TSTP Solution File: NUM623+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM623+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n018.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 13:10:58 EDT 2022
% Result : Theorem 0.48s 0.54s
% Output : Proof 0.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 88
% Syntax : Number of formulae : 188 ( 50 unt; 19 typ; 0 def)
% Number of atoms : 1566 ( 287 equ)
% Maximal formula atoms : 36 ( 9 avg)
% Number of connectives : 2648 (1330 ~; 940 |; 221 &)
% ( 128 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 79 ( 79 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 9 >; 4 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 10 con; 0-2 aty)
% Number of variables : 311 ( 288 !; 0 ?; 311 :)
% Comments :
%------------------------------------------------------------------------------
tff(aSet0_type,type,
aSet0: $i > $o ).
tff(sdtlpdtrp0_type,type,
sdtlpdtrp0: ( $i * $i ) > $i ).
tff(xm_type,type,
xm: $i ).
tff(xN_type,type,
xN: $i ).
tff(slbdtrb0_type,type,
slbdtrb0: $i > $i ).
tff(sz00_type,type,
sz00: $i ).
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(xQ_type,type,
xQ: $i ).
tff(szmzizndt0_type,type,
szmzizndt0: $i > $i ).
tff(xe_type,type,
xe: $i ).
tff(xx_type,type,
xx: $i ).
tff(xp_type,type,
xp: $i ).
tff(aSubsetOf0_type,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff(szDzozmdt0_type,type,
szDzozmdt0: $i > $i ).
tff(isCountable0_type,type,
isCountable0: $i > $o ).
tff(szNzAzT0_type,type,
szNzAzT0: $i ).
tff(slcrc0_type,type,
slcrc0: $i ).
tff(xO_type,type,
xO: $i ).
tff(tptp_fun_W2_1_type,type,
tptp_fun_W2_1: ( $i * $i ) > $i ).
tff(1,plain,
( ( xx = szmzizndt0(sdtlpdtrp0(xN,xm)) )
<=> ( sdtlpdtrp0(xe,xm) = szmzizndt0(sdtlpdtrp0(xN,xm)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ( xx = szmzizndt0(sdtlpdtrp0(xN,xm)) )
<=> ( xx = szmzizndt0(sdtlpdtrp0(xN,xm)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(3,axiom,
xx = szmzizndt0(sdtlpdtrp0(xN,xm)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5401) ).
tff(4,plain,
xx = szmzizndt0(sdtlpdtrp0(xN,xm)),
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
sdtlpdtrp0(xe,xm) = szmzizndt0(sdtlpdtrp0(xN,xm)),
inference(modus_ponens,[status(thm)],[4,1]) ).
tff(6,plain,
szmzizndt0(sdtlpdtrp0(xN,xm)) = sdtlpdtrp0(xe,xm),
inference(symmetry,[status(thm)],[5]) ).
tff(7,plain,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xm)),xQ)
<=> aElementOf0(sdtlpdtrp0(xe,xm),xQ) ),
inference(monotonicity,[status(thm)],[6]) ).
tff(8,plain,
( aElementOf0(sdtlpdtrp0(xe,xm),xQ)
<=> aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xm)),xQ) ),
inference(symmetry,[status(thm)],[7]) ).
tff(9,plain,
( aElementOf0(xx,xQ)
<=> aElementOf0(sdtlpdtrp0(xe,xm),xQ) ),
inference(rewrite,[status(thm)],]) ).
tff(10,plain,
( aElementOf0(xx,xQ)
<=> aElementOf0(xx,xQ) ),
inference(rewrite,[status(thm)],]) ).
tff(11,axiom,
( aElementOf0(xp,sdtlpdtrp0(xN,xm))
& aElementOf0(xx,xQ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5481) ).
tff(12,plain,
aElementOf0(xx,xQ),
inference(and_elim,[status(thm)],[11]) ).
tff(13,plain,
aElementOf0(xx,xQ),
inference(modus_ponens,[status(thm)],[12,10]) ).
tff(14,plain,
aElementOf0(sdtlpdtrp0(xe,xm),xQ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xm)),xQ),
inference(modus_ponens,[status(thm)],[14,8]) ).
tff(16,plain,
( aElementOf0(xm,szNzAzT0)
<=> aElementOf0(xm,szDzozmdt0(xN)) ),
inference(rewrite,[status(thm)],]) ).
tff(17,plain,
( aElementOf0(xm,szNzAzT0)
<=> aElementOf0(xm,szNzAzT0) ),
inference(rewrite,[status(thm)],]) ).
tff(18,axiom,
( aElementOf0(xm,szNzAzT0)
& ( xx = sdtlpdtrp0(xe,xm) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5389) ).
tff(19,plain,
aElementOf0(xm,szNzAzT0),
inference(and_elim,[status(thm)],[18]) ).
tff(20,plain,
aElementOf0(xm,szNzAzT0),
inference(modus_ponens,[status(thm)],[19,17]) ).
tff(21,plain,
aElementOf0(xm,szDzozmdt0(xN)),
inference(modus_ponens,[status(thm)],[20,16]) ).
tff(22,plain,
^ [W0: $i] :
refl(
( ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,W0)) ) )
<=> ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,W0)) ) ) )),
inference(bind,[status(th)],]) ).
tff(23,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,W0)) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,W0)) ) ) ),
inference(quant_intro,[status(thm)],[22]) ).
tff(24,plain,
^ [W0: $i] :
rewrite(
( ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
& isCountable0(sdtlpdtrp0(xN,W0)) ) )
<=> ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,W0)) ) ) )),
inference(bind,[status(th)],]) ).
