TSTP Solution File: NUM584+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM584+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 18 13:10:40 EDT 2022
% Result : Theorem 1.13s 0.99s
% Output : Proof 1.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 84
% Syntax : Number of formulae : 166 ( 40 unt; 25 typ; 0 def)
% Number of atoms : 2018 ( 435 equ)
% Maximal formula atoms : 48 ( 14 avg)
% Number of connectives : 3889 (2081 ~;1303 |; 149 &)
% ( 341 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 8 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of FOOLs : 69 ( 69 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 24 ( 15 >; 9 *; 0 +; 0 <<)
% Number of predicates : 14 ( 12 usr; 1 prp; 0-3 aty)
% Number of functors : 20 ( 20 usr; 10 con; 0-3 aty)
% Number of variables : 487 ( 463 !; 0 ?; 487 :)
% Comments :
%------------------------------------------------------------------------------
tff(szszuzczcdt0_type,type,
szszuzczcdt0: $i > $i ).
tff(xk_type,type,
xk: $i ).
tff(sbrdtbr0_type,type,
sbrdtbr0: $i > $i ).
tff(sdtpldt0_type,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(szmzizndt0_type,type,
szmzizndt0: $i > $i ).
tff(sdtlpdtrp0_type,type,
sdtlpdtrp0: ( $i * $i ) > $i ).
tff(xi_type,type,
xi: $i ).
tff(xN_type,type,
xN: $i ).
tff(xQ_type,type,
xQ: $i ).
tff(aSubsetOf0_type,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff(sz00_type,type,
sz00: $i ).
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(slbdtsldtrb0_type,type,
slbdtsldtrb0: ( $i * $i ) > $i ).
tff(xS_type,type,
xS: $i ).
tff(xK_type,type,
xK: $i ).
tff(szDzozmdt0_type,type,
szDzozmdt0: $i > $i ).
tff(xc_type,type,
xc: $i ).
tff(aFunction0_type,type,
aFunction0: $i > $o ).
tff(xT_type,type,
xT: $i ).
tff(sdtlcdtrc0_type,type,
sdtlcdtrc0: ( $i * $i ) > $i ).
tff(aSet0_type,type,
aSet0: $i > $o ).
tff(tptp_fun_W3_10_type,type,
tptp_fun_W3_10: ( $i * $i * $i ) > $i ).
tff(tptp_fun_W2_1_type,type,
tptp_fun_W2_1: ( $i * $i ) > $i ).
tff(szNzAzT0_type,type,
szNzAzT0: $i ).
tff(isCountable0_type,type,
isCountable0: $i > $o ).
tff(1,plain,
( aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)
<=> aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),sdtlpdtrp0(xN,sz00)) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)
<=> aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS) ),
inference(rewrite,[status(thm)],]) ).
tff(3,axiom,
aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4024) ).
tff(4,plain,
aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS),
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),sdtlpdtrp0(xN,sz00)),
inference(modus_ponens,[status(thm)],[4,1]) ).
tff(6,plain,
( ( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK )
<=> ( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = szszuzczcdt0(xk) ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,plain,
( ( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK )
<=> ( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK ) ),
inference(rewrite,[status(thm)],]) ).
tff(8,axiom,
sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4007) ).
tff(9,plain,
sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK,
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = szszuzczcdt0(xk),
inference(modus_ponens,[status(thm)],[9,6]) ).
tff(11,plain,
( ~ ( ~ aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) != szszuzczcdt0(xk) ) )
| ~ aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) != szszuzczcdt0(xk) ) ),
inference(tautology,[status(thm)],]) ).
tff(12,plain,
~ ( ~ aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) != szszuzczcdt0(xk) ) ),
inference(unit_resolution,[status(thm)],[11,10,5]) ).
tff(13,plain,
( ( szDzozmdt0(xc) = slbdtsldtrb0(xS,xK) )
<=> ( szDzozmdt0(xc) = slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(14,plain,
( ( szDzozmdt0(xc) = slbdtsldtrb0(xS,xK) )
<=> ( szDzozmdt0(xc) = slbdtsldtrb0(xS,xK) ) ),
inference(rewrite,[status(thm)],]) ).
tff(15,axiom,
( aFunction0(xc)
& ( szDzozmdt0(xc) = slbdtsldtrb0(xS,xK) )
& aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3453) ).
tff(16,plain,
( aFunction0(xc)
& ( szDzozmdt0(xc) = slbdtsldtrb0(xS,xK) ) ),
inference(and_elim,[status(thm)],[15]) ).
tff(17,plain,
szDzozmdt0(xc) = slbdtsldtrb0(xS,xK),
inference(and_elim,[status(thm)],[16]) ).
tff(18,plain,
szDzozmdt0(xc) = slbdtsldtrb0(xS,xK),
inference(modus_ponens,[status(thm)],[17,14]) ).
tff(19,plain,
szDzozmdt0(xc) = slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)),
inference(modus_ponens,[status(thm)],[18,13]) ).
tff(20,plain,
slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)) = szDzozmdt0(xc),
inference(symmetry,[status(thm)],[19]) ).
tff(21,plain,
( aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)))
<=> aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),szDzozmdt0(xc)) ),
inference(monotonicity,[status(thm)],[20]) ).
tff(22,plain,
( aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),szDzozmdt0(xc))
<=> aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk))) ),
inference(symmetry,[status(thm)],[21]) ).
tff(23,plain,
( ~ aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),szDzozmdt0(xc))
<=> ~ aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk))) ),
inference(monotonicity,[status(thm)],[22]) ).
tff(24,plain,
( ~ aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)))
<=> ~ aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),szDzozmdt0(xc)) ),
inference(rewrite,[status(thm)],]) ).
tff(25,plain,
( ~ aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(xS,xK))
<=> ~ aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk))) ),
inference(rewrite,[status(thm)],]) ).
tff(26,plain,
( ~ aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(xS,xK))
<=> ~ aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(xS,xK)) ),
inference(rewrite,[status(thm)],]) ).
