TSTP Solution File: NUM610+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM610+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 18 13:10:52 EDT 2022
% Result : Theorem 0.17s 0.50s
% Output : Proof 0.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 55
% Syntax : Number of formulae : 105 ( 26 unt; 15 typ; 0 def)
% Number of atoms : 1076 ( 3 equ)
% Maximal formula atoms : 36 ( 11 avg)
% Number of connectives : 1949 (1009 ~; 737 |; 102 &)
% ( 78 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 8 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 46 ( 46 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 9 >; 6 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 272 ( 256 !; 0 ?; 272 :)
% Comments :
%------------------------------------------------------------------------------
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(sdtlcdtrc0_type,type,
sdtlcdtrc0: ( $i * $i ) > $i ).
tff(sdtlbdtrb0_type,type,
sdtlbdtrb0: ( $i * $i ) > $i ).
tff(szDzizrdt0_type,type,
szDzizrdt0: $i > $i ).
tff(xd_type,type,
xd: $i ).
tff(xe_type,type,
xe: $i ).
tff(xQ_type,type,
xQ: $i ).
tff(aSet0_type,type,
aSet0: $i > $o ).
tff(aSubsetOf0_type,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff(tptp_fun_W2_1_type,type,
tptp_fun_W2_1: ( $i * $i ) > $i ).
tff(sdtmndt0_type,type,
sdtmndt0: ( $i * $i ) > $i ).
tff(szmzizndt0_type,type,
szmzizndt0: $i > $i ).
tff(xO_type,type,
xO: $i ).
tff(xP_type,type,
xP: $i ).
tff(slcrc0_type,type,
slcrc0: $i ).
tff(1,plain,
( ~ aSubsetOf0(xP,xO)
<=> ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ~ aSubsetOf0(xP,xO)
<=> ~ aSubsetOf0(xP,xO) ),
inference(rewrite,[status(thm)],]) ).
tff(3,axiom,
~ aSubsetOf0(xP,xO),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(4,plain,
~ aSubsetOf0(xP,xO),
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),
inference(modus_ponens,[status(thm)],[4,1]) ).
tff(6,plain,
( aSubsetOf0(xP,xQ)
<=> aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,plain,
( aSubsetOf0(xP,xQ)
<=> aSubsetOf0(xP,xQ) ),
inference(rewrite,[status(thm)],]) ).
tff(8,axiom,
aSubsetOf0(xP,xQ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5195) ).
tff(9,plain,
aSubsetOf0(xP,xQ),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ),
inference(modus_ponens,[status(thm)],[9,6]) ).
tff(11,plain,
( aSet0(xP)
<=> aSet0(sdtmndt0(xQ,szmzizndt0(xQ))) ),
inference(rewrite,[status(thm)],]) ).
tff(12,plain,
( aSet0(xP)
<=> aSet0(xP) ),
inference(rewrite,[status(thm)],]) ).
tff(13,axiom,
( aSet0(xP)
& ( xP = sdtmndt0(xQ,szmzizndt0(xQ)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5164) ).
tff(14,plain,
aSet0(xP),
inference(and_elim,[status(thm)],[13]) ).
tff(15,plain,
aSet0(xP),
inference(modus_ponens,[status(thm)],[14,12]) ).
tff(16,plain,
aSet0(sdtmndt0(xQ,szmzizndt0(xQ))),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( aSubsetOf0(xQ,xO)
<=> aSubsetOf0(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ),
inference(rewrite,[status(thm)],]) ).
tff(18,plain,
( aSubsetOf0(xQ,xO)
<=> aSubsetOf0(xQ,xO) ),
inference(rewrite,[status(thm)],]) ).
tff(19,axiom,
( aSubsetOf0(xQ,xO)
& ( xQ != slcrc0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5093) ).
tff(20,plain,
aSubsetOf0(xQ,xO),
inference(and_elim,[status(thm)],[19]) ).
tff(21,plain,
aSubsetOf0(xQ,xO),
inference(modus_ponens,[status(thm)],[20,18]) ).
tff(22,plain,
aSubsetOf0(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),
inference(modus_ponens,[status(thm)],[21,17]) ).
tff(23,plain,
( aSet0(xO)
<=> aSet0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
( aSet0(xO)
<=> aSet0(xO) ),
inference(rewrite,[status(thm)],]) ).
