TSTP Solution File: NUM609+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM609+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 18 13:10:52 EDT 2022
% Result : Theorem 12.60s 8.42s
% Output : Proof 12.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 88
% Syntax : Number of formulae : 182 ( 36 unt; 18 typ; 0 def)
% Number of atoms : 2618 ( 394 equ)
% Maximal formula atoms : 56 ( 15 avg)
% Number of connectives : 4942 (2568 ~;1802 |; 199 &)
% ( 343 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 9 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of FOOLs : 80 ( 80 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 19 ( 11 >; 8 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 7 con; 0-3 aty)
% Number of variables : 606 ( 580 !; 0 ?; 606 :)
% Comments :
%------------------------------------------------------------------------------
tff(szmzizndt0_type,type,
szmzizndt0: $i > $i ).
tff(xQ_type,type,
xQ: $i ).
tff(tptp_fun_W2_1_type,type,
tptp_fun_W2_1: ( $i * $i ) > $i ).
tff(sdtmndt0_type,type,
sdtmndt0: ( $i * $i ) > $i ).
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(aElement0_type,type,
aElement0: $i > $o ).
tff(aSet0_type,type,
aSet0: $i > $o ).
tff(aSubsetOf0_type,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff(sdtlcdtrc0_type,type,
sdtlcdtrc0: ( $i * $i ) > $i ).
tff(sdtlbdtrb0_type,type,
sdtlbdtrb0: ( $i * $i ) > $i ).
tff(szDzizrdt0_type,type,
szDzizrdt0: $i > $i ).
tff(xd_type,type,
xd: $i ).
tff(xe_type,type,
xe: $i ).
tff(xO_type,type,
xO: $i ).
tff(slcrc0_type,type,
slcrc0: $i ).
tff(xP_type,type,
xP: $i ).
tff(tptp_fun_W3_3_type,type,
tptp_fun_W3_3: ( $i * $i * $i ) > $i ).
tff(xp_type,type,
xp: $i ).
tff(1,plain,
( aSet0(xO)
<=> aSet0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( aSet0(xO)
<=> aSet0(xO) ),
inference(rewrite,[status(thm)],]) ).
tff(3,axiom,
( aSet0(xO)
& ( xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4891) ).
tff(4,plain,
aSet0(xO),
inference(and_elim,[status(thm)],[3]) ).
tff(5,plain,
aSet0(xO),
inference(modus_ponens,[status(thm)],[4,2]) ).
tff(6,plain,
aSet0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),
inference(modus_ponens,[status(thm)],[5,1]) ).
tff(7,plain,
^ [W0: $i] :
rewrite(
( ( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(8,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
^ [W0: $i] :
refl(
( ( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(10,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) ),
inference(quant_intro,[status(thm)],[9]) ).
tff(11,plain,
^ [W0: $i] :
rewrite(
( ( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(12,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) ),
inference(transitivity,[status(thm)],[12,10]) ).
tff(14,plain,
^ [W0: $i] :
rewrite(
( ( ~ aSet0(W0)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,W0)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
& ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(15,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,W0)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
& ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) ),
inference(quant_intro,[status(thm)],[14]) ).
tff(16,plain,
^ [W0: $i] :
rewrite(
( ( ~ aSet0(W0)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,W0)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
& ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,W0)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
& ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(17,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,W0)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
& ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,W0)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
& ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(19,plain,
^ [W0: $i] :
trans(
monotonicity(
quant_intro(
proof_bind(
^ [W1: $i] :
rewrite(
( ( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) ) ) )
<=> ( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ))),
( ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) ) ) )
<=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) )),
( ( aSet0(W0)
=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) ) ) ) )
<=> ( aSet0(W0)
=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )),
rewrite(
( ( aSet0(W0)
=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )),
( ( aSet0(W0)
=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) ) ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(20,plain,
( ! [W0: $i] :
( aSet0(W0)
=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,axiom,
! [W0: $i] :
( aSet0(W0)
=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSub) ).
tff(22,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ),
inference(modus_ponens,[status(thm)],[22,18]) ).
tff(24,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,W0)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
& ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ),
inference(skolemize,[status(sab)],[23]) ).
tff(25,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,W0)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
& ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ),
inference(modus_ponens,[status(thm)],[24,17]) ).
tff(26,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ),
inference(modus_ponens,[status(thm)],[25,15]) ).
tff(27,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ),
inference(modus_ponens,[status(thm)],[26,13]) ).
tff(28,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[27,8]) ).
tff(29,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),W1)
| aElementOf0(tptp_fun_W2_1(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) )
| ~ ( ~ aSubsetOf0(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) )
<=> ( ~ ! [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(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),W1)
| aElementOf0(tptp_fun_W2_1(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) )
| ~ ( ~ aSubsetOf0(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,plain,
( ( ~ aSet0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),W1)
| aElementOf0(tptp_fun_W2_1(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) )
| ~ ( ~ aSubsetOf0(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) )
<=> ( ~ aSet0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),W1)
| aElementOf0(tptp_fun_W2_1(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) )
| ~ ( ~ aSubsetOf0(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(31,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),W1)
| aElementOf0(tptp_fun_W2_1(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) )
| ~ ( ~ aSubsetOf0(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) )
<=> ( ~ ! [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(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),W1)
| aElementOf0(tptp_fun_W2_1(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) )
| ~ ( ~ aSubsetOf0(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[30]) ).
tff(32,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),W1)
| aElementOf0(tptp_fun_W2_1(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) )
| ~ ( ~ aSubsetOf0(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) )
<=> ( ~ ! [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(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),W1)
| aElementOf0(tptp_fun_W2_1(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) )
| ~ ( ~ aSubsetOf0(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[31,29]) ).
tff(33,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),W1)
| aElementOf0(tptp_fun_W2_1(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) )
| ~ ( ~ aSubsetOf0(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(34,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),W1)
| aElementOf0(tptp_fun_W2_1(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) )
| ~ ( ~ aSubsetOf0(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),W1)
| aElementOf0(tptp_fun_W2_1(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) )
| ~ ( ~ aSubsetOf0(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ),
inference(unit_resolution,[status(thm)],[34,28,6]) ).
tff(36,plain,
( ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),W1)
| aElementOf0(tptp_fun_W2_1(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) )
| ~ ( ~ aSubsetOf0(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) )
| ~ ( ~ ( aSubsetOf0(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSet0(xQ)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),xQ)
| aElementOf0(tptp_fun_W2_1(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) )
| ~ ( ~ aSubsetOf0(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(xQ)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xQ)
| aElementOf0(W2,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) )
<=> ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),W1)
| aElementOf0(tptp_fun_W2_1(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) )
| ~ ( ~ aSubsetOf0(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) )
| ~ ( ~ ( aSubsetOf0(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSet0(xQ)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),xQ)
| aElementOf0(tptp_fun_W2_1(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) )
| ~ ( ~ aSubsetOf0(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(xQ)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xQ)
| aElementOf0(W2,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(37,plain,
( ~ ( ~ ( ~ aSet0(xQ)
| aSubsetOf0(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),xQ)
| aElementOf0(tptp_fun_W2_1(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) )
| ~ ( ~ aSubsetOf0(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(xQ)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xQ)
| aElementOf0(W2,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) )
<=> ~ ( ~ ( aSubsetOf0(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSet0(xQ)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),xQ)
| aElementOf0(tptp_fun_W2_1(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) )
| ~ ( ~ aSubsetOf0(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(xQ)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xQ)
| aElementOf0(W2,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(38,plain,
( ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),W1)
| aElementOf0(tptp_fun_W2_1(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) )
| ~ ( ~ aSubsetOf0(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) )
| ~ ( ~ ( ~ aSet0(xQ)
| aSubsetOf0(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),xQ)
| aElementOf0(tptp_fun_W2_1(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) )
| ~ ( ~ aSubsetOf0(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(xQ)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xQ)
| aElementOf0(W2,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) )
<=> ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),W1)
| aElementOf0(tptp_fun_W2_1(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) )
| ~ ( ~ aSubsetOf0(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) )
| ~ ( ~ ( aSubsetOf0(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSet0(xQ)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),xQ)
| aElementOf0(tptp_fun_W2_1(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) )
| ~ ( ~ aSubsetOf0(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(xQ)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xQ)
| aElementOf0(W2,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[37]) ).