tff(27,axiom,
~ aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(xS,xK)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(28,plain,
~ aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(xS,xK)),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
~ aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk))),
inference(modus_ponens,[status(thm)],[28,25]) ).
tff(30,plain,
~ aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),szDzozmdt0(xc)),
inference(modus_ponens,[status(thm)],[29,24]) ).
tff(31,plain,
~ aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk))),
inference(modus_ponens,[status(thm)],[30,23]) ).
tff(32,plain,
( ~ ( aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)))
<=> ~ ( ~ aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) != szszuzczcdt0(xk) ) ) )
| aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)))
| ~ aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) != szszuzczcdt0(xk) ) ),
inference(tautology,[status(thm)],]) ).
tff(33,plain,
~ ( aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)))
<=> ~ ( ~ aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) != szszuzczcdt0(xk) ) ) ),
inference(unit_resolution,[status(thm)],[32,31,12]) ).
tff(34,plain,
( aSet0(szNzAzT0)
<=> aSet0(szDzozmdt0(xN)) ),
inference(rewrite,[status(thm)],]) ).
tff(35,plain,
( aSet0(szNzAzT0)
<=> aSet0(szNzAzT0) ),
inference(rewrite,[status(thm)],]) ).
tff(36,axiom,
( aSet0(szNzAzT0)
& isCountable0(szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNATSet) ).
tff(37,plain,
aSet0(szNzAzT0),
inference(and_elim,[status(thm)],[36]) ).
tff(38,plain,
aSet0(szNzAzT0),
inference(modus_ponens,[status(thm)],[37,35]) ).
tff(39,plain,
aSet0(szDzozmdt0(xN)),
inference(modus_ponens,[status(thm)],[38,34]) ).
tff(40,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(41,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)],[40]) ).
tff(42,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(43,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)],[42]) ).
tff(44,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(45,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ! [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)],[44]) ).
tff(46,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ! [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)],[45,43]) ).
tff(47,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(48,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,W0)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
& ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ! [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)],[47]) ).
tff(49,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(50,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)],[49]) ).
tff(51,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(52,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(53,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)],[52]) ).
tff(54,axiom,
! [W0: $i] :
( aSet0(W0)
=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSub) ).
tff(55,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)],[54,53]) ).
tff(56,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)],[55,51]) ).
tff(57,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)],[56]) ).
tff(58,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)],[57,50]) ).
tff(59,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)],[58,48]) ).
tff(60,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)],[59,46]) ).
tff(61,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)],[60,41]) ).
tff(62,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(szDzozmdt0(xN))
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),W1)
| aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),szDzozmdt0(xN)) ) )
| ~ ( ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ) ) )
<=> ( ~ ! [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(szDzozmdt0(xN))
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),W1)
| aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),szDzozmdt0(xN)) ) )
| ~ ( ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(63,plain,
( ( ~ aSet0(szDzozmdt0(xN))
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,szDzozmdt0(xN))
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),W1)
| aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),szDzozmdt0(xN)) ) )
| ~ ( ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ) ) )
<=> ( ~ aSet0(szDzozmdt0(xN))
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),W1)
| aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),szDzozmdt0(xN)) ) )
| ~ ( ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(64,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(szDzozmdt0(xN))
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,szDzozmdt0(xN))
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),W1)
| aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),szDzozmdt0(xN)) ) )
| ~ ( ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ) ) )
<=> ( ~ ! [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(szDzozmdt0(xN))
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),W1)
| aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),szDzozmdt0(xN)) ) )
| ~ ( ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[63]) ).
tff(65,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(szDzozmdt0(xN))
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,szDzozmdt0(xN))
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),W1)
| aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),szDzozmdt0(xN)) ) )
| ~ ( ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ) ) )
<=> ( ~ ! [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(szDzozmdt0(xN))
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),W1)
| aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),szDzozmdt0(xN)) ) )
| ~ ( ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[64,62]) ).
tff(66,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(szDzozmdt0(xN))
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,szDzozmdt0(xN))
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),W1)
| aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),szDzozmdt0(xN)) ) )
| ~ ( ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(67,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(szDzozmdt0(xN))
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),W1)
| aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),szDzozmdt0(xN)) ) )
| ~ ( ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),W1)
| aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),szDzozmdt0(xN)) ) )
| ~ ( ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ) ),
inference(unit_resolution,[status(thm)],[67,61,39]) ).
tff(69,plain,
( ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),W1)
| aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),szDzozmdt0(xN)) ) )
| ~ ( ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ) )
| ~ ( ~ ( aSubsetOf0(sdtlpdtrp0(xN,sz00),szDzozmdt0(xN))
| ~ aSet0(sdtlpdtrp0(xN,sz00))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,sz00),szDzozmdt0(xN)),sdtlpdtrp0(xN,sz00))
| aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,sz00),szDzozmdt0(xN)),szDzozmdt0(xN)) ) )
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,sz00),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,sz00))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,sz00))
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ) ) )
<=> ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),W1)
| aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),szDzozmdt0(xN)) ) )
| ~ ( ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ) )
| ~ ( ~ ( aSubsetOf0(sdtlpdtrp0(xN,sz00),szDzozmdt0(xN))
| ~ aSet0(sdtlpdtrp0(xN,sz00))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,sz00),szDzozmdt0(xN)),sdtlpdtrp0(xN,sz00))
| aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,sz00),szDzozmdt0(xN)),szDzozmdt0(xN)) ) )
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,sz00),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,sz00))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,sz00))
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(70,plain,
( ~ ( ~ ( ~ aSet0(sdtlpdtrp0(xN,sz00))
| aSubsetOf0(sdtlpdtrp0(xN,sz00),szDzozmdt0(xN))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,sz00),szDzozmdt0(xN)),sdtlpdtrp0(xN,sz00))
| aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,sz00),szDzozmdt0(xN)),szDzozmdt0(xN)) ) )
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,sz00),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,sz00))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,sz00))
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ) )
<=> ~ ( ~ ( aSubsetOf0(sdtlpdtrp0(xN,sz00),szDzozmdt0(xN))
| ~ aSet0(sdtlpdtrp0(xN,sz00))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,sz00),szDzozmdt0(xN)),sdtlpdtrp0(xN,sz00))
| aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,sz00),szDzozmdt0(xN)),szDzozmdt0(xN)) ) )
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,sz00),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,sz00))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,sz00))
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(71,plain,
( ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),W1)
| aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),szDzozmdt0(xN)) ) )
| ~ ( ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ) )
| ~ ( ~ ( ~ aSet0(sdtlpdtrp0(xN,sz00))
| aSubsetOf0(sdtlpdtrp0(xN,sz00),szDzozmdt0(xN))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,sz00),szDzozmdt0(xN)),sdtlpdtrp0(xN,sz00))
| aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,sz00),szDzozmdt0(xN)),szDzozmdt0(xN)) ) )
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,sz00),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,sz00))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,sz00))
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ) ) )
<=> ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),W1)
| aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),szDzozmdt0(xN)) ) )
| ~ ( ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ) )
| ~ ( ~ ( aSubsetOf0(sdtlpdtrp0(xN,sz00),szDzozmdt0(xN))
| ~ aSet0(sdtlpdtrp0(xN,sz00))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,sz00),szDzozmdt0(xN)),sdtlpdtrp0(xN,sz00))
| aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,sz00),szDzozmdt0(xN)),szDzozmdt0(xN)) ) )
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,sz00),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,sz00))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,sz00))
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[70]) ).