tff(25,axiom,
( aSet0(xO)
& ( xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4891) ).
tff(26,plain,
aSet0(xO),
inference(and_elim,[status(thm)],[25]) ).
tff(27,plain,
aSet0(xO),
inference(modus_ponens,[status(thm)],[26,24]) ).
tff(28,plain,
aSet0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),
inference(modus_ponens,[status(thm)],[27,23]) ).
tff(29,plain,
^ [W0: $i,W1: $i,W2: $i] :
refl(
( ( aSubsetOf0(W0,W2)
| ~ aSet0(W2)
| ~ aSubsetOf0(W1,W2)
| ~ aSet0(W1)
| ~ aSubsetOf0(W0,W1)
| ~ aSet0(W0) )
<=> ( aSubsetOf0(W0,W2)
| ~ aSet0(W2)
| ~ aSubsetOf0(W1,W2)
| ~ aSet0(W1)
| ~ aSubsetOf0(W0,W1)
| ~ aSet0(W0) ) )),
inference(bind,[status(th)],]) ).
tff(30,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( aSubsetOf0(W0,W2)
| ~ aSet0(W2)
| ~ aSubsetOf0(W1,W2)
| ~ aSet0(W1)
| ~ aSubsetOf0(W0,W1)
| ~ aSet0(W0) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( aSubsetOf0(W0,W2)
| ~ aSet0(W2)
| ~ aSubsetOf0(W1,W2)
| ~ aSet0(W1)
| ~ aSubsetOf0(W0,W1)
| ~ aSet0(W0) ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,plain,
^ [W0: $i,W1: $i,W2: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( aSubsetOf0(W0,W1)
& aSubsetOf0(W1,W2) )
<=> ~ ( ~ aSubsetOf0(W1,W2)
| ~ aSubsetOf0(W0,W1) ) )),
( ~ ( aSubsetOf0(W0,W1)
& aSubsetOf0(W1,W2) )
<=> ~ ~ ( ~ aSubsetOf0(W1,W2)
| ~ aSubsetOf0(W0,W1) ) )),
rewrite(
( ~ ~ ( ~ aSubsetOf0(W1,W2)
| ~ aSubsetOf0(W0,W1) )
<=> ( ~ aSubsetOf0(W1,W2)
| ~ aSubsetOf0(W0,W1) ) )),
( ~ ( aSubsetOf0(W0,W1)
& aSubsetOf0(W1,W2) )
<=> ( ~ aSubsetOf0(W1,W2)
| ~ aSubsetOf0(W0,W1) ) )),
trans(
monotonicity(
rewrite(
( ( aSet0(W0)
& aSet0(W1)
& aSet0(W2) )
<=> ~ ( ~ aSet0(W2)
| ~ aSet0(W1)
| ~ aSet0(W0) ) )),
( ~ ( aSet0(W0)
& aSet0(W1)
& aSet0(W2) )
<=> ~ ~ ( ~ aSet0(W2)
| ~ aSet0(W1)
| ~ aSet0(W0) ) )),
rewrite(
( ~ ~ ( ~ aSet0(W2)
| ~ aSet0(W1)
| ~ aSet0(W0) )
<=> ( ~ aSet0(W2)
| ~ aSet0(W1)
| ~ aSet0(W0) ) )),
( ~ ( aSet0(W0)
& aSet0(W1)
& aSet0(W2) )
<=> ( ~ aSet0(W2)
| ~ aSet0(W1)
| ~ aSet0(W0) ) )),
( ( aSubsetOf0(W0,W2)
| ~ ( aSubsetOf0(W0,W1)
& aSubsetOf0(W1,W2) )
| ~ ( aSet0(W0)
& aSet0(W1)
& aSet0(W2) ) )
<=> ( aSubsetOf0(W0,W2)
| ~ aSubsetOf0(W1,W2)
| ~ aSubsetOf0(W0,W1)
| ~ aSet0(W2)
| ~ aSet0(W1)
| ~ aSet0(W0) ) )),
rewrite(
( ( aSubsetOf0(W0,W2)
| ~ aSubsetOf0(W1,W2)
| ~ aSubsetOf0(W0,W1)
| ~ aSet0(W2)
| ~ aSet0(W1)
| ~ aSet0(W0) )
<=> ( aSubsetOf0(W0,W2)
| ~ aSet0(W2)
| ~ aSubsetOf0(W1,W2)
| ~ aSet0(W1)
| ~ aSubsetOf0(W0,W1)
| ~ aSet0(W0) ) )),
( ( aSubsetOf0(W0,W2)
| ~ ( aSubsetOf0(W0,W1)
& aSubsetOf0(W1,W2) )
| ~ ( aSet0(W0)
& aSet0(W1)
& aSet0(W2) ) )
<=> ( aSubsetOf0(W0,W2)
| ~ aSet0(W2)
| ~ aSubsetOf0(W1,W2)
| ~ aSet0(W1)
| ~ aSubsetOf0(W0,W1)
| ~ aSet0(W0) ) )),
inference(bind,[status(th)],]) ).