tff(25,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
& isCountable0(sdtlpdtrp0(xN,W0)) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,W0)) ) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
^ [W0: $i] :
rewrite(
( ( ~ aElementOf0(W0,szNzAzT0)
| ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) ) )
<=> ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
& isCountable0(sdtlpdtrp0(xN,W0)) ) ) )),
inference(bind,[status(th)],]) ).
tff(27,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
& isCountable0(sdtlpdtrp0(xN,W0)) ) ) ),
inference(quant_intro,[status(thm)],[26]) ).
tff(28,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(29,plain,
^ [W0: $i] :
rewrite(
( ( aElementOf0(W0,szNzAzT0)
=> ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) ) )
<=> ( ~ aElementOf0(W0,szNzAzT0)
| ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) ) ) )),
inference(bind,[status(th)],]) ).
tff(30,plain,
( ! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) ) ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,axiom,
! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3671) ).
tff(32,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) ) ),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) ) ),
inference(modus_ponens,[status(thm)],[32,28]) ).
tff(34,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
& isCountable0(sdtlpdtrp0(xN,W0)) ) ),
inference(modus_ponens,[status(thm)],[33,27]) ).
tff(35,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
& isCountable0(sdtlpdtrp0(xN,W0)) ) ),
inference(skolemize,[status(sab)],[34]) ).
tff(36,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,W0)) ) ),
inference(modus_ponens,[status(thm)],[35,25]) ).
tff(37,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,W0)) ) ),
inference(modus_ponens,[status(thm)],[36,23]) ).
tff(38,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,W0)) ) )
| ~ aElementOf0(xm,szDzozmdt0(xN))
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,xm)) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,W0)) ) )
| ~ aElementOf0(xm,szDzozmdt0(xN))
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,xm)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(39,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,W0)) ) )
| ~ aElementOf0(xm,szDzozmdt0(xN))
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,xm)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(40,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,W0)) ) )
| ~ aElementOf0(xm,szDzozmdt0(xN))
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,xm)) ) ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,xm)) ),
inference(unit_resolution,[status(thm)],[40,37,21]) ).
tff(42,plain,
( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,xm))
| aSubsetOf0(sdtlpdtrp0(xN,xm),szDzozmdt0(xN)) ),
inference(tautology,[status(thm)],]) ).
tff(43,plain,
aSubsetOf0(sdtlpdtrp0(xN,xm),szDzozmdt0(xN)),
inference(unit_resolution,[status(thm)],[42,41]) ).
tff(44,plain,
( ( sdtlpdtrp0(xe,xm) = szmzizndt0(xQ) )
<=> ( szmzizndt0(xQ) = sdtlpdtrp0(xe,xm) ) ),
inference(commutativity,[status(thm)],]) ).
tff(45,plain,
( ( szmzizndt0(sdtlpdtrp0(xN,xm)) = szmzizndt0(xQ) )
<=> ( sdtlpdtrp0(xe,xm) = szmzizndt0(xQ) ) ),
inference(monotonicity,[status(thm)],[6]) ).
tff(46,plain,
( ( szmzizndt0(sdtlpdtrp0(xN,xm)) = szmzizndt0(xQ) )
<=> ( szmzizndt0(xQ) = sdtlpdtrp0(xe,xm) ) ),
inference(transitivity,[status(thm)],[45,44]) ).
tff(47,plain,
( ( szmzizndt0(xQ) = sdtlpdtrp0(xe,xm) )
<=> ( szmzizndt0(sdtlpdtrp0(xN,xm)) = szmzizndt0(xQ) ) ),
inference(symmetry,[status(thm)],[46]) ).
tff(48,plain,
( ( szmzizndt0(xQ) != sdtlpdtrp0(xe,xm) )
<=> ( szmzizndt0(sdtlpdtrp0(xN,xm)) != szmzizndt0(xQ) ) ),
inference(monotonicity,[status(thm)],[47]) ).
tff(49,plain,
( ( xp != xx )
<=> ( szmzizndt0(xQ) != sdtlpdtrp0(xe,xm) ) ),
inference(rewrite,[status(thm)],]) ).
tff(50,plain,
( ( xp != xx )
<=> ( xp != xx ) ),
inference(rewrite,[status(thm)],]) ).
tff(51,axiom,
xp != xx,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(52,plain,
xp != xx,
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
szmzizndt0(xQ) != sdtlpdtrp0(xe,xm),
inference(modus_ponens,[status(thm)],[52,49]) ).
tff(54,plain,
szmzizndt0(sdtlpdtrp0(xN,xm)) != szmzizndt0(xQ),
inference(modus_ponens,[status(thm)],[53,48]) ).
tff(55,plain,
( aElementOf0(xp,sdtlpdtrp0(xN,xm))
<=> aElementOf0(szmzizndt0(xQ),sdtlpdtrp0(xN,xm)) ),
inference(rewrite,[status(thm)],]) ).
tff(56,plain,
( aElementOf0(xp,sdtlpdtrp0(xN,xm))
<=> aElementOf0(xp,sdtlpdtrp0(xN,xm)) ),
inference(rewrite,[status(thm)],]) ).
tff(57,plain,
aElementOf0(xp,sdtlpdtrp0(xN,xm)),
inference(and_elim,[status(thm)],[11]) ).
tff(58,plain,
aElementOf0(xp,sdtlpdtrp0(xN,xm)),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
aElementOf0(szmzizndt0(xQ),sdtlpdtrp0(xN,xm)),
inference(modus_ponens,[status(thm)],[58,55]) ).
tff(60,plain,
( aSubsetOf0(xQ,szNzAzT0)
<=> aSubsetOf0(xQ,szDzozmdt0(xN)) ),
inference(rewrite,[status(thm)],]) ).