tff(72,plain,
( ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),W1)
| aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),szDzozmdt0(xN)) ) )
| ~ ( ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ) )
| ~ ( ~ ( ~ aSet0(sdtlpdtrp0(xN,sz00))
| aSubsetOf0(sdtlpdtrp0(xN,sz00),szDzozmdt0(xN))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,sz00),szDzozmdt0(xN)),sdtlpdtrp0(xN,sz00))
| aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,sz00),szDzozmdt0(xN)),szDzozmdt0(xN)) ) )
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,sz00),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,sz00))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,sz00))
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ) ) )
<=> ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),W1)
| aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),szDzozmdt0(xN)) ) )
| ~ ( ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ) )
| ~ ( ~ ( aSubsetOf0(sdtlpdtrp0(xN,sz00),szDzozmdt0(xN))
| ~ aSet0(sdtlpdtrp0(xN,sz00))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,sz00),szDzozmdt0(xN)),sdtlpdtrp0(xN,sz00))
| aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,sz00),szDzozmdt0(xN)),szDzozmdt0(xN)) ) )
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,sz00),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,sz00))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,sz00))
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[71,69]) ).
tff(73,plain,
( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),W1)
| aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),szDzozmdt0(xN)) ) )
| ~ ( ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ) )
| ~ ( ~ ( ~ aSet0(sdtlpdtrp0(xN,sz00))
| aSubsetOf0(sdtlpdtrp0(xN,sz00),szDzozmdt0(xN))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,sz00),szDzozmdt0(xN)),sdtlpdtrp0(xN,sz00))
| aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,sz00),szDzozmdt0(xN)),szDzozmdt0(xN)) ) )
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,sz00),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,sz00))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,sz00))
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(74,plain,
( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),W1)
| aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),szDzozmdt0(xN)) ) )
| ~ ( ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ) )
| ~ ( ~ ( aSubsetOf0(sdtlpdtrp0(xN,sz00),szDzozmdt0(xN))
| ~ aSet0(sdtlpdtrp0(xN,sz00))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,sz00),szDzozmdt0(xN)),sdtlpdtrp0(xN,sz00))
| aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,sz00),szDzozmdt0(xN)),szDzozmdt0(xN)) ) )
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,sz00),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,sz00))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,sz00))
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[73,72]) ).
tff(75,plain,
~ ( ~ ( aSubsetOf0(sdtlpdtrp0(xN,sz00),szDzozmdt0(xN))
| ~ aSet0(sdtlpdtrp0(xN,sz00))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,sz00),szDzozmdt0(xN)),sdtlpdtrp0(xN,sz00))
| aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,sz00),szDzozmdt0(xN)),szDzozmdt0(xN)) ) )
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,sz00),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,sz00))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,sz00))
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ) ),
inference(unit_resolution,[status(thm)],[74,68]) ).
tff(76,plain,
( ~ ( aSubsetOf0(sdtlpdtrp0(xN,sz00),szDzozmdt0(xN))
| ~ aSet0(sdtlpdtrp0(xN,sz00))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,sz00),szDzozmdt0(xN)),sdtlpdtrp0(xN,sz00))
| aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,sz00),szDzozmdt0(xN)),szDzozmdt0(xN)) ) )
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,sz00),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,sz00))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,sz00))
| aElementOf0(W2,szDzozmdt0(xN)) ) ) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,sz00),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,sz00))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,sz00))
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(77,plain,
( ~ aSubsetOf0(sdtlpdtrp0(xN,sz00),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,sz00))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,sz00))
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ),
inference(unit_resolution,[status(thm)],[76,75]) ).
tff(78,plain,
( aSubsetOf0(xS,szNzAzT0)
<=> aSubsetOf0(sdtlpdtrp0(xN,sz00),szDzozmdt0(xN)) ),
inference(rewrite,[status(thm)],]) ).
tff(79,plain,
( aSubsetOf0(xS,szNzAzT0)
<=> aSubsetOf0(xS,szNzAzT0) ),
inference(rewrite,[status(thm)],]) ).
tff(80,axiom,
( aSubsetOf0(xS,szNzAzT0)
& isCountable0(xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3435) ).
tff(81,plain,
aSubsetOf0(xS,szNzAzT0),
inference(and_elim,[status(thm)],[80]) ).
tff(82,plain,
aSubsetOf0(xS,szNzAzT0),
inference(modus_ponens,[status(thm)],[81,79]) ).
