%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM563+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:21:24 AM UTC 2025
% Result : Theorem 211.70s 211.96s
% Output : Proof 212.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 148
% Syntax : Number of formulae : 379 ( 88 unt; 0 typ; 0 def)
% Number of atoms : 3698 ( 756 equ)
% Maximal formula atoms : 48 ( 9 avg)
% Number of connectives : 6735 (3596 ~;2370 |; 236 &)
% ( 478 <=>; 55 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 180 ( 180 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 20 ( 17 usr; 1 prp; 0-4 aty)
% Number of functors : 17 ( 17 usr; 7 con; 0-3 aty)
% Number of variables : 938 ( 862 !; 26 ?; 938 :)
% Comments :
%------------------------------------------------------------------------------
tff(sdtlpdtrp0_type,type,
sdtlpdtrp0: ( $i * $i ) > $i ).
tff(slcrc0_type,type,
slcrc0: $i ).
tff(xc_type,type,
xc: $i ).
tff(tptp_fun_W2_21_type,type,
tptp_fun_W2_21: ( $i * $i ) > $i ).
tff(xS_type,type,
xS: $i ).
tff(sz00_type,type,
sz00: $i ).
tff(sbrdtbr0_type,type,
sbrdtbr0: $i > $i ).
tff(aSet0_type,type,
aSet0: $i > $o ).
tff(aElementOf0_type,type,
aElementOf0: ( $i * $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(szNzAzT0_type,type,
szNzAzT0: $i ).
tff(isCountable0_type,type,
isCountable0: $i > $o ).
tff(slbdtsldtrb0_type,type,
slbdtsldtrb0: ( $i * $i ) > $i ).
tff(xK_type,type,
xK: $i ).
tff(tptp_fun_W3_10_type,type,
tptp_fun_W3_10: ( $i * $i * $i ) > $i ).
tff(xT_type,type,
xT: $i ).
tff(sdtlcdtrc0_type,type,
sdtlcdtrc0: ( $i * $i ) > $i ).
tff(szDzozmdt0_type,type,
szDzozmdt0: $i > $i ).
tff(tptp_fun_W1_0_type,type,
tptp_fun_W1_0: $i > $i ).
tff(aFunction0_type,type,
aFunction0: $i > $o ).
tff(slbdtrb0_type,type,
slbdtrb0: $i > $i ).
tff(isFinite0_type,type,
isFinite0: $i > $o ).
tff(1,plain,
( aSet0(szNzAzT0)
<=> aSet0(szNzAzT0) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
( aSet0(szNzAzT0)
& isCountable0(szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNATSet) ).
tff(3,plain,
aSet0(szNzAzT0),
inference(and_elim,[status(thm)],[2]) ).
tff(4,plain,
aSet0(szNzAzT0),
inference(modus_ponens,[status(thm)],[3,1]) ).
tff(5,plain,
^ [W0: $i] :
rewrite(( ( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(6,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[5]) ).
tff(7,plain,
^ [W0: $i] :
refl(( ( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
^ [W0: $i] :
rewrite(( ( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(10,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) ),
inference(quant_intro,[status(thm)],[9]) ).
tff(11,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) ),
inference(transitivity,[status(thm)],[10,8]) ).
tff(12,plain,
^ [W0: $i] :
rewrite(( ( ~ aSet0(W0)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,W0)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
& ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(13,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,W0)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
& ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) ),
inference(quant_intro,[status(thm)],[12]) ).
tff(14,plain,
^ [W0: $i] :
rewrite(( ( ~ aSet0(W0)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,W0)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
& ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,W0)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
& ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(15,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,W0)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
& ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,W0)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
& ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) ),
inference(quant_intro,[status(thm)],[14]) ).
tff(16,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(17,plain,
^ [W0: $i] :
trans(monotonicity(quant_intro(proof_bind(^ [W1: $i] :
rewrite(( ( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) ) ) )
<=> ( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ))),
( ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) ) ) )
<=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) )),
( ( aSet0(W0)
=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) ) ) ) )
<=> ( aSet0(W0)
=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )),
rewrite(( ( aSet0(W0)
=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )),
( ( aSet0(W0)
=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) ) ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(18,plain,
( ! [W0: $i] :
( aSet0(W0)
=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) ),
inference(quant_intro,[status(thm)],[17]) ).
tff(19,axiom,
! [W0: $i] :
( aSet0(W0)
=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSub) ).
tff(20,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ),
inference(modus_ponens,[status(thm)],[20,16]) ).
tff(22,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,W0)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
& ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ),
inference(skolemize,[status(sab)],[21]) ).
tff(23,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,W0)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
& ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ),
inference(modus_ponens,[status(thm)],[22,15]) ).
tff(24,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ),
inference(modus_ponens,[status(thm)],[23,13]) ).
tff(25,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ),
inference(modus_ponens,[status(thm)],[24,11]) ).
tff(26,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[25,6]) ).
tff(27,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(szNzAzT0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,szNzAzT0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,szNzAzT0),W1)
| aElementOf0(tptp_fun_W2_1(W1,szNzAzT0),szNzAzT0) ) )
| ~ ( ~ aSubsetOf0(W1,szNzAzT0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,szNzAzT0) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(szNzAzT0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,szNzAzT0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,szNzAzT0),W1)
| aElementOf0(tptp_fun_W2_1(W1,szNzAzT0),szNzAzT0) ) )
| ~ ( ~ aSubsetOf0(W1,szNzAzT0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,szNzAzT0) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(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) ) ) ) ) )
| ~ aSet0(szNzAzT0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,szNzAzT0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,szNzAzT0),W1)
| aElementOf0(tptp_fun_W2_1(W1,szNzAzT0),szNzAzT0) ) )
| ~ ( ~ aSubsetOf0(W1,szNzAzT0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,szNzAzT0) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(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(szNzAzT0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,szNzAzT0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,szNzAzT0),W1)
| aElementOf0(tptp_fun_W2_1(W1,szNzAzT0),szNzAzT0) ) )
| ~ ( ~ aSubsetOf0(W1,szNzAzT0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,szNzAzT0) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,szNzAzT0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,szNzAzT0),W1)
| aElementOf0(tptp_fun_W2_1(W1,szNzAzT0),szNzAzT0) ) )
| ~ ( ~ aSubsetOf0(W1,szNzAzT0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,szNzAzT0) ) ) ) ),
inference(unit_resolution,[status(thm)],[29,26,4]) ).
tff(31,plain,
( ~ ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,szNzAzT0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,szNzAzT0),W1)
| aElementOf0(tptp_fun_W2_1(W1,szNzAzT0),szNzAzT0) ) )
| ~ ( ~ aSubsetOf0(W1,szNzAzT0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,szNzAzT0) ) ) ) )
| ~ ( ~ ( aSubsetOf0(xS,szNzAzT0)
| ~ aSet0(xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(xS,szNzAzT0),xS)
| aElementOf0(tptp_fun_W2_1(xS,szNzAzT0),szNzAzT0) ) )
| ~ ( ~ aSubsetOf0(xS,szNzAzT0)
| ~ ( ~ aSet0(xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xS)
| aElementOf0(W2,szNzAzT0) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(32,plain,
~ ( ~ ( aSubsetOf0(xS,szNzAzT0)
| ~ aSet0(xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(xS,szNzAzT0),xS)
| aElementOf0(tptp_fun_W2_1(xS,szNzAzT0),szNzAzT0) ) )
| ~ ( ~ aSubsetOf0(xS,szNzAzT0)
| ~ ( ~ aSet0(xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xS)
| aElementOf0(W2,szNzAzT0) ) ) ) ),
inference(unit_resolution,[status(thm)],[31,30]) ).
tff(33,plain,
( ~ ( aSubsetOf0(xS,szNzAzT0)
| ~ aSet0(xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(xS,szNzAzT0),xS)
| aElementOf0(tptp_fun_W2_1(xS,szNzAzT0),szNzAzT0) ) )
| ~ ( ~ aSubsetOf0(xS,szNzAzT0)
| ~ ( ~ aSet0(xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xS)
| aElementOf0(W2,szNzAzT0) ) ) )
| ~ aSubsetOf0(xS,szNzAzT0)
| ~ ( ~ aSet0(xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xS)
| aElementOf0(W2,szNzAzT0) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(34,plain,
( ~ aSubsetOf0(xS,szNzAzT0)
| ~ ( ~ aSet0(xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xS)
| aElementOf0(W2,szNzAzT0) ) ) ),
inference(unit_resolution,[status(thm)],[33,32]) ).
tff(35,plain,
( aSubsetOf0(xS,szNzAzT0)
<=> aSubsetOf0(xS,szNzAzT0) ),
inference(rewrite,[status(thm)],[]) ).
tff(36,axiom,
( aSubsetOf0(xS,szNzAzT0)
& isCountable0(xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3435) ).
tff(37,plain,
aSubsetOf0(xS,szNzAzT0),
inference(and_elim,[status(thm)],[36]) ).
tff(38,plain,
aSubsetOf0(xS,szNzAzT0),
inference(modus_ponens,[status(thm)],[37,35]) ).
tff(39,plain,
( ~ ( ~ aSubsetOf0(xS,szNzAzT0)
| ~ ( ~ aSet0(xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xS)
| aElementOf0(W2,szNzAzT0) ) ) )
| ~ aSubsetOf0(xS,szNzAzT0)
| ~ ( ~ aSet0(xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xS)
| aElementOf0(W2,szNzAzT0) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(40,plain,
( ~ ( ~ aSubsetOf0(xS,szNzAzT0)
| ~ ( ~ aSet0(xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xS)
| aElementOf0(W2,szNzAzT0) ) ) )
| ~ ( ~ aSet0(xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xS)
| aElementOf0(W2,szNzAzT0) ) ) ),
inference(unit_resolution,[status(thm)],[39,38]) ).
tff(41,plain,
~ ( ~ aSet0(xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xS)
| aElementOf0(W2,szNzAzT0) ) ),
inference(unit_resolution,[status(thm)],[40,34]) ).
tff(42,plain,
( ~ aSet0(xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xS)
| aElementOf0(W2,szNzAzT0) )
| aSet0(xS) ),
inference(tautology,[status(thm)],[]) ).
tff(43,plain,
aSet0(xS),
inference(unit_resolution,[status(thm)],[42,41]) ).
tff(44,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(xS)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,xS)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xS),W1)
| aElementOf0(tptp_fun_W2_1(W1,xS),xS) ) )
| ~ ( ~ aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xS) ) ) ) ) )
<=> ( ~ ! [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(xS)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,xS)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xS),W1)
| aElementOf0(tptp_fun_W2_1(W1,xS),xS) ) )
| ~ ( ~ aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xS) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(45,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(xS)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,xS)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xS),W1)
| aElementOf0(tptp_fun_W2_1(W1,xS),xS) ) )
| ~ ( ~ aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xS) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(46,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(xS)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,xS)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xS),W1)
| aElementOf0(tptp_fun_W2_1(W1,xS),xS) ) )
| ~ ( ~ aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xS) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,xS)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xS),W1)
| aElementOf0(tptp_fun_W2_1(W1,xS),xS) ) )
| ~ ( ~ aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xS) ) ) ) ),
inference(unit_resolution,[status(thm)],[46,26,43]) ).
tff(48,plain,
( ~ ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,xS)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xS),W1)
| aElementOf0(tptp_fun_W2_1(W1,xS),xS) ) )
| ~ ( ~ aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xS) ) ) ) )
| ~ ( ~ ( aSubsetOf0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)),xS)
| ~ aSet0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)),xS),tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(tptp_fun_W2_1(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)),xS),xS) ) )
| ~ ( ~ aSubsetOf0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)),xS)
| ~ ( ~ aSet0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W2,xS) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(49,plain,
~ ( ~ ( aSubsetOf0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)),xS)
| ~ aSet0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)),xS),tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(tptp_fun_W2_1(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)),xS),xS) ) )
| ~ ( ~ aSubsetOf0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)),xS)
| ~ ( ~ aSet0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W2,xS) ) ) ) ),
inference(unit_resolution,[status(thm)],[48,47]) ).