tff(61,plain,
( aSubsetOf0(xQ,szNzAzT0)
<=> aSubsetOf0(xQ,szNzAzT0) ),
inference(rewrite,[status(thm)],]) ).
tff(62,axiom,
aSubsetOf0(xQ,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5106) ).
tff(63,plain,
aSubsetOf0(xQ,szNzAzT0),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
aSubsetOf0(xQ,szDzozmdt0(xN)),
inference(modus_ponens,[status(thm)],[63,60]) ).
tff(65,plain,
( ( xQ != slcrc0 )
<=> ( xQ != slbdtrb0(sz00) ) ),
inference(rewrite,[status(thm)],]) ).
tff(66,plain,
( ( xQ != slcrc0 )
<=> ( xQ != slcrc0 ) ),
inference(rewrite,[status(thm)],]) ).
tff(67,axiom,
( aSubsetOf0(xQ,xO)
& ( xQ != slcrc0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5093) ).
tff(68,plain,
xQ != slcrc0,
inference(and_elim,[status(thm)],[67]) ).
tff(69,plain,
xQ != slcrc0,
inference(modus_ponens,[status(thm)],[68,66]) ).
tff(70,plain,
xQ != slbdtrb0(sz00),
inference(modus_ponens,[status(thm)],[69,65]) ).
tff(71,plain,
^ [W0: $i,W1: $i] :
refl(
( ( ( szmzizndt0(W0) = szmzizndt0(W1) )
| ( W1 = slbdtrb0(sz00) )
| ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(szmzizndt0(W0),W1)
| ~ aElementOf0(szmzizndt0(W1),W0)
| ~ aSubsetOf0(W0,szDzozmdt0(xN)) )
<=> ( ( szmzizndt0(W0) = szmzizndt0(W1) )
| ( W1 = slbdtrb0(sz00) )
| ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(szmzizndt0(W0),W1)
| ~ aElementOf0(szmzizndt0(W1),W0)
| ~ aSubsetOf0(W0,szDzozmdt0(xN)) ) )),
inference(bind,[status(th)],]) ).
tff(72,plain,
( ! [W0: $i,W1: $i] :
( ( szmzizndt0(W0) = szmzizndt0(W1) )
| ( W1 = slbdtrb0(sz00) )
| ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(szmzizndt0(W0),W1)
| ~ aElementOf0(szmzizndt0(W1),W0)
| ~ aSubsetOf0(W0,szDzozmdt0(xN)) )
<=> ! [W0: $i,W1: $i] :
( ( szmzizndt0(W0) = szmzizndt0(W1) )
| ( W1 = slbdtrb0(sz00) )
| ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(szmzizndt0(W0),W1)
| ~ aElementOf0(szmzizndt0(W1),W0)
| ~ aSubsetOf0(W0,szDzozmdt0(xN)) ) ),
inference(quant_intro,[status(thm)],[71]) ).
tff(73,plain,
^ [W0: $i,W1: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( aElementOf0(szmzizndt0(W0),W1)
& aElementOf0(szmzizndt0(W1),W0) )
<=> ~ ( ~ aElementOf0(szmzizndt0(W0),W1)
| ~ aElementOf0(szmzizndt0(W1),W0) ) )),
( ~ ( aElementOf0(szmzizndt0(W0),W1)
& aElementOf0(szmzizndt0(W1),W0) )
<=> ~ ~ ( ~ aElementOf0(szmzizndt0(W0),W1)
| ~ aElementOf0(szmzizndt0(W1),W0) ) )),
rewrite(
( ~ ~ ( ~ aElementOf0(szmzizndt0(W0),W1)
| ~ aElementOf0(szmzizndt0(W1),W0) )
<=> ( ~ aElementOf0(szmzizndt0(W0),W1)
| ~ aElementOf0(szmzizndt0(W1),W0) ) )),
( ~ ( aElementOf0(szmzizndt0(W0),W1)
& aElementOf0(szmzizndt0(W1),W0) )
<=> ( ~ aElementOf0(szmzizndt0(W0),W1)
| ~ aElementOf0(szmzizndt0(W1),W0) ) )),
trans(
monotonicity(
rewrite(
( ( aSubsetOf0(W0,szDzozmdt0(xN))
& aSubsetOf0(W1,szDzozmdt0(xN))
& ( W0 != slbdtrb0(sz00) )
& ( W1 != slbdtrb0(sz00) ) )
<=> ~ ( ( W1 = slbdtrb0(sz00) )
| ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ~ aSubsetOf0(W0,szDzozmdt0(xN)) ) )),
( ~ ( aSubsetOf0(W0,szDzozmdt0(xN))
& aSubsetOf0(W1,szDzozmdt0(xN))
& ( W0 != slbdtrb0(sz00) )
& ( W1 != slbdtrb0(sz00) ) )
<=> ~ ~ ( ( W1 = slbdtrb0(sz00) )
| ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ~ aSubsetOf0(W0,szDzozmdt0(xN)) ) )),
rewrite(
( ~ ~ ( ( W1 = slbdtrb0(sz00) )
| ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ~ aSubsetOf0(W0,szDzozmdt0(xN)) )
<=> ( ( W1 = slbdtrb0(sz00) )
| ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ~ aSubsetOf0(W0,szDzozmdt0(xN)) ) )),
( ~ ( aSubsetOf0(W0,szDzozmdt0(xN))
& aSubsetOf0(W1,szDzozmdt0(xN))
& ( W0 != slbdtrb0(sz00) )
& ( W1 != slbdtrb0(sz00) ) )
<=> ( ( W1 = slbdtrb0(sz00) )
| ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ~ aSubsetOf0(W0,szDzozmdt0(xN)) ) )),
( ( ( szmzizndt0(W0) = szmzizndt0(W1) )
| ~ ( aElementOf0(szmzizndt0(W0),W1)
& aElementOf0(szmzizndt0(W1),W0) )
| ~ ( aSubsetOf0(W0,szDzozmdt0(xN))
& aSubsetOf0(W1,szDzozmdt0(xN))
& ( W0 != slbdtrb0(sz00) )
& ( W1 != slbdtrb0(sz00) ) ) )
<=> ( ( szmzizndt0(W0) = szmzizndt0(W1) )
| ~ aElementOf0(szmzizndt0(W0),W1)
| ~ aElementOf0(szmzizndt0(W1),W0)
| ( W1 = slbdtrb0(sz00) )
| ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ~ aSubsetOf0(W0,szDzozmdt0(xN)) ) )),
rewrite(
( ( ( szmzizndt0(W0) = szmzizndt0(W1) )
| ~ aElementOf0(szmzizndt0(W0),W1)
| ~ aElementOf0(szmzizndt0(W1),W0)
| ( W1 = slbdtrb0(sz00) )
| ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ~ aSubsetOf0(W0,szDzozmdt0(xN)) )
<=> ( ( szmzizndt0(W0) = szmzizndt0(W1) )
| ( W1 = slbdtrb0(sz00) )
| ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(szmzizndt0(W0),W1)
| ~ aElementOf0(szmzizndt0(W1),W0)
| ~ aSubsetOf0(W0,szDzozmdt0(xN)) ) )),
( ( ( szmzizndt0(W0) = szmzizndt0(W1) )
| ~ ( aElementOf0(szmzizndt0(W0),W1)
& aElementOf0(szmzizndt0(W1),W0) )
| ~ ( aSubsetOf0(W0,szDzozmdt0(xN))
& aSubsetOf0(W1,szDzozmdt0(xN))
& ( W0 != slbdtrb0(sz00) )
& ( W1 != slbdtrb0(sz00) ) ) )
<=> ( ( szmzizndt0(W0) = szmzizndt0(W1) )
| ( W1 = slbdtrb0(sz00) )
| ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(szmzizndt0(W0),W1)
| ~ aElementOf0(szmzizndt0(W1),W0)
| ~ aSubsetOf0(W0,szDzozmdt0(xN)) ) )),
inference(bind,[status(th)],]) ).
tff(74,plain,
( ! [W0: $i,W1: $i] :
( ( szmzizndt0(W0) = szmzizndt0(W1) )
| ~ ( aElementOf0(szmzizndt0(W0),W1)
& aElementOf0(szmzizndt0(W1),W0) )
| ~ ( aSubsetOf0(W0,szDzozmdt0(xN))
& aSubsetOf0(W1,szDzozmdt0(xN))
& ( W0 != slbdtrb0(sz00) )
& ( W1 != slbdtrb0(sz00) ) ) )
<=> ! [W0: $i,W1: $i] :
( ( szmzizndt0(W0) = szmzizndt0(W1) )
| ( W1 = slbdtrb0(sz00) )
| ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(szmzizndt0(W0),W1)
| ~ aElementOf0(szmzizndt0(W1),W0)
| ~ aSubsetOf0(W0,szDzozmdt0(xN)) ) ),
inference(quant_intro,[status(thm)],[73]) ).
tff(75,plain,
^ [W0: $i,W1: $i] :
trans(
monotonicity(
rewrite(
( ~ ( aSubsetOf0(W0,szNzAzT0)
& aSubsetOf0(W1,szNzAzT0)
& ( W0 != slcrc0 )
& ( W1 != slcrc0 ) )
<=> ~ ( aSubsetOf0(W0,szDzozmdt0(xN))
& aSubsetOf0(W1,szDzozmdt0(xN))
& ( W0 != slbdtrb0(sz00) )
& ( W1 != slbdtrb0(sz00) ) ) )),
( ( ( szmzizndt0(W0) = szmzizndt0(W1) )
| ~ ( aElementOf0(szmzizndt0(W0),W1)
& aElementOf0(szmzizndt0(W1),W0) )
| ~ ( aSubsetOf0(W0,szNzAzT0)
& aSubsetOf0(W1,szNzAzT0)
& ( W0 != slcrc0 )
& ( W1 != slcrc0 ) ) )
<=> ( ( szmzizndt0(W0) = szmzizndt0(W1) )
| ~ ( aElementOf0(szmzizndt0(W0),W1)
& aElementOf0(szmzizndt0(W1),W0) )
| ~ ( aSubsetOf0(W0,szDzozmdt0(xN))
& aSubsetOf0(W1,szDzozmdt0(xN))
& ( W0 != slbdtrb0(sz00) )
& ( W1 != slbdtrb0(sz00) ) ) ) )),
rewrite(
( ( ( szmzizndt0(W0) = szmzizndt0(W1) )
