%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM597+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:21:32 AM UTC 2025
% Result : Theorem 262.23s 262.43s
% Output : Proof 262.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 128
% Syntax : Number of formulae : 323 ( 70 unt; 0 typ; 0 def)
% Number of atoms : 4553 ( 988 equ)
% Maximal formula atoms : 72 ( 14 avg)
% Number of connectives : 8995 (4927 ~;3199 |; 339 &)
% ( 472 <=>; 58 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 9 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of FOOLs : 162 ( 162 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 : 20 ( 20 usr; 7 con; 0-3 aty)
% Number of variables : 1220 (1150 !; 21 ?;1220 :)
% Comments :
%------------------------------------------------------------------------------
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(szNzAzT0_type,type,
szNzAzT0: $i ).
tff(tptp_fun_W1_0_type,type,
tptp_fun_W1_0: $i > $i ).
tff(sdtlbdtrb0_type,type,
sdtlbdtrb0: ( $i * $i ) > $i ).
tff(szDzizrdt0_type,type,
szDzizrdt0: $i > $i ).
tff(xd_type,type,
xd: $i ).
tff(aSet0_type,type,
aSet0: $i > $o ).
tff(slcrc0_type,type,
slcrc0: $i ).
tff(aSubsetOf0_type,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff(tptp_fun_W2_1_type,type,
tptp_fun_W2_1: ( $i * $i ) > $i ).
tff(isCountable0_type,type,
isCountable0: $i > $o ).
tff(szDzozmdt0_type,type,
szDzozmdt0: $i > $i ).
tff(aFunction0_type,type,
aFunction0: $i > $o ).
tff(sdtlpdtrp0_type,type,
sdtlpdtrp0: ( $i * $i ) > $i ).
tff(xC_type,type,
xC: $i ).
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(isFinite0_type,type,
isFinite0: $i > $o ).
tff(sdtlcdtrc0_type,type,
sdtlcdtrc0: ( $i * $i ) > $i ).
tff(xT_type,type,
xT: $i ).
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,
^ [W0: $i] :
rewrite(( ~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ~ ( ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) )
| ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [W0: $i] :
~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ! [W0: $i] :
~ ( ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) )
| ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [W0: $i] :
refl(( ~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(4,plain,
( ! [W0: $i] :
~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ! [W0: $i] :
~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
^ [W0: $i] :
rewrite(( ~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(6,plain,
( ! [W0: $i] :
~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ! [W0: $i] :
~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) ),
inference(quant_intro,[status(thm)],[5]) ).
tff(7,plain,
( ! [W0: $i] :
~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ! [W0: $i] :
~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) ),
inference(transitivity,[status(thm)],[6,4]) ).
tff(8,plain,
^ [W0: $i] :
trans(monotonicity(rewrite(( ( ( W0 != slcrc0 )
| ( aSet0(W0)
& ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
<=> ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) ) )),
rewrite(( ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) )
<=> ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )),
( ( ( ( W0 != slcrc0 )
| ( aSet0(W0)
& ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ( ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) )),
rewrite(( ( ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) )),
( ( ( ( W0 != slcrc0 )
| ( aSet0(W0)
& ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(9,plain,
( ! [W0: $i] :
( ( ( W0 != slcrc0 )
| ( aSet0(W0)
& ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ! [W0: $i] :
~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
^ [W0: $i] :
rewrite(( ( ( ( W0 != slcrc0 )
| ( aSet0(W0)
& ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ( ( ( W0 != slcrc0 )
| ( aSet0(W0)
& ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [W0: $i] :
( ( ( W0 != slcrc0 )
| ( aSet0(W0)
& ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ! [W0: $i] :
( ( ( W0 != slcrc0 )
| ( aSet0(W0)
& ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [W0: $i] :
( ( W0 = slcrc0 )
<=> ( aSet0(W0)
& ~ ? [W1: $i] : aElementOf0(W1,W0) ) )
<=> ! [W0: $i] :
( ( W0 = slcrc0 )
<=> ( aSet0(W0)
& ~ ? [W1: $i] : aElementOf0(W1,W0) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
! [W0: $i] :
( ( W0 = slcrc0 )
<=> ( aSet0(W0)
& ~ ? [W1: $i] : aElementOf0(W1,W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefEmp) ).
