain,
( ~ isCountable0(szDzozmdt0(xd))
| ~ ( ~ aElement0(szDzizrdt0(xd))
| ~ isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd))) )
| ~ isFinite0(sdtlcdtrc0(xd,szDzozmdt0(xd))) ),
inference(unit_resolution,[status(thm)],[176,173,160]) ).
tff(178,plain,
~ ( ~ aElement0(szDzizrdt0(xd))
| ~ isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
inference(unit_resolution,[status(thm)],[177,157,151]) ).
tff(179,plain,
( ~ aElement0(szDzizrdt0(xd))
| ~ isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aElement0(szDzizrdt0(xd)) ),
inference(tautology,[status(thm)],[]) ).
tff(180,plain,
aElement0(szDzizrdt0(xd)),
inference(unit_resolution,[status(thm)],[179,178]) ).
tff(181,plain,
^ [W0: $i,W1: $i] :
refl(( ( aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0))
| ~ aElement0(W1)
| ~ aFunction0(W0) )
<=> ( aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0))
| ~ aElement0(W1)
| ~ aFunction0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(182,plain,
( ! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0))
| ~ aElement0(W1)
| ~ aFunction0(W0) )
<=> ! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0))
| ~ aElement0(W1)
| ~ aFunction0(W0) ) ),
inference(quant_intro,[status(thm)],[181]) ).
tff(183,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aFunction0(W0)
& aElement0(W1) )
<=> ~ ( ~ aElement0(W1)
| ~ aFunction0(W0) ) )),
( ~ ( aFunction0(W0)
& aElement0(W1) )
<=> ~ ~ ( ~ aElement0(W1)
| ~ aFunction0(W0) ) )),
rewrite(( ~ ~ ( ~ aElement0(W1)
| ~ aFunction0(W0) )
<=> ( ~ aElement0(W1)
| ~ aFunction0(W0) ) )),
( ~ ( aFunction0(W0)
& aElement0(W1) )
<=> ( ~ aElement0(W1)
| ~ aFunction0(W0) ) )),
( ( ~ ( aFunction0(W0)
& aElement0(W1) )
| aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0)) )
<=> ( ~ aElement0(W1)
| ~ aFunction0(W0)
| aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0)) ) )),
rewrite(( ( ~ aElement0(W1)
| ~ aFunction0(W0)
| aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0)) )
<=> ( aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0))
| ~ aElement0(W1)
| ~ aFunction0(W0) ) )),
( ( ~ ( aFunction0(W0)
& aElement0(W1) )
| aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0)) )
<=> ( aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0))
| ~ aElement0(W1)
| ~ aFunction0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(184,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aFunction0(W0)
& aElement0(W1) )
| aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0)) )
<=> ! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0))
| ~ aElement0(W1)
| ~ aFunction0(W0) ) ),
inference(quant_intro,[status(thm)],[183]) ).
tff(185,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aFunction0(W0)
& aElement0(W1) )
| aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0)) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aFunction0(W0)
& aElement0(W1) )
| aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(186,plain,
^ [W0: $i,W1: $i] :
rewrite(( ( ( aFunction0(W0)
& aElement0(W1) )
=> aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0)) )
<=> ( ~ ( aFunction0(W0)
& aElement0(W1) )
| aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0)) ) )),
inference(bind,[status(th)],[]) ).
tff(187,plain,
( ! [W0: $i,W1: $i] :
( ( aFunction0(W0)
& aElement0(W1) )
=> aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0)) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aFunction0(W0)
& aElement0(W1) )
| aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0)) ) ),
inference(quant_intro,[status(thm)],[186]) ).
tff(188,axiom,
! [W0: $i,W1: $i] :
( ( aFunction0(W0)
& aElement0(W1) )
=> aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mPttSet) ).
tff(189,plain,
! [W0: $i,W1: $i] :
( ~ ( aFunction0(W0)
& aElement0(W1) )
| aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0)) ),
inference(modus_ponens,[status(thm)],[188,187]) ).
tff(190,plain,
! [W0: $i,W1: $i] :
( ~ ( aFunction0(W0)
& aElement0(W1) )
| aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0)) ),
inference(modus_ponens,[status(thm)],[189,185]) ).
tff(191,plain,
! [W0: $i,W1: $i] :
( ~ ( aFunction0(W0)
& aElement0(W1) )
| aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0)) ),
inference(skolemize,[status(sab)],[190]) ).
tff(192,plain,
! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0))
| ~ aElement0(W1)
| ~ aFunction0(W0) ),
inference(modus_ponens,[status(thm)],[191,184]) ).
tff(193,plain,
! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0))
| ~ aElement0(W1)
| ~ aFunction0(W0) ),
inference(modus_ponens,[status(thm)],[192,182]) ).
tff(194,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0))
| ~ aElement0(W1)
| ~ aFunction0(W0) )
| ~ aElement0(szDzizrdt0(xd))
| ~ aFunction0(xd)
| aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzozmdt0(xd)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0))
| ~ aElement0(W1)
| ~ aFunction0(W0) )
| ~ aElement0(szDzizrdt0(xd))
| ~ aFunction0(xd)
| aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzozmdt0(xd)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(195,plain,
( ( aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzozmdt0(xd))
| ~ aElement0(szDzizrdt0(xd))
| ~ aFunction0(xd) )
<=> ( ~ aElement0(szDzizrdt0(xd))
| ~ aFunction0(xd)
| aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzozmdt0(xd)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(196,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0))
| ~ aElement0(W1)
| ~ aFunction0(W0) )
| aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzozmdt0(xd))
| ~ aElement0(szDzizrdt0(xd))
| ~ aFunction0(xd) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0))
| ~ aElement0(W1)
| ~ aFunction0(W0) )
| ~ aElement0(szDzizrdt0(xd))
| ~ aFunction0(xd)
| aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzozmdt0(xd)) ) ),
inference(monotonicity,[status(thm)],[195]) ).
tff(197,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0))
| ~ aElement0(W1)
| ~ aFunction0(W0) )
| aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzozmdt0(xd))
| ~ aElement0(szDzizrdt0(xd))
| ~ aFunction0(xd) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0))
| ~ aElement0(W1)
| ~ aFunction0(W0) )
| ~ aElement0(szDzizrdt0(xd))
| ~ aFunction0(xd)
| aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzozmdt0(xd)) ) ),
inference(transitivity,[status(thm)],[196,194]) ).
tff(198,plain,
( ~ ! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0))
| ~ aElement0(W1)
| ~ aFunction0(W0) )
| aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzozmdt0(xd))
| ~ aElement0(szDzizrdt0(xd))
| ~ aFunction0(xd) ),
inference(quant_inst,[status(thm)],[]) ).
tff(199,plain,
( ~ ! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0))
| ~ aElement0(W1)
| ~ aFunction0(W0) )
| ~ aElement0(szDzizrdt0(xd))
| ~ aFunction0(xd)
| aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzozmdt0(xd)) ),
inference(modus_ponens,[status(thm)],[198,197]) ).
tff(200,plain,
aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzozmdt0(xd)),
inference(unit_resolution,[status(thm)],[199,193,160,180]) ).
tff(201,plain,
aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szNzAzT0),
inference(modus_ponens,[status(thm)],[200,144]) ).
tff(202,plain,
( ~ ( ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szNzAzT0)
| ~ ( ~ aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aElementOf0(W2,szNzAzT0) ) ) )
| ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szNzAzT0)
| ~ ( ~ aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aElementOf0(W2,szNzAzT0) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(203,plain,
( ~ ( ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szNzAzT0)
| ~ ( ~ aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aElementOf0(W2,szNzAzT0) ) ) )
| ~ ( ~ aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aElementOf0(W2,szNzAzT0) ) ) ),
inference(unit_resolution,[status(thm)],[202,201]) ).
tff(204,plain,
~ ( ~ aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aElementOf0(W2,szNzAzT0) ) ),
inference(unit_resolution,[status(thm)],[203,138]) ).
tff(205,plain,
( ~ aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aElementOf0(W2,szNzAzT0) )
| aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
inference(tautology,[status(thm)],[]) ).
tff(206,plain,
aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd))),
inference(unit_resolution,[status(thm)],[205,204]) ).
tff(207,plain,
( ~ aElement0(szDzizrdt0(xd))
| ~ isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
inference(tautology,[status(thm)],[]) ).
tff(208,plain,
isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd))),
inference(unit_resolution,[status(thm)],[207,178]) ).
tff(209,plain,
^ [W0: $i] :
refl(( ( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) )
<=> ( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(210,plain,
( ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) )
<=> ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) ) ),
inference(quant_intro,[status(thm)],[209]) ).
tff(211,plain,
^ [W0: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aSet0(W0)
& isCountable0(W0) )
<=> ~ ( ~ aSet0(W0)
| ~ isCountable0(W0) ) )),
( ~ ( aSet0(W0)
& isCountable0(W0) )
<=> ~ ~ ( ~ aSet0(W0)
| ~ isCountable0(W0) ) )),
rewrite(( ~ ~ ( ~ aSet0(W0)
| ~ isCountable0(W0) )
<=> ( ~ aSet0(W0)
| ~ isCountable0(W0) ) )),
( ~ ( aSet0(W0)
& isCountable0(W0) )
<=> ( ~ aSet0(W0)
| ~ isCountable0(W0) ) )),
( ( ~ isFinite0(W0)
| ~ ( aSet0(W0)
& isCountable0(W0) ) )
<=> ( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) ) )),
rewrite(( ( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) )
<=> ( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) ) )),
( ( ~ isFinite0(W0)
| ~ ( aSet0(W0)
& isCountable0(W0) ) )
<=> ( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(212,plain,
( ! [W0: $i] :
( ~ isFinite0(W0)
| ~ ( aSet0(W0)
& isCountable0(W0) ) )
<=> ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) ) ),
inference(quant_intro,[status(thm)],[211]) ).
tff(213,plain,
( ! [W0: $i] :
( ~ isFinite0(W0)
| ~ ( aSet0(W0)
& isCountable0(W0) ) )
<=> ! [W0: $i] :
( ~ isFinite0(W0)
| ~ ( aSet0(W0)
& isCountable0(W0) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(214,plain,
^ [W0: $i] :
rewrite(( ( ( aSet0(W0)
& isCountable0(W0) )
=> ~ isFinite0(W0) )
<=> ( ~ isFinite0(W0)
| ~ ( aSet0(W0)
& isCountable0(W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(215,plain,
( ! [W0: $i] :
( ( aSet0(W0)
& isCountable0(W0) )
=> ~ isFinite0(W0) )
<=> ! [W0: $i] :
( ~ isFinite0(W0)
| ~ ( aSet0(W0)
& isCountable0(W0) ) ) ),
inference(quant_intro,[status(thm)],[214]) ).
tff(216,axiom,
! [W0: $i] :
( ( aSet0(W0)
& isCountable0(W0) )
=> ~ isFinite0(W0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCountNFin) ).
tff(217,plain,
! [W0: $i] :
( ~ isFinite0(W0)
| ~ ( aSet0(W0)
& isCountable0(W0) ) ),
inference(modus_ponens,[status(thm)],[216,215]) ).
tff(218,plain,
! [W0: $i] :
( ~ isFinite0(W0)
| ~ ( aSet0(W0)
& isCountable0(W0) ) ),
inference(modus_ponens,[status(thm)],[217,213]) ).
tff(219,plain,
! [W0: $i] :
( ~ isFinite0(W0)
| ~ ( aSet0(W0)
& isCountable0(W0) ) ),
inference(skolemize,[status(sab)],[218]) ).
tff(220,plain,
! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) ),
inference(modus_ponens,[status(thm)],[219,212]) ).
tff(221,plain,
! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) ),
inference(modus_ponens,[status(thm)],[220,210]) ).
tff(222,plain,
( ( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) )
| ~ isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ isFinite0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd))) )
<=> ( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) )
| ~ isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ isFinite0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(223,plain,
( ( ~ isFinite0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd))) )
<=> ( ~ isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ isFinite0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(224,plain,
( ( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) )
| ~ isFinite0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd))) )
<=> ( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) )
| ~ isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ isFinite0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd))) ) ),
inference(monotonicity,[status(thm)],[223]) ).
tff(225,plain,
( ( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) )
| ~ isFinite0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd))) )
<=> ( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) )
| ~ isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ isFinite0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd))) ) ),
inference(transitivity,[status(thm)],[224,222]) ).
tff(226,plain,
( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) )
| ~ isFinite0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(227,plain,
( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) )
| ~ isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ isFinite0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
inference(modus_ponens,[status(thm)],[226,225]) ).
tff(228,plain,
( ~ isFinite0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
inference(unit_resolution,[status(thm)],[227,221,208]) ).
tff(229,plain,
~ isFinite0(sdtlbdtrb0(xd,szDzizrdt0(xd))),
inference(unit_resolution,[status(thm)],[228,206]) ).
tff(230,plain,
( ( ~ ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))) )
| isFinite0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))) )
<=> ( ~ ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))) )
| isFinite0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(231,plain,
( ~ ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))) )
| isFinite0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(232,plain,
( ~ ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))) )
| isFinite0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))) ),
inference(modus_ponens,[status(thm)],[231,230]) ).
tff(233,plain,
~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),
inference(unit_resolution,[status(thm)],[232,229,126]) ).
tff(234,plain,
( ~ ( ~ aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aElementOf0(tptp_fun_W2_1(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))) ) )
| ~ aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aElementOf0(tptp_fun_W2_1(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))) ) ),
inference(tautology,[status(thm)],[]) ).
tff(235,plain,
( ~ ( ~ aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aElementOf0(tptp_fun_W2_1(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))) ) )
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aElementOf0(tptp_fun_W2_1(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))) ) ),
inference(unit_resolution,[status(thm)],[234,206,233]) ).
tff(236,plain,
~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aElementOf0(tptp_fun_W2_1(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))) ),
inference(unit_resolution,[status(thm)],[235,92]) ).
tff(237,plain,
( ~ aElementOf0(tptp_fun_W2_1(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aElementOf0(tptp_fun_W2_1(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))
| aElementOf0(tptp_fun_W2_1(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
inference(tautology,[status(thm)],[]) ).
tff(238,plain,
aElementOf0(tptp_fun_W2_1(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),sdtlbdtrb0(xd,szDzizrdt0(xd))),
inference(unit_resolution,[status(thm)],[237,236]) ).
tff(239,plain,
( ~ aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aElementOf0(W2,szNzAzT0) )
| ! [W2: $i] :
( ~ aElementOf0(W2,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aElementOf0(W2,szNzAzT0) ) ),
inference(tautology,[status(thm)],[]) ).
tff(240,plain,
! [W2: $i] :
( ~ aElementOf0(W2,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aElementOf0(W2,szNzAzT0) ),
inference(unit_resolution,[status(thm)],[239,204]) ).
tff(241,plain,
( ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aElementOf0(W2,szNzAzT0) )
| ~ aElementOf0(tptp_fun_W2_1(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aElementOf0(tptp_fun_W2_1(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),szNzAzT0) )
<=> ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aElementOf0(W2,szNzAzT0) )
| ~ aElementOf0(tptp_fun_W2_1(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aElementOf0(tptp_fun_W2_1(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),szNzAzT0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(242,plain,
( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aElementOf0(W2,szNzAzT0) )
| ~ aElementOf0(tptp_fun_W2_1(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aElementOf0(tptp_fun_W2_1(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),szNzAzT0) ),
inference(quant_inst,[status(thm)],[]) ).
tff(243,plain,
( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aElementOf0(W2,szNzAzT0) )
| ~ aElementOf0(tptp_fun_W2_1(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aElementOf0(tptp_fun_W2_1(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),szNzAzT0) ),
inference(modus_ponens,[status(thm)],[242,241]) ).