tff(83,plain,
aSubsetOf0(sdtlpdtrp0(xN,sz00),szDzozmdt0(xN)),
inference(modus_ponens,[status(thm)],[82,78]) ).
tff(84,plain,
( ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,sz00),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,sz00))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,sz00))
| aElementOf0(W2,szDzozmdt0(xN)) ) ) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,sz00),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,sz00))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,sz00))
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(85,plain,
( ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,sz00),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,sz00))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,sz00))
| aElementOf0(W2,szDzozmdt0(xN)) ) ) )
| ~ ( ~ aSet0(sdtlpdtrp0(xN,sz00))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,sz00))
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ),
inference(unit_resolution,[status(thm)],[84,83]) ).
tff(86,plain,
~ ( ~ aSet0(sdtlpdtrp0(xN,sz00))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,sz00))
| aElementOf0(W2,szDzozmdt0(xN)) ) ),
inference(unit_resolution,[status(thm)],[85,77]) ).
tff(87,plain,
( ~ aSet0(sdtlpdtrp0(xN,sz00))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,sz00))
| aElementOf0(W2,szDzozmdt0(xN)) )
| aSet0(sdtlpdtrp0(xN,sz00)) ),
inference(tautology,[status(thm)],]) ).
tff(88,plain,
aSet0(sdtlpdtrp0(xN,sz00)),
inference(unit_resolution,[status(thm)],[87,86]) ).
tff(89,plain,
( aElementOf0(xK,szNzAzT0)
<=> aElementOf0(szszuzczcdt0(xk),szDzozmdt0(xN)) ),
inference(rewrite,[status(thm)],]) ).
tff(90,plain,
( aElementOf0(xK,szNzAzT0)
<=> aElementOf0(xK,szNzAzT0) ),
inference(rewrite,[status(thm)],]) ).
tff(91,axiom,
aElementOf0(xK,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3418) ).
tff(92,plain,
aElementOf0(xK,szNzAzT0),
inference(modus_ponens,[status(thm)],[91,90]) ).
tff(93,plain,
aElementOf0(szszuzczcdt0(xk),szDzozmdt0(xN)),
inference(modus_ponens,[status(thm)],[92,89]) ).
tff(94,plain,
^ [W0: $i,W1: $i] :
trans(
monotonicity(
quant_intro(
proof_bind(
^ [W2: $i] :
rewrite(
( ~ ( ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) ) ) ) )
| ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) ) ) ) )
<=> ~ ( ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) ) ) )
| ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) ) ) ) ) ) ))),
( ! [W2: $i] :
~ ( ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) ) ) ) )
| ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) ) ) ) )
<=> ! [W2: $i] :
~ ( ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) ) ) )
| ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) ) ) ) ) ) )),
( ( ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) ) ) ) )
| ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) ) ) ) ) )
<=> ( ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) ) ) )
| ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) ) ) ) ) ) ) )),
rewrite(
( ( ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) ) ) )
| ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) ) ) ) ) ) )
<=> ( ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) ) ) )
| ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) ) ) ) ) ) ) )),
( ( ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) ) ) ) )
| ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) ) ) ) ) )
<=> ( ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) ) ) )
| ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) ) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(95,plain,
( ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) ) ) ) )
| ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) ) ) )
| ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) ) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[94]) ).
tff(96,plain,
^ [W0: $i,W1: $i] :
refl(
( ( ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) ) ) ) )
| ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) ) ) ) ) )
<=> ( ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) ) ) ) )
| ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(97,plain,
( ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) ) ) ) )
| ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) ) ) ) )
| ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[96]) ).
tff(98,plain,
^ [W0: $i,W1: $i] :
rewrite(
( ( ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) ) ) ) )
| ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) ) ) ) ) )
<=> ( ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) ) ) ) )
| ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(99,plain,
( ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) ) ) ) )
| ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) ) ) ) )
| ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[98]) ).
tff(100,plain,
( ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) ) ) ) )
| ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) ) ) ) )
| ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[99,97]) ).
tff(101,plain,
^ [W0: $i,W1: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( aSet0(W0)
& aElementOf0(W1,szDzozmdt0(xN)) )
<=> ~ ( ~ aSet0(W0)
| ~ aElementOf0(W1,szDzozmdt0(xN)) ) )),
( ~ ( aSet0(W0)
& aElementOf0(W1,szDzozmdt0(xN)) )
<=> ~ ~ ( ~ aSet0(W0)
| ~ aElementOf0(W1,szDzozmdt0(xN)) ) )),
rewrite(
( ~ ~ ( ~ aSet0(W0)
| ~ aElementOf0(W1,szDzozmdt0(xN)) )
<=> ( ~ aSet0(W0)
| ~ aElementOf0(W1,szDzozmdt0(xN)) ) )),
( ~ ( aSet0(W0)
& aElementOf0(W1,szDzozmdt0(xN)) )
<=> ( ~ aSet0(W0)
| ~ aElementOf0(W1,szDzozmdt0(xN)) ) )),
quant_intro(
proof_bind(
^ [W2: $i] :
trans(
monotonicity(
rewrite(
( ( ( W2 != slbdtsldtrb0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& ( sbrdtbr0(W3) = W1 ) ) ) ) )
<=> ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) ) ) ) ) )),
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
& ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) = W1 ) )
<=> ~ ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) ) )),
( ( ~ aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
& ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) = W1 ) ) )
<=> ( ~ aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ~ ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) ) ) )),
rewrite(
( ( ~ aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ~ ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) ) )
<=> ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) ) ) )),
( ( ~ aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
& ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) = W1 ) ) )
<=> ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) ) ) )),
( ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ~ aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
& ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) = W1 ) ) ) )
<=> ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) ) ) ) )),
rewrite(
( ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) ) ) )
<=> ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) ) ) ) )),
( ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ~ aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
& ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) = W1 ) ) ) )
<=> ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) ) ) ) )),
( ( ( ( W2 != slbdtsldtrb0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& ( sbrdtbr0(W3) = W1 ) ) ) ) )
& ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ~ aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
& ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) = W1 ) ) ) ) )