tff(32,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( aSubsetOf0(W0,W2)
| ~ ( aSubsetOf0(W0,W1)
& aSubsetOf0(W1,W2) )
| ~ ( aSet0(W0)
& aSet0(W1)
& aSet0(W2) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( aSubsetOf0(W0,W2)
| ~ aSet0(W2)
| ~ aSubsetOf0(W1,W2)
| ~ aSet0(W1)
| ~ aSubsetOf0(W0,W1)
| ~ aSet0(W0) ) ),
inference(quant_intro,[status(thm)],[31]) ).
tff(33,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( aSubsetOf0(W0,W2)
| ~ ( aSubsetOf0(W0,W1)
& aSubsetOf0(W1,W2) )
| ~ ( aSet0(W0)
& aSet0(W1)
& aSet0(W2) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( aSubsetOf0(W0,W2)
| ~ ( aSubsetOf0(W0,W1)
& aSubsetOf0(W1,W2) )
| ~ ( aSet0(W0)
& aSet0(W1)
& aSet0(W2) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(34,plain,
^ [W0: $i,W1: $i,W2: $i] :
trans(
monotonicity(
rewrite(
( ( aSet0(W0)
& aSet0(W1)
& aSet0(W2) )
<=> ( aSet0(W0)
& aSet0(W1)
& aSet0(W2) ) )),
rewrite(
( ( ( aSubsetOf0(W0,W1)
& aSubsetOf0(W1,W2) )
=> aSubsetOf0(W0,W2) )
<=> ( ~ ( aSubsetOf0(W0,W1)
& aSubsetOf0(W1,W2) )
| aSubsetOf0(W0,W2) ) )),
( ( ( aSet0(W0)
& aSet0(W1)
& aSet0(W2) )
=> ( ( aSubsetOf0(W0,W1)
& aSubsetOf0(W1,W2) )
=> aSubsetOf0(W0,W2) ) )
<=> ( ( aSet0(W0)
& aSet0(W1)
& aSet0(W2) )
=> ( ~ ( aSubsetOf0(W0,W1)
& aSubsetOf0(W1,W2) )
| aSubsetOf0(W0,W2) ) ) )),
rewrite(
( ( ( aSet0(W0)
& aSet0(W1)
& aSet0(W2) )
=> ( ~ ( aSubsetOf0(W0,W1)
& aSubsetOf0(W1,W2) )
| aSubsetOf0(W0,W2) ) )
<=> ( aSubsetOf0(W0,W2)
| ~ ( aSubsetOf0(W0,W1)
& aSubsetOf0(W1,W2) )
| ~ ( aSet0(W0)
& aSet0(W1)
& aSet0(W2) ) ) )),
( ( ( aSet0(W0)
& aSet0(W1)
& aSet0(W2) )
=> ( ( aSubsetOf0(W0,W1)
& aSubsetOf0(W1,W2) )
=> aSubsetOf0(W0,W2) ) )
<=> ( aSubsetOf0(W0,W2)
| ~ ( aSubsetOf0(W0,W1)
& aSubsetOf0(W1,W2) )
| ~ ( aSet0(W0)
& aSet0(W1)
& aSet0(W2) ) ) )),
inference(bind,[status(th)],]) ).