tff(244,plain,
aElementOf0(tptp_fun_W2_1(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),szNzAzT0),
inference(unit_resolution,[status(thm)],[243,240,238]) ).
tff(245,plain,
^ [W0: $i,W1: $i] :
rewrite(( ( ~ aElement0(W1)
| ~ aFunction0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtlbdtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = sdtlbdtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElementOf0(tptp_fun_W3_12(W2,W1,W0),szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,tptp_fun_W3_12(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_12(W2,W1,W0),W2) ) ) ) )
<=> ( ~ aElement0(W1)
| ~ aFunction0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtlbdtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElementOf0(tptp_fun_W3_12(W2,W1,W0),szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,tptp_fun_W3_12(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_12(W2,W1,W0),W2) ) )
| ~ ( ( W2 != sdtlbdtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(246,plain,
( ! [W0: $i,W1: $i] :
( ~ aElement0(W1)
| ~ aFunction0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtlbdtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = sdtlbdtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElementOf0(tptp_fun_W3_12(W2,W1,W0),szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,tptp_fun_W3_12(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_12(W2,W1,W0),W2) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aElement0(W1)
| ~ aFunction0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtlbdtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElementOf0(tptp_fun_W3_12(W2,W1,W0),szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,tptp_fun_W3_12(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_12(W2,W1,W0),W2) ) )
| ~ ( ( W2 != sdtlbdtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[245]) ).
tff(247,plain,
^ [W0: $i,W1: $i] :
refl(( ( ~ aElement0(W1)
| ~ aFunction0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtlbdtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = sdtlbdtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElementOf0(tptp_fun_W3_12(W2,W1,W0),szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,tptp_fun_W3_12(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_12(W2,W1,W0),W2) ) ) ) )
<=> ( ~ aElement0(W1)
| ~ aFunction0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtlbdtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = sdtlbdtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElementOf0(tptp_fun_W3_12(W2,W1,W0),szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,tptp_fun_W3_12(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_12(W2,W1,W0),W2) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(248,plain,
( ! [W0: $i,W1: $i] :
( ~ aElement0(W1)
| ~ aFunction0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtlbdtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = sdtlbdtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElementOf0(tptp_fun_W3_12(W2,W1,W0),szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,tptp_fun_W3_12(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_12(W2,W1,W0),W2) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aElement0(W1)
| ~ aFunction0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtlbdtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = sdtlbdtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElementOf0(tptp_fun_W3_12(W2,W1,W0),szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,tptp_fun_W3_12(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_12(W2,W1,W0),W2) ) ) ) ) ),
inference(quant_intro,[status(thm)],[247]) ).
tff(249,plain,
^ [W0: $i,W1: $i] :
rewrite(( ( ~ aElement0(W1)
| ~ aFunction0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtlbdtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = sdtlbdtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElementOf0(tptp_fun_W3_12(W2,W1,W0),szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,tptp_fun_W3_12(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_12(W2,W1,W0),W2) ) ) ) )
<=> ( ~ aElement0(W1)
| ~ aFunction0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtlbdtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = sdtlbdtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElementOf0(tptp_fun_W3_12(W2,W1,W0),szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,tptp_fun_W3_12(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_12(W2,W1,W0),W2) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(250,plain,
( ! [W0: $i,W1: $i] :
( ~ aElement0(W1)
| ~ aFunction0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtlbdtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = sdtlbdtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElementOf0(tptp_fun_W3_12(W2,W1,W0),szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,tptp_fun_W3_12(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_12(W2,W1,W0),W2) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aElement0(W1)
| ~ aFunction0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtlbdtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = sdtlbdtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElementOf0(tptp_fun_W3_12(W2,W1,W0),szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,tptp_fun_W3_12(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_12(W2,W1,W0),W2) ) ) ) ) ),
inference(quant_intro,[status(thm)],[249]) ).
tff(251,plain,
( ! [W0: $i,W1: $i] :
( ~ aElement0(W1)
| ~ aFunction0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtlbdtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = sdtlbdtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElementOf0(tptp_fun_W3_12(W2,W1,W0),szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,tptp_fun_W3_12(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_12(W2,W1,W0),W2) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aElement0(W1)
| ~ aFunction0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtlbdtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = sdtlbdtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElementOf0(tptp_fun_W3_12(W2,W1,W0),szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,tptp_fun_W3_12(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_12(W2,W1,W0),W2) ) ) ) ) ),
inference(transitivity,[status(thm)],[250,248]) ).
tff(252,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aFunction0(W0)
& aElement0(W1) )
<=> ~ ( ~ aElement0(W1)
| ~ aFunction0(W0) ) )),
( ~ ( aFunction0(W0)
& aElement0(W1) )
<=> ~ ~ ( ~ aElement0(W1)
| ~ aFunction0(W0) ) )),
rewrite(( ~ ~ ( ~ aElement0(W1)
| ~ aFunction0(W0) )
<=> ( ~ aElement0(W1)
| ~ aFunction0(W0) ) )),
( ~ ( aFunction0(W0)
& aElement0(W1) )
<=> ( ~ aElement0(W1)
| ~ aFunction0(W0) ) )),
quant_intro(proof_bind(^ [W2: $i] :
trans(monotonicity(rewrite(( ( ( W2 != sdtlbdtrb0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElementOf0(W3,szDzozmdt0(W0))
& ( sdtlpdtrp0(W0,W3) = W1 ) ) ) ) )
<=> ( ( W2 != sdtlbdtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) ) )),
trans(monotonicity(trans(monotonicity(trans(trans(monotonicity(rewrite(( ( aElementOf0(tptp_fun_W3_12(W2,W1,W0),szDzozmdt0(W0))
& ( sdtlpdtrp0(W0,tptp_fun_W3_12(W2,W1,W0)) = W1 ) )
<=> ~ ( ~ aElementOf0(tptp_fun_W3_12(W2,W1,W0),szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,tptp_fun_W3_12(W2,W1,W0)) != W1 ) ) )),
( ( aElementOf0(tptp_fun_W3_12(W2,W1,W0),W2)
<=> ( aElementOf0(tptp_fun_W3_12(W2,W1,W0),szDzozmdt0(W0))
& ( sdtlpdtrp0(W0,tptp_fun_W3_12(W2,W1,W0)) = W1 ) ) )
<=> ( aElementOf0(tptp_fun_W3_12(W2,W1,W0),W2)
<=> ~ ( ~ aElementOf0(tptp_fun_W3_12(W2,W1,W0),szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,tptp_fun_W3_12(W2,W1,W0)) != W1 ) ) ) )),
rewrite(( ( aElementOf0(tptp_fun_W3_12(W2,W1,W0),W2)
<=> ~ ( ~ aElementOf0(tptp_fun_W3_12(W2,W1,W0),szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,tptp_fun_W3_12(W2,W1,W0)) != W1 ) ) )
<=> ~ ( ( ~ aElementOf0(tptp_fun_W3_12(W2,W1,W0),szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,tptp_fun_W3_12(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_12(W2,W1,W0),W2) ) )),
( ( aElementOf0(tptp_fun_W3_12(W2,W1,W0),W2)
<=> ( aElementOf0(tptp_fun_W3_12(W2,W1,W0),szDzozmdt0(W0))
& ( sdtlpdtrp0(W0,tptp_fun_W3_12(W2,W1,W0)) = W1 ) ) )
<=> ~ ( ( ~ aElementOf0(tptp_fun_W3_12(W2,W1,W0),szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,tptp_fun_W3_12(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_12(W2,W1,W0),W2) ) )),
rewrite(( ~ ( ( ~ aElementOf0(tptp_fun_W3_12(W2,W1,W0),szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,tptp_fun_W3_12(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_12(W2,W1,W0),W2) )
<=> ~ ( ( ~ aElementOf0(tptp_fun_W3_12(W2,W1,W0),szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,tptp_fun_W3_12(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_12(W2,W1,W0),W2) ) )),
( ( aElementOf0(tptp_fun_W3_12(W2,W1,W0),W2)
<=> ( aElementOf0(tptp_fun_W3_12(W2,W1,W0),szDzozmdt0(W0))
& ( sdtlpdtrp0(W0,tptp_fun_W3_12(W2,W1,W0)) = W1 ) ) )
<=> ~ ( ( ~ aElementOf0(tptp_fun_W3_12(W2,W1,W0),szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,tptp_fun_W3_12(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_12(W2,W1,W0),W2) ) )),
( ~ ( aElementOf0(tptp_fun_W3_12(W2,W1,W0),W2)
<=> ( aElementOf0(tptp_fun_W3_12(W2,W1,W0),szDzozmdt0(W0))
& ( sdtlpdtrp0(W0,tptp_fun_W3_12(W2,W1,W0)) = W1 ) ) )
<=> ~ ~ ( ( ~ aElementOf0(tptp_fun_W3_12(W2,W1,W0),szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,tptp_fun_W3_12(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_12(W2,W1,W0),W2) ) )),
rewrite(( ~ ~ ( ( ~ aElementOf0(tptp_fun_W3_12(W2,W1,W0),szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,tptp_fun_W3_12(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_12(W2,W1,W0),W2) )
<=> ( ( ~ aElementOf0(tptp_fun_W3_12(W2,W1,W0),szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,tptp_fun_W3_12(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_12(W2,W1,W0),W2) ) )),
( ~ ( aElementOf0(tptp_fun_W3_12(W2,W1,W0),W2)
<=> ( aElementOf0(tptp_fun_W3_12(W2,W1,W0),szDzozmdt0(W0))
& ( sdtlpdtrp0(W0,tptp_fun_W3_12(W2,W1,W0)) = W1 ) ) )
<=> ( ( ~ aElementOf0(tptp_fun_W3_12(W2,W1,W0),szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,tptp_fun_W3_12(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_12(W2,W1,W0),W2) ) )),
( ( ( W2 = sdtlbdtrb0(W0,W1) )
| ~ aSet0(W2)
| ~ ( aElementOf0(tptp_fun_W3_12(W2,W1,W0),W2)
<=> ( aElementOf0(tptp_fun_W3_12(W2,W1,W0),szDzozmdt0(W0))
& ( sdtlpdtrp0(W0,tptp_fun_W3_12(W2,W1,W0)) = W1 ) ) ) )
<=> ( ( W2 = sdtlbdtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElementOf0(tptp_fun_W3_12(W2,W1,W0),szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,tptp_fun_W3_12(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_12(W2,W1,W0),W2) ) ) )),
rewrite(( ( ( W2 = sdtlbdtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElementOf0(tptp_fun_W3_12(W2,W1,W0),szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,tptp_fun_W3_12(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_12(W2,W1,W0),W2) ) )
<=> ( ( W2 = sdtlbdtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElementOf0(tptp_fun_W3_12(W2,W1,W0),szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,tptp_fun_W3_12(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_12(W2,W1,W0),W2) ) ) )),
( ( ( W2 = sdtlbdtrb0(W0,W1) )
| ~ aSet0(W2)
| ~ ( aElementOf0(tptp_fun_W3_12(W2,W1,W0),W2)
<=> ( aElementOf0(tptp_fun_W3_12(W2,W1,W0),szDzozmdt0(W0))
& ( sdtlpdtrp0(W0,tptp_fun_W3_12(W2,W1,W0)) = W1 ) ) ) )
<=> ( ( W2 = sdtlbdtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElementOf0(tptp_fun_W3_12(W2,W1,W0),szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,tptp_fun_W3_12(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_12(W2,W1,W0),W2) ) ) )),
( ( ( ( W2 != sdtlbdtrb0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElementOf0(W3,szDzozmdt0(W0))
& ( sdtlpdtrp0(W0,W3) = W1 ) ) ) ) )
& ( ( W2 = sdtlbdtrb0(W0,W1) )
| ~ aSet0(W2)
| ~ ( aElementOf0(tptp_fun_W3_12(W2,W1,W0),W2)
<=> ( aElementOf0(tptp_fun_W3_12(W2,W1,W0),szDzozmdt0(W0))
& ( sdtlpdtrp0(W0,tptp_fun_W3_12(W2,W1,W0)) = W1 ) ) ) ) )
<=> ( ( ( W2 != sdtlbdtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
& ( ( W2 = sdtlbdtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElementOf0(tptp_fun_W3_12(W2,W1,W0),szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,tptp_fun_W3_12(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_12(W2,W1,W0),W2) ) ) ) )),
rewrite(( ( ( ( W2 != sdtlbdtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
& ( ( W2 = sdtlbdtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElementOf0(tptp_fun_W3_12(W2,W1,W0),szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,tptp_fun_W3_12(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_12(W2,W1,W0),W2) ) ) )
<=> ~ ( ~ ( ( W2 != sdtlbdtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = sdtlbdtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElementOf0(tptp_fun_W3_12(W2,W1,W0),szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,tptp_fun_W3_12(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_12(W2,W1,W0),W2) ) ) ) )),
( ( ( ( W2 != sdtlbdtrb0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElementOf0(W3,szDzozmdt0(W0))
& ( sdtlpdtrp0(W0,W3) = W1 ) ) ) ) )
& ( ( W2 = sdtlbdtrb0(W0,W1) )
| ~ aSet0(W2)
| ~ ( aElementOf0(tptp_fun_W3_12(W2,W1,W0),W2)
<=> ( aElementOf0(tptp_fun_W3_12(W2,W1,W0),szDzozmdt0(W0))
& ( sdtlpdtrp0(W0,tptp_fun_W3_12(W2,W1,W0)) = W1 ) ) ) ) )
<=> ~ ( ~ ( ( W2 != sdtlbdtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = sdtlbdtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElementOf0(tptp_fun_W3_12(W2,W1,W0),szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,tptp_fun_W3_12(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_12(W2,W1,W0),W2) ) ) ) ))),
( ! [W2: $i] :
( ( ( W2 != sdtlbdtrb0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElementOf0(W3,szDzozmdt0(W0))
& ( sdtlpdtrp0(W0,W3) = W1 ) ) ) ) )
& ( ( W2 = sdtlbdtrb0(W0,W1) )
| ~ aSet0(W2)
| ~ ( aElementOf0(tptp_fun_W3_12(W2,W1,W0),W2)
<=> ( aElementOf0(tptp_fun_W3_12(W2,W1,W0),szDzozmdt0(W0))
& ( sdtlpdtrp0(W0,tptp_fun_W3_12(W2,W1,W0)) = W1 ) ) ) ) )
<=> ! [W2: $i] :
~ ( ~ ( ( W2 != sdtlbdtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = sdtlbdtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElementOf0(tptp_fun_W3_12(W2,W1,W0),szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,tptp_fun_W3_12(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_12(W2,W1,W0),W2) ) ) ) )),
( ( ~ ( aFunction0(W0)
& aElement0(W1) )
| ! [W2: $i] :
( ( ( W2 != sdtlbdtrb0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElementOf0(W3,szDzozmdt0(W0))
& ( sdtlpdtrp0(W0,W3) = W1 ) ) ) ) )
& ( ( W2 = sdtlbdtrb0(W0,W1) )
| ~ aSet0(W2)
| ~ ( aElementOf0(tptp_fun_W3_12(W2,W1,W0),W2)
<=> ( aElementOf0(tptp_fun_W3_12(W2,W1,W0),szDzozmdt0(W0))
& ( sdtlpdtrp0(W0,tptp_fun_W3_12(W2,W1,W0)) = W1 ) ) ) ) ) )
<=> ( ~ aElement0(W1)
| ~ aFunction0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtlbdtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = sdtlbdtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElementOf0(tptp_fun_W3_12(W2,W1,W0),szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,tptp_fun_W3_12(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_12(W2,W1,W0),W2) ) ) ) ) )),
rewrite(( ( ~ aElement0(W1)
| ~ aFunction0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtlbdtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = sdtlbdtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElementOf0(tptp_fun_W3_12(W2,W1,W0),szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,tptp_fun_W3_12(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_12(W2,W1,W0),W2) ) ) ) )
<=> ( ~ aElement0(W1)
| ~ aFunction0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtlbdtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = sdtlbdtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElementOf0(tptp_fun_W3_12(W2,W1,W0),szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,tptp_fun_W3_12(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_12(W2,W1,W0),W2) ) ) ) ) )),
( ( ~ ( aFunction0(W0)
& aElement0(W1) )
| ! [W2: $i] :
( ( ( W2 != sdtlbdtrb0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElementOf0(W3,szDzozmdt0(W0))
& ( sdtlpdtrp0(W0,W3) = W1 ) ) ) ) )
& ( ( W2 = sdtlbdtrb0(W0,W1) )
| ~ aSet0(W2)
| ~ ( aElementOf0(tptp_fun_W3_12(W2,W1,W0),W2)
<=> ( aElementOf0(tptp_fun_W3_12(W2,W1,W0),szDzozmdt0(W0))
& ( sdtlpdtrp0(W0,tptp_fun_W3_12(W2,W1,W0)) = W1 ) ) ) ) ) )
<=> ( ~ aElement0(W1)
| ~ aFunction0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtlbdtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = sdtlbdtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElementOf0(tptp_fun_W3_12(W2,W1,W0),szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,tptp_fun_W3_12(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_12(W2,W1,W0),W2) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(253,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aFunction0(W0)
& aElement0(W1) )
| ! [W2: $i] :
( ( ( W2 != sdtlbdtrb0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElementOf0(W3,szDzozmdt0(W0))
& ( sdtlpdtrp0(W0,W3) = W1 ) ) ) ) )
& ( ( W2 = sdtlbdtrb0(W0,W1) )
| ~ aSet0(W2)
| ~ ( aElementOf0(tptp_fun_W3_12(W2,W1,W0),W2)
<=> ( aElementOf0(tptp_fun_W3_12(W2,W1,W0),szDzozmdt0(W0))
& ( sdtlpdtrp0(W0,tptp_fun_W3_12(W2,W1,W0)) = W1 ) ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aElement0(W1)
| ~ aFunction0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtlbdtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = sdtlbdtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElementOf0(tptp_fun_W3_12(W2,W1,W0),szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,tptp_fun_W3_12(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_12(W2,W1,W0),W2) ) ) ) ) ),
inference(quant_intro,[status(thm)],[252]) ).
