TSTP Solution File: NUM625+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM625+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n020.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 13:10:59 EDT 2022
% Result : Theorem 4.56s 3.16s
% Output : Proof 4.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 81
% Syntax : Number of formulae : 168 ( 32 unt; 20 typ; 0 def)
% Number of atoms : 2314 ( 405 equ)
% Maximal formula atoms : 56 ( 15 avg)
% Number of connectives : 4207 (2121 ~;1499 |; 199 &)
% ( 358 <=>; 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 : 21 ( 12 >; 9 *; 0 +; 0 <<)
% Number of predicates : 14 ( 11 usr; 2 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 8 con; 0-3 aty)
% Number of variables : 539 ( 513 !; 0 ?; 539 :)
% Comments :
%------------------------------------------------------------------------------
tff(szmzizndt0_type,type,
szmzizndt0: $i > $i ).
tff(xQ_type,type,
xQ: $i ).
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(aElement0_type,type,
aElement0: $i > $o ).
tff(sdtmndt0_type,type,
sdtmndt0: ( $i * $i ) > $i ).
tff(aSet0_type,type,
aSet0: $i > $o ).
tff(tptp_fun_W3_3_type,type,
tptp_fun_W3_3: ( $i * $i * $i ) > $i ).
tff(xP_type,type,
xP: $i ).
tff(sdtlpdtrp0_type,type,
sdtlpdtrp0: ( $i * $i ) > $i ).
tff(xm_type,type,
xm: $i ).
tff(xe_type,type,
xe: $i ).
tff(xx_type,type,
xx: $i ).
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(aSubsetOf0_type,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff(tptp_fun_W2_1_type,type,
tptp_fun_W2_1: ( $i * $i ) > $i ).
tff(xO_type,type,
xO: $i ).
tff(slcrc0_type,type,
slcrc0: $i ).
tff(1,plain,
( aSet0(xP)
<=> aSet0(sdtmndt0(xQ,szmzizndt0(xQ))) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( aSet0(xP)
<=> aSet0(xP) ),
inference(rewrite,[status(thm)],]) ).
tff(3,axiom,
( aSet0(xP)
& ( xP = sdtmndt0(xQ,szmzizndt0(xQ)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5164) ).
tff(4,plain,
aSet0(xP),
inference(and_elim,[status(thm)],[3]) ).
tff(5,plain,
aSet0(xP),
inference(modus_ponens,[status(thm)],[4,2]) ).
tff(6,plain,
aSet0(sdtmndt0(xQ,szmzizndt0(xQ))),
inference(modus_ponens,[status(thm)],[5,1]) ).
tff(7,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(8,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)],[7]) ).
tff(9,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(10,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)],[9]) ).
tff(11,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)],[10,8]) ).
tff(12,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(13,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(14,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)],[13]) ).
tff(15,axiom,
! [W0: $i] :
( aSet0(W0)
=> ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
tff(16,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[18,11]) ).
tff(20,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,sdtmndt0(xQ,szmzizndt0(xQ))) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,sdtmndt0(xQ,szmzizndt0(xQ))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(21,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,sdtmndt0(xQ,szmzizndt0(xQ))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(22,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,sdtmndt0(xQ,szmzizndt0(xQ))) ) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,sdtmndt0(xQ,szmzizndt0(xQ))) ),
inference(unit_resolution,[status(thm)],[22,19,6]) ).
tff(24,plain,
( aElementOf0(sdtlpdtrp0(xe,xm),sdtmndt0(xQ,szmzizndt0(xQ)))
<=> aElementOf0(szmzizndt0(xQ),sdtmndt0(xQ,szmzizndt0(xQ))) ),
inference(rewrite,[status(thm)],]) ).
tff(25,plain,
( aElementOf0(xx,xP)
<=> aElementOf0(sdtlpdtrp0(xe,xm),sdtmndt0(xQ,szmzizndt0(xQ))) ),
inference(rewrite,[status(thm)],]) ).
tff(26,plain,
( aElementOf0(xx,xP)
<=> aElementOf0(xx,xP) ),
inference(rewrite,[status(thm)],]) ).
tff(27,axiom,
aElementOf0(xx,xP),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5348) ).
