TSTP Solution File: NUM604+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM604+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n022.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 13:10:49 EDT 2022
% Result : Theorem 176.15s 112.07s
% Output : Proof 176.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 150
% Syntax : Number of formulae : 328 ( 70 unt; 26 typ; 0 def)
% Number of atoms : 3205 ( 423 equ)
% Maximal formula atoms : 40 ( 10 avg)
% Number of connectives : 5985 (3214 ~;2259 |; 236 &)
% ( 222 <=>; 54 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 7 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 132 ( 132 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 24 ( 16 >; 8 *; 0 +; 0 <<)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-3 aty)
% Number of functors : 20 ( 20 usr; 10 con; 0-2 aty)
% Number of variables : 777 ( 713 !; 20 ?; 777 :)
% Comments :
%------------------------------------------------------------------------------
tff(sdtlseqdt0_type,type,
sdtlseqdt0: ( $i * $i ) > $o ).
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(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(tptp_fun_W1_24_type,type,
tptp_fun_W1_24: $i > $i ).
tff(xe_type,type,
xe: $i ).
tff(tptp_fun_W2_6_type,type,
tptp_fun_W2_6: ( $i * $i ) > $i ).
tff(sz00_type,type,
sz00: $i ).
tff(aSet0_type,type,
aSet0: $i > $o ).
tff(aSubsetOf0_type,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff(tptp_fun_W2_1_type,type,
tptp_fun_W2_1: ( $i * $i ) > $i ).
tff(szDzozmdt0_type,type,
szDzozmdt0: $i > $i ).
tff(szNzAzT0_type,type,
szNzAzT0: $i ).
tff(isCountable0_type,type,
isCountable0: $i > $o ).
tff(xS_type,type,
xS: $i ).
tff(sdtlbdtrb0_type,type,
sdtlbdtrb0: ( $i * $i ) > $i ).
tff(szDzizrdt0_type,type,
szDzizrdt0: $i > $i ).
tff(xd_type,type,
xd: $i ).
tff(sdtlcdtrc0_type,type,
sdtlcdtrc0: ( $i * $i ) > $i ).
tff(xO_type,type,
xO: $i ).
tff(xx_type,type,
xx: $i ).
tff(aFunction0_type,type,
aFunction0: $i > $o ).
tff(slbdtrb0_type,type,
slbdtrb0: $i > $i ).
tff(slcrc0_type,type,
slcrc0: $i ).
tff(1,plain,
( aSet0(szNzAzT0)
<=> aSet0(szDzozmdt0(xN)) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( aSet0(szNzAzT0)
<=> aSet0(szNzAzT0) ),
inference(rewrite,[status(thm)],]) ).
tff(3,axiom,
( aSet0(szNzAzT0)
& isCountable0(szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNATSet) ).
tff(4,plain,
aSet0(szNzAzT0),
inference(and_elim,[status(thm)],[3]) ).
tff(5,plain,
aSet0(szNzAzT0),
inference(modus_ponens,[status(thm)],[4,2]) ).
tff(6,plain,
aSet0(szDzozmdt0(xN)),
inference(modus_ponens,[status(thm)],[5,1]) ).
tff(7,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(8,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ 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)],[7]) ).
tff(9,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(10,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) ),
inference(quant_intro,[status(thm)],[9]) ).
tff(11,plain,
^ [W0: $i] :
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(12,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)],[11]) ).
tff(13,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) ),
inference(transitivity,[status(thm)],[12,10]) ).
tff(14,plain,
^ [W0: $i] :
rewrite(
( ( ~ aSet0(W0)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,W0)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
& ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(15,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,W0)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
& ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) ),
inference(quant_intro,[status(thm)],[14]) ).
tff(16,plain,
^ [W0: $i] :
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(17,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)],[16]) ).
tff(18,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(19,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(20,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)],[19]) ).
tff(21,axiom,
! [W0: $i] :
( aSet0(W0)
=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSub) ).
tff(22,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)],[21,20]) ).
tff(23,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)],[22,18]) ).
tff(24,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,W0)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
& ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ),
inference(skolemize,[status(sab)],[23]) ).
tff(25,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,W0)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
& ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ),
inference(modus_ponens,[status(thm)],[24,17]) ).
tff(26,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)],[25,15]) ).
tff(27,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)],[26,13]) ).
tff(28,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)],[27,8]) ).
tff(29,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(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(30,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(31,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(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)],[30]) ).
tff(32,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(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)],[31,29]) ).
tff(33,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(34,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)],[33,32]) ).
tff(35,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)],[34,28,6]) ).
tff(36,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(37,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(38,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)],[37]) ).
tff(39,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)],[38,36]) ).
tff(40,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(41,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)],[40,39]) ).
tff(42,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)],[41,35]) ).
tff(43,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(44,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)],[43,42]) ).
tff(45,plain,
( aSubsetOf0(xS,szNzAzT0)
<=> aSubsetOf0(sdtlpdtrp0(xN,sz00),szDzozmdt0(xN)) ),
inference(rewrite,[status(thm)],]) ).
tff(46,plain,
( aSubsetOf0(xS,szNzAzT0)
<=> aSubsetOf0(xS,szNzAzT0) ),
inference(rewrite,[status(thm)],]) ).
tff(47,axiom,
( aSubsetOf0(xS,szNzAzT0)
& isCountable0(xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3435) ).
tff(48,plain,
aSubsetOf0(xS,szNzAzT0),
inference(and_elim,[status(thm)],[47]) ).
tff(49,plain,
aSubsetOf0(xS,szNzAzT0),
inference(modus_ponens,[status(thm)],[48,46]) ).
tff(50,plain,
aSubsetOf0(sdtlpdtrp0(xN,sz00),szDzozmdt0(xN)),
inference(modus_ponens,[status(thm)],[49,45]) ).
tff(51,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(52,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)],[51,50]) ).
tff(53,plain,
~ ( ~ aSet0(sdtlpdtrp0(xN,sz00))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,sz00))
| aElementOf0(W2,szDzozmdt0(xN)) ) ),
inference(unit_resolution,[status(thm)],[52,44]) ).
tff(54,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(55,plain,
aSet0(sdtlpdtrp0(xN,sz00)),
inference(unit_resolution,[status(thm)],[54,53]) ).
tff(56,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(sdtlpdtrp0(xN,sz00))
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,sdtlpdtrp0(xN,sz00)),W1)
| aElementOf0(tptp_fun_W2_1(W1,sdtlpdtrp0(xN,sz00)),sdtlpdtrp0(xN,sz00)) ) )
| ~ ( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlpdtrp0(xN,sz00)) ) ) ) ) )
<=> ( ~ ! [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(sdtlpdtrp0(xN,sz00))
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,sdtlpdtrp0(xN,sz00)),W1)
| aElementOf0(tptp_fun_W2_1(W1,sdtlpdtrp0(xN,sz00)),sdtlpdtrp0(xN,sz00)) ) )
| ~ ( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlpdtrp0(xN,sz00)) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(57,plain,
( ( ~ aSet0(sdtlpdtrp0(xN,sz00))
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,sdtlpdtrp0(xN,sz00)),W1)
| aElementOf0(tptp_fun_W2_1(W1,sdtlpdtrp0(xN,sz00)),sdtlpdtrp0(xN,sz00)) ) )
| ~ ( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlpdtrp0(xN,sz00)) ) ) ) ) )
<=> ( ~ aSet0(sdtlpdtrp0(xN,sz00))
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,sdtlpdtrp0(xN,sz00)),W1)
| aElementOf0(tptp_fun_W2_1(W1,sdtlpdtrp0(xN,sz00)),sdtlpdtrp0(xN,sz00)) ) )
| ~ ( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlpdtrp0(xN,sz00)) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(58,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(sdtlpdtrp0(xN,sz00))
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,sdtlpdtrp0(xN,sz00)),W1)
| aElementOf0(tptp_fun_W2_1(W1,sdtlpdtrp0(xN,sz00)),sdtlpdtrp0(xN,sz00)) ) )
| ~ ( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlpdtrp0(xN,sz00)) ) ) ) ) )
<=> ( ~ ! [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(sdtlpdtrp0(xN,sz00))
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,sdtlpdtrp0(xN,sz00)),W1)
| aElementOf0(tptp_fun_W2_1(W1,sdtlpdtrp0(xN,sz00)),sdtlpdtrp0(xN,sz00)) ) )
| ~ ( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlpdtrp0(xN,sz00)) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[57]) ).
tff(59,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(sdtlpdtrp0(xN,sz00))
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,sdtlpdtrp0(xN,sz00)),W1)
| aElementOf0(tptp_fun_W2_1(W1,sdtlpdtrp0(xN,sz00)),sdtlpdtrp0(xN,sz00)) ) )
| ~ ( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlpdtrp0(xN,sz00)) ) ) ) ) )
<=> ( ~ ! [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(sdtlpdtrp0(xN,sz00))
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,sdtlpdtrp0(xN,sz00)),W1)
| aElementOf0(tptp_fun_W2_1(W1,sdtlpdtrp0(xN,sz00)),sdtlpdtrp0(xN,sz00)) ) )
| ~ ( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlpdtrp0(xN,sz00)) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[58,56]) ).
tff(60,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(sdtlpdtrp0(xN,sz00))
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,sdtlpdtrp0(xN,sz00)),W1)
| aElementOf0(tptp_fun_W2_1(W1,sdtlpdtrp0(xN,sz00)),sdtlpdtrp0(xN,sz00)) ) )
| ~ ( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlpdtrp0(xN,sz00)) ) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
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) ) ) ) ) )
| ~ aSet0(sdtlpdtrp0(xN,sz00))
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,sdtlpdtrp0(xN,sz00)),W1)
| aElementOf0(tptp_fun_W2_1(W1,sdtlpdtrp0(xN,sz00)),sdtlpdtrp0(xN,sz00)) ) )
| ~ ( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlpdtrp0(xN,sz00)) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,sdtlpdtrp0(xN,sz00)),W1)
| aElementOf0(tptp_fun_W2_1(W1,sdtlpdtrp0(xN,sz00)),sdtlpdtrp0(xN,sz00)) ) )
| ~ ( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlpdtrp0(xN,sz00)) ) ) ) ),
inference(unit_resolution,[status(thm)],[61,28,55]) ).
tff(63,plain,
( ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,sdtlpdtrp0(xN,sz00)),W1)
| aElementOf0(tptp_fun_W2_1(W1,sdtlpdtrp0(xN,sz00)),sdtlpdtrp0(xN,sz00)) ) )
| ~ ( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlpdtrp0(xN,sz00)) ) ) ) )
| ~ ( ~ ( aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),sdtlpdtrp0(xN,sz00))
| ~ aSet0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),sdtlpdtrp0(xN,sz00)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),sdtlpdtrp0(xN,sz00)),sdtlpdtrp0(xN,sz00)) ) )
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),sdtlpdtrp0(xN,sz00))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aElementOf0(W2,sdtlpdtrp0(xN,sz00)) ) ) ) ) )
<=> ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,sdtlpdtrp0(xN,sz00)),W1)
| aElementOf0(tptp_fun_W2_1(W1,sdtlpdtrp0(xN,sz00)),sdtlpdtrp0(xN,sz00)) ) )
| ~ ( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlpdtrp0(xN,sz00)) ) ) ) )
| ~ ( ~ ( aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),sdtlpdtrp0(xN,sz00))
| ~ aSet0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),sdtlpdtrp0(xN,sz00)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),sdtlpdtrp0(xN,sz00)),sdtlpdtrp0(xN,sz00)) ) )
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),sdtlpdtrp0(xN,sz00))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aElementOf0(W2,sdtlpdtrp0(xN,sz00)) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(64,plain,
( ~ ( ~ ( ~ aSet0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),sdtlpdtrp0(xN,sz00))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),sdtlpdtrp0(xN,sz00)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),sdtlpdtrp0(xN,sz00)),sdtlpdtrp0(xN,sz00)) ) )
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),sdtlpdtrp0(xN,sz00))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aElementOf0(W2,sdtlpdtrp0(xN,sz00)) ) ) ) )
<=> ~ ( ~ ( aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),sdtlpdtrp0(xN,sz00))
| ~ aSet0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),sdtlpdtrp0(xN,sz00)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),sdtlpdtrp0(xN,sz00)),sdtlpdtrp0(xN,sz00)) ) )
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),sdtlpdtrp0(xN,sz00))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aElementOf0(W2,sdtlpdtrp0(xN,sz00)) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(65,plain,
( ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,sdtlpdtrp0(xN,sz00)),W1)
| aElementOf0(tptp_fun_W2_1(W1,sdtlpdtrp0(xN,sz00)),sdtlpdtrp0(xN,sz00)) ) )
| ~ ( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlpdtrp0(xN,sz00)) ) ) ) )
| ~ ( ~ ( ~ aSet0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),sdtlpdtrp0(xN,sz00))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),sdtlpdtrp0(xN,sz00)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),sdtlpdtrp0(xN,sz00)),sdtlpdtrp0(xN,sz00)) ) )
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),sdtlpdtrp0(xN,sz00))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aElementOf0(W2,sdtlpdtrp0(xN,sz00)) ) ) ) ) )
<=> ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,sdtlpdtrp0(xN,sz00)),W1)
| aElementOf0(tptp_fun_W2_1(W1,sdtlpdtrp0(xN,sz00)),sdtlpdtrp0(xN,sz00)) ) )
| ~ ( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlpdtrp0(xN,sz00)) ) ) ) )
| ~ ( ~ ( aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),sdtlpdtrp0(xN,sz00))
| ~ aSet0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),sdtlpdtrp0(xN,sz00)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),sdtlpdtrp0(xN,sz00)),sdtlpdtrp0(xN,sz00)) ) )
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),sdtlpdtrp0(xN,sz00))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aElementOf0(W2,sdtlpdtrp0(xN,sz00)) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[64]) ).