tff(254,plain,
^ [W0: $i,W1: $i] :
rewrite(( ( ~ ( aFunction0(W0)
& aElement0(W1) )
| ! [W2: $i] :
( ( ( W2 != sdtlbdtrb0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElementOf0(W3,szDzozmdt0(W0))
& ( sdtlpdtrp0(W0,W3) = W1 ) ) ) ) )
& ( ( W2 = sdtlbdtrb0(W0,W1) )
| ~ aSet0(W2)
| ~ ( aElementOf0(tptp_fun_W3_12(W2,W1,W0),W2)
<=> ( aElementOf0(tptp_fun_W3_12(W2,W1,W0),szDzozmdt0(W0))
& ( sdtlpdtrp0(W0,tptp_fun_W3_12(W2,W1,W0)) = W1 ) ) ) ) ) )
<=> ( ~ ( aFunction0(W0)
& aElement0(W1) )
| ! [W2: $i] :
( ( ( W2 != sdtlbdtrb0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElementOf0(W3,szDzozmdt0(W0))
& ( sdtlpdtrp0(W0,W3) = W1 ) ) ) ) )
& ( ( W2 = sdtlbdtrb0(W0,W1) )
| ~ aSet0(W2)
| ~ ( aElementOf0(tptp_fun_W3_12(W2,W1,W0),W2)
<=> ( aElementOf0(tptp_fun_W3_12(W2,W1,W0),szDzozmdt0(W0))
& ( sdtlpdtrp0(W0,tptp_fun_W3_12(W2,W1,W0)) = W1 ) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(255,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aFunction0(W0)
& aElement0(W1) )
| ! [W2: $i] :
( ( ( W2 != sdtlbdtrb0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElementOf0(W3,szDzozmdt0(W0))
& ( sdtlpdtrp0(W0,W3) = W1 ) ) ) ) )
& ( ( W2 = sdtlbdtrb0(W0,W1) )
| ~ aSet0(W2)
| ~ ( aElementOf0(tptp_fun_W3_12(W2,W1,W0),W2)
<=> ( aElementOf0(tptp_fun_W3_12(W2,W1,W0),szDzozmdt0(W0))
& ( sdtlpdtrp0(W0,tptp_fun_W3_12(W2,W1,W0)) = W1 ) ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aFunction0(W0)
& aElement0(W1) )
| ! [W2: $i] :
( ( ( W2 != sdtlbdtrb0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElementOf0(W3,szDzozmdt0(W0))
& ( sdtlpdtrp0(W0,W3) = W1 ) ) ) ) )
& ( ( W2 = sdtlbdtrb0(W0,W1) )
| ~ aSet0(W2)
| ~ ( aElementOf0(tptp_fun_W3_12(W2,W1,W0),W2)
<=> ( aElementOf0(tptp_fun_W3_12(W2,W1,W0),szDzozmdt0(W0))
& ( sdtlpdtrp0(W0,tptp_fun_W3_12(W2,W1,W0)) = W1 ) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[254]) ).
tff(256,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aFunction0(W0)
& aElement0(W1) )
| ! [W2: $i] :
( ( W2 = sdtlbdtrb0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElementOf0(W3,szDzozmdt0(W0))
& ( sdtlpdtrp0(W0,W3) = W1 ) ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aFunction0(W0)
& aElement0(W1) )
| ! [W2: $i] :
( ( W2 = sdtlbdtrb0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElementOf0(W3,szDzozmdt0(W0))
& ( sdtlpdtrp0(W0,W3) = W1 ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(257,plain,
^ [W0: $i,W1: $i] :
rewrite(( ( ( aFunction0(W0)
& aElement0(W1) )
=> ! [W2: $i] :
( ( W2 = sdtlbdtrb0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElementOf0(W3,szDzozmdt0(W0))
& ( sdtlpdtrp0(W0,W3) = W1 ) ) ) ) ) )
<=> ( ~ ( aFunction0(W0)
& aElement0(W1) )
| ! [W2: $i] :
( ( W2 = sdtlbdtrb0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElementOf0(W3,szDzozmdt0(W0))
& ( sdtlpdtrp0(W0,W3) = W1 ) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(258,plain,
( ! [W0: $i,W1: $i] :
( ( aFunction0(W0)
& aElement0(W1) )
=> ! [W2: $i] :
( ( W2 = sdtlbdtrb0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElementOf0(W3,szDzozmdt0(W0))
& ( sdtlpdtrp0(W0,W3) = W1 ) ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aFunction0(W0)
& aElement0(W1) )
| ! [W2: $i] :
( ( W2 = sdtlbdtrb0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElementOf0(W3,szDzozmdt0(W0))
& ( sdtlpdtrp0(W0,W3) = W1 ) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[257]) ).
tff(259,axiom,
! [W0: $i,W1: $i] :
( ( aFunction0(W0)
& aElement0(W1) )
=> ! [W2: $i] :
( ( W2 = sdtlbdtrb0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElementOf0(W3,szDzozmdt0(W0))
& ( sdtlpdtrp0(W0,W3) = W1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefPtt) ).
tff(260,plain,
! [W0: $i,W1: $i] :
( ~ ( aFunction0(W0)
& aElement0(W1) )
| ! [W2: $i] :
( ( W2 = sdtlbdtrb0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElementOf0(W3,szDzozmdt0(W0))
& ( sdtlpdtrp0(W0,W3) = W1 ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[259,258]) ).
tff(261,plain,
! [W0: $i,W1: $i] :
( ~ ( aFunction0(W0)
& aElement0(W1) )
| ! [W2: $i] :
( ( W2 = sdtlbdtrb0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElementOf0(W3,szDzozmdt0(W0))
& ( sdtlpdtrp0(W0,W3) = W1 ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[260,256]) ).
tff(262,plain,
! [W0: $i,W1: $i] :
( ~ ( aFunction0(W0)
& aElement0(W1) )
| ! [W2: $i] :
( ( ( W2 != sdtlbdtrb0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElementOf0(W3,szDzozmdt0(W0))
& ( sdtlpdtrp0(W0,W3) = W1 ) ) ) ) )
& ( ( W2 = sdtlbdtrb0(W0,W1) )
| ~ aSet0(W2)
| ~ ( aElementOf0(tptp_fun_W3_12(W2,W1,W0),W2)
<=> ( aElementOf0(tptp_fun_W3_12(W2,W1,W0),szDzozmdt0(W0))
& ( sdtlpdtrp0(W0,tptp_fun_W3_12(W2,W1,W0)) = W1 ) ) ) ) ) ),
inference(skolemize,[status(sab)],[261]) ).
tff(263,plain,
! [W0: $i,W1: $i] :
( ~ ( aFunction0(W0)
& aElement0(W1) )
| ! [W2: $i] :
( ( ( W2 != sdtlbdtrb0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElementOf0(W3,szDzozmdt0(W0))
& ( sdtlpdtrp0(W0,W3) = W1 ) ) ) ) )
& ( ( W2 = sdtlbdtrb0(W0,W1) )
| ~ aSet0(W2)
| ~ ( aElementOf0(tptp_fun_W3_12(W2,W1,W0),W2)
<=> ( aElementOf0(tptp_fun_W3_12(W2,W1,W0),szDzozmdt0(W0))
& ( sdtlpdtrp0(W0,tptp_fun_W3_12(W2,W1,W0)) = W1 ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[262,255]) ).
tff(264,plain,
! [W0: $i,W1: $i] :
( ~ aElement0(W1)
| ~ aFunction0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtlbdtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = sdtlbdtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElementOf0(tptp_fun_W3_12(W2,W1,W0),szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,tptp_fun_W3_12(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_12(W2,W1,W0),W2) ) ) ) ),
inference(modus_ponens,[status(thm)],[263,253]) ).
tff(265,plain,
! [W0: $i,W1: $i] :
( ~ aElement0(W1)
| ~ aFunction0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtlbdtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = sdtlbdtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElementOf0(tptp_fun_W3_12(W2,W1,W0),szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,tptp_fun_W3_12(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_12(W2,W1,W0),W2) ) ) ) ),
inference(modus_ponens,[status(thm)],[264,251]) ).
tff(266,plain,
! [W0: $i,W1: $i] :
( ~ aElement0(W1)
| ~ aFunction0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtlbdtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElementOf0(tptp_fun_W3_12(W2,W1,W0),szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,tptp_fun_W3_12(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_12(W2,W1,W0),W2) ) )
| ~ ( ( W2 != sdtlbdtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[265,246]) ).
tff(267,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aElement0(W1)
| ~ aFunction0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtlbdtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElementOf0(tptp_fun_W3_12(W2,W1,W0),szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,tptp_fun_W3_12(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_12(W2,W1,W0),W2) ) )
| ~ ( ( W2 != sdtlbdtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) ) ) )
| ~ aElement0(szDzizrdt0(xd))
| ~ aFunction0(xd)
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlbdtrb0(xd,szDzizrdt0(xd)) )
| ( ( ~ aElementOf0(tptp_fun_W3_12(W2,szDzizrdt0(xd),xd),szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,tptp_fun_W3_12(W2,szDzizrdt0(xd),xd)) != szDzizrdt0(xd) ) )
<=> aElementOf0(tptp_fun_W3_12(W2,szDzizrdt0(xd),xd),W2) ) )
| ~ ( ( W2 != sdtlbdtrb0(xd,szDzizrdt0(xd)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,W3) != szDzizrdt0(xd) ) )
<=> aElementOf0(W3,W2) ) ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aElement0(W1)
| ~ aFunction0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtlbdtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElementOf0(tptp_fun_W3_12(W2,W1,W0),szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,tptp_fun_W3_12(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_12(W2,W1,W0),W2) ) )
| ~ ( ( W2 != sdtlbdtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) ) ) )
| ~ aElement0(szDzizrdt0(xd))
| ~ aFunction0(xd)
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlbdtrb0(xd,szDzizrdt0(xd)) )
| ( ( ~ aElementOf0(tptp_fun_W3_12(W2,szDzizrdt0(xd),xd),szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,tptp_fun_W3_12(W2,szDzizrdt0(xd),xd)) != szDzizrdt0(xd) ) )
<=> aElementOf0(tptp_fun_W3_12(W2,szDzizrdt0(xd),xd),W2) ) )
| ~ ( ( W2 != sdtlbdtrb0(xd,szDzizrdt0(xd)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,W3) != szDzizrdt0(xd) ) )
<=> aElementOf0(W3,W2) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(268,plain,
( ( ~ aElement0(szDzizrdt0(xd))
| ~ aFunction0(xd)
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlbdtrb0(xd,szDzizrdt0(xd)) )
| ( ( ~ aElementOf0(tptp_fun_W3_12(W2,szDzizrdt0(xd),xd),szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,tptp_fun_W3_12(W2,szDzizrdt0(xd),xd)) != szDzizrdt0(xd) ) )
<=> aElementOf0(tptp_fun_W3_12(W2,szDzizrdt0(xd),xd),W2) ) )
| ~ ( ( W2 != sdtlbdtrb0(xd,szDzizrdt0(xd)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,W3) != szDzizrdt0(xd) ) )
<=> aElementOf0(W3,W2) ) ) ) ) )
<=> ( ~ aElement0(szDzizrdt0(xd))
| ~ aFunction0(xd)
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlbdtrb0(xd,szDzizrdt0(xd)) )
| ( ( ~ aElementOf0(tptp_fun_W3_12(W2,szDzizrdt0(xd),xd),szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,tptp_fun_W3_12(W2,szDzizrdt0(xd),xd)) != szDzizrdt0(xd) ) )
<=> aElementOf0(tptp_fun_W3_12(W2,szDzizrdt0(xd),xd),W2) ) )
| ~ ( ( W2 != sdtlbdtrb0(xd,szDzizrdt0(xd)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,W3) != szDzizrdt0(xd) ) )
<=> aElementOf0(W3,W2) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(269,plain,
^ [W2: $i] :
rewrite(( ~ ( ~ ( ( W2 = sdtlbdtrb0(xd,szDzizrdt0(xd)) )
| ~ aSet0(W2)
| ( ( ~ aElementOf0(tptp_fun_W3_12(W2,szDzizrdt0(xd),xd),szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,tptp_fun_W3_12(W2,szDzizrdt0(xd),xd)) != szDzizrdt0(xd) ) )
<=> aElementOf0(tptp_fun_W3_12(W2,szDzizrdt0(xd),xd),W2) ) )
| ~ ( ( W2 != sdtlbdtrb0(xd,szDzizrdt0(xd)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,W3) != szDzizrdt0(xd) ) )
<=> aElementOf0(W3,W2) ) ) ) )
<=> ~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlbdtrb0(xd,szDzizrdt0(xd)) )
| ( ( ~ aElementOf0(tptp_fun_W3_12(W2,szDzizrdt0(xd),xd),szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,tptp_fun_W3_12(W2,szDzizrdt0(xd),xd)) != szDzizrdt0(xd) ) )
<=> aElementOf0(tptp_fun_W3_12(W2,szDzizrdt0(xd),xd),W2) ) )
| ~ ( ( W2 != sdtlbdtrb0(xd,szDzizrdt0(xd)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,W3) != szDzizrdt0(xd) ) )
<=> aElementOf0(W3,W2) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(270,plain,
( ! [W2: $i] :
~ ( ~ ( ( W2 = sdtlbdtrb0(xd,szDzizrdt0(xd)) )
| ~ aSet0(W2)
| ( ( ~ aElementOf0(tptp_fun_W3_12(W2,szDzizrdt0(xd),xd),szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,tptp_fun_W3_12(W2,szDzizrdt0(xd),xd)) != szDzizrdt0(xd) ) )
<=> aElementOf0(tptp_fun_W3_12(W2,szDzizrdt0(xd),xd),W2) ) )
| ~ ( ( W2 != sdtlbdtrb0(xd,szDzizrdt0(xd)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,W3) != szDzizrdt0(xd) ) )
<=> aElementOf0(W3,W2) ) ) ) )
<=> ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlbdtrb0(xd,szDzizrdt0(xd)) )
| ( ( ~ aElementOf0(tptp_fun_W3_12(W2,szDzizrdt0(xd),xd),szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,tptp_fun_W3_12(W2,szDzizrdt0(xd),xd)) != szDzizrdt0(xd) ) )
<=> aElementOf0(tptp_fun_W3_12(W2,szDzizrdt0(xd),xd),W2) ) )
| ~ ( ( W2 != sdtlbdtrb0(xd,szDzizrdt0(xd)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,W3) != szDzizrdt0(xd) ) )
<=> aElementOf0(W3,W2) ) ) ) ) ),
inference(quant_intro,[status(thm)],[269]) ).