tff(14,plain,
! [W0: $i] :
( ( W0 = slcrc0 )
<=> ( aSet0(W0)
& ~ ? [W1: $i] : aElementOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [W0: $i] :
( ( ( W0 != slcrc0 )
| ( aSet0(W0)
& ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [W0: $i] :
( ( ( W0 != slcrc0 )
| ( aSet0(W0)
& ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
! [W0: $i] :
~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ),
inference(modus_ponens,[status(thm)],[16,9]) ).
tff(18,plain,
! [W0: $i] :
~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ),
inference(modus_ponens,[status(thm)],[17,7]) ).
tff(19,plain,
! [W0: $i] :
~ ( ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) )
| ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) ) ),
inference(modus_ponens,[status(thm)],[18,2]) ).
tff(20,plain,
( ~ ! [W0: $i] :
~ ( ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) )
| ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) ) )
| ~ ( ~ ( ( sdtlbdtrb0(xd,szDzizrdt0(xd)) = slcrc0 )
| ~ aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aElementOf0(tptp_fun_W1_0(sdtlbdtrb0(xd,szDzizrdt0(xd))),sdtlbdtrb0(xd,szDzizrdt0(xd))) )
| ~ ( ( sdtlbdtrb0(xd,szDzizrdt0(xd)) != slcrc0 )
| ~ ( ~ aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ ! [W1: $i] : ~ aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(21,plain,
~ ( ~ ( ( sdtlbdtrb0(xd,szDzizrdt0(xd)) = slcrc0 )
| ~ aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aElementOf0(tptp_fun_W1_0(sdtlbdtrb0(xd,szDzizrdt0(xd))),sdtlbdtrb0(xd,szDzizrdt0(xd))) )
| ~ ( ( sdtlbdtrb0(xd,szDzizrdt0(xd)) != slcrc0 )
| ~ ( ~ aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ ! [W1: $i] : ~ aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) ) ),
inference(unit_resolution,[status(thm)],[20,19]) ).
tff(22,plain,
( ~ ( ( sdtlbdtrb0(xd,szDzizrdt0(xd)) = slcrc0 )
| ~ aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aElementOf0(tptp_fun_W1_0(sdtlbdtrb0(xd,szDzizrdt0(xd))),sdtlbdtrb0(xd,szDzizrdt0(xd))) )
| ~ ( ( sdtlbdtrb0(xd,szDzizrdt0(xd)) != slcrc0 )
| ~ ( ~ aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ ! [W1: $i] : ~ aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) )
| ( sdtlbdtrb0(xd,szDzizrdt0(xd)) = slcrc0 )
| ~ aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aElementOf0(tptp_fun_W1_0(sdtlbdtrb0(xd,szDzizrdt0(xd))),sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
inference(tautology,[status(thm)],[]) ).
tff(23,plain,
( ( sdtlbdtrb0(xd,szDzizrdt0(xd)) = slcrc0 )
| ~ aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aElementOf0(tptp_fun_W1_0(sdtlbdtrb0(xd,szDzizrdt0(xd))),sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
inference(unit_resolution,[status(thm)],[22,21]) ).
tff(24,plain,
( aSet0(szNzAzT0)
<=> aSet0(szNzAzT0) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,axiom,
( aSet0(szNzAzT0)
& isCountable0(szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNATSet) ).
tff(26,plain,
aSet0(szNzAzT0),
inference(and_elim,[status(thm)],[25]) ).
tff(27,plain,
aSet0(szNzAzT0),
inference(modus_ponens,[status(thm)],[26,24]) ).
tff(28,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(29,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)],[28]) ).
tff(30,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(31,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)],[30]) ).
tff(32,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(33,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)],[32]) ).
tff(34,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)],[33,31]) ).
tff(35,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(36,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)],[35]) ).
tff(37,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(38,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)],[37]) ).
tff(39,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(40,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(41,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)],[40]) ).
tff(42,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(43,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)],[42,41]) ).
tff(44,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)],[43,39]) ).
tff(45,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)],[44]) ).
tff(46,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)],[45,38]) ).
tff(47,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)],[46,36]) ).
tff(48,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)],[47,34]) ).
tff(49,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)],[48,29]) ).
tff(50,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(51,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(52,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)],[51,50]) ).
tff(53,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)],[52,49,27]) ).
tff(54,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(55,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)],[54,53]) ).
