%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM566+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 05:21:25 AM UTC 2025
% Result : Theorem 1.97s 2.21s
% Output : Proof 2.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 76
% Syntax : Number of formulae : 195 ( 48 unt; 0 typ; 0 def)
% Number of atoms : 3054 ( 398 equ)
% Maximal formula atoms : 52 ( 15 avg)
% Number of connectives : 5435 (2752 ~;2055 |; 418 &)
% ( 137 <=>; 73 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 9 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 176 ( 176 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 22 ( 19 usr; 1 prp; 0-6 aty)
% Number of functors : 16 ( 16 usr; 7 con; 0-2 aty)
% Number of variables : 670 ( 599 !; 47 ?; 670 :)
% Comments :
%------------------------------------------------------------------------------
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(slbdtsldtrb0_type,type,
slbdtsldtrb0: ( $i * $i ) > $i ).
tff(sz00_type,type,
sz00: $i ).
tff(xS_type,type,
xS: $i ).
tff(tptp_fun_W2_30_type,type,
tptp_fun_W2_30: ( $i * $i ) > $i ).
tff(sdtlpdtrp0_type,type,
sdtlpdtrp0: ( $i * $i ) > $i ).
tff(slcrc0_type,type,
slcrc0: $i ).
tff(xc_type,type,
xc: $i ).
tff(tptp_fun_W1_19_type,type,
tptp_fun_W1_19: $i > $i ).
tff(aSet0_type,type,
aSet0: $i > $o ).
tff(aSubsetOf0_type,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff(sbrdtbr0_type,type,
sbrdtbr0: $i > $i ).
tff(xK_type,type,
xK: $i ).
tff(tptp_fun_W2_29_type,type,
tptp_fun_W2_29: $i > $i ).
tff(isCountable0_type,type,
isCountable0: $i > $o ).
tff(xT_type,type,
xT: $i ).
tff(sdtlcdtrc0_type,type,
sdtlcdtrc0: ( $i * $i ) > $i ).
tff(szDzozmdt0_type,type,
szDzozmdt0: $i > $i ).
tff(tptp_fun_W2_1_type,type,
tptp_fun_W2_1: ( $i * $i ) > $i ).
tff(isFinite0_type,type,
isFinite0: $i > $o ).
tff(aFunction0_type,type,
aFunction0: $i > $o ).
tff(szNzAzT0_type,type,
szNzAzT0: $i ).
tff(1,plain,
( aSet0(xT)
<=> aSet0(xT) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
( aSet0(xT)
& isFinite0(xT) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3291) ).
tff(3,plain,
aSet0(xT),
inference(and_elim,[status(thm)],[2]) ).
tff(4,plain,
aSet0(xT),
inference(modus_ponens,[status(thm)],[3,1]) ).
tff(5,plain,
^ [W0: $i] :
rewrite(( ( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(6,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[5]) ).
tff(7,plain,
^ [W0: $i] :
refl(( ( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
^ [W0: $i] :
rewrite(( ( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(10,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) ),
inference(quant_intro,[status(thm)],[9]) ).
tff(11,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) ),
inference(transitivity,[status(thm)],[10,8]) ).
tff(12,plain,
^ [W0: $i] :
rewrite(( ( ~ aSet0(W0)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,W0)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
& ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(13,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,W0)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
& ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) ),
inference(quant_intro,[status(thm)],[12]) ).
tff(14,plain,
^ [W0: $i] :
rewrite(( ( ~ aSet0(W0)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,W0)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
& ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,W0)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
& ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(15,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,W0)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
& ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,W0)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
& ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) ),
inference(quant_intro,[status(thm)],[14]) ).
tff(16,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(17,plain,
^ [W0: $i] :
trans(monotonicity(quant_intro(proof_bind(^ [W1: $i] :
rewrite(( ( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) ) ) )
<=> ( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ))),
( ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) ) ) )
<=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) )),
( ( aSet0(W0)
=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) ) ) ) )
<=> ( aSet0(W0)
=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )),
rewrite(( ( aSet0(W0)
=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )),
( ( aSet0(W0)
=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) ) ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(18,plain,
( ! [W0: $i] :
( aSet0(W0)
=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) ),
inference(quant_intro,[status(thm)],[17]) ).
tff(19,axiom,
! [W0: $i] :
( aSet0(W0)
=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSub) ).
tff(20,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ),
inference(modus_ponens,[status(thm)],[20,16]) ).
tff(22,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,W0)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
& ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ),
inference(skolemize,[status(sab)],[21]) ).
tff(23,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,W0)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
& ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ),
inference(modus_ponens,[status(thm)],[22,15]) ).
tff(24,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ),
inference(modus_ponens,[status(thm)],[23,13]) ).
tff(25,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ),
inference(modus_ponens,[status(thm)],[24,11]) ).
tff(26,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[25,6]) ).
tff(27,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(xT)
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(xT)
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(28,plain,
( ( ~ aSet0(xT)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,xT)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) ) )
<=> ( ~ aSet0(xT)
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(xT)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,xT)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(xT)
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[28]) ).
tff(30,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(xT)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,xT)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(xT)
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[29,27]) ).
tff(31,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(xT)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,xT)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(32,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(xT)
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) ),
inference(unit_resolution,[status(thm)],[32,26,4]) ).
tff(34,plain,
( ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) )
| ~ ( ~ ( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),xT) ) )
| ~ ( ~ aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| 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(xc,szDzozmdt0(xc)),xT)
| ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),xT) ) )
| ~ ( ~ aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,plain,
( ~ ( ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),xT) ) )
| ~ ( ~ aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ) ) )
<=> ~ ( ~ ( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),xT) ) )
| ~ ( ~ aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(36,plain,
( ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) )
| ~ ( ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),xT) ) )
| ~ ( ~ aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| 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(xc,szDzozmdt0(xc)),xT)
| ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),xT) ) )
| ~ ( ~ aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[35]) ).
tff(37,plain,
( ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) )
| ~ ( ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),xT) ) )
| ~ ( ~ aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| 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(xc,szDzozmdt0(xc)),xT)
| ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),xT) ) )
| ~ ( ~ aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[36,34]) ).
tff(38,plain,
( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) )
| ~ ( ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),xT) ) )
| ~ ( ~ aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(39,plain,
( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) )
| ~ ( ~ ( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),xT) ) )
| ~ ( ~ aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
~ ( ~ ( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),xT) ) )
| ~ ( ~ aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ) ) ),
inference(unit_resolution,[status(thm)],[39,33]) ).
tff(41,plain,
( ~ ( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),xT) ) )
| ~ ( ~ aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ) )
| ~ aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(42,plain,
( ~ aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ) ),
inference(unit_resolution,[status(thm)],[41,40]) ).
tff(43,plain,
( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
<=> aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT) ),
inference(rewrite,[status(thm)],[]) ).
tff(44,axiom,
( aFunction0(xc)
& ! [W0: $i] :
( ( aElementOf0(W0,szDzozmdt0(xc))
=> ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& ( sbrdtbr0(W0) = xK ) ) )
& ( ( ( ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) ) )
| aSubsetOf0(W0,xS) )
& ( sbrdtbr0(W0) = xK ) )
=> aElementOf0(W0,szDzozmdt0(xc)) ) )
& ( szDzozmdt0(xc) = slbdtsldtrb0(xS,xK) )
& aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
& ! [W0: $i] :
( aElementOf0(W0,sdtlcdtrc0(xc,szDzozmdt0(xc)))
<=> ? [W1: $i] :
( aElementOf0(W1,szDzozmdt0(xc))
& ( sdtlpdtrp0(xc,W1) = W0 ) ) )
& ! [W0: $i] :
( aElementOf0(W0,sdtlcdtrc0(xc,szDzozmdt0(xc)))
=> aElementOf0(W0,xT) )
& aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3453) ).
tff(45,plain,
aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),
inference(and_elim,[status(thm)],[44]) ).
tff(46,plain,
aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),
inference(modus_ponens,[status(thm)],[45,43]) ).
tff(47,plain,
( ~ ( ~ aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ) )
| ~ aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(48,plain,
( ~ ( ~ aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ) )
| ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ) ),
inference(unit_resolution,[status(thm)],[47,46]) ).
tff(49,plain,
~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ),
inference(unit_resolution,[status(thm)],[48,42]) ).
tff(50,plain,
( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) )
| ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ),
inference(tautology,[status(thm)],[]) ).
tff(51,plain,
! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ),
inference(unit_resolution,[status(thm)],[50,49]) ).
tff(52,plain,
( aFunction0(xc)
<=> aFunction0(xc) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,plain,
( aFunction0(xc)
& ! [W0: $i] :
( ( aElementOf0(W0,szDzozmdt0(xc))
=> ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& ( sbrdtbr0(W0) = xK ) ) )
& ( ( ( ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) ) )
| aSubsetOf0(W0,xS) )
& ( sbrdtbr0(W0) = xK ) )
=> aElementOf0(W0,szDzozmdt0(xc)) ) )
& ( szDzozmdt0(xc) = slbdtsldtrb0(xS,xK) )
& aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
& ! [W0: $i] :
( aElementOf0(W0,sdtlcdtrc0(xc,szDzozmdt0(xc)))
<=> ? [W1: $i] :
( aElementOf0(W1,szDzozmdt0(xc))
& ( sdtlpdtrp0(xc,W1) = W0 ) ) )
& ! [W0: $i] :
( aElementOf0(W0,sdtlcdtrc0(xc,szDzozmdt0(xc)))
=> aElementOf0(W0,xT) ) ),
inference(and_elim,[status(thm)],[44]) ).
tff(54,plain,
( aFunction0(xc)
& ! [W0: $i] :
( ( aElementOf0(W0,szDzozmdt0(xc))
=> ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& ( sbrdtbr0(W0) = xK ) ) )
& ( ( ( ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) ) )
| aSubsetOf0(W0,xS) )
& ( sbrdtbr0(W0) = xK ) )
=> aElementOf0(W0,szDzozmdt0(xc)) ) )
& ( szDzozmdt0(xc) = slbdtsldtrb0(xS,xK) )
& aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
& ! [W0: $i] :
( aElementOf0(W0,sdtlcdtrc0(xc,szDzozmdt0(xc)))
<=> ? [W1: $i] :
( aElementOf0(W1,szDzozmdt0(xc))
& ( sdtlpdtrp0(xc,W1) = W0 ) ) ) ),
inference(and_elim,[status(thm)],[53]) ).
tff(55,plain,
( aFunction0(xc)
& ! [W0: $i] :
( ( aElementOf0(W0,szDzozmdt0(xc))
=> ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& ( sbrdtbr0(W0) = xK ) ) )
& ( ( ( ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) ) )
| aSubsetOf0(W0,xS) )
& ( sbrdtbr0(W0) = xK ) )
=> aElementOf0(W0,szDzozmdt0(xc)) ) )
& ( szDzozmdt0(xc) = slbdtsldtrb0(xS,xK) )
& aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc))) ),
inference(and_elim,[status(thm)],[54]) ).