tff(271,plain,
( ( ~ aElement0(szDzizrdt0(xd))
| ~ aFunction0(xd)
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtlbdtrb0(xd,szDzizrdt0(xd)) )
| ~ aSet0(W2)
| ( ( ~ aElementOf0(tptp_fun_W3_12(W2,szDzizrdt0(xd),xd),szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,tptp_fun_W3_12(W2,szDzizrdt0(xd),xd)) != szDzizrdt0(xd) ) )
<=> aElementOf0(tptp_fun_W3_12(W2,szDzizrdt0(xd),xd),W2) ) )
| ~ ( ( W2 != sdtlbdtrb0(xd,szDzizrdt0(xd)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,W3) != szDzizrdt0(xd) ) )
<=> aElementOf0(W3,W2) ) ) ) ) )
<=> ( ~ aElement0(szDzizrdt0(xd))
| ~ aFunction0(xd)
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlbdtrb0(xd,szDzizrdt0(xd)) )
| ( ( ~ aElementOf0(tptp_fun_W3_12(W2,szDzizrdt0(xd),xd),szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,tptp_fun_W3_12(W2,szDzizrdt0(xd),xd)) != szDzizrdt0(xd) ) )
<=> aElementOf0(tptp_fun_W3_12(W2,szDzizrdt0(xd),xd),W2) ) )
| ~ ( ( W2 != sdtlbdtrb0(xd,szDzizrdt0(xd)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,W3) != szDzizrdt0(xd) ) )
<=> aElementOf0(W3,W2) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[270]) ).
tff(272,plain,
( ( ~ aElement0(szDzizrdt0(xd))
| ~ aFunction0(xd)
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtlbdtrb0(xd,szDzizrdt0(xd)) )
| ~ aSet0(W2)
| ( ( ~ aElementOf0(tptp_fun_W3_12(W2,szDzizrdt0(xd),xd),szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,tptp_fun_W3_12(W2,szDzizrdt0(xd),xd)) != szDzizrdt0(xd) ) )
<=> aElementOf0(tptp_fun_W3_12(W2,szDzizrdt0(xd),xd),W2) ) )
| ~ ( ( W2 != sdtlbdtrb0(xd,szDzizrdt0(xd)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,W3) != szDzizrdt0(xd) ) )
<=> aElementOf0(W3,W2) ) ) ) ) )
<=> ( ~ aElement0(szDzizrdt0(xd))
| ~ aFunction0(xd)
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlbdtrb0(xd,szDzizrdt0(xd)) )
| ( ( ~ aElementOf0(tptp_fun_W3_12(W2,szDzizrdt0(xd),xd),szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,tptp_fun_W3_12(W2,szDzizrdt0(xd),xd)) != szDzizrdt0(xd) ) )
<=> aElementOf0(tptp_fun_W3_12(W2,szDzizrdt0(xd),xd),W2) ) )
| ~ ( ( W2 != sdtlbdtrb0(xd,szDzizrdt0(xd)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,W3) != szDzizrdt0(xd) ) )
<=> aElementOf0(W3,W2) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[271,268]) ).
tff(273,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aElement0(W1)
| ~ aFunction0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtlbdtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElementOf0(tptp_fun_W3_12(W2,W1,W0),szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,tptp_fun_W3_12(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_12(W2,W1,W0),W2) ) )
| ~ ( ( W2 != sdtlbdtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) ) ) )
| ~ aElement0(szDzizrdt0(xd))
| ~ aFunction0(xd)
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtlbdtrb0(xd,szDzizrdt0(xd)) )
| ~ aSet0(W2)
| ( ( ~ aElementOf0(tptp_fun_W3_12(W2,szDzizrdt0(xd),xd),szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,tptp_fun_W3_12(W2,szDzizrdt0(xd),xd)) != szDzizrdt0(xd) ) )
<=> aElementOf0(tptp_fun_W3_12(W2,szDzizrdt0(xd),xd),W2) ) )
| ~ ( ( W2 != sdtlbdtrb0(xd,szDzizrdt0(xd)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,W3) != szDzizrdt0(xd) ) )
<=> aElementOf0(W3,W2) ) ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aElement0(W1)
| ~ aFunction0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtlbdtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElementOf0(tptp_fun_W3_12(W2,W1,W0),szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,tptp_fun_W3_12(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_12(W2,W1,W0),W2) ) )
| ~ ( ( W2 != sdtlbdtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) ) ) )
| ~ aElement0(szDzizrdt0(xd))
| ~ aFunction0(xd)
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlbdtrb0(xd,szDzizrdt0(xd)) )
| ( ( ~ aElementOf0(tptp_fun_W3_12(W2,szDzizrdt0(xd),xd),szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,tptp_fun_W3_12(W2,szDzizrdt0(xd),xd)) != szDzizrdt0(xd) ) )
<=> aElementOf0(tptp_fun_W3_12(W2,szDzizrdt0(xd),xd),W2) ) )
| ~ ( ( W2 != sdtlbdtrb0(xd,szDzizrdt0(xd)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,W3) != szDzizrdt0(xd) ) )
<=> aElementOf0(W3,W2) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[272]) ).
tff(274,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aElement0(W1)
| ~ aFunction0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtlbdtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElementOf0(tptp_fun_W3_12(W2,W1,W0),szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,tptp_fun_W3_12(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_12(W2,W1,W0),W2) ) )
| ~ ( ( W2 != sdtlbdtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) ) ) )
| ~ aElement0(szDzizrdt0(xd))
| ~ aFunction0(xd)
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtlbdtrb0(xd,szDzizrdt0(xd)) )
| ~ aSet0(W2)
| ( ( ~ aElementOf0(tptp_fun_W3_12(W2,szDzizrdt0(xd),xd),szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,tptp_fun_W3_12(W2,szDzizrdt0(xd),xd)) != szDzizrdt0(xd) ) )
<=> aElementOf0(tptp_fun_W3_12(W2,szDzizrdt0(xd),xd),W2) ) )
| ~ ( ( W2 != sdtlbdtrb0(xd,szDzizrdt0(xd)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,W3) != szDzizrdt0(xd) ) )
<=> aElementOf0(W3,W2) ) ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aElement0(W1)
| ~ aFunction0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtlbdtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElementOf0(tptp_fun_W3_12(W2,W1,W0),szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,tptp_fun_W3_12(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_12(W2,W1,W0),W2) ) )
| ~ ( ( W2 != sdtlbdtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) ) ) )
| ~ aElement0(szDzizrdt0(xd))
| ~ aFunction0(xd)
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlbdtrb0(xd,szDzizrdt0(xd)) )
| ( ( ~ aElementOf0(tptp_fun_W3_12(W2,szDzizrdt0(xd),xd),szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,tptp_fun_W3_12(W2,szDzizrdt0(xd),xd)) != szDzizrdt0(xd) ) )
<=> aElementOf0(tptp_fun_W3_12(W2,szDzizrdt0(xd),xd),W2) ) )
| ~ ( ( W2 != sdtlbdtrb0(xd,szDzizrdt0(xd)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,W3) != szDzizrdt0(xd) ) )
<=> aElementOf0(W3,W2) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[273,267]) ).
tff(275,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aElement0(W1)
| ~ aFunction0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtlbdtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElementOf0(tptp_fun_W3_12(W2,W1,W0),szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,tptp_fun_W3_12(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_12(W2,W1,W0),W2) ) )
| ~ ( ( W2 != sdtlbdtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) ) ) )
| ~ aElement0(szDzizrdt0(xd))
| ~ aFunction0(xd)
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtlbdtrb0(xd,szDzizrdt0(xd)) )
| ~ aSet0(W2)
| ( ( ~ aElementOf0(tptp_fun_W3_12(W2,szDzizrdt0(xd),xd),szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,tptp_fun_W3_12(W2,szDzizrdt0(xd),xd)) != szDzizrdt0(xd) ) )
<=> aElementOf0(tptp_fun_W3_12(W2,szDzizrdt0(xd),xd),W2) ) )
| ~ ( ( W2 != sdtlbdtrb0(xd,szDzizrdt0(xd)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,W3) != szDzizrdt0(xd) ) )
<=> aElementOf0(W3,W2) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(276,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aElement0(W1)
| ~ aFunction0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtlbdtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElementOf0(tptp_fun_W3_12(W2,W1,W0),szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,tptp_fun_W3_12(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_12(W2,W1,W0),W2) ) )
| ~ ( ( W2 != sdtlbdtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(W0))
| ( sdtlpdtrp0(W0,W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) ) ) )
| ~ aElement0(szDzizrdt0(xd))
| ~ aFunction0(xd)
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlbdtrb0(xd,szDzizrdt0(xd)) )
| ( ( ~ aElementOf0(tptp_fun_W3_12(W2,szDzizrdt0(xd),xd),szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,tptp_fun_W3_12(W2,szDzizrdt0(xd),xd)) != szDzizrdt0(xd) ) )
<=> aElementOf0(tptp_fun_W3_12(W2,szDzizrdt0(xd),xd),W2) ) )
| ~ ( ( W2 != sdtlbdtrb0(xd,szDzizrdt0(xd)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,W3) != szDzizrdt0(xd) ) )
<=> aElementOf0(W3,W2) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[275,274]) ).
tff(277,plain,
! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlbdtrb0(xd,szDzizrdt0(xd)) )
| ( ( ~ aElementOf0(tptp_fun_W3_12(W2,szDzizrdt0(xd),xd),szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,tptp_fun_W3_12(W2,szDzizrdt0(xd),xd)) != szDzizrdt0(xd) ) )
<=> aElementOf0(tptp_fun_W3_12(W2,szDzizrdt0(xd),xd),W2) ) )
| ~ ( ( W2 != sdtlbdtrb0(xd,szDzizrdt0(xd)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,W3) != szDzizrdt0(xd) ) )
<=> aElementOf0(W3,W2) ) ) ) ),
inference(unit_resolution,[status(thm)],[276,266,160,180]) ).
tff(278,plain,
( ( ~ ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlbdtrb0(xd,szDzizrdt0(xd)) )
| ( ( ~ aElementOf0(tptp_fun_W3_12(W2,szDzizrdt0(xd),xd),szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,tptp_fun_W3_12(W2,szDzizrdt0(xd),xd)) != szDzizrdt0(xd) ) )
<=> aElementOf0(tptp_fun_W3_12(W2,szDzizrdt0(xd),xd),W2) ) )
| ~ ( ( W2 != sdtlbdtrb0(xd,szDzizrdt0(xd)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,W3) != szDzizrdt0(xd) ) )
<=> aElementOf0(W3,W2) ) ) ) )
| ~ ( ~ aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,W3) != szDzizrdt0(xd) ) )
<=> aElementOf0(W3,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) ) )
<=> ( ~ ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlbdtrb0(xd,szDzizrdt0(xd)) )
| ( ( ~ aElementOf0(tptp_fun_W3_12(W2,szDzizrdt0(xd),xd),szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,tptp_fun_W3_12(W2,szDzizrdt0(xd),xd)) != szDzizrdt0(xd) ) )
<=> aElementOf0(tptp_fun_W3_12(W2,szDzizrdt0(xd),xd),W2) ) )
| ~ ( ( W2 != sdtlbdtrb0(xd,szDzizrdt0(xd)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,W3) != szDzizrdt0(xd) ) )
<=> aElementOf0(W3,W2) ) ) ) )
| ~ ( ~ aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,W3) != szDzizrdt0(xd) ) )
<=> aElementOf0(W3,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(279,plain,
( ~ ( ~ ( ~ aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlbdtrb0(xd,szDzizrdt0(xd)) = sdtlbdtrb0(xd,szDzizrdt0(xd)) )
| ( ( ~ aElementOf0(tptp_fun_W3_12(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzizrdt0(xd),xd),szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,tptp_fun_W3_12(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzizrdt0(xd),xd)) != szDzizrdt0(xd) ) )
<=> aElementOf0(tptp_fun_W3_12(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzizrdt0(xd),xd),sdtlbdtrb0(xd,szDzizrdt0(xd))) ) )
| ~ ( ( sdtlbdtrb0(xd,szDzizrdt0(xd)) != sdtlbdtrb0(xd,szDzizrdt0(xd)) )
| ~ ( ~ aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,W3) != szDzizrdt0(xd) ) )
<=> aElementOf0(W3,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) ) ) )
<=> ~ ( ~ aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,W3) != szDzizrdt0(xd) ) )
<=> aElementOf0(W3,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(280,plain,
( ( ~ ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlbdtrb0(xd,szDzizrdt0(xd)) )
| ( ( ~ aElementOf0(tptp_fun_W3_12(W2,szDzizrdt0(xd),xd),szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,tptp_fun_W3_12(W2,szDzizrdt0(xd),xd)) != szDzizrdt0(xd) ) )
<=> aElementOf0(tptp_fun_W3_12(W2,szDzizrdt0(xd),xd),W2) ) )
| ~ ( ( W2 != sdtlbdtrb0(xd,szDzizrdt0(xd)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,W3) != szDzizrdt0(xd) ) )
<=> aElementOf0(W3,W2) ) ) ) )
| ~ ( ~ ( ~ aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlbdtrb0(xd,szDzizrdt0(xd)) = sdtlbdtrb0(xd,szDzizrdt0(xd)) )
| ( ( ~ aElementOf0(tptp_fun_W3_12(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzizrdt0(xd),xd),szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,tptp_fun_W3_12(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzizrdt0(xd),xd)) != szDzizrdt0(xd) ) )
<=> aElementOf0(tptp_fun_W3_12(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzizrdt0(xd),xd),sdtlbdtrb0(xd,szDzizrdt0(xd))) ) )
| ~ ( ( sdtlbdtrb0(xd,szDzizrdt0(xd)) != sdtlbdtrb0(xd,szDzizrdt0(xd)) )
| ~ ( ~ aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,W3) != szDzizrdt0(xd) ) )
<=> aElementOf0(W3,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) ) ) ) )
<=> ( ~ ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlbdtrb0(xd,szDzizrdt0(xd)) )
| ( ( ~ aElementOf0(tptp_fun_W3_12(W2,szDzizrdt0(xd),xd),szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,tptp_fun_W3_12(W2,szDzizrdt0(xd),xd)) != szDzizrdt0(xd) ) )
<=> aElementOf0(tptp_fun_W3_12(W2,szDzizrdt0(xd),xd),W2) ) )
| ~ ( ( W2 != sdtlbdtrb0(xd,szDzizrdt0(xd)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,W3) != szDzizrdt0(xd) ) )
<=> aElementOf0(W3,W2) ) ) ) )
| ~ ( ~ aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,W3) != szDzizrdt0(xd) ) )
<=> aElementOf0(W3,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) ) ) ),
inference(monotonicity,[status(thm)],[279]) ).