tff(66,plain,
( ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,sdtlpdtrp0(xN,sz00)),W1)
| aElementOf0(tptp_fun_W2_1(W1,sdtlpdtrp0(xN,sz00)),sdtlpdtrp0(xN,sz00)) ) )
| ~ ( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlpdtrp0(xN,sz00)) ) ) ) )
| ~ ( ~ ( ~ aSet0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),sdtlpdtrp0(xN,sz00))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),sdtlpdtrp0(xN,sz00)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),sdtlpdtrp0(xN,sz00)),sdtlpdtrp0(xN,sz00)) ) )
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),sdtlpdtrp0(xN,sz00))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aElementOf0(W2,sdtlpdtrp0(xN,sz00)) ) ) ) ) )
<=> ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,sdtlpdtrp0(xN,sz00)),W1)
| aElementOf0(tptp_fun_W2_1(W1,sdtlpdtrp0(xN,sz00)),sdtlpdtrp0(xN,sz00)) ) )
| ~ ( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlpdtrp0(xN,sz00)) ) ) ) )
| ~ ( ~ ( aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),sdtlpdtrp0(xN,sz00))
| ~ aSet0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),sdtlpdtrp0(xN,sz00)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),sdtlpdtrp0(xN,sz00)),sdtlpdtrp0(xN,sz00)) ) )
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),sdtlpdtrp0(xN,sz00))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aElementOf0(W2,sdtlpdtrp0(xN,sz00)) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[65,63]) ).
tff(67,plain,
( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,sdtlpdtrp0(xN,sz00)),W1)
| aElementOf0(tptp_fun_W2_1(W1,sdtlpdtrp0(xN,sz00)),sdtlpdtrp0(xN,sz00)) ) )
| ~ ( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlpdtrp0(xN,sz00)) ) ) ) )
| ~ ( ~ ( ~ aSet0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),sdtlpdtrp0(xN,sz00))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),sdtlpdtrp0(xN,sz00)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),sdtlpdtrp0(xN,sz00)),sdtlpdtrp0(xN,sz00)) ) )
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),sdtlpdtrp0(xN,sz00))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aElementOf0(W2,sdtlpdtrp0(xN,sz00)) ) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(68,plain,
( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,sdtlpdtrp0(xN,sz00)),W1)
| aElementOf0(tptp_fun_W2_1(W1,sdtlpdtrp0(xN,sz00)),sdtlpdtrp0(xN,sz00)) ) )
| ~ ( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlpdtrp0(xN,sz00)) ) ) ) )
| ~ ( ~ ( aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),sdtlpdtrp0(xN,sz00))
| ~ aSet0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),sdtlpdtrp0(xN,sz00)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),sdtlpdtrp0(xN,sz00)),sdtlpdtrp0(xN,sz00)) ) )
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),sdtlpdtrp0(xN,sz00))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aElementOf0(W2,sdtlpdtrp0(xN,sz00)) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
~ ( ~ ( aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),sdtlpdtrp0(xN,sz00))
| ~ aSet0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),sdtlpdtrp0(xN,sz00)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),sdtlpdtrp0(xN,sz00)),sdtlpdtrp0(xN,sz00)) ) )
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),sdtlpdtrp0(xN,sz00))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aElementOf0(W2,sdtlpdtrp0(xN,sz00)) ) ) ) ),
inference(unit_resolution,[status(thm)],[68,62]) ).
tff(70,plain,
( ~ ( aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),sdtlpdtrp0(xN,sz00))
| ~ aSet0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),sdtlpdtrp0(xN,sz00)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),sdtlpdtrp0(xN,sz00)),sdtlpdtrp0(xN,sz00)) ) )
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),sdtlpdtrp0(xN,sz00))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aElementOf0(W2,sdtlpdtrp0(xN,sz00)) ) ) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),sdtlpdtrp0(xN,sz00))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aElementOf0(W2,sdtlpdtrp0(xN,sz00)) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(71,plain,
( ~ aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),sdtlpdtrp0(xN,sz00))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aElementOf0(W2,sdtlpdtrp0(xN,sz00)) ) ) ),
inference(unit_resolution,[status(thm)],[70,69]) ).
tff(72,plain,
( aElementOf0(xx,xO)
<=> aElementOf0(sdtlpdtrp0(xe,xi),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ),
inference(rewrite,[status(thm)],]) ).
tff(73,plain,
( aElementOf0(xx,xO)
<=> aElementOf0(xx,xO) ),
inference(rewrite,[status(thm)],]) ).
tff(74,axiom,
aElementOf0(xx,xO),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5009) ).
tff(75,plain,
aElementOf0(xx,xO),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
aElementOf0(sdtlpdtrp0(xe,xi),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),
inference(modus_ponens,[status(thm)],[75,72]) ).
tff(77,plain,
^ [W0: $i] :
refl(
( ( ~ aElementOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aElementOf0(tptp_fun_W1_24(W0),szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_24(W0),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,tptp_fun_W1_24(W0)) != W0 ) ) )
<=> ( ~ aElementOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aElementOf0(tptp_fun_W1_24(W0),szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_24(W0),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,tptp_fun_W1_24(W0)) != W0 ) ) ) )),
inference(bind,[status(th)],]) ).
tff(78,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aElementOf0(tptp_fun_W1_24(W0),szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_24(W0),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,tptp_fun_W1_24(W0)) != W0 ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aElementOf0(tptp_fun_W1_24(W0),szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_24(W0),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,tptp_fun_W1_24(W0)) != W0 ) ) ) ),
inference(quant_intro,[status(thm)],[77]) ).
tff(79,plain,
^ [W0: $i] :
rewrite(
( ( ~ aElementOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ( aElementOf0(tptp_fun_W1_24(W0),szDzozmdt0(xN))
& aElementOf0(tptp_fun_W1_24(W0),sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ( sdtlpdtrp0(xe,tptp_fun_W1_24(W0)) = W0 ) ) )
<=> ( ~ aElementOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aElementOf0(tptp_fun_W1_24(W0),szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_24(W0),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,tptp_fun_W1_24(W0)) != W0 ) ) ) )),
inference(bind,[status(th)],]) ).
tff(80,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ( aElementOf0(tptp_fun_W1_24(W0),szDzozmdt0(xN))
& aElementOf0(tptp_fun_W1_24(W0),sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ( sdtlpdtrp0(xe,tptp_fun_W1_24(W0)) = W0 ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aElementOf0(tptp_fun_W1_24(W0),szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_24(W0),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,tptp_fun_W1_24(W0)) != W0 ) ) ) ),
inference(quant_intro,[status(thm)],[79]) ).
tff(81,plain,
^ [W0: $i] :
rewrite(
( ( ~ aElementOf0(W0,xO)
| ? [W1: $i] :
( aElementOf0(W1,szNzAzT0)
& aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ( sdtlpdtrp0(xe,W1) = W0 ) ) )
<=> ( ~ aElementOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ? [W1: $i] :
( aElementOf0(W1,szDzozmdt0(xN))
& aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ( sdtlpdtrp0(xe,W1) = W0 ) ) ) )),
inference(bind,[status(th)],]) ).
tff(82,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xO)
| ? [W1: $i] :
( aElementOf0(W1,szNzAzT0)
& aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ( sdtlpdtrp0(xe,W1) = W0 ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ? [W1: $i] :
( aElementOf0(W1,szDzozmdt0(xN))
& aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ( sdtlpdtrp0(xe,W1) = W0 ) ) ) ),
inference(quant_intro,[status(thm)],[81]) ).
tff(83,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xO)
| ? [W1: $i] :
( aElementOf0(W1,szNzAzT0)
& aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ( sdtlpdtrp0(xe,W1) = W0 ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xO)
| ? [W1: $i] :
( aElementOf0(W1,szNzAzT0)
& aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ( sdtlpdtrp0(xe,W1) = W0 ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(84,plain,
^ [W0: $i] :
trans(
monotonicity(
quant_intro(
proof_bind(
^ [W1: $i] :
rewrite(
( ( aElementOf0(W1,szNzAzT0)
& aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ( sdtlpdtrp0(xe,W1) = W0 ) )
<=> ( aElementOf0(W1,szNzAzT0)
& aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ( sdtlpdtrp0(xe,W1) = W0 ) ) ))),
( ? [W1: $i] :
( aElementOf0(W1,szNzAzT0)
& aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ( sdtlpdtrp0(xe,W1) = W0 ) )
<=> ? [W1: $i] :
( aElementOf0(W1,szNzAzT0)
& aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ( sdtlpdtrp0(xe,W1) = W0 ) ) )),
( ( aElementOf0(W0,xO)
=> ? [W1: $i] :
( aElementOf0(W1,szNzAzT0)
& aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ( sdtlpdtrp0(xe,W1) = W0 ) ) )
<=> ( aElementOf0(W0,xO)
=> ? [W1: $i] :
( aElementOf0(W1,szNzAzT0)
& aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ( sdtlpdtrp0(xe,W1) = W0 ) ) ) )),
rewrite(
( ( aElementOf0(W0,xO)
=> ? [W1: $i] :
( aElementOf0(W1,szNzAzT0)
& aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ( sdtlpdtrp0(xe,W1) = W0 ) ) )
<=> ( ~ aElementOf0(W0,xO)
| ? [W1: $i] :
( aElementOf0(W1,szNzAzT0)
& aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ( sdtlpdtrp0(xe,W1) = W0 ) ) ) )),
( ( aElementOf0(W0,xO)
=> ? [W1: $i] :
( aElementOf0(W1,szNzAzT0)
& aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ( sdtlpdtrp0(xe,W1) = W0 ) ) )
<=> ( ~ aElementOf0(W0,xO)
| ? [W1: $i] :
( aElementOf0(W1,szNzAzT0)
& aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ( sdtlpdtrp0(xe,W1) = W0 ) ) ) )),
inference(bind,[status(th)],]) ).
tff(85,plain,
( ! [W0: $i] :
( aElementOf0(W0,xO)
=> ? [W1: $i] :
( aElementOf0(W1,szNzAzT0)
& aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ( sdtlpdtrp0(xe,W1) = W0 ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xO)
| ? [W1: $i] :
( aElementOf0(W1,szNzAzT0)
& aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ( sdtlpdtrp0(xe,W1) = W0 ) ) ) ),
inference(quant_intro,[status(thm)],[84]) ).
tff(86,axiom,
! [W0: $i] :
( aElementOf0(W0,xO)
=> ? [W1: $i] :
( aElementOf0(W1,szNzAzT0)
& aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ( sdtlpdtrp0(xe,W1) = W0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4982) ).
tff(87,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xO)
| ? [W1: $i] :
( aElementOf0(W1,szNzAzT0)
& aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ( sdtlpdtrp0(xe,W1) = W0 ) ) ),
inference(modus_ponens,[status(thm)],[86,85]) ).
tff(88,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xO)
| ? [W1: $i] :
( aElementOf0(W1,szNzAzT0)
& aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ( sdtlpdtrp0(xe,W1) = W0 ) ) ),
inference(modus_ponens,[status(thm)],[87,83]) ).
tff(89,plain,
! [W0: $i] :
( ~ aElementOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ? [W1: $i] :
( aElementOf0(W1,szDzozmdt0(xN))
& aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ( sdtlpdtrp0(xe,W1) = W0 ) ) ),
inference(modus_ponens,[status(thm)],[88,82]) ).
tff(90,plain,
! [W0: $i] :
( ~ aElementOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ( aElementOf0(tptp_fun_W1_24(W0),szDzozmdt0(xN))
& aElementOf0(tptp_fun_W1_24(W0),sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ( sdtlpdtrp0(xe,tptp_fun_W1_24(W0)) = W0 ) ) ),
inference(skolemize,[status(sab)],[89]) ).
tff(91,plain,
! [W0: $i] :
( ~ aElementOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aElementOf0(tptp_fun_W1_24(W0),szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_24(W0),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,tptp_fun_W1_24(W0)) != W0 ) ) ),
inference(modus_ponens,[status(thm)],[90,80]) ).
tff(92,plain,
! [W0: $i] :
( ~ aElementOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aElementOf0(tptp_fun_W1_24(W0),szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_24(W0),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,tptp_fun_W1_24(W0)) != W0 ) ) ),
inference(modus_ponens,[status(thm)],[91,78]) ).