tff(56,plain,
( aFunction0(xc)
& ! [W0: $i] :
( ( aElementOf0(W0,szDzozmdt0(xc))
=> ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& ( sbrdtbr0(W0) = xK ) ) )
& ( ( ( ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) ) )
| aSubsetOf0(W0,xS) )
& ( sbrdtbr0(W0) = xK ) )
=> aElementOf0(W0,szDzozmdt0(xc)) ) )
& ( szDzozmdt0(xc) = slbdtsldtrb0(xS,xK) ) ),
inference(and_elim,[status(thm)],[55]) ).
tff(57,plain,
( aFunction0(xc)
& ! [W0: $i] :
( ( aElementOf0(W0,szDzozmdt0(xc))
=> ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& ( sbrdtbr0(W0) = xK ) ) )
& ( ( ( ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) ) )
| aSubsetOf0(W0,xS) )
& ( sbrdtbr0(W0) = xK ) )
=> aElementOf0(W0,szDzozmdt0(xc)) ) ) ),
inference(and_elim,[status(thm)],[56]) ).
tff(58,plain,
aFunction0(xc),
inference(and_elim,[status(thm)],[57]) ).
tff(59,plain,
aFunction0(xc),
inference(modus_ponens,[status(thm)],[58,52]) ).
tff(60,plain,
^ [W0: $i] :
refl(( ( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) )
<=> ( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ) )),
inference(bind,[status(th)],[]) ).
tff(61,plain,
( ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) )
<=> ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ) ),
inference(quant_intro,[status(thm)],[60]) ).
tff(62,plain,
^ [W0: $i] :
rewrite(( ( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) )
<=> ( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ) )),
inference(bind,[status(th)],[]) ).
tff(63,plain,
( ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) )
<=> ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ) ),
inference(quant_intro,[status(thm)],[62]) ).
tff(64,plain,
( ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) )
<=> ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ) ),
inference(transitivity,[status(thm)],[63,61]) ).
tff(65,plain,
( ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) )
<=> ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(66,plain,
^ [W0: $i] :
trans(monotonicity(quant_intro(proof_bind(^ [W1: $i] :
rewrite(( ( aElementOf0(W1,szDzozmdt0(W0))
=> aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) )
<=> ( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ))),
( ! [W1: $i] :
( aElementOf0(W1,szDzozmdt0(W0))
=> aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) )
<=> ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) )),
( ( aFunction0(W0)
=> ! [W1: $i] :
( aElementOf0(W1,szDzozmdt0(W0))
=> aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) )
<=> ( aFunction0(W0)
=> ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ) )),
rewrite(( ( aFunction0(W0)
=> ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) )
<=> ( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ) )),
( ( aFunction0(W0)
=> ! [W1: $i] :
( aElementOf0(W1,szDzozmdt0(W0))
=> aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) )
<=> ( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ) )),
inference(bind,[status(th)],[]) ).
tff(67,plain,
( ! [W0: $i] :
( aFunction0(W0)
=> ! [W1: $i] :
( aElementOf0(W1,szDzozmdt0(W0))
=> aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) )
<=> ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ) ),
inference(quant_intro,[status(thm)],[66]) ).
tff(68,axiom,
! [W0: $i] :
( aFunction0(W0)
=> ! [W1: $i] :
( aElementOf0(W1,szDzozmdt0(W0))
=> aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mImgRng) ).
tff(69,plain,
! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ),
inference(modus_ponens,[status(thm)],[68,67]) ).
tff(70,plain,
! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ),
inference(modus_ponens,[status(thm)],[69,65]) ).
tff(71,plain,
! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ),
inference(skolemize,[status(sab)],[70]) ).
tff(72,plain,
! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ),
inference(modus_ponens,[status(thm)],[71,64]) ).
tff(73,plain,
( ( ~ ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) )
| ~ aFunction0(xc)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(xc))
| aElementOf0(sdtlpdtrp0(xc,W1),sdtlcdtrc0(xc,szDzozmdt0(xc))) ) )
<=> ( ~ ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) )
| ~ aFunction0(xc)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(xc))
| aElementOf0(sdtlpdtrp0(xc,W1),sdtlcdtrc0(xc,szDzozmdt0(xc))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(74,plain,
( ~ ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) )
| ~ aFunction0(xc)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(xc))
| aElementOf0(sdtlpdtrp0(xc,W1),sdtlcdtrc0(xc,szDzozmdt0(xc))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(75,plain,
( ~ ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) )
| ~ aFunction0(xc)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(xc))
| aElementOf0(sdtlpdtrp0(xc,W1),sdtlcdtrc0(xc,szDzozmdt0(xc))) ) ),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(xc))
| aElementOf0(sdtlpdtrp0(xc,W1),sdtlcdtrc0(xc,szDzozmdt0(xc))) ),
inference(unit_resolution,[status(thm)],[75,72,59]) ).
tff(77,plain,
( ( xK = sz00 )
<=> ( xK = sz00 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(78,axiom,
xK = sz00,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3462) ).
tff(79,plain,
xK = sz00,
inference(modus_ponens,[status(thm)],[78,77]) ).
tff(80,plain,
sz00 = xK,
inference(symmetry,[status(thm)],[79]) ).
tff(81,plain,
slbdtsldtrb0(xS,sz00) = slbdtsldtrb0(xS,xK),
inference(monotonicity,[status(thm)],[80]) ).
tff(82,plain,
slbdtsldtrb0(xS,xK) = slbdtsldtrb0(xS,sz00),
inference(symmetry,[status(thm)],[81]) ).
tff(83,plain,
( ( szDzozmdt0(xc) = slbdtsldtrb0(xS,xK) )
<=> ( szDzozmdt0(xc) = slbdtsldtrb0(xS,xK) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(84,plain,
szDzozmdt0(xc) = slbdtsldtrb0(xS,xK),
inference(and_elim,[status(thm)],[56]) ).
tff(85,plain,
szDzozmdt0(xc) = slbdtsldtrb0(xS,xK),
inference(modus_ponens,[status(thm)],[84,83]) ).
tff(86,plain,
szDzozmdt0(xc) = slbdtsldtrb0(xS,sz00),
inference(transitivity,[status(thm)],[85,82]) ).
tff(87,plain,
( aElementOf0(slcrc0,szDzozmdt0(xc))
<=> aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)) ),
inference(monotonicity,[status(thm)],[86]) ).
tff(88,plain,
( aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00))
<=> aElementOf0(slcrc0,szDzozmdt0(xc)) ),
inference(symmetry,[status(thm)],[87]) ).
tff(89,plain,
( aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00))
<=> aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)) ),
inference(rewrite,[status(thm)],[]) ).
tff(90,axiom,
( aSet0(slcrc0)
& ~ ? [W0: $i] : aElementOf0(W0,slcrc0)
& ! [W0: $i] :
( aElementOf0(W0,slcrc0)
=> aElementOf0(W0,xS) )
& aSubsetOf0(slcrc0,xS)
& aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3476) ).
tff(91,plain,
aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)),
inference(and_elim,[status(thm)],[90]) ).
tff(92,plain,
aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)),
inference(modus_ponens,[status(thm)],[91,89]) ).
tff(93,plain,
aElementOf0(slcrc0,szDzozmdt0(xc)),
inference(modus_ponens,[status(thm)],[92,88]) ).
tff(94,plain,
( ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(xc))
| aElementOf0(sdtlpdtrp0(xc,W1),sdtlcdtrc0(xc,szDzozmdt0(xc))) )
| ~ aElementOf0(slcrc0,szDzozmdt0(xc))
| aElementOf0(sdtlpdtrp0(xc,slcrc0),sdtlcdtrc0(xc,szDzozmdt0(xc))) )
<=> ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(xc))
| aElementOf0(sdtlpdtrp0(xc,W1),sdtlcdtrc0(xc,szDzozmdt0(xc))) )
| ~ aElementOf0(slcrc0,szDzozmdt0(xc))
| aElementOf0(sdtlpdtrp0(xc,slcrc0),sdtlcdtrc0(xc,szDzozmdt0(xc))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(95,plain,
( ~ ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(xc))
| aElementOf0(sdtlpdtrp0(xc,W1),sdtlcdtrc0(xc,szDzozmdt0(xc))) )
| ~ aElementOf0(slcrc0,szDzozmdt0(xc))
| aElementOf0(sdtlpdtrp0(xc,slcrc0),sdtlcdtrc0(xc,szDzozmdt0(xc))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(96,plain,
( ~ ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(xc))
| aElementOf0(sdtlpdtrp0(xc,W1),sdtlcdtrc0(xc,szDzozmdt0(xc))) )
| ~ aElementOf0(slcrc0,szDzozmdt0(xc))
| aElementOf0(sdtlpdtrp0(xc,slcrc0),sdtlcdtrc0(xc,szDzozmdt0(xc))) ),
inference(modus_ponens,[status(thm)],[95,94]) ).
tff(97,plain,
aElementOf0(sdtlpdtrp0(xc,slcrc0),sdtlcdtrc0(xc,szDzozmdt0(xc))),
inference(unit_resolution,[status(thm)],[96,93,76]) ).
tff(98,plain,
( ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) )
| ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(sdtlpdtrp0(xc,slcrc0),xT) )
<=> ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) )
| ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(sdtlpdtrp0(xc,slcrc0),xT) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(99,plain,
( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) )
| ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(sdtlpdtrp0(xc,slcrc0),xT) ),
inference(quant_inst,[status(thm)],[]) ).
tff(100,plain,
( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) )
| ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(sdtlpdtrp0(xc,slcrc0),xT) ),
inference(modus_ponens,[status(thm)],[99,98]) ).
tff(101,plain,
aElementOf0(sdtlpdtrp0(xc,slcrc0),xT),
inference(unit_resolution,[status(thm)],[100,97,51]) ).
tff(102,plain,
^ [W0: $i] :
rewrite(( ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_30(W1,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) )
| ~ aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK)) ) ) )
<=> ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_30(W1,W0))
| ~ aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(103,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_30(W1,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) )
| ~ aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK)) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_30(W1,W0))
| ~ aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) ) ) ) ) ),
inference(quant_intro,[status(thm)],[102]) ).
tff(104,plain,
^ [W0: $i] :
refl(( ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_30(W1,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) )
| ~ aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK)) ) ) )
<=> ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_30(W1,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) )
| ~ aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(105,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_30(W1,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) )
| ~ aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK)) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_30(W1,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) )
| ~ aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK)) ) ) ) ),
inference(quant_intro,[status(thm)],[104]) ).
tff(106,plain,
^ [W0: $i] :
rewrite(( ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_30(W1,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) )
| ~ aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK)) ) ) )
<=> ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_30(W1,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) )
| ~ aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(107,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_30(W1,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) )
| ~ aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK)) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_30(W1,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) )
| ~ aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK)) ) ) ) ),
inference(quant_intro,[status(thm)],[106]) ).
tff(108,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_30(W1,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) )
| ~ aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK)) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_30(W1,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) )
| ~ aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK)) ) ) ) ),
inference(transitivity,[status(thm)],[107,105]) ).