<=> ( ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) ) ) ) )
& ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) ) ) ) ) )),
rewrite(
( ( ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) ) ) ) )
& ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) ) ) ) )
<=> ~ ( ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) ) ) ) )
| ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) ) ) ) ) )),
( ( ( ( W2 != slbdtsldtrb0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& ( sbrdtbr0(W3) = W1 ) ) ) ) )
& ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ~ aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
& ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) = W1 ) ) ) ) )
<=> ~ ( ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) ) ) ) )
| ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) ) ) ) ) ))),
( ! [W2: $i] :
( ( ( W2 != slbdtsldtrb0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& ( sbrdtbr0(W3) = W1 ) ) ) ) )
& ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ~ aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
& ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) = W1 ) ) ) ) )
<=> ! [W2: $i] :
~ ( ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) ) ) ) )
| ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) ) ) ) ) )),
( ( ~ ( aSet0(W0)
& aElementOf0(W1,szDzozmdt0(xN)) )
| ! [W2: $i] :
( ( ( W2 != slbdtsldtrb0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& ( sbrdtbr0(W3) = W1 ) ) ) ) )
& ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ~ aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
& ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) = W1 ) ) ) ) ) )
<=> ( ~ aSet0(W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ! [W2: $i] :
~ ( ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) ) ) ) )
| ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) ) ) ) ) ) )),
rewrite(
( ( ~ aSet0(W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ! [W2: $i] :
~ ( ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) ) ) ) )
| ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) ) ) ) ) )
<=> ( ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) ) ) ) )
| ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) ) ) ) ) ) )),
( ( ~ ( aSet0(W0)
& aElementOf0(W1,szDzozmdt0(xN)) )
| ! [W2: $i] :
( ( ( W2 != slbdtsldtrb0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& ( sbrdtbr0(W3) = W1 ) ) ) ) )
& ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ~ aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
& ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) = W1 ) ) ) ) ) )
<=> ( ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) ) ) ) )
| ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(102,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aSet0(W0)
& aElementOf0(W1,szDzozmdt0(xN)) )
| ! [W2: $i] :
( ( ( W2 != slbdtsldtrb0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& ( sbrdtbr0(W3) = W1 ) ) ) ) )
& ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ~ aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
& ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) = W1 ) ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) ) ) ) )
| ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[101]) ).
tff(103,plain,
^ [W0: $i,W1: $i] :
rewrite(
( ( ~ ( aSet0(W0)
& aElementOf0(W1,szDzozmdt0(xN)) )
| ! [W2: $i] :
( ( ( W2 != slbdtsldtrb0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& ( sbrdtbr0(W3) = W1 ) ) ) ) )
& ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ~ ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
& ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) = W1 ) ) ) ) ) )
<=> ( ~ ( aSet0(W0)
& aElementOf0(W1,szDzozmdt0(xN)) )
| ! [W2: $i] :
( ( ( W2 != slbdtsldtrb0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& ( sbrdtbr0(W3) = W1 ) ) ) ) )
& ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ~ aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
& ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) = W1 ) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(104,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aSet0(W0)
& aElementOf0(W1,szDzozmdt0(xN)) )
| ! [W2: $i] :
( ( ( W2 != slbdtsldtrb0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& ( sbrdtbr0(W3) = W1 ) ) ) ) )
& ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ~ ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
& ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) = W1 ) ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aSet0(W0)
& aElementOf0(W1,szDzozmdt0(xN)) )
| ! [W2: $i] :
( ( ( W2 != slbdtsldtrb0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& ( sbrdtbr0(W3) = W1 ) ) ) ) )
& ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ~ aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
& ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) = W1 ) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[103]) ).
tff(105,plain,
^ [W0: $i,W1: $i] :
rewrite(
( ( ~ ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) )
| ! [W2: $i] :
( ( W2 = slbdtsldtrb0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& ( sbrdtbr0(W3) = W1 ) ) ) ) ) )
<=> ( ~ ( aSet0(W0)
& aElementOf0(W1,szDzozmdt0(xN)) )
| ! [W2: $i] :
( ( W2 = slbdtsldtrb0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& ( sbrdtbr0(W3) = W1 ) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(106,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) )
| ! [W2: $i] :
( ( W2 = slbdtsldtrb0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& ( sbrdtbr0(W3) = W1 ) ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aSet0(W0)
& aElementOf0(W1,szDzozmdt0(xN)) )
| ! [W2: $i] :
( ( W2 = slbdtsldtrb0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& ( sbrdtbr0(W3) = W1 ) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[105]) ).
tff(107,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) )
| ! [W2: $i] :
( ( W2 = slbdtsldtrb0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& ( sbrdtbr0(W3) = W1 ) ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) )
| ! [W2: $i] :
( ( W2 = slbdtsldtrb0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& ( sbrdtbr0(W3) = W1 ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(108,plain,
^ [W0: $i,W1: $i] :
rewrite(
( ( ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) )
=> ! [W2: $i] :
( ( W2 = slbdtsldtrb0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& ( sbrdtbr0(W3) = W1 ) ) ) ) ) )
<=> ( ~ ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) )
| ! [W2: $i] :
( ( W2 = slbdtsldtrb0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& ( sbrdtbr0(W3) = W1 ) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(109,plain,
( ! [W0: $i,W1: $i] :
( ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) )
=> ! [W2: $i] :
( ( W2 = slbdtsldtrb0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& ( sbrdtbr0(W3) = W1 ) ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) )
| ! [W2: $i] :
( ( W2 = slbdtsldtrb0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& ( sbrdtbr0(W3) = W1 ) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[108]) ).
tff(110,axiom,
! [W0: $i,W1: $i] :
( ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) )
=> ! [W2: $i] :
( ( W2 = slbdtsldtrb0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& ( sbrdtbr0(W3) = W1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSel) ).
tff(111,plain,
! [W0: $i,W1: $i] :
( ~ ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) )
| ! [W2: $i] :
( ( W2 = slbdtsldtrb0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& ( sbrdtbr0(W3) = W1 ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[110,109]) ).