tff(39,plain,
( ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),W1)
| aElementOf0(tptp_fun_W2_1(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) )
| ~ ( ~ aSubsetOf0(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) )
| ~ ( ~ ( ~ aSet0(xQ)
| aSubsetOf0(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),xQ)
| aElementOf0(tptp_fun_W2_1(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) )
| ~ ( ~ aSubsetOf0(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(xQ)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xQ)
| aElementOf0(W2,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) )
<=> ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),W1)
| aElementOf0(tptp_fun_W2_1(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) )
| ~ ( ~ aSubsetOf0(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) )
| ~ ( ~ ( aSubsetOf0(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSet0(xQ)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),xQ)
| aElementOf0(tptp_fun_W2_1(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) )
| ~ ( ~ aSubsetOf0(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(xQ)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xQ)
| aElementOf0(W2,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[38,36]) ).
tff(40,plain,
( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),W1)
| aElementOf0(tptp_fun_W2_1(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) )
| ~ ( ~ aSubsetOf0(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) )
| ~ ( ~ ( ~ aSet0(xQ)
| aSubsetOf0(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),xQ)
| aElementOf0(tptp_fun_W2_1(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) )
| ~ ( ~ aSubsetOf0(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(xQ)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xQ)
| aElementOf0(W2,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(41,plain,
( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),W1)
| aElementOf0(tptp_fun_W2_1(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) )
| ~ ( ~ aSubsetOf0(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) )
| ~ ( ~ ( aSubsetOf0(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSet0(xQ)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),xQ)
| aElementOf0(tptp_fun_W2_1(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) )
| ~ ( ~ aSubsetOf0(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(xQ)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xQ)
| aElementOf0(W2,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
~ ( ~ ( aSubsetOf0(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSet0(xQ)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),xQ)
| aElementOf0(tptp_fun_W2_1(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) )
| ~ ( ~ aSubsetOf0(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(xQ)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xQ)
| aElementOf0(W2,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ) ),
inference(unit_resolution,[status(thm)],[41,35]) ).
tff(43,plain,
( ~ ( aSubsetOf0(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSet0(xQ)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),xQ)
| aElementOf0(tptp_fun_W2_1(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) )
| ~ ( ~ aSubsetOf0(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(xQ)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xQ)
| aElementOf0(W2,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) )
| ~ aSubsetOf0(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(xQ)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xQ)
| aElementOf0(W2,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(44,plain,
( ~ aSubsetOf0(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(xQ)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xQ)
| aElementOf0(W2,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ),
inference(unit_resolution,[status(thm)],[43,42]) ).
tff(45,plain,
( aSubsetOf0(xQ,xO)
<=> aSubsetOf0(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ),
inference(rewrite,[status(thm)],]) ).
tff(46,plain,
( aSubsetOf0(xQ,xO)
<=> aSubsetOf0(xQ,xO) ),
inference(rewrite,[status(thm)],]) ).
tff(47,axiom,
( aSubsetOf0(xQ,xO)
& ( xQ != slcrc0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5093) ).
tff(48,plain,
aSubsetOf0(xQ,xO),
inference(and_elim,[status(thm)],[47]) ).
tff(49,plain,
aSubsetOf0(xQ,xO),
inference(modus_ponens,[status(thm)],[48,46]) ).
tff(50,plain,
aSubsetOf0(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),
inference(modus_ponens,[status(thm)],[49,45]) ).
tff(51,plain,
( ~ ( ~ aSubsetOf0(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(xQ)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xQ)
| aElementOf0(W2,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) )
| ~ aSubsetOf0(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(xQ)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xQ)
| aElementOf0(W2,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(52,plain,
( ~ ( ~ aSubsetOf0(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(xQ)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xQ)
| aElementOf0(W2,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) )
| ~ ( ~ aSet0(xQ)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xQ)
| aElementOf0(W2,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ),
inference(unit_resolution,[status(thm)],[51,50]) ).
tff(53,plain,
~ ( ~ aSet0(xQ)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xQ)
| aElementOf0(W2,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ),
inference(unit_resolution,[status(thm)],[52,44]) ).
tff(54,plain,
( ~ aSet0(xQ)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xQ)
| aElementOf0(W2,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) )
| aSet0(xQ) ),
inference(tautology,[status(thm)],]) ).
tff(55,plain,
aSet0(xQ),
inference(unit_resolution,[status(thm)],[54,53]) ).
tff(56,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(xQ)
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xQ)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xQ),W1)
| aElementOf0(tptp_fun_W2_1(W1,xQ),xQ) ) )
| ~ ( ~ aSubsetOf0(W1,xQ)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xQ) ) ) ) ) )
<=> ( ~ ! [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(xQ)
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xQ)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xQ),W1)
| aElementOf0(tptp_fun_W2_1(W1,xQ),xQ) ) )
| ~ ( ~ aSubsetOf0(W1,xQ)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xQ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(57,plain,
( ( ~ aSet0(xQ)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,xQ)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xQ),W1)
| aElementOf0(tptp_fun_W2_1(W1,xQ),xQ) ) )
| ~ ( ~ aSubsetOf0(W1,xQ)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xQ) ) ) ) ) )
<=> ( ~ aSet0(xQ)
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xQ)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xQ),W1)
| aElementOf0(tptp_fun_W2_1(W1,xQ),xQ) ) )
| ~ ( ~ aSubsetOf0(W1,xQ)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xQ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(58,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(xQ)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,xQ)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xQ),W1)
| aElementOf0(tptp_fun_W2_1(W1,xQ),xQ) ) )
| ~ ( ~ aSubsetOf0(W1,xQ)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xQ) ) ) ) ) )
<=> ( ~ ! [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(xQ)
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xQ)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xQ),W1)
| aElementOf0(tptp_fun_W2_1(W1,xQ),xQ) ) )
| ~ ( ~ aSubsetOf0(W1,xQ)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xQ) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[57]) ).
tff(59,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(xQ)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,xQ)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xQ),W1)
| aElementOf0(tptp_fun_W2_1(W1,xQ),xQ) ) )
| ~ ( ~ aSubsetOf0(W1,xQ)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xQ) ) ) ) ) )
<=> ( ~ ! [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(xQ)
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xQ)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xQ),W1)
| aElementOf0(tptp_fun_W2_1(W1,xQ),xQ) ) )
| ~ ( ~ aSubsetOf0(W1,xQ)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xQ) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[58,56]) ).
tff(60,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(xQ)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,xQ)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xQ),W1)
| aElementOf0(tptp_fun_W2_1(W1,xQ),xQ) ) )
| ~ ( ~ aSubsetOf0(W1,xQ)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xQ) ) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(61,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(xQ)
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xQ)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xQ),W1)
| aElementOf0(tptp_fun_W2_1(W1,xQ),xQ) ) )
| ~ ( ~ aSubsetOf0(W1,xQ)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xQ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xQ)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xQ),W1)
| aElementOf0(tptp_fun_W2_1(W1,xQ),xQ) ) )
| ~ ( ~ aSubsetOf0(W1,xQ)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xQ) ) ) ) ),
inference(unit_resolution,[status(thm)],[61,28,55]) ).
tff(63,plain,
( ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xQ)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xQ),W1)
| aElementOf0(tptp_fun_W2_1(W1,xQ),xQ) ) )
| ~ ( ~ aSubsetOf0(W1,xQ)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xQ) ) ) ) )
| ~ ( ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ)
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtmndt0(xQ,szmzizndt0(xQ)),xQ),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W2_1(sdtmndt0(xQ,szmzizndt0(xQ)),xQ),xQ) ) )
| ~ ( ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ)
| ~ ( ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(W2,xQ) ) ) ) ) )
<=> ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xQ)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xQ),W1)
| aElementOf0(tptp_fun_W2_1(W1,xQ),xQ) ) )
| ~ ( ~ aSubsetOf0(W1,xQ)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xQ) ) ) ) )
| ~ ( ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ)
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtmndt0(xQ,szmzizndt0(xQ)),xQ),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W2_1(sdtmndt0(xQ,szmzizndt0(xQ)),xQ),xQ) ) )
| ~ ( ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ)
| ~ ( ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(W2,xQ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(64,plain,
( ~ ( ~ ( ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtmndt0(xQ,szmzizndt0(xQ)),xQ),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W2_1(sdtmndt0(xQ,szmzizndt0(xQ)),xQ),xQ) ) )
| ~ ( ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ)
| ~ ( ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(W2,xQ) ) ) ) )
<=> ~ ( ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ)
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtmndt0(xQ,szmzizndt0(xQ)),xQ),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W2_1(sdtmndt0(xQ,szmzizndt0(xQ)),xQ),xQ) ) )
| ~ ( ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ)
| ~ ( ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(W2,xQ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(65,plain,
( ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xQ)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xQ),W1)
| aElementOf0(tptp_fun_W2_1(W1,xQ),xQ) ) )
| ~ ( ~ aSubsetOf0(W1,xQ)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xQ) ) ) ) )
| ~ ( ~ ( ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtmndt0(xQ,szmzizndt0(xQ)),xQ),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W2_1(sdtmndt0(xQ,szmzizndt0(xQ)),xQ),xQ) ) )
| ~ ( ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ)
| ~ ( ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(W2,xQ) ) ) ) ) )
<=> ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xQ)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xQ),W1)
| aElementOf0(tptp_fun_W2_1(W1,xQ),xQ) ) )
| ~ ( ~ aSubsetOf0(W1,xQ)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xQ) ) ) ) )
| ~ ( ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ)
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtmndt0(xQ,szmzizndt0(xQ)),xQ),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W2_1(sdtmndt0(xQ,szmzizndt0(xQ)),xQ),xQ) ) )
| ~ ( ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ)
| ~ ( ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(W2,xQ) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[64]) ).