tff(35,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ( aSet0(W0)
& aSet0(W1)
& aSet0(W2) )
=> ( ( aSubsetOf0(W0,W1)
& aSubsetOf0(W1,W2) )
=> aSubsetOf0(W0,W2) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( aSubsetOf0(W0,W2)
| ~ ( aSubsetOf0(W0,W1)
& aSubsetOf0(W1,W2) )
| ~ ( aSet0(W0)
& aSet0(W1)
& aSet0(W2) ) ) ),
inference(quant_intro,[status(thm)],[34]) ).
tff(36,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( aSet0(W0)
& aSet0(W1)
& aSet0(W2) )
=> ( ( aSubsetOf0(W0,W1)
& aSubsetOf0(W1,W2) )
=> aSubsetOf0(W0,W2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSubTrans) ).
tff(37,plain,
! [W0: $i,W1: $i,W2: $i] :
( aSubsetOf0(W0,W2)
| ~ ( aSubsetOf0(W0,W1)
& aSubsetOf0(W1,W2) )
| ~ ( aSet0(W0)
& aSet0(W1)
& aSet0(W2) ) ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
! [W0: $i,W1: $i,W2: $i] :
( aSubsetOf0(W0,W2)
| ~ ( aSubsetOf0(W0,W1)
& aSubsetOf0(W1,W2) )
| ~ ( aSet0(W0)
& aSet0(W1)
& aSet0(W2) ) ),
inference(modus_ponens,[status(thm)],[37,33]) ).
tff(39,plain,
! [W0: $i,W1: $i,W2: $i] :
( aSubsetOf0(W0,W2)
| ~ ( aSubsetOf0(W0,W1)
& aSubsetOf0(W1,W2) )
| ~ ( aSet0(W0)
& aSet0(W1)
& aSet0(W2) ) ),
inference(skolemize,[status(sab)],[38]) ).
tff(40,plain,
! [W0: $i,W1: $i,W2: $i] :
( aSubsetOf0(W0,W2)
| ~ aSet0(W2)
| ~ aSubsetOf0(W1,W2)
| ~ aSet0(W1)
| ~ aSubsetOf0(W0,W1)
| ~ aSet0(W0) ),
inference(modus_ponens,[status(thm)],[39,32]) ).
tff(41,plain,
! [W0: $i,W1: $i,W2: $i] :
( aSubsetOf0(W0,W2)
| ~ aSet0(W2)
| ~ aSubsetOf0(W1,W2)
| ~ aSet0(W1)
| ~ aSubsetOf0(W0,W1)
| ~ aSet0(W0) ),
inference(modus_ponens,[status(thm)],[40,30]) ).
tff(42,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( aSubsetOf0(W0,W2)
| ~ aSet0(W2)
| ~ aSubsetOf0(W1,W2)
| ~ aSet0(W1)
| ~ aSubsetOf0(W0,W1)
| ~ aSet0(W0) )
| aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSet0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ aSubsetOf0(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSet0(xQ)
| ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( aSubsetOf0(W0,W2)
| ~ aSet0(W2)
| ~ aSubsetOf0(W1,W2)
| ~ aSet0(W1)
| ~ aSubsetOf0(W0,W1)
| ~ aSet0(W0) )
| aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSet0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ aSubsetOf0(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSet0(xQ)
| ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(43,plain,
( ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSet0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSubsetOf0(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSet0(xQ)
| ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ)
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ))) )
<=> ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSet0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ aSubsetOf0(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSet0(xQ)
| ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(44,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( aSubsetOf0(W0,W2)
| ~ aSet0(W2)
| ~ aSubsetOf0(W1,W2)
| ~ aSet0(W1)
| ~ aSubsetOf0(W0,W1)
| ~ aSet0(W0) )
| aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSet0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSubsetOf0(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSet0(xQ)
| ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ)
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ))) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( aSubsetOf0(W0,W2)
| ~ aSet0(W2)
| ~ aSubsetOf0(W1,W2)
| ~ aSet0(W1)
| ~ aSubsetOf0(W0,W1)
| ~ aSet0(W0) )
| aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSet0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ aSubsetOf0(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSet0(xQ)
| ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ) ) ),
inference(monotonicity,[status(thm)],[43]) ).