tff(56,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(57,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)],[56,55]) ).
tff(58,plain,
( ( szDzozmdt0(xd) = szNzAzT0 )
<=> ( szDzozmdt0(xd) = szNzAzT0 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(59,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(60,plain,
( aFunction0(xd)
& ( szDzozmdt0(xd) = szNzAzT0 ) ),
inference(and_elim,[status(thm)],[59]) ).
tff(61,plain,
szDzozmdt0(xd) = szNzAzT0,
inference(and_elim,[status(thm)],[60]) ).
tff(62,plain,
szDzozmdt0(xd) = szNzAzT0,
inference(modus_ponens,[status(thm)],[61,58]) ).
tff(63,plain,
szNzAzT0 = szDzozmdt0(xd),
inference(symmetry,[status(thm)],[62]) ).
tff(64,plain,
( aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szNzAzT0)
<=> aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzozmdt0(xd)) ),
inference(monotonicity,[status(thm)],[63]) ).
tff(65,plain,
( aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzozmdt0(xd))
<=> aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szNzAzT0) ),
inference(symmetry,[status(thm)],[64]) ).
tff(66,plain,
( isFinite0(xT)
<=> isFinite0(xT) ),
inference(rewrite,[status(thm)],[]) ).
tff(67,axiom,
( aSet0(xT)
& isFinite0(xT) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3291) ).
tff(68,plain,
isFinite0(xT),
inference(and_elim,[status(thm)],[67]) ).
tff(69,plain,
isFinite0(xT),
inference(modus_ponens,[status(thm)],[68,66]) ).
tff(70,plain,
( aSet0(xT)
<=> aSet0(xT) ),
inference(rewrite,[status(thm)],[]) ).
tff(71,plain,
aSet0(xT),
inference(and_elim,[status(thm)],[67]) ).
tff(72,plain,
aSet0(xT),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,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(74,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)],[73]) ).
tff(75,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(76,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)],[75]) ).
tff(77,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)],[76,74]) ).
tff(78,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(79,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)],[78]) ).
tff(80,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(81,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(82,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)],[81]) ).
tff(83,axiom,
! [W0: $i] :
( ( aSet0(W0)
& isFinite0(W0) )
=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
=> isFinite0(W1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubFSet) ).
tff(84,plain,
! [W0: $i] :
( ~ ( aSet0(W0)
& isFinite0(W0) )
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
! [W0: $i] :
( ~ ( aSet0(W0)
& isFinite0(W0) )
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[84,80]) ).
tff(86,plain,
! [W0: $i] :
( ~ ( aSet0(W0)
& isFinite0(W0) )
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) ),
inference(skolemize,[status(sab)],[85]) ).
tff(87,plain,
! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[86,79]) ).
tff(88,plain,
! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[87,77]) ).
tff(89,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(90,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(91,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)],[90]) ).
tff(92,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)],[91,89]) ).
tff(93,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(94,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)],[93,92]) ).
tff(95,plain,
! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,xT) ),
inference(unit_resolution,[status(thm)],[94,88,72,69]) ).
tff(96,plain,
( aSubsetOf0(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT)
<=> aSubsetOf0(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT) ),
inference(rewrite,[status(thm)],[]) ).
tff(97,axiom,
aSubsetOf0(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4758) ).
tff(98,plain,
aSubsetOf0(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT),
inference(modus_ponens,[status(thm)],[97,96]) ).
tff(99,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(100,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(101,plain,
( ~ ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,xT) )
| isFinite0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ aSubsetOf0(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT) ),
inference(modus_ponens,[status(thm)],[100,99]) ).
tff(102,plain,
isFinite0(sdtlcdtrc0(xd,szDzozmdt0(xd))),
inference(unit_resolution,[status(thm)],[101,98,95]) ).
tff(103,plain,
( isCountable0(szDzozmdt0(xd))
<=> isCountable0(szNzAzT0) ),
inference(monotonicity,[status(thm)],[62]) ).
tff(104,plain,
( isCountable0(szNzAzT0)
<=> isCountable0(szDzozmdt0(xd)) ),
inference(symmetry,[status(thm)],[103]) ).
tff(105,plain,
( isCountable0(szNzAzT0)
<=> isCountable0(szNzAzT0) ),
inference(rewrite,[status(thm)],[]) ).