tff(93,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aElementOf0(tptp_fun_W1_24(W0),szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_24(W0),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,tptp_fun_W1_24(W0)) != W0 ) ) )
| ~ aElementOf0(sdtlpdtrp0(xe,xi),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aElementOf0(tptp_fun_W1_24(sdtlpdtrp0(xe,xi)),szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_24(sdtlpdtrp0(xe,xi)),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))) != sdtlpdtrp0(xe,xi) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aElementOf0(tptp_fun_W1_24(W0),szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_24(W0),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,tptp_fun_W1_24(W0)) != W0 ) ) )
| ~ aElementOf0(sdtlpdtrp0(xe,xi),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aElementOf0(tptp_fun_W1_24(sdtlpdtrp0(xe,xi)),szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_24(sdtlpdtrp0(xe,xi)),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))) != sdtlpdtrp0(xe,xi) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(94,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aElementOf0(tptp_fun_W1_24(W0),szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_24(W0),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,tptp_fun_W1_24(W0)) != W0 ) ) )
| ~ aElementOf0(sdtlpdtrp0(xe,xi),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aElementOf0(tptp_fun_W1_24(sdtlpdtrp0(xe,xi)),szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_24(sdtlpdtrp0(xe,xi)),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))) != sdtlpdtrp0(xe,xi) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(95,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aElementOf0(tptp_fun_W1_24(W0),szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_24(W0),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,tptp_fun_W1_24(W0)) != W0 ) ) )
| ~ aElementOf0(sdtlpdtrp0(xe,xi),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aElementOf0(tptp_fun_W1_24(sdtlpdtrp0(xe,xi)),szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_24(sdtlpdtrp0(xe,xi)),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))) != sdtlpdtrp0(xe,xi) ) ) ),
inference(modus_ponens,[status(thm)],[94,93]) ).
tff(96,plain,
~ ( ~ aElementOf0(tptp_fun_W1_24(sdtlpdtrp0(xe,xi)),szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_24(sdtlpdtrp0(xe,xi)),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))) != sdtlpdtrp0(xe,xi) ) ),
inference(unit_resolution,[status(thm)],[95,92,76]) ).
tff(97,plain,
( ~ aElementOf0(tptp_fun_W1_24(sdtlpdtrp0(xe,xi)),szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_24(sdtlpdtrp0(xe,xi)),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))) != sdtlpdtrp0(xe,xi) )
| aElementOf0(tptp_fun_W1_24(sdtlpdtrp0(xe,xi)),szDzozmdt0(xN)) ),
inference(tautology,[status(thm)],]) ).
tff(98,plain,
aElementOf0(tptp_fun_W1_24(sdtlpdtrp0(xe,xi)),szDzozmdt0(xN)),
inference(unit_resolution,[status(thm)],[97,96]) ).
tff(99,plain,
^ [W0: $i] :
refl(
( ( ~ aElementOf0(W0,szDzozmdt0(xN))
| sdtlseqdt0(sz00,W0) )
<=> ( ~ aElementOf0(W0,szDzozmdt0(xN))
| sdtlseqdt0(sz00,W0) ) )),
inference(bind,[status(th)],]) ).
tff(100,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| sdtlseqdt0(sz00,W0) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| sdtlseqdt0(sz00,W0) ) ),
inference(quant_intro,[status(thm)],[99]) ).
tff(101,plain,
^ [W0: $i] :
rewrite(
( ( ~ aElementOf0(W0,szNzAzT0)
| sdtlseqdt0(sz00,W0) )
<=> ( ~ aElementOf0(W0,szDzozmdt0(xN))
| sdtlseqdt0(sz00,W0) ) )),
inference(bind,[status(th)],]) ).
tff(102,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| sdtlseqdt0(sz00,W0) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| sdtlseqdt0(sz00,W0) ) ),
inference(quant_intro,[status(thm)],[101]) ).
tff(103,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| sdtlseqdt0(sz00,W0) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| sdtlseqdt0(sz00,W0) ) ),
inference(rewrite,[status(thm)],]) ).
tff(104,plain,
^ [W0: $i] :
rewrite(
( ( aElementOf0(W0,szNzAzT0)
=> sdtlseqdt0(sz00,W0) )
<=> ( ~ aElementOf0(W0,szNzAzT0)
| sdtlseqdt0(sz00,W0) ) )),
inference(bind,[status(th)],]) ).
tff(105,plain,
( ! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> sdtlseqdt0(sz00,W0) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| sdtlseqdt0(sz00,W0) ) ),
inference(quant_intro,[status(thm)],[104]) ).
tff(106,axiom,
! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> sdtlseqdt0(sz00,W0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroLess) ).
tff(107,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| sdtlseqdt0(sz00,W0) ),
inference(modus_ponens,[status(thm)],[106,105]) ).
tff(108,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| sdtlseqdt0(sz00,W0) ),
inference(modus_ponens,[status(thm)],[107,103]) ).
tff(109,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| sdtlseqdt0(sz00,W0) ),
inference(modus_ponens,[status(thm)],[108,102]) ).
tff(110,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| sdtlseqdt0(sz00,W0) ),
inference(skolemize,[status(sab)],[109]) ).
tff(111,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| sdtlseqdt0(sz00,W0) ),
inference(modus_ponens,[status(thm)],[110,100]) ).
tff(112,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| sdtlseqdt0(sz00,W0) )
| ~ aElementOf0(tptp_fun_W1_24(sdtlpdtrp0(xe,xi)),szDzozmdt0(xN))
| sdtlseqdt0(sz00,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| sdtlseqdt0(sz00,W0) )
| ~ aElementOf0(tptp_fun_W1_24(sdtlpdtrp0(xe,xi)),szDzozmdt0(xN))
| sdtlseqdt0(sz00,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(113,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| sdtlseqdt0(sz00,W0) )
| ~ aElementOf0(tptp_fun_W1_24(sdtlpdtrp0(xe,xi)),szDzozmdt0(xN))
| sdtlseqdt0(sz00,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))) ),
inference(quant_inst,[status(thm)],]) ).
tff(114,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| sdtlseqdt0(sz00,W0) )
| ~ aElementOf0(tptp_fun_W1_24(sdtlpdtrp0(xe,xi)),szDzozmdt0(xN))
| sdtlseqdt0(sz00,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))) ),
inference(modus_ponens,[status(thm)],[113,112]) ).
tff(115,plain,
sdtlseqdt0(sz00,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),
inference(unit_resolution,[status(thm)],[114,111,98]) ).
tff(116,plain,
^ [W0: $i,W1: $i] :
refl(
( ( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
<=> ( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ) )),
inference(bind,[status(th)],]) ).
tff(117,plain,
( ! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
<=> ! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ) ),
inference(quant_intro,[status(thm)],[116]) ).
tff(118,plain,
^ [W0: $i,W1: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) )
<=> ~ ( ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ) )),
( ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) )
<=> ~ ~ ( ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ) )),
rewrite(
( ~ ~ ( ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
<=> ( ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ) )),
( ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) )
<=> ( ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ) )),
( ( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ sdtlseqdt0(W1,W0)
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) )
<=> ( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ) )),
rewrite(
( ( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
<=> ( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ) )),
( ( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ sdtlseqdt0(W1,W0)
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) )
<=> ( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ) )),
inference(bind,[status(th)],]) ).
tff(119,plain,
( ! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ sdtlseqdt0(W1,W0)
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) )
<=> ! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ) ),
inference(quant_intro,[status(thm)],[118]) ).
tff(120,plain,
^ [W0: $i,W1: $i] :
trans(
monotonicity(
rewrite(
( ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
<=> ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) )),
( ( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ sdtlseqdt0(W1,W0) )
<=> ( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) )
| ~ sdtlseqdt0(W1,W0) ) )),
rewrite(
( ( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) )
| ~ sdtlseqdt0(W1,W0) )
<=> ( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ sdtlseqdt0(W1,W0)
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) ) )),
( ( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ sdtlseqdt0(W1,W0) )
<=> ( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ sdtlseqdt0(W1,W0)
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) ) )),
inference(bind,[status(th)],]) ).
tff(121,plain,
( ! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ sdtlseqdt0(W1,W0) )
<=> ! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ sdtlseqdt0(W1,W0)
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) ) ),
inference(quant_intro,[status(thm)],[120]) ).
tff(122,plain,
( ! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ sdtlseqdt0(W1,W0) )
<=> ! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ sdtlseqdt0(W1,W0) ) ),
inference(rewrite,[status(thm)],]) ).
tff(123,plain,
^ [W0: $i,W1: $i] :
trans(
monotonicity(
rewrite(
( ( sdtlseqdt0(W1,W0)
=> aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) )
<=> ( ~ sdtlseqdt0(W1,W0)
| aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) )),
( ( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( sdtlseqdt0(W1,W0)
=> aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) )
<=> ( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( ~ sdtlseqdt0(W1,W0)
| aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) ) )),
rewrite(
( ( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( ~ sdtlseqdt0(W1,W0)
| aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) )
<=> ( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ sdtlseqdt0(W1,W0) ) )),
( ( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( sdtlseqdt0(W1,W0)
=> aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) )
<=> ( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ sdtlseqdt0(W1,W0) ) )),
inference(bind,[status(th)],]) ).
tff(124,plain,
( ! [W0: $i,W1: $i] :
( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( sdtlseqdt0(W1,W0)
=> aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) )
<=> ! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ sdtlseqdt0(W1,W0) ) ),
inference(quant_intro,[status(thm)],[123]) ).
tff(125,axiom,
! [W0: $i,W1: $i] :
( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( sdtlseqdt0(W1,W0)
=> aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3754) ).
tff(126,plain,
! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ sdtlseqdt0(W1,W0) ),
inference(modus_ponens,[status(thm)],[125,124]) ).
tff(127,plain,
! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ sdtlseqdt0(W1,W0) ),
inference(modus_ponens,[status(thm)],[126,122]) ).
tff(128,plain,
! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ sdtlseqdt0(W1,W0)
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) ),
inference(modus_ponens,[status(thm)],[127,121]) ).
tff(129,plain,
! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ sdtlseqdt0(W1,W0)
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) ),
inference(skolemize,[status(sab)],[128]) ).
tff(130,plain,
! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ),
inference(modus_ponens,[status(thm)],[129,119]) ).
tff(131,plain,
! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ),
inference(modus_ponens,[status(thm)],[130,117]) ).
tff(132,plain,
( aElementOf0(sz00,szNzAzT0)
<=> aElementOf0(sz00,szDzozmdt0(xN)) ),
inference(rewrite,[status(thm)],]) ).
tff(133,plain,
( aElementOf0(sz00,szNzAzT0)
<=> aElementOf0(sz00,szNzAzT0) ),
inference(rewrite,[status(thm)],]) ).
tff(134,axiom,
aElementOf0(sz00,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroNum) ).
tff(135,plain,
aElementOf0(sz00,szNzAzT0),
inference(modus_ponens,[status(thm)],[134,133]) ).
tff(136,plain,
aElementOf0(sz00,szDzozmdt0(xN)),
inference(modus_ponens,[status(thm)],[135,132]) ).
tff(137,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| ~ aElementOf0(sz00,szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_24(sdtlpdtrp0(xe,xi)),szDzozmdt0(xN))
| aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),sdtlpdtrp0(xN,sz00))
| ~ sdtlseqdt0(sz00,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| ~ aElementOf0(sz00,szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_24(sdtlpdtrp0(xe,xi)),szDzozmdt0(xN))
| aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),sdtlpdtrp0(xN,sz00))
| ~ sdtlseqdt0(sz00,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(138,plain,
( ( aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),sdtlpdtrp0(xN,sz00))
| ~ sdtlseqdt0(sz00,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))
| ~ aElementOf0(sz00,szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_24(sdtlpdtrp0(xe,xi)),szDzozmdt0(xN)) )
<=> ( ~ aElementOf0(sz00,szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_24(sdtlpdtrp0(xe,xi)),szDzozmdt0(xN))
| aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),sdtlpdtrp0(xN,sz00))
| ~ sdtlseqdt0(sz00,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(139,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),sdtlpdtrp0(xN,sz00))
| ~ sdtlseqdt0(sz00,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))
| ~ aElementOf0(sz00,szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_24(sdtlpdtrp0(xe,xi)),szDzozmdt0(xN)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| ~ aElementOf0(sz00,szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_24(sdtlpdtrp0(xe,xi)),szDzozmdt0(xN))
| aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),sdtlpdtrp0(xN,sz00))
| ~ sdtlseqdt0(sz00,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))) ) ),
inference(monotonicity,[status(thm)],[138]) ).
tff(140,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),sdtlpdtrp0(xN,sz00))
| ~ sdtlseqdt0(sz00,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))
| ~ aElementOf0(sz00,szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_24(sdtlpdtrp0(xe,xi)),szDzozmdt0(xN)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| ~ aElementOf0(sz00,szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_24(sdtlpdtrp0(xe,xi)),szDzozmdt0(xN))
| aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),sdtlpdtrp0(xN,sz00))
| ~ sdtlseqdt0(sz00,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))) ) ),
inference(transitivity,[status(thm)],[139,137]) ).
tff(141,plain,
( ~ ! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),sdtlpdtrp0(xN,sz00))
| ~ sdtlseqdt0(sz00,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))
| ~ aElementOf0(sz00,szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_24(sdtlpdtrp0(xe,xi)),szDzozmdt0(xN)) ),
inference(quant_inst,[status(thm)],]) ).
tff(142,plain,
( ~ ! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| ~ aElementOf0(sz00,szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_24(sdtlpdtrp0(xe,xi)),szDzozmdt0(xN))
| aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),sdtlpdtrp0(xN,sz00))
| ~ sdtlseqdt0(sz00,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))) ),
inference(modus_ponens,[status(thm)],[141,140]) ).
tff(143,plain,
aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),sdtlpdtrp0(xN,sz00)),
inference(unit_resolution,[status(thm)],[142,136,131,98,115]) ).