tff(281,plain,
( ( ~ ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlbdtrb0(xd,szDzizrdt0(xd)) )
| ( ( ~ aElementOf0(tptp_fun_W3_12(W2,szDzizrdt0(xd),xd),szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,tptp_fun_W3_12(W2,szDzizrdt0(xd),xd)) != szDzizrdt0(xd) ) )
<=> aElementOf0(tptp_fun_W3_12(W2,szDzizrdt0(xd),xd),W2) ) )
| ~ ( ( W2 != sdtlbdtrb0(xd,szDzizrdt0(xd)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,W3) != szDzizrdt0(xd) ) )
<=> aElementOf0(W3,W2) ) ) ) )
| ~ ( ~ ( ~ aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlbdtrb0(xd,szDzizrdt0(xd)) = sdtlbdtrb0(xd,szDzizrdt0(xd)) )
| ( ( ~ aElementOf0(tptp_fun_W3_12(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzizrdt0(xd),xd),szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,tptp_fun_W3_12(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzizrdt0(xd),xd)) != szDzizrdt0(xd) ) )
<=> aElementOf0(tptp_fun_W3_12(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzizrdt0(xd),xd),sdtlbdtrb0(xd,szDzizrdt0(xd))) ) )
| ~ ( ( sdtlbdtrb0(xd,szDzizrdt0(xd)) != sdtlbdtrb0(xd,szDzizrdt0(xd)) )
| ~ ( ~ aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,W3) != szDzizrdt0(xd) ) )
<=> aElementOf0(W3,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) ) ) ) )
<=> ( ~ ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlbdtrb0(xd,szDzizrdt0(xd)) )
| ( ( ~ aElementOf0(tptp_fun_W3_12(W2,szDzizrdt0(xd),xd),szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,tptp_fun_W3_12(W2,szDzizrdt0(xd),xd)) != szDzizrdt0(xd) ) )
<=> aElementOf0(tptp_fun_W3_12(W2,szDzizrdt0(xd),xd),W2) ) )
| ~ ( ( W2 != sdtlbdtrb0(xd,szDzizrdt0(xd)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,W3) != szDzizrdt0(xd) ) )
<=> aElementOf0(W3,W2) ) ) ) )
| ~ ( ~ aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,W3) != szDzizrdt0(xd) ) )
<=> aElementOf0(W3,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) ) ) ),
inference(transitivity,[status(thm)],[280,278]) ).
tff(282,plain,
( ~ ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlbdtrb0(xd,szDzizrdt0(xd)) )
| ( ( ~ aElementOf0(tptp_fun_W3_12(W2,szDzizrdt0(xd),xd),szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,tptp_fun_W3_12(W2,szDzizrdt0(xd),xd)) != szDzizrdt0(xd) ) )
<=> aElementOf0(tptp_fun_W3_12(W2,szDzizrdt0(xd),xd),W2) ) )
| ~ ( ( W2 != sdtlbdtrb0(xd,szDzizrdt0(xd)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,W3) != szDzizrdt0(xd) ) )
<=> aElementOf0(W3,W2) ) ) ) )
| ~ ( ~ ( ~ aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlbdtrb0(xd,szDzizrdt0(xd)) = sdtlbdtrb0(xd,szDzizrdt0(xd)) )
| ( ( ~ aElementOf0(tptp_fun_W3_12(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzizrdt0(xd),xd),szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,tptp_fun_W3_12(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzizrdt0(xd),xd)) != szDzizrdt0(xd) ) )
<=> aElementOf0(tptp_fun_W3_12(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzizrdt0(xd),xd),sdtlbdtrb0(xd,szDzizrdt0(xd))) ) )
| ~ ( ( sdtlbdtrb0(xd,szDzizrdt0(xd)) != sdtlbdtrb0(xd,szDzizrdt0(xd)) )
| ~ ( ~ aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,W3) != szDzizrdt0(xd) ) )
<=> aElementOf0(W3,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(283,plain,
( ~ ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlbdtrb0(xd,szDzizrdt0(xd)) )
| ( ( ~ aElementOf0(tptp_fun_W3_12(W2,szDzizrdt0(xd),xd),szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,tptp_fun_W3_12(W2,szDzizrdt0(xd),xd)) != szDzizrdt0(xd) ) )
<=> aElementOf0(tptp_fun_W3_12(W2,szDzizrdt0(xd),xd),W2) ) )
| ~ ( ( W2 != sdtlbdtrb0(xd,szDzizrdt0(xd)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,W3) != szDzizrdt0(xd) ) )
<=> aElementOf0(W3,W2) ) ) ) )
| ~ ( ~ aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,W3) != szDzizrdt0(xd) ) )
<=> aElementOf0(W3,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) ) ),
inference(modus_ponens,[status(thm)],[282,281]) ).
tff(284,plain,
~ ( ~ aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,W3) != szDzizrdt0(xd) ) )
<=> aElementOf0(W3,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) ),
inference(unit_resolution,[status(thm)],[283,277]) ).
tff(285,plain,
( ~ aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,W3) != szDzizrdt0(xd) ) )
<=> aElementOf0(W3,sdtlbdtrb0(xd,szDzizrdt0(xd))) )
| ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,W3) != szDzizrdt0(xd) ) )
<=> aElementOf0(W3,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) ),
inference(tautology,[status(thm)],[]) ).
tff(286,plain,
! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,W3) != szDzizrdt0(xd) ) )
<=> aElementOf0(W3,sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
inference(unit_resolution,[status(thm)],[285,284]) ).
tff(287,plain,
( ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,W3) != szDzizrdt0(xd) ) )
<=> aElementOf0(W3,sdtlbdtrb0(xd,szDzizrdt0(xd))) )
| ~ ( ( ~ aElementOf0(tptp_fun_W2_1(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,tptp_fun_W2_1(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))) != szDzizrdt0(xd) ) )
<=> aElementOf0(tptp_fun_W2_1(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),sdtlbdtrb0(xd,szDzizrdt0(xd))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(288,plain,
~ ( ( ~ aElementOf0(tptp_fun_W2_1(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,tptp_fun_W2_1(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))) != szDzizrdt0(xd) ) )
<=> aElementOf0(tptp_fun_W2_1(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
inference(unit_resolution,[status(thm)],[287,286]) ).
tff(289,plain,
( ( ( ~ aElementOf0(tptp_fun_W2_1(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,tptp_fun_W2_1(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))) != szDzizrdt0(xd) ) )
<=> aElementOf0(tptp_fun_W2_1(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),sdtlbdtrb0(xd,szDzizrdt0(xd))) )
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,tptp_fun_W2_1(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))) != szDzizrdt0(xd) ) )
| ~ aElementOf0(tptp_fun_W2_1(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
inference(tautology,[status(thm)],[]) ).
tff(290,plain,
( ( ( ~ aElementOf0(tptp_fun_W2_1(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,tptp_fun_W2_1(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))) != szDzizrdt0(xd) ) )
<=> aElementOf0(tptp_fun_W2_1(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),sdtlbdtrb0(xd,szDzizrdt0(xd))) )
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,tptp_fun_W2_1(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))) != szDzizrdt0(xd) ) ) ),
inference(unit_resolution,[status(thm)],[289,238]) ).
tff(291,plain,
~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,tptp_fun_W2_1(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))) != szDzizrdt0(xd) ) ),
inference(unit_resolution,[status(thm)],[290,288]) ).
tff(292,plain,
( ~ aElementOf0(tptp_fun_W2_1(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,tptp_fun_W2_1(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))) != szDzizrdt0(xd) )
| ( sdtlpdtrp0(xd,tptp_fun_W2_1(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))) = szDzizrdt0(xd) ) ),
inference(tautology,[status(thm)],[]) ).
tff(293,plain,
sdtlpdtrp0(xd,tptp_fun_W2_1(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))) = szDzizrdt0(xd),
inference(unit_resolution,[status(thm)],[292,291]) ).
tff(294,plain,
( aSubsetOf0(szNzAzT0,szDzozmdt0(xd))
<=> aSubsetOf0(szNzAzT0,szNzAzT0) ),
inference(monotonicity,[status(thm)],[143]) ).
tff(295,plain,
( aSubsetOf0(szNzAzT0,szNzAzT0)
<=> aSubsetOf0(szNzAzT0,szDzozmdt0(xd)) ),
inference(symmetry,[status(thm)],[294]) ).
tff(296,plain,
^ [W0: $i] :
refl(( ( ~ aSet0(W0)
| aSubsetOf0(W0,W0) )
<=> ( ~ aSet0(W0)
| aSubsetOf0(W0,W0) ) )),
inference(bind,[status(th)],[]) ).
tff(297,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) ) ),
inference(quant_intro,[status(thm)],[296]) ).
tff(298,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(299,plain,
^ [W0: $i] :
rewrite(( ( aSet0(W0)
=> aSubsetOf0(W0,W0) )
<=> ( ~ aSet0(W0)
| aSubsetOf0(W0,W0) ) )),
inference(bind,[status(th)],[]) ).
tff(300,plain,
( ! [W0: $i] :
( aSet0(W0)
=> aSubsetOf0(W0,W0) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) ) ),
inference(quant_intro,[status(thm)],[299]) ).
tff(301,axiom,
! [W0: $i] :
( aSet0(W0)
=> aSubsetOf0(W0,W0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubRefl) ).
tff(302,plain,
! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) ),
inference(modus_ponens,[status(thm)],[301,300]) ).
tff(303,plain,
! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) ),
inference(modus_ponens,[status(thm)],[302,298]) ).
tff(304,plain,
! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) ),
inference(skolemize,[status(sab)],[303]) ).
tff(305,plain,
! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) ),
inference(modus_ponens,[status(thm)],[304,297]) ).
tff(306,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) )
| ~ aSet0(szNzAzT0)
| aSubsetOf0(szNzAzT0,szNzAzT0) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) )
| ~ aSet0(szNzAzT0)
| aSubsetOf0(szNzAzT0,szNzAzT0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(307,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) )
| ~ aSet0(szNzAzT0)
| aSubsetOf0(szNzAzT0,szNzAzT0) ),
inference(quant_inst,[status(thm)],[]) ).
tff(308,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) )
| ~ aSet0(szNzAzT0)
| aSubsetOf0(szNzAzT0,szNzAzT0) ),
inference(modus_ponens,[status(thm)],[307,306]) ).
tff(309,plain,
aSubsetOf0(szNzAzT0,szNzAzT0),
inference(unit_resolution,[status(thm)],[308,305,130]) ).
tff(310,plain,
aSubsetOf0(szNzAzT0,szDzozmdt0(xd)),
inference(modus_ponens,[status(thm)],[309,295]) ).
tff(311,plain,
^ [W0: $i] :
rewrite(( ( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtlcdtrc0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_13(W3,W1,W0)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != W3 ) ) ) ) ) )
| ~ ( ( W2 = sdtlcdtrc0(W0,W1) )
| ~ aSet0(W2)
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_15(W2,W1,W0)) != tptp_fun_W3_14(W2,W1,W0) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != tptp_fun_W3_14(W2,W1,W0) ) ) ) ) ) ) ) )
<=> ( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtlcdtrc0(W0,W1) )
| ~ aSet0(W2)
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_15(W2,W1,W0)) != tptp_fun_W3_14(W2,W1,W0) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != tptp_fun_W3_14(W2,W1,W0) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_13(W3,W1,W0)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != W3 ) ) ) ) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(312,plain,
( ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtlcdtrc0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_13(W3,W1,W0)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != W3 ) ) ) ) ) )
| ~ ( ( W2 = sdtlcdtrc0(W0,W1) )
| ~ aSet0(W2)
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_15(W2,W1,W0)) != tptp_fun_W3_14(W2,W1,W0) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != tptp_fun_W3_14(W2,W1,W0) ) ) ) ) ) ) ) )
<=> ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtlcdtrc0(W0,W1) )
| ~ aSet0(W2)
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_15(W2,W1,W0)) != tptp_fun_W3_14(W2,W1,W0) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != tptp_fun_W3_14(W2,W1,W0) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_13(W3,W1,W0)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != W3 ) ) ) ) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[311]) ).
tff(313,plain,
^ [W0: $i] :
refl(( ( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtlcdtrc0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_13(W3,W1,W0)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != W3 ) ) ) ) ) )
| ~ ( ( W2 = sdtlcdtrc0(W0,W1) )
| ~ aSet0(W2)
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_15(W2,W1,W0)) != tptp_fun_W3_14(W2,W1,W0) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != tptp_fun_W3_14(W2,W1,W0) ) ) ) ) ) ) ) )
<=> ( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtlcdtrc0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_13(W3,W1,W0)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != W3 ) ) ) ) ) )
| ~ ( ( W2 = sdtlcdtrc0(W0,W1) )
| ~ aSet0(W2)
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_15(W2,W1,W0)) != tptp_fun_W3_14(W2,W1,W0) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != tptp_fun_W3_14(W2,W1,W0) ) ) ) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(314,plain,
( ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtlcdtrc0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_13(W3,W1,W0)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != W3 ) ) ) ) ) )
| ~ ( ( W2 = sdtlcdtrc0(W0,W1) )
| ~ aSet0(W2)
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_15(W2,W1,W0)) != tptp_fun_W3_14(W2,W1,W0) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != tptp_fun_W3_14(W2,W1,W0) ) ) ) ) ) ) ) )
<=> ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtlcdtrc0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_13(W3,W1,W0)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != W3 ) ) ) ) ) )
| ~ ( ( W2 = sdtlcdtrc0(W0,W1) )
| ~ aSet0(W2)
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_15(W2,W1,W0)) != tptp_fun_W3_14(W2,W1,W0) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != tptp_fun_W3_14(W2,W1,W0) ) ) ) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[313]) ).
tff(315,plain,
^ [W0: $i] :
rewrite(( ( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtlcdtrc0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_13(W3,W1,W0)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != W3 ) ) ) ) ) )
| ~ ( ( W2 = sdtlcdtrc0(W0,W1) )
| ~ aSet0(W2)
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_15(W2,W1,W0)) != tptp_fun_W3_14(W2,W1,W0) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != tptp_fun_W3_14(W2,W1,W0) ) ) ) ) ) ) ) )
<=> ( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtlcdtrc0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_13(W3,W1,W0)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != W3 ) ) ) ) ) )
| ~ ( ( W2 = sdtlcdtrc0(W0,W1) )
| ~ aSet0(W2)
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_15(W2,W1,W0)) != tptp_fun_W3_14(W2,W1,W0) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != tptp_fun_W3_14(W2,W1,W0) ) ) ) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(316,plain,
( ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtlcdtrc0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_13(W3,W1,W0)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != W3 ) ) ) ) ) )
| ~ ( ( W2 = sdtlcdtrc0(W0,W1) )
| ~ aSet0(W2)
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_15(W2,W1,W0)) != tptp_fun_W3_14(W2,W1,W0) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != tptp_fun_W3_14(W2,W1,W0) ) ) ) ) ) ) ) )
<=> ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtlcdtrc0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_13(W3,W1,W0)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != W3 ) ) ) ) ) )
| ~ ( ( W2 = sdtlcdtrc0(W0,W1) )
| ~ aSet0(W2)
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_15(W2,W1,W0)) != tptp_fun_W3_14(W2,W1,W0) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != tptp_fun_W3_14(W2,W1,W0) ) ) ) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[315]) ).