tff(50,plain,
( ~ ( aSubsetOf0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)),xS)
| ~ aSet0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)),xS),tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(tptp_fun_W2_1(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)),xS),xS) ) )
| ~ ( ~ aSubsetOf0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)),xS)
| ~ ( ~ aSet0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W2,xS) ) ) )
| ~ aSubsetOf0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)),xS)
| ~ ( ~ aSet0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W2,xS) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(51,plain,
( ~ aSubsetOf0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)),xS)
| ~ ( ~ aSet0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W2,xS) ) ) ),
inference(unit_resolution,[status(thm)],[50,49]) ).
tff(52,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(quant_intro(proof_bind(^ [W2: $i] :
rewrite(( ~ ( ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) ) )
<=> ~ ( ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) ) ) ))),
( ! [W2: $i] :
~ ( ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) ) )
<=> ! [W2: $i] :
~ ( ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) ) ) )),
( ( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) ) ) )
<=> ( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) ) ) ) )),
rewrite(( ( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) ) ) )
<=> ( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) ) ) ) )),
( ( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) ) ) )
<=> ( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(53,plain,
( ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[52]) ).
tff(54,plain,
^ [W0: $i,W1: $i] :
refl(( ( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) ) ) )
<=> ( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(55,plain,
( ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) ) ) ) ),
inference(quant_intro,[status(thm)],[54]) ).
tff(56,plain,
^ [W0: $i,W1: $i] :
rewrite(( ( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) ) ) )
<=> ( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(57,plain,
( ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) ) ) ) ),
inference(quant_intro,[status(thm)],[56]) ).
tff(58,plain,
( ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) ) ) ) ),
inference(transitivity,[status(thm)],[57,55]) ).
tff(59,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) )
<=> ~ ( ~ aSet0(W0)
| ~ aElementOf0(W1,szNzAzT0) ) )),
( ~ ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) )
<=> ~ ~ ( ~ aSet0(W0)
| ~ aElementOf0(W1,szNzAzT0) ) )),
rewrite(( ~ ~ ( ~ aSet0(W0)
| ~ aElementOf0(W1,szNzAzT0) )
<=> ( ~ aSet0(W0)
| ~ aElementOf0(W1,szNzAzT0) ) )),
( ~ ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) )
<=> ( ~ aSet0(W0)
| ~ aElementOf0(W1,szNzAzT0) ) )),
quant_intro(proof_bind(^ [W2: $i] :
trans(monotonicity(rewrite(( ( ( W2 != slbdtsldtrb0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& ( sbrdtbr0(W3) = W1 ) ) ) ) )
<=> ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) ) )),
trans(monotonicity(trans(monotonicity(trans(trans(monotonicity(rewrite(( ( aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
& ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) = W1 ) )
<=> ~ ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) ) )),
( ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
& ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) = W1 ) ) )
<=> ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ~ ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) ) ) )),
rewrite(( ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ~ ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) ) )
<=> ~ ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) )),
( ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
& ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) = W1 ) ) )
<=> ~ ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) )),
rewrite(( ~ ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) )
<=> ~ ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) )),
( ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
& ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) = W1 ) ) )
<=> ~ ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) )),
( ~ ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
& ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) = W1 ) ) )
<=> ~ ~ ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) )),
rewrite(( ~ ~ ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) )
<=> ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) )),
( ~ ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
& ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) = W1 ) ) )
<=> ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) )),
( ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ~ ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
& ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) = W1 ) ) ) )
<=> ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) ) )),
rewrite(( ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) )
<=> ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) ) )),
( ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ~ ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
& ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) = W1 ) ) ) )
<=> ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) ) )),
( ( ( ( W2 != slbdtsldtrb0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& ( sbrdtbr0(W3) = W1 ) ) ) ) )
& ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ~ ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
& ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) = W1 ) ) ) ) )
<=> ( ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
& ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) ) ) )),
rewrite(( ( ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
& ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) ) )
<=> ~ ( ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) ) ) )),
( ( ( ( W2 != slbdtsldtrb0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& ( sbrdtbr0(W3) = W1 ) ) ) ) )
& ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ~ ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
& ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) = W1 ) ) ) ) )
<=> ~ ( ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) ) ) ))),
( ! [W2: $i] :
( ( ( W2 != slbdtsldtrb0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& ( sbrdtbr0(W3) = W1 ) ) ) ) )
& ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ~ ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
& ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) = W1 ) ) ) ) )
<=> ! [W2: $i] :
~ ( ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) ) ) )),
( ( ~ ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) )
| ! [W2: $i] :
( ( ( W2 != slbdtsldtrb0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& ( sbrdtbr0(W3) = W1 ) ) ) ) )
& ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ~ ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
& ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) = W1 ) ) ) ) ) )
<=> ( ~ aSet0(W0)
| ~ aElementOf0(W1,szNzAzT0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) ) ) ) )),
rewrite(( ( ~ aSet0(W0)
| ~ aElementOf0(W1,szNzAzT0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) ) ) )
<=> ( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) ) ) ) )),
( ( ~ ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) )
| ! [W2: $i] :
( ( ( W2 != slbdtsldtrb0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& ( sbrdtbr0(W3) = W1 ) ) ) ) )
& ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ~ ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
& ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) = W1 ) ) ) ) ) )
<=> ( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(60,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) )
| ! [W2: $i] :
( ( ( W2 != slbdtsldtrb0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& ( sbrdtbr0(W3) = W1 ) ) ) ) )
& ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ~ ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
& ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) = W1 ) ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) ) ) ) ),
inference(quant_intro,[status(thm)],[59]) ).
tff(61,plain,
^ [W0: $i,W1: $i] :
rewrite(( ( ~ ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) )
| ! [W2: $i] :
( ( ( W2 != slbdtsldtrb0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& ( sbrdtbr0(W3) = W1 ) ) ) ) )
& ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ~ ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
& ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) = W1 ) ) ) ) ) )
<=> ( ~ ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) )
| ! [W2: $i] :
( ( ( W2 != slbdtsldtrb0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& ( sbrdtbr0(W3) = W1 ) ) ) ) )
& ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ~ ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
& ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) = W1 ) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(62,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) )
| ! [W2: $i] :
( ( ( W2 != slbdtsldtrb0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& ( sbrdtbr0(W3) = W1 ) ) ) ) )
& ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ~ ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
& ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) = W1 ) ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) )
| ! [W2: $i] :
( ( ( W2 != slbdtsldtrb0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& ( sbrdtbr0(W3) = W1 ) ) ) ) )
& ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ~ ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
& ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) = W1 ) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[61]) ).
tff(63,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) )
| ! [W2: $i] :
( ( W2 = slbdtsldtrb0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& ( sbrdtbr0(W3) = W1 ) ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) )
| ! [W2: $i] :
( ( W2 = slbdtsldtrb0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& ( sbrdtbr0(W3) = W1 ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(64,plain,
^ [W0: $i,W1: $i] :
rewrite(( ( ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) )
=> ! [W2: $i] :
( ( W2 = slbdtsldtrb0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& ( sbrdtbr0(W3) = W1 ) ) ) ) ) )
<=> ( ~ ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) )
| ! [W2: $i] :
( ( W2 = slbdtsldtrb0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& ( sbrdtbr0(W3) = W1 ) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(65,plain,
( ! [W0: $i,W1: $i] :
( ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) )
=> ! [W2: $i] :
( ( W2 = slbdtsldtrb0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& ( sbrdtbr0(W3) = W1 ) ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) )
| ! [W2: $i] :
( ( W2 = slbdtsldtrb0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& ( sbrdtbr0(W3) = W1 ) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[64]) ).
tff(66,axiom,
! [W0: $i,W1: $i] :
( ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) )
=> ! [W2: $i] :
( ( W2 = slbdtsldtrb0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& ( sbrdtbr0(W3) = W1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSel) ).
tff(67,plain,
! [W0: $i,W1: $i] :
( ~ ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) )
| ! [W2: $i] :
( ( W2 = slbdtsldtrb0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& ( sbrdtbr0(W3) = W1 ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
! [W0: $i,W1: $i] :
( ~ ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) )
| ! [W2: $i] :
( ( W2 = slbdtsldtrb0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& ( sbrdtbr0(W3) = W1 ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[67,63]) ).
tff(69,plain,
! [W0: $i,W1: $i] :
( ~ ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) )
| ! [W2: $i] :
( ( ( W2 != slbdtsldtrb0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& ( sbrdtbr0(W3) = W1 ) ) ) ) )
& ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ~ ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
& ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) = W1 ) ) ) ) ) ),
inference(skolemize,[status(sab)],[68]) ).
tff(70,plain,
! [W0: $i,W1: $i] :
( ~ ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) )
| ! [W2: $i] :
( ( ( W2 != slbdtsldtrb0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& ( sbrdtbr0(W3) = W1 ) ) ) ) )
& ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ~ ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
& ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) = W1 ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[69,62]) ).
tff(71,plain,
! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) ) ) ),
inference(modus_ponens,[status(thm)],[70,60]) ).
tff(72,plain,
! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) ) ) ),
inference(modus_ponens,[status(thm)],[71,58]) ).
tff(73,plain,
! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[72,53]) ).
tff(74,plain,
( aElementOf0(sz00,szNzAzT0)
<=> aElementOf0(sz00,szNzAzT0) ),
inference(rewrite,[status(thm)],[]) ).
tff(75,axiom,
aElementOf0(sz00,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroNum) ).
tff(76,plain,
aElementOf0(sz00,szNzAzT0),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) ) ) )
| ~ aSet0(xS)
| ~ aElementOf0(sz00,szNzAzT0)
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(xS,sz00) )
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,sz00,xS)) != sz00 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,sz00,xS),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) )
<=> aElementOf0(W3,W2) ) ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) ) ) )
| ~ aSet0(xS)
| ~ aElementOf0(sz00,szNzAzT0)
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(xS,sz00) )
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,sz00,xS)) != sz00 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,sz00,xS),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) )
<=> aElementOf0(W3,W2) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(78,plain,
( ( ~ aElementOf0(sz00,szNzAzT0)
| ~ aSet0(xS)
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(xS,sz00) )
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,sz00,xS)) != sz00 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,sz00,xS),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) )
<=> aElementOf0(W3,W2) ) ) ) ) )
<=> ( ~ aSet0(xS)
| ~ aElementOf0(sz00,szNzAzT0)
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(xS,sz00) )
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,sz00,xS)) != sz00 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,sz00,xS),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) )
<=> aElementOf0(W3,W2) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(79,plain,
^ [W2: $i] :
rewrite(( ~ ( ~ ( ( W2 = slbdtsldtrb0(xS,sz00) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,sz00,xS)) != sz00 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,sz00,xS),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) )
<=> aElementOf0(W3,W2) ) ) ) )
<=> ~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(xS,sz00) )
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,sz00,xS)) != sz00 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,sz00,xS),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) )
<=> aElementOf0(W3,W2) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(80,plain,
( ! [W2: $i] :
~ ( ~ ( ( W2 = slbdtsldtrb0(xS,sz00) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,sz00,xS)) != sz00 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,sz00,xS),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) )
<=> aElementOf0(W3,W2) ) ) ) )
<=> ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(xS,sz00) )
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,sz00,xS)) != sz00 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,sz00,xS),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) )
<=> aElementOf0(W3,W2) ) ) ) ) ),
inference(quant_intro,[status(thm)],[79]) ).