tff(144,plain,
( ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),sdtlpdtrp0(xN,sz00))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aElementOf0(W2,sdtlpdtrp0(xN,sz00)) ) ) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),sdtlpdtrp0(xN,sz00))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aElementOf0(W2,sdtlpdtrp0(xN,sz00)) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(145,plain,
( ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),sdtlpdtrp0(xN,sz00))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aElementOf0(W2,sdtlpdtrp0(xN,sz00)) ) ) )
| ~ ( ~ aSet0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aElementOf0(W2,sdtlpdtrp0(xN,sz00)) ) ) ),
inference(unit_resolution,[status(thm)],[144,143]) ).
tff(146,plain,
~ ( ~ aSet0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aElementOf0(W2,sdtlpdtrp0(xN,sz00)) ) ),
inference(unit_resolution,[status(thm)],[145,71]) ).
tff(147,plain,
( ~ aSet0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aElementOf0(W2,sdtlpdtrp0(xN,sz00)) )
| ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aElementOf0(W2,sdtlpdtrp0(xN,sz00)) ) ),
inference(tautology,[status(thm)],]) ).
tff(148,plain,
! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aElementOf0(W2,sdtlpdtrp0(xN,sz00)) ),
inference(unit_resolution,[status(thm)],[147,146]) ).
tff(149,plain,
( aElementOf0(xi,szNzAzT0)
<=> aElementOf0(xi,szDzozmdt0(xN)) ),
inference(rewrite,[status(thm)],]) ).
tff(150,plain,
( aElementOf0(xi,szNzAzT0)
<=> aElementOf0(xi,szNzAzT0) ),
inference(rewrite,[status(thm)],]) ).
tff(151,axiom,
( aElementOf0(xi,szNzAzT0)
& ( sdtlpdtrp0(xe,xi) = xx ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5034) ).
tff(152,plain,
aElementOf0(xi,szNzAzT0),
inference(and_elim,[status(thm)],[151]) ).
tff(153,plain,
aElementOf0(xi,szNzAzT0),
inference(modus_ponens,[status(thm)],[152,150]) ).
tff(154,plain,
aElementOf0(xi,szDzozmdt0(xN)),
inference(modus_ponens,[status(thm)],[153,149]) ).
tff(155,plain,
^ [W0: $i] :
refl(
( ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )),
inference(bind,[status(th)],]) ).
tff(156,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ),
inference(quant_intro,[status(thm)],[155]) ).
tff(157,plain,
^ [W0: $i] :
rewrite(
( ( ~ aElementOf0(W0,szNzAzT0)
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )),
inference(bind,[status(th)],]) ).
tff(158,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ),
inference(quant_intro,[status(thm)],[157]) ).
tff(159,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(160,plain,
^ [W0: $i] :
rewrite(
( ( aElementOf0(W0,szNzAzT0)
=> ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> ( ~ aElementOf0(W0,szNzAzT0)
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )),
inference(bind,[status(th)],]) ).
tff(161,plain,
( ! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ),
inference(quant_intro,[status(thm)],[160]) ).
tff(162,axiom,
( aFunction0(xe)
& ( szDzozmdt0(xe) = szNzAzT0 )
& ! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4660) ).
tff(163,plain,
! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ),
inference(and_elim,[status(thm)],[162]) ).
tff(164,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ),
inference(modus_ponens,[status(thm)],[163,161]) ).
tff(165,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ),
inference(modus_ponens,[status(thm)],[164,159]) ).
tff(166,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ),
inference(modus_ponens,[status(thm)],[165,158]) ).
tff(167,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ),
inference(skolemize,[status(sab)],[166]) ).
tff(168,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ),
inference(modus_ponens,[status(thm)],[167,156]) ).
tff(169,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
| ~ aElementOf0(xi,szDzozmdt0(xN))
| ( sdtlpdtrp0(xe,xi) = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
| ~ aElementOf0(xi,szDzozmdt0(xN))
| ( sdtlpdtrp0(xe,xi) = szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(170,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
| ~ aElementOf0(xi,szDzozmdt0(xN))
| ( sdtlpdtrp0(xe,xi) = szmzizndt0(sdtlpdtrp0(xN,xi)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(171,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
| ~ aElementOf0(xi,szDzozmdt0(xN))
| ( sdtlpdtrp0(xe,xi) = szmzizndt0(sdtlpdtrp0(xN,xi)) ) ),
inference(modus_ponens,[status(thm)],[170,169]) ).
tff(172,plain,
sdtlpdtrp0(xe,xi) = szmzizndt0(sdtlpdtrp0(xN,xi)),
inference(unit_resolution,[status(thm)],[171,168,154]) ).
tff(173,plain,
szmzizndt0(sdtlpdtrp0(xN,xi)) = sdtlpdtrp0(xe,xi),
inference(symmetry,[status(thm)],[172]) ).
tff(174,plain,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,sz00))
<=> aElementOf0(sdtlpdtrp0(xe,xi),sdtlpdtrp0(xN,sz00)) ),
inference(monotonicity,[status(thm)],[173]) ).
tff(175,plain,
( aElementOf0(sdtlpdtrp0(xe,xi),sdtlpdtrp0(xN,sz00))
<=> aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,sz00)) ),
inference(symmetry,[status(thm)],[174]) ).
tff(176,plain,
( ~ aElementOf0(sdtlpdtrp0(xe,xi),sdtlpdtrp0(xN,sz00))
<=> ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,sz00)) ),
inference(monotonicity,[status(thm)],[175]) ).
tff(177,plain,
( ~ aElementOf0(xx,xS)
<=> ~ aElementOf0(sdtlpdtrp0(xe,xi),sdtlpdtrp0(xN,sz00)) ),
inference(rewrite,[status(thm)],]) ).
tff(178,plain,
( ~ aElementOf0(xx,xS)
<=> ~ aElementOf0(xx,xS) ),
inference(rewrite,[status(thm)],]) ).
tff(179,axiom,
~ aElementOf0(xx,xS),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(180,plain,
~ aElementOf0(xx,xS),
inference(modus_ponens,[status(thm)],[179,178]) ).
tff(181,plain,
~ aElementOf0(sdtlpdtrp0(xe,xi),sdtlpdtrp0(xN,sz00)),
inference(modus_ponens,[status(thm)],[180,177]) ).
tff(182,plain,
~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,sz00)),
inference(modus_ponens,[status(thm)],[181,176]) ).
tff(183,plain,
( ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aElementOf0(W2,sdtlpdtrp0(xN,sz00)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,sz00)) )
<=> ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aElementOf0(W2,sdtlpdtrp0(xN,sz00)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,sz00)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(184,plain,
( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aElementOf0(W2,sdtlpdtrp0(xN,sz00)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,sz00)) ),
inference(quant_inst,[status(thm)],]) ).
tff(185,plain,
( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aElementOf0(W2,sdtlpdtrp0(xN,sz00)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,sz00)) ),
inference(modus_ponens,[status(thm)],[184,183]) ).
tff(186,plain,
~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))),
inference(unit_resolution,[status(thm)],[185,182,148]) ).
tff(187,plain,
( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) ),
inference(tautology,[status(thm)],]) ).
tff(188,plain,
( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) ) ),
inference(unit_resolution,[status(thm)],[187,186]) ).
tff(189,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
| ~ aElementOf0(tptp_fun_W1_24(sdtlpdtrp0(xe,xi)),szDzozmdt0(xN))
| ( sdtlpdtrp0(xe,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))) = szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
| ~ aElementOf0(tptp_fun_W1_24(sdtlpdtrp0(xe,xi)),szDzozmdt0(xN))
| ( sdtlpdtrp0(xe,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))) = szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(190,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
| ~ aElementOf0(tptp_fun_W1_24(sdtlpdtrp0(xe,xi)),szDzozmdt0(xN))
| ( sdtlpdtrp0(xe,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))) = szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(191,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
| ~ aElementOf0(tptp_fun_W1_24(sdtlpdtrp0(xe,xi)),szDzozmdt0(xN))
| ( sdtlpdtrp0(xe,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))) = szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) ) ),
inference(modus_ponens,[status(thm)],[190,189]) ).
tff(192,plain,
sdtlpdtrp0(xe,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))) = szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))),
inference(unit_resolution,[status(thm)],[191,168,98]) ).
tff(193,plain,
( ~ aElementOf0(tptp_fun_W1_24(sdtlpdtrp0(xe,xi)),szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_24(sdtlpdtrp0(xe,xi)),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))) != sdtlpdtrp0(xe,xi) )
| ( sdtlpdtrp0(xe,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))) = sdtlpdtrp0(xe,xi) ) ),
inference(tautology,[status(thm)],]) ).
tff(194,plain,
sdtlpdtrp0(xe,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))) = sdtlpdtrp0(xe,xi),
inference(unit_resolution,[status(thm)],[193,96]) ).
tff(195,plain,
sdtlpdtrp0(xe,xi) = sdtlpdtrp0(xe,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),
inference(symmetry,[status(thm)],[194]) ).
tff(196,plain,
szmzizndt0(sdtlpdtrp0(xN,xi)) = szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))),
inference(transitivity,[status(thm)],[173,195,192]) ).
tff(197,plain,
( ~ ( ( szmzizndt0(sdtlpdtrp0(xN,xi)) != szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) ) ) )
| ( szmzizndt0(sdtlpdtrp0(xN,xi)) != szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(198,plain,
~ ( ( szmzizndt0(sdtlpdtrp0(xN,xi)) != szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) ) ) ),
inference(unit_resolution,[status(thm)],[197,196,188]) ).
tff(199,plain,
( ~ ( ( szmzizndt0(sdtlpdtrp0(xN,xi)) = szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ( ~ aElementOf0(tptp_fun_W2_6(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),tptp_fun_W2_6(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))) ) )
| ~ ( ( szmzizndt0(sdtlpdtrp0(xN,xi)) != szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) ) ) )
| ( szmzizndt0(sdtlpdtrp0(xN,xi)) != szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(200,plain,
( ~ ( ( szmzizndt0(sdtlpdtrp0(xN,xi)) = szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ( ~ aElementOf0(tptp_fun_W2_6(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),tptp_fun_W2_6(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))) ) )
| ~ ( ( szmzizndt0(sdtlpdtrp0(xN,xi)) != szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) ) ) ) ),
inference(unit_resolution,[status(thm)],[199,198]) ).
tff(201,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,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),szDzozmdt0(xN))
| ~ aSet0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),szDzozmdt0(xN)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),szDzozmdt0(xN)),szDzozmdt0(xN)) ) )
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| 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,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),szDzozmdt0(xN))
| ~ aSet0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),szDzozmdt0(xN)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),szDzozmdt0(xN)),szDzozmdt0(xN)) ) )
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(202,plain,
( ~ ( ~ ( ~ aSet0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),szDzozmdt0(xN))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),szDzozmdt0(xN)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),szDzozmdt0(xN)),szDzozmdt0(xN)) ) )
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ) )
<=> ~ ( ~ ( aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),szDzozmdt0(xN))
| ~ aSet0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),szDzozmdt0(xN)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),szDzozmdt0(xN)),szDzozmdt0(xN)) ) )
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(203,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,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),szDzozmdt0(xN))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),szDzozmdt0(xN)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),szDzozmdt0(xN)),szDzozmdt0(xN)) ) )
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| 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,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),szDzozmdt0(xN))
| ~ aSet0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),szDzozmdt0(xN)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),szDzozmdt0(xN)),szDzozmdt0(xN)) ) )
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[202]) ).
tff(204,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,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),szDzozmdt0(xN))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),szDzozmdt0(xN)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),szDzozmdt0(xN)),szDzozmdt0(xN)) ) )
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| 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,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),szDzozmdt0(xN))
| ~ aSet0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),szDzozmdt0(xN)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),szDzozmdt0(xN)),szDzozmdt0(xN)) ) )
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[203,201]) ).
tff(205,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,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),szDzozmdt0(xN))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),szDzozmdt0(xN)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),szDzozmdt0(xN)),szDzozmdt0(xN)) ) )
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(206,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,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),szDzozmdt0(xN))
| ~ aSet0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),szDzozmdt0(xN)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),szDzozmdt0(xN)),szDzozmdt0(xN)) ) )
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[205,204]) ).
tff(207,plain,
~ ( ~ ( aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),szDzozmdt0(xN))
| ~ aSet0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),szDzozmdt0(xN)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),szDzozmdt0(xN)),szDzozmdt0(xN)) ) )
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ) ),
inference(unit_resolution,[status(thm)],[206,35]) ).
tff(208,plain,
( ~ ( aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),szDzozmdt0(xN))
| ~ aSet0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),szDzozmdt0(xN)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),szDzozmdt0(xN)),szDzozmdt0(xN)) ) )
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aElementOf0(W2,szDzozmdt0(xN)) ) ) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(209,plain,
( ~ aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ),
inference(unit_resolution,[status(thm)],[208,207]) ).
tff(210,plain,
^ [W0: $i] :
refl(
( ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,W0)) ) )
<=> ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,W0)) ) ) )),
inference(bind,[status(th)],]) ).
tff(211,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,W0)) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,W0)) ) ) ),
inference(quant_intro,[status(thm)],[210]) ).
tff(212,plain,
^ [W0: $i] :
rewrite(
( ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
& isCountable0(sdtlpdtrp0(xN,W0)) ) )
<=> ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,W0)) ) ) )),
inference(bind,[status(th)],]) ).