tff(317,plain,
( ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtlcdtrc0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_13(W3,W1,W0)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != W3 ) ) ) ) ) )
| ~ ( ( W2 = sdtlcdtrc0(W0,W1) )
| ~ aSet0(W2)
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_15(W2,W1,W0)) != tptp_fun_W3_14(W2,W1,W0) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != tptp_fun_W3_14(W2,W1,W0) ) ) ) ) ) ) ) )
<=> ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtlcdtrc0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_13(W3,W1,W0)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != W3 ) ) ) ) ) )
| ~ ( ( W2 = sdtlcdtrc0(W0,W1) )
| ~ aSet0(W2)
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_15(W2,W1,W0)) != tptp_fun_W3_14(W2,W1,W0) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != tptp_fun_W3_14(W2,W1,W0) ) ) ) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[316,314]) ).
tff(318,plain,
^ [W0: $i] :
rewrite(( ( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
( ( ( W2 != sdtlcdtrc0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( ( ~ aElementOf0(W3,W2)
| ( aElementOf0(tptp_fun_W4_13(W3,W1,W0),W1)
& ( sdtlpdtrp0(W0,tptp_fun_W4_13(W3,W1,W0)) = W3 ) ) )
& ( aElementOf0(W3,W2)
| ! [W4: $i] :
~ ( aElementOf0(W4,W1)
& ( sdtlpdtrp0(W0,W4) = W3 ) ) ) ) ) )
& ( ( W2 = sdtlcdtrc0(W0,W1) )
| ~ aSet0(W2)
| ( ( aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ( aElementOf0(tptp_fun_W4_15(W2,W1,W0),W1)
& ( sdtlpdtrp0(W0,tptp_fun_W4_15(W2,W1,W0)) = tptp_fun_W3_14(W2,W1,W0) ) ) )
& ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ! [W4: $i] :
~ ( aElementOf0(W4,W1)
& ( sdtlpdtrp0(W0,W4) = tptp_fun_W3_14(W2,W1,W0) ) ) ) ) ) ) ) )
<=> ( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtlcdtrc0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_13(W3,W1,W0)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != W3 ) ) ) ) ) )
| ~ ( ( W2 = sdtlcdtrc0(W0,W1) )
| ~ aSet0(W2)
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_15(W2,W1,W0)) != tptp_fun_W3_14(W2,W1,W0) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != tptp_fun_W3_14(W2,W1,W0) ) ) ) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(319,plain,
( ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
( ( ( W2 != sdtlcdtrc0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( ( ~ aElementOf0(W3,W2)
| ( aElementOf0(tptp_fun_W4_13(W3,W1,W0),W1)
& ( sdtlpdtrp0(W0,tptp_fun_W4_13(W3,W1,W0)) = W3 ) ) )
& ( aElementOf0(W3,W2)
| ! [W4: $i] :
~ ( aElementOf0(W4,W1)
& ( sdtlpdtrp0(W0,W4) = W3 ) ) ) ) ) )
& ( ( W2 = sdtlcdtrc0(W0,W1) )
| ~ aSet0(W2)
| ( ( aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ( aElementOf0(tptp_fun_W4_15(W2,W1,W0),W1)
& ( sdtlpdtrp0(W0,tptp_fun_W4_15(W2,W1,W0)) = tptp_fun_W3_14(W2,W1,W0) ) ) )
& ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ! [W4: $i] :
~ ( aElementOf0(W4,W1)
& ( sdtlpdtrp0(W0,W4) = tptp_fun_W3_14(W2,W1,W0) ) ) ) ) ) ) ) )
<=> ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtlcdtrc0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_13(W3,W1,W0)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != W3 ) ) ) ) ) )
| ~ ( ( W2 = sdtlcdtrc0(W0,W1) )
| ~ aSet0(W2)
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_15(W2,W1,W0)) != tptp_fun_W3_14(W2,W1,W0) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != tptp_fun_W3_14(W2,W1,W0) ) ) ) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[318]) ).
tff(320,plain,
^ [W0: $i] :
rewrite(( ( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
( ( ( W2 != sdtlcdtrc0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( ( ~ aElementOf0(W3,W2)
| ( aElementOf0(tptp_fun_W4_13(W3,W1,W0),W1)
& ( sdtlpdtrp0(W0,tptp_fun_W4_13(W3,W1,W0)) = W3 ) ) )
& ( aElementOf0(W3,W2)
| ! [W4: $i] :
~ ( aElementOf0(W4,W1)
& ( sdtlpdtrp0(W0,W4) = W3 ) ) ) ) ) )
& ( ( W2 = sdtlcdtrc0(W0,W1) )
| ~ aSet0(W2)
| ( ( aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ( aElementOf0(tptp_fun_W4_15(W2,W1,W0),W1)
& ( sdtlpdtrp0(W0,tptp_fun_W4_15(W2,W1,W0)) = tptp_fun_W3_14(W2,W1,W0) ) ) )
& ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ! [W4: $i] :
~ ( aElementOf0(W4,W1)
& ( sdtlpdtrp0(W0,W4) = tptp_fun_W3_14(W2,W1,W0) ) ) ) ) ) ) ) )
<=> ( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
( ( ( W2 != sdtlcdtrc0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( ( ~ aElementOf0(W3,W2)
| ( aElementOf0(tptp_fun_W4_13(W3,W1,W0),W1)
& ( sdtlpdtrp0(W0,tptp_fun_W4_13(W3,W1,W0)) = W3 ) ) )
& ( aElementOf0(W3,W2)
| ! [W4: $i] :
~ ( aElementOf0(W4,W1)
& ( sdtlpdtrp0(W0,W4) = W3 ) ) ) ) ) )
& ( ( W2 = sdtlcdtrc0(W0,W1) )
| ~ aSet0(W2)
| ( ( aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ( aElementOf0(tptp_fun_W4_15(W2,W1,W0),W1)
& ( sdtlpdtrp0(W0,tptp_fun_W4_15(W2,W1,W0)) = tptp_fun_W3_14(W2,W1,W0) ) ) )
& ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ! [W4: $i] :
~ ( aElementOf0(W4,W1)
& ( sdtlpdtrp0(W0,W4) = tptp_fun_W3_14(W2,W1,W0) ) ) ) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(321,plain,
( ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
( ( ( W2 != sdtlcdtrc0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( ( ~ aElementOf0(W3,W2)
| ( aElementOf0(tptp_fun_W4_13(W3,W1,W0),W1)
& ( sdtlpdtrp0(W0,tptp_fun_W4_13(W3,W1,W0)) = W3 ) ) )
& ( aElementOf0(W3,W2)
| ! [W4: $i] :
~ ( aElementOf0(W4,W1)
& ( sdtlpdtrp0(W0,W4) = W3 ) ) ) ) ) )
& ( ( W2 = sdtlcdtrc0(W0,W1) )
| ~ aSet0(W2)
| ( ( aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ( aElementOf0(tptp_fun_W4_15(W2,W1,W0),W1)
& ( sdtlpdtrp0(W0,tptp_fun_W4_15(W2,W1,W0)) = tptp_fun_W3_14(W2,W1,W0) ) ) )
& ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ! [W4: $i] :
~ ( aElementOf0(W4,W1)
& ( sdtlpdtrp0(W0,W4) = tptp_fun_W3_14(W2,W1,W0) ) ) ) ) ) ) ) )
<=> ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
( ( ( W2 != sdtlcdtrc0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( ( ~ aElementOf0(W3,W2)
| ( aElementOf0(tptp_fun_W4_13(W3,W1,W0),W1)
& ( sdtlpdtrp0(W0,tptp_fun_W4_13(W3,W1,W0)) = W3 ) ) )
& ( aElementOf0(W3,W2)
| ! [W4: $i] :
~ ( aElementOf0(W4,W1)
& ( sdtlpdtrp0(W0,W4) = W3 ) ) ) ) ) )
& ( ( W2 = sdtlcdtrc0(W0,W1) )
| ~ aSet0(W2)
| ( ( aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ( aElementOf0(tptp_fun_W4_15(W2,W1,W0),W1)
& ( sdtlpdtrp0(W0,tptp_fun_W4_15(W2,W1,W0)) = tptp_fun_W3_14(W2,W1,W0) ) ) )
& ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ! [W4: $i] :
~ ( aElementOf0(W4,W1)
& ( sdtlpdtrp0(W0,W4) = tptp_fun_W3_14(W2,W1,W0) ) ) ) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[320]) ).
tff(322,plain,
( ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
( ( W2 = sdtlcdtrc0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ? [W4: $i] :
( aElementOf0(W4,W1)
& ( sdtlpdtrp0(W0,W4) = W3 ) ) ) ) ) ) )
<=> ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
( ( W2 = sdtlcdtrc0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ? [W4: $i] :
( aElementOf0(W4,W1)
& ( sdtlpdtrp0(W0,W4) = W3 ) ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(323,plain,
^ [W0: $i] :
trans(monotonicity(quant_intro(proof_bind(^ [W1: $i] :
rewrite(( ( aSubsetOf0(W1,szDzozmdt0(W0))
=> ! [W2: $i] :
( ( W2 = sdtlcdtrc0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ? [W4: $i] :
( aElementOf0(W4,W1)
& ( sdtlpdtrp0(W0,W4) = W3 ) ) ) ) ) )
<=> ( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
( ( W2 = sdtlcdtrc0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ? [W4: $i] :
( aElementOf0(W4,W1)
& ( sdtlpdtrp0(W0,W4) = W3 ) ) ) ) ) ) ))),
( ! [W1: $i] :
( aSubsetOf0(W1,szDzozmdt0(W0))
=> ! [W2: $i] :
( ( W2 = sdtlcdtrc0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ? [W4: $i] :
( aElementOf0(W4,W1)
& ( sdtlpdtrp0(W0,W4) = W3 ) ) ) ) ) )
<=> ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
( ( W2 = sdtlcdtrc0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ? [W4: $i] :
( aElementOf0(W4,W1)
& ( sdtlpdtrp0(W0,W4) = W3 ) ) ) ) ) ) )),
( ( aFunction0(W0)
=> ! [W1: $i] :
( aSubsetOf0(W1,szDzozmdt0(W0))
=> ! [W2: $i] :
( ( W2 = sdtlcdtrc0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ? [W4: $i] :
( aElementOf0(W4,W1)
& ( sdtlpdtrp0(W0,W4) = W3 ) ) ) ) ) ) )
<=> ( aFunction0(W0)
=> ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
( ( W2 = sdtlcdtrc0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ? [W4: $i] :
( aElementOf0(W4,W1)
& ( sdtlpdtrp0(W0,W4) = W3 ) ) ) ) ) ) ) )),
rewrite(( ( aFunction0(W0)
=> ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
( ( W2 = sdtlcdtrc0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ? [W4: $i] :
( aElementOf0(W4,W1)
& ( sdtlpdtrp0(W0,W4) = W3 ) ) ) ) ) ) )
<=> ( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
( ( W2 = sdtlcdtrc0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ? [W4: $i] :
( aElementOf0(W4,W1)
& ( sdtlpdtrp0(W0,W4) = W3 ) ) ) ) ) ) ) )),
( ( aFunction0(W0)
=> ! [W1: $i] :
( aSubsetOf0(W1,szDzozmdt0(W0))
=> ! [W2: $i] :
( ( W2 = sdtlcdtrc0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ? [W4: $i] :
( aElementOf0(W4,W1)
& ( sdtlpdtrp0(W0,W4) = W3 ) ) ) ) ) ) )
<=> ( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
( ( W2 = sdtlcdtrc0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ? [W4: $i] :
( aElementOf0(W4,W1)
& ( sdtlpdtrp0(W0,W4) = W3 ) ) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(324,plain,
( ! [W0: $i] :
( aFunction0(W0)
=> ! [W1: $i] :
( aSubsetOf0(W1,szDzozmdt0(W0))
=> ! [W2: $i] :
( ( W2 = sdtlcdtrc0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ? [W4: $i] :
( aElementOf0(W4,W1)
& ( sdtlpdtrp0(W0,W4) = W3 ) ) ) ) ) ) )
<=> ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
( ( W2 = sdtlcdtrc0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ? [W4: $i] :
( aElementOf0(W4,W1)
& ( sdtlpdtrp0(W0,W4) = W3 ) ) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[323]) ).
tff(325,axiom,
! [W0: $i] :
( aFunction0(W0)
=> ! [W1: $i] :
( aSubsetOf0(W1,szDzozmdt0(W0))
=> ! [W2: $i] :
( ( W2 = sdtlcdtrc0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ? [W4: $i] :
( aElementOf0(W4,W1)
& ( sdtlpdtrp0(W0,W4) = W3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSImg) ).
tff(326,plain,
! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
( ( W2 = sdtlcdtrc0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ? [W4: $i] :
( aElementOf0(W4,W1)
& ( sdtlpdtrp0(W0,W4) = W3 ) ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[325,324]) ).
tff(327,plain,
! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
( ( W2 = sdtlcdtrc0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ? [W4: $i] :
( aElementOf0(W4,W1)
& ( sdtlpdtrp0(W0,W4) = W3 ) ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[326,322]) ).
tff(328,plain,
! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
( ( ( W2 != sdtlcdtrc0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( ( ~ aElementOf0(W3,W2)
| ( aElementOf0(tptp_fun_W4_13(W3,W1,W0),W1)
& ( sdtlpdtrp0(W0,tptp_fun_W4_13(W3,W1,W0)) = W3 ) ) )
& ( aElementOf0(W3,W2)
| ! [W4: $i] :
~ ( aElementOf0(W4,W1)
& ( sdtlpdtrp0(W0,W4) = W3 ) ) ) ) ) )
& ( ( W2 = sdtlcdtrc0(W0,W1) )
| ~ aSet0(W2)
| ( ( aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ( aElementOf0(tptp_fun_W4_15(W2,W1,W0),W1)
& ( sdtlpdtrp0(W0,tptp_fun_W4_15(W2,W1,W0)) = tptp_fun_W3_14(W2,W1,W0) ) ) )
& ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ! [W4: $i] :
~ ( aElementOf0(W4,W1)
& ( sdtlpdtrp0(W0,W4) = tptp_fun_W3_14(W2,W1,W0) ) ) ) ) ) ) ) ),
inference(skolemize,[status(sab)],[327]) ).
tff(329,plain,
! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
( ( ( W2 != sdtlcdtrc0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( ( ~ aElementOf0(W3,W2)
| ( aElementOf0(tptp_fun_W4_13(W3,W1,W0),W1)
& ( sdtlpdtrp0(W0,tptp_fun_W4_13(W3,W1,W0)) = W3 ) ) )
& ( aElementOf0(W3,W2)
| ! [W4: $i] :
~ ( aElementOf0(W4,W1)
& ( sdtlpdtrp0(W0,W4) = W3 ) ) ) ) ) )
& ( ( W2 = sdtlcdtrc0(W0,W1) )
| ~ aSet0(W2)
| ( ( aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ( aElementOf0(tptp_fun_W4_15(W2,W1,W0),W1)
& ( sdtlpdtrp0(W0,tptp_fun_W4_15(W2,W1,W0)) = tptp_fun_W3_14(W2,W1,W0) ) ) )
& ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ! [W4: $i] :
~ ( aElementOf0(W4,W1)
& ( sdtlpdtrp0(W0,W4) = tptp_fun_W3_14(W2,W1,W0) ) ) ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[328,321]) ).