tff(81,plain,
( ( ~ aElementOf0(sz00,szNzAzT0)
| ~ aSet0(xS)
| ! [W2: $i] :
~ ( ~ ( ( W2 = slbdtsldtrb0(xS,sz00) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,sz00,xS)) != sz00 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,sz00,xS),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) )
<=> aElementOf0(W3,W2) ) ) ) ) )
<=> ( ~ aElementOf0(sz00,szNzAzT0)
| ~ aSet0(xS)
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(xS,sz00) )
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,sz00,xS)) != sz00 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,sz00,xS),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) )
<=> aElementOf0(W3,W2) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[80]) ).
tff(82,plain,
( ( ~ aElementOf0(sz00,szNzAzT0)
| ~ aSet0(xS)
| ! [W2: $i] :
~ ( ~ ( ( W2 = slbdtsldtrb0(xS,sz00) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,sz00,xS)) != sz00 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,sz00,xS),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) )
<=> aElementOf0(W3,W2) ) ) ) ) )
<=> ( ~ aSet0(xS)
| ~ aElementOf0(sz00,szNzAzT0)
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(xS,sz00) )
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,sz00,xS)) != sz00 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,sz00,xS),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) )
<=> aElementOf0(W3,W2) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[81,78]) ).
tff(83,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) ) ) )
| ~ aElementOf0(sz00,szNzAzT0)
| ~ aSet0(xS)
| ! [W2: $i] :
~ ( ~ ( ( W2 = slbdtsldtrb0(xS,sz00) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,sz00,xS)) != sz00 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,sz00,xS),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) )
<=> aElementOf0(W3,W2) ) ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) ) ) )
| ~ aSet0(xS)
| ~ aElementOf0(sz00,szNzAzT0)
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(xS,sz00) )
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,sz00,xS)) != sz00 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,sz00,xS),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) )
<=> aElementOf0(W3,W2) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[82]) ).
tff(84,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) ) ) )
| ~ aElementOf0(sz00,szNzAzT0)
| ~ aSet0(xS)
| ! [W2: $i] :
~ ( ~ ( ( W2 = slbdtsldtrb0(xS,sz00) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,sz00,xS)) != sz00 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,sz00,xS),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) )
<=> aElementOf0(W3,W2) ) ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) ) ) )
| ~ aSet0(xS)
| ~ aElementOf0(sz00,szNzAzT0)
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(xS,sz00) )
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,sz00,xS)) != sz00 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,sz00,xS),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) )
<=> aElementOf0(W3,W2) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[83,77]) ).
tff(85,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) ) ) )
| ~ aElementOf0(sz00,szNzAzT0)
| ~ aSet0(xS)
| ! [W2: $i] :
~ ( ~ ( ( W2 = slbdtsldtrb0(xS,sz00) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,sz00,xS)) != sz00 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,sz00,xS),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) )
<=> aElementOf0(W3,W2) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(86,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) ) ) )
| ~ aSet0(xS)
| ~ aElementOf0(sz00,szNzAzT0)
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(xS,sz00) )
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,sz00,xS)) != sz00 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,sz00,xS),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) )
<=> aElementOf0(W3,W2) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[85,84]) ).
tff(87,plain,
( ~ aSet0(xS)
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(xS,sz00) )
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,sz00,xS)) != sz00 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,sz00,xS),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) )
<=> aElementOf0(W3,W2) ) ) ) ) ),
inference(unit_resolution,[status(thm)],[86,76,73]) ).
tff(88,plain,
! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(xS,sz00) )
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,sz00,xS)) != sz00 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,sz00,xS),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) )
<=> aElementOf0(W3,W2) ) ) ) ),
inference(unit_resolution,[status(thm)],[87,43]) ).
tff(89,plain,
( ~ ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(xS,sz00) )
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,sz00,xS)) != sz00 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,sz00,xS),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) )
<=> aElementOf0(W3,W2) ) ) ) )
| ~ ( ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ( slbdtsldtrb0(xS,xK) = slbdtsldtrb0(xS,sz00) )
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(slbdtsldtrb0(xS,xK),sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(slbdtsldtrb0(xS,xK),sz00,xS)) != sz00 ) )
<=> aElementOf0(tptp_fun_W3_10(slbdtsldtrb0(xS,xK),sz00,xS),slbdtsldtrb0(xS,xK)) ) )
| ~ ( ( slbdtsldtrb0(xS,xK) != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) )
<=> aElementOf0(W3,slbdtsldtrb0(xS,xK)) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(90,plain,
~ ( ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ( slbdtsldtrb0(xS,xK) = slbdtsldtrb0(xS,sz00) )
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(slbdtsldtrb0(xS,xK),sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(slbdtsldtrb0(xS,xK),sz00,xS)) != sz00 ) )
<=> aElementOf0(tptp_fun_W3_10(slbdtsldtrb0(xS,xK),sz00,xS),slbdtsldtrb0(xS,xK)) ) )
| ~ ( ( slbdtsldtrb0(xS,xK) != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) )
<=> aElementOf0(W3,slbdtsldtrb0(xS,xK)) ) ) ) ),
inference(unit_resolution,[status(thm)],[89,88]) ).
tff(91,plain,
( ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ( slbdtsldtrb0(xS,xK) = slbdtsldtrb0(xS,sz00) )
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(slbdtsldtrb0(xS,xK),sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(slbdtsldtrb0(xS,xK),sz00,xS)) != sz00 ) )
<=> aElementOf0(tptp_fun_W3_10(slbdtsldtrb0(xS,xK),sz00,xS),slbdtsldtrb0(xS,xK)) ) )
| ~ ( ( slbdtsldtrb0(xS,xK) != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) )
<=> aElementOf0(W3,slbdtsldtrb0(xS,xK)) ) ) )
| ( slbdtsldtrb0(xS,xK) != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) )
<=> aElementOf0(W3,slbdtsldtrb0(xS,xK)) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(92,plain,
( ( slbdtsldtrb0(xS,xK) != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) )
<=> aElementOf0(W3,slbdtsldtrb0(xS,xK)) ) ) ),
inference(unit_resolution,[status(thm)],[91,90]) ).
tff(93,plain,
( ( xK = sz00 )
<=> ( xK = sz00 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(94,plain,
( ~ ( ( xK = sz00 )
=> ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( aSubsetOf0(W1,xS)
& isCountable0(W1)
& ! [W2: $i] :
( aElementOf0(W2,slbdtsldtrb0(W1,xK))
=> ( sdtlpdtrp0(xc,W2) = W0 ) ) ) ) )
<=> ~ ( ( xK != sz00 )
| ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( aSubsetOf0(W1,xS)
& isCountable0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,W2) = W0 ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(95,axiom,
~ ( ( xK = sz00 )
=> ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( aSubsetOf0(W1,xS)
& isCountable0(W1)
& ! [W2: $i] :
( aElementOf0(W2,slbdtsldtrb0(W1,xK))
=> ( sdtlpdtrp0(xc,W2) = W0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(96,plain,
~ ( ( xK != sz00 )
| ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( aSubsetOf0(W1,xS)
& isCountable0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,W2) = W0 ) ) ) ) ),
inference(modus_ponens,[status(thm)],[95,94]) ).
tff(97,plain,
xK = sz00,
inference(or_elim,[status(thm)],[96]) ).
tff(98,plain,
xK = sz00,
inference(modus_ponens,[status(thm)],[97,93]) ).
tff(99,plain,
sz00 = xK,
inference(symmetry,[status(thm)],[98]) ).
tff(100,plain,
slbdtsldtrb0(xS,sz00) = slbdtsldtrb0(xS,xK),
inference(monotonicity,[status(thm)],[99]) ).
tff(101,plain,
slbdtsldtrb0(xS,xK) = slbdtsldtrb0(xS,sz00),
inference(symmetry,[status(thm)],[100]) ).
tff(102,plain,
( ~ ( ( slbdtsldtrb0(xS,xK) != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) )
<=> aElementOf0(W3,slbdtsldtrb0(xS,xK)) ) ) )
| ( slbdtsldtrb0(xS,xK) != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) )
<=> aElementOf0(W3,slbdtsldtrb0(xS,xK)) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(103,plain,
( ~ ( ( slbdtsldtrb0(xS,xK) != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) )
<=> aElementOf0(W3,slbdtsldtrb0(xS,xK)) ) ) )
| ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) )
<=> aElementOf0(W3,slbdtsldtrb0(xS,xK)) ) ) ),
inference(unit_resolution,[status(thm)],[102,101]) ).
tff(104,plain,
~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) )
<=> aElementOf0(W3,slbdtsldtrb0(xS,xK)) ) ),
inference(unit_resolution,[status(thm)],[103,92]) ).
tff(105,plain,
( ~ aSet0(slbdtsldtrb0(xS,xK))
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) )
<=> aElementOf0(W3,slbdtsldtrb0(xS,xK)) )
| ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) )
<=> aElementOf0(W3,slbdtsldtrb0(xS,xK)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(106,plain,
! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) )
<=> aElementOf0(W3,slbdtsldtrb0(xS,xK)) ),
inference(unit_resolution,[status(thm)],[105,104]) ).
tff(107,plain,
( ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) )
<=> aElementOf0(W3,slbdtsldtrb0(xS,xK)) )
| ~ ( ( ~ aSubsetOf0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)),xS)
| ( sbrdtbr0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0))) != sz00 ) )
<=> aElementOf0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(xS,xK)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(108,plain,
~ ( ( ~ aSubsetOf0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)),xS)
| ( sbrdtbr0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0))) != sz00 ) )
<=> aElementOf0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(xS,xK)) ),
inference(unit_resolution,[status(thm)],[107,106]) ).
tff(109,plain,
( ~ ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,xS)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xS),W1)
| aElementOf0(tptp_fun_W2_1(W1,xS),xS) ) )
| ~ ( ~ aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xS) ) ) ) )
| ~ ( ~ ( aSubsetOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),xS)
| ~ aSet0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),xS),tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| aElementOf0(tptp_fun_W2_1(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),xS),xS) ) )
| ~ ( ~ aSubsetOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),xS)
| ~ ( ~ aSet0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| aElementOf0(W2,xS) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(110,plain,
~ ( ~ ( aSubsetOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),xS)
| ~ aSet0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),xS),tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| aElementOf0(tptp_fun_W2_1(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),xS),xS) ) )
| ~ ( ~ aSubsetOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),xS)
| ~ ( ~ aSet0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| aElementOf0(W2,xS) ) ) ) ),
inference(unit_resolution,[status(thm)],[109,47]) ).
tff(111,plain,
( ~ ( aSubsetOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),xS)
| ~ aSet0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),xS),tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| aElementOf0(tptp_fun_W2_1(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),xS),xS) ) )
| ~ ( ~ aSubsetOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),xS)
| ~ ( ~ aSet0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| aElementOf0(W2,xS) ) ) )
| ~ aSubsetOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),xS)
| ~ ( ~ aSet0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| aElementOf0(W2,xS) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(112,plain,
( ~ aSubsetOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),xS)
| ~ ( ~ aSet0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| aElementOf0(W2,xS) ) ) ),
inference(unit_resolution,[status(thm)],[111,110]) ).
tff(113,plain,
( ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) )
<=> aElementOf0(W3,slbdtsldtrb0(xS,xK)) )
| ~ ( ( ~ aSubsetOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),xS)
| ( sbrdtbr0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))) != sz00 ) )
<=> aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),slbdtsldtrb0(xS,xK)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(114,plain,
~ ( ( ~ aSubsetOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),xS)
| ( sbrdtbr0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))) != sz00 ) )
<=> aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),slbdtsldtrb0(xS,xK)) ),
inference(unit_resolution,[status(thm)],[113,106]) ).
tff(115,plain,
^ [W0: $i] :
rewrite(( ~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ~ ( ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) )
| ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(116,plain,
( ! [W0: $i] :
~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ! [W0: $i] :
~ ( ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) )
| ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[115]) ).