tff(213,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
& isCountable0(sdtlpdtrp0(xN,W0)) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,W0)) ) ) ),
inference(quant_intro,[status(thm)],[212]) ).
tff(214,plain,
^ [W0: $i] :
rewrite(
( ( ~ aElementOf0(W0,szNzAzT0)
| ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) ) )
<=> ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
& isCountable0(sdtlpdtrp0(xN,W0)) ) ) )),
inference(bind,[status(th)],]) ).
tff(215,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
& isCountable0(sdtlpdtrp0(xN,W0)) ) ) ),
inference(quant_intro,[status(thm)],[214]) ).
tff(216,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(217,plain,
^ [W0: $i] :
rewrite(
( ( aElementOf0(W0,szNzAzT0)
=> ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) ) )
<=> ( ~ aElementOf0(W0,szNzAzT0)
| ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) ) ) )),
inference(bind,[status(th)],]) ).
tff(218,plain,
( ! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) ) ) ),
inference(quant_intro,[status(thm)],[217]) ).
tff(219,axiom,
! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3671) ).
tff(220,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) ) ),
inference(modus_ponens,[status(thm)],[219,218]) ).
tff(221,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) ) ),
inference(modus_ponens,[status(thm)],[220,216]) ).
tff(222,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
& isCountable0(sdtlpdtrp0(xN,W0)) ) ),
inference(modus_ponens,[status(thm)],[221,215]) ).
tff(223,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
& isCountable0(sdtlpdtrp0(xN,W0)) ) ),
inference(skolemize,[status(sab)],[222]) ).
tff(224,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,W0)) ) ),
inference(modus_ponens,[status(thm)],[223,213]) ).
tff(225,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,W0)) ) ),
inference(modus_ponens,[status(thm)],[224,211]) ).
tff(226,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,W0)) ) )
| ~ aElementOf0(tptp_fun_W1_24(sdtlpdtrp0(xe,xi)),szDzozmdt0(xN))
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,W0)) ) )
| ~ aElementOf0(tptp_fun_W1_24(sdtlpdtrp0(xe,xi)),szDzozmdt0(xN))
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(227,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,W0)) ) )
| ~ aElementOf0(tptp_fun_W1_24(sdtlpdtrp0(xe,xi)),szDzozmdt0(xN))
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(228,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,W0)) ) )
| ~ aElementOf0(tptp_fun_W1_24(sdtlpdtrp0(xe,xi)),szDzozmdt0(xN))
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) ) ),
inference(modus_ponens,[status(thm)],[227,226]) ).
tff(229,plain,
~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) ),
inference(unit_resolution,[status(thm)],[228,225,98]) ).
tff(230,plain,
( ~ aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),szDzozmdt0(xN)) ),
inference(tautology,[status(thm)],]) ).
tff(231,plain,
aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),szDzozmdt0(xN)),
inference(unit_resolution,[status(thm)],[230,229]) ).
tff(232,plain,
( ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aElementOf0(W2,szDzozmdt0(xN)) ) ) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(233,plain,
( ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aElementOf0(W2,szDzozmdt0(xN)) ) ) )
| ~ ( ~ aSet0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ),
inference(unit_resolution,[status(thm)],[232,231]) ).
tff(234,plain,
~ ( ~ aSet0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aElementOf0(W2,szDzozmdt0(xN)) ) ),
inference(unit_resolution,[status(thm)],[233,209]) ).
tff(235,plain,
( ~ aSet0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| aElementOf0(W2,szDzozmdt0(xN)) )
| aSet0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) ),
inference(tautology,[status(thm)],]) ).
tff(236,plain,
aSet0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))),
inference(unit_resolution,[status(thm)],[235,234]) ).
tff(237,plain,
( ~ aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| isCountable0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) ),
inference(tautology,[status(thm)],]) ).
tff(238,plain,
isCountable0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))),
inference(unit_resolution,[status(thm)],[237,229]) ).
tff(239,plain,
^ [W0: $i] :
refl(
( ( ~ aSet0(W0)
| ( W0 != slbdtrb0(sz00) )
| ~ isCountable0(W0) )
<=> ( ~ aSet0(W0)
| ( W0 != slbdtrb0(sz00) )
| ~ isCountable0(W0) ) )),
inference(bind,[status(th)],]) ).
tff(240,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ( W0 != slbdtrb0(sz00) )
| ~ isCountable0(W0) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ( W0 != slbdtrb0(sz00) )
| ~ isCountable0(W0) ) ),
inference(quant_intro,[status(thm)],[239]) ).
tff(241,plain,
^ [W0: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( aSet0(W0)
& isCountable0(W0) )
<=> ~ ( ~ aSet0(W0)
| ~ isCountable0(W0) ) )),
( ~ ( aSet0(W0)
& isCountable0(W0) )
<=> ~ ~ ( ~ aSet0(W0)
| ~ isCountable0(W0) ) )),
rewrite(
( ~ ~ ( ~ aSet0(W0)
| ~ isCountable0(W0) )
<=> ( ~ aSet0(W0)
| ~ isCountable0(W0) ) )),
( ~ ( aSet0(W0)
& isCountable0(W0) )
<=> ( ~ aSet0(W0)
| ~ isCountable0(W0) ) )),
( ( ( W0 != slbdtrb0(sz00) )
| ~ ( aSet0(W0)
& isCountable0(W0) ) )
<=> ( ( W0 != slbdtrb0(sz00) )
| ~ aSet0(W0)
| ~ isCountable0(W0) ) )),
rewrite(
( ( ( W0 != slbdtrb0(sz00) )
| ~ aSet0(W0)
| ~ isCountable0(W0) )
<=> ( ~ aSet0(W0)
| ( W0 != slbdtrb0(sz00) )
| ~ isCountable0(W0) ) )),
( ( ( W0 != slbdtrb0(sz00) )
| ~ ( aSet0(W0)
& isCountable0(W0) ) )
<=> ( ~ aSet0(W0)
| ( W0 != slbdtrb0(sz00) )
| ~ isCountable0(W0) ) )),
inference(bind,[status(th)],]) ).
tff(242,plain,
( ! [W0: $i] :
( ( W0 != slbdtrb0(sz00) )
| ~ ( aSet0(W0)
& isCountable0(W0) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ( W0 != slbdtrb0(sz00) )
| ~ isCountable0(W0) ) ),
inference(quant_intro,[status(thm)],[241]) ).
tff(243,plain,
^ [W0: $i] :
rewrite(
( ( ( W0 != slcrc0 )
| ~ ( aSet0(W0)
& isCountable0(W0) ) )
<=> ( ( W0 != slbdtrb0(sz00) )
| ~ ( aSet0(W0)
& isCountable0(W0) ) ) )),
inference(bind,[status(th)],]) ).
tff(244,plain,
( ! [W0: $i] :
( ( W0 != slcrc0 )
| ~ ( aSet0(W0)
& isCountable0(W0) ) )
<=> ! [W0: $i] :
( ( W0 != slbdtrb0(sz00) )
| ~ ( aSet0(W0)
& isCountable0(W0) ) ) ),
inference(quant_intro,[status(thm)],[243]) ).
tff(245,plain,
( ! [W0: $i] :
( ( W0 != slcrc0 )
| ~ ( aSet0(W0)
& isCountable0(W0) ) )
<=> ! [W0: $i] :
( ( W0 != slcrc0 )
| ~ ( aSet0(W0)
& isCountable0(W0) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(246,plain,
^ [W0: $i] :
rewrite(
( ( ( aSet0(W0)
& isCountable0(W0) )
=> ( W0 != slcrc0 ) )
<=> ( ( W0 != slcrc0 )
| ~ ( aSet0(W0)
& isCountable0(W0) ) ) )),
inference(bind,[status(th)],]) ).
tff(247,plain,
( ! [W0: $i] :
( ( aSet0(W0)
& isCountable0(W0) )
=> ( W0 != slcrc0 ) )
<=> ! [W0: $i] :
( ( W0 != slcrc0 )
| ~ ( aSet0(W0)
& isCountable0(W0) ) ) ),
inference(quant_intro,[status(thm)],[246]) ).
tff(248,axiom,
! [W0: $i] :
( ( aSet0(W0)
& isCountable0(W0) )
=> ( W0 != slcrc0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCountNFin_01) ).
tff(249,plain,
! [W0: $i] :
( ( W0 != slcrc0 )
| ~ ( aSet0(W0)
& isCountable0(W0) ) ),
inference(modus_ponens,[status(thm)],[248,247]) ).
tff(250,plain,
! [W0: $i] :
( ( W0 != slcrc0 )
| ~ ( aSet0(W0)
& isCountable0(W0) ) ),
inference(modus_ponens,[status(thm)],[249,245]) ).
tff(251,plain,
! [W0: $i] :
( ( W0 != slbdtrb0(sz00) )
| ~ ( aSet0(W0)
& isCountable0(W0) ) ),
inference(modus_ponens,[status(thm)],[250,244]) ).
tff(252,plain,
! [W0: $i] :
( ( W0 != slbdtrb0(sz00) )
| ~ ( aSet0(W0)
& isCountable0(W0) ) ),
inference(skolemize,[status(sab)],[251]) ).
tff(253,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ( W0 != slbdtrb0(sz00) )
| ~ isCountable0(W0) ),
inference(modus_ponens,[status(thm)],[252,242]) ).
tff(254,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ( W0 != slbdtrb0(sz00) )
| ~ isCountable0(W0) ),
inference(modus_ponens,[status(thm)],[253,240]) ).
tff(255,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( W0 != slbdtrb0(sz00) )
| ~ isCountable0(W0) )
| ~ isCountable0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ aSet0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ( sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))) != slbdtrb0(sz00) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( W0 != slbdtrb0(sz00) )
| ~ isCountable0(W0) )
| ~ isCountable0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ aSet0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ( sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))) != slbdtrb0(sz00) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(256,plain,
( ( ~ aSet0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ( sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))) != slbdtrb0(sz00) )
| ~ isCountable0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) )
<=> ( ~ isCountable0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ aSet0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ( sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))) != slbdtrb0(sz00) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(257,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( W0 != slbdtrb0(sz00) )
| ~ isCountable0(W0) )
| ~ aSet0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ( sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))) != slbdtrb0(sz00) )
| ~ isCountable0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( W0 != slbdtrb0(sz00) )
| ~ isCountable0(W0) )
| ~ isCountable0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ aSet0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ( sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))) != slbdtrb0(sz00) ) ) ),
inference(monotonicity,[status(thm)],[256]) ).
tff(258,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( W0 != slbdtrb0(sz00) )
| ~ isCountable0(W0) )
| ~ aSet0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ( sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))) != slbdtrb0(sz00) )
| ~ isCountable0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( W0 != slbdtrb0(sz00) )
| ~ isCountable0(W0) )
| ~ isCountable0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ aSet0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ( sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))) != slbdtrb0(sz00) ) ) ),
inference(transitivity,[status(thm)],[257,255]) ).
tff(259,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( W0 != slbdtrb0(sz00) )
| ~ isCountable0(W0) )
| ~ aSet0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ( sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))) != slbdtrb0(sz00) )
| ~ isCountable0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(260,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( W0 != slbdtrb0(sz00) )
| ~ isCountable0(W0) )
| ~ isCountable0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ aSet0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ( sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))) != slbdtrb0(sz00) ) ),
inference(modus_ponens,[status(thm)],[259,258]) ).
tff(261,plain,
( ~ aSet0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ( sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))) != slbdtrb0(sz00) ) ),
inference(unit_resolution,[status(thm)],[260,254,238]) ).
tff(262,plain,
sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))) != slbdtrb0(sz00),
inference(unit_resolution,[status(thm)],[261,236]) ).