tff(112,plain,
! [W0: $i,W1: $i] :
( ~ ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) )
| ! [W2: $i] :
( ( W2 = slbdtsldtrb0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& ( sbrdtbr0(W3) = W1 ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[111,107]) ).
tff(113,plain,
! [W0: $i,W1: $i] :
( ~ ( aSet0(W0)
& aElementOf0(W1,szDzozmdt0(xN)) )
| ! [W2: $i] :
( ( W2 = slbdtsldtrb0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& ( sbrdtbr0(W3) = W1 ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[112,106]) ).
tff(114,plain,
! [W0: $i,W1: $i] :
( ~ ( aSet0(W0)
& aElementOf0(W1,szDzozmdt0(xN)) )
| ! [W2: $i] :
( ( ( W2 != slbdtsldtrb0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& ( sbrdtbr0(W3) = W1 ) ) ) ) )
& ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ~ ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
& ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) = W1 ) ) ) ) ) ),
inference(skolemize,[status(sab)],[113]) ).
tff(115,plain,
! [W0: $i,W1: $i] :
( ~ ( aSet0(W0)
& aElementOf0(W1,szDzozmdt0(xN)) )
| ! [W2: $i] :
( ( ( W2 != slbdtsldtrb0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& ( sbrdtbr0(W3) = W1 ) ) ) ) )
& ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ~ aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
& ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) = W1 ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[114,104]) ).
tff(116,plain,
! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) ) ) ) )
| ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[115,102]) ).
tff(117,plain,
! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) ) ) ) )
| ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[116,100]) ).
tff(118,plain,
! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) ) ) )
| ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[117,95]) ).
tff(119,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) ) ) )
| ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) ) ) ) ) ) )
| ~ aSet0(sdtlpdtrp0(xN,sz00))
| ~ aElementOf0(szszuzczcdt0(xk),szDzozmdt0(xN))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)) )
| ( aElementOf0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00)),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00)),sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00))) != szszuzczcdt0(xk) ) ) ) )
| ~ ( ( W2 != slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(W3) != szszuzczcdt0(xk) ) ) ) ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) ) ) )
| ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) ) ) ) ) ) )
| ~ aSet0(sdtlpdtrp0(xN,sz00))
| ~ aElementOf0(szszuzczcdt0(xk),szDzozmdt0(xN))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)) )
| ( aElementOf0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00)),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00)),sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00))) != szszuzczcdt0(xk) ) ) ) )
| ~ ( ( W2 != slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(W3) != szszuzczcdt0(xk) ) ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(120,plain,
( ( ~ aElementOf0(szszuzczcdt0(xk),szDzozmdt0(xN))
| ~ aSet0(sdtlpdtrp0(xN,sz00))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)) )
| ( aElementOf0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00)),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00)),sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00))) != szszuzczcdt0(xk) ) ) ) )
| ~ ( ( W2 != slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(W3) != szszuzczcdt0(xk) ) ) ) ) ) ) )
<=> ( ~ aSet0(sdtlpdtrp0(xN,sz00))
| ~ aElementOf0(szszuzczcdt0(xk),szDzozmdt0(xN))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)) )
| ( aElementOf0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00)),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00)),sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00))) != szszuzczcdt0(xk) ) ) ) )
| ~ ( ( W2 != slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(W3) != szszuzczcdt0(xk) ) ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(121,plain,
^ [W2: $i] :
rewrite(
( ~ ( ~ ( ( W2 = slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00)),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00)),sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00))) != szszuzczcdt0(xk) ) ) ) )
| ~ ( ( W2 != slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(W3) != szszuzczcdt0(xk) ) ) ) ) ) )
<=> ~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)) )
| ( aElementOf0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00)),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00)),sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00))) != szszuzczcdt0(xk) ) ) ) )
| ~ ( ( W2 != slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(W3) != szszuzczcdt0(xk) ) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(122,plain,
( ! [W2: $i] :
~ ( ~ ( ( W2 = slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00)),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00)),sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00))) != szszuzczcdt0(xk) ) ) ) )
| ~ ( ( W2 != slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(W3) != szszuzczcdt0(xk) ) ) ) ) ) )
<=> ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)) )
| ( aElementOf0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00)),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00)),sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00))) != szszuzczcdt0(xk) ) ) ) )
| ~ ( ( W2 != slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(W3) != szszuzczcdt0(xk) ) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[121]) ).
tff(123,plain,
( ( ~ aElementOf0(szszuzczcdt0(xk),szDzozmdt0(xN))
| ~ aSet0(sdtlpdtrp0(xN,sz00))
| ! [W2: $i] :
~ ( ~ ( ( W2 = slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00)),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00)),sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00))) != szszuzczcdt0(xk) ) ) ) )
| ~ ( ( W2 != slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(W3) != szszuzczcdt0(xk) ) ) ) ) ) ) )
<=> ( ~ aElementOf0(szszuzczcdt0(xk),szDzozmdt0(xN))
| ~ aSet0(sdtlpdtrp0(xN,sz00))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)) )
| ( aElementOf0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00)),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00)),sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00))) != szszuzczcdt0(xk) ) ) ) )
| ~ ( ( W2 != slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(W3) != szszuzczcdt0(xk) ) ) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[122]) ).
tff(124,plain,
( ( ~ aElementOf0(szszuzczcdt0(xk),szDzozmdt0(xN))
| ~ aSet0(sdtlpdtrp0(xN,sz00))
| ! [W2: $i] :
~ ( ~ ( ( W2 = slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00)),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00)),sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00))) != szszuzczcdt0(xk) ) ) ) )
| ~ ( ( W2 != slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(W3) != szszuzczcdt0(xk) ) ) ) ) ) ) )
<=> ( ~ aSet0(sdtlpdtrp0(xN,sz00))
| ~ aElementOf0(szszuzczcdt0(xk),szDzozmdt0(xN))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)) )
| ( aElementOf0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00)),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00)),sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00))) != szszuzczcdt0(xk) ) ) ) )
| ~ ( ( W2 != slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(W3) != szszuzczcdt0(xk) ) ) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[123,120]) ).