tff(330,plain,
! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtlcdtrc0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_13(W3,W1,W0)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != W3 ) ) ) ) ) )
| ~ ( ( W2 = sdtlcdtrc0(W0,W1) )
| ~ aSet0(W2)
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_15(W2,W1,W0)) != tptp_fun_W3_14(W2,W1,W0) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != tptp_fun_W3_14(W2,W1,W0) ) ) ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[329,319]) ).
tff(331,plain,
! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtlcdtrc0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_13(W3,W1,W0)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != W3 ) ) ) ) ) )
| ~ ( ( W2 = sdtlcdtrc0(W0,W1) )
| ~ aSet0(W2)
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_15(W2,W1,W0)) != tptp_fun_W3_14(W2,W1,W0) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != tptp_fun_W3_14(W2,W1,W0) ) ) ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[330,317]) ).
tff(332,plain,
! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtlcdtrc0(W0,W1) )
| ~ aSet0(W2)
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_15(W2,W1,W0)) != tptp_fun_W3_14(W2,W1,W0) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != tptp_fun_W3_14(W2,W1,W0) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_13(W3,W1,W0)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != W3 ) ) ) ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[331,312]) ).
tff(333,plain,
( ( ~ ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtlcdtrc0(W0,W1) )
| ~ aSet0(W2)
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_15(W2,W1,W0)) != tptp_fun_W3_14(W2,W1,W0) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != tptp_fun_W3_14(W2,W1,W0) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_13(W3,W1,W0)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != W3 ) ) ) ) ) ) ) ) )
| ~ aFunction0(xd)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(xd))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlcdtrc0(xd,W1) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,W1,xd) ) ) )
| ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,W1,xd)) != tptp_fun_W3_14(W2,W1,xd) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,W1,xd)) != W3 ) ) ) ) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtlcdtrc0(W0,W1) )
| ~ aSet0(W2)
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_15(W2,W1,W0)) != tptp_fun_W3_14(W2,W1,W0) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != tptp_fun_W3_14(W2,W1,W0) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_13(W3,W1,W0)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != W3 ) ) ) ) ) ) ) ) )
| ~ aFunction0(xd)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(xd))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlcdtrc0(xd,W1) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,W1,xd) ) ) )
| ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,W1,xd)) != tptp_fun_W3_14(W2,W1,xd) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,W1,xd)) != W3 ) ) ) ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(334,plain,
( ( ~ aFunction0(xd)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(xd))
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtlcdtrc0(xd,W1) )
| ~ aSet0(W2)
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,W1,xd)) != tptp_fun_W3_14(W2,W1,xd) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,W1,xd) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,W1,xd)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) ) ) ) ) ) ) )
<=> ( ~ aFunction0(xd)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(xd))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlcdtrc0(xd,W1) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,W1,xd) ) ) )
| ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,W1,xd)) != tptp_fun_W3_14(W2,W1,xd) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,W1,xd)) != W3 ) ) ) ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(335,plain,
( ( ~ ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtlcdtrc0(W0,W1) )
| ~ aSet0(W2)
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_15(W2,W1,W0)) != tptp_fun_W3_14(W2,W1,W0) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != tptp_fun_W3_14(W2,W1,W0) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_13(W3,W1,W0)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != W3 ) ) ) ) ) ) ) ) )
| ~ aFunction0(xd)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(xd))
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtlcdtrc0(xd,W1) )
| ~ aSet0(W2)
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,W1,xd)) != tptp_fun_W3_14(W2,W1,xd) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,W1,xd) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,W1,xd)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) ) ) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtlcdtrc0(W0,W1) )
| ~ aSet0(W2)
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_15(W2,W1,W0)) != tptp_fun_W3_14(W2,W1,W0) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != tptp_fun_W3_14(W2,W1,W0) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_13(W3,W1,W0)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != W3 ) ) ) ) ) ) ) ) )
| ~ aFunction0(xd)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(xd))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlcdtrc0(xd,W1) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,W1,xd) ) ) )
| ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,W1,xd)) != tptp_fun_W3_14(W2,W1,xd) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,W1,xd)) != W3 ) ) ) ) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[334]) ).
tff(336,plain,
( ( ~ ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtlcdtrc0(W0,W1) )
| ~ aSet0(W2)
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_15(W2,W1,W0)) != tptp_fun_W3_14(W2,W1,W0) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != tptp_fun_W3_14(W2,W1,W0) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_13(W3,W1,W0)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != W3 ) ) ) ) ) ) ) ) )
| ~ aFunction0(xd)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(xd))
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtlcdtrc0(xd,W1) )
| ~ aSet0(W2)
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,W1,xd)) != tptp_fun_W3_14(W2,W1,xd) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,W1,xd) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,W1,xd)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) ) ) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtlcdtrc0(W0,W1) )
| ~ aSet0(W2)
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_15(W2,W1,W0)) != tptp_fun_W3_14(W2,W1,W0) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != tptp_fun_W3_14(W2,W1,W0) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_13(W3,W1,W0)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != W3 ) ) ) ) ) ) ) ) )
| ~ aFunction0(xd)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(xd))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlcdtrc0(xd,W1) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,W1,xd) ) ) )
| ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,W1,xd)) != tptp_fun_W3_14(W2,W1,xd) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,W1,xd)) != W3 ) ) ) ) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[335,333]) ).
tff(337,plain,
( ~ ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtlcdtrc0(W0,W1) )
| ~ aSet0(W2)
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_15(W2,W1,W0)) != tptp_fun_W3_14(W2,W1,W0) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != tptp_fun_W3_14(W2,W1,W0) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_13(W3,W1,W0)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != W3 ) ) ) ) ) ) ) ) )
| ~ aFunction0(xd)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(xd))
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtlcdtrc0(xd,W1) )
| ~ aSet0(W2)
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,W1,xd)) != tptp_fun_W3_14(W2,W1,xd) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,W1,xd) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,W1,xd)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) ) ) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(338,plain,
( ~ ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtlcdtrc0(W0,W1) )
| ~ aSet0(W2)
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_15(W2,W1,W0)) != tptp_fun_W3_14(W2,W1,W0) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != tptp_fun_W3_14(W2,W1,W0) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_13(W3,W1,W0)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != W3 ) ) ) ) ) ) ) ) )
| ~ aFunction0(xd)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(xd))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlcdtrc0(xd,W1) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,W1,xd) ) ) )
| ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,W1,xd)) != tptp_fun_W3_14(W2,W1,xd) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,W1,xd)) != W3 ) ) ) ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[337,336]) ).
tff(339,plain,
! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(xd))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlcdtrc0(xd,W1) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,W1,xd) ) ) )
| ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,W1,xd)) != tptp_fun_W3_14(W2,W1,xd) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,W1,xd)) != W3 ) ) ) ) ) ) ) ),
inference(unit_resolution,[status(thm)],[338,332,160]) ).
tff(340,plain,
( ( ~ ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(xd))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlcdtrc0(xd,W1) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,W1,xd) ) ) )
| ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,W1,xd)) != tptp_fun_W3_14(W2,W1,xd) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,W1,xd)) != W3 ) ) ) ) ) ) ) )
| ~ aSubsetOf0(szNzAzT0,szDzozmdt0(xd))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlcdtrc0(xd,szNzAzT0) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,szNzAzT0,xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,szNzAzT0,xd) ) ) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,szNzAzT0,xd)) != tptp_fun_W3_14(W2,szNzAzT0,xd) ) )
| aElementOf0(tptp_fun_W3_14(W2,szNzAzT0,xd),W2) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,szNzAzT0) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szNzAzT0,xd)) != W3 ) ) ) ) ) ) ) )
<=> ( ~ ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(xd))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlcdtrc0(xd,W1) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,W1,xd) ) ) )
| ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,W1,xd)) != tptp_fun_W3_14(W2,W1,xd) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,W1,xd)) != W3 ) ) ) ) ) ) ) )
| ~ aSubsetOf0(szNzAzT0,szDzozmdt0(xd))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlcdtrc0(xd,szNzAzT0) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,szNzAzT0,xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,szNzAzT0,xd) ) ) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,szNzAzT0,xd)) != tptp_fun_W3_14(W2,szNzAzT0,xd) ) )
| aElementOf0(tptp_fun_W3_14(W2,szNzAzT0,xd),W2) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,szNzAzT0) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szNzAzT0,xd)) != W3 ) ) ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(341,plain,
( ( ~ aSubsetOf0(szNzAzT0,szDzozmdt0(xd))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlcdtrc0(xd,szNzAzT0) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,szNzAzT0,xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,szNzAzT0,xd) ) ) )
| ~ ( aElementOf0(tptp_fun_W3_14(W2,szNzAzT0,xd),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,szNzAzT0,xd)) != tptp_fun_W3_14(W2,szNzAzT0,xd) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,szNzAzT0) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szNzAzT0,xd)) != W3 ) ) ) ) ) ) ) )
<=> ( ~ aSubsetOf0(szNzAzT0,szDzozmdt0(xd))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlcdtrc0(xd,szNzAzT0) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,szNzAzT0,xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,szNzAzT0,xd) ) ) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,szNzAzT0,xd)) != tptp_fun_W3_14(W2,szNzAzT0,xd) ) )
| aElementOf0(tptp_fun_W3_14(W2,szNzAzT0,xd),W2) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,szNzAzT0) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szNzAzT0,xd)) != W3 ) ) ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(342,plain,
( ( ~ ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(xd))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlcdtrc0(xd,W1) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,W1,xd) ) ) )
| ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,W1,xd)) != tptp_fun_W3_14(W2,W1,xd) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,W1,xd)) != W3 ) ) ) ) ) ) ) )
| ~ aSubsetOf0(szNzAzT0,szDzozmdt0(xd))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlcdtrc0(xd,szNzAzT0) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,szNzAzT0,xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,szNzAzT0,xd) ) ) )
| ~ ( aElementOf0(tptp_fun_W3_14(W2,szNzAzT0,xd),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,szNzAzT0,xd)) != tptp_fun_W3_14(W2,szNzAzT0,xd) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,szNzAzT0) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szNzAzT0,xd)) != W3 ) ) ) ) ) ) ) )
<=> ( ~ ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(xd))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlcdtrc0(xd,W1) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,W1,xd) ) ) )
| ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,W1,xd)) != tptp_fun_W3_14(W2,W1,xd) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,W1,xd)) != W3 ) ) ) ) ) ) ) )
| ~ aSubsetOf0(szNzAzT0,szDzozmdt0(xd))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlcdtrc0(xd,szNzAzT0) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,szNzAzT0,xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,szNzAzT0,xd) ) ) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,szNzAzT0,xd)) != tptp_fun_W3_14(W2,szNzAzT0,xd) ) )
| aElementOf0(tptp_fun_W3_14(W2,szNzAzT0,xd),W2) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,szNzAzT0) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szNzAzT0,xd)) != W3 ) ) ) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[341]) ).
tff(343,plain,
( ( ~ ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(xd))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlcdtrc0(xd,W1) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,W1,xd) ) ) )
| ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,W1,xd)) != tptp_fun_W3_14(W2,W1,xd) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,W1,xd)) != W3 ) ) ) ) ) ) ) )
| ~ aSubsetOf0(szNzAzT0,szDzozmdt0(xd))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlcdtrc0(xd,szNzAzT0) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,szNzAzT0,xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,szNzAzT0,xd) ) ) )
| ~ ( aElementOf0(tptp_fun_W3_14(W2,szNzAzT0,xd),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,szNzAzT0,xd)) != tptp_fun_W3_14(W2,szNzAzT0,xd) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,szNzAzT0) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szNzAzT0,xd)) != W3 ) ) ) ) ) ) ) )
<=> ( ~ ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(xd))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlcdtrc0(xd,W1) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,W1,xd) ) ) )
| ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,W1,xd)) != tptp_fun_W3_14(W2,W1,xd) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,W1,xd)) != W3 ) ) ) ) ) ) ) )
| ~ aSubsetOf0(szNzAzT0,szDzozmdt0(xd))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlcdtrc0(xd,szNzAzT0) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,szNzAzT0,xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,szNzAzT0,xd) ) ) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,szNzAzT0,xd)) != tptp_fun_W3_14(W2,szNzAzT0,xd) ) )
| aElementOf0(tptp_fun_W3_14(W2,szNzAzT0,xd),W2) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,szNzAzT0) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szNzAzT0,xd)) != W3 ) ) ) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[342,340]) ).
tff(344,plain,
( ~ ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(xd))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlcdtrc0(xd,W1) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,W1,xd) ) ) )
| ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,W1,xd)) != tptp_fun_W3_14(W2,W1,xd) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,W1,xd)) != W3 ) ) ) ) ) ) ) )
| ~ aSubsetOf0(szNzAzT0,szDzozmdt0(xd))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlcdtrc0(xd,szNzAzT0) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,szNzAzT0,xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,szNzAzT0,xd) ) ) )
| ~ ( aElementOf0(tptp_fun_W3_14(W2,szNzAzT0,xd),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,szNzAzT0,xd)) != tptp_fun_W3_14(W2,szNzAzT0,xd) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,szNzAzT0) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szNzAzT0,xd)) != W3 ) ) ) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(345,plain,
( ~ ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(xd))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlcdtrc0(xd,W1) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,W1,xd) ) ) )
| ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,W1,xd)) != tptp_fun_W3_14(W2,W1,xd) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,W1,xd)) != W3 ) ) ) ) ) ) ) )
| ~ aSubsetOf0(szNzAzT0,szDzozmdt0(xd))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlcdtrc0(xd,szNzAzT0) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,szNzAzT0,xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,szNzAzT0,xd) ) ) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,szNzAzT0,xd)) != tptp_fun_W3_14(W2,szNzAzT0,xd) ) )
| aElementOf0(tptp_fun_W3_14(W2,szNzAzT0,xd),W2) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,szNzAzT0) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szNzAzT0,xd)) != W3 ) ) ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[344,343]) ).
tff(346,plain,
( ~ aSubsetOf0(szNzAzT0,szDzozmdt0(xd))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlcdtrc0(xd,szNzAzT0) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,szNzAzT0,xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,szNzAzT0,xd) ) ) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,szNzAzT0,xd)) != tptp_fun_W3_14(W2,szNzAzT0,xd) ) )
| aElementOf0(tptp_fun_W3_14(W2,szNzAzT0,xd),W2) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,szNzAzT0) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szNzAzT0,xd)) != W3 ) ) ) ) ) ) ) ),
inference(unit_resolution,[status(thm)],[345,339]) ).
tff(347,plain,
! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlcdtrc0(xd,szNzAzT0) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,szNzAzT0,xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,szNzAzT0,xd) ) ) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,szNzAzT0,xd)) != tptp_fun_W3_14(W2,szNzAzT0,xd) ) )
| aElementOf0(tptp_fun_W3_14(W2,szNzAzT0,xd),W2) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,szNzAzT0) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szNzAzT0,xd)) != W3 ) ) ) ) ) ) ),
inference(unit_resolution,[status(thm)],[346,310]) ).