tff(106,plain,
isCountable0(szNzAzT0),
inference(and_elim,[status(thm)],[25]) ).
tff(107,plain,
isCountable0(szNzAzT0),
inference(modus_ponens,[status(thm)],[106,105]) ).
tff(108,plain,
isCountable0(szDzozmdt0(xd)),
inference(modus_ponens,[status(thm)],[107,104]) ).
tff(109,plain,
( aFunction0(xd)
<=> aFunction0(xd) ),
inference(rewrite,[status(thm)],[]) ).
tff(110,plain,
aFunction0(xd),
inference(and_elim,[status(thm)],[60]) ).
tff(111,plain,
aFunction0(xd),
inference(modus_ponens,[status(thm)],[110,109]) ).
tff(112,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(113,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)],[112]) ).
tff(114,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(115,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)],[114]) ).
tff(116,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(117,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(118,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)],[117]) ).
tff(119,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(120,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)],[119,118]) ).
tff(121,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)],[120,116]) ).
tff(122,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)],[121]) ).
tff(123,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)],[122,115]) ).
tff(124,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)],[123,113]) ).
tff(125,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(126,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(127,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)],[126,125]) ).
tff(128,plain,
( ~ isCountable0(szDzozmdt0(xd))
| ~ ( ~ aElement0(szDzizrdt0(xd))
| ~ isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd))) )
| ~ isFinite0(sdtlcdtrc0(xd,szDzozmdt0(xd))) ),
inference(unit_resolution,[status(thm)],[127,124,111]) ).
tff(129,plain,
~ ( ~ aElement0(szDzizrdt0(xd))
| ~ isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
inference(unit_resolution,[status(thm)],[128,108,102]) ).
tff(130,plain,
( ~ aElement0(szDzizrdt0(xd))
| ~ isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aElement0(szDzizrdt0(xd)) ),
inference(tautology,[status(thm)],[]) ).
tff(131,plain,
aElement0(szDzizrdt0(xd)),
inference(unit_resolution,[status(thm)],[130,129]) ).
tff(132,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(133,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)],[132]) ).
tff(134,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(135,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)],[134]) ).
tff(136,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(137,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(138,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)],[137]) ).
tff(139,axiom,
! [W0: $i,W1: $i] :
( ( aFunction0(W0)
& aElement0(W1) )
=> aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mPttSet) ).
tff(140,plain,
! [W0: $i,W1: $i] :
( ~ ( aFunction0(W0)
& aElement0(W1) )
| aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0)) ),
inference(modus_ponens,[status(thm)],[139,138]) ).
tff(141,plain,
! [W0: $i,W1: $i] :
( ~ ( aFunction0(W0)
& aElement0(W1) )
| aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0)) ),
inference(modus_ponens,[status(thm)],[140,136]) ).
tff(142,plain,
! [W0: $i,W1: $i] :
( ~ ( aFunction0(W0)
& aElement0(W1) )
| aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0)) ),
inference(skolemize,[status(sab)],[141]) ).
tff(143,plain,
! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0))
| ~ aElement0(W1)
| ~ aFunction0(W0) ),
inference(modus_ponens,[status(thm)],[142,135]) ).
tff(144,plain,
! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0))
| ~ aElement0(W1)
| ~ aFunction0(W0) ),
inference(modus_ponens,[status(thm)],[143,133]) ).
tff(145,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(146,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(147,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)],[146]) ).
tff(148,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)],[147,145]) ).
tff(149,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(150,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)],[149,148]) ).
tff(151,plain,
( ~ aElement0(szDzizrdt0(xd))
| aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzozmdt0(xd)) ),
inference(unit_resolution,[status(thm)],[150,144,111]) ).
tff(152,plain,
aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzozmdt0(xd)),
inference(unit_resolution,[status(thm)],[151,131]) ).
tff(153,plain,
aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szNzAzT0),
inference(modus_ponens,[status(thm)],[152,65]) ).
tff(154,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(155,plain,
~ ( ~ aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aElementOf0(W2,szNzAzT0) ) ),
inference(unit_resolution,[status(thm)],[154,153,57]) ).
tff(156,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(157,plain,
aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd))),
inference(unit_resolution,[status(thm)],[156,155]) ).