tff(125,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) ) ) )
| ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) ) ) ) ) ) )
| ~ aElementOf0(szszuzczcdt0(xk),szDzozmdt0(xN))
| ~ aSet0(sdtlpdtrp0(xN,sz00))
| ! [W2: $i] :
~ ( ~ ( ( W2 = slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00)),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00)),sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00))) != szszuzczcdt0(xk) ) ) ) )
| ~ ( ( W2 != slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(W3) != szszuzczcdt0(xk) ) ) ) ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) ) ) )
| ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) ) ) ) ) ) )
| ~ aSet0(sdtlpdtrp0(xN,sz00))
| ~ aElementOf0(szszuzczcdt0(xk),szDzozmdt0(xN))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)) )
| ( aElementOf0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00)),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00)),sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00))) != szszuzczcdt0(xk) ) ) ) )
| ~ ( ( W2 != slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(W3) != szszuzczcdt0(xk) ) ) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[124]) ).
tff(126,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) ) ) )
| ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) ) ) ) ) ) )
| ~ aElementOf0(szszuzczcdt0(xk),szDzozmdt0(xN))
| ~ aSet0(sdtlpdtrp0(xN,sz00))
| ! [W2: $i] :
~ ( ~ ( ( W2 = slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00)),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00)),sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00))) != szszuzczcdt0(xk) ) ) ) )
| ~ ( ( W2 != slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(W3) != szszuzczcdt0(xk) ) ) ) ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) ) ) )
| ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) ) ) ) ) ) )
| ~ aSet0(sdtlpdtrp0(xN,sz00))
| ~ aElementOf0(szszuzczcdt0(xk),szDzozmdt0(xN))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)) )
| ( aElementOf0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00)),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00)),sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00))) != szszuzczcdt0(xk) ) ) ) )
| ~ ( ( W2 != slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(W3) != szszuzczcdt0(xk) ) ) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[125,119]) ).
tff(127,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) ) ) )
| ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) ) ) ) ) ) )
| ~ aElementOf0(szszuzczcdt0(xk),szDzozmdt0(xN))
| ~ aSet0(sdtlpdtrp0(xN,sz00))
| ! [W2: $i] :
~ ( ~ ( ( W2 = slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00)),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00)),sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00))) != szszuzczcdt0(xk) ) ) ) )
| ~ ( ( W2 != slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(W3) != szszuzczcdt0(xk) ) ) ) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(128,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) ) ) )
| ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) ) ) ) ) ) )
| ~ aSet0(sdtlpdtrp0(xN,sz00))
| ~ aElementOf0(szszuzczcdt0(xk),szDzozmdt0(xN))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)) )
| ( aElementOf0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00)),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00)),sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00))) != szszuzczcdt0(xk) ) ) ) )
| ~ ( ( W2 != slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(W3) != szszuzczcdt0(xk) ) ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[127,126]) ).
tff(129,plain,
( ~ aSet0(sdtlpdtrp0(xN,sz00))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)) )
| ( aElementOf0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00)),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00)),sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00))) != szszuzczcdt0(xk) ) ) ) )
| ~ ( ( W2 != slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(W3) != szszuzczcdt0(xk) ) ) ) ) ) ) ),
inference(unit_resolution,[status(thm)],[128,118,93]) ).
tff(130,plain,
! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)) )
| ( aElementOf0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00)),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00)),sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00))) != szszuzczcdt0(xk) ) ) ) )
| ~ ( ( W2 != slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(W3) != szszuzczcdt0(xk) ) ) ) ) ) ),
inference(unit_resolution,[status(thm)],[129,88]) ).
tff(131,plain,
( ( ~ ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)) )
| ( aElementOf0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00)),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00)),sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00))) != szszuzczcdt0(xk) ) ) ) )
| ~ ( ( W2 != slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(W3) != szszuzczcdt0(xk) ) ) ) ) ) )
| ~ ( ~ aSet0(slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)))
| ~ ! [W3: $i] :
( aElementOf0(W3,slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)))
<=> ~ ( ~ aSubsetOf0(W3,sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(W3) != szszuzczcdt0(xk) ) ) ) ) )
<=> ( ~ ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)) )
| ( aElementOf0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00)),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00)),sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00))) != szszuzczcdt0(xk) ) ) ) )
| ~ ( ( W2 != slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(W3) != szszuzczcdt0(xk) ) ) ) ) ) )
| ~ ( ~ aSet0(slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)))
| ~ ! [W3: $i] :
( aElementOf0(W3,slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)))
<=> ~ ( ~ aSubsetOf0(W3,sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(W3) != szszuzczcdt0(xk) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(132,plain,
( ~ ( ~ ( ~ aSet0(slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)))
| ( slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)) = slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)) )
| ( aElementOf0(tptp_fun_W3_10(slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)),szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00)),slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)))
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)),szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00)),sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(tptp_fun_W3_10(slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)),szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00))) != szszuzczcdt0(xk) ) ) ) )
| ~ ( ( slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)) != slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)) )
| ~ ( ~ aSet0(slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)))
| ~ ! [W3: $i] :
( aElementOf0(W3,slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)))
<=> ~ ( ~ aSubsetOf0(W3,sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(W3) != szszuzczcdt0(xk) ) ) ) ) ) )
<=> ~ ( ~ aSet0(slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)))
| ~ ! [W3: $i] :
( aElementOf0(W3,slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)))
<=> ~ ( ~ aSubsetOf0(W3,sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(W3) != szszuzczcdt0(xk) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(133,plain,
( ( ~ ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)) )
| ( aElementOf0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00)),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00)),sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00))) != szszuzczcdt0(xk) ) ) ) )
| ~ ( ( W2 != slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(W3) != szszuzczcdt0(xk) ) ) ) ) ) )
| ~ ( ~ ( ~ aSet0(slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)))
| ( slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)) = slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)) )
| ( aElementOf0(tptp_fun_W3_10(slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)),szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00)),slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)))
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)),szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00)),sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(tptp_fun_W3_10(slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)),szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00))) != szszuzczcdt0(xk) ) ) ) )
| ~ ( ( slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)) != slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)) )
| ~ ( ~ aSet0(slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)))
| ~ ! [W3: $i] :
( aElementOf0(W3,slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)))
<=> ~ ( ~ aSubsetOf0(W3,sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(W3) != szszuzczcdt0(xk) ) ) ) ) ) ) )
<=> ( ~ ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)) )
| ( aElementOf0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00)),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00)),sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00))) != szszuzczcdt0(xk) ) ) ) )
| ~ ( ( W2 != slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(W3) != szszuzczcdt0(xk) ) ) ) ) ) )
| ~ ( ~ aSet0(slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)))
| ~ ! [W3: $i] :
( aElementOf0(W3,slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)))
<=> ~ ( ~ aSubsetOf0(W3,sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(W3) != szszuzczcdt0(xk) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[132]) ).