tff(263,plain,
^ [W0: $i] :
trans(
monotonicity(
quant_intro(
proof_bind(
^ [W1: $i] :
rewrite(
( ~ ( ~ ( ( W1 != szmzizndt0(W0) )
| ~ ( ~ aElementOf0(W1,W0)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| sdtlseqdt0(W1,W2) ) ) )
| ~ ( ~ aElementOf0(W1,W0)
| ( W1 = szmzizndt0(W0) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,W0),W0)
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,W0)) ) ) )
<=> ~ ( ~ ( ~ aElementOf0(W1,W0)
| ( W1 = szmzizndt0(W0) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,W0),W0)
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,W0)) ) )
| ~ ( ( W1 != szmzizndt0(W0) )
| ~ ( ~ aElementOf0(W1,W0)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| sdtlseqdt0(W1,W2) ) ) ) ) ))),
( ! [W1: $i] :
~ ( ~ ( ( W1 != szmzizndt0(W0) )
| ~ ( ~ aElementOf0(W1,W0)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| sdtlseqdt0(W1,W2) ) ) )
| ~ ( ~ aElementOf0(W1,W0)
| ( W1 = szmzizndt0(W0) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,W0),W0)
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,W0)) ) ) )
<=> ! [W1: $i] :
~ ( ~ ( ~ aElementOf0(W1,W0)
| ( W1 = szmzizndt0(W0) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,W0),W0)
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,W0)) ) )
| ~ ( ( W1 != szmzizndt0(W0) )
| ~ ( ~ aElementOf0(W1,W0)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| sdtlseqdt0(W1,W2) ) ) ) ) )),
( ( ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
~ ( ~ ( ( W1 != szmzizndt0(W0) )
| ~ ( ~ aElementOf0(W1,W0)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| sdtlseqdt0(W1,W2) ) ) )
| ~ ( ~ aElementOf0(W1,W0)
| ( W1 = szmzizndt0(W0) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,W0),W0)
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,W0)) ) ) ) )
<=> ( ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
~ ( ~ ( ~ aElementOf0(W1,W0)
| ( W1 = szmzizndt0(W0) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,W0),W0)
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,W0)) ) )
| ~ ( ( W1 != szmzizndt0(W0) )
| ~ ( ~ aElementOf0(W1,W0)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| sdtlseqdt0(W1,W2) ) ) ) ) ) )),
rewrite(
( ( ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
~ ( ~ ( ~ aElementOf0(W1,W0)
| ( W1 = szmzizndt0(W0) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,W0),W0)
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,W0)) ) )
| ~ ( ( W1 != szmzizndt0(W0) )
| ~ ( ~ aElementOf0(W1,W0)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| sdtlseqdt0(W1,W2) ) ) ) ) )
<=> ( ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
~ ( ~ ( ~ aElementOf0(W1,W0)
| ( W1 = szmzizndt0(W0) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,W0),W0)
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,W0)) ) )
| ~ ( ( W1 != szmzizndt0(W0) )
| ~ ( ~ aElementOf0(W1,W0)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| sdtlseqdt0(W1,W2) ) ) ) ) ) )),
( ( ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
~ ( ~ ( ( W1 != szmzizndt0(W0) )
| ~ ( ~ aElementOf0(W1,W0)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| sdtlseqdt0(W1,W2) ) ) )
| ~ ( ~ aElementOf0(W1,W0)
| ( W1 = szmzizndt0(W0) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,W0),W0)
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,W0)) ) ) ) )
<=> ( ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
~ ( ~ ( ~ aElementOf0(W1,W0)
| ( W1 = szmzizndt0(W0) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,W0),W0)
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,W0)) ) )
| ~ ( ( W1 != szmzizndt0(W0) )
| ~ ( ~ aElementOf0(W1,W0)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| sdtlseqdt0(W1,W2) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(264,plain,
( ! [W0: $i] :
( ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
~ ( ~ ( ( W1 != szmzizndt0(W0) )
| ~ ( ~ aElementOf0(W1,W0)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| sdtlseqdt0(W1,W2) ) ) )
| ~ ( ~ aElementOf0(W1,W0)
| ( W1 = szmzizndt0(W0) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,W0),W0)
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,W0)) ) ) ) )
<=> ! [W0: $i] :
( ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
~ ( ~ ( ~ aElementOf0(W1,W0)
| ( W1 = szmzizndt0(W0) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,W0),W0)
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,W0)) ) )
| ~ ( ( W1 != szmzizndt0(W0) )
| ~ ( ~ aElementOf0(W1,W0)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| sdtlseqdt0(W1,W2) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[263]) ).
tff(265,plain,
^ [W0: $i] :
refl(
( ( ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
~ ( ~ ( ( W1 != szmzizndt0(W0) )
| ~ ( ~ aElementOf0(W1,W0)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| sdtlseqdt0(W1,W2) ) ) )
| ~ ( ~ aElementOf0(W1,W0)
| ( W1 = szmzizndt0(W0) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,W0),W0)
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,W0)) ) ) ) )
<=> ( ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
~ ( ~ ( ( W1 != szmzizndt0(W0) )
| ~ ( ~ aElementOf0(W1,W0)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| sdtlseqdt0(W1,W2) ) ) )
| ~ ( ~ aElementOf0(W1,W0)
| ( W1 = szmzizndt0(W0) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,W0),W0)
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,W0)) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(266,plain,
( ! [W0: $i] :
( ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
~ ( ~ ( ( W1 != szmzizndt0(W0) )
| ~ ( ~ aElementOf0(W1,W0)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| sdtlseqdt0(W1,W2) ) ) )
| ~ ( ~ aElementOf0(W1,W0)
| ( W1 = szmzizndt0(W0) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,W0),W0)
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,W0)) ) ) ) )
<=> ! [W0: $i] :
( ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
~ ( ~ ( ( W1 != szmzizndt0(W0) )
| ~ ( ~ aElementOf0(W1,W0)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| sdtlseqdt0(W1,W2) ) ) )
| ~ ( ~ aElementOf0(W1,W0)
| ( W1 = szmzizndt0(W0) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,W0),W0)
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,W0)) ) ) ) ) ),
inference(quant_intro,[status(thm)],[265]) ).
tff(267,plain,
^ [W0: $i] :
rewrite(
( ( ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
~ ( ~ ( ( W1 != szmzizndt0(W0) )
| ~ ( ~ aElementOf0(W1,W0)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| sdtlseqdt0(W1,W2) ) ) )
| ~ ( ~ aElementOf0(W1,W0)
| ( W1 = szmzizndt0(W0) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,W0),W0)
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,W0)) ) ) ) )
<=> ( ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
~ ( ~ ( ( W1 != szmzizndt0(W0) )
| ~ ( ~ aElementOf0(W1,W0)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| sdtlseqdt0(W1,W2) ) ) )
| ~ ( ~ aElementOf0(W1,W0)
| ( W1 = szmzizndt0(W0) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,W0),W0)
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,W0)) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(268,plain,
( ! [W0: $i] :
( ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
~ ( ~ ( ( W1 != szmzizndt0(W0) )
| ~ ( ~ aElementOf0(W1,W0)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| sdtlseqdt0(W1,W2) ) ) )
| ~ ( ~ aElementOf0(W1,W0)
| ( W1 = szmzizndt0(W0) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,W0),W0)
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,W0)) ) ) ) )
<=> ! [W0: $i] :
( ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
~ ( ~ ( ( W1 != szmzizndt0(W0) )
| ~ ( ~ aElementOf0(W1,W0)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| sdtlseqdt0(W1,W2) ) ) )
| ~ ( ~ aElementOf0(W1,W0)
| ( W1 = szmzizndt0(W0) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,W0),W0)
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,W0)) ) ) ) ) ),
inference(quant_intro,[status(thm)],[267]) ).
tff(269,plain,
( ! [W0: $i] :
( ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
~ ( ~ ( ( W1 != szmzizndt0(W0) )
| ~ ( ~ aElementOf0(W1,W0)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| sdtlseqdt0(W1,W2) ) ) )
| ~ ( ~ aElementOf0(W1,W0)
| ( W1 = szmzizndt0(W0) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,W0),W0)
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,W0)) ) ) ) )
<=> ! [W0: $i] :
( ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
~ ( ~ ( ( W1 != szmzizndt0(W0) )
| ~ ( ~ aElementOf0(W1,W0)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| sdtlseqdt0(W1,W2) ) ) )
| ~ ( ~ aElementOf0(W1,W0)
| ( W1 = szmzizndt0(W0) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,W0),W0)
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,W0)) ) ) ) ) ),
inference(transitivity,[status(thm)],[268,266]) ).
tff(270,plain,
^ [W0: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( aSubsetOf0(W0,szDzozmdt0(xN))
& ( W0 != slbdtrb0(sz00) ) )
<=> ~ ( ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ( W0 = slbdtrb0(sz00) ) ) )),
( ~ ( aSubsetOf0(W0,szDzozmdt0(xN))
& ( W0 != slbdtrb0(sz00) ) )
<=> ~ ~ ( ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ( W0 = slbdtrb0(sz00) ) ) )),
rewrite(
( ~ ~ ( ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ( W0 = slbdtrb0(sz00) ) )
<=> ( ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ( W0 = slbdtrb0(sz00) ) ) )),
( ~ ( aSubsetOf0(W0,szDzozmdt0(xN))
& ( W0 != slbdtrb0(sz00) ) )
<=> ( ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ( W0 = slbdtrb0(sz00) ) ) )),
quant_intro(
proof_bind(
^ [W1: $i] :
trans(
monotonicity(
rewrite(
( ( ( W1 != szmzizndt0(W0) )
| ( aElementOf0(W1,W0)
& ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| sdtlseqdt0(W1,W2) ) ) )
<=> ( ( W1 != szmzizndt0(W0) )
| ~ ( ~ aElementOf0(W1,W0)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| sdtlseqdt0(W1,W2) ) ) ) )),
rewrite(
( ( ~ aElementOf0(W1,W0)
| ( W1 = szmzizndt0(W0) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,W0),W0)
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,W0)) ) )
<=> ( ~ aElementOf0(W1,W0)
| ( W1 = szmzizndt0(W0) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,W0),W0)
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,W0)) ) ) )),
( ( ( ( W1 != szmzizndt0(W0) )
| ( aElementOf0(W1,W0)
& ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| sdtlseqdt0(W1,W2) ) ) )
& ( ~ aElementOf0(W1,W0)
| ( W1 = szmzizndt0(W0) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,W0),W0)
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,W0)) ) ) )
<=> ( ( ( W1 != szmzizndt0(W0) )
| ~ ( ~ aElementOf0(W1,W0)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| sdtlseqdt0(W1,W2) ) ) )
& ( ~ aElementOf0(W1,W0)
| ( W1 = szmzizndt0(W0) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,W0),W0)
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,W0)) ) ) ) )),
rewrite(
( ( ( ( W1 != szmzizndt0(W0) )
| ~ ( ~ aElementOf0(W1,W0)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| sdtlseqdt0(W1,W2) ) ) )
& ( ~ aElementOf0(W1,W0)
| ( W1 = szmzizndt0(W0) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,W0),W0)
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,W0)) ) ) )
<=> ~ ( ~ ( ( W1 != szmzizndt0(W0) )
| ~ ( ~ aElementOf0(W1,W0)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| sdtlseqdt0(W1,W2) ) ) )
| ~ ( ~ aElementOf0(W1,W0)
| ( W1 = szmzizndt0(W0) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,W0),W0)
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,W0)) ) ) ) )),
( ( ( ( W1 != szmzizndt0(W0) )
| ( aElementOf0(W1,W0)
& ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| sdtlseqdt0(W1,W2) ) ) )
& ( ~ aElementOf0(W1,W0)
| ( W1 = szmzizndt0(W0) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,W0),W0)
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,W0)) ) ) )
<=> ~ ( ~ ( ( W1 != szmzizndt0(W0) )
| ~ ( ~ aElementOf0(W1,W0)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| sdtlseqdt0(W1,W2) ) ) )
| ~ ( ~ aElementOf0(W1,W0)
| ( W1 = szmzizndt0(W0) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,W0),W0)
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,W0)) ) ) ) ))),
( ! [W1: $i] :
( ( ( W1 != szmzizndt0(W0) )
| ( aElementOf0(W1,W0)
& ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| sdtlseqdt0(W1,W2) ) ) )
& ( ~ aElementOf0(W1,W0)
| ( W1 = szmzizndt0(W0) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,W0),W0)
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,W0)) ) ) )
<=> ! [W1: $i] :
~ ( ~ ( ( W1 != szmzizndt0(W0) )
| ~ ( ~ aElementOf0(W1,W0)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| sdtlseqdt0(W1,W2) ) ) )
| ~ ( ~ aElementOf0(W1,W0)
| ( W1 = szmzizndt0(W0) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,W0),W0)
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,W0)) ) ) ) )),
( ( ~ ( aSubsetOf0(W0,szDzozmdt0(xN))
& ( W0 != slbdtrb0(sz00) ) )
| ! [W1: $i] :
( ( ( W1 != szmzizndt0(W0) )
| ( aElementOf0(W1,W0)
& ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| sdtlseqdt0(W1,W2) ) ) )
& ( ~ aElementOf0(W1,W0)
| ( W1 = szmzizndt0(W0) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,W0),W0)
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,W0)) ) ) ) )
<=> ( ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ( W0 = slbdtrb0(sz00) )
| ! [W1: $i] :
~ ( ~ ( ( W1 != szmzizndt0(W0) )
| ~ ( ~ aElementOf0(W1,W0)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| sdtlseqdt0(W1,W2) ) ) )
| ~ ( ~ aElementOf0(W1,W0)
| ( W1 = szmzizndt0(W0) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,W0),W0)
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,W0)) ) ) ) ) )),
rewrite(
( ( ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ( W0 = slbdtrb0(sz00) )
| ! [W1: $i] :
~ ( ~ ( ( W1 != szmzizndt0(W0) )
| ~ ( ~ aElementOf0(W1,W0)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| sdtlseqdt0(W1,W2) ) ) )
| ~ ( ~ aElementOf0(W1,W0)
| ( W1 = szmzizndt0(W0) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,W0),W0)
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,W0)) ) ) ) )
<=> ( ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
~ ( ~ ( ( W1 != szmzizndt0(W0) )
| ~ ( ~ aElementOf0(W1,W0)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| sdtlseqdt0(W1,W2) ) ) )
| ~ ( ~ aElementOf0(W1,W0)
| ( W1 = szmzizndt0(W0) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,W0),W0)
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,W0)) ) ) ) ) )),
( ( ~ ( aSubsetOf0(W0,szDzozmdt0(xN))
& ( W0 != slbdtrb0(sz00) ) )
| ! [W1: $i] :
( ( ( W1 != szmzizndt0(W0) )
| ( aElementOf0(W1,W0)
& ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| sdtlseqdt0(W1,W2) ) ) )
& ( ~ aElementOf0(W1,W0)
| ( W1 = szmzizndt0(W0) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,W0),W0)
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,W0)) ) ) ) )
<=> ( ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
~ ( ~ ( ( W1 != szmzizndt0(W0) )
| ~ ( ~ aElementOf0(W1,W0)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| sdtlseqdt0(W1,W2) ) ) )
| ~ ( ~ aElementOf0(W1,W0)
| ( W1 = szmzizndt0(W0) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,W0),W0)
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,W0)) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(271,plain,
( ! [W0: $i] :
( ~ ( aSubsetOf0(W0,szDzozmdt0(xN))
& ( W0 != slbdtrb0(sz00) ) )
| ! [W1: $i] :
( ( ( W1 != szmzizndt0(W0) )
| ( aElementOf0(W1,W0)
& ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| sdtlseqdt0(W1,W2) ) ) )
& ( ~ aElementOf0(W1,W0)
| ( W1 = szmzizndt0(W0) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,W0),W0)
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,W0)) ) ) ) )
<=> ! [W0: $i] :
( ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
~ ( ~ ( ( W1 != szmzizndt0(W0) )
| ~ ( ~ aElementOf0(W1,W0)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| sdtlseqdt0(W1,W2) ) ) )
| ~ ( ~ aElementOf0(W1,W0)
| ( W1 = szmzizndt0(W0) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,W0),W0)
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,W0)) ) ) ) ) ),
inference(quant_intro,[status(thm)],[270]) ).