tff(109,plain,
^ [W0: $i] :
rewrite(( ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ( ~ aSubsetOf0(W1,xS)
& ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ( aSet0(tptp_fun_W2_30(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) = xK )
& aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK))
& ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) != W0 ) ) ) )
<=> ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_30(W1,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) )
| ~ aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(110,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ( ~ aSubsetOf0(W1,xS)
& ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ( aSet0(tptp_fun_W2_30(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) = xK )
& aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK))
& ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) != W0 ) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_30(W1,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) )
| ~ aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK)) ) ) ) ),
inference(quant_intro,[status(thm)],[109]) ).
tff(111,plain,
^ [W0: $i] :
rewrite(( ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,xS)
& ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ isCountable0(W1)
| ( aSet0(tptp_fun_W2_30(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) = xK )
& aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK))
& ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) != W0 ) ) ) )
<=> ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ( ~ aSubsetOf0(W1,xS)
& ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ( aSet0(tptp_fun_W2_30(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) = xK )
& aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK))
& ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) != W0 ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(112,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,xS)
& ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ isCountable0(W1)
| ( aSet0(tptp_fun_W2_30(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) = xK )
& aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK))
& ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) != W0 ) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ( ~ aSubsetOf0(W1,xS)
& ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ( aSet0(tptp_fun_W2_30(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) = xK )
& aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK))
& ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) != W0 ) ) ) ) ),
inference(quant_intro,[status(thm)],[111]) ).
tff(113,plain,
( ~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( ( aSubsetOf0(W1,xS)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xS) ) ) )
& isCountable0(W1)
& ! [W2: $i] :
( ~ ( aSet0(W2)
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) )
& aSubsetOf0(W2,W1)
& ( sbrdtbr0(W2) = xK )
& aElementOf0(W2,slbdtsldtrb0(W1,xK)) )
| ( sdtlpdtrp0(xc,W2) = W0 ) ) ) )
<=> ~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( ( aSubsetOf0(W1,xS)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xS) ) ) )
& isCountable0(W1)
& ! [W2: $i] :
( ~ ( aSet0(W2)
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) )
& aSubsetOf0(W2,W1)
& ( sbrdtbr0(W2) = xK )
& aElementOf0(W2,slbdtsldtrb0(W1,xK)) )
| ( sdtlpdtrp0(xc,W2) = W0 ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(114,plain,
( ~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( ( ( aSet0(W1)
& ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,xS) ) )
| aSubsetOf0(W1,xS) )
& isCountable0(W1)
& ! [W2: $i] :
( ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
=> aElementOf0(W3,W1) )
& aSubsetOf0(W2,W1)
& ( sbrdtbr0(W2) = xK )
& aElementOf0(W2,slbdtsldtrb0(W1,xK)) )
=> ( sdtlpdtrp0(xc,W2) = W0 ) ) ) )
<=> ~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( ( aSubsetOf0(W1,xS)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xS) ) ) )
& isCountable0(W1)
& ! [W2: $i] :
( ~ ( aSet0(W2)
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) )
& aSubsetOf0(W2,W1)
& ( sbrdtbr0(W2) = xK )
& aElementOf0(W2,slbdtsldtrb0(W1,xK)) )
| ( sdtlpdtrp0(xc,W2) = W0 ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(115,axiom,
~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( ( ( aSet0(W1)
& ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,xS) ) )
| aSubsetOf0(W1,xS) )
& isCountable0(W1)
& ! [W2: $i] :
( ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
=> aElementOf0(W3,W1) )
& aSubsetOf0(W2,W1)
& ( sbrdtbr0(W2) = xK )
& aElementOf0(W2,slbdtsldtrb0(W1,xK)) )
=> ( sdtlpdtrp0(xc,W2) = W0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(116,plain,
~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( ( aSubsetOf0(W1,xS)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xS) ) ) )
& isCountable0(W1)
& ! [W2: $i] :
( ~ ( aSet0(W2)
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) )
& aSubsetOf0(W2,W1)
& ( sbrdtbr0(W2) = xK )
& aElementOf0(W2,slbdtsldtrb0(W1,xK)) )
| ( sdtlpdtrp0(xc,W2) = W0 ) ) ) ),
inference(modus_ponens,[status(thm)],[115,114]) ).
tff(117,plain,
~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( ( aSubsetOf0(W1,xS)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xS) ) ) )
& isCountable0(W1)
& ! [W2: $i] :
( ~ ( aSet0(W2)
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) )
& aSubsetOf0(W2,W1)
& ( sbrdtbr0(W2) = xK )
& aElementOf0(W2,slbdtsldtrb0(W1,xK)) )
| ( sdtlpdtrp0(xc,W2) = W0 ) ) ) ),
inference(modus_ponens,[status(thm)],[116,113]) ).
tff(118,plain,
~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( ( aSubsetOf0(W1,xS)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xS) ) ) )
& isCountable0(W1)
& ! [W2: $i] :
( ~ ( aSet0(W2)
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) )
& aSubsetOf0(W2,W1)
& ( sbrdtbr0(W2) = xK )
& aElementOf0(W2,slbdtsldtrb0(W1,xK)) )
| ( sdtlpdtrp0(xc,W2) = W0 ) ) ) ),
inference(modus_ponens,[status(thm)],[117,113]) ).
tff(119,plain,
~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( ( aSubsetOf0(W1,xS)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xS) ) ) )
& isCountable0(W1)
& ! [W2: $i] :
( ~ ( aSet0(W2)
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) )
& aSubsetOf0(W2,W1)
& ( sbrdtbr0(W2) = xK )
& aElementOf0(W2,slbdtsldtrb0(W1,xK)) )
| ( sdtlpdtrp0(xc,W2) = W0 ) ) ) ),
inference(modus_ponens,[status(thm)],[118,113]) ).
tff(120,plain,
^ [W0: $i] :
nnf_neg(refl($oeq(~ aElementOf0(W0,xT),~ aElementOf0(W0,xT))),
nnf_neg(proof_bind(^ [W1: $i] :
nnf_neg(nnf_neg(refl($oeq(~ aSubsetOf0(W1,xS),~ aSubsetOf0(W1,xS))),
nnf_neg(refl($oeq(~ aSet0(W1),~ aSet0(W1))),
sk($oeq(~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xS) ),
~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ))),
$oeq(~ ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xS) ) ),
( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ))),
$oeq(~ ( aSubsetOf0(W1,xS)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xS) ) ) ),
( ~ aSubsetOf0(W1,xS)
& ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) ))),refl($oeq(~ isCountable0(W1),~ isCountable0(W1))),
trans(sk($oeq(~ ! [W2: $i] :
( ~ ( aSet0(W2)
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) )
& aSubsetOf0(W2,W1)
& ( sbrdtbr0(W2) = xK )
& aElementOf0(W2,slbdtsldtrb0(W1,xK)) )
| ( sdtlpdtrp0(xc,W2) = W0 ) ),
~ ( ~ ( aSet0(tptp_fun_W2_30(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) = xK )
& aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK)) )
| ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) = W0 ) ))),
nnf_neg(nnf_neg(monotonicity(refl($oeq(aSet0(tptp_fun_W2_30(W1,W0)),aSet0(tptp_fun_W2_30(W1,W0)))),
nnf_pos(proof_bind(^ [W3: $i] :
refl($oeq(( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) ),
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) )))),
$oeq(! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) ),
! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) ))),
refl($oeq(aSubsetOf0(tptp_fun_W2_30(W1,W0),W1),aSubsetOf0(tptp_fun_W2_30(W1,W0),W1))),refl($oeq(sbrdtbr0(tptp_fun_W2_30(W1,W0)) = xK,sbrdtbr0(tptp_fun_W2_30(W1,W0)) = xK)),refl($oeq(aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK)),aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK)))),
$oeq(( aSet0(tptp_fun_W2_30(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) = xK )
& aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK)) ),
( aSet0(tptp_fun_W2_30(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) = xK )
& aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK)) ))),
$oeq(~ ~ ( aSet0(tptp_fun_W2_30(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) = xK )
& aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK)) ),
( aSet0(tptp_fun_W2_30(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) = xK )
& aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK)) ))),refl($oeq(sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) != W0,sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) != W0)),
$oeq(~ ( ~ ( aSet0(tptp_fun_W2_30(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) = xK )
& aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK)) )
| ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) = W0 ) ),
( aSet0(tptp_fun_W2_30(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) = xK )
& aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK))
& ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) != W0 ) ))),
$oeq(~ ! [W2: $i] :
( ~ ( aSet0(W2)
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) )
& aSubsetOf0(W2,W1)
& ( sbrdtbr0(W2) = xK )
& aElementOf0(W2,slbdtsldtrb0(W1,xK)) )
| ( sdtlpdtrp0(xc,W2) = W0 ) ),
( aSet0(tptp_fun_W2_30(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) = xK )
& aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK))
& ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) != W0 ) ))),
$oeq(~ ( ( aSubsetOf0(W1,xS)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xS) ) ) )
& isCountable0(W1)
& ! [W2: $i] :
( ~ ( aSet0(W2)
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) )
& aSubsetOf0(W2,W1)
& ( sbrdtbr0(W2) = xK )
& aElementOf0(W2,slbdtsldtrb0(W1,xK)) )
| ( sdtlpdtrp0(xc,W2) = W0 ) ) ),
( ( ~ aSubsetOf0(W1,xS)
& ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ isCountable0(W1)
| ( aSet0(tptp_fun_W2_30(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) = xK )
& aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK))
& ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) != W0 ) ) )))),
$oeq(~ ? [W1: $i] :
( ( aSubsetOf0(W1,xS)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xS) ) ) )
& isCountable0(W1)
& ! [W2: $i] :
( ~ ( aSet0(W2)
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) )
& aSubsetOf0(W2,W1)
& ( sbrdtbr0(W2) = xK )
& aElementOf0(W2,slbdtsldtrb0(W1,xK)) )
| ( sdtlpdtrp0(xc,W2) = W0 ) ) ),
! [W1: $i] :
( ( ~ aSubsetOf0(W1,xS)
& ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ isCountable0(W1)
| ( aSet0(tptp_fun_W2_30(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) = xK )
& aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK))
& ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) != W0 ) ) ))),
$oeq(~ ( aElementOf0(W0,xT)
& ? [W1: $i] :
( ( aSubsetOf0(W1,xS)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xS) ) ) )
& isCountable0(W1)
& ! [W2: $i] :
( ~ ( aSet0(W2)
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) )
& aSubsetOf0(W2,W1)
& ( sbrdtbr0(W2) = xK )
& aElementOf0(W2,slbdtsldtrb0(W1,xK)) )
| ( sdtlpdtrp0(xc,W2) = W0 ) ) ) ),
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,xS)
& ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ isCountable0(W1)
| ( aSet0(tptp_fun_W2_30(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) = xK )
& aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK))
& ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) != W0 ) ) ) ))),
inference(bind,[status(th)],[]) ).
tff(121,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,xS)
& ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ isCountable0(W1)
| ( aSet0(tptp_fun_W2_30(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) = xK )
& aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK))
& ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) != W0 ) ) ) ),
inference(nnf-neg,[status(sab)],[119,120]) ).