tff(66,plain,
( ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xQ)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xQ),W1)
| aElementOf0(tptp_fun_W2_1(W1,xQ),xQ) ) )
| ~ ( ~ aSubsetOf0(W1,xQ)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xQ) ) ) ) )
| ~ ( ~ ( ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtmndt0(xQ,szmzizndt0(xQ)),xQ),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W2_1(sdtmndt0(xQ,szmzizndt0(xQ)),xQ),xQ) ) )
| ~ ( ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ)
| ~ ( ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(W2,xQ) ) ) ) ) )
<=> ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xQ)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xQ),W1)
| aElementOf0(tptp_fun_W2_1(W1,xQ),xQ) ) )
| ~ ( ~ aSubsetOf0(W1,xQ)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xQ) ) ) ) )
| ~ ( ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ)
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtmndt0(xQ,szmzizndt0(xQ)),xQ),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W2_1(sdtmndt0(xQ,szmzizndt0(xQ)),xQ),xQ) ) )
| ~ ( ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ)
| ~ ( ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(W2,xQ) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[65,63]) ).
tff(67,plain,
( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xQ)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xQ),W1)
| aElementOf0(tptp_fun_W2_1(W1,xQ),xQ) ) )
| ~ ( ~ aSubsetOf0(W1,xQ)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xQ) ) ) ) )
| ~ ( ~ ( ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtmndt0(xQ,szmzizndt0(xQ)),xQ),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W2_1(sdtmndt0(xQ,szmzizndt0(xQ)),xQ),xQ) ) )
| ~ ( ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ)
| ~ ( ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(W2,xQ) ) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(68,plain,
( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xQ)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xQ),W1)
| aElementOf0(tptp_fun_W2_1(W1,xQ),xQ) ) )
| ~ ( ~ aSubsetOf0(W1,xQ)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xQ) ) ) ) )
| ~ ( ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ)
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtmndt0(xQ,szmzizndt0(xQ)),xQ),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W2_1(sdtmndt0(xQ,szmzizndt0(xQ)),xQ),xQ) ) )
| ~ ( ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ)
| ~ ( ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(W2,xQ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
~ ( ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ)
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtmndt0(xQ,szmzizndt0(xQ)),xQ),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W2_1(sdtmndt0(xQ,szmzizndt0(xQ)),xQ),xQ) ) )
| ~ ( ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ)
| ~ ( ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(W2,xQ) ) ) ) ),
inference(unit_resolution,[status(thm)],[68,62]) ).
tff(70,plain,
( ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ)
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtmndt0(xQ,szmzizndt0(xQ)),xQ),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W2_1(sdtmndt0(xQ,szmzizndt0(xQ)),xQ),xQ) ) )
| ~ ( ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ)
| ~ ( ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(W2,xQ) ) ) )
| aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ)
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtmndt0(xQ,szmzizndt0(xQ)),xQ),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W2_1(sdtmndt0(xQ,szmzizndt0(xQ)),xQ),xQ) ) ),
inference(tautology,[status(thm)],]) ).
tff(71,plain,
( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ)
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtmndt0(xQ,szmzizndt0(xQ)),xQ),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W2_1(sdtmndt0(xQ,szmzizndt0(xQ)),xQ),xQ) ) ),
inference(unit_resolution,[status(thm)],[70,69]) ).
tff(72,plain,
( ~ aSubsetOf0(xP,xQ)
<=> ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ) ),
inference(rewrite,[status(thm)],]) ).
tff(73,plain,
( ~ aSubsetOf0(xP,xQ)
<=> ~ aSubsetOf0(xP,xQ) ),
inference(rewrite,[status(thm)],]) ).
tff(74,axiom,
~ aSubsetOf0(xP,xQ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(75,plain,
~ aSubsetOf0(xP,xQ),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ),
inference(modus_ponens,[status(thm)],[75,72]) ).
tff(77,plain,
( aSet0(xP)
<=> aSet0(sdtmndt0(xQ,szmzizndt0(xQ))) ),
inference(rewrite,[status(thm)],]) ).
tff(78,plain,
( aSet0(xP)
<=> aSet0(xP) ),
inference(rewrite,[status(thm)],]) ).
tff(79,axiom,
( aSet0(xP)
& ( xP = sdtmndt0(xQ,szmzizndt0(xQ)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5164) ).
tff(80,plain,
aSet0(xP),
inference(and_elim,[status(thm)],[79]) ).
tff(81,plain,
aSet0(xP),
inference(modus_ponens,[status(thm)],[80,78]) ).
tff(82,plain,
aSet0(sdtmndt0(xQ,szmzizndt0(xQ))),
inference(modus_ponens,[status(thm)],[81,77]) ).
tff(83,plain,
( ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ)
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtmndt0(xQ,szmzizndt0(xQ)),xQ),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W2_1(sdtmndt0(xQ,szmzizndt0(xQ)),xQ),xQ) ) )
| aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ)
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtmndt0(xQ,szmzizndt0(xQ)),xQ),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W2_1(sdtmndt0(xQ,szmzizndt0(xQ)),xQ),xQ) ) ),
inference(tautology,[status(thm)],]) ).
tff(84,plain,
( ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ)
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtmndt0(xQ,szmzizndt0(xQ)),xQ),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W2_1(sdtmndt0(xQ,szmzizndt0(xQ)),xQ),xQ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtmndt0(xQ,szmzizndt0(xQ)),xQ),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W2_1(sdtmndt0(xQ,szmzizndt0(xQ)),xQ),xQ) ) ),
inference(unit_resolution,[status(thm)],[83,82,76]) ).
tff(85,plain,
~ ( ~ aElementOf0(tptp_fun_W2_1(sdtmndt0(xQ,szmzizndt0(xQ)),xQ),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W2_1(sdtmndt0(xQ,szmzizndt0(xQ)),xQ),xQ) ),
inference(unit_resolution,[status(thm)],[84,71]) ).
tff(86,plain,
( ~ aElementOf0(tptp_fun_W2_1(sdtmndt0(xQ,szmzizndt0(xQ)),xQ),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W2_1(sdtmndt0(xQ,szmzizndt0(xQ)),xQ),xQ)
| ~ aElementOf0(tptp_fun_W2_1(sdtmndt0(xQ,szmzizndt0(xQ)),xQ),xQ) ),
inference(tautology,[status(thm)],]) ).
tff(87,plain,
~ aElementOf0(tptp_fun_W2_1(sdtmndt0(xQ,szmzizndt0(xQ)),xQ),xQ),
inference(unit_resolution,[status(thm)],[86,85]) ).
tff(88,plain,
( ~ aElement0(tptp_fun_W2_1(sdtmndt0(xQ,szmzizndt0(xQ)),xQ))
| ~ aElementOf0(tptp_fun_W2_1(sdtmndt0(xQ,szmzizndt0(xQ)),xQ),xQ)
| ( tptp_fun_W2_1(sdtmndt0(xQ,szmzizndt0(xQ)),xQ) = szmzizndt0(xQ) )
| aElementOf0(tptp_fun_W2_1(sdtmndt0(xQ,szmzizndt0(xQ)),xQ),xQ) ),
inference(tautology,[status(thm)],]) ).