tff(272,plain,
^ [W0: $i] :
rewrite(
( ( ~ ( aSubsetOf0(W0,szDzozmdt0(xN))
& ( W0 != slbdtrb0(sz00) ) )
| ! [W1: $i] :
( ( ( W1 != szmzizndt0(W0) )
| ( aElementOf0(W1,W0)
& ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| sdtlseqdt0(W1,W2) ) ) )
& ( ( W1 = szmzizndt0(W0) )
| ~ aElementOf0(W1,W0)
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,W0),W0)
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,W0)) ) ) ) )
<=> ( ~ ( aSubsetOf0(W0,szDzozmdt0(xN))
& ( W0 != slbdtrb0(sz00) ) )
| ! [W1: $i] :
( ( ( W1 != szmzizndt0(W0) )
| ( aElementOf0(W1,W0)
& ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| sdtlseqdt0(W1,W2) ) ) )
& ( ~ aElementOf0(W1,W0)
| ( W1 = szmzizndt0(W0) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,W0),W0)
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,W0)) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(273,plain,
( ! [W0: $i] :
( ~ ( aSubsetOf0(W0,szDzozmdt0(xN))
& ( W0 != slbdtrb0(sz00) ) )
| ! [W1: $i] :
( ( ( W1 != szmzizndt0(W0) )
| ( aElementOf0(W1,W0)
& ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| sdtlseqdt0(W1,W2) ) ) )
& ( ( W1 = szmzizndt0(W0) )
| ~ aElementOf0(W1,W0)
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,W0),W0)
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,W0)) ) ) ) )
<=> ! [W0: $i] :
( ~ ( aSubsetOf0(W0,szDzozmdt0(xN))
& ( W0 != slbdtrb0(sz00) ) )
| ! [W1: $i] :
( ( ( W1 != szmzizndt0(W0) )
| ( aElementOf0(W1,W0)
& ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| sdtlseqdt0(W1,W2) ) ) )
& ( ~ aElementOf0(W1,W0)
| ( W1 = szmzizndt0(W0) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,W0),W0)
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,W0)) ) ) ) ) ),
inference(quant_intro,[status(thm)],[272]) ).
tff(274,plain,
^ [W0: $i] :
rewrite(
( ( ~ ( aSubsetOf0(W0,szNzAzT0)
& ( W0 != slcrc0 ) )
| ! [W1: $i] :
( ( W1 = szmzizndt0(W0) )
<=> ( aElementOf0(W1,W0)
& ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| sdtlseqdt0(W1,W2) ) ) ) )
<=> ( ~ ( aSubsetOf0(W0,szDzozmdt0(xN))
& ( W0 != slbdtrb0(sz00) ) )
| ! [W1: $i] :
( ( W1 = szmzizndt0(W0) )
<=> ( aElementOf0(W1,W0)
& ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| sdtlseqdt0(W1,W2) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(275,plain,
( ! [W0: $i] :
( ~ ( aSubsetOf0(W0,szNzAzT0)
& ( W0 != slcrc0 ) )
| ! [W1: $i] :
( ( W1 = szmzizndt0(W0) )
<=> ( aElementOf0(W1,W0)
& ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| sdtlseqdt0(W1,W2) ) ) ) )
<=> ! [W0: $i] :
( ~ ( aSubsetOf0(W0,szDzozmdt0(xN))
& ( W0 != slbdtrb0(sz00) ) )
| ! [W1: $i] :
( ( W1 = szmzizndt0(W0) )
<=> ( aElementOf0(W1,W0)
& ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| sdtlseqdt0(W1,W2) ) ) ) ) ),
inference(quant_intro,[status(thm)],[274]) ).
tff(276,plain,
( ! [W0: $i] :
( ~ ( aSubsetOf0(W0,szNzAzT0)
& ( W0 != slcrc0 ) )
| ! [W1: $i] :
( ( W1 = szmzizndt0(W0) )
<=> ( aElementOf0(W1,W0)
& ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| sdtlseqdt0(W1,W2) ) ) ) )
<=> ! [W0: $i] :
( ~ ( aSubsetOf0(W0,szNzAzT0)
& ( W0 != slcrc0 ) )
| ! [W1: $i] :
( ( W1 = szmzizndt0(W0) )
<=> ( aElementOf0(W1,W0)
& ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| sdtlseqdt0(W1,W2) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(277,plain,
^ [W0: $i] :
trans(
monotonicity(
quant_intro(
proof_bind(
^ [W1: $i] :
rewrite(
( ( ( W1 = szmzizndt0(W0) )
<=> ( aElementOf0(W1,W0)
& ! [W2: $i] :
( aElementOf0(W2,W0)
=> sdtlseqdt0(W1,W2) ) ) )
<=> ( ( W1 = szmzizndt0(W0) )
<=> ( aElementOf0(W1,W0)
& ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| sdtlseqdt0(W1,W2) ) ) ) ))),
( ! [W1: $i] :
( ( W1 = szmzizndt0(W0) )
<=> ( aElementOf0(W1,W0)
& ! [W2: $i] :
( aElementOf0(W2,W0)
=> sdtlseqdt0(W1,W2) ) ) )
<=> ! [W1: $i] :
( ( W1 = szmzizndt0(W0) )
<=> ( aElementOf0(W1,W0)
& ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| sdtlseqdt0(W1,W2) ) ) ) )),
( ( ( aSubsetOf0(W0,szNzAzT0)
& ( W0 != slcrc0 ) )
=> ! [W1: $i] :
( ( W1 = szmzizndt0(W0) )
<=> ( aElementOf0(W1,W0)
& ! [W2: $i] :
( aElementOf0(W2,W0)
=> sdtlseqdt0(W1,W2) ) ) ) )
<=> ( ( aSubsetOf0(W0,szNzAzT0)
& ( W0 != slcrc0 ) )
=> ! [W1: $i] :
( ( W1 = szmzizndt0(W0) )
<=> ( aElementOf0(W1,W0)
& ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| sdtlseqdt0(W1,W2) ) ) ) ) )),
rewrite(
( ( ( aSubsetOf0(W0,szNzAzT0)
& ( W0 != slcrc0 ) )
=> ! [W1: $i] :
( ( W1 = szmzizndt0(W0) )
<=> ( aElementOf0(W1,W0)
& ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| sdtlseqdt0(W1,W2) ) ) ) )
<=> ( ~ ( aSubsetOf0(W0,szNzAzT0)
& ( W0 != slcrc0 ) )
| ! [W1: $i] :
( ( W1 = szmzizndt0(W0) )
<=> ( aElementOf0(W1,W0)
& ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| sdtlseqdt0(W1,W2) ) ) ) ) )),
( ( ( aSubsetOf0(W0,szNzAzT0)
& ( W0 != slcrc0 ) )
=> ! [W1: $i] :
( ( W1 = szmzizndt0(W0) )
<=> ( aElementOf0(W1,W0)
& ! [W2: $i] :
( aElementOf0(W2,W0)
=> sdtlseqdt0(W1,W2) ) ) ) )
<=> ( ~ ( aSubsetOf0(W0,szNzAzT0)
& ( W0 != slcrc0 ) )
| ! [W1: $i] :
( ( W1 = szmzizndt0(W0) )
<=> ( aElementOf0(W1,W0)
& ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| sdtlseqdt0(W1,W2) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(278,plain,
( ! [W0: $i] :
( ( aSubsetOf0(W0,szNzAzT0)
& ( W0 != slcrc0 ) )
=> ! [W1: $i] :
( ( W1 = szmzizndt0(W0) )
<=> ( aElementOf0(W1,W0)
& ! [W2: $i] :
( aElementOf0(W2,W0)
=> sdtlseqdt0(W1,W2) ) ) ) )
<=> ! [W0: $i] :
( ~ ( aSubsetOf0(W0,szNzAzT0)
& ( W0 != slcrc0 ) )
| ! [W1: $i] :
( ( W1 = szmzizndt0(W0) )
<=> ( aElementOf0(W1,W0)
& ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| sdtlseqdt0(W1,W2) ) ) ) ) ),
inference(quant_intro,[status(thm)],[277]) ).
tff(279,axiom,
! [W0: $i] :
( ( aSubsetOf0(W0,szNzAzT0)
& ( W0 != slcrc0 ) )
=> ! [W1: $i] :
( ( W1 = szmzizndt0(W0) )
<=> ( aElementOf0(W1,W0)
& ! [W2: $i] :
( aElementOf0(W2,W0)
=> sdtlseqdt0(W1,W2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefMin) ).
tff(280,plain,
! [W0: $i] :
( ~ ( aSubsetOf0(W0,szNzAzT0)
& ( W0 != slcrc0 ) )
| ! [W1: $i] :
( ( W1 = szmzizndt0(W0) )
<=> ( aElementOf0(W1,W0)
& ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| sdtlseqdt0(W1,W2) ) ) ) ),
inference(modus_ponens,[status(thm)],[279,278]) ).
tff(281,plain,
! [W0: $i] :
( ~ ( aSubsetOf0(W0,szNzAzT0)
& ( W0 != slcrc0 ) )
| ! [W1: $i] :
( ( W1 = szmzizndt0(W0) )
<=> ( aElementOf0(W1,W0)
& ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| sdtlseqdt0(W1,W2) ) ) ) ),
inference(modus_ponens,[status(thm)],[280,276]) ).
tff(282,plain,
! [W0: $i] :
( ~ ( aSubsetOf0(W0,szDzozmdt0(xN))
& ( W0 != slbdtrb0(sz00) ) )
| ! [W1: $i] :
( ( W1 = szmzizndt0(W0) )
<=> ( aElementOf0(W1,W0)
& ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| sdtlseqdt0(W1,W2) ) ) ) ),
inference(modus_ponens,[status(thm)],[281,275]) ).
tff(283,plain,
! [W0: $i] :
( ~ ( aSubsetOf0(W0,szDzozmdt0(xN))
& ( W0 != slbdtrb0(sz00) ) )
| ! [W1: $i] :
( ( ( W1 != szmzizndt0(W0) )
| ( aElementOf0(W1,W0)
& ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| sdtlseqdt0(W1,W2) ) ) )
& ( ( W1 = szmzizndt0(W0) )
| ~ aElementOf0(W1,W0)
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,W0),W0)
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,W0)) ) ) ) ),
inference(skolemize,[status(sab)],[282]) ).
tff(284,plain,
! [W0: $i] :
( ~ ( aSubsetOf0(W0,szDzozmdt0(xN))
& ( W0 != slbdtrb0(sz00) ) )
| ! [W1: $i] :
( ( ( W1 != szmzizndt0(W0) )
| ( aElementOf0(W1,W0)
& ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| sdtlseqdt0(W1,W2) ) ) )
& ( ~ aElementOf0(W1,W0)
| ( W1 = szmzizndt0(W0) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,W0),W0)
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,W0)) ) ) ) ),
inference(modus_ponens,[status(thm)],[283,273]) ).
tff(285,plain,
! [W0: $i] :
( ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
~ ( ~ ( ( W1 != szmzizndt0(W0) )
| ~ ( ~ aElementOf0(W1,W0)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| sdtlseqdt0(W1,W2) ) ) )
| ~ ( ~ aElementOf0(W1,W0)
| ( W1 = szmzizndt0(W0) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,W0),W0)
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,W0)) ) ) ) ),
inference(modus_ponens,[status(thm)],[284,271]) ).
tff(286,plain,
! [W0: $i] :
( ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
~ ( ~ ( ( W1 != szmzizndt0(W0) )
| ~ ( ~ aElementOf0(W1,W0)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| sdtlseqdt0(W1,W2) ) ) )
| ~ ( ~ aElementOf0(W1,W0)
| ( W1 = szmzizndt0(W0) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,W0),W0)
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,W0)) ) ) ) ),
inference(modus_ponens,[status(thm)],[285,269]) ).