tff(117,plain,
^ [W0: $i] :
refl(( ~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(118,plain,
( ! [W0: $i] :
~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ! [W0: $i] :
~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) ),
inference(quant_intro,[status(thm)],[117]) ).
tff(119,plain,
^ [W0: $i] :
rewrite(( ~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(120,plain,
( ! [W0: $i] :
~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ! [W0: $i] :
~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) ),
inference(quant_intro,[status(thm)],[119]) ).
tff(121,plain,
( ! [W0: $i] :
~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ! [W0: $i] :
~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) ),
inference(transitivity,[status(thm)],[120,118]) ).
tff(122,plain,
^ [W0: $i] :
trans(monotonicity(rewrite(( ( ( W0 != slcrc0 )
| ( aSet0(W0)
& ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
<=> ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) ) )),
rewrite(( ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) )
<=> ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )),
( ( ( ( W0 != slcrc0 )
| ( aSet0(W0)
& ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ( ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) )),
rewrite(( ( ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) )),
( ( ( ( W0 != slcrc0 )
| ( aSet0(W0)
& ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(123,plain,
( ! [W0: $i] :
( ( ( W0 != slcrc0 )
| ( aSet0(W0)
& ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ! [W0: $i] :
~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) ),
inference(quant_intro,[status(thm)],[122]) ).
tff(124,plain,
^ [W0: $i] :
rewrite(( ( ( ( W0 != slcrc0 )
| ( aSet0(W0)
& ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ( ( ( W0 != slcrc0 )
| ( aSet0(W0)
& ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(125,plain,
( ! [W0: $i] :
( ( ( W0 != slcrc0 )
| ( aSet0(W0)
& ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ! [W0: $i] :
( ( ( W0 != slcrc0 )
| ( aSet0(W0)
& ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) ),
inference(quant_intro,[status(thm)],[124]) ).
tff(126,plain,
( ! [W0: $i] :
( ( W0 = slcrc0 )
<=> ( aSet0(W0)
& ~ ? [W1: $i] : aElementOf0(W1,W0) ) )
<=> ! [W0: $i] :
( ( W0 = slcrc0 )
<=> ( aSet0(W0)
& ~ ? [W1: $i] : aElementOf0(W1,W0) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(127,axiom,
! [W0: $i] :
( ( W0 = slcrc0 )
<=> ( aSet0(W0)
& ~ ? [W1: $i] : aElementOf0(W1,W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefEmp) ).
tff(128,plain,
! [W0: $i] :
( ( W0 = slcrc0 )
<=> ( aSet0(W0)
& ~ ? [W1: $i] : aElementOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[127,126]) ).
tff(129,plain,
! [W0: $i] :
( ( ( W0 != slcrc0 )
| ( aSet0(W0)
& ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ),
inference(skolemize,[status(sab)],[128]) ).
tff(130,plain,
! [W0: $i] :
( ( ( W0 != slcrc0 )
| ( aSet0(W0)
& ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ),
inference(modus_ponens,[status(thm)],[129,125]) ).
tff(131,plain,
! [W0: $i] :
~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ),
inference(modus_ponens,[status(thm)],[130,123]) ).
tff(132,plain,
! [W0: $i] :
~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ),
inference(modus_ponens,[status(thm)],[131,121]) ).
tff(133,plain,
! [W0: $i] :
~ ( ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) )
| ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) ) ),
inference(modus_ponens,[status(thm)],[132,116]) ).
tff(134,plain,
( ( ~ ! [W0: $i] :
~ ( ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) )
| ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) ) )
| ~ ( ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ( slbdtsldtrb0(xS,xK) = slcrc0 )
| aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),slbdtsldtrb0(xS,xK)) )
| ~ ( ( slbdtsldtrb0(xS,xK) != slcrc0 )
| ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ~ ! [W1: $i] : ~ aElementOf0(W1,slbdtsldtrb0(xS,xK)) ) ) ) )
<=> ( ~ ! [W0: $i] :
~ ( ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) )
| ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) ) )
| ~ ( ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ( slbdtsldtrb0(xS,xK) = slcrc0 )
| aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),slbdtsldtrb0(xS,xK)) )
| ~ ( ( slbdtsldtrb0(xS,xK) != slcrc0 )
| ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ~ ! [W1: $i] : ~ aElementOf0(W1,slbdtsldtrb0(xS,xK)) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(135,plain,
( ~ ( ~ ( ( slbdtsldtrb0(xS,xK) = slcrc0 )
| ~ aSet0(slbdtsldtrb0(xS,xK))
| aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),slbdtsldtrb0(xS,xK)) )
| ~ ( ( slbdtsldtrb0(xS,xK) != slcrc0 )
| ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ~ ! [W1: $i] : ~ aElementOf0(W1,slbdtsldtrb0(xS,xK)) ) ) )
<=> ~ ( ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ( slbdtsldtrb0(xS,xK) = slcrc0 )
| aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),slbdtsldtrb0(xS,xK)) )
| ~ ( ( slbdtsldtrb0(xS,xK) != slcrc0 )
| ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ~ ! [W1: $i] : ~ aElementOf0(W1,slbdtsldtrb0(xS,xK)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(136,plain,
( ( ~ ! [W0: $i] :
~ ( ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) )
| ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) ) )
| ~ ( ~ ( ( slbdtsldtrb0(xS,xK) = slcrc0 )
| ~ aSet0(slbdtsldtrb0(xS,xK))
| aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),slbdtsldtrb0(xS,xK)) )
| ~ ( ( slbdtsldtrb0(xS,xK) != slcrc0 )
| ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ~ ! [W1: $i] : ~ aElementOf0(W1,slbdtsldtrb0(xS,xK)) ) ) ) )
<=> ( ~ ! [W0: $i] :
~ ( ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) )
| ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) ) )
| ~ ( ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ( slbdtsldtrb0(xS,xK) = slcrc0 )
| aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),slbdtsldtrb0(xS,xK)) )
| ~ ( ( slbdtsldtrb0(xS,xK) != slcrc0 )
| ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ~ ! [W1: $i] : ~ aElementOf0(W1,slbdtsldtrb0(xS,xK)) ) ) ) ) ),
inference(monotonicity,[status(thm)],[135]) ).
tff(137,plain,
( ( ~ ! [W0: $i] :
~ ( ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) )
| ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) ) )
| ~ ( ~ ( ( slbdtsldtrb0(xS,xK) = slcrc0 )
| ~ aSet0(slbdtsldtrb0(xS,xK))
| aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),slbdtsldtrb0(xS,xK)) )
| ~ ( ( slbdtsldtrb0(xS,xK) != slcrc0 )
| ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ~ ! [W1: $i] : ~ aElementOf0(W1,slbdtsldtrb0(xS,xK)) ) ) ) )
<=> ( ~ ! [W0: $i] :
~ ( ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) )
| ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) ) )
| ~ ( ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ( slbdtsldtrb0(xS,xK) = slcrc0 )
| aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),slbdtsldtrb0(xS,xK)) )
| ~ ( ( slbdtsldtrb0(xS,xK) != slcrc0 )
| ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ~ ! [W1: $i] : ~ aElementOf0(W1,slbdtsldtrb0(xS,xK)) ) ) ) ) ),
inference(transitivity,[status(thm)],[136,134]) ).
tff(138,plain,
( ~ ! [W0: $i] :
~ ( ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) )
| ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) ) )
| ~ ( ~ ( ( slbdtsldtrb0(xS,xK) = slcrc0 )
| ~ aSet0(slbdtsldtrb0(xS,xK))
| aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),slbdtsldtrb0(xS,xK)) )
| ~ ( ( slbdtsldtrb0(xS,xK) != slcrc0 )
| ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ~ ! [W1: $i] : ~ aElementOf0(W1,slbdtsldtrb0(xS,xK)) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(139,plain,
( ~ ! [W0: $i] :
~ ( ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) )
| ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) ) )
| ~ ( ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ( slbdtsldtrb0(xS,xK) = slcrc0 )
| aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),slbdtsldtrb0(xS,xK)) )
| ~ ( ( slbdtsldtrb0(xS,xK) != slcrc0 )
| ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ~ ! [W1: $i] : ~ aElementOf0(W1,slbdtsldtrb0(xS,xK)) ) ) ) ),
inference(modus_ponens,[status(thm)],[138,137]) ).
tff(140,plain,
~ ( ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ( slbdtsldtrb0(xS,xK) = slcrc0 )
| aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),slbdtsldtrb0(xS,xK)) )
| ~ ( ( slbdtsldtrb0(xS,xK) != slcrc0 )
| ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ~ ! [W1: $i] : ~ aElementOf0(W1,slbdtsldtrb0(xS,xK)) ) ) ),
inference(unit_resolution,[status(thm)],[139,133]) ).
tff(141,plain,
( ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ( slbdtsldtrb0(xS,xK) = slcrc0 )
| aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),slbdtsldtrb0(xS,xK)) )
| ~ ( ( slbdtsldtrb0(xS,xK) != slcrc0 )
| ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ~ ! [W1: $i] : ~ aElementOf0(W1,slbdtsldtrb0(xS,xK)) ) )
| ~ aSet0(slbdtsldtrb0(xS,xK))
| ( slbdtsldtrb0(xS,xK) = slcrc0 )
| aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),slbdtsldtrb0(xS,xK)) ),
inference(tautology,[status(thm)],[]) ).
tff(142,plain,
( ~ aSet0(slbdtsldtrb0(xS,xK))
| ( slbdtsldtrb0(xS,xK) = slcrc0 )
| aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),slbdtsldtrb0(xS,xK)) ),
inference(unit_resolution,[status(thm)],[141,140]) ).
tff(143,plain,
( ( szDzozmdt0(xc) = slbdtsldtrb0(xS,xK) )
<=> ( szDzozmdt0(xc) = slbdtsldtrb0(xS,xK) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(144,axiom,
( aFunction0(xc)
& ( szDzozmdt0(xc) = slbdtsldtrb0(xS,xK) )
& aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3453) ).
tff(145,plain,
( aFunction0(xc)
& ( szDzozmdt0(xc) = slbdtsldtrb0(xS,xK) ) ),
inference(and_elim,[status(thm)],[144]) ).
tff(146,plain,
szDzozmdt0(xc) = slbdtsldtrb0(xS,xK),
inference(and_elim,[status(thm)],[145]) ).
tff(147,plain,
szDzozmdt0(xc) = slbdtsldtrb0(xS,xK),
inference(modus_ponens,[status(thm)],[146,143]) ).
tff(148,plain,
slbdtsldtrb0(xS,xK) = szDzozmdt0(xc),
inference(symmetry,[status(thm)],[147]) ).
tff(149,plain,
( aSet0(slbdtsldtrb0(xS,xK))
<=> aSet0(szDzozmdt0(xc)) ),
inference(monotonicity,[status(thm)],[148]) ).
tff(150,plain,
( aSet0(szDzozmdt0(xc))
<=> aSet0(slbdtsldtrb0(xS,xK)) ),
inference(symmetry,[status(thm)],[149]) ).
tff(151,plain,
( aFunction0(xc)
<=> aFunction0(xc) ),
inference(rewrite,[status(thm)],[]) ).
tff(152,plain,
aFunction0(xc),
inference(and_elim,[status(thm)],[145]) ).
tff(153,plain,
aFunction0(xc),
inference(modus_ponens,[status(thm)],[152,151]) ).
tff(154,plain,
^ [W0: $i] :
refl(( ( aSet0(szDzozmdt0(W0))
| ~ aFunction0(W0) )
<=> ( aSet0(szDzozmdt0(W0))
| ~ aFunction0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(155,plain,
( ! [W0: $i] :
( aSet0(szDzozmdt0(W0))
| ~ aFunction0(W0) )
<=> ! [W0: $i] :
( aSet0(szDzozmdt0(W0))
| ~ aFunction0(W0) ) ),
inference(quant_intro,[status(thm)],[154]) ).