tff(89,plain,
( ~ aElement0(tptp_fun_W2_1(sdtmndt0(xQ,szmzizndt0(xQ)),xQ))
| ~ aElementOf0(tptp_fun_W2_1(sdtmndt0(xQ,szmzizndt0(xQ)),xQ),xQ)
| ( tptp_fun_W2_1(sdtmndt0(xQ,szmzizndt0(xQ)),xQ) = szmzizndt0(xQ) ) ),
inference(unit_resolution,[status(thm)],[88,87]) ).
tff(90,plain,
( ~ aElementOf0(tptp_fun_W2_1(sdtmndt0(xQ,szmzizndt0(xQ)),xQ),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W2_1(sdtmndt0(xQ,szmzizndt0(xQ)),xQ),xQ)
| aElementOf0(tptp_fun_W2_1(sdtmndt0(xQ,szmzizndt0(xQ)),xQ),sdtmndt0(xQ,szmzizndt0(xQ))) ),
inference(tautology,[status(thm)],]) ).
tff(91,plain,
aElementOf0(tptp_fun_W2_1(sdtmndt0(xQ,szmzizndt0(xQ)),xQ),sdtmndt0(xQ,szmzizndt0(xQ))),
inference(unit_resolution,[status(thm)],[90,85]) ).
tff(92,plain,
( ~ ( aElementOf0(tptp_fun_W2_1(sdtmndt0(xQ,szmzizndt0(xQ)),xQ),sdtmndt0(xQ,szmzizndt0(xQ)))
<=> ~ ( ~ aElement0(tptp_fun_W2_1(sdtmndt0(xQ,szmzizndt0(xQ)),xQ))
| ~ aElementOf0(tptp_fun_W2_1(sdtmndt0(xQ,szmzizndt0(xQ)),xQ),xQ)
| ( tptp_fun_W2_1(sdtmndt0(xQ,szmzizndt0(xQ)),xQ) = szmzizndt0(xQ) ) ) )
| ~ aElementOf0(tptp_fun_W2_1(sdtmndt0(xQ,szmzizndt0(xQ)),xQ),sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ ( ~ aElement0(tptp_fun_W2_1(sdtmndt0(xQ,szmzizndt0(xQ)),xQ))
| ~ aElementOf0(tptp_fun_W2_1(sdtmndt0(xQ,szmzizndt0(xQ)),xQ),xQ)
| ( tptp_fun_W2_1(sdtmndt0(xQ,szmzizndt0(xQ)),xQ) = szmzizndt0(xQ) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(93,plain,
~ ( aElementOf0(tptp_fun_W2_1(sdtmndt0(xQ,szmzizndt0(xQ)),xQ),sdtmndt0(xQ,szmzizndt0(xQ)))
<=> ~ ( ~ aElement0(tptp_fun_W2_1(sdtmndt0(xQ,szmzizndt0(xQ)),xQ))
| ~ aElementOf0(tptp_fun_W2_1(sdtmndt0(xQ,szmzizndt0(xQ)),xQ),xQ)
| ( tptp_fun_W2_1(sdtmndt0(xQ,szmzizndt0(xQ)),xQ) = szmzizndt0(xQ) ) ) ),
inference(unit_resolution,[status(thm)],[92,91,89]) ).
tff(94,plain,
^ [W0: $i] :
refl(
( ( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) )),
inference(bind,[status(th)],]) ).
tff(95,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) ),
inference(quant_intro,[status(thm)],[94]) ).
tff(96,plain,
^ [W0: $i] :
rewrite(
( ( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) )),
inference(bind,[status(th)],]) ).
tff(97,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) ),
inference(quant_intro,[status(thm)],[96]) ).
tff(98,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) ),
inference(transitivity,[status(thm)],[97,95]) ).
tff(99,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(100,plain,
^ [W0: $i] :
trans(
monotonicity(
quant_intro(
proof_bind(
^ [W1: $i] :
rewrite(
( ( aElementOf0(W1,W0)
=> aElement0(W1) )
<=> ( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ))),
( ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElement0(W1) )
<=> ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )),
( ( aSet0(W0)
=> ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) )
<=> ( aSet0(W0)
=> ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) )),
rewrite(
( ( aSet0(W0)
=> ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) )),
( ( aSet0(W0)
=> ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) )),
inference(bind,[status(th)],]) ).
tff(101,plain,
( ! [W0: $i] :
( aSet0(W0)
=> ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) ),
inference(quant_intro,[status(thm)],[100]) ).
tff(102,axiom,
! [W0: $i] :
( aSet0(W0)
=> ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
tff(103,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[102,101]) ).
tff(104,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[103,99]) ).
tff(105,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ),
inference(skolemize,[status(sab)],[104]) ).
tff(106,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[105,98]) ).
tff(107,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(108,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(109,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ),
inference(modus_ponens,[status(thm)],[108,107]) ).
tff(110,plain,
! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ),
inference(unit_resolution,[status(thm)],[109,106,6]) ).
tff(111,plain,
( aElementOf0(xp,xO)
<=> aElementOf0(szmzizndt0(xQ),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ),
inference(rewrite,[status(thm)],]) ).
tff(112,plain,
( aElementOf0(xp,xO)
<=> aElementOf0(xp,xO) ),
inference(rewrite,[status(thm)],]) ).
tff(113,axiom,
aElementOf0(xp,xO),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5182) ).
tff(114,plain,
aElementOf0(xp,xO),
inference(modus_ponens,[status(thm)],[113,112]) ).
tff(115,plain,
aElementOf0(szmzizndt0(xQ),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),
inference(modus_ponens,[status(thm)],[114,111]) ).
tff(116,plain,
( ( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) )
| aElement0(szmzizndt0(xQ))
| ~ aElementOf0(szmzizndt0(xQ),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) )
<=> ( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) )
| aElement0(szmzizndt0(xQ))
| ~ aElementOf0(szmzizndt0(xQ),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(117,plain,
( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) )
| aElement0(szmzizndt0(xQ))
| ~ aElementOf0(szmzizndt0(xQ),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(118,plain,
( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) )
| aElement0(szmzizndt0(xQ))
| ~ aElementOf0(szmzizndt0(xQ),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ),
inference(modus_ponens,[status(thm)],[117,116]) ).
tff(119,plain,
aElement0(szmzizndt0(xQ)),
inference(unit_resolution,[status(thm)],[118,115,110]) ).
tff(120,plain,
^ [W0: $i,W1: $i] :
rewrite(
( ( ~ aElement0(W1)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtmndt0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| ( W3 = W1 ) ) ) ) )
| ~ ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) ) ) ) ) )
<=> ( ~ aElement0(W1)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) ) ) )
| ~ ( ( W2 != sdtmndt0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| ( W3 = W1 ) ) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(121,plain,
( ! [W0: $i,W1: $i] :
( ~ aElement0(W1)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtmndt0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| ( W3 = W1 ) ) ) ) )
| ~ ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aElement0(W1)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) ) ) )
| ~ ( ( W2 != sdtmndt0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| ( W3 = W1 ) ) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[120]) ).
tff(122,plain,
^ [W0: $i,W1: $i] :
refl(
( ( ~ aElement0(W1)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtmndt0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| ( W3 = W1 ) ) ) ) )
| ~ ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) ) ) ) ) )
<=> ( ~ aElement0(W1)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtmndt0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| ( W3 = W1 ) ) ) ) )
| ~ ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(123,plain,
( ! [W0: $i,W1: $i] :
( ~ aElement0(W1)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtmndt0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| ( W3 = W1 ) ) ) ) )
| ~ ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aElement0(W1)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtmndt0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| ( W3 = W1 ) ) ) ) )
| ~ ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[122]) ).
tff(124,plain,
^ [W0: $i,W1: $i] :
rewrite(
( ( ~ aElement0(W1)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtmndt0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| ( W3 = W1 ) ) ) ) )
| ~ ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) ) ) ) ) )
<=> ( ~ aElement0(W1)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtmndt0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| ( W3 = W1 ) ) ) ) )
| ~ ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(125,plain,
( ! [W0: $i,W1: $i] :
( ~ aElement0(W1)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtmndt0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| ( W3 = W1 ) ) ) ) )
| ~ ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aElement0(W1)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtmndt0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| ( W3 = W1 ) ) ) ) )
| ~ ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[124]) ).
tff(126,plain,
( ! [W0: $i,W1: $i] :
( ~ aElement0(W1)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtmndt0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| ( W3 = W1 ) ) ) ) )
| ~ ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aElement0(W1)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtmndt0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| ( W3 = W1 ) ) ) ) )
| ~ ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[125,123]) ).