tff(287,plain,
! [W0: $i] :
( ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
~ ( ~ ( ~ aElementOf0(W1,W0)
| ( W1 = szmzizndt0(W0) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,W0),W0)
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,W0)) ) )
| ~ ( ( W1 != szmzizndt0(W0) )
| ~ ( ~ aElementOf0(W1,W0)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| sdtlseqdt0(W1,W2) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[286,264]) ).
tff(288,plain,
( ( ~ ! [W0: $i] :
( ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
~ ( ~ ( ~ aElementOf0(W1,W0)
| ( W1 = szmzizndt0(W0) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,W0),W0)
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,W0)) ) )
| ~ ( ( W1 != szmzizndt0(W0) )
| ~ ( ~ aElementOf0(W1,W0)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| sdtlseqdt0(W1,W2) ) ) ) ) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),szDzozmdt0(xN))
| ( sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))) = slbdtrb0(sz00) )
| ! [W1: $i] :
~ ( ~ ( ~ aElementOf0(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ( W1 = szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))) ) )
| ~ ( ( W1 != szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) )
| ~ ( ~ aElementOf0(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| sdtlseqdt0(W1,W2) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
~ ( ~ ( ~ aElementOf0(W1,W0)
| ( W1 = szmzizndt0(W0) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,W0),W0)
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,W0)) ) )
| ~ ( ( W1 != szmzizndt0(W0) )
| ~ ( ~ aElementOf0(W1,W0)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| sdtlseqdt0(W1,W2) ) ) ) ) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),szDzozmdt0(xN))
| ( sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))) = slbdtrb0(sz00) )
| ! [W1: $i] :
~ ( ~ ( ~ aElementOf0(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ( W1 = szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))) ) )
| ~ ( ( W1 != szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) )
| ~ ( ~ aElementOf0(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| sdtlseqdt0(W1,W2) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(289,plain,
( ( ( sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))) = slbdtrb0(sz00) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),szDzozmdt0(xN))
| ! [W1: $i] :
~ ( ~ ( ~ aElementOf0(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ( W1 = szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))) ) )
| ~ ( ( W1 != szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) )
| ~ ( ~ aElementOf0(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| sdtlseqdt0(W1,W2) ) ) ) ) )
<=> ( ~ aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),szDzozmdt0(xN))
| ( sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))) = slbdtrb0(sz00) )
| ! [W1: $i] :
~ ( ~ ( ~ aElementOf0(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ( W1 = szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))) ) )
| ~ ( ( W1 != szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) )
| ~ ( ~ aElementOf0(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| sdtlseqdt0(W1,W2) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(290,plain,
( ( ~ ! [W0: $i] :
( ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
~ ( ~ ( ~ aElementOf0(W1,W0)
| ( W1 = szmzizndt0(W0) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,W0),W0)
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,W0)) ) )
| ~ ( ( W1 != szmzizndt0(W0) )
| ~ ( ~ aElementOf0(W1,W0)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| sdtlseqdt0(W1,W2) ) ) ) ) )
| ( sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))) = slbdtrb0(sz00) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),szDzozmdt0(xN))
| ! [W1: $i] :
~ ( ~ ( ~ aElementOf0(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ( W1 = szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))) ) )
| ~ ( ( W1 != szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) )
| ~ ( ~ aElementOf0(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| sdtlseqdt0(W1,W2) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
~ ( ~ ( ~ aElementOf0(W1,W0)
| ( W1 = szmzizndt0(W0) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,W0),W0)
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,W0)) ) )
| ~ ( ( W1 != szmzizndt0(W0) )
| ~ ( ~ aElementOf0(W1,W0)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| sdtlseqdt0(W1,W2) ) ) ) ) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),szDzozmdt0(xN))
| ( sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))) = slbdtrb0(sz00) )
| ! [W1: $i] :
~ ( ~ ( ~ aElementOf0(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ( W1 = szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))) ) )
| ~ ( ( W1 != szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) )
| ~ ( ~ aElementOf0(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| sdtlseqdt0(W1,W2) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[289]) ).
tff(291,plain,
( ( ~ ! [W0: $i] :
( ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
~ ( ~ ( ~ aElementOf0(W1,W0)
| ( W1 = szmzizndt0(W0) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,W0),W0)
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,W0)) ) )
| ~ ( ( W1 != szmzizndt0(W0) )
| ~ ( ~ aElementOf0(W1,W0)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| sdtlseqdt0(W1,W2) ) ) ) ) )
| ( sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))) = slbdtrb0(sz00) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),szDzozmdt0(xN))
| ! [W1: $i] :
~ ( ~ ( ~ aElementOf0(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ( W1 = szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))) ) )
| ~ ( ( W1 != szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) )
| ~ ( ~ aElementOf0(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| sdtlseqdt0(W1,W2) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
~ ( ~ ( ~ aElementOf0(W1,W0)
| ( W1 = szmzizndt0(W0) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,W0),W0)
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,W0)) ) )
| ~ ( ( W1 != szmzizndt0(W0) )
| ~ ( ~ aElementOf0(W1,W0)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| sdtlseqdt0(W1,W2) ) ) ) ) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),szDzozmdt0(xN))
| ( sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))) = slbdtrb0(sz00) )
| ! [W1: $i] :
~ ( ~ ( ~ aElementOf0(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ( W1 = szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))) ) )
| ~ ( ( W1 != szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) )
| ~ ( ~ aElementOf0(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| sdtlseqdt0(W1,W2) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[290,288]) ).
tff(292,plain,
( ~ ! [W0: $i] :
( ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
~ ( ~ ( ~ aElementOf0(W1,W0)
| ( W1 = szmzizndt0(W0) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,W0),W0)
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,W0)) ) )
| ~ ( ( W1 != szmzizndt0(W0) )
| ~ ( ~ aElementOf0(W1,W0)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| sdtlseqdt0(W1,W2) ) ) ) ) )
| ( sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))) = slbdtrb0(sz00) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),szDzozmdt0(xN))
| ! [W1: $i] :
~ ( ~ ( ~ aElementOf0(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ( W1 = szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))) ) )
| ~ ( ( W1 != szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) )
| ~ ( ~ aElementOf0(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| sdtlseqdt0(W1,W2) ) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(293,plain,
( ~ ! [W0: $i] :
( ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
~ ( ~ ( ~ aElementOf0(W1,W0)
| ( W1 = szmzizndt0(W0) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,W0),W0)
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,W0)) ) )
| ~ ( ( W1 != szmzizndt0(W0) )
| ~ ( ~ aElementOf0(W1,W0)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| sdtlseqdt0(W1,W2) ) ) ) ) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))),szDzozmdt0(xN))
| ( sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))) = slbdtrb0(sz00) )
| ! [W1: $i] :
~ ( ~ ( ~ aElementOf0(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ( W1 = szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))) ) )
| ~ ( ( W1 != szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) )
| ~ ( ~ aElementOf0(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| sdtlseqdt0(W1,W2) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[292,291]) ).
tff(294,plain,
( ( sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))) = slbdtrb0(sz00) )
| ! [W1: $i] :
~ ( ~ ( ~ aElementOf0(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ( W1 = szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))) ) )
| ~ ( ( W1 != szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) )
| ~ ( ~ aElementOf0(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| sdtlseqdt0(W1,W2) ) ) ) ) ),
inference(unit_resolution,[status(thm)],[293,287,231]) ).
tff(295,plain,
! [W1: $i] :
~ ( ~ ( ~ aElementOf0(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ( W1 = szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))) ) )
| ~ ( ( W1 != szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) )
| ~ ( ~ aElementOf0(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| sdtlseqdt0(W1,W2) ) ) ) ),
inference(unit_resolution,[status(thm)],[294,262]) ).
tff(296,plain,
( ( ~ ! [W1: $i] :
~ ( ~ ( ~ aElementOf0(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ( W1 = szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))) ) )
| ~ ( ( W1 != szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) )
| ~ ( ~ aElementOf0(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| sdtlseqdt0(W1,W2) ) ) ) )
| ~ ( ~ ( ( szmzizndt0(sdtlpdtrp0(xN,xi)) = szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ( ~ aElementOf0(tptp_fun_W2_6(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),tptp_fun_W2_6(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))) ) )
| ~ ( ( szmzizndt0(sdtlpdtrp0(xN,xi)) != szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) ) ) ) ) )
<=> ( ~ ! [W1: $i] :
~ ( ~ ( ~ aElementOf0(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ( W1 = szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))) ) )
| ~ ( ( W1 != szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) )
| ~ ( ~ aElementOf0(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| sdtlseqdt0(W1,W2) ) ) ) )
| ~ ( ~ ( ( szmzizndt0(sdtlpdtrp0(xN,xi)) = szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ( ~ aElementOf0(tptp_fun_W2_6(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),tptp_fun_W2_6(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))) ) )
| ~ ( ( szmzizndt0(sdtlpdtrp0(xN,xi)) != szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(297,plain,
( ~ ( ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ( szmzizndt0(sdtlpdtrp0(xN,xi)) = szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),tptp_fun_W2_6(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))) ) )
| ~ ( ( szmzizndt0(sdtlpdtrp0(xN,xi)) != szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) ) ) ) )
<=> ~ ( ~ ( ( szmzizndt0(sdtlpdtrp0(xN,xi)) = szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ( ~ aElementOf0(tptp_fun_W2_6(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),tptp_fun_W2_6(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))) ) )
| ~ ( ( szmzizndt0(sdtlpdtrp0(xN,xi)) != szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(298,plain,
( ( ~ ! [W1: $i] :
~ ( ~ ( ~ aElementOf0(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ( W1 = szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))) ) )
| ~ ( ( W1 != szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) )
| ~ ( ~ aElementOf0(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| sdtlseqdt0(W1,W2) ) ) ) )
| ~ ( ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ( szmzizndt0(sdtlpdtrp0(xN,xi)) = szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),tptp_fun_W2_6(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))) ) )
| ~ ( ( szmzizndt0(sdtlpdtrp0(xN,xi)) != szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) ) ) ) ) )
<=> ( ~ ! [W1: $i] :
~ ( ~ ( ~ aElementOf0(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ( W1 = szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))) ) )
| ~ ( ( W1 != szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) )
| ~ ( ~ aElementOf0(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| sdtlseqdt0(W1,W2) ) ) ) )
| ~ ( ~ ( ( szmzizndt0(sdtlpdtrp0(xN,xi)) = szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ( ~ aElementOf0(tptp_fun_W2_6(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),tptp_fun_W2_6(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))) ) )
| ~ ( ( szmzizndt0(sdtlpdtrp0(xN,xi)) != szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[297]) ).
tff(299,plain,
( ( ~ ! [W1: $i] :
~ ( ~ ( ~ aElementOf0(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ( W1 = szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))) ) )
| ~ ( ( W1 != szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) )
| ~ ( ~ aElementOf0(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| sdtlseqdt0(W1,W2) ) ) ) )
| ~ ( ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ( szmzizndt0(sdtlpdtrp0(xN,xi)) = szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),tptp_fun_W2_6(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))) ) )
| ~ ( ( szmzizndt0(sdtlpdtrp0(xN,xi)) != szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) ) ) ) ) )
<=> ( ~ ! [W1: $i] :
~ ( ~ ( ~ aElementOf0(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ( W1 = szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))) ) )
| ~ ( ( W1 != szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) )
| ~ ( ~ aElementOf0(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| sdtlseqdt0(W1,W2) ) ) ) )
| ~ ( ~ ( ( szmzizndt0(sdtlpdtrp0(xN,xi)) = szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ( ~ aElementOf0(tptp_fun_W2_6(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),tptp_fun_W2_6(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))) ) )
| ~ ( ( szmzizndt0(sdtlpdtrp0(xN,xi)) != szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[298,296]) ).
tff(300,plain,
( ~ ! [W1: $i] :
~ ( ~ ( ~ aElementOf0(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ( W1 = szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))) ) )
| ~ ( ( W1 != szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) )
| ~ ( ~ aElementOf0(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| sdtlseqdt0(W1,W2) ) ) ) )
| ~ ( ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ( szmzizndt0(sdtlpdtrp0(xN,xi)) = szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),tptp_fun_W2_6(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))) ) )
| ~ ( ( szmzizndt0(sdtlpdtrp0(xN,xi)) != szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) ) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(301,plain,
( ~ ! [W1: $i] :
~ ( ~ ( ~ aElementOf0(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ( W1 = szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) )
| ~ ( ~ aElementOf0(tptp_fun_W2_6(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| sdtlseqdt0(W1,tptp_fun_W2_6(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))) ) )
| ~ ( ( W1 != szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) )
| ~ ( ~ aElementOf0(W1,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| sdtlseqdt0(W1,W2) ) ) ) )
| ~ ( ~ ( ( szmzizndt0(sdtlpdtrp0(xN,xi)) = szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ( ~ aElementOf0(tptp_fun_W2_6(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),tptp_fun_W2_6(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))) ) )
| ~ ( ( szmzizndt0(sdtlpdtrp0(xN,xi)) != szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi)))) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,tptp_fun_W1_24(sdtlpdtrp0(xe,xi))))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[300,299]) ).
tff(302,plain,
$false,
inference(unit_resolution,[status(thm)],[301,295,200]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM604+1 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n022.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri Sep 2 12:18:25 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 176.15/112.07 % SZS status Theorem
% 176.15/112.07 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------