| ~ ( aElementOf0(szmzizndt0(W0),W1)
& aElementOf0(szmzizndt0(W1),W0) )
| ~ ( aSubsetOf0(W0,szDzozmdt0(xN))
& aSubsetOf0(W1,szDzozmdt0(xN))
& ( W0 != slbdtrb0(sz00) )
& ( W1 != slbdtrb0(sz00) ) ) )
<=> ( ( szmzizndt0(W0) = szmzizndt0(W1) )
| ~ ( aElementOf0(szmzizndt0(W0),W1)
& aElementOf0(szmzizndt0(W1),W0) )
| ~ ( aSubsetOf0(W0,szDzozmdt0(xN))
& aSubsetOf0(W1,szDzozmdt0(xN))
& ( W0 != slbdtrb0(sz00) )
& ( W1 != slbdtrb0(sz00) ) ) ) )),
( ( ( szmzizndt0(W0) = szmzizndt0(W1) )
| ~ ( aElementOf0(szmzizndt0(W0),W1)
& aElementOf0(szmzizndt0(W1),W0) )
| ~ ( aSubsetOf0(W0,szNzAzT0)
& aSubsetOf0(W1,szNzAzT0)
& ( W0 != slcrc0 )
& ( W1 != slcrc0 ) ) )
<=> ( ( szmzizndt0(W0) = szmzizndt0(W1) )
| ~ ( aElementOf0(szmzizndt0(W0),W1)
& aElementOf0(szmzizndt0(W1),W0) )
| ~ ( aSubsetOf0(W0,szDzozmdt0(xN))
& aSubsetOf0(W1,szDzozmdt0(xN))
& ( W0 != slbdtrb0(sz00) )
& ( W1 != slbdtrb0(sz00) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(76,plain,
( ! [W0: $i,W1: $i] :
( ( szmzizndt0(W0) = szmzizndt0(W1) )
| ~ ( aElementOf0(szmzizndt0(W0),W1)
& aElementOf0(szmzizndt0(W1),W0) )
| ~ ( aSubsetOf0(W0,szNzAzT0)
& aSubsetOf0(W1,szNzAzT0)
& ( W0 != slcrc0 )
& ( W1 != slcrc0 ) ) )
<=> ! [W0: $i,W1: $i] :
( ( szmzizndt0(W0) = szmzizndt0(W1) )
| ~ ( aElementOf0(szmzizndt0(W0),W1)
& aElementOf0(szmzizndt0(W1),W0) )
| ~ ( aSubsetOf0(W0,szDzozmdt0(xN))
& aSubsetOf0(W1,szDzozmdt0(xN))
& ( W0 != slbdtrb0(sz00) )
& ( W1 != slbdtrb0(sz00) ) ) ) ),
inference(quant_intro,[status(thm)],[75]) ).
tff(77,plain,
( ! [W0: $i,W1: $i] :
( ( szmzizndt0(W0) = szmzizndt0(W1) )
| ~ ( aElementOf0(szmzizndt0(W0),W1)
& aElementOf0(szmzizndt0(W1),W0) )
| ~ ( aSubsetOf0(W0,szNzAzT0)
& aSubsetOf0(W1,szNzAzT0)
& ( W0 != slcrc0 )
& ( W1 != slcrc0 ) ) )
<=> ! [W0: $i,W1: $i] :
( ( szmzizndt0(W0) = szmzizndt0(W1) )
| ~ ( aElementOf0(szmzizndt0(W0),W1)
& aElementOf0(szmzizndt0(W1),W0) )
| ~ ( aSubsetOf0(W0,szNzAzT0)
& aSubsetOf0(W1,szNzAzT0)
& ( W0 != slcrc0 )
& ( W1 != slcrc0 ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(78,plain,
^ [W0: $i,W1: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( aSubsetOf0(W0,szNzAzT0)
& aSubsetOf0(W1,szNzAzT0)
& ( W0 != slcrc0 ) )
<=> ( aSubsetOf0(W0,szNzAzT0)
& aSubsetOf0(W1,szNzAzT0)
& ( W0 != slcrc0 ) ) )),
( ( aSubsetOf0(W0,szNzAzT0)
& aSubsetOf0(W1,szNzAzT0)
& ( W0 != slcrc0 )
& ( W1 != slcrc0 ) )
<=> ( aSubsetOf0(W0,szNzAzT0)
& aSubsetOf0(W1,szNzAzT0)
& ( W0 != slcrc0 )
& ( W1 != slcrc0 ) ) )),
rewrite(
( ( aSubsetOf0(W0,szNzAzT0)
& aSubsetOf0(W1,szNzAzT0)
& ( W0 != slcrc0 )
& ( W1 != slcrc0 ) )
<=> ( aSubsetOf0(W0,szNzAzT0)
& aSubsetOf0(W1,szNzAzT0)
& ( W0 != slcrc0 )
& ( W1 != slcrc0 ) ) )),
( ( aSubsetOf0(W0,szNzAzT0)
& aSubsetOf0(W1,szNzAzT0)
& ( W0 != slcrc0 )
& ( W1 != slcrc0 ) )
<=> ( aSubsetOf0(W0,szNzAzT0)
& aSubsetOf0(W1,szNzAzT0)
& ( W0 != slcrc0 )
& ( W1 != slcrc0 ) ) )),
rewrite(
( ( ( aElementOf0(szmzizndt0(W0),W1)
& aElementOf0(szmzizndt0(W1),W0) )
=> ( szmzizndt0(W0) = szmzizndt0(W1) ) )
<=> ( ~ ( aElementOf0(szmzizndt0(W0),W1)
& aElementOf0(szmzizndt0(W1),W0) )
| ( szmzizndt0(W0) = szmzizndt0(W1) ) ) )),
( ( ( aSubsetOf0(W0,szNzAzT0)
& aSubsetOf0(W1,szNzAzT0)
& ( W0 != slcrc0 )
& ( W1 != slcrc0 ) )
=> ( ( aElementOf0(szmzizndt0(W0),W1)
& aElementOf0(szmzizndt0(W1),W0) )