tff(122,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ( ~ aSubsetOf0(W1,xS)
& ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ( aSet0(tptp_fun_W2_30(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) = xK )
& aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK))
& ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) != W0 ) ) ) ),
inference(modus_ponens,[status(thm)],[121,112]) ).
tff(123,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_30(W1,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) )
| ~ aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK)) ) ) ),
inference(modus_ponens,[status(thm)],[122,110]) ).
tff(124,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_30(W1,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) )
| ~ aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK)) ) ) ),
inference(modus_ponens,[status(thm)],[123,108]) ).
tff(125,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_30(W1,W0))
| ~ aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) ) ) ) ),
inference(modus_ponens,[status(thm)],[124,103]) ).
tff(126,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_30(W1,W0))
| ~ aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) ) ) ) )
| ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W3,W1) )
| ~ aElementOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(W1,xK))
| ( sbrdtbr0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) != xK )
| ~ aSubsetOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),W1)
| ~ aSet0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_30(W1,W0))
| ~ aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) ) ) ) )
| ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W3,W1) )
| ~ aElementOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(W1,xK))
| ( sbrdtbr0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) != xK )
| ~ aSubsetOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),W1)
| ~ aSet0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(127,plain,
( ( ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) )
| ~ aSet0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| ~ aSubsetOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),W1)
| ( sbrdtbr0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) != xK )
| ~ aElementOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(W1,xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W3,W1) ) ) ) )
<=> ( ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W3,W1) )
| ~ aElementOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(W1,xK))
| ( sbrdtbr0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) != xK )
| ~ aSubsetOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),W1)
| ~ aSet0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(128,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_30(W1,W0))
| ~ aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) ) ) ) )
| ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) )
| ~ aSet0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| ~ aSubsetOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),W1)
| ( sbrdtbr0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) != xK )
| ~ aElementOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(W1,xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W3,W1) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_30(W1,W0))
| ~ aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) ) ) ) )
| ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W3,W1) )
| ~ aElementOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(W1,xK))
| ( sbrdtbr0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) != xK )
| ~ aSubsetOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),W1)
| ~ aSet0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) ) ) ) ) ),
inference(monotonicity,[status(thm)],[127]) ).
tff(129,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_30(W1,W0))
| ~ aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) ) ) ) )
| ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) )
| ~ aSet0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| ~ aSubsetOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),W1)
| ( sbrdtbr0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) != xK )
| ~ aElementOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(W1,xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W3,W1) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_30(W1,W0))
| ~ aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) ) ) ) )
| ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W3,W1) )
| ~ aElementOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(W1,xK))
| ( sbrdtbr0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) != xK )
| ~ aSubsetOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),W1)
| ~ aSet0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) ) ) ) ) ),
inference(transitivity,[status(thm)],[128,126]) ).
tff(130,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_30(W1,W0))
| ~ aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) ) ) ) )
| ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) )
| ~ aSet0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| ~ aSubsetOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),W1)
| ( sbrdtbr0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) != xK )
| ~ aElementOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(W1,xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W3,W1) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(131,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_30(W1,W0))
| ~ aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) ) ) ) )
| ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W3,W1) )
| ~ aElementOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(W1,xK))
| ( sbrdtbr0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) != xK )
| ~ aSubsetOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),W1)
| ~ aSet0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) ) ) ) ),
inference(modus_ponens,[status(thm)],[130,129]) ).
tff(132,plain,
! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W3,W1) )
| ~ aElementOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(W1,xK))
| ( sbrdtbr0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) != xK )
| ~ aSubsetOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),W1)
| ~ aSet0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) ) ) ),
inference(unit_resolution,[status(thm)],[131,125,101]) ).
tff(133,plain,
( aSet0(xS)
<=> aSet0(xS) ),
inference(rewrite,[status(thm)],[]) ).
tff(134,axiom,
( aSet0(xS)
& ! [W0: $i] :
( aElementOf0(W0,xS)
=> aElementOf0(W0,szNzAzT0) )
& aSubsetOf0(xS,szNzAzT0)
& isCountable0(xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3435) ).
tff(135,plain,
( aSet0(xS)
& ! [W0: $i] :
( aElementOf0(W0,xS)
=> aElementOf0(W0,szNzAzT0) )
& aSubsetOf0(xS,szNzAzT0) ),
inference(and_elim,[status(thm)],[134]) ).
tff(136,plain,
( aSet0(xS)
& ! [W0: $i] :
( aElementOf0(W0,xS)
=> aElementOf0(W0,szNzAzT0) ) ),
inference(and_elim,[status(thm)],[135]) ).
tff(137,plain,
aSet0(xS),
inference(and_elim,[status(thm)],[136]) ).
tff(138,plain,
aSet0(xS),
inference(modus_ponens,[status(thm)],[137,133]) ).
tff(139,plain,
( aSet0(xS)
| aSubsetOf0(xS,xS)
| ~ aSet0(xS) ),
inference(tautology,[status(thm)],[]) ).
tff(140,plain,
( aSet0(xS)
| aSubsetOf0(xS,xS) ),
inference(unit_resolution,[status(thm)],[139,138]) ).
tff(141,plain,
( isCountable0(xS)
<=> isCountable0(xS) ),
inference(rewrite,[status(thm)],[]) ).
tff(142,plain,
isCountable0(xS),
inference(and_elim,[status(thm)],[134]) ).
tff(143,plain,
isCountable0(xS),
inference(modus_ponens,[status(thm)],[142,141]) ).
tff(144,plain,
( ( ~ ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W3,W1) )
| ~ aElementOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(W1,xK))
| ( sbrdtbr0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) != xK )
| ~ aSubsetOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),W1)
| ~ aSet0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) ) ) )
| ~ isCountable0(xS)
| ~ ( aSet0(xS)
| aSubsetOf0(xS,xS) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) )
| ~ aSet0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| ~ aSubsetOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),xS)
| ( sbrdtbr0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) != xK )
| ~ aElementOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(xS,xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W3,xS) ) ) )
<=> ( ~ ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W3,W1) )
| ~ aElementOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(W1,xK))
| ( sbrdtbr0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) != xK )
| ~ aSubsetOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),W1)
| ~ aSet0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) ) ) )
| ~ isCountable0(xS)
| ~ ( aSet0(xS)
| aSubsetOf0(xS,xS) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) )
| ~ aSet0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| ~ aSubsetOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),xS)
| ( sbrdtbr0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) != xK )
| ~ aElementOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(xS,xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W3,xS) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(145,plain,
( ( ~ isCountable0(xS)
| ~ ( aSubsetOf0(xS,xS)
| ~ ( ~ aSet0(xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(xS),xS)
| aElementOf0(tptp_fun_W2_29(xS),xS) ) ) )
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W3,xS) )
| ~ aElementOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(xS,xK))
| ( sbrdtbr0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) != xK )
| ~ aSubsetOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),xS)
| ~ aSet0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) ) ) )
<=> ( ~ isCountable0(xS)
| ~ ( aSet0(xS)
| aSubsetOf0(xS,xS) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) )
| ~ aSet0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| ~ aSubsetOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),xS)
| ( sbrdtbr0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) != xK )
| ~ aElementOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(xS,xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W3,xS) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(146,plain,
( ( ~ ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W3,W1) )
| ~ aElementOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(W1,xK))
| ( sbrdtbr0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) != xK )
| ~ aSubsetOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),W1)
| ~ aSet0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) ) ) )
| ~ isCountable0(xS)
| ~ ( aSubsetOf0(xS,xS)
| ~ ( ~ aSet0(xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(xS),xS)
| aElementOf0(tptp_fun_W2_29(xS),xS) ) ) )
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W3,xS) )
| ~ aElementOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(xS,xK))
| ( sbrdtbr0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) != xK )
| ~ aSubsetOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),xS)
| ~ aSet0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) ) ) )
<=> ( ~ ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W3,W1) )
| ~ aElementOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(W1,xK))
| ( sbrdtbr0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) != xK )
| ~ aSubsetOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),W1)
| ~ aSet0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) ) ) )
| ~ isCountable0(xS)
| ~ ( aSet0(xS)
| aSubsetOf0(xS,xS) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) )
| ~ aSet0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| ~ aSubsetOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),xS)
| ( sbrdtbr0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) != xK )
| ~ aElementOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(xS,xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W3,xS) ) ) ) ),
inference(monotonicity,[status(thm)],[145]) ).
tff(147,plain,
( ( ~ ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W3,W1) )
| ~ aElementOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(W1,xK))
| ( sbrdtbr0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) != xK )
| ~ aSubsetOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),W1)
| ~ aSet0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) ) ) )
| ~ isCountable0(xS)
| ~ ( aSubsetOf0(xS,xS)
| ~ ( ~ aSet0(xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(xS),xS)
| aElementOf0(tptp_fun_W2_29(xS),xS) ) ) )
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W3,xS) )
| ~ aElementOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(xS,xK))
| ( sbrdtbr0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) != xK )
| ~ aSubsetOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),xS)
| ~ aSet0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) ) ) )
<=> ( ~ ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W3,W1) )
| ~ aElementOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(W1,xK))
| ( sbrdtbr0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) != xK )
| ~ aSubsetOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),W1)
| ~ aSet0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) ) ) )
| ~ isCountable0(xS)
| ~ ( aSet0(xS)
| aSubsetOf0(xS,xS) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) )
| ~ aSet0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| ~ aSubsetOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),xS)
| ( sbrdtbr0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) != xK )
| ~ aElementOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(xS,xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W3,xS) ) ) ) ),
inference(transitivity,[status(thm)],[146,144]) ).
tff(148,plain,
( ~ ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W3,W1) )
| ~ aElementOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(W1,xK))
| ( sbrdtbr0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) != xK )
| ~ aSubsetOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),W1)
| ~ aSet0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) ) ) )
| ~ isCountable0(xS)
| ~ ( aSubsetOf0(xS,xS)
| ~ ( ~ aSet0(xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(xS),xS)
| aElementOf0(tptp_fun_W2_29(xS),xS) ) ) )
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W3,xS) )
| ~ aElementOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(xS,xK))
| ( sbrdtbr0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) != xK )
| ~ aSubsetOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),xS)
| ~ aSet0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(149,plain,
( ~ ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W3,W1) )
| ~ aElementOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(W1,xK))
| ( sbrdtbr0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) != xK )
| ~ aSubsetOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),W1)
| ~ aSet0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) ) ) )
| ~ isCountable0(xS)
| ~ ( aSet0(xS)
| aSubsetOf0(xS,xS) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) )
| ~ aSet0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| ~ aSubsetOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),xS)
| ( sbrdtbr0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) != xK )
| ~ aElementOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(xS,xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W3,xS) ) ) ),
inference(modus_ponens,[status(thm)],[148,147]) ).
tff(150,plain,
~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) )
| ~ aSet0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| ~ aSubsetOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),xS)
| ( sbrdtbr0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) != xK )
| ~ aElementOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(xS,xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W3,xS) ) ),
inference(unit_resolution,[status(thm)],[149,143,140,132]) ).