tff(127,plain,
^ [W0: $i,W1: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( aSet0(W0)
& aElement0(W1) )
<=> ~ ( ~ aElement0(W1)
| ~ aSet0(W0) ) )),
( ~ ( aSet0(W0)
& aElement0(W1) )
<=> ~ ~ ( ~ aElement0(W1)
| ~ aSet0(W0) ) )),
rewrite(
( ~ ~ ( ~ aElement0(W1)
| ~ aSet0(W0) )
<=> ( ~ aElement0(W1)
| ~ aSet0(W0) ) )),
( ~ ( aSet0(W0)
& aElement0(W1) )
<=> ( ~ aElement0(W1)
| ~ aSet0(W0) ) )),
quant_intro(
proof_bind(
^ [W2: $i] :
trans(
monotonicity(
rewrite(
( ( ( W2 != sdtmndt0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElement0(W3)
& aElementOf0(W3,W0)
& ( W3 != W1 ) ) ) ) )
<=> ( ( W2 != sdtmndt0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| ( W3 = W1 ) ) ) ) ) )),
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( aElement0(tptp_fun_W3_3(W2,W1,W0))
& aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
& ( tptp_fun_W3_3(W2,W1,W0) != W1 ) )
<=> ~ ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) ) )),
( ( ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( aElement0(tptp_fun_W3_3(W2,W1,W0))
& aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
& ( tptp_fun_W3_3(W2,W1,W0) != W1 ) ) )
<=> ( ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ~ ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) ) ) )),
rewrite(
( ( ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ~ ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) ) )
<=> ( aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) ) ) )),
( ( ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( aElement0(tptp_fun_W3_3(W2,W1,W0))
& aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
& ( tptp_fun_W3_3(W2,W1,W0) != W1 ) ) )
<=> ( aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) ) ) )),
( ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( aElement0(tptp_fun_W3_3(W2,W1,W0))
& aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
& ( tptp_fun_W3_3(W2,W1,W0) != W1 ) ) ) )
<=> ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) ) ) ) )),
rewrite(
( ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) ) ) )
<=> ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) ) ) ) )),
( ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( aElement0(tptp_fun_W3_3(W2,W1,W0))
& aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
& ( tptp_fun_W3_3(W2,W1,W0) != W1 ) ) ) )
<=> ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) ) ) ) )),
( ( ( ( W2 != sdtmndt0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElement0(W3)
& aElementOf0(W3,W0)
& ( W3 != W1 ) ) ) ) )
& ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( aElement0(tptp_fun_W3_3(W2,W1,W0))
& aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
& ( tptp_fun_W3_3(W2,W1,W0) != W1 ) ) ) ) )
<=> ( ( ( W2 != sdtmndt0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| ( W3 = W1 ) ) ) ) )
& ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) ) ) ) ) )),
rewrite(
( ( ( ( W2 != sdtmndt0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| ( W3 = W1 ) ) ) ) )
& ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) ) ) ) )
<=> ~ ( ~ ( ( W2 != sdtmndt0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| ( W3 = W1 ) ) ) ) )
| ~ ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) ) ) ) ) )),
( ( ( ( W2 != sdtmndt0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElement0(W3)
& aElementOf0(W3,W0)
& ( W3 != W1 ) ) ) ) )
& ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( aElement0(tptp_fun_W3_3(W2,W1,W0))
& aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
& ( tptp_fun_W3_3(W2,W1,W0) != W1 ) ) ) ) )
<=> ~ ( ~ ( ( W2 != sdtmndt0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| ( W3 = W1 ) ) ) ) )
| ~ ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) ) ) ) ) ))),
( ! [W2: $i] :
( ( ( W2 != sdtmndt0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElement0(W3)
& aElementOf0(W3,W0)
& ( W3 != W1 ) ) ) ) )
& ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( aElement0(tptp_fun_W3_3(W2,W1,W0))
& aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
& ( tptp_fun_W3_3(W2,W1,W0) != W1 ) ) ) ) )
<=> ! [W2: $i] :
~ ( ~ ( ( W2 != sdtmndt0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| ( W3 = W1 ) ) ) ) )
| ~ ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) ) ) ) ) )),
( ( ~ ( aSet0(W0)
& aElement0(W1) )
| ! [W2: $i] :
( ( ( W2 != sdtmndt0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElement0(W3)
& aElementOf0(W3,W0)
& ( W3 != W1 ) ) ) ) )
& ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( aElement0(tptp_fun_W3_3(W2,W1,W0))
& aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
& ( tptp_fun_W3_3(W2,W1,W0) != W1 ) ) ) ) ) )
<=> ( ~ aElement0(W1)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtmndt0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| ( W3 = W1 ) ) ) ) )
| ~ ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) ) ) ) ) ) )),
rewrite(
( ( ~ aElement0(W1)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtmndt0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| ( W3 = W1 ) ) ) ) )
| ~ ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) ) ) ) ) )
<=> ( ~ aElement0(W1)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtmndt0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| ( W3 = W1 ) ) ) ) )
| ~ ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) ) ) ) ) ) )),
( ( ~ ( aSet0(W0)
& aElement0(W1) )
| ! [W2: $i] :
( ( ( W2 != sdtmndt0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElement0(W3)
& aElementOf0(W3,W0)
& ( W3 != W1 ) ) ) ) )
& ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( aElement0(tptp_fun_W3_3(W2,W1,W0))
& aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
& ( tptp_fun_W3_3(W2,W1,W0) != W1 ) ) ) ) ) )
<=> ( ~ aElement0(W1)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtmndt0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| ( W3 = W1 ) ) ) ) )
| ~ ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(128,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aSet0(W0)
& aElement0(W1) )
| ! [W2: $i] :
( ( ( W2 != sdtmndt0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElement0(W3)
& aElementOf0(W3,W0)
& ( W3 != W1 ) ) ) ) )
& ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( aElement0(tptp_fun_W3_3(W2,W1,W0))
& aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
& ( tptp_fun_W3_3(W2,W1,W0) != W1 ) ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aElement0(W1)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtmndt0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| ( W3 = W1 ) ) ) ) )
| ~ ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[127]) ).
tff(129,plain,
^ [W0: $i,W1: $i] :
rewrite(
( ( ~ ( aSet0(W0)
& aElement0(W1) )
| ! [W2: $i] :
( ( ( W2 != sdtmndt0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElement0(W3)
& aElementOf0(W3,W0)
& ( W3 != W1 ) ) ) ) )
& ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ~ ( aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( aElement0(tptp_fun_W3_3(W2,W1,W0))
& aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
& ( tptp_fun_W3_3(W2,W1,W0) != W1 ) ) ) ) ) )
<=> ( ~ ( aSet0(W0)
& aElement0(W1) )
| ! [W2: $i] :
( ( ( W2 != sdtmndt0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElement0(W3)
& aElementOf0(W3,W0)
& ( W3 != W1 ) ) ) ) )
& ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( aElement0(tptp_fun_W3_3(W2,W1,W0))
& aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
& ( tptp_fun_W3_3(W2,W1,W0) != W1 ) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(130,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aSet0(W0)
& aElement0(W1) )
| ! [W2: $i] :
( ( ( W2 != sdtmndt0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElement0(W3)
& aElementOf0(W3,W0)
& ( W3 != W1 ) ) ) ) )
& ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ~ ( aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( aElement0(tptp_fun_W3_3(W2,W1,W0))
& aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
& ( tptp_fun_W3_3(W2,W1,W0) != W1 ) ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aSet0(W0)
& aElement0(W1) )
| ! [W2: $i] :
( ( ( W2 != sdtmndt0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElement0(W3)
& aElementOf0(W3,W0)
& ( W3 != W1 ) ) ) ) )
& ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( aElement0(tptp_fun_W3_3(W2,W1,W0))
& aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
& ( tptp_fun_W3_3(W2,W1,W0) != W1 ) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[129]) ).