tff(28,plain,
aElementOf0(xx,xP),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
aElementOf0(sdtlpdtrp0(xe,xm),sdtmndt0(xQ,szmzizndt0(xQ))),
inference(modus_ponens,[status(thm)],[28,25]) ).
tff(30,plain,
aElementOf0(szmzizndt0(xQ),sdtmndt0(xQ,szmzizndt0(xQ))),
inference(modus_ponens,[status(thm)],[29,24]) ).
tff(31,plain,
( ( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,sdtmndt0(xQ,szmzizndt0(xQ))) )
| aElement0(szmzizndt0(xQ))
| ~ aElementOf0(szmzizndt0(xQ),sdtmndt0(xQ,szmzizndt0(xQ))) )
<=> ( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,sdtmndt0(xQ,szmzizndt0(xQ))) )
| aElement0(szmzizndt0(xQ))
| ~ aElementOf0(szmzizndt0(xQ),sdtmndt0(xQ,szmzizndt0(xQ))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(32,plain,
( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,sdtmndt0(xQ,szmzizndt0(xQ))) )
| aElement0(szmzizndt0(xQ))
| ~ aElementOf0(szmzizndt0(xQ),sdtmndt0(xQ,szmzizndt0(xQ))) ),
inference(quant_inst,[status(thm)],]) ).
tff(33,plain,
( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,sdtmndt0(xQ,szmzizndt0(xQ))) )
| aElement0(szmzizndt0(xQ))
| ~ aElementOf0(szmzizndt0(xQ),sdtmndt0(xQ,szmzizndt0(xQ))) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
aElement0(szmzizndt0(xQ)),
inference(unit_resolution,[status(thm)],[33,30,23]) ).
tff(35,plain,
( aSet0(xO)
<=> aSet0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ),
inference(rewrite,[status(thm)],]) ).
tff(36,plain,
( aSet0(xO)
<=> aSet0(xO) ),
inference(rewrite,[status(thm)],]) ).
tff(37,axiom,
( aSet0(xO)
& ( xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4891) ).
tff(38,plain,
aSet0(xO),
inference(and_elim,[status(thm)],[37]) ).
tff(39,plain,
aSet0(xO),
inference(modus_ponens,[status(thm)],[38,36]) ).
tff(40,plain,
aSet0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),
inference(modus_ponens,[status(thm)],[39,35]) ).
tff(41,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(42,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)],[41]) ).
tff(43,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(44,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)],[43]) ).
tff(45,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(46,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) ),
inference(quant_intro,[status(thm)],[45]) ).
tff(47,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)],[46,44]) ).
tff(48,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(49,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)],[48]) ).
tff(50,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(51,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)],[50]) ).
tff(52,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(53,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(54,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)],[53]) ).
tff(55,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(56,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,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)],[56,52]) ).
tff(58,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,W0)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
& ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ),
inference(skolemize,[status(sab)],[57]) ).
tff(59,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,W0)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
& ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ),
inference(modus_ponens,[status(thm)],[58,51]) ).
tff(60,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ),
inference(modus_ponens,[status(thm)],[59,49]) ).
tff(61,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)],[60,47]) ).
tff(62,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[61,42]) ).
tff(63,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(64,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(65,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(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)],[64]) ).
tff(66,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(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)],[65,63]) ).
tff(67,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(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(68,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)],[67,66]) ).
tff(69,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)],[68,62,40]) ).
tff(70,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(71,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(72,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)],[71]) ).
tff(73,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)],[72,70]) ).
tff(74,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(75,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)],[74,73]) ).
tff(76,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)],[75,69]) ).
tff(77,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(78,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)],[77,76]) ).
tff(79,plain,
( aSubsetOf0(xQ,xO)
<=> aSubsetOf0(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ),
inference(rewrite,[status(thm)],]) ).
tff(80,plain,
( aSubsetOf0(xQ,xO)
<=> aSubsetOf0(xQ,xO) ),
inference(rewrite,[status(thm)],]) ).
tff(81,axiom,
( aSubsetOf0(xQ,xO)
& ( xQ != slcrc0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5093) ).
tff(82,plain,
aSubsetOf0(xQ,xO),
inference(and_elim,[status(thm)],[81]) ).
tff(83,plain,
aSubsetOf0(xQ,xO),
inference(modus_ponens,[status(thm)],[82,80]) ).