tff(151,plain,
( ( sdtlpdtrp0(xc,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) )
| ~ aSet0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| ~ aSubsetOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),xS)
| ( sbrdtbr0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) != xK )
| ~ aElementOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(xS,xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W3,xS) )
| aSubsetOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),xS) ),
inference(tautology,[status(thm)],[]) ).
tff(152,plain,
aSubsetOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),xS),
inference(unit_resolution,[status(thm)],[151,150]) ).
tff(153,plain,
( aSubsetOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),xS)
| ~ ( ~ aSet0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| ~ ( ~ aElementOf0(tptp_fun_W1_19(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))),tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(tptp_fun_W1_19(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))),xS) ) )
| ~ aSubsetOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),xS) ),
inference(tautology,[status(thm)],[]) ).
tff(154,plain,
( aSubsetOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),xS)
| ~ ( ~ aSet0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| ~ ( ~ aElementOf0(tptp_fun_W1_19(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))),tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(tptp_fun_W1_19(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))),xS) ) ) ),
inference(unit_resolution,[status(thm)],[153,152]) ).
tff(155,plain,
( ( sdtlpdtrp0(xc,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) )
| ~ aSet0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| ~ aSubsetOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),xS)
| ( sbrdtbr0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) != xK )
| ~ aElementOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(xS,xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W3,xS) )
| ( sbrdtbr0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) = xK ) ),
inference(tautology,[status(thm)],[]) ).
tff(156,plain,
sbrdtbr0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) = xK,
inference(unit_resolution,[status(thm)],[155,150]) ).
tff(157,plain,
sbrdtbr0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) = sz00,
inference(transitivity,[status(thm)],[156,79]) ).
tff(158,plain,
( ~ ( ( sbrdtbr0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) != sz00 )
| ~ ( aSubsetOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),xS)
| ~ ( ~ aSet0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| ~ ( ~ aElementOf0(tptp_fun_W1_19(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))),tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(tptp_fun_W1_19(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))),xS) ) ) ) )
| ( sbrdtbr0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) != sz00 )
| ~ ( aSubsetOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),xS)
| ~ ( ~ aSet0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| ~ ( ~ aElementOf0(tptp_fun_W1_19(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))),tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(tptp_fun_W1_19(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))),xS) ) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(159,plain,
~ ( ( sbrdtbr0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) != sz00 )
| ~ ( aSubsetOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),xS)
| ~ ( ~ aSet0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| ~ ( ~ aElementOf0(tptp_fun_W1_19(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))),tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(tptp_fun_W1_19(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))),xS) ) ) ) ),
inference(unit_resolution,[status(thm)],[158,157,154]) ).
tff(160,plain,
( ~ ( ( sbrdtbr0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) != sz00 )
| ~ ( aSubsetOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),xS)
| ~ ( ~ aSet0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| ~ ( ~ aElementOf0(tptp_fun_W1_19(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))),tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(tptp_fun_W1_19(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))),xS) ) ) ) )
| aElementOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(xS,sz00))
| ( sbrdtbr0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) != sz00 )
| ~ ( aSubsetOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),xS)
| ~ ( ~ aSet0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| ~ ( ~ aElementOf0(tptp_fun_W1_19(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))),tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(tptp_fun_W1_19(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))),xS) ) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(161,plain,
( ~ ( ( sbrdtbr0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) != sz00 )
| ~ ( aSubsetOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),xS)
| ~ ( ~ aSet0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| ~ ( ~ aElementOf0(tptp_fun_W1_19(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))),tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(tptp_fun_W1_19(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))),xS) ) ) ) )
| aElementOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(xS,sz00)) ),
inference(unit_resolution,[status(thm)],[160,159]) ).
tff(162,plain,
( ( sdtlpdtrp0(xc,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) )
| ~ aSet0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| ~ aSubsetOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),xS)
| ( sbrdtbr0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) != xK )
| ~ aElementOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(xS,xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W3,xS) )
| ( sdtlpdtrp0(xc,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) != sdtlpdtrp0(xc,slcrc0) ) ),
inference(tautology,[status(thm)],[]) ).
tff(163,plain,
sdtlpdtrp0(xc,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) != sdtlpdtrp0(xc,slcrc0),
inference(unit_resolution,[status(thm)],[162,150]) ).
tff(164,plain,
( ~ aSet0(slcrc0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,slcrc0)
| ( sdtlpdtrp0(xc,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) != sdtlpdtrp0(xc,slcrc0) )
| ( sdtlpdtrp0(xc,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) ) ),
inference(tautology,[status(thm)],[]) ).
tff(165,plain,
( ~ aSet0(slcrc0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,slcrc0)
| ( sdtlpdtrp0(xc,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) != sdtlpdtrp0(xc,slcrc0) ) ),
inference(unit_resolution,[status(thm)],[164,163]) ).
tff(166,plain,
^ [W0: $i] :
trans(monotonicity(rewrite(( ~ ( aElementOf0(W0,slbdtsldtrb0(xS,sz00))
| ~ ( ( sbrdtbr0(W0) != sz00 )
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) ) )
<=> ~ ( aElementOf0(W0,slbdtsldtrb0(xS,sz00))
| ~ ( ( sbrdtbr0(W0) != sz00 )
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) ) ) )),
rewrite(( ~ ( ~ aSet0(slcrc0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,slcrc0)
| ( sdtlpdtrp0(xc,W0) != sdtlpdtrp0(xc,slcrc0) ) )
<=> ~ ( ~ aSet0(slcrc0)
| ( sdtlpdtrp0(xc,W0) != sdtlpdtrp0(xc,slcrc0) )
| ~ ! [W1: $i] : ~ aElementOf0(W1,slcrc0) ) )),
( ( ~ ( aElementOf0(W0,slbdtsldtrb0(xS,sz00))
| ~ ( ( sbrdtbr0(W0) != sz00 )
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) ) )
| ~ ( ~ aSet0(slcrc0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,slcrc0)
| ( sdtlpdtrp0(xc,W0) != sdtlpdtrp0(xc,slcrc0) ) ) )
<=> ( ~ ( aElementOf0(W0,slbdtsldtrb0(xS,sz00))
| ~ ( ( sbrdtbr0(W0) != sz00 )
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) ) )
| ~ ( ~ aSet0(slcrc0)
| ( sdtlpdtrp0(xc,W0) != sdtlpdtrp0(xc,slcrc0) )
| ~ ! [W1: $i] : ~ aElementOf0(W1,slcrc0) ) ) )),
rewrite(( ( ~ ( aElementOf0(W0,slbdtsldtrb0(xS,sz00))
| ~ ( ( sbrdtbr0(W0) != sz00 )
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) ) )
| ~ ( ~ aSet0(slcrc0)
| ( sdtlpdtrp0(xc,W0) != sdtlpdtrp0(xc,slcrc0) )
| ~ ! [W1: $i] : ~ aElementOf0(W1,slcrc0) ) )
<=> ( ~ ( aElementOf0(W0,slbdtsldtrb0(xS,sz00))
| ~ ( ( sbrdtbr0(W0) != sz00 )
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) ) )
| ~ ( ~ aSet0(slcrc0)
| ( sdtlpdtrp0(xc,W0) != sdtlpdtrp0(xc,slcrc0) )
| ~ ! [W1: $i] : ~ aElementOf0(W1,slcrc0) ) ) )),
( ( ~ ( aElementOf0(W0,slbdtsldtrb0(xS,sz00))
| ~ ( ( sbrdtbr0(W0) != sz00 )
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) ) )
| ~ ( ~ aSet0(slcrc0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,slcrc0)
| ( sdtlpdtrp0(xc,W0) != sdtlpdtrp0(xc,slcrc0) ) ) )
<=> ( ~ ( aElementOf0(W0,slbdtsldtrb0(xS,sz00))
| ~ ( ( sbrdtbr0(W0) != sz00 )
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) ) )
| ~ ( ~ aSet0(slcrc0)
| ( sdtlpdtrp0(xc,W0) != sdtlpdtrp0(xc,slcrc0) )
| ~ ! [W1: $i] : ~ aElementOf0(W1,slcrc0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(167,plain,
( ! [W0: $i] :
( ~ ( aElementOf0(W0,slbdtsldtrb0(xS,sz00))
| ~ ( ( sbrdtbr0(W0) != sz00 )
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) ) )
| ~ ( ~ aSet0(slcrc0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,slcrc0)
| ( sdtlpdtrp0(xc,W0) != sdtlpdtrp0(xc,slcrc0) ) ) )
<=> ! [W0: $i] :
( ~ ( aElementOf0(W0,slbdtsldtrb0(xS,sz00))
| ~ ( ( sbrdtbr0(W0) != sz00 )
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) ) )
| ~ ( ~ aSet0(slcrc0)
| ( sdtlpdtrp0(xc,W0) != sdtlpdtrp0(xc,slcrc0) )
| ~ ! [W1: $i] : ~ aElementOf0(W1,slcrc0) ) ) ),
inference(quant_intro,[status(thm)],[166]) ).
tff(168,plain,
^ [W0: $i] :
refl(( ( ~ ( aElementOf0(W0,slbdtsldtrb0(xS,sz00))
| ~ ( ( sbrdtbr0(W0) != sz00 )
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) ) )
| ~ ( ~ aSet0(slcrc0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,slcrc0)
| ( sdtlpdtrp0(xc,W0) != sdtlpdtrp0(xc,slcrc0) ) ) )
<=> ( ~ ( aElementOf0(W0,slbdtsldtrb0(xS,sz00))
| ~ ( ( sbrdtbr0(W0) != sz00 )
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) ) )
| ~ ( ~ aSet0(slcrc0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,slcrc0)
| ( sdtlpdtrp0(xc,W0) != sdtlpdtrp0(xc,slcrc0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(169,plain,
( ! [W0: $i] :
( ~ ( aElementOf0(W0,slbdtsldtrb0(xS,sz00))
| ~ ( ( sbrdtbr0(W0) != sz00 )
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) ) )
| ~ ( ~ aSet0(slcrc0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,slcrc0)
| ( sdtlpdtrp0(xc,W0) != sdtlpdtrp0(xc,slcrc0) ) ) )
<=> ! [W0: $i] :
( ~ ( aElementOf0(W0,slbdtsldtrb0(xS,sz00))
| ~ ( ( sbrdtbr0(W0) != sz00 )
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) ) )
| ~ ( ~ aSet0(slcrc0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,slcrc0)
| ( sdtlpdtrp0(xc,W0) != sdtlpdtrp0(xc,slcrc0) ) ) ) ),
inference(quant_intro,[status(thm)],[168]) ).