tff(131,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aSet0(W0)
& aElement0(W1) )
| ! [W2: $i] :
( ( W2 = sdtmndt0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElement0(W3)
& aElementOf0(W3,W0)
& ( W3 != W1 ) ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aSet0(W0)
& aElement0(W1) )
| ! [W2: $i] :
( ( W2 = sdtmndt0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElement0(W3)
& aElementOf0(W3,W0)
& ( W3 != W1 ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(132,plain,
^ [W0: $i,W1: $i] :
trans(
monotonicity(
quant_intro(
proof_bind(
^ [W2: $i] :
rewrite(
( ( ( W2 = sdtmndt0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElement0(W3)
& aElementOf0(W3,W0)
& ( W3 != W1 ) ) ) ) )
<=> ( ( W2 = sdtmndt0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElement0(W3)
& aElementOf0(W3,W0)
& ( W3 != W1 ) ) ) ) ) ))),
( ! [W2: $i] :
( ( W2 = sdtmndt0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElement0(W3)
& aElementOf0(W3,W0)
& ( W3 != W1 ) ) ) ) )
<=> ! [W2: $i] :
( ( W2 = sdtmndt0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElement0(W3)
& aElementOf0(W3,W0)
& ( W3 != W1 ) ) ) ) ) )),
( ( ( aSet0(W0)
& aElement0(W1) )
=> ! [W2: $i] :
( ( W2 = sdtmndt0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElement0(W3)
& aElementOf0(W3,W0)
& ( W3 != W1 ) ) ) ) ) )
<=> ( ( aSet0(W0)
& aElement0(W1) )
=> ! [W2: $i] :
( ( W2 = sdtmndt0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElement0(W3)
& aElementOf0(W3,W0)
& ( W3 != W1 ) ) ) ) ) ) )),
rewrite(
( ( ( aSet0(W0)
& aElement0(W1) )
=> ! [W2: $i] :
( ( W2 = sdtmndt0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElement0(W3)
& aElementOf0(W3,W0)
& ( W3 != W1 ) ) ) ) ) )
<=> ( ~ ( aSet0(W0)
& aElement0(W1) )
| ! [W2: $i] :
( ( W2 = sdtmndt0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElement0(W3)
& aElementOf0(W3,W0)
& ( W3 != W1 ) ) ) ) ) ) )),
( ( ( aSet0(W0)
& aElement0(W1) )
=> ! [W2: $i] :
( ( W2 = sdtmndt0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElement0(W3)
& aElementOf0(W3,W0)
& ( W3 != W1 ) ) ) ) ) )
<=> ( ~ ( aSet0(W0)
& aElement0(W1) )
| ! [W2: $i] :
( ( W2 = sdtmndt0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElement0(W3)
& aElementOf0(W3,W0)
& ( W3 != W1 ) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(133,plain,
( ! [W0: $i,W1: $i] :
( ( aSet0(W0)
& aElement0(W1) )
=> ! [W2: $i] :
( ( W2 = sdtmndt0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElement0(W3)
& aElementOf0(W3,W0)
& ( W3 != W1 ) ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aSet0(W0)
& aElement0(W1) )
| ! [W2: $i] :
( ( W2 = sdtmndt0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElement0(W3)
& aElementOf0(W3,W0)
& ( W3 != W1 ) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[132]) ).
tff(134,axiom,
! [W0: $i,W1: $i] :
( ( aSet0(W0)
& aElement0(W1) )
=> ! [W2: $i] :
( ( W2 = sdtmndt0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElement0(W3)
& aElementOf0(W3,W0)
& ( W3 != W1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiff) ).
tff(135,plain,
! [W0: $i,W1: $i] :
( ~ ( aSet0(W0)
& aElement0(W1) )
| ! [W2: $i] :
( ( W2 = sdtmndt0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElement0(W3)
& aElementOf0(W3,W0)
& ( W3 != W1 ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[134,133]) ).
tff(136,plain,
! [W0: $i,W1: $i] :
( ~ ( aSet0(W0)
& aElement0(W1) )
| ! [W2: $i] :
( ( W2 = sdtmndt0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElement0(W3)
& aElementOf0(W3,W0)
& ( W3 != W1 ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[135,131]) ).
tff(137,plain,
! [W0: $i,W1: $i] :
( ~ ( aSet0(W0)
& aElement0(W1) )
| ! [W2: $i] :
( ( ( W2 != sdtmndt0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElement0(W3)
& aElementOf0(W3,W0)
& ( W3 != W1 ) ) ) ) )
& ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ~ ( aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( aElement0(tptp_fun_W3_3(W2,W1,W0))
& aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
& ( tptp_fun_W3_3(W2,W1,W0) != W1 ) ) ) ) ) ),
inference(skolemize,[status(sab)],[136]) ).
tff(138,plain,
! [W0: $i,W1: $i] :
( ~ ( aSet0(W0)
& aElement0(W1) )
| ! [W2: $i] :
( ( ( W2 != sdtmndt0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElement0(W3)
& aElementOf0(W3,W0)
& ( W3 != W1 ) ) ) ) )
& ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( aElement0(tptp_fun_W3_3(W2,W1,W0))
& aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
& ( tptp_fun_W3_3(W2,W1,W0) != W1 ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[137,130]) ).
tff(139,plain,
! [W0: $i,W1: $i] :
( ~ aElement0(W1)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtmndt0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| ( W3 = W1 ) ) ) ) )
| ~ ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[138,128]) ).
tff(140,plain,
! [W0: $i,W1: $i] :
( ~ aElement0(W1)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtmndt0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| ( W3 = W1 ) ) ) ) )
| ~ ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[139,126]) ).
tff(141,plain,
! [W0: $i,W1: $i] :
( ~ aElement0(W1)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) ) ) )
| ~ ( ( W2 != sdtmndt0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| ( W3 = W1 ) ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[140,121]) ).
tff(142,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aElement0(W1)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) ) ) )
| ~ ( ( W2 != sdtmndt0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| ( W3 = W1 ) ) ) ) ) ) )
| ~ aSet0(xQ)
| ~ aElement0(szmzizndt0(xQ))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtmndt0(xQ,szmzizndt0(xQ)) )
| ( aElementOf0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ),W2)
<=> ( ~ aElement0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ))
| ~ aElementOf0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ),xQ)
| ( tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ) = szmzizndt0(xQ) ) ) ) )
| ~ ( ( W2 != sdtmndt0(xQ,szmzizndt0(xQ)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = szmzizndt0(xQ) ) ) ) ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aElement0(W1)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) ) ) )
| ~ ( ( W2 != sdtmndt0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| ( W3 = W1 ) ) ) ) ) ) )
| ~ aSet0(xQ)
| ~ aElement0(szmzizndt0(xQ))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtmndt0(xQ,szmzizndt0(xQ)) )
| ( aElementOf0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ),W2)
<=> ( ~ aElement0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ))
| ~ aElementOf0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ),xQ)
| ( tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ) = szmzizndt0(xQ) ) ) ) )
| ~ ( ( W2 != sdtmndt0(xQ,szmzizndt0(xQ)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = szmzizndt0(xQ) ) ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(143,plain,
( ( ~ aElement0(szmzizndt0(xQ))
| ~ aSet0(xQ)
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtmndt0(xQ,szmzizndt0(xQ)) )
| ( aElementOf0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ),W2)
<=> ( ~ aElement0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ))
| ~ aElementOf0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ),xQ)
| ( tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ) = szmzizndt0(xQ) ) ) ) )
| ~ ( ( W2 != sdtmndt0(xQ,szmzizndt0(xQ)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = szmzizndt0(xQ) ) ) ) ) ) ) )
<=> ( ~ aSet0(xQ)
| ~ aElement0(szmzizndt0(xQ))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtmndt0(xQ,szmzizndt0(xQ)) )
| ( aElementOf0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ),W2)
<=> ( ~ aElement0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ))
| ~ aElementOf0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ),xQ)
| ( tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ) = szmzizndt0(xQ) ) ) ) )
| ~ ( ( W2 != sdtmndt0(xQ,szmzizndt0(xQ)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = szmzizndt0(xQ) ) ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(144,plain,
^ [W2: $i] :
rewrite(
( ~ ( ~ ( ( W2 = sdtmndt0(xQ,szmzizndt0(xQ)) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ),W2)
<=> ( ~ aElement0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ))
| ~ aElementOf0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ),xQ)
| ( tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ) = szmzizndt0(xQ) ) ) ) )
| ~ ( ( W2 != sdtmndt0(xQ,szmzizndt0(xQ)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = szmzizndt0(xQ) ) ) ) ) ) )
<=> ~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtmndt0(xQ,szmzizndt0(xQ)) )
| ( aElementOf0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ),W2)
<=> ( ~ aElement0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ))
| ~ aElementOf0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ),xQ)
| ( tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ) = szmzizndt0(xQ) ) ) ) )
| ~ ( ( W2 != sdtmndt0(xQ,szmzizndt0(xQ)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = szmzizndt0(xQ) ) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(145,plain,
( ! [W2: $i] :
~ ( ~ ( ( W2 = sdtmndt0(xQ,szmzizndt0(xQ)) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ),W2)
<=> ( ~ aElement0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ))
| ~ aElementOf0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ),xQ)
| ( tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ) = szmzizndt0(xQ) ) ) ) )
| ~ ( ( W2 != sdtmndt0(xQ,szmzizndt0(xQ)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = szmzizndt0(xQ) ) ) ) ) ) )
<=> ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtmndt0(xQ,szmzizndt0(xQ)) )
| ( aElementOf0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ),W2)
<=> ( ~ aElement0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ))
| ~ aElementOf0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ),xQ)
| ( tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ) = szmzizndt0(xQ) ) ) ) )
| ~ ( ( W2 != sdtmndt0(xQ,szmzizndt0(xQ)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = szmzizndt0(xQ) ) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[144]) ).