tff(84,plain,
aSubsetOf0(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),
inference(modus_ponens,[status(thm)],[83,79]) ).
tff(85,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(86,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)],[85,84]) ).
tff(87,plain,
~ ( ~ aSet0(xQ)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xQ)
| aElementOf0(W2,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ),
inference(unit_resolution,[status(thm)],[86,78]) ).
tff(88,plain,
( ~ aSet0(xQ)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xQ)
| aElementOf0(W2,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) )
| aSet0(xQ) ),
inference(tautology,[status(thm)],]) ).
tff(89,plain,
aSet0(xQ),
inference(unit_resolution,[status(thm)],[88,87]) ).
tff(90,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(91,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)],[90]) ).
tff(92,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(93,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)],[92]) ).
tff(94,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(95,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)],[94]) ).
tff(96,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)],[95,93]) ).
tff(97,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(98,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)],[97]) ).
tff(99,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(100,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)],[99]) ).
tff(101,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(102,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(103,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)],[102]) ).
tff(104,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(105,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)],[104,103]) ).
tff(106,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)],[105,101]) ).
tff(107,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)],[106]) ).
tff(108,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)],[107,100]) ).
tff(109,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)],[108,98]) ).
tff(110,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)],[109,96]) ).
tff(111,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)],[110,91]) ).
tff(112,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(113,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(114,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(115,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)],[114]) ).
tff(116,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)],[115]) ).
tff(117,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)],[116,113]) ).
tff(118,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)],[117]) ).
tff(119,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)],[118,112]) ).
tff(120,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(121,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)],[120,119]) ).
tff(122,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)],[121,111]) ).
tff(123,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)],[122,89,34]) ).
tff(124,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(125,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(126,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)],[125]) ).
tff(127,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)],[126,124]) ).
tff(128,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(129,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)],[128,127]) ).
tff(130,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)],[129,123]) ).
tff(131,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(132,plain,
! [W3: $i] :
( aElementOf0(W3,sdtmndt0(xQ,szmzizndt0(xQ)))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = szmzizndt0(xQ) ) ) ),
inference(unit_resolution,[status(thm)],[131,130]) ).
tff(133,plain,
( ( ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(xQ,szmzizndt0(xQ)))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = szmzizndt0(xQ) ) ) )
| ~ aElementOf0(szmzizndt0(xQ),sdtmndt0(xQ,szmzizndt0(xQ))) )
<=> ( ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(xQ,szmzizndt0(xQ)))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = szmzizndt0(xQ) ) ) )
| ~ aElementOf0(szmzizndt0(xQ),sdtmndt0(xQ,szmzizndt0(xQ))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(134,plain,
( ( aElementOf0(szmzizndt0(xQ),sdtmndt0(xQ,szmzizndt0(xQ)))
<=> $false )
<=> ~ aElementOf0(szmzizndt0(xQ),sdtmndt0(xQ,szmzizndt0(xQ))) ),
inference(rewrite,[status(thm)],]) ).
tff(135,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(136,plain,
( ( ~ aElement0(szmzizndt0(xQ))
| ~ aElementOf0(szmzizndt0(xQ),xQ)
| $true )
<=> $true ),
inference(rewrite,[status(thm)],]) ).
tff(137,plain,
( ( szmzizndt0(xQ) = szmzizndt0(xQ) )
<=> $true ),
inference(rewrite,[status(thm)],]) ).
tff(138,plain,
( ( ~ aElement0(szmzizndt0(xQ))
| ~ aElementOf0(szmzizndt0(xQ),xQ)
| ( szmzizndt0(xQ) = szmzizndt0(xQ) ) )
<=> ( ~ aElement0(szmzizndt0(xQ))
| ~ aElementOf0(szmzizndt0(xQ),xQ)
| $true ) ),
inference(monotonicity,[status(thm)],[137]) ).
tff(139,plain,
( ( ~ aElement0(szmzizndt0(xQ))
| ~ aElementOf0(szmzizndt0(xQ),xQ)
| ( szmzizndt0(xQ) = szmzizndt0(xQ) ) )
<=> $true ),
inference(transitivity,[status(thm)],[138,136]) ).