tff(170,plain,
^ [W0: $i] :
rewrite(( ( ~ ( aElementOf0(W0,slbdtsldtrb0(xS,sz00))
| ~ ( ( sbrdtbr0(W0) != sz00 )
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) ) )
| ~ ( ~ aSet0(slcrc0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,slcrc0)
| ( sdtlpdtrp0(xc,W0) != sdtlpdtrp0(xc,slcrc0) ) ) )
<=> ( ~ ( aElementOf0(W0,slbdtsldtrb0(xS,sz00))
| ~ ( ( sbrdtbr0(W0) != sz00 )
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) ) )
| ~ ( ~ aSet0(slcrc0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,slcrc0)
| ( sdtlpdtrp0(xc,W0) != sdtlpdtrp0(xc,slcrc0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(171,plain,
( ! [W0: $i] :
( ~ ( aElementOf0(W0,slbdtsldtrb0(xS,sz00))
| ~ ( ( sbrdtbr0(W0) != sz00 )
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) ) )
| ~ ( ~ aSet0(slcrc0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,slcrc0)
| ( sdtlpdtrp0(xc,W0) != sdtlpdtrp0(xc,slcrc0) ) ) )
<=> ! [W0: $i] :
( ~ ( aElementOf0(W0,slbdtsldtrb0(xS,sz00))
| ~ ( ( sbrdtbr0(W0) != sz00 )
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) ) )
| ~ ( ~ aSet0(slcrc0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,slcrc0)
| ( sdtlpdtrp0(xc,W0) != sdtlpdtrp0(xc,slcrc0) ) ) ) ),
inference(quant_intro,[status(thm)],[170]) ).
tff(172,plain,
( ! [W0: $i] :
( ~ ( aElementOf0(W0,slbdtsldtrb0(xS,sz00))
| ~ ( ( sbrdtbr0(W0) != sz00 )
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) ) )
| ~ ( ~ aSet0(slcrc0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,slcrc0)
| ( sdtlpdtrp0(xc,W0) != sdtlpdtrp0(xc,slcrc0) ) ) )
<=> ! [W0: $i] :
( ~ ( aElementOf0(W0,slbdtsldtrb0(xS,sz00))
| ~ ( ( sbrdtbr0(W0) != sz00 )
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) ) )
| ~ ( ~ aSet0(slcrc0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,slcrc0)
| ( sdtlpdtrp0(xc,W0) != sdtlpdtrp0(xc,slcrc0) ) ) ) ),
inference(transitivity,[status(thm)],[171,169]) ).
tff(173,plain,
^ [W0: $i] :
trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(( ( ~ aSubsetOf0(W0,xS)
& ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) )
<=> ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) )),
( ( ( ~ aSubsetOf0(W0,xS)
& ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) )
| ( sbrdtbr0(W0) != sz00 ) )
<=> ( ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) )
| ( sbrdtbr0(W0) != sz00 ) ) )),
rewrite(( ( ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) )
| ( sbrdtbr0(W0) != sz00 ) )
<=> ( ( sbrdtbr0(W0) != sz00 )
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) ) )),
( ( ( ~ aSubsetOf0(W0,xS)
& ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) )
| ( sbrdtbr0(W0) != sz00 ) )
<=> ( ( sbrdtbr0(W0) != sz00 )
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) ) )),
( ( ~ aElementOf0(W0,slbdtsldtrb0(xS,sz00))
& ( ( ~ aSubsetOf0(W0,xS)
& ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) )
| ( sbrdtbr0(W0) != sz00 ) ) )
<=> ( ~ aElementOf0(W0,slbdtsldtrb0(xS,sz00))
& ( ( sbrdtbr0(W0) != sz00 )
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) ) ) )),
rewrite(( ( ~ aElementOf0(W0,slbdtsldtrb0(xS,sz00))
& ( ( sbrdtbr0(W0) != sz00 )
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) ) )
<=> ~ ( aElementOf0(W0,slbdtsldtrb0(xS,sz00))
| ~ ( ( sbrdtbr0(W0) != sz00 )
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) ) ) )),
( ( ~ aElementOf0(W0,slbdtsldtrb0(xS,sz00))
& ( ( ~ aSubsetOf0(W0,xS)
& ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) )
| ( sbrdtbr0(W0) != sz00 ) ) )
<=> ~ ( aElementOf0(W0,slbdtsldtrb0(xS,sz00))
| ~ ( ( sbrdtbr0(W0) != sz00 )
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) ) ) )),
rewrite(( ( aSet0(slcrc0)
& ! [W1: $i] : ~ aElementOf0(W1,slcrc0)
& ( sdtlpdtrp0(xc,W0) = sdtlpdtrp0(xc,slcrc0) ) )
<=> ~ ( ~ aSet0(slcrc0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,slcrc0)
| ( sdtlpdtrp0(xc,W0) != sdtlpdtrp0(xc,slcrc0) ) ) )),
( ( ( ~ aElementOf0(W0,slbdtsldtrb0(xS,sz00))
& ( ( ~ aSubsetOf0(W0,xS)
& ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) )
| ( sbrdtbr0(W0) != sz00 ) ) )
| ( aSet0(slcrc0)
& ! [W1: $i] : ~ aElementOf0(W1,slcrc0)
& ( sdtlpdtrp0(xc,W0) = sdtlpdtrp0(xc,slcrc0) ) ) )
<=> ( ~ ( aElementOf0(W0,slbdtsldtrb0(xS,sz00))
| ~ ( ( sbrdtbr0(W0) != sz00 )
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) ) )
| ~ ( ~ aSet0(slcrc0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,slcrc0)
| ( sdtlpdtrp0(xc,W0) != sdtlpdtrp0(xc,slcrc0) ) ) ) )),
rewrite(( ( ~ ( aElementOf0(W0,slbdtsldtrb0(xS,sz00))
| ~ ( ( sbrdtbr0(W0) != sz00 )
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) ) )
| ~ ( ~ aSet0(slcrc0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,slcrc0)
| ( sdtlpdtrp0(xc,W0) != sdtlpdtrp0(xc,slcrc0) ) ) )
<=> ( ~ ( aElementOf0(W0,slbdtsldtrb0(xS,sz00))
| ~ ( ( sbrdtbr0(W0) != sz00 )
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) ) )
| ~ ( ~ aSet0(slcrc0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,slcrc0)
| ( sdtlpdtrp0(xc,W0) != sdtlpdtrp0(xc,slcrc0) ) ) ) )),
( ( ( ~ aElementOf0(W0,slbdtsldtrb0(xS,sz00))
& ( ( ~ aSubsetOf0(W0,xS)
& ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) )
| ( sbrdtbr0(W0) != sz00 ) ) )
| ( aSet0(slcrc0)
& ! [W1: $i] : ~ aElementOf0(W1,slcrc0)
& ( sdtlpdtrp0(xc,W0) = sdtlpdtrp0(xc,slcrc0) ) ) )
<=> ( ~ ( aElementOf0(W0,slbdtsldtrb0(xS,sz00))
| ~ ( ( sbrdtbr0(W0) != sz00 )
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) ) )
| ~ ( ~ aSet0(slcrc0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,slcrc0)
| ( sdtlpdtrp0(xc,W0) != sdtlpdtrp0(xc,slcrc0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(174,plain,
( ! [W0: $i] :
( ( ~ aElementOf0(W0,slbdtsldtrb0(xS,sz00))
& ( ( ~ aSubsetOf0(W0,xS)
& ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) )
| ( sbrdtbr0(W0) != sz00 ) ) )
| ( aSet0(slcrc0)
& ! [W1: $i] : ~ aElementOf0(W1,slcrc0)
& ( sdtlpdtrp0(xc,W0) = sdtlpdtrp0(xc,slcrc0) ) ) )
<=> ! [W0: $i] :
( ~ ( aElementOf0(W0,slbdtsldtrb0(xS,sz00))
| ~ ( ( sbrdtbr0(W0) != sz00 )
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) ) )
| ~ ( ~ aSet0(slcrc0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,slcrc0)
| ( sdtlpdtrp0(xc,W0) != sdtlpdtrp0(xc,slcrc0) ) ) ) ),
inference(quant_intro,[status(thm)],[173]) ).
tff(175,plain,
( ! [W0: $i] :
( ~ ( aElementOf0(W0,slbdtsldtrb0(xS,sz00))
| ( ( aSubsetOf0(W0,xS)
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) ) ) )
& ( sbrdtbr0(W0) = sz00 ) ) )
| ( aSet0(slcrc0)
& ~ ? [W1: $i] : aElementOf0(W1,slcrc0)
& ( sdtlpdtrp0(xc,W0) = sdtlpdtrp0(xc,slcrc0) ) ) )
<=> ! [W0: $i] :
( ~ ( aElementOf0(W0,slbdtsldtrb0(xS,sz00))
| ( ( aSubsetOf0(W0,xS)
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) ) ) )
& ( sbrdtbr0(W0) = sz00 ) ) )
| ( aSet0(slcrc0)
& ~ ? [W1: $i] : aElementOf0(W1,slcrc0)
& ( sdtlpdtrp0(xc,W0) = sdtlpdtrp0(xc,slcrc0) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(176,plain,