tff(146,plain,
( ( ~ aElement0(szmzizndt0(xQ))
| ~ aSet0(xQ)
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtmndt0(xQ,szmzizndt0(xQ)) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ),W2)
<=> ( ~ aElement0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ))
| ~ aElementOf0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ),xQ)
| ( tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ) = szmzizndt0(xQ) ) ) ) )
| ~ ( ( W2 != sdtmndt0(xQ,szmzizndt0(xQ)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = szmzizndt0(xQ) ) ) ) ) ) ) )
<=> ( ~ aElement0(szmzizndt0(xQ))
| ~ aSet0(xQ)
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtmndt0(xQ,szmzizndt0(xQ)) )
| ( aElementOf0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ),W2)
<=> ( ~ aElement0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ))
| ~ aElementOf0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ),xQ)
| ( tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ) = szmzizndt0(xQ) ) ) ) )
| ~ ( ( W2 != sdtmndt0(xQ,szmzizndt0(xQ)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = szmzizndt0(xQ) ) ) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[145]) ).
tff(147,plain,
( ( ~ aElement0(szmzizndt0(xQ))
| ~ aSet0(xQ)
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtmndt0(xQ,szmzizndt0(xQ)) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ),W2)
<=> ( ~ aElement0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ))
| ~ aElementOf0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ),xQ)
| ( tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ) = szmzizndt0(xQ) ) ) ) )
| ~ ( ( W2 != sdtmndt0(xQ,szmzizndt0(xQ)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = szmzizndt0(xQ) ) ) ) ) ) ) )
<=> ( ~ aSet0(xQ)
| ~ aElement0(szmzizndt0(xQ))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtmndt0(xQ,szmzizndt0(xQ)) )
| ( aElementOf0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ),W2)
<=> ( ~ aElement0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ))
| ~ aElementOf0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ),xQ)
| ( tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ) = szmzizndt0(xQ) ) ) ) )
| ~ ( ( W2 != sdtmndt0(xQ,szmzizndt0(xQ)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = szmzizndt0(xQ) ) ) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[146,143]) ).
tff(148,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aElement0(W1)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) ) ) )
| ~ ( ( W2 != sdtmndt0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| ( W3 = W1 ) ) ) ) ) ) )
| ~ aElement0(szmzizndt0(xQ))
| ~ aSet0(xQ)
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtmndt0(xQ,szmzizndt0(xQ)) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ),W2)
<=> ( ~ aElement0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ))
| ~ aElementOf0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ),xQ)
| ( tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ) = szmzizndt0(xQ) ) ) ) )
| ~ ( ( W2 != sdtmndt0(xQ,szmzizndt0(xQ)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = szmzizndt0(xQ) ) ) ) ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aElement0(W1)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) ) ) )
| ~ ( ( W2 != sdtmndt0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| ( W3 = W1 ) ) ) ) ) ) )
| ~ aSet0(xQ)
| ~ aElement0(szmzizndt0(xQ))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtmndt0(xQ,szmzizndt0(xQ)) )
| ( aElementOf0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ),W2)
<=> ( ~ aElement0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ))
| ~ aElementOf0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ),xQ)
| ( tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ) = szmzizndt0(xQ) ) ) ) )
| ~ ( ( W2 != sdtmndt0(xQ,szmzizndt0(xQ)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = szmzizndt0(xQ) ) ) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[147]) ).
tff(149,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aElement0(W1)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) ) ) )
| ~ ( ( W2 != sdtmndt0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| ( W3 = W1 ) ) ) ) ) ) )
| ~ aElement0(szmzizndt0(xQ))
| ~ aSet0(xQ)
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtmndt0(xQ,szmzizndt0(xQ)) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ),W2)
<=> ( ~ aElement0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ))
| ~ aElementOf0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ),xQ)
| ( tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ) = szmzizndt0(xQ) ) ) ) )
| ~ ( ( W2 != sdtmndt0(xQ,szmzizndt0(xQ)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = szmzizndt0(xQ) ) ) ) ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aElement0(W1)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) ) ) )
| ~ ( ( W2 != sdtmndt0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| ( W3 = W1 ) ) ) ) ) ) )
| ~ aSet0(xQ)
| ~ aElement0(szmzizndt0(xQ))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtmndt0(xQ,szmzizndt0(xQ)) )
| ( aElementOf0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ),W2)
<=> ( ~ aElement0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ))
| ~ aElementOf0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ),xQ)
| ( tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ) = szmzizndt0(xQ) ) ) ) )
| ~ ( ( W2 != sdtmndt0(xQ,szmzizndt0(xQ)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = szmzizndt0(xQ) ) ) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[148,142]) ).
tff(150,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aElement0(W1)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) ) ) )
| ~ ( ( W2 != sdtmndt0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| ( W3 = W1 ) ) ) ) ) ) )
| ~ aElement0(szmzizndt0(xQ))
| ~ aSet0(xQ)
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtmndt0(xQ,szmzizndt0(xQ)) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ),W2)
<=> ( ~ aElement0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ))
| ~ aElementOf0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ),xQ)
| ( tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ) = szmzizndt0(xQ) ) ) ) )
| ~ ( ( W2 != sdtmndt0(xQ,szmzizndt0(xQ)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = szmzizndt0(xQ) ) ) ) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(151,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aElement0(W1)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) ) ) )
| ~ ( ( W2 != sdtmndt0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| ( W3 = W1 ) ) ) ) ) ) )
| ~ aSet0(xQ)
| ~ aElement0(szmzizndt0(xQ))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtmndt0(xQ,szmzizndt0(xQ)) )
| ( aElementOf0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ),W2)
<=> ( ~ aElement0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ))
| ~ aElementOf0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ),xQ)
| ( tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ) = szmzizndt0(xQ) ) ) ) )
| ~ ( ( W2 != sdtmndt0(xQ,szmzizndt0(xQ)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = szmzizndt0(xQ) ) ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[150,149]) ).
tff(152,plain,
( ~ aSet0(xQ)
| ~ aElement0(szmzizndt0(xQ))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtmndt0(xQ,szmzizndt0(xQ)) )
| ( aElementOf0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ),W2)
<=> ( ~ aElement0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ))
| ~ aElementOf0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ),xQ)
| ( tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ) = szmzizndt0(xQ) ) ) ) )
| ~ ( ( W2 != sdtmndt0(xQ,szmzizndt0(xQ)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = szmzizndt0(xQ) ) ) ) ) ) ) ),
inference(unit_resolution,[status(thm)],[151,141]) ).
tff(153,plain,
! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtmndt0(xQ,szmzizndt0(xQ)) )
| ( aElementOf0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ),W2)
<=> ( ~ aElement0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ))
| ~ aElementOf0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ),xQ)
| ( tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ) = szmzizndt0(xQ) ) ) ) )
| ~ ( ( W2 != sdtmndt0(xQ,szmzizndt0(xQ)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = szmzizndt0(xQ) ) ) ) ) ) ),
inference(unit_resolution,[status(thm)],[152,55,119]) ).