tff(158,plain,
( ( sdtlbdtrb0(xd,szDzizrdt0(xd)) != slcrc0 )
<=> ( sdtlbdtrb0(xd,szDzizrdt0(xd)) != slcrc0 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(159,axiom,
sdtlbdtrb0(xd,szDzizrdt0(xd)) != slcrc0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4868) ).
tff(160,plain,
sdtlbdtrb0(xd,szDzizrdt0(xd)) != slcrc0,
inference(modus_ponens,[status(thm)],[159,158]) ).
tff(161,plain,
( ~ ( ( sdtlbdtrb0(xd,szDzizrdt0(xd)) = slcrc0 )
| ~ aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aElementOf0(tptp_fun_W1_0(sdtlbdtrb0(xd,szDzizrdt0(xd))),sdtlbdtrb0(xd,szDzizrdt0(xd))) )
| ( sdtlbdtrb0(xd,szDzizrdt0(xd)) = slcrc0 )
| ~ aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aElementOf0(tptp_fun_W1_0(sdtlbdtrb0(xd,szDzizrdt0(xd))),sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
inference(tautology,[status(thm)],[]) ).
tff(162,plain,
( ~ ( ( sdtlbdtrb0(xd,szDzizrdt0(xd)) = slcrc0 )
| ~ aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aElementOf0(tptp_fun_W1_0(sdtlbdtrb0(xd,szDzizrdt0(xd))),sdtlbdtrb0(xd,szDzizrdt0(xd))) )
| aElementOf0(tptp_fun_W1_0(sdtlbdtrb0(xd,szDzizrdt0(xd))),sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
inference(unit_resolution,[status(thm)],[161,160,157]) ).
tff(163,plain,
aElementOf0(tptp_fun_W1_0(sdtlbdtrb0(xd,szDzizrdt0(xd))),sdtlbdtrb0(xd,szDzizrdt0(xd))),
inference(unit_resolution,[status(thm)],[162,23]) ).
tff(164,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(165,plain,
! [W2: $i] :
( ~ aElementOf0(W2,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aElementOf0(W2,szNzAzT0) ),
inference(unit_resolution,[status(thm)],[164,155]) ).
tff(166,plain,
( ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aElementOf0(W2,szNzAzT0) )
| ~ aElementOf0(tptp_fun_W1_0(sdtlbdtrb0(xd,szDzizrdt0(xd))),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aElementOf0(tptp_fun_W1_0(sdtlbdtrb0(xd,szDzizrdt0(xd))),szNzAzT0) )
<=> ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aElementOf0(W2,szNzAzT0) )
| ~ aElementOf0(tptp_fun_W1_0(sdtlbdtrb0(xd,szDzizrdt0(xd))),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aElementOf0(tptp_fun_W1_0(sdtlbdtrb0(xd,szDzizrdt0(xd))),szNzAzT0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(167,plain,
( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aElementOf0(W2,szNzAzT0) )
| ~ aElementOf0(tptp_fun_W1_0(sdtlbdtrb0(xd,szDzizrdt0(xd))),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aElementOf0(tptp_fun_W1_0(sdtlbdtrb0(xd,szDzizrdt0(xd))),szNzAzT0) ),
inference(quant_inst,[status(thm)],[]) ).
tff(168,plain,
( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aElementOf0(W2,szNzAzT0) )
| ~ aElementOf0(tptp_fun_W1_0(sdtlbdtrb0(xd,szDzizrdt0(xd))),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aElementOf0(tptp_fun_W1_0(sdtlbdtrb0(xd,szDzizrdt0(xd))),szNzAzT0) ),
inference(modus_ponens,[status(thm)],[167,166]) ).
tff(169,plain,
aElementOf0(tptp_fun_W1_0(sdtlbdtrb0(xd,szDzizrdt0(xd))),szNzAzT0),
inference(unit_resolution,[status(thm)],[168,165,163]) ).
tff(170,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(171,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)],[170]) ).
tff(172,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(173,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)],[172]) ).
tff(174,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(175,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)],[174]) ).
tff(176,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)],[175,173]) ).
tff(177,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(178,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)],[177]) ).
tff(179,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(180,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)],[179]) ).
tff(181,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(182,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(183,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)],[182]) ).
tff(184,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(185,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)],[184,183]) ).
tff(186,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)],[185,181]) ).
tff(187,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)],[186]) ).
tff(188,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)],[187,180]) ).
tff(189,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)],[188,178]) ).