^ [W0: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( ( ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) ) )
| aSubsetOf0(W0,xS) )
& ( sbrdtbr0(W0) = sz00 ) )
<=> ( ( aSubsetOf0(W0,xS)
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) ) ) )
& ( sbrdtbr0(W0) = sz00 ) ) )),
( ( ( ( ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) ) )
| aSubsetOf0(W0,xS) )
& ( sbrdtbr0(W0) = sz00 ) )
| aElementOf0(W0,slbdtsldtrb0(xS,sz00)) )
<=> ( ( ( aSubsetOf0(W0,xS)
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) ) ) )
& ( sbrdtbr0(W0) = sz00 ) )
| aElementOf0(W0,slbdtsldtrb0(xS,sz00)) ) )),
rewrite(( ( ( ( aSubsetOf0(W0,xS)
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) ) ) )
& ( sbrdtbr0(W0) = sz00 ) )
| aElementOf0(W0,slbdtsldtrb0(xS,sz00)) )
<=> ( aElementOf0(W0,slbdtsldtrb0(xS,sz00))
| ( ( aSubsetOf0(W0,xS)
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) ) ) )
& ( sbrdtbr0(W0) = sz00 ) ) ) )),
( ( ( ( ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) ) )
| aSubsetOf0(W0,xS) )
& ( sbrdtbr0(W0) = sz00 ) )
| aElementOf0(W0,slbdtsldtrb0(xS,sz00)) )
<=> ( aElementOf0(W0,slbdtsldtrb0(xS,sz00))
| ( ( aSubsetOf0(W0,xS)
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) ) ) )
& ( sbrdtbr0(W0) = sz00 ) ) ) )),
trans(monotonicity(monotonicity(rewrite(( ~ ? [W1: $i] : aElementOf0(W1,slcrc0)
<=> ~ ? [W1: $i] : aElementOf0(W1,slcrc0) )),
( ( aSet0(slcrc0)
& ~ ? [W1: $i] : aElementOf0(W1,slcrc0) )
<=> ( aSet0(slcrc0)
& ~ ? [W1: $i] : aElementOf0(W1,slcrc0) ) )),
( ( aSet0(slcrc0)
& ~ ? [W1: $i] : aElementOf0(W1,slcrc0)
& ( sdtlpdtrp0(xc,W0) = sdtlpdtrp0(xc,slcrc0) ) )
<=> ( aSet0(slcrc0)
& ~ ? [W1: $i] : aElementOf0(W1,slcrc0)
& ( sdtlpdtrp0(xc,W0) = sdtlpdtrp0(xc,slcrc0) ) ) )),
rewrite(( ( aSet0(slcrc0)
& ~ ? [W1: $i] : aElementOf0(W1,slcrc0)
& ( sdtlpdtrp0(xc,W0) = sdtlpdtrp0(xc,slcrc0) ) )
<=> ( aSet0(slcrc0)
& ~ ? [W1: $i] : aElementOf0(W1,slcrc0)
& ( sdtlpdtrp0(xc,W0) = sdtlpdtrp0(xc,slcrc0) ) ) )),
( ( aSet0(slcrc0)
& ~ ? [W1: $i] : aElementOf0(W1,slcrc0)
& ( sdtlpdtrp0(xc,W0) = sdtlpdtrp0(xc,slcrc0) ) )
<=> ( aSet0(slcrc0)
& ~ ? [W1: $i] : aElementOf0(W1,slcrc0)
& ( sdtlpdtrp0(xc,W0) = sdtlpdtrp0(xc,slcrc0) ) ) )),
( ( ( ( ( ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) ) )
| aSubsetOf0(W0,xS) )
& ( sbrdtbr0(W0) = sz00 ) )
| aElementOf0(W0,slbdtsldtrb0(xS,sz00)) )
=> ( aSet0(slcrc0)
& ~ ? [W1: $i] : aElementOf0(W1,slcrc0)
& ( sdtlpdtrp0(xc,W0) = sdtlpdtrp0(xc,slcrc0) ) ) )
<=> ( ( aElementOf0(W0,slbdtsldtrb0(xS,sz00))
| ( ( aSubsetOf0(W0,xS)
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) ) ) )
& ( sbrdtbr0(W0) = sz00 ) ) )
=> ( aSet0(slcrc0)
& ~ ? [W1: $i] : aElementOf0(W1,slcrc0)
& ( sdtlpdtrp0(xc,W0) = sdtlpdtrp0(xc,slcrc0) ) ) ) )),
rewrite(( ( ( aElementOf0(W0,slbdtsldtrb0(xS,sz00))
| ( ( aSubsetOf0(W0,xS)
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) ) ) )
& ( sbrdtbr0(W0) = sz00 ) ) )
=> ( aSet0(slcrc0)
& ~ ? [W1: $i] : aElementOf0(W1,slcrc0)
& ( sdtlpdtrp0(xc,W0) = sdtlpdtrp0(xc,slcrc0) ) ) )
<=> ( ~ ( aElementOf0(W0,slbdtsldtrb0(xS,sz00))
| ( ( aSubsetOf0(W0,xS)
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) ) ) )
& ( sbrdtbr0(W0) = sz00 ) ) )
| ( aSet0(slcrc0)
& ~ ? [W1: $i] : aElementOf0(W1,slcrc0)
& ( sdtlpdtrp0(xc,W0) = sdtlpdtrp0(xc,slcrc0) ) ) ) )),
( ( ( ( ( ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) ) )
| aSubsetOf0(W0,xS) )
& ( sbrdtbr0(W0) = sz00 ) )
| aElementOf0(W0,slbdtsldtrb0(xS,sz00)) )
=> ( aSet0(slcrc0)
& ~ ? [W1: $i] : aElementOf0(W1,slcrc0)
& ( sdtlpdtrp0(xc,W0) = sdtlpdtrp0(xc,slcrc0) ) ) )
<=> ( ~ ( aElementOf0(W0,slbdtsldtrb0(xS,sz00))
| ( ( aSubsetOf0(W0,xS)
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) ) ) )
& ( sbrdtbr0(W0) = sz00 ) ) )
| ( aSet0(slcrc0)
& ~ ? [W1: $i] : aElementOf0(W1,slcrc0)
& ( sdtlpdtrp0(xc,W0) = sdtlpdtrp0(xc,slcrc0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(177,plain,
( ! [W0: $i] :
( ( ( ( ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) ) )
| aSubsetOf0(W0,xS) )
& ( sbrdtbr0(W0) = sz00 ) )
| aElementOf0(W0,slbdtsldtrb0(xS,sz00)) )
=> ( aSet0(slcrc0)
& ~ ? [W1: $i] : aElementOf0(W1,slcrc0)
& ( sdtlpdtrp0(xc,W0) = sdtlpdtrp0(xc,slcrc0) ) ) )
<=> ! [W0: $i] :
( ~ ( aElementOf0(W0,slbdtsldtrb0(xS,sz00))
| ( ( aSubsetOf0(W0,xS)
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) ) ) )
& ( sbrdtbr0(W0) = sz00 ) ) )
| ( aSet0(slcrc0)
& ~ ? [W1: $i] : aElementOf0(W1,slcrc0)
& ( sdtlpdtrp0(xc,W0) = sdtlpdtrp0(xc,slcrc0) ) ) ) ),
inference(quant_intro,[status(thm)],[176]) ).
tff(178,axiom,
! [W0: $i] :
( ( ( ( ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) ) )
| aSubsetOf0(W0,xS) )
& ( sbrdtbr0(W0) = sz00 ) )
| aElementOf0(W0,slbdtsldtrb0(xS,sz00)) )
=> ( aSet0(slcrc0)
& ~ ? [W1: $i] : aElementOf0(W1,slcrc0)
& ( sdtlpdtrp0(xc,W0) = sdtlpdtrp0(xc,slcrc0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3507) ).
tff(179,plain,
! [W0: $i] :
( ~ ( aElementOf0(W0,slbdtsldtrb0(xS,sz00))
| ( ( aSubsetOf0(W0,xS)
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) ) ) )
& ( sbrdtbr0(W0) = sz00 ) ) )
| ( aSet0(slcrc0)
& ~ ? [W1: $i] : aElementOf0(W1,slcrc0)
& ( sdtlpdtrp0(xc,W0) = sdtlpdtrp0(xc,slcrc0) ) ) ),
inference(modus_ponens,[status(thm)],[178,177]) ).
tff(180,plain,
! [W0: $i] :
( ~ ( aElementOf0(W0,slbdtsldtrb0(xS,sz00))
| ( ( aSubsetOf0(W0,xS)
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) ) ) )
& ( sbrdtbr0(W0) = sz00 ) ) )
| ( aSet0(slcrc0)
& ~ ? [W1: $i] : aElementOf0(W1,slcrc0)
& ( sdtlpdtrp0(xc,W0) = sdtlpdtrp0(xc,slcrc0) ) ) ),
inference(modus_ponens,[status(thm)],[179,175]) ).
tff(181,plain,
! [W0: $i] :
( ( ~ aElementOf0(W0,slbdtsldtrb0(xS,sz00))
& ( ( ~ aSubsetOf0(W0,xS)
& ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) )
| ( sbrdtbr0(W0) != sz00 ) ) )
| ( aSet0(slcrc0)
& ! [W1: $i] : ~ aElementOf0(W1,slcrc0)
& ( sdtlpdtrp0(xc,W0) = sdtlpdtrp0(xc,slcrc0) ) ) ),
inference(skolemize,[status(sab)],[180]) ).
tff(182,plain,
! [W0: $i] :
( ~ ( aElementOf0(W0,slbdtsldtrb0(xS,sz00))
| ~ ( ( sbrdtbr0(W0) != sz00 )
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) ) )
| ~ ( ~ aSet0(slcrc0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,slcrc0)
| ( sdtlpdtrp0(xc,W0) != sdtlpdtrp0(xc,slcrc0) ) ) ),
inference(modus_ponens,[status(thm)],[181,174]) ).
tff(183,plain,
! [W0: $i] :
( ~ ( aElementOf0(W0,slbdtsldtrb0(xS,sz00))
| ~ ( ( sbrdtbr0(W0) != sz00 )
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) ) )
| ~ ( ~ aSet0(slcrc0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,slcrc0)
| ( sdtlpdtrp0(xc,W0) != sdtlpdtrp0(xc,slcrc0) ) ) ),
inference(modus_ponens,[status(thm)],[182,172]) ).
tff(184,plain,
! [W0: $i] :
( ~ ( aElementOf0(W0,slbdtsldtrb0(xS,sz00))
| ~ ( ( sbrdtbr0(W0) != sz00 )
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) ) )
| ~ ( ~ aSet0(slcrc0)
| ( sdtlpdtrp0(xc,W0) != sdtlpdtrp0(xc,slcrc0) )
| ~ ! [W1: $i] : ~ aElementOf0(W1,slcrc0) ) ),
inference(modus_ponens,[status(thm)],[183,167]) ).