=> ( szmzizndt0(W0) = szmzizndt0(W1) ) ) )
<=> ( ( aSubsetOf0(W0,szNzAzT0)
& aSubsetOf0(W1,szNzAzT0)
& ( W0 != slcrc0 )
& ( W1 != slcrc0 ) )
=> ( ~ ( aElementOf0(szmzizndt0(W0),W1)
& aElementOf0(szmzizndt0(W1),W0) )
| ( szmzizndt0(W0) = szmzizndt0(W1) ) ) ) )),
rewrite(
( ( ( aSubsetOf0(W0,szNzAzT0)
& aSubsetOf0(W1,szNzAzT0)
& ( W0 != slcrc0 )
& ( W1 != slcrc0 ) )
=> ( ~ ( aElementOf0(szmzizndt0(W0),W1)
& aElementOf0(szmzizndt0(W1),W0) )
| ( szmzizndt0(W0) = szmzizndt0(W1) ) ) )
<=> ( ( szmzizndt0(W0) = szmzizndt0(W1) )
| ~ ( aElementOf0(szmzizndt0(W0),W1)
& aElementOf0(szmzizndt0(W1),W0) )
| ~ ( aSubsetOf0(W0,szNzAzT0)
& aSubsetOf0(W1,szNzAzT0)
& ( W0 != slcrc0 )
& ( W1 != slcrc0 ) ) ) )),
( ( ( aSubsetOf0(W0,szNzAzT0)
& aSubsetOf0(W1,szNzAzT0)
& ( W0 != slcrc0 )
& ( W1 != slcrc0 ) )
=> ( ( aElementOf0(szmzizndt0(W0),W1)
& aElementOf0(szmzizndt0(W1),W0) )
=> ( szmzizndt0(W0) = szmzizndt0(W1) ) ) )
<=> ( ( szmzizndt0(W0) = szmzizndt0(W1) )
| ~ ( aElementOf0(szmzizndt0(W0),W1)
& aElementOf0(szmzizndt0(W1),W0) )
| ~ ( aSubsetOf0(W0,szNzAzT0)
& aSubsetOf0(W1,szNzAzT0)
& ( W0 != slcrc0 )
& ( W1 != slcrc0 ) ) ) )),
inference(bind,[status(th)],]) ).
tff(79,plain,
( ! [W0: $i,W1: $i] :
( ( aSubsetOf0(W0,szNzAzT0)
& aSubsetOf0(W1,szNzAzT0)
& ( W0 != slcrc0 )
& ( W1 != slcrc0 ) )
=> ( ( aElementOf0(szmzizndt0(W0),W1)
& aElementOf0(szmzizndt0(W1),W0) )
=> ( szmzizndt0(W0) = szmzizndt0(W1) ) ) )
<=> ! [W0: $i,W1: $i] :
( ( szmzizndt0(W0) = szmzizndt0(W1) )
| ~ ( aElementOf0(szmzizndt0(W0),W1)
& aElementOf0(szmzizndt0(W1),W0) )
| ~ ( aSubsetOf0(W0,szNzAzT0)
& aSubsetOf0(W1,szNzAzT0)
& ( W0 != slcrc0 )
& ( W1 != slcrc0 ) ) ) ),
inference(quant_intro,[status(thm)],[78]) ).
tff(80,axiom,
! [W0: $i,W1: $i] :
( ( aSubsetOf0(W0,szNzAzT0)
& aSubsetOf0(W1,szNzAzT0)
& ( W0 != slcrc0 )
& ( W1 != slcrc0 ) )
=> ( ( aElementOf0(szmzizndt0(W0),W1)
& aElementOf0(szmzizndt0(W1),W0) )
=> ( szmzizndt0(W0) = szmzizndt0(W1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMinMin) ).
tff(81,plain,
! [W0: $i,W1: $i] :
( ( szmzizndt0(W0) = szmzizndt0(W1) )
| ~ ( aElementOf0(szmzizndt0(W0),W1)
& aElementOf0(szmzizndt0(W1),W0) )
| ~ ( aSubsetOf0(W0,szNzAzT0)
& aSubsetOf0(W1,szNzAzT0)
& ( W0 != slcrc0 )
& ( W1 != slcrc0 ) ) ),
inference(modus_ponens,[status(thm)],[80,79]) ).
tff(82,plain,
! [W0: $i,W1: $i] :
( ( szmzizndt0(W0) = szmzizndt0(W1) )
| ~ ( aElementOf0(szmzizndt0(W0),W1)
& aElementOf0(szmzizndt0(W1),W0) )
| ~ ( aSubsetOf0(W0,szNzAzT0)
& aSubsetOf0(W1,szNzAzT0)
& ( W0 != slcrc0 )
& ( W1 != slcrc0 ) ) ),
inference(modus_ponens,[status(thm)],[81,77]) ).
tff(83,plain,
! [W0: $i,W1: $i] :
( ( szmzizndt0(W0) = szmzizndt0(W1) )
| ~ ( aElementOf0(szmzizndt0(W0),W1)
& aElementOf0(szmzizndt0(W1),W0) )
| ~ ( aSubsetOf0(W0,szDzozmdt0(xN))
& aSubsetOf0(W1,szDzozmdt0(xN))
& ( W0 != slbdtrb0(sz00) )
& ( W1 != slbdtrb0(sz00) ) ) ),
inference(modus_ponens,[status(thm)],[82,76]) ).
tff(84,plain,
! [W0: $i,W1: $i] :
( ( szmzizndt0(W0) = szmzizndt0(W1) )
| ~ ( aElementOf0(szmzizndt0(W0),W1)
& aElementOf0(szmzizndt0(W1),W0) )
| ~ ( aSubsetOf0(W0,szDzozmdt0(xN))
& aSubsetOf0(W1,szDzozmdt0(xN))
& ( W0 != slbdtrb0(sz00) )
& ( W1 != slbdtrb0(sz00) ) ) ),
inference(skolemize,[status(sab)],[83]) ).