tff(156,plain,
( ! [W0: $i] :
( aSet0(szDzozmdt0(W0))
| ~ aFunction0(W0) )
<=> ! [W0: $i] :
( aSet0(szDzozmdt0(W0))
| ~ aFunction0(W0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(157,plain,
^ [W0: $i] :
rewrite(( ( aFunction0(W0)
=> aSet0(szDzozmdt0(W0)) )
<=> ( aSet0(szDzozmdt0(W0))
| ~ aFunction0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(158,plain,
( ! [W0: $i] :
( aFunction0(W0)
=> aSet0(szDzozmdt0(W0)) )
<=> ! [W0: $i] :
( aSet0(szDzozmdt0(W0))
| ~ aFunction0(W0) ) ),
inference(quant_intro,[status(thm)],[157]) ).
tff(159,axiom,
! [W0: $i] :
( aFunction0(W0)
=> aSet0(szDzozmdt0(W0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDomSet) ).
tff(160,plain,
! [W0: $i] :
( aSet0(szDzozmdt0(W0))
| ~ aFunction0(W0) ),
inference(modus_ponens,[status(thm)],[159,158]) ).
tff(161,plain,
! [W0: $i] :
( aSet0(szDzozmdt0(W0))
| ~ aFunction0(W0) ),
inference(modus_ponens,[status(thm)],[160,156]) ).
tff(162,plain,
! [W0: $i] :
( aSet0(szDzozmdt0(W0))
| ~ aFunction0(W0) ),
inference(skolemize,[status(sab)],[161]) ).
tff(163,plain,
! [W0: $i] :
( aSet0(szDzozmdt0(W0))
| ~ aFunction0(W0) ),
inference(modus_ponens,[status(thm)],[162,155]) ).
tff(164,plain,
( ( ~ ! [W0: $i] :
( aSet0(szDzozmdt0(W0))
| ~ aFunction0(W0) )
| aSet0(szDzozmdt0(xc))
| ~ aFunction0(xc) )
<=> ( ~ ! [W0: $i] :
( aSet0(szDzozmdt0(W0))
| ~ aFunction0(W0) )
| aSet0(szDzozmdt0(xc))
| ~ aFunction0(xc) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(165,plain,
( ~ ! [W0: $i] :
( aSet0(szDzozmdt0(W0))
| ~ aFunction0(W0) )
| aSet0(szDzozmdt0(xc))
| ~ aFunction0(xc) ),
inference(quant_inst,[status(thm)],[]) ).
tff(166,plain,
( ~ ! [W0: $i] :
( aSet0(szDzozmdt0(W0))
| ~ aFunction0(W0) )
| aSet0(szDzozmdt0(xc))
| ~ aFunction0(xc) ),
inference(modus_ponens,[status(thm)],[165,164]) ).
tff(167,plain,
aSet0(szDzozmdt0(xc)),
inference(unit_resolution,[status(thm)],[166,163,153]) ).
tff(168,plain,
aSet0(slbdtsldtrb0(xS,xK)),
inference(modus_ponens,[status(thm)],[167,150]) ).
tff(169,plain,
( ( slbdtrb0(sz00) = slcrc0 )
<=> ( slbdtrb0(sz00) = slcrc0 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(170,axiom,
slbdtrb0(sz00) = slcrc0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSegZero) ).
tff(171,plain,
slbdtrb0(sz00) = slcrc0,
inference(modus_ponens,[status(thm)],[170,169]) ).
tff(172,plain,
slcrc0 = slbdtrb0(sz00),
inference(symmetry,[status(thm)],[171]) ).
tff(173,plain,
( ( slbdtsldtrb0(xS,xK) = slcrc0 )
<=> ( slbdtsldtrb0(xS,xK) = slbdtrb0(sz00) ) ),
inference(monotonicity,[status(thm)],[172]) ).
tff(174,plain,
( ( slbdtsldtrb0(xS,xK) = slbdtrb0(sz00) )
<=> ( slbdtsldtrb0(xS,xK) = slcrc0 ) ),
inference(symmetry,[status(thm)],[173]) ).
tff(175,plain,
( ( slbdtsldtrb0(xS,sz00) = slcrc0 )
<=> ( slbdtsldtrb0(xS,xK) = slbdtrb0(sz00) ) ),
inference(monotonicity,[status(thm)],[100,172]) ).
tff(176,plain,
( ( slbdtsldtrb0(xS,sz00) = slcrc0 )
<=> ( slbdtsldtrb0(xS,xK) = slcrc0 ) ),
inference(transitivity,[status(thm)],[175,174]) ).
tff(177,plain,
( ( slbdtsldtrb0(xS,sz00) != slcrc0 )
<=> ( slbdtsldtrb0(xS,xK) != slcrc0 ) ),
inference(monotonicity,[status(thm)],[176]) ).
tff(178,plain,
( isCountable0(xS)
<=> isCountable0(xS) ),
inference(rewrite,[status(thm)],[]) ).
tff(179,plain,
isCountable0(xS),
inference(and_elim,[status(thm)],[36]) ).
tff(180,plain,
isCountable0(xS),
inference(modus_ponens,[status(thm)],[179,178]) ).
tff(181,plain,
^ [W0: $i] :
refl(( ( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) )
<=> ( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(182,plain,
( ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) )
<=> ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) ) ),
inference(quant_intro,[status(thm)],[181]) ).
tff(183,plain,
^ [W0: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aSet0(W0)
& isCountable0(W0) )
<=> ~ ( ~ aSet0(W0)
| ~ isCountable0(W0) ) )),
( ~ ( aSet0(W0)
& isCountable0(W0) )
<=> ~ ~ ( ~ aSet0(W0)
| ~ isCountable0(W0) ) )),
rewrite(( ~ ~ ( ~ aSet0(W0)
| ~ isCountable0(W0) )
<=> ( ~ aSet0(W0)
| ~ isCountable0(W0) ) )),
( ~ ( aSet0(W0)
& isCountable0(W0) )
<=> ( ~ aSet0(W0)
| ~ isCountable0(W0) ) )),
( ( ~ isFinite0(W0)
| ~ ( aSet0(W0)
& isCountable0(W0) ) )
<=> ( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) ) )),
rewrite(( ( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) )
<=> ( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) ) )),
( ( ~ isFinite0(W0)
| ~ ( aSet0(W0)
& isCountable0(W0) ) )
<=> ( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(184,plain,
( ! [W0: $i] :
( ~ isFinite0(W0)
| ~ ( aSet0(W0)
& isCountable0(W0) ) )
<=> ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) ) ),
inference(quant_intro,[status(thm)],[183]) ).
tff(185,plain,
( ! [W0: $i] :
( ~ isFinite0(W0)
| ~ ( aSet0(W0)
& isCountable0(W0) ) )
<=> ! [W0: $i] :
( ~ isFinite0(W0)
| ~ ( aSet0(W0)
& isCountable0(W0) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(186,plain,
^ [W0: $i] :
rewrite(( ( ( aSet0(W0)
& isCountable0(W0) )
=> ~ isFinite0(W0) )
<=> ( ~ isFinite0(W0)
| ~ ( aSet0(W0)
& isCountable0(W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(187,plain,
( ! [W0: $i] :
( ( aSet0(W0)
& isCountable0(W0) )
=> ~ isFinite0(W0) )
<=> ! [W0: $i] :
( ~ isFinite0(W0)
| ~ ( aSet0(W0)
& isCountable0(W0) ) ) ),
inference(quant_intro,[status(thm)],[186]) ).
tff(188,axiom,
! [W0: $i] :
( ( aSet0(W0)
& isCountable0(W0) )
=> ~ isFinite0(W0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCountNFin) ).
tff(189,plain,
! [W0: $i] :
( ~ isFinite0(W0)
| ~ ( aSet0(W0)
& isCountable0(W0) ) ),
inference(modus_ponens,[status(thm)],[188,187]) ).
tff(190,plain,
! [W0: $i] :
( ~ isFinite0(W0)
| ~ ( aSet0(W0)
& isCountable0(W0) ) ),
inference(modus_ponens,[status(thm)],[189,185]) ).
tff(191,plain,
! [W0: $i] :
( ~ isFinite0(W0)
| ~ ( aSet0(W0)
& isCountable0(W0) ) ),
inference(skolemize,[status(sab)],[190]) ).
tff(192,plain,
! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) ),
inference(modus_ponens,[status(thm)],[191,184]) ).
tff(193,plain,
! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) ),
inference(modus_ponens,[status(thm)],[192,182]) ).
tff(194,plain,
( ( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) )
| ~ isFinite0(xS)
| ~ aSet0(xS)
| ~ isCountable0(xS) )
<=> ( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) )
| ~ isFinite0(xS)
| ~ aSet0(xS)
| ~ isCountable0(xS) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(195,plain,
( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) )
| ~ isFinite0(xS)
| ~ aSet0(xS)
| ~ isCountable0(xS) ),
inference(quant_inst,[status(thm)],[]) ).
tff(196,plain,
( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) )
| ~ isFinite0(xS)
| ~ aSet0(xS)
| ~ isCountable0(xS) ),
inference(modus_ponens,[status(thm)],[195,194]) ).
tff(197,plain,
( ~ isFinite0(xS)
| ~ aSet0(xS) ),
inference(unit_resolution,[status(thm)],[196,193,180]) ).
tff(198,plain,
~ isFinite0(xS),
inference(unit_resolution,[status(thm)],[197,43]) ).
tff(199,plain,
^ [W0: $i] :
refl(( ( isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) )
<=> ( isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(200,plain,
( ! [W0: $i] :
( isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) )
<=> ! [W0: $i] :
( isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) ) ),
inference(quant_intro,[status(thm)],[199]) ).
tff(201,plain,
^ [W0: $i] :
rewrite(( ( isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) )
<=> ( isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(202,plain,
( ! [W0: $i] :
( isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) )
<=> ! [W0: $i] :
( isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) ) ),
inference(quant_intro,[status(thm)],[201]) ).
tff(203,plain,
( ! [W0: $i] :
( isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) )
<=> ! [W0: $i] :
( isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) ) ),
inference(transitivity,[status(thm)],[202,200]) ).
tff(204,plain,
^ [W0: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aSet0(W0)
& ~ isFinite0(W0) )
<=> ~ ( isFinite0(W0)
| ~ aSet0(W0) ) )),
( ~ ( aSet0(W0)
& ~ isFinite0(W0) )
<=> ~ ~ ( isFinite0(W0)
| ~ aSet0(W0) ) )),
rewrite(( ~ ~ ( isFinite0(W0)
| ~ aSet0(W0) )
<=> ( isFinite0(W0)
| ~ aSet0(W0) ) )),
( ~ ( aSet0(W0)
& ~ isFinite0(W0) )
<=> ( isFinite0(W0)
| ~ aSet0(W0) ) )),
( ( ~ ( aSet0(W0)
& ~ isFinite0(W0) )
| ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) )
<=> ( isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) ) )),
rewrite(( ( isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) )
<=> ( isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) ) )),
( ( ~ ( aSet0(W0)
& ~ isFinite0(W0) )
| ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) )
<=> ( isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(205,plain,
( ! [W0: $i] :
( ~ ( aSet0(W0)
& ~ isFinite0(W0) )
| ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) )
<=> ! [W0: $i] :
( isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) ) ),
inference(quant_intro,[status(thm)],[204]) ).