tff(154,plain,
( ( ~ ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtmndt0(xQ,szmzizndt0(xQ)) )
| ( aElementOf0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ),W2)
<=> ( ~ aElement0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ))
| ~ aElementOf0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ),xQ)
| ( tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ) = szmzizndt0(xQ) ) ) ) )
| ~ ( ( W2 != sdtmndt0(xQ,szmzizndt0(xQ)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = szmzizndt0(xQ) ) ) ) ) ) )
| ~ ( ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(xQ,szmzizndt0(xQ)))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = szmzizndt0(xQ) ) ) ) ) )
<=> ( ~ ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtmndt0(xQ,szmzizndt0(xQ)) )
| ( aElementOf0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ),W2)
<=> ( ~ aElement0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ))
| ~ aElementOf0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ),xQ)
| ( tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ) = szmzizndt0(xQ) ) ) ) )
| ~ ( ( W2 != sdtmndt0(xQ,szmzizndt0(xQ)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = szmzizndt0(xQ) ) ) ) ) ) )
| ~ ( ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(xQ,szmzizndt0(xQ)))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = szmzizndt0(xQ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(155,plain,
( ~ ( ~ ( ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ( sdtmndt0(xQ,szmzizndt0(xQ)) = sdtmndt0(xQ,szmzizndt0(xQ)) )
| ( aElementOf0(tptp_fun_W3_3(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(xQ),xQ),sdtmndt0(xQ,szmzizndt0(xQ)))
<=> ( ~ aElement0(tptp_fun_W3_3(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(xQ),xQ))
| ~ aElementOf0(tptp_fun_W3_3(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(xQ),xQ),xQ)
| ( tptp_fun_W3_3(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(xQ),xQ) = szmzizndt0(xQ) ) ) ) )
| ~ ( ( sdtmndt0(xQ,szmzizndt0(xQ)) != sdtmndt0(xQ,szmzizndt0(xQ)) )
| ~ ( ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(xQ,szmzizndt0(xQ)))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = szmzizndt0(xQ) ) ) ) ) ) )
<=> ~ ( ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(xQ,szmzizndt0(xQ)))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = szmzizndt0(xQ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(156,plain,
( ( ~ ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtmndt0(xQ,szmzizndt0(xQ)) )
| ( aElementOf0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ),W2)
<=> ( ~ aElement0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ))
| ~ aElementOf0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ),xQ)
| ( tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ) = szmzizndt0(xQ) ) ) ) )
| ~ ( ( W2 != sdtmndt0(xQ,szmzizndt0(xQ)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = szmzizndt0(xQ) ) ) ) ) ) )
| ~ ( ~ ( ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ( sdtmndt0(xQ,szmzizndt0(xQ)) = sdtmndt0(xQ,szmzizndt0(xQ)) )
| ( aElementOf0(tptp_fun_W3_3(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(xQ),xQ),sdtmndt0(xQ,szmzizndt0(xQ)))
<=> ( ~ aElement0(tptp_fun_W3_3(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(xQ),xQ))
| ~ aElementOf0(tptp_fun_W3_3(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(xQ),xQ),xQ)
| ( tptp_fun_W3_3(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(xQ),xQ) = szmzizndt0(xQ) ) ) ) )
| ~ ( ( sdtmndt0(xQ,szmzizndt0(xQ)) != sdtmndt0(xQ,szmzizndt0(xQ)) )
| ~ ( ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(xQ,szmzizndt0(xQ)))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = szmzizndt0(xQ) ) ) ) ) ) ) )
<=> ( ~ ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtmndt0(xQ,szmzizndt0(xQ)) )
| ( aElementOf0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ),W2)
<=> ( ~ aElement0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ))
| ~ aElementOf0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ),xQ)
| ( tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ) = szmzizndt0(xQ) ) ) ) )
| ~ ( ( W2 != sdtmndt0(xQ,szmzizndt0(xQ)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = szmzizndt0(xQ) ) ) ) ) ) )
| ~ ( ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(xQ,szmzizndt0(xQ)))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = szmzizndt0(xQ) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[155]) ).
tff(157,plain,
( ( ~ ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtmndt0(xQ,szmzizndt0(xQ)) )
| ( aElementOf0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ),W2)
<=> ( ~ aElement0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ))
| ~ aElementOf0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ),xQ)
| ( tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ) = szmzizndt0(xQ) ) ) ) )
| ~ ( ( W2 != sdtmndt0(xQ,szmzizndt0(xQ)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = szmzizndt0(xQ) ) ) ) ) ) )
| ~ ( ~ ( ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ( sdtmndt0(xQ,szmzizndt0(xQ)) = sdtmndt0(xQ,szmzizndt0(xQ)) )
| ( aElementOf0(tptp_fun_W3_3(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(xQ),xQ),sdtmndt0(xQ,szmzizndt0(xQ)))
<=> ( ~ aElement0(tptp_fun_W3_3(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(xQ),xQ))
| ~ aElementOf0(tptp_fun_W3_3(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(xQ),xQ),xQ)
| ( tptp_fun_W3_3(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(xQ),xQ) = szmzizndt0(xQ) ) ) ) )
| ~ ( ( sdtmndt0(xQ,szmzizndt0(xQ)) != sdtmndt0(xQ,szmzizndt0(xQ)) )
| ~ ( ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(xQ,szmzizndt0(xQ)))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = szmzizndt0(xQ) ) ) ) ) ) ) )
<=> ( ~ ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtmndt0(xQ,szmzizndt0(xQ)) )
| ( aElementOf0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ),W2)
<=> ( ~ aElement0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ))
| ~ aElementOf0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ),xQ)
| ( tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ) = szmzizndt0(xQ) ) ) ) )
| ~ ( ( W2 != sdtmndt0(xQ,szmzizndt0(xQ)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = szmzizndt0(xQ) ) ) ) ) ) )
| ~ ( ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(xQ,szmzizndt0(xQ)))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = szmzizndt0(xQ) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[156,154]) ).
tff(158,plain,
( ~ ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtmndt0(xQ,szmzizndt0(xQ)) )
| ( aElementOf0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ),W2)
<=> ( ~ aElement0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ))
| ~ aElementOf0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ),xQ)
| ( tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ) = szmzizndt0(xQ) ) ) ) )
| ~ ( ( W2 != sdtmndt0(xQ,szmzizndt0(xQ)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = szmzizndt0(xQ) ) ) ) ) ) )
| ~ ( ~ ( ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ( sdtmndt0(xQ,szmzizndt0(xQ)) = sdtmndt0(xQ,szmzizndt0(xQ)) )
| ( aElementOf0(tptp_fun_W3_3(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(xQ),xQ),sdtmndt0(xQ,szmzizndt0(xQ)))
<=> ( ~ aElement0(tptp_fun_W3_3(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(xQ),xQ))
| ~ aElementOf0(tptp_fun_W3_3(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(xQ),xQ),xQ)
| ( tptp_fun_W3_3(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(xQ),xQ) = szmzizndt0(xQ) ) ) ) )
| ~ ( ( sdtmndt0(xQ,szmzizndt0(xQ)) != sdtmndt0(xQ,szmzizndt0(xQ)) )
| ~ ( ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(xQ,szmzizndt0(xQ)))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = szmzizndt0(xQ) ) ) ) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(159,plain,
( ~ ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtmndt0(xQ,szmzizndt0(xQ)) )
| ( aElementOf0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ),W2)
<=> ( ~ aElement0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ))
| ~ aElementOf0(tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ),xQ)
| ( tptp_fun_W3_3(W2,szmzizndt0(xQ),xQ) = szmzizndt0(xQ) ) ) ) )
| ~ ( ( W2 != sdtmndt0(xQ,szmzizndt0(xQ)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = szmzizndt0(xQ) ) ) ) ) ) )
| ~ ( ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(xQ,szmzizndt0(xQ)))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = szmzizndt0(xQ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[158,157]) ).
tff(160,plain,
~ ( ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(xQ,szmzizndt0(xQ)))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = szmzizndt0(xQ) ) ) ) ),
inference(unit_resolution,[status(thm)],[159,153]) ).
tff(161,plain,
( ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(xQ,szmzizndt0(xQ)))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = szmzizndt0(xQ) ) ) )
| ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(xQ,szmzizndt0(xQ)))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = szmzizndt0(xQ) ) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(162,plain,
! [W3: $i] :
( aElementOf0(W3,sdtmndt0(xQ,szmzizndt0(xQ)))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = szmzizndt0(xQ) ) ) ),
inference(unit_resolution,[status(thm)],[161,160]) ).
tff(163,plain,
( ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(xQ,szmzizndt0(xQ)))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = szmzizndt0(xQ) ) ) )
| ( aElementOf0(tptp_fun_W2_1(sdtmndt0(xQ,szmzizndt0(xQ)),xQ),sdtmndt0(xQ,szmzizndt0(xQ)))
<=> ~ ( ~ aElement0(tptp_fun_W2_1(sdtmndt0(xQ,szmzizndt0(xQ)),xQ))
| ~ aElementOf0(tptp_fun_W2_1(sdtmndt0(xQ,szmzizndt0(xQ)),xQ),xQ)
| ( tptp_fun_W2_1(sdtmndt0(xQ,szmzizndt0(xQ)),xQ) = szmzizndt0(xQ) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(164,plain,
$false,
inference(unit_resolution,[status(thm)],[163,162,93]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM609+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n012.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Sep 2 12:18:49 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 12.60/8.42 % SZS status Theorem
% 12.60/8.42 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------