tff(85,plain,
! [W0: $i,W1: $i] :
( ( szmzizndt0(W0) = szmzizndt0(W1) )
| ( W1 = slbdtrb0(sz00) )
| ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(szmzizndt0(W0),W1)
| ~ aElementOf0(szmzizndt0(W1),W0)
| ~ aSubsetOf0(W0,szDzozmdt0(xN)) ),
inference(modus_ponens,[status(thm)],[84,74]) ).
tff(86,plain,
! [W0: $i,W1: $i] :
( ( szmzizndt0(W0) = szmzizndt0(W1) )
| ( W1 = slbdtrb0(sz00) )
| ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(szmzizndt0(W0),W1)
| ~ aElementOf0(szmzizndt0(W1),W0)
| ~ aSubsetOf0(W0,szDzozmdt0(xN)) ),
inference(modus_ponens,[status(thm)],[85,72]) ).
tff(87,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( szmzizndt0(W0) = szmzizndt0(W1) )
| ( W1 = slbdtrb0(sz00) )
| ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(szmzizndt0(W0),W1)
| ~ aElementOf0(szmzizndt0(W1),W0)
| ~ aSubsetOf0(W0,szDzozmdt0(xN)) )
| ( xQ = slbdtrb0(sz00) )
| ( sdtlpdtrp0(xN,xm) = slbdtrb0(sz00) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szDzozmdt0(xN))
| ( szmzizndt0(sdtlpdtrp0(xN,xm)) = szmzizndt0(xQ) )
| ~ aSubsetOf0(xQ,szDzozmdt0(xN))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xm)),xQ)
| ~ aElementOf0(szmzizndt0(xQ),sdtlpdtrp0(xN,xm)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( szmzizndt0(W0) = szmzizndt0(W1) )
| ( W1 = slbdtrb0(sz00) )
| ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(szmzizndt0(W0),W1)
| ~ aElementOf0(szmzizndt0(W1),W0)
| ~ aSubsetOf0(W0,szDzozmdt0(xN)) )
| ( xQ = slbdtrb0(sz00) )
| ( sdtlpdtrp0(xN,xm) = slbdtrb0(sz00) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szDzozmdt0(xN))
| ( szmzizndt0(sdtlpdtrp0(xN,xm)) = szmzizndt0(xQ) )
| ~ aSubsetOf0(xQ,szDzozmdt0(xN))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xm)),xQ)
| ~ aElementOf0(szmzizndt0(xQ),sdtlpdtrp0(xN,xm)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(88,plain,
( ( ( szmzizndt0(sdtlpdtrp0(xN,xm)) = szmzizndt0(xQ) )
| ( xQ = slbdtrb0(sz00) )
| ( sdtlpdtrp0(xN,xm) = slbdtrb0(sz00) )
| ~ aSubsetOf0(xQ,szDzozmdt0(xN))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xm)),xQ)
| ~ aElementOf0(szmzizndt0(xQ),sdtlpdtrp0(xN,xm))
| ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szDzozmdt0(xN)) )
<=> ( ( xQ = slbdtrb0(sz00) )
| ( sdtlpdtrp0(xN,xm) = slbdtrb0(sz00) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szDzozmdt0(xN))
| ( szmzizndt0(sdtlpdtrp0(xN,xm)) = szmzizndt0(xQ) )
| ~ aSubsetOf0(xQ,szDzozmdt0(xN))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xm)),xQ)
| ~ aElementOf0(szmzizndt0(xQ),sdtlpdtrp0(xN,xm)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(89,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( szmzizndt0(W0) = szmzizndt0(W1) )
| ( W1 = slbdtrb0(sz00) )
| ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(szmzizndt0(W0),W1)
| ~ aElementOf0(szmzizndt0(W1),W0)
| ~ aSubsetOf0(W0,szDzozmdt0(xN)) )
| ( szmzizndt0(sdtlpdtrp0(xN,xm)) = szmzizndt0(xQ) )
| ( xQ = slbdtrb0(sz00) )
| ( sdtlpdtrp0(xN,xm) = slbdtrb0(sz00) )
| ~ aSubsetOf0(xQ,szDzozmdt0(xN))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xm)),xQ)
| ~ aElementOf0(szmzizndt0(xQ),sdtlpdtrp0(xN,xm))
| ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szDzozmdt0(xN)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( szmzizndt0(W0) = szmzizndt0(W1) )
| ( W1 = slbdtrb0(sz00) )
| ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(szmzizndt0(W0),W1)
| ~ aElementOf0(szmzizndt0(W1),W0)
| ~ aSubsetOf0(W0,szDzozmdt0(xN)) )
| ( xQ = slbdtrb0(sz00) )
| ( sdtlpdtrp0(xN,xm) = slbdtrb0(sz00) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szDzozmdt0(xN))
| ( szmzizndt0(sdtlpdtrp0(xN,xm)) = szmzizndt0(xQ) )
| ~ aSubsetOf0(xQ,szDzozmdt0(xN))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xm)),xQ)
| ~ aElementOf0(szmzizndt0(xQ),sdtlpdtrp0(xN,xm)) ) ),
inference(monotonicity,[status(thm)],[88]) ).