tff(185,plain,
( ( ~ ! [W0: $i] :
( ~ ( aElementOf0(W0,slbdtsldtrb0(xS,sz00))
| ~ ( ( sbrdtbr0(W0) != sz00 )
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) ) )
| ~ ( ~ aSet0(slcrc0)
| ( sdtlpdtrp0(xc,W0) != sdtlpdtrp0(xc,slcrc0) )
| ~ ! [W1: $i] : ~ aElementOf0(W1,slcrc0) ) )
| ~ ( ~ aSet0(slcrc0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,slcrc0)
| ( sdtlpdtrp0(xc,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) != sdtlpdtrp0(xc,slcrc0) ) )
| ~ ( ~ ( ( sbrdtbr0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) != sz00 )
| ~ ( aSubsetOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),xS)
| ~ ( ~ aSet0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| ~ ( ~ aElementOf0(tptp_fun_W1_19(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))),tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(tptp_fun_W1_19(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))),xS) ) ) ) )
| aElementOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(xS,sz00)) ) )
<=> ( ~ ! [W0: $i] :
( ~ ( aElementOf0(W0,slbdtsldtrb0(xS,sz00))
| ~ ( ( sbrdtbr0(W0) != sz00 )
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) ) )
| ~ ( ~ aSet0(slcrc0)
| ( sdtlpdtrp0(xc,W0) != sdtlpdtrp0(xc,slcrc0) )
| ~ ! [W1: $i] : ~ aElementOf0(W1,slcrc0) ) )
| ~ ( ~ aSet0(slcrc0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,slcrc0)
| ( sdtlpdtrp0(xc,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) != sdtlpdtrp0(xc,slcrc0) ) )
| ~ ( ~ ( ( sbrdtbr0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) != sz00 )
| ~ ( aSubsetOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),xS)
| ~ ( ~ aSet0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| ~ ( ~ aElementOf0(tptp_fun_W1_19(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))),tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(tptp_fun_W1_19(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))),xS) ) ) ) )
| aElementOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(xS,sz00)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(186,plain,
( ( ~ ( ~ ( ( sbrdtbr0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) != sz00 )
| ~ ( aSubsetOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),xS)
| ~ ( ~ aSet0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| ~ ( ~ aElementOf0(tptp_fun_W1_19(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))),tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(tptp_fun_W1_19(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))),xS) ) ) ) )
| aElementOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(xS,sz00)) )
| ~ ( ~ aSet0(slcrc0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,slcrc0)
| ( sdtlpdtrp0(xc,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) != sdtlpdtrp0(xc,slcrc0) ) ) )
<=> ( ~ ( ~ aSet0(slcrc0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,slcrc0)
| ( sdtlpdtrp0(xc,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) != sdtlpdtrp0(xc,slcrc0) ) )
| ~ ( ~ ( ( sbrdtbr0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) != sz00 )
| ~ ( aSubsetOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),xS)
| ~ ( ~ aSet0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| ~ ( ~ aElementOf0(tptp_fun_W1_19(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))),tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(tptp_fun_W1_19(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))),xS) ) ) ) )
| aElementOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(xS,sz00)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(187,plain,
( ~ ( ~ aSet0(slcrc0)
| ( sdtlpdtrp0(xc,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) != sdtlpdtrp0(xc,slcrc0) )
| ~ ! [W1: $i] : ~ aElementOf0(W1,slcrc0) )
<=> ~ ( ~ aSet0(slcrc0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,slcrc0)
| ( sdtlpdtrp0(xc,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) != sdtlpdtrp0(xc,slcrc0) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(188,plain,
( ~ ( aElementOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(xS,sz00))
| ~ ( ( sbrdtbr0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) != sz00 )
| ~ ( aSubsetOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),xS)
| ~ ( ~ aSet0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| ~ ( ~ aElementOf0(tptp_fun_W1_19(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))),tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(tptp_fun_W1_19(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))),xS) ) ) ) ) )
<=> ~ ( ~ ( ( sbrdtbr0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) != sz00 )
| ~ ( aSubsetOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),xS)
| ~ ( ~ aSet0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| ~ ( ~ aElementOf0(tptp_fun_W1_19(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))),tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(tptp_fun_W1_19(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))),xS) ) ) ) )
| aElementOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(xS,sz00)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(189,plain,
( ( ~ ( aElementOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(xS,sz00))
| ~ ( ( sbrdtbr0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) != sz00 )
| ~ ( aSubsetOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),xS)
| ~ ( ~ aSet0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| ~ ( ~ aElementOf0(tptp_fun_W1_19(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))),tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(tptp_fun_W1_19(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))),xS) ) ) ) ) )
| ~ ( ~ aSet0(slcrc0)
| ( sdtlpdtrp0(xc,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) != sdtlpdtrp0(xc,slcrc0) )
| ~ ! [W1: $i] : ~ aElementOf0(W1,slcrc0) ) )
<=> ( ~ ( ~ ( ( sbrdtbr0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) != sz00 )
| ~ ( aSubsetOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),xS)
| ~ ( ~ aSet0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| ~ ( ~ aElementOf0(tptp_fun_W1_19(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))),tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(tptp_fun_W1_19(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))),xS) ) ) ) )
| aElementOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(xS,sz00)) )
| ~ ( ~ aSet0(slcrc0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,slcrc0)
| ( sdtlpdtrp0(xc,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) != sdtlpdtrp0(xc,slcrc0) ) ) ) ),
inference(monotonicity,[status(thm)],[188,187]) ).
tff(190,plain,
( ( ~ ( aElementOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(xS,sz00))
| ~ ( ( sbrdtbr0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) != sz00 )
| ~ ( aSubsetOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),xS)
| ~ ( ~ aSet0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| ~ ( ~ aElementOf0(tptp_fun_W1_19(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))),tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(tptp_fun_W1_19(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))),xS) ) ) ) ) )
| ~ ( ~ aSet0(slcrc0)
| ( sdtlpdtrp0(xc,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) != sdtlpdtrp0(xc,slcrc0) )
| ~ ! [W1: $i] : ~ aElementOf0(W1,slcrc0) ) )
<=> ( ~ ( ~ aSet0(slcrc0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,slcrc0)
| ( sdtlpdtrp0(xc,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) != sdtlpdtrp0(xc,slcrc0) ) )
| ~ ( ~ ( ( sbrdtbr0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) != sz00 )
| ~ ( aSubsetOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),xS)
| ~ ( ~ aSet0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| ~ ( ~ aElementOf0(tptp_fun_W1_19(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))),tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(tptp_fun_W1_19(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))),xS) ) ) ) )
| aElementOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(xS,sz00)) ) ) ),
inference(transitivity,[status(thm)],[189,186]) ).
tff(191,plain,
( ( ~ ! [W0: $i] :
( ~ ( aElementOf0(W0,slbdtsldtrb0(xS,sz00))
| ~ ( ( sbrdtbr0(W0) != sz00 )
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) ) )
| ~ ( ~ aSet0(slcrc0)
| ( sdtlpdtrp0(xc,W0) != sdtlpdtrp0(xc,slcrc0) )
| ~ ! [W1: $i] : ~ aElementOf0(W1,slcrc0) ) )
| ~ ( aElementOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(xS,sz00))
| ~ ( ( sbrdtbr0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) != sz00 )
| ~ ( aSubsetOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),xS)
| ~ ( ~ aSet0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| ~ ( ~ aElementOf0(tptp_fun_W1_19(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))),tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(tptp_fun_W1_19(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))),xS) ) ) ) ) )
| ~ ( ~ aSet0(slcrc0)
| ( sdtlpdtrp0(xc,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) != sdtlpdtrp0(xc,slcrc0) )
| ~ ! [W1: $i] : ~ aElementOf0(W1,slcrc0) ) )
<=> ( ~ ! [W0: $i] :
( ~ ( aElementOf0(W0,slbdtsldtrb0(xS,sz00))
| ~ ( ( sbrdtbr0(W0) != sz00 )
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) ) )
| ~ ( ~ aSet0(slcrc0)
| ( sdtlpdtrp0(xc,W0) != sdtlpdtrp0(xc,slcrc0) )
| ~ ! [W1: $i] : ~ aElementOf0(W1,slcrc0) ) )
| ~ ( ~ aSet0(slcrc0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,slcrc0)
| ( sdtlpdtrp0(xc,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) != sdtlpdtrp0(xc,slcrc0) ) )
| ~ ( ~ ( ( sbrdtbr0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) != sz00 )
| ~ ( aSubsetOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),xS)
| ~ ( ~ aSet0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| ~ ( ~ aElementOf0(tptp_fun_W1_19(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))),tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(tptp_fun_W1_19(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))),xS) ) ) ) )
| aElementOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(xS,sz00)) ) ) ),
inference(monotonicity,[status(thm)],[190]) ).
tff(192,plain,
( ( ~ ! [W0: $i] :
( ~ ( aElementOf0(W0,slbdtsldtrb0(xS,sz00))
| ~ ( ( sbrdtbr0(W0) != sz00 )
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) ) )
| ~ ( ~ aSet0(slcrc0)
| ( sdtlpdtrp0(xc,W0) != sdtlpdtrp0(xc,slcrc0) )
| ~ ! [W1: $i] : ~ aElementOf0(W1,slcrc0) ) )
| ~ ( aElementOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(xS,sz00))
| ~ ( ( sbrdtbr0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) != sz00 )
| ~ ( aSubsetOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),xS)
| ~ ( ~ aSet0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| ~ ( ~ aElementOf0(tptp_fun_W1_19(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))),tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(tptp_fun_W1_19(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))),xS) ) ) ) ) )
| ~ ( ~ aSet0(slcrc0)
| ( sdtlpdtrp0(xc,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) != sdtlpdtrp0(xc,slcrc0) )
| ~ ! [W1: $i] : ~ aElementOf0(W1,slcrc0) ) )
<=> ( ~ ! [W0: $i] :
( ~ ( aElementOf0(W0,slbdtsldtrb0(xS,sz00))
| ~ ( ( sbrdtbr0(W0) != sz00 )
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) ) )
| ~ ( ~ aSet0(slcrc0)
| ( sdtlpdtrp0(xc,W0) != sdtlpdtrp0(xc,slcrc0) )
| ~ ! [W1: $i] : ~ aElementOf0(W1,slcrc0) ) )
| ~ ( ~ aSet0(slcrc0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,slcrc0)
| ( sdtlpdtrp0(xc,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) != sdtlpdtrp0(xc,slcrc0) ) )
| ~ ( ~ ( ( sbrdtbr0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) != sz00 )
| ~ ( aSubsetOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),xS)
| ~ ( ~ aSet0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| ~ ( ~ aElementOf0(tptp_fun_W1_19(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))),tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(tptp_fun_W1_19(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))),xS) ) ) ) )
| aElementOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(xS,sz00)) ) ) ),
inference(transitivity,[status(thm)],[191,185]) ).
tff(193,plain,
( ~ ! [W0: $i] :
( ~ ( aElementOf0(W0,slbdtsldtrb0(xS,sz00))
| ~ ( ( sbrdtbr0(W0) != sz00 )
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) ) )
| ~ ( ~ aSet0(slcrc0)
| ( sdtlpdtrp0(xc,W0) != sdtlpdtrp0(xc,slcrc0) )
| ~ ! [W1: $i] : ~ aElementOf0(W1,slcrc0) ) )
| ~ ( aElementOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(xS,sz00))
| ~ ( ( sbrdtbr0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) != sz00 )
| ~ ( aSubsetOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),xS)
| ~ ( ~ aSet0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| ~ ( ~ aElementOf0(tptp_fun_W1_19(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))),tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(tptp_fun_W1_19(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))),xS) ) ) ) ) )
| ~ ( ~ aSet0(slcrc0)
| ( sdtlpdtrp0(xc,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) != sdtlpdtrp0(xc,slcrc0) )
| ~ ! [W1: $i] : ~ aElementOf0(W1,slcrc0) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(194,plain,
( ~ ! [W0: $i] :
( ~ ( aElementOf0(W0,slbdtsldtrb0(xS,sz00))
| ~ ( ( sbrdtbr0(W0) != sz00 )
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) ) )
| ~ ( ~ aSet0(slcrc0)
| ( sdtlpdtrp0(xc,W0) != sdtlpdtrp0(xc,slcrc0) )
| ~ ! [W1: $i] : ~ aElementOf0(W1,slcrc0) ) )
| ~ ( ~ aSet0(slcrc0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,slcrc0)
| ( sdtlpdtrp0(xc,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) != sdtlpdtrp0(xc,slcrc0) ) )
| ~ ( ~ ( ( sbrdtbr0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) != sz00 )
| ~ ( aSubsetOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),xS)
| ~ ( ~ aSet0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| ~ ( ~ aElementOf0(tptp_fun_W1_19(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))),tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(tptp_fun_W1_19(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))),xS) ) ) ) )
| aElementOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(xS,sz00)) ) ),
inference(modus_ponens,[status(thm)],[193,192]) ).
tff(195,plain,
$false,
inference(unit_resolution,[status(thm)],[194,184,165,161]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.12 % Problem : NUM566+3 : TPTP v9.0.0. Released v4.0.0.
% 0.02/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n009.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 01:26:48 EDT 2025
% 0.12/0.33 % CPUTime :
% 1.97/2.21 % SZS status Theorem
% 1.97/2.21 % SZS output start Proof
% See solution above
% 2.06/2.26 % E exiting
%------------------------------------------------------------------------------