tff(140,plain,
( ~ ( ~ aElement0(szmzizndt0(xQ))
| ~ aElementOf0(szmzizndt0(xQ),xQ)
| ( szmzizndt0(xQ) = szmzizndt0(xQ) ) )
<=> ~ $true ),
inference(monotonicity,[status(thm)],[139]) ).
tff(141,plain,
( ~ ( ~ aElement0(szmzizndt0(xQ))
| ~ aElementOf0(szmzizndt0(xQ),xQ)
| ( szmzizndt0(xQ) = szmzizndt0(xQ) ) )
<=> $false ),
inference(transitivity,[status(thm)],[140,135]) ).
tff(142,plain,
( ( aElementOf0(szmzizndt0(xQ),sdtmndt0(xQ,szmzizndt0(xQ)))
<=> ~ ( ~ aElement0(szmzizndt0(xQ))
| ~ aElementOf0(szmzizndt0(xQ),xQ)
| ( szmzizndt0(xQ) = szmzizndt0(xQ) ) ) )
<=> ( aElementOf0(szmzizndt0(xQ),sdtmndt0(xQ,szmzizndt0(xQ)))
<=> $false ) ),
inference(monotonicity,[status(thm)],[141]) ).
tff(143,plain,
( ( aElementOf0(szmzizndt0(xQ),sdtmndt0(xQ,szmzizndt0(xQ)))
<=> ~ ( ~ aElement0(szmzizndt0(xQ))
| ~ aElementOf0(szmzizndt0(xQ),xQ)
| ( szmzizndt0(xQ) = szmzizndt0(xQ) ) ) )
<=> ~ aElementOf0(szmzizndt0(xQ),sdtmndt0(xQ,szmzizndt0(xQ))) ),
inference(transitivity,[status(thm)],[142,134]) ).
tff(144,plain,
( ( ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(xQ,szmzizndt0(xQ)))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = szmzizndt0(xQ) ) ) )
| ( aElementOf0(szmzizndt0(xQ),sdtmndt0(xQ,szmzizndt0(xQ)))
<=> ~ ( ~ aElement0(szmzizndt0(xQ))
| ~ aElementOf0(szmzizndt0(xQ),xQ)
| ( szmzizndt0(xQ) = szmzizndt0(xQ) ) ) ) )
<=> ( ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(xQ,szmzizndt0(xQ)))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = szmzizndt0(xQ) ) ) )
| ~ aElementOf0(szmzizndt0(xQ),sdtmndt0(xQ,szmzizndt0(xQ))) ) ),
inference(monotonicity,[status(thm)],[143]) ).
tff(145,plain,
( ( ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(xQ,szmzizndt0(xQ)))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = szmzizndt0(xQ) ) ) )
| ( aElementOf0(szmzizndt0(xQ),sdtmndt0(xQ,szmzizndt0(xQ)))
<=> ~ ( ~ aElement0(szmzizndt0(xQ))
| ~ aElementOf0(szmzizndt0(xQ),xQ)
| ( szmzizndt0(xQ) = szmzizndt0(xQ) ) ) ) )
<=> ( ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(xQ,szmzizndt0(xQ)))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = szmzizndt0(xQ) ) ) )
| ~ aElementOf0(szmzizndt0(xQ),sdtmndt0(xQ,szmzizndt0(xQ))) ) ),
inference(transitivity,[status(thm)],[144,133]) ).
tff(146,plain,
( ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(xQ,szmzizndt0(xQ)))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = szmzizndt0(xQ) ) ) )
| ( aElementOf0(szmzizndt0(xQ),sdtmndt0(xQ,szmzizndt0(xQ)))
<=> ~ ( ~ aElement0(szmzizndt0(xQ))
| ~ aElementOf0(szmzizndt0(xQ),xQ)
| ( szmzizndt0(xQ) = szmzizndt0(xQ) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(147,plain,
( ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(xQ,szmzizndt0(xQ)))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = szmzizndt0(xQ) ) ) )
| ~ aElementOf0(szmzizndt0(xQ),sdtmndt0(xQ,szmzizndt0(xQ))) ),
inference(modus_ponens,[status(thm)],[146,145]) ).
tff(148,plain,
$false,
inference(unit_resolution,[status(thm)],[147,30,132]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : NUM625+1 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n020.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Sep 2 12:30:14 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 4.56/3.16 % SZS status Theorem
% 4.56/3.16 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------