tff(190,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)],[189,176]) ).
tff(191,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)],[190,171]) ).
tff(192,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(193,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(194,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(195,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)],[194]) ).
tff(196,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)],[195]) ).
tff(197,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)],[196,193]) ).
tff(198,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)],[197]) ).
tff(199,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)],[198,192]) ).
tff(200,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(201,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)],[200,199]) ).
tff(202,plain,
( ~ aElement0(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) ) ) ) ) ),
inference(unit_resolution,[status(thm)],[201,191,111]) ).
tff(203,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)],[202,131]) ).
tff(204,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(205,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(206,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)],[205]) ).
tff(207,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)],[206,204]) ).
tff(208,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(209,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)],[208,207]) ).
tff(210,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)],[209,203]) ).
tff(211,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(212,plain,
! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,W3) != szDzizrdt0(xd) ) )
<=> aElementOf0(W3,sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
inference(unit_resolution,[status(thm)],[211,210]) ).
tff(213,plain,
( ~ ! [W3: $i] :
~ ( ( ~ aElementOf0(W3,szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,W3) != szDzizrdt0(xd) ) )
<=> aElementOf0(W3,sdtlbdtrb0(xd,szDzizrdt0(xd))) )
| ~ ( ( ~ aElementOf0(tptp_fun_W1_0(sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,tptp_fun_W1_0(sdtlbdtrb0(xd,szDzizrdt0(xd)))) != szDzizrdt0(xd) ) )
<=> aElementOf0(tptp_fun_W1_0(sdtlbdtrb0(xd,szDzizrdt0(xd))),sdtlbdtrb0(xd,szDzizrdt0(xd))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(214,plain,
~ ( ( ~ aElementOf0(tptp_fun_W1_0(sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,tptp_fun_W1_0(sdtlbdtrb0(xd,szDzizrdt0(xd)))) != szDzizrdt0(xd) ) )
<=> aElementOf0(tptp_fun_W1_0(sdtlbdtrb0(xd,szDzizrdt0(xd))),sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
inference(unit_resolution,[status(thm)],[213,212]) ).
tff(215,plain,
( ( ( ~ aElementOf0(tptp_fun_W1_0(sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,tptp_fun_W1_0(sdtlbdtrb0(xd,szDzizrdt0(xd)))) != szDzizrdt0(xd) ) )
<=> aElementOf0(tptp_fun_W1_0(sdtlbdtrb0(xd,szDzizrdt0(xd))),sdtlbdtrb0(xd,szDzizrdt0(xd))) )
| ~ ( ~ aElementOf0(tptp_fun_W1_0(sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,tptp_fun_W1_0(sdtlbdtrb0(xd,szDzizrdt0(xd)))) != szDzizrdt0(xd) ) )
| ~ aElementOf0(tptp_fun_W1_0(sdtlbdtrb0(xd,szDzizrdt0(xd))),sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
inference(tautology,[status(thm)],[]) ).
tff(216,plain,
( ( ( ~ aElementOf0(tptp_fun_W1_0(sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,tptp_fun_W1_0(sdtlbdtrb0(xd,szDzizrdt0(xd)))) != szDzizrdt0(xd) ) )
<=> aElementOf0(tptp_fun_W1_0(sdtlbdtrb0(xd,szDzizrdt0(xd))),sdtlbdtrb0(xd,szDzizrdt0(xd))) )
| ~ ( ~ aElementOf0(tptp_fun_W1_0(sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,tptp_fun_W1_0(sdtlbdtrb0(xd,szDzizrdt0(xd)))) != szDzizrdt0(xd) ) ) ),
inference(unit_resolution,[status(thm)],[215,163]) ).
tff(217,plain,
~ ( ~ aElementOf0(tptp_fun_W1_0(sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,tptp_fun_W1_0(sdtlbdtrb0(xd,szDzizrdt0(xd)))) != szDzizrdt0(xd) ) ),
inference(unit_resolution,[status(thm)],[216,214]) ).
tff(218,plain,
( ~ aElementOf0(tptp_fun_W1_0(sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzozmdt0(xd))
| ( sdtlpdtrp0(xd,tptp_fun_W1_0(sdtlbdtrb0(xd,szDzizrdt0(xd)))) != szDzizrdt0(xd) )
| ( sdtlpdtrp0(xd,tptp_fun_W1_0(sdtlbdtrb0(xd,szDzizrdt0(xd)))) = szDzizrdt0(xd) ) ),
inference(tautology,[status(thm)],[]) ).