tff(206,plain,
( ! [W0: $i] :
( ~ ( aSet0(W0)
& ~ isFinite0(W0) )
| ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) )
<=> ! [W0: $i] :
( ~ ( aSet0(W0)
& ~ isFinite0(W0) )
| ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(207,plain,
^ [W0: $i] :
trans(monotonicity(quant_intro(proof_bind(^ [W1: $i] :
rewrite(( ( aElementOf0(W1,szNzAzT0)
=> ( slbdtsldtrb0(W0,W1) != slcrc0 ) )
<=> ( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) ))),
( ! [W1: $i] :
( aElementOf0(W1,szNzAzT0)
=> ( slbdtsldtrb0(W0,W1) != slcrc0 ) )
<=> ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) )),
( ( ( aSet0(W0)
& ~ isFinite0(W0) )
=> ! [W1: $i] :
( aElementOf0(W1,szNzAzT0)
=> ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) )
<=> ( ( aSet0(W0)
& ~ isFinite0(W0) )
=> ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) ) )),
rewrite(( ( ( aSet0(W0)
& ~ isFinite0(W0) )
=> ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) )
<=> ( ~ ( aSet0(W0)
& ~ isFinite0(W0) )
| ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) ) )),
( ( ( aSet0(W0)
& ~ isFinite0(W0) )
=> ! [W1: $i] :
( aElementOf0(W1,szNzAzT0)
=> ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) )
<=> ( ~ ( aSet0(W0)
& ~ isFinite0(W0) )
| ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(208,plain,
( ! [W0: $i] :
( ( aSet0(W0)
& ~ isFinite0(W0) )
=> ! [W1: $i] :
( aElementOf0(W1,szNzAzT0)
=> ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) )
<=> ! [W0: $i] :
( ~ ( aSet0(W0)
& ~ isFinite0(W0) )
| ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) ) ),
inference(quant_intro,[status(thm)],[207]) ).
tff(209,axiom,
! [W0: $i] :
( ( aSet0(W0)
& ~ isFinite0(W0) )
=> ! [W1: $i] :
( aElementOf0(W1,szNzAzT0)
=> ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSelNSet) ).
tff(210,plain,
! [W0: $i] :
( ~ ( aSet0(W0)
& ~ isFinite0(W0) )
| ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) ),
inference(modus_ponens,[status(thm)],[209,208]) ).
tff(211,plain,
! [W0: $i] :
( ~ ( aSet0(W0)
& ~ isFinite0(W0) )
| ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) ),
inference(modus_ponens,[status(thm)],[210,206]) ).
tff(212,plain,
! [W0: $i] :
( ~ ( aSet0(W0)
& ~ isFinite0(W0) )
| ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) ),
inference(skolemize,[status(sab)],[211]) ).
tff(213,plain,
! [W0: $i] :
( isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) ),
inference(modus_ponens,[status(thm)],[212,205]) ).
tff(214,plain,
! [W0: $i] :
( isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) ),
inference(modus_ponens,[status(thm)],[213,203]) ).
tff(215,plain,
( ( ~ ! [W0: $i] :
( isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) )
| isFinite0(xS)
| ~ aSet0(xS)
| ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(xS,W1) != slcrc0 ) ) )
<=> ( ~ ! [W0: $i] :
( isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) )
| isFinite0(xS)
| ~ aSet0(xS)
| ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(xS,W1) != slcrc0 ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(216,plain,
( ~ ! [W0: $i] :
( isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) )
| isFinite0(xS)
| ~ aSet0(xS)
| ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(xS,W1) != slcrc0 ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(217,plain,
( ~ ! [W0: $i] :
( isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) )
| isFinite0(xS)
| ~ aSet0(xS)
| ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(xS,W1) != slcrc0 ) ) ),
inference(modus_ponens,[status(thm)],[216,215]) ).
tff(218,plain,
! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(xS,W1) != slcrc0 ) ),
inference(unit_resolution,[status(thm)],[217,214,198,43]) ).
tff(219,plain,
( ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(xS,W1) != slcrc0 ) )
| ~ aElementOf0(sz00,szNzAzT0)
| ( slbdtsldtrb0(xS,sz00) != slcrc0 ) )
<=> ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(xS,W1) != slcrc0 ) )
| ~ aElementOf0(sz00,szNzAzT0)
| ( slbdtsldtrb0(xS,sz00) != slcrc0 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(220,plain,
( ~ ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(xS,W1) != slcrc0 ) )
| ~ aElementOf0(sz00,szNzAzT0)
| ( slbdtsldtrb0(xS,sz00) != slcrc0 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(221,plain,
( ~ ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(xS,W1) != slcrc0 ) )
| ~ aElementOf0(sz00,szNzAzT0)
| ( slbdtsldtrb0(xS,sz00) != slcrc0 ) ),
inference(modus_ponens,[status(thm)],[220,219]) ).
tff(222,plain,
slbdtsldtrb0(xS,sz00) != slcrc0,
inference(unit_resolution,[status(thm)],[221,76,218]) ).
tff(223,plain,
slbdtsldtrb0(xS,xK) != slcrc0,
inference(modus_ponens,[status(thm)],[222,177]) ).
tff(224,plain,
( ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ( slbdtsldtrb0(xS,xK) = slcrc0 )
| aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),slbdtsldtrb0(xS,xK)) )
| ~ aSet0(slbdtsldtrb0(xS,xK))
| ( slbdtsldtrb0(xS,xK) = slcrc0 )
| aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),slbdtsldtrb0(xS,xK)) ),
inference(tautology,[status(thm)],[]) ).
tff(225,plain,
aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),slbdtsldtrb0(xS,xK)),
inference(unit_resolution,[status(thm)],[224,223,168,142]) ).
tff(226,plain,
( ( ( ~ aSubsetOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),xS)
| ( sbrdtbr0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))) != sz00 ) )
<=> aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),slbdtsldtrb0(xS,xK)) )
| ~ ( ~ aSubsetOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),xS)
| ( sbrdtbr0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))) != sz00 ) )
| ~ aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),slbdtsldtrb0(xS,xK)) ),
inference(tautology,[status(thm)],[]) ).
tff(227,plain,
( ( ( ~ aSubsetOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),xS)
| ( sbrdtbr0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))) != sz00 ) )
<=> aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),slbdtsldtrb0(xS,xK)) )
| ~ ( ~ aSubsetOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),xS)
| ( sbrdtbr0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))) != sz00 ) ) ),
inference(unit_resolution,[status(thm)],[226,225]) ).
tff(228,plain,
~ ( ~ aSubsetOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),xS)
| ( sbrdtbr0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))) != sz00 ) ),
inference(unit_resolution,[status(thm)],[227,114]) ).
tff(229,plain,
( ~ aSubsetOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),xS)
| ( sbrdtbr0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))) != sz00 )
| aSubsetOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),xS) ),
inference(tautology,[status(thm)],[]) ).
tff(230,plain,
aSubsetOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),xS),
inference(unit_resolution,[status(thm)],[229,228]) ).
tff(231,plain,
( ~ ( ~ aSubsetOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),xS)
| ~ ( ~ aSet0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| aElementOf0(W2,xS) ) ) )
| ~ aSubsetOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),xS)
| ~ ( ~ aSet0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| aElementOf0(W2,xS) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(232,plain,
( ~ ( ~ aSubsetOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),xS)
| ~ ( ~ aSet0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| aElementOf0(W2,xS) ) ) )
| ~ ( ~ aSet0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| aElementOf0(W2,xS) ) ) ),
inference(unit_resolution,[status(thm)],[231,230]) ).
tff(233,plain,
~ ( ~ aSet0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| aElementOf0(W2,xS) ) ),
inference(unit_resolution,[status(thm)],[232,112]) ).
tff(234,plain,
( ~ aSet0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| aElementOf0(W2,xS) )
| aSet0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))) ),
inference(tautology,[status(thm)],[]) ).
tff(235,plain,
aSet0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))),
inference(unit_resolution,[status(thm)],[234,233]) ).
tff(236,plain,
^ [W0: $i] :
refl(( ( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) )
<=> ( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(237,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) ) ),
inference(quant_intro,[status(thm)],[236]) ).
tff(238,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(239,plain,
^ [W0: $i] :
rewrite(( ( aSet0(W0)
=> ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) )
<=> ( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(240,plain,
( ! [W0: $i] :
( aSet0(W0)
=> ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) ) ),
inference(quant_intro,[status(thm)],[239]) ).
tff(241,axiom,
! [W0: $i] :
( aSet0(W0)
=> ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardEmpty) ).
tff(242,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) ),
inference(modus_ponens,[status(thm)],[241,240]) ).
tff(243,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) ),
inference(modus_ponens,[status(thm)],[242,238]) ).
tff(244,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) ),
inference(skolemize,[status(sab)],[243]) ).
tff(245,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) ),
inference(modus_ponens,[status(thm)],[244,237]) ).
tff(246,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) )
| ~ aSet0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| ( ( sbrdtbr0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))) = sz00 )
<=> ( tptp_fun_W1_0(slbdtsldtrb0(xS,xK)) = slcrc0 ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) )
| ~ aSet0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| ( ( sbrdtbr0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))) = sz00 )
<=> ( tptp_fun_W1_0(slbdtsldtrb0(xS,xK)) = slcrc0 ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(247,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) )
| ~ aSet0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| ( ( sbrdtbr0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))) = sz00 )
<=> ( tptp_fun_W1_0(slbdtsldtrb0(xS,xK)) = slcrc0 ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(248,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) )
| ~ aSet0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| ( ( sbrdtbr0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))) = sz00 )
<=> ( tptp_fun_W1_0(slbdtsldtrb0(xS,xK)) = slcrc0 ) ) ),
inference(modus_ponens,[status(thm)],[247,246]) ).
tff(249,plain,
( ~ aSet0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| ( ( sbrdtbr0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))) = sz00 )
<=> ( tptp_fun_W1_0(slbdtsldtrb0(xS,xK)) = slcrc0 ) ) ),
inference(unit_resolution,[status(thm)],[248,245]) ).
tff(250,plain,
( ( sbrdtbr0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))) = sz00 )
<=> ( tptp_fun_W1_0(slbdtsldtrb0(xS,xK)) = slcrc0 ) ),
inference(unit_resolution,[status(thm)],[249,235]) ).
tff(251,plain,
( ~ aSubsetOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),xS)
| ( sbrdtbr0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))) != sz00 )
| ( sbrdtbr0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))) = sz00 ) ),
inference(tautology,[status(thm)],[]) ).
tff(252,plain,
sbrdtbr0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))) = sz00,
inference(unit_resolution,[status(thm)],[251,228]) ).
tff(253,plain,
( ~ ( ( sbrdtbr0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))) = sz00 )
<=> ( tptp_fun_W1_0(slbdtsldtrb0(xS,xK)) = slcrc0 ) )
| ( sbrdtbr0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))) != sz00 )
| ( tptp_fun_W1_0(slbdtsldtrb0(xS,xK)) = slcrc0 ) ),
inference(tautology,[status(thm)],[]) ).
tff(254,plain,
( ~ ( ( sbrdtbr0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))) = sz00 )
<=> ( tptp_fun_W1_0(slbdtsldtrb0(xS,xK)) = slcrc0 ) )
| ( tptp_fun_W1_0(slbdtsldtrb0(xS,xK)) = slcrc0 ) ),
inference(unit_resolution,[status(thm)],[253,252]) ).
tff(255,plain,
tptp_fun_W1_0(slbdtsldtrb0(xS,xK)) = slcrc0,
inference(unit_resolution,[status(thm)],[254,250]) ).
tff(256,plain,
sdtlpdtrp0(xc,tptp_fun_W1_0(slbdtsldtrb0(xS,xK))) = sdtlpdtrp0(xc,slcrc0),
inference(monotonicity,[status(thm)],[255]) ).
tff(257,plain,
( aElementOf0(sdtlpdtrp0(xc,tptp_fun_W1_0(slbdtsldtrb0(xS,xK))),sdtlcdtrc0(xc,szDzozmdt0(xc)))
<=> aElementOf0(sdtlpdtrp0(xc,slcrc0),sdtlcdtrc0(xc,szDzozmdt0(xc))) ),
inference(monotonicity,[status(thm)],[256]) ).