tff(348,plain,
( ~ ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlcdtrc0(xd,szNzAzT0) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,szNzAzT0,xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,szNzAzT0,xd) ) ) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,szNzAzT0,xd)) != tptp_fun_W3_14(W2,szNzAzT0,xd) ) )
| aElementOf0(tptp_fun_W3_14(W2,szNzAzT0,xd),W2) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,szNzAzT0) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szNzAzT0,xd)) != W3 ) ) ) ) ) ) )
| ~ ( ~ ( ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ( sdtlcdtrc0(xd,szDzozmdt0(xd)) = sdtlcdtrc0(xd,szNzAzT0) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W3_14(sdtlcdtrc0(xd,szDzozmdt0(xd)),szNzAzT0,xd),sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(sdtlcdtrc0(xd,szDzozmdt0(xd)),szNzAzT0,xd) ) ) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W4_15(sdtlcdtrc0(xd,szDzozmdt0(xd)),szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(sdtlcdtrc0(xd,szDzozmdt0(xd)),szNzAzT0,xd)) != tptp_fun_W3_14(sdtlcdtrc0(xd,szDzozmdt0(xd)),szNzAzT0,xd) ) )
| aElementOf0(tptp_fun_W3_14(sdtlcdtrc0(xd,szDzozmdt0(xd)),szNzAzT0,xd),sdtlcdtrc0(xd,szDzozmdt0(xd))) ) ) )
| ~ ( ( sdtlcdtrc0(xd,szDzozmdt0(xd)) != sdtlcdtrc0(xd,szNzAzT0) )
| ~ ( ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szNzAzT0,xd)) != W3 ) ) ) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(349,plain,
~ ( ~ ( ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ( sdtlcdtrc0(xd,szDzozmdt0(xd)) = sdtlcdtrc0(xd,szNzAzT0) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W3_14(sdtlcdtrc0(xd,szDzozmdt0(xd)),szNzAzT0,xd),sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(sdtlcdtrc0(xd,szDzozmdt0(xd)),szNzAzT0,xd) ) ) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W4_15(sdtlcdtrc0(xd,szDzozmdt0(xd)),szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(sdtlcdtrc0(xd,szDzozmdt0(xd)),szNzAzT0,xd)) != tptp_fun_W3_14(sdtlcdtrc0(xd,szDzozmdt0(xd)),szNzAzT0,xd) ) )
| aElementOf0(tptp_fun_W3_14(sdtlcdtrc0(xd,szDzozmdt0(xd)),szNzAzT0,xd),sdtlcdtrc0(xd,szDzozmdt0(xd))) ) ) )
| ~ ( ( sdtlcdtrc0(xd,szDzozmdt0(xd)) != sdtlcdtrc0(xd,szNzAzT0) )
| ~ ( ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szNzAzT0,xd)) != W3 ) ) ) ) ) ) ),
inference(unit_resolution,[status(thm)],[348,347]) ).
tff(350,plain,
( ~ ( ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ( sdtlcdtrc0(xd,szDzozmdt0(xd)) = sdtlcdtrc0(xd,szNzAzT0) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W3_14(sdtlcdtrc0(xd,szDzozmdt0(xd)),szNzAzT0,xd),sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(sdtlcdtrc0(xd,szDzozmdt0(xd)),szNzAzT0,xd) ) ) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W4_15(sdtlcdtrc0(xd,szDzozmdt0(xd)),szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(sdtlcdtrc0(xd,szDzozmdt0(xd)),szNzAzT0,xd)) != tptp_fun_W3_14(sdtlcdtrc0(xd,szDzozmdt0(xd)),szNzAzT0,xd) ) )
| aElementOf0(tptp_fun_W3_14(sdtlcdtrc0(xd,szDzozmdt0(xd)),szNzAzT0,xd),sdtlcdtrc0(xd,szDzozmdt0(xd))) ) ) )
| ~ ( ( sdtlcdtrc0(xd,szDzozmdt0(xd)) != sdtlcdtrc0(xd,szNzAzT0) )
| ~ ( ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szNzAzT0,xd)) != W3 ) ) ) ) ) )
| ( sdtlcdtrc0(xd,szDzozmdt0(xd)) != sdtlcdtrc0(xd,szNzAzT0) )
| ~ ( ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szNzAzT0,xd)) != W3 ) ) ) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(351,plain,
( ( sdtlcdtrc0(xd,szDzozmdt0(xd)) != sdtlcdtrc0(xd,szNzAzT0) )
| ~ ( ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szNzAzT0,xd)) != W3 ) ) ) ) ) ),
inference(unit_resolution,[status(thm)],[350,349]) ).
tff(352,plain,
szNzAzT0 = szDzozmdt0(xd),
inference(symmetry,[status(thm)],[143]) ).
tff(353,plain,
sdtlcdtrc0(xd,szNzAzT0) = sdtlcdtrc0(xd,szDzozmdt0(xd)),
inference(monotonicity,[status(thm)],[352]) ).
tff(354,plain,
sdtlcdtrc0(xd,szDzozmdt0(xd)) = sdtlcdtrc0(xd,szNzAzT0),
inference(symmetry,[status(thm)],[353]) ).
tff(355,plain,
( ~ ( ( sdtlcdtrc0(xd,szDzozmdt0(xd)) != sdtlcdtrc0(xd,szNzAzT0) )
| ~ ( ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szNzAzT0,xd)) != W3 ) ) ) ) ) )
| ( sdtlcdtrc0(xd,szDzozmdt0(xd)) != sdtlcdtrc0(xd,szNzAzT0) )
| ~ ( ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szNzAzT0,xd)) != W3 ) ) ) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(356,plain,
( ~ ( ( sdtlcdtrc0(xd,szDzozmdt0(xd)) != sdtlcdtrc0(xd,szNzAzT0) )
| ~ ( ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szNzAzT0,xd)) != W3 ) ) ) ) ) )
| ~ ( ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szNzAzT0,xd)) != W3 ) ) ) ) ) ),
inference(unit_resolution,[status(thm)],[355,354]) ).
tff(357,plain,
~ ( ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szNzAzT0,xd)) != W3 ) ) ) ) ),
inference(unit_resolution,[status(thm)],[356,351]) ).
tff(358,plain,
( ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szNzAzT0,xd)) != W3 ) ) ) )
| ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szNzAzT0,xd)) != W3 ) ) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(359,plain,
! [W3: $i] :
~ ( ~ ( aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szNzAzT0,xd)) != W3 ) ) ) ),
inference(unit_resolution,[status(thm)],[358,357]) ).
tff(360,plain,
( ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szNzAzT0,xd)) != W3 ) ) ) )
| ~ ( ~ ( aElementOf0(szDzizrdt0(xd),sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != szDzizrdt0(xd) ) ) )
| ~ ( ~ aElementOf0(szDzizrdt0(xd),sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ( ~ aElementOf0(tptp_fun_W4_13(szDzizrdt0(xd),szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(szDzizrdt0(xd),szNzAzT0,xd)) != szDzizrdt0(xd) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(361,plain,
~ ( ~ ( aElementOf0(szDzizrdt0(xd),sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != szDzizrdt0(xd) ) ) )
| ~ ( ~ aElementOf0(szDzizrdt0(xd),sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ( ~ aElementOf0(tptp_fun_W4_13(szDzizrdt0(xd),szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(szDzizrdt0(xd),szNzAzT0,xd)) != szDzizrdt0(xd) ) ) ) ),
inference(unit_resolution,[status(thm)],[360,359]) ).
tff(362,plain,
( ~ ( aElementOf0(szDzizrdt0(xd),sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != szDzizrdt0(xd) ) ) )
| ~ ( ~ aElementOf0(szDzizrdt0(xd),sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ( ~ aElementOf0(tptp_fun_W4_13(szDzizrdt0(xd),szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(szDzizrdt0(xd),szNzAzT0,xd)) != szDzizrdt0(xd) ) ) )
| aElementOf0(szDzizrdt0(xd),sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != szDzizrdt0(xd) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(363,plain,
( aElementOf0(szDzizrdt0(xd),sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != szDzizrdt0(xd) ) ) ),
inference(unit_resolution,[status(thm)],[362,361]) ).
tff(364,plain,
( ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) )
| ~ ( ~ ( aSubsetOf0(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT)
| ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT),sdtlcdtrc0(xd,szDzozmdt0(xd)))
| aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT),xT) ) )
| ~ ( ~ aSubsetOf0(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| aElementOf0(W2,xT) ) ) ) ) )
<=> ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) )
| ~ ( ~ ( aSubsetOf0(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT)
| ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT),sdtlcdtrc0(xd,szDzozmdt0(xd)))
| aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT),xT) ) )
| ~ ( ~ aSubsetOf0(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| aElementOf0(W2,xT) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(365,plain,
( ~ ( ~ ( ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
| aSubsetOf0(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT),sdtlcdtrc0(xd,szDzozmdt0(xd)))
| aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT),xT) ) )
| ~ ( ~ aSubsetOf0(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| aElementOf0(W2,xT) ) ) ) )
<=> ~ ( ~ ( aSubsetOf0(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT)
| ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT),sdtlcdtrc0(xd,szDzozmdt0(xd)))
| aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT),xT) ) )
| ~ ( ~ aSubsetOf0(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| aElementOf0(W2,xT) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(366,plain,
( ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) )
| ~ ( ~ ( ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
| aSubsetOf0(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT),sdtlcdtrc0(xd,szDzozmdt0(xd)))
| aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT),xT) ) )
| ~ ( ~ aSubsetOf0(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| aElementOf0(W2,xT) ) ) ) ) )
<=> ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) )
| ~ ( ~ ( aSubsetOf0(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT)
| ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT),sdtlcdtrc0(xd,szDzozmdt0(xd)))
| aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT),xT) ) )
| ~ ( ~ aSubsetOf0(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| aElementOf0(W2,xT) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[365]) ).
tff(367,plain,
( ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) )
| ~ ( ~ ( ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
| aSubsetOf0(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT),sdtlcdtrc0(xd,szDzozmdt0(xd)))
| aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT),xT) ) )
| ~ ( ~ aSubsetOf0(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| aElementOf0(W2,xT) ) ) ) ) )
<=> ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) )
| ~ ( ~ ( aSubsetOf0(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT)
| ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT),sdtlcdtrc0(xd,szDzozmdt0(xd)))
| aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT),xT) ) )
| ~ ( ~ aSubsetOf0(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| aElementOf0(W2,xT) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[366,364]) ).
tff(368,plain,
( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) )
| ~ ( ~ ( ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
| aSubsetOf0(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT),sdtlcdtrc0(xd,szDzozmdt0(xd)))
| aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT),xT) ) )
| ~ ( ~ aSubsetOf0(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| aElementOf0(W2,xT) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(369,plain,
( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) )
| ~ ( ~ ( aSubsetOf0(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT)
| ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT),sdtlcdtrc0(xd,szDzozmdt0(xd)))
| aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT),xT) ) )
| ~ ( ~ aSubsetOf0(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| aElementOf0(W2,xT) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[368,367]) ).
tff(370,plain,
~ ( ~ ( aSubsetOf0(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT)
| ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT),sdtlcdtrc0(xd,szDzozmdt0(xd)))
| aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT),xT) ) )
| ~ ( ~ aSubsetOf0(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| aElementOf0(W2,xT) ) ) ) ),
inference(unit_resolution,[status(thm)],[369,33]) ).
tff(371,plain,
( ~ ( aSubsetOf0(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT)
| ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT),sdtlcdtrc0(xd,szDzozmdt0(xd)))
| aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT),xT) ) )
| ~ ( ~ aSubsetOf0(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| aElementOf0(W2,xT) ) ) )
| ~ aSubsetOf0(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| aElementOf0(W2,xT) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(372,plain,
( ~ aSubsetOf0(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| aElementOf0(W2,xT) ) ) ),
inference(unit_resolution,[status(thm)],[371,370]) ).
tff(373,plain,
( ~ ( ~ aSubsetOf0(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| aElementOf0(W2,xT) ) ) )
| ~ aSubsetOf0(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| aElementOf0(W2,xT) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(374,plain,
( ~ ( ~ aSubsetOf0(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| aElementOf0(W2,xT) ) ) )
| ~ ( ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| aElementOf0(W2,xT) ) ) ),
inference(unit_resolution,[status(thm)],[373,147]) ).
tff(375,plain,
~ ( ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| aElementOf0(W2,xT) ) ),
inference(unit_resolution,[status(thm)],[374,372]) ).
tff(376,plain,
( ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| aElementOf0(W2,xT) )
| ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| aElementOf0(W2,xT) ) ),
inference(tautology,[status(thm)],[]) ).
tff(377,plain,
! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| aElementOf0(W2,xT) ),
inference(unit_resolution,[status(thm)],[376,375]) ).
tff(378,plain,
( ~ aElementOf0(szDzizrdt0(xd),xT)
<=> ~ aElementOf0(szDzizrdt0(xd),xT) ),
inference(rewrite,[status(thm)],[]) ).
tff(379,axiom,
~ aElementOf0(szDzizrdt0(xd),xT),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(380,plain,
~ aElementOf0(szDzizrdt0(xd),xT),
inference(modus_ponens,[status(thm)],[379,378]) ).
tff(381,plain,
( ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| aElementOf0(W2,xT) )
| ~ aElementOf0(szDzizrdt0(xd),sdtlcdtrc0(xd,szDzozmdt0(xd)))
| aElementOf0(szDzizrdt0(xd),xT) )
<=> ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| aElementOf0(W2,xT) )
| ~ aElementOf0(szDzizrdt0(xd),sdtlcdtrc0(xd,szDzozmdt0(xd)))
| aElementOf0(szDzizrdt0(xd),xT) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(382,plain,
( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| aElementOf0(W2,xT) )
| ~ aElementOf0(szDzizrdt0(xd),sdtlcdtrc0(xd,szDzozmdt0(xd)))
| aElementOf0(szDzizrdt0(xd),xT) ),
inference(quant_inst,[status(thm)],[]) ).
tff(383,plain,
( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| aElementOf0(W2,xT) )
| ~ aElementOf0(szDzizrdt0(xd),sdtlcdtrc0(xd,szDzozmdt0(xd)))
| aElementOf0(szDzizrdt0(xd),xT) ),
inference(modus_ponens,[status(thm)],[382,381]) ).
tff(384,plain,
~ aElementOf0(szDzizrdt0(xd),sdtlcdtrc0(xd,szDzozmdt0(xd))),
inference(unit_resolution,[status(thm)],[383,380,377]) ).
tff(385,plain,
( ~ ( aElementOf0(szDzizrdt0(xd),sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != szDzizrdt0(xd) ) ) )
| aElementOf0(szDzizrdt0(xd),sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != szDzizrdt0(xd) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(386,plain,
( ~ ( aElementOf0(szDzizrdt0(xd),sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != szDzizrdt0(xd) ) ) )
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != szDzizrdt0(xd) ) ) ),
inference(unit_resolution,[status(thm)],[385,384]) ).
tff(387,plain,
! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != szDzizrdt0(xd) ) ),
inference(unit_resolution,[status(thm)],[386,363]) ).
tff(388,plain,
( ( ~ ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != szDzizrdt0(xd) ) )
| ~ aElementOf0(tptp_fun_W2_1(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W2_1(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))) != szDzizrdt0(xd) ) )
<=> ( ~ ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != szDzizrdt0(xd) ) )
| ~ aElementOf0(tptp_fun_W2_1(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W2_1(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))) != szDzizrdt0(xd) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(389,plain,
( ~ ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != szDzizrdt0(xd) ) )
| ~ aElementOf0(tptp_fun_W2_1(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W2_1(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))) != szDzizrdt0(xd) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(390,plain,
( ~ ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != szDzizrdt0(xd) ) )
| ~ aElementOf0(tptp_fun_W2_1(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT))))),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W2_1(sdtlbdtrb0(xd,szDzizrdt0(xd)),sdtlcdtrc0(sdtlpdtrp0(xC,sbrdtbr0(xT)),szDzozmdt0(sdtlpdtrp0(xC,sbrdtbr0(xT)))))) != szDzizrdt0(xd) ) ),
inference(modus_ponens,[status(thm)],[389,388]) ).
tff(391,plain,
$false,
inference(unit_resolution,[status(thm)],[390,387,293,244]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM596+1 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n012.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 01:32:25 EDT 2025
% 0.12/0.34 % CPUTime :
% 255.30/255.63 % SZS status Theorem
% 255.30/255.63 % SZS output start Proof
% See solution above
% 256.31/256.70 % E exiting
%------------------------------------------------------------------------------