tff(219,plain,
sdtlpdtrp0(xd,tptp_fun_W1_0(sdtlbdtrb0(xd,szDzizrdt0(xd)))) = szDzizrdt0(xd),
inference(unit_resolution,[status(thm)],[218,217]) ).
tff(220,plain,
( aSubsetOf0(szNzAzT0,szDzozmdt0(xd))
<=> aSubsetOf0(szNzAzT0,szNzAzT0) ),
inference(monotonicity,[status(thm)],[62]) ).
tff(221,plain,
( aSubsetOf0(szNzAzT0,szNzAzT0)
<=> aSubsetOf0(szNzAzT0,szDzozmdt0(xd)) ),
inference(symmetry,[status(thm)],[220]) ).
tff(222,plain,
^ [W0: $i] :
refl(( ( ~ aSet0(W0)
| aSubsetOf0(W0,W0) )
<=> ( ~ aSet0(W0)
| aSubsetOf0(W0,W0) ) )),
inference(bind,[status(th)],[]) ).
tff(223,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) ) ),
inference(quant_intro,[status(thm)],[222]) ).
tff(224,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(225,plain,
^ [W0: $i] :
rewrite(( ( aSet0(W0)
=> aSubsetOf0(W0,W0) )
<=> ( ~ aSet0(W0)
| aSubsetOf0(W0,W0) ) )),
inference(bind,[status(th)],[]) ).
tff(226,plain,
( ! [W0: $i] :
( aSet0(W0)
=> aSubsetOf0(W0,W0) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) ) ),
inference(quant_intro,[status(thm)],[225]) ).
tff(227,axiom,
! [W0: $i] :
( aSet0(W0)
=> aSubsetOf0(W0,W0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubRefl) ).
tff(228,plain,
! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) ),
inference(modus_ponens,[status(thm)],[227,226]) ).
tff(229,plain,
! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) ),
inference(modus_ponens,[status(thm)],[228,224]) ).
tff(230,plain,
! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) ),
inference(skolemize,[status(sab)],[229]) ).
tff(231,plain,
! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) ),
inference(modus_ponens,[status(thm)],[230,223]) ).
tff(232,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(233,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) )
| ~ aSet0(szNzAzT0)
| aSubsetOf0(szNzAzT0,szNzAzT0) ),
inference(quant_inst,[status(thm)],[]) ).
tff(234,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) )
| ~ aSet0(szNzAzT0)
| aSubsetOf0(szNzAzT0,szNzAzT0) ),
inference(modus_ponens,[status(thm)],[233,232]) ).
tff(235,plain,
aSubsetOf0(szNzAzT0,szNzAzT0),
inference(unit_resolution,[status(thm)],[234,231,27]) ).
tff(236,plain,
aSubsetOf0(szNzAzT0,szDzozmdt0(xd)),
inference(modus_ponens,[status(thm)],[235,221]) ).
tff(237,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(238,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)],[237]) ).
tff(239,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(240,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)],[239]) ).
tff(241,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(242,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)],[241]) ).
tff(243,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)],[242,240]) ).
tff(244,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(245,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)],[244]) ).
tff(246,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(247,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)],[246]) ).
tff(248,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(249,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(250,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)],[249]) ).
tff(251,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(252,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)],[251,250]) ).
tff(253,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)],[252,248]) ).
tff(254,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)],[253]) ).
tff(255,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)],[254,247]) ).
tff(256,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)],[255,245]) ).
tff(257,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)],[256,243]) ).
tff(258,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)],[257,238]) ).
tff(259,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(260,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(261,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)],[260]) ).
tff(262,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)],[261,259]) ).
tff(263,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(264,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)],[263,262]) ).
tff(265,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)],[264,258,111]) ).
tff(266,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(267,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(268,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)],[267]) ).
tff(269,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)],[268,266]) ).
tff(270,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(271,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)],[270,269]) ).
tff(272,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)],[271,265]) ).
tff(273,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)],[272,236]) ).
tff(274,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(275,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)],[274,273]) ).
tff(276,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(277,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)],[276,275]) ).