tff(258,plain,
( aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),szDzozmdt0(xc))
<=> aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),slbdtsldtrb0(xS,xK)) ),
inference(monotonicity,[status(thm)],[147]) ).
tff(259,plain,
( aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),slbdtsldtrb0(xS,xK))
<=> aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),szDzozmdt0(xc)) ),
inference(symmetry,[status(thm)],[258]) ).
tff(260,plain,
aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),szDzozmdt0(xc)),
inference(modus_ponens,[status(thm)],[225,259]) ).
tff(261,plain,
^ [W0: $i] :
refl(( ( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) )
<=> ( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ) )),
inference(bind,[status(th)],[]) ).
tff(262,plain,
( ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) )
<=> ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ) ),
inference(quant_intro,[status(thm)],[261]) ).
tff(263,plain,
^ [W0: $i] :
rewrite(( ( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) )
<=> ( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ) )),
inference(bind,[status(th)],[]) ).
tff(264,plain,
( ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) )
<=> ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ) ),
inference(quant_intro,[status(thm)],[263]) ).
tff(265,plain,
( ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) )
<=> ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ) ),
inference(transitivity,[status(thm)],[264,262]) ).
tff(266,plain,
( ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) )
<=> ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(267,plain,
^ [W0: $i] :
trans(monotonicity(quant_intro(proof_bind(^ [W1: $i] :
rewrite(( ( aElementOf0(W1,szDzozmdt0(W0))
=> aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) )
<=> ( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ))),
( ! [W1: $i] :
( aElementOf0(W1,szDzozmdt0(W0))
=> aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) )
<=> ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) )),
( ( aFunction0(W0)
=> ! [W1: $i] :
( aElementOf0(W1,szDzozmdt0(W0))
=> aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) )
<=> ( aFunction0(W0)
=> ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ) )),
rewrite(( ( aFunction0(W0)
=> ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) )
<=> ( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ) )),
( ( aFunction0(W0)
=> ! [W1: $i] :
( aElementOf0(W1,szDzozmdt0(W0))
=> aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) )
<=> ( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ) )),
inference(bind,[status(th)],[]) ).
tff(268,plain,
( ! [W0: $i] :
( aFunction0(W0)
=> ! [W1: $i] :
( aElementOf0(W1,szDzozmdt0(W0))
=> aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) )
<=> ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ) ),
inference(quant_intro,[status(thm)],[267]) ).
tff(269,axiom,
! [W0: $i] :
( aFunction0(W0)
=> ! [W1: $i] :
( aElementOf0(W1,szDzozmdt0(W0))
=> aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mImgRng) ).
tff(270,plain,
! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ),
inference(modus_ponens,[status(thm)],[269,268]) ).
tff(271,plain,
! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ),
inference(modus_ponens,[status(thm)],[270,266]) ).
tff(272,plain,
! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ),
inference(skolemize,[status(sab)],[271]) ).
tff(273,plain,
! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ),
inference(modus_ponens,[status(thm)],[272,265]) ).
tff(274,plain,
( ( ~ ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) )
| ~ aFunction0(xc)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(xc))
| aElementOf0(sdtlpdtrp0(xc,W1),sdtlcdtrc0(xc,szDzozmdt0(xc))) ) )
<=> ( ~ ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) )
| ~ aFunction0(xc)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(xc))
| aElementOf0(sdtlpdtrp0(xc,W1),sdtlcdtrc0(xc,szDzozmdt0(xc))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(275,plain,
( ~ ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) )
| ~ aFunction0(xc)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(xc))
| aElementOf0(sdtlpdtrp0(xc,W1),sdtlcdtrc0(xc,szDzozmdt0(xc))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(276,plain,
( ~ ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) )
| ~ aFunction0(xc)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(xc))
| aElementOf0(sdtlpdtrp0(xc,W1),sdtlcdtrc0(xc,szDzozmdt0(xc))) ) ),
inference(modus_ponens,[status(thm)],[275,274]) ).
tff(277,plain,
! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(xc))
| aElementOf0(sdtlpdtrp0(xc,W1),sdtlcdtrc0(xc,szDzozmdt0(xc))) ),
inference(unit_resolution,[status(thm)],[276,273,153]) ).
tff(278,plain,
( ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(xc))
| aElementOf0(sdtlpdtrp0(xc,W1),sdtlcdtrc0(xc,szDzozmdt0(xc))) )
| ~ aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),szDzozmdt0(xc))
| aElementOf0(sdtlpdtrp0(xc,tptp_fun_W1_0(slbdtsldtrb0(xS,xK))),sdtlcdtrc0(xc,szDzozmdt0(xc))) )
<=> ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(xc))
| aElementOf0(sdtlpdtrp0(xc,W1),sdtlcdtrc0(xc,szDzozmdt0(xc))) )
| ~ aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),szDzozmdt0(xc))
| aElementOf0(sdtlpdtrp0(xc,tptp_fun_W1_0(slbdtsldtrb0(xS,xK))),sdtlcdtrc0(xc,szDzozmdt0(xc))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(279,plain,
( ~ ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(xc))
| aElementOf0(sdtlpdtrp0(xc,W1),sdtlcdtrc0(xc,szDzozmdt0(xc))) )
| ~ aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),szDzozmdt0(xc))
| aElementOf0(sdtlpdtrp0(xc,tptp_fun_W1_0(slbdtsldtrb0(xS,xK))),sdtlcdtrc0(xc,szDzozmdt0(xc))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(280,plain,
( ~ ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(xc))
| aElementOf0(sdtlpdtrp0(xc,W1),sdtlcdtrc0(xc,szDzozmdt0(xc))) )
| ~ aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),szDzozmdt0(xc))
| aElementOf0(sdtlpdtrp0(xc,tptp_fun_W1_0(slbdtsldtrb0(xS,xK))),sdtlcdtrc0(xc,szDzozmdt0(xc))) ),
inference(modus_ponens,[status(thm)],[279,278]) ).
tff(281,plain,
( ~ aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),szDzozmdt0(xc))
| aElementOf0(sdtlpdtrp0(xc,tptp_fun_W1_0(slbdtsldtrb0(xS,xK))),sdtlcdtrc0(xc,szDzozmdt0(xc))) ),
inference(unit_resolution,[status(thm)],[280,277]) ).
tff(282,plain,
aElementOf0(sdtlpdtrp0(xc,tptp_fun_W1_0(slbdtsldtrb0(xS,xK))),sdtlcdtrc0(xc,szDzozmdt0(xc))),
inference(unit_resolution,[status(thm)],[281,260]) ).
tff(283,plain,
aElementOf0(sdtlpdtrp0(xc,slcrc0),sdtlcdtrc0(xc,szDzozmdt0(xc))),
inference(modus_ponens,[status(thm)],[282,257]) ).
tff(284,plain,
( aSet0(xT)
<=> aSet0(xT) ),
inference(rewrite,[status(thm)],[]) ).
tff(285,axiom,
( aSet0(xT)
& isFinite0(xT) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3291) ).
tff(286,plain,
aSet0(xT),
inference(and_elim,[status(thm)],[285]) ).
tff(287,plain,
aSet0(xT),
inference(modus_ponens,[status(thm)],[286,284]) ).
tff(288,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(xT)
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(xT)
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(289,plain,
( ( ~ aSet0(xT)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,xT)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) ) )
<=> ( ~ aSet0(xT)
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(290,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(xT)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,xT)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(xT)
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[289]) ).
tff(291,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(xT)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,xT)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(xT)
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[290,288]) ).
tff(292,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(xT)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,xT)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(293,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(xT)
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[292,291]) ).
tff(294,plain,
! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) ),
inference(unit_resolution,[status(thm)],[293,26,287]) ).
tff(295,plain,
( ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) )
| ~ ( ~ ( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),xT) ) )
| ~ ( ~ aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ) ) ) )
<=> ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) )
| ~ ( ~ ( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),xT) ) )
| ~ ( ~ aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(296,plain,
( ~ ( ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),xT) ) )
| ~ ( ~ aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ) ) )
<=> ~ ( ~ ( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),xT) ) )
| ~ ( ~ aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(297,plain,
( ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) )
| ~ ( ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),xT) ) )
| ~ ( ~ aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ) ) ) )
<=> ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) )
| ~ ( ~ ( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),xT) ) )
| ~ ( ~ aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[296]) ).
tff(298,plain,
( ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) )
| ~ ( ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),xT) ) )
| ~ ( ~ aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ) ) ) )
<=> ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) )
| ~ ( ~ ( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),xT) ) )
| ~ ( ~ aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[297,295]) ).
tff(299,plain,
( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) )
| ~ ( ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),xT) ) )
| ~ ( ~ aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(300,plain,
( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) )
| ~ ( ~ ( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),xT) ) )
| ~ ( ~ aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[299,298]) ).
tff(301,plain,
~ ( ~ ( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),xT) ) )
| ~ ( ~ aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ) ) ),
inference(unit_resolution,[status(thm)],[300,294]) ).
tff(302,plain,
( ~ ( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),xT) ) )
| ~ ( ~ aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ) )
| ~ aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(303,plain,
( ~ aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ) ),
inference(unit_resolution,[status(thm)],[302,301]) ).
tff(304,plain,
( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
<=> aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT) ),
inference(rewrite,[status(thm)],[]) ).
tff(305,plain,
aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),
inference(and_elim,[status(thm)],[144]) ).
tff(306,plain,
aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),
inference(modus_ponens,[status(thm)],[305,304]) ).
tff(307,plain,
( ~ ( ~ aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ) )
| ~ aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(308,plain,
( ~ ( ~ aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ) )
| ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ) ),
inference(unit_resolution,[status(thm)],[307,306]) ).
tff(309,plain,
~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ),
inference(unit_resolution,[status(thm)],[308,303]) ).
tff(310,plain,
( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) )
| ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ),
inference(tautology,[status(thm)],[]) ).
tff(311,plain,
! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ),
inference(unit_resolution,[status(thm)],[310,309]) ).
tff(312,plain,
( ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) )
| ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(sdtlpdtrp0(xc,slcrc0),xT) )
<=> ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) )
| ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(sdtlpdtrp0(xc,slcrc0),xT) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(313,plain,
( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) )
| ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(sdtlpdtrp0(xc,slcrc0),xT) ),
inference(quant_inst,[status(thm)],[]) ).
tff(314,plain,
( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) )
| ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(sdtlpdtrp0(xc,slcrc0),xT) ),
inference(modus_ponens,[status(thm)],[313,312]) ).
tff(315,plain,
aElementOf0(sdtlpdtrp0(xc,slcrc0),xT),
inference(unit_resolution,[status(thm)],[314,311,283]) ).
tff(316,plain,
^ [W0: $i] :
refl(( ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(W1,W0)) = W0 ) ) ) )
<=> ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(W1,W0)) = W0 ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(317,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(W1,W0)) = W0 ) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(W1,W0)) = W0 ) ) ) ) ),
inference(quant_intro,[status(thm)],[316]) ).
tff(318,plain,
^ [W0: $i] :
rewrite(( ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(W1,W0)) = W0 ) ) ) )
<=> ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(W1,W0)) = W0 ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(319,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(W1,W0)) = W0 ) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(W1,W0)) = W0 ) ) ) ) ),
inference(quant_intro,[status(thm)],[318]) ).
tff(320,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(W1,W0)) = W0 ) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(W1,W0)) = W0 ) ) ) ) ),
inference(transitivity,[status(thm)],[319,317]) ).
tff(321,plain,
^ [W0: $i] :
rewrite(( ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,xS)
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(W1,W0)) = W0 ) ) ) )
<=> ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(W1,W0)) = W0 ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(322,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,xS)
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(W1,W0)) = W0 ) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(W1,W0)) = W0 ) ) ) ) ),
inference(quant_intro,[status(thm)],[321]) ).