tff(134,plain,
( ( ~ ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)) )
| ( aElementOf0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00)),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00)),sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00))) != szszuzczcdt0(xk) ) ) ) )
| ~ ( ( W2 != slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(W3) != szszuzczcdt0(xk) ) ) ) ) ) )
| ~ ( ~ ( ~ aSet0(slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)))
| ( slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)) = slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)) )
| ( aElementOf0(tptp_fun_W3_10(slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)),szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00)),slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)))
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)),szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00)),sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(tptp_fun_W3_10(slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)),szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00))) != szszuzczcdt0(xk) ) ) ) )
| ~ ( ( slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)) != slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)) )
| ~ ( ~ aSet0(slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)))
| ~ ! [W3: $i] :
( aElementOf0(W3,slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)))
<=> ~ ( ~ aSubsetOf0(W3,sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(W3) != szszuzczcdt0(xk) ) ) ) ) ) ) )
<=> ( ~ ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)) )
| ( aElementOf0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00)),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00)),sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00))) != szszuzczcdt0(xk) ) ) ) )
| ~ ( ( W2 != slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(W3) != szszuzczcdt0(xk) ) ) ) ) ) )
| ~ ( ~ aSet0(slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)))
| ~ ! [W3: $i] :
( aElementOf0(W3,slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)))
<=> ~ ( ~ aSubsetOf0(W3,sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(W3) != szszuzczcdt0(xk) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[133,131]) ).
tff(135,plain,
( ~ ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)) )
| ( aElementOf0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00)),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00)),sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00))) != szszuzczcdt0(xk) ) ) ) )
| ~ ( ( W2 != slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(W3) != szszuzczcdt0(xk) ) ) ) ) ) )
| ~ ( ~ ( ~ aSet0(slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)))
| ( slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)) = slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)) )
| ( aElementOf0(tptp_fun_W3_10(slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)),szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00)),slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)))
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)),szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00)),sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(tptp_fun_W3_10(slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)),szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00))) != szszuzczcdt0(xk) ) ) ) )
| ~ ( ( slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)) != slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)) )
| ~ ( ~ aSet0(slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)))
| ~ ! [W3: $i] :
( aElementOf0(W3,slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)))
<=> ~ ( ~ aSubsetOf0(W3,sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(W3) != szszuzczcdt0(xk) ) ) ) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(136,plain,
( ~ ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)) )
| ( aElementOf0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00)),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00)),sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(tptp_fun_W3_10(W2,szszuzczcdt0(xk),sdtlpdtrp0(xN,sz00))) != szszuzczcdt0(xk) ) ) ) )
| ~ ( ( W2 != slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(W3) != szszuzczcdt0(xk) ) ) ) ) ) )
| ~ ( ~ aSet0(slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)))
| ~ ! [W3: $i] :
( aElementOf0(W3,slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)))
<=> ~ ( ~ aSubsetOf0(W3,sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(W3) != szszuzczcdt0(xk) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[135,134]) ).
tff(137,plain,
~ ( ~ aSet0(slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)))
| ~ ! [W3: $i] :
( aElementOf0(W3,slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)))
<=> ~ ( ~ aSubsetOf0(W3,sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(W3) != szszuzczcdt0(xk) ) ) ) ),
inference(unit_resolution,[status(thm)],[136,130]) ).
tff(138,plain,
( ~ aSet0(slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)))
| ~ ! [W3: $i] :
( aElementOf0(W3,slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)))
<=> ~ ( ~ aSubsetOf0(W3,sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(W3) != szszuzczcdt0(xk) ) ) )
| ! [W3: $i] :
( aElementOf0(W3,slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)))
<=> ~ ( ~ aSubsetOf0(W3,sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(W3) != szszuzczcdt0(xk) ) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(139,plain,
! [W3: $i] :
( aElementOf0(W3,slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)))
<=> ~ ( ~ aSubsetOf0(W3,sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(W3) != szszuzczcdt0(xk) ) ) ),
inference(unit_resolution,[status(thm)],[138,137]) ).
tff(140,plain,
( ~ ! [W3: $i] :
( aElementOf0(W3,slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)))
<=> ~ ( ~ aSubsetOf0(W3,sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(W3) != szszuzczcdt0(xk) ) ) )
| ( aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)))
<=> ~ ( ~ aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),sdtlpdtrp0(xN,sz00))
| ( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) != szszuzczcdt0(xk) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(141,plain,
$false,
inference(unit_resolution,[status(thm)],[140,139,33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM584+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n007.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Sep 2 11:47:33 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 1.13/0.99 % SZS status Theorem
% 1.13/0.99 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------