tff(278,plain,
sdtlcdtrc0(xd,szNzAzT0) = sdtlcdtrc0(xd,szDzozmdt0(xd)),
inference(monotonicity,[status(thm)],[63]) ).
tff(279,plain,
sdtlcdtrc0(xd,szDzozmdt0(xd)) = sdtlcdtrc0(xd,szNzAzT0),
inference(symmetry,[status(thm)],[278]) ).
tff(280,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(281,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)],[280,279]) ).
tff(282,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)],[281,277]) ).
tff(283,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(284,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)],[283,282]) ).
tff(285,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(286,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)],[285,284]) ).
tff(287,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(288,plain,
( aElementOf0(szDzizrdt0(xd),sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != szDzizrdt0(xd) ) ) ),
inference(unit_resolution,[status(thm)],[287,286]) ).
tff(289,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(290,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(291,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)],[290]) ).
tff(292,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)],[291,289]) ).
tff(293,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(294,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)],[293,292]) ).
tff(295,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)],[294,49,72]) ).
tff(296,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(297,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(298,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)],[297]) ).
tff(299,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)],[298,296]) ).
tff(300,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(301,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)],[300,299]) ).
tff(302,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)],[301,295]) ).
tff(303,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(304,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)],[303,302]) ).
tff(305,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(306,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)],[305,98]) ).
tff(307,plain,
~ ( ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| aElementOf0(W2,xT) ) ),
inference(unit_resolution,[status(thm)],[306,304]) ).
tff(308,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(309,plain,
! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| aElementOf0(W2,xT) ),
inference(unit_resolution,[status(thm)],[308,307]) ).
tff(310,plain,
( ~ aElementOf0(szDzizrdt0(xd),xT)
<=> ~ aElementOf0(szDzizrdt0(xd),xT) ),
inference(rewrite,[status(thm)],[]) ).
tff(311,axiom,
~ aElementOf0(szDzizrdt0(xd),xT),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(312,plain,
~ aElementOf0(szDzizrdt0(xd),xT),
inference(modus_ponens,[status(thm)],[311,310]) ).
tff(313,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(314,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(315,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)],[314,313]) ).
tff(316,plain,
~ aElementOf0(szDzizrdt0(xd),sdtlcdtrc0(xd,szDzozmdt0(xd))),
inference(unit_resolution,[status(thm)],[315,312,309]) ).
tff(317,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(318,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)],[317,316]) ).
tff(319,plain,
! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != szDzizrdt0(xd) ) ),
inference(unit_resolution,[status(thm)],[318,288]) ).
tff(320,plain,
( ( ~ ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != szDzizrdt0(xd) ) )
| ~ aElementOf0(tptp_fun_W1_0(sdtlbdtrb0(xd,szDzizrdt0(xd))),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W1_0(sdtlbdtrb0(xd,szDzizrdt0(xd)))) != szDzizrdt0(xd) ) )
<=> ( ~ ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != szDzizrdt0(xd) ) )
| ~ aElementOf0(tptp_fun_W1_0(sdtlbdtrb0(xd,szDzizrdt0(xd))),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W1_0(sdtlbdtrb0(xd,szDzizrdt0(xd)))) != szDzizrdt0(xd) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(321,plain,
( ~ ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != szDzizrdt0(xd) ) )
| ~ aElementOf0(tptp_fun_W1_0(sdtlbdtrb0(xd,szDzizrdt0(xd))),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W1_0(sdtlbdtrb0(xd,szDzizrdt0(xd)))) != szDzizrdt0(xd) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(322,plain,
( ~ ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != szDzizrdt0(xd) ) )
| ~ aElementOf0(tptp_fun_W1_0(sdtlbdtrb0(xd,szDzizrdt0(xd))),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W1_0(sdtlbdtrb0(xd,szDzizrdt0(xd)))) != szDzizrdt0(xd) ) ),
inference(modus_ponens,[status(thm)],[321,320]) ).
tff(323,plain,
$false,
inference(unit_resolution,[status(thm)],[322,319,219,169]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM597+1 : TPTP v9.0.0. Released v4.0.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n001.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 01:37:04 EDT 2025
% 0.12/0.34 % CPUTime :
% 262.23/262.43 % SZS status Theorem
% 262.23/262.43 % SZS output start Proof
% See solution above
% 263.16/263.39 % E exiting
%------------------------------------------------------------------------------