tff(323,plain,
( ~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( aSubsetOf0(W1,xS)
& isCountable0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,W2) = W0 ) ) ) )
<=> ~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( aSubsetOf0(W1,xS)
& isCountable0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,W2) = W0 ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(324,plain,
~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( aSubsetOf0(W1,xS)
& isCountable0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,W2) = W0 ) ) ) ),
inference(or_elim,[status(thm)],[96]) ).
tff(325,plain,
~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( aSubsetOf0(W1,xS)
& isCountable0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,W2) = W0 ) ) ) ),
inference(modus_ponens,[status(thm)],[324,323]) ).
tff(326,plain,
~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( aSubsetOf0(W1,xS)
& isCountable0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,W2) = W0 ) ) ) ),
inference(modus_ponens,[status(thm)],[325,323]) ).
tff(327,plain,
~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( aSubsetOf0(W1,xS)
& isCountable0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,W2) = W0 ) ) ) ),
inference(modus_ponens,[status(thm)],[326,323]) ).
tff(328,plain,
^ [W0: $i] :
nnf_neg(refl($oeq(~ aElementOf0(W0,xT),~ aElementOf0(W0,xT))),
nnf_neg(proof_bind(^ [W1: $i] :
nnf_neg(refl($oeq(~ aSubsetOf0(W1,xS),~ aSubsetOf0(W1,xS))),refl($oeq(~ isCountable0(W1),~ isCountable0(W1))),
sk($oeq(~ ! [W2: $i] :
( ~ aElementOf0(W2,slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,W2) = W0 ) ),
~ ( ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(W1,W0)) = W0 ) ))),
$oeq(~ ( aSubsetOf0(W1,xS)
& isCountable0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,W2) = W0 ) ) ),
( ~ aSubsetOf0(W1,xS)
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(W1,W0)) = W0 ) ) )))),
$oeq(~ ? [W1: $i] :
( aSubsetOf0(W1,xS)
& isCountable0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,W2) = W0 ) ) ),
! [W1: $i] :
( ~ aSubsetOf0(W1,xS)
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(W1,W0)) = W0 ) ) ))),
$oeq(~ ( aElementOf0(W0,xT)
& ? [W1: $i] :
( aSubsetOf0(W1,xS)
& isCountable0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,W2) = W0 ) ) ) ),
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,xS)
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(W1,W0)) = W0 ) ) ) ))),
inference(bind,[status(th)],[]) ).
tff(329,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,xS)
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(W1,W0)) = W0 ) ) ) ),
inference(nnf-neg,[status(sab)],[327,328]) ).
tff(330,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(W1,W0)) = W0 ) ) ) ),
inference(modus_ponens,[status(thm)],[329,322]) ).
tff(331,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(W1,W0)) = W0 ) ) ) ),
inference(modus_ponens,[status(thm)],[330,320]) ).
tff(332,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(W1,W0)) = W0 ) ) ) )
| ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(W1,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(W1,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(W1,W0)) = W0 ) ) ) )
| ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(W1,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(W1,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(333,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(W1,W0)) = W0 ) ) ) )
| ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(W1,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(W1,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(334,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(W1,W0)) = W0 ) ) ) )
| ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(W1,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(W1,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) ) ) ) ),
inference(modus_ponens,[status(thm)],[333,332]) ).
tff(335,plain,
! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(W1,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(W1,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) ) ) ),
inference(unit_resolution,[status(thm)],[334,331,315]) ).
tff(336,plain,
^ [W0: $i] :
refl(( ( ~ aSet0(W0)
| aSubsetOf0(W0,W0) )
<=> ( ~ aSet0(W0)
| aSubsetOf0(W0,W0) ) )),
inference(bind,[status(th)],[]) ).
tff(337,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) ) ),
inference(quant_intro,[status(thm)],[336]) ).
tff(338,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(339,plain,
^ [W0: $i] :
rewrite(( ( aSet0(W0)
=> aSubsetOf0(W0,W0) )
<=> ( ~ aSet0(W0)
| aSubsetOf0(W0,W0) ) )),
inference(bind,[status(th)],[]) ).
tff(340,plain,
( ! [W0: $i] :
( aSet0(W0)
=> aSubsetOf0(W0,W0) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) ) ),
inference(quant_intro,[status(thm)],[339]) ).
tff(341,axiom,
! [W0: $i] :
( aSet0(W0)
=> aSubsetOf0(W0,W0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubRefl) ).
tff(342,plain,
! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) ),
inference(modus_ponens,[status(thm)],[341,340]) ).
tff(343,plain,
! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) ),
inference(modus_ponens,[status(thm)],[342,338]) ).
tff(344,plain,
! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) ),
inference(skolemize,[status(sab)],[343]) ).
tff(345,plain,
! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) ),
inference(modus_ponens,[status(thm)],[344,337]) ).
tff(346,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) )
| ~ aSet0(xS)
| aSubsetOf0(xS,xS) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) )
| ~ aSet0(xS)
| aSubsetOf0(xS,xS) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(347,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) )
| ~ aSet0(xS)
| aSubsetOf0(xS,xS) ),
inference(quant_inst,[status(thm)],[]) ).
tff(348,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) )
| ~ aSet0(xS)
| aSubsetOf0(xS,xS) ),
inference(modus_ponens,[status(thm)],[347,346]) ).
tff(349,plain,
aSubsetOf0(xS,xS),
inference(unit_resolution,[status(thm)],[348,345,43]) ).
tff(350,plain,
( ( ~ ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(W1,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(W1,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) ) ) )
| ~ isCountable0(xS)
| ~ aSubsetOf0(xS,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(xS,xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) ) ) )
<=> ( ~ ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(W1,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(W1,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) ) ) )
| ~ isCountable0(xS)
| ~ aSubsetOf0(xS,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(xS,xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(351,plain,
( ~ ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(W1,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(W1,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) ) ) )
| ~ isCountable0(xS)
| ~ aSubsetOf0(xS,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(xS,xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(352,plain,
( ~ ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(W1,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(W1,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) ) ) )
| ~ isCountable0(xS)
| ~ aSubsetOf0(xS,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(xS,xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) ) ) ),
inference(modus_ponens,[status(thm)],[351,350]) ).
tff(353,plain,
~ ( ~ aElementOf0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(xS,xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) ) ),
inference(unit_resolution,[status(thm)],[352,180,349,335]) ).
tff(354,plain,
( ~ aElementOf0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(xS,xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) )
| aElementOf0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(xS,xK)) ),
inference(tautology,[status(thm)],[]) ).
tff(355,plain,
aElementOf0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(xS,xK)),
inference(unit_resolution,[status(thm)],[354,353]) ).
tff(356,plain,
( ( ( ~ aSubsetOf0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)),xS)
| ( sbrdtbr0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0))) != sz00 ) )
<=> aElementOf0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(xS,xK)) )
| ~ ( ~ aSubsetOf0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)),xS)
| ( sbrdtbr0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0))) != sz00 ) )
| ~ aElementOf0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(xS,xK)) ),
inference(tautology,[status(thm)],[]) ).
tff(357,plain,
( ( ( ~ aSubsetOf0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)),xS)
| ( sbrdtbr0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0))) != sz00 ) )
<=> aElementOf0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(xS,xK)) )
| ~ ( ~ aSubsetOf0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)),xS)
| ( sbrdtbr0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0))) != sz00 ) ) ),
inference(unit_resolution,[status(thm)],[356,355]) ).
tff(358,plain,
~ ( ~ aSubsetOf0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)),xS)
| ( sbrdtbr0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0))) != sz00 ) ),
inference(unit_resolution,[status(thm)],[357,108]) ).
tff(359,plain,
( ~ aSubsetOf0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)),xS)
| ( sbrdtbr0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0))) != sz00 )
| aSubsetOf0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)),xS) ),
inference(tautology,[status(thm)],[]) ).
tff(360,plain,
aSubsetOf0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)),xS),
inference(unit_resolution,[status(thm)],[359,358]) ).
tff(361,plain,
( ~ ( ~ aSubsetOf0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)),xS)
| ~ ( ~ aSet0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W2,xS) ) ) )
| ~ aSubsetOf0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)),xS)
| ~ ( ~ aSet0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W2,xS) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(362,plain,
( ~ ( ~ aSubsetOf0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)),xS)
| ~ ( ~ aSet0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W2,xS) ) ) )
| ~ ( ~ aSet0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W2,xS) ) ) ),
inference(unit_resolution,[status(thm)],[361,360]) ).
tff(363,plain,
~ ( ~ aSet0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W2,xS) ) ),
inference(unit_resolution,[status(thm)],[362,51]) ).
tff(364,plain,
( ~ aSet0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W2,xS) )
| aSet0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0))) ),
inference(tautology,[status(thm)],[]) ).
tff(365,plain,
aSet0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0))),
inference(unit_resolution,[status(thm)],[364,363]) ).
tff(366,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) )
| ~ aSet0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)))
| ( ( sbrdtbr0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0))) = sz00 )
<=> ( tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)) = slcrc0 ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) )
| ~ aSet0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)))
| ( ( sbrdtbr0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0))) = sz00 )
<=> ( tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)) = slcrc0 ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(367,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) )
| ~ aSet0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)))
| ( ( sbrdtbr0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0))) = sz00 )
<=> ( tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)) = slcrc0 ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(368,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) )
| ~ aSet0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)))
| ( ( sbrdtbr0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0))) = sz00 )
<=> ( tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)) = slcrc0 ) ) ),
inference(modus_ponens,[status(thm)],[367,366]) ).
tff(369,plain,
( ~ aSet0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)))
| ( ( sbrdtbr0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0))) = sz00 )
<=> ( tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)) = slcrc0 ) ) ),
inference(unit_resolution,[status(thm)],[368,245]) ).
tff(370,plain,
( ( sbrdtbr0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0))) = sz00 )
<=> ( tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)) = slcrc0 ) ),
inference(unit_resolution,[status(thm)],[369,365]) ).
tff(371,plain,
( ~ aSubsetOf0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)),xS)
| ( sbrdtbr0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0))) != sz00 )
| ( sbrdtbr0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0))) = sz00 ) ),
inference(tautology,[status(thm)],[]) ).
tff(372,plain,
sbrdtbr0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0))) = sz00,
inference(unit_resolution,[status(thm)],[371,358]) ).
tff(373,plain,
( ~ ( ( sbrdtbr0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0))) = sz00 )
<=> ( tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)) = slcrc0 ) )
| ( sbrdtbr0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0))) != sz00 )
| ( tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)) = slcrc0 ) ),
inference(tautology,[status(thm)],[]) ).
tff(374,plain,
( ~ ( ( sbrdtbr0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0))) = sz00 )
<=> ( tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)) = slcrc0 ) )
| ( tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)) = slcrc0 ) ),
inference(unit_resolution,[status(thm)],[373,372]) ).
tff(375,plain,
tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)) = slcrc0,
inference(unit_resolution,[status(thm)],[374,370]) ).
tff(376,plain,
sdtlpdtrp0(xc,tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0),
inference(monotonicity,[status(thm)],[375]) ).
tff(377,plain,
( ~ aElementOf0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(xS,xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) )
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0))) != sdtlpdtrp0(xc,slcrc0) ) ),
inference(tautology,[status(thm)],[]) ).
tff(378,plain,
sdtlpdtrp0(xc,tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slcrc0))) != sdtlpdtrp0(xc,slcrc0),
inference(unit_resolution,[status(thm)],[377,353]) ).
tff(379,plain,
$false,
inference(unit_resolution,[status(thm)],[378,376]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : NUM563+1 : TPTP v9.0.0. Released v4.0.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n005.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 01:27:05 EDT 2025
% 0.12/0.34 % CPUTime :
% 211.70/211.96 % SZS status Theorem
% 211.70/211.96 % SZS output start Proof
% See solution above
% 212.52/212.76 % E exiting
%------------------------------------------------------------------------------