tff(45,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( aSubsetOf0(W0,W2)
| ~ aSet0(W2)
| ~ aSubsetOf0(W1,W2)
| ~ aSet0(W1)
| ~ aSubsetOf0(W0,W1)
| ~ aSet0(W0) )
| aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSet0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSubsetOf0(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSet0(xQ)
| ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ)
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ))) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( aSubsetOf0(W0,W2)
| ~ aSet0(W2)
| ~ aSubsetOf0(W1,W2)
| ~ aSet0(W1)
| ~ aSubsetOf0(W0,W1)
| ~ aSet0(W0) )
| aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSet0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ aSubsetOf0(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSet0(xQ)
| ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ) ) ),
inference(transitivity,[status(thm)],[44,42]) ).
tff(46,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( aSubsetOf0(W0,W2)
| ~ aSet0(W2)
| ~ aSubsetOf0(W1,W2)
| ~ aSet0(W1)
| ~ aSubsetOf0(W0,W1)
| ~ aSet0(W0) )
| aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSet0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSubsetOf0(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSet0(xQ)
| ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ)
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ))) ),
inference(quant_inst,[status(thm)],]) ).
tff(47,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( aSubsetOf0(W0,W2)
| ~ aSet0(W2)
| ~ aSubsetOf0(W1,W2)
| ~ aSet0(W1)
| ~ aSubsetOf0(W0,W1)
| ~ aSet0(W0) )
| aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSet0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ aSubsetOf0(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSet0(xQ)
| ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
~ aSet0(xQ),
inference(unit_resolution,[status(thm)],[47,41,28,22,16,10,5]) ).
tff(49,plain,
( ~ aSet0(xQ)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xQ)
| aElementOf0(W2,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) )
| aSet0(xQ) ),
inference(tautology,[status(thm)],]) ).
tff(50,plain,
( ~ aSet0(xQ)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xQ)
| aElementOf0(W2,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ),
inference(unit_resolution,[status(thm)],[49,48]) ).
tff(51,plain,
( ~ ( ~ aSubsetOf0(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(xQ)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xQ)
| aElementOf0(W2,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) )
| ~ aSubsetOf0(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(xQ)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xQ)
| aElementOf0(W2,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(52,plain,
~ ( ~ aSubsetOf0(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aSet0(xQ)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xQ)
| aElementOf0(W2,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ) ),
inference(unit_resolution,[status(thm)],[51,22,50]) ).
tff(53,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(54,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)],[53,52]) ).
tff(55,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(56,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)],[55]) ).
tff(57,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(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) ) ) ) )
<=> ! [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)],[57]) ).
tff(59,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(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) ) ) ) )
<=> ! [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)],[59]) ).
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) ) ) ) )
<=> ! [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)],[60,58]) ).
tff(62,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(63,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)],[62]) ).
tff(64,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(65,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)],[64]) ).
tff(66,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(67,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(68,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)],[67]) ).
tff(69,axiom,
! [W0: $i] :
( aSet0(W0)
=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSub) ).
tff(70,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)],[69,68]) ).
tff(71,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)],[70,66]) ).
tff(72,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)],[71]) ).
tff(73,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)],[72,65]) ).
tff(74,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)],[73,63]) ).
tff(75,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)],[74,61]) ).
tff(76,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)],[75,56]) ).
tff(77,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(78,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(79,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)],[78]) ).
tff(80,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)],[79,77]) ).
tff(81,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(82,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)],[81,80]) ).
tff(83,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)],[82,76,28]) ).
tff(84,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(85,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(86,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)],[85]) ).
tff(87,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)],[86,84]) ).
tff(88,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(89,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)],[88,87]) ).
tff(90,plain,
$false,
inference(unit_resolution,[status(thm)],[89,83,54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : NUM610+1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.32 % Computer : n014.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Sep 2 12:21:01 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.11/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.33 Usage: tptp [options] [-file:]file
% 0.11/0.33 -h, -? prints this message.
% 0.11/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.11/0.33 -m, -model generate model.
% 0.11/0.33 -p, -proof generate proof.
% 0.11/0.33 -c, -core generate unsat core of named formulas.
% 0.11/0.33 -st, -statistics display statistics.
% 0.11/0.33 -t:timeout set timeout (in second).
% 0.11/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.11/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.33 -<param>:<value> configuration parameter and value.
% 0.11/0.33 -o:<output-file> file to place output in.
% 0.17/0.50 % SZS status Theorem
% 0.17/0.50 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------