tff(90,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( szmzizndt0(W0) = szmzizndt0(W1) )
| ( W1 = slbdtrb0(sz00) )
| ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(szmzizndt0(W0),W1)
| ~ aElementOf0(szmzizndt0(W1),W0)
| ~ aSubsetOf0(W0,szDzozmdt0(xN)) )
| ( szmzizndt0(sdtlpdtrp0(xN,xm)) = szmzizndt0(xQ) )
| ( xQ = slbdtrb0(sz00) )
| ( sdtlpdtrp0(xN,xm) = slbdtrb0(sz00) )
| ~ aSubsetOf0(xQ,szDzozmdt0(xN))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xm)),xQ)
| ~ aElementOf0(szmzizndt0(xQ),sdtlpdtrp0(xN,xm))
| ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szDzozmdt0(xN)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( szmzizndt0(W0) = szmzizndt0(W1) )
| ( W1 = slbdtrb0(sz00) )
| ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(szmzizndt0(W0),W1)
| ~ aElementOf0(szmzizndt0(W1),W0)
| ~ aSubsetOf0(W0,szDzozmdt0(xN)) )
| ( xQ = slbdtrb0(sz00) )
| ( sdtlpdtrp0(xN,xm) = slbdtrb0(sz00) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szDzozmdt0(xN))
| ( szmzizndt0(sdtlpdtrp0(xN,xm)) = szmzizndt0(xQ) )
| ~ aSubsetOf0(xQ,szDzozmdt0(xN))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xm)),xQ)
| ~ aElementOf0(szmzizndt0(xQ),sdtlpdtrp0(xN,xm)) ) ),
inference(transitivity,[status(thm)],[89,87]) ).
tff(91,plain,
( ~ ! [W0: $i,W1: $i] :
( ( szmzizndt0(W0) = szmzizndt0(W1) )
| ( W1 = slbdtrb0(sz00) )
| ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(szmzizndt0(W0),W1)
| ~ aElementOf0(szmzizndt0(W1),W0)
| ~ aSubsetOf0(W0,szDzozmdt0(xN)) )
| ( szmzizndt0(sdtlpdtrp0(xN,xm)) = szmzizndt0(xQ) )
| ( xQ = slbdtrb0(sz00) )
| ( sdtlpdtrp0(xN,xm) = slbdtrb0(sz00) )
| ~ aSubsetOf0(xQ,szDzozmdt0(xN))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xm)),xQ)
| ~ aElementOf0(szmzizndt0(xQ),sdtlpdtrp0(xN,xm))
| ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szDzozmdt0(xN)) ),
inference(quant_inst,[status(thm)],]) ).
tff(92,plain,
( ~ ! [W0: $i,W1: $i] :
( ( szmzizndt0(W0) = szmzizndt0(W1) )
| ( W1 = slbdtrb0(sz00) )
| ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(szmzizndt0(W0),W1)
| ~ aElementOf0(szmzizndt0(W1),W0)
| ~ aSubsetOf0(W0,szDzozmdt0(xN)) )
| ( xQ = slbdtrb0(sz00) )
| ( sdtlpdtrp0(xN,xm) = slbdtrb0(sz00) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szDzozmdt0(xN))
| ( szmzizndt0(sdtlpdtrp0(xN,xm)) = szmzizndt0(xQ) )
| ~ aSubsetOf0(xQ,szDzozmdt0(xN))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xm)),xQ)
| ~ aElementOf0(szmzizndt0(xQ),sdtlpdtrp0(xN,xm)) ),
inference(modus_ponens,[status(thm)],[91,90]) ).
tff(93,plain,
( ( sdtlpdtrp0(xN,xm) = slbdtrb0(sz00) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szDzozmdt0(xN))
| ( szmzizndt0(sdtlpdtrp0(xN,xm)) = szmzizndt0(xQ) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xm)),xQ) ),
inference(unit_resolution,[status(thm)],[92,86,70,64,59]) ).
tff(94,plain,
sdtlpdtrp0(xN,xm) = slbdtrb0(sz00),
inference(unit_resolution,[status(thm)],[93,54,43,15]) ).
tff(95,plain,
( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,xm))
| isCountable0(sdtlpdtrp0(xN,xm)) ),
inference(tautology,[status(thm)],]) ).
tff(96,plain,
isCountable0(sdtlpdtrp0(xN,xm)),
inference(unit_resolution,[status(thm)],[95,41]) ).
tff(97,plain,
^ [W0: $i] :
refl(
( ( ~ aSet0(W0)
| ( W0 != slbdtrb0(sz00) )
| ~ isCountable0(W0) )
<=> ( ~ aSet0(W0)
| ( W0 != slbdtrb0(sz00) )
| ~ isCountable0(W0) ) )),
inference(bind,[status(th)],]) ).
tff(98,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ( W0 != slbdtrb0(sz00) )
| ~ isCountable0(W0) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ( W0 != slbdtrb0(sz00) )
| ~ isCountable0(W0) ) ),
inference(quant_intro,[status(thm)],[97]) ).
tff(99,plain,
^ [W0: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( aSet0(W0)
& isCountable0(W0) )
<=> ~ ( ~ aSet0(W0)
| ~ isCountable0(W0) ) )),
( ~ ( aSet0(W0)
& isCountable0(W0) )
<=> ~ ~ ( ~ aSet0(W0)
| ~ isCountable0(W0) ) )),
rewrite(
( ~ ~ ( ~ aSet0(W0)
| ~ isCountable0(W0) )
<=> ( ~ aSet0(W0)
| ~ isCountable0(W0) ) )),
( ~ ( aSet0(W0)
& isCountable0(W0) )
<=> ( ~ aSet0(W0)
| ~ isCountable0(W0) ) )),
( ( ( W0 != slbdtrb0(sz00) )
| ~ ( aSet0(W0)
& isCountable0(W0) ) )
<=> ( ( W0 != slbdtrb0(sz00) )
| ~ aSet0(W0)
| ~ isCountable0(W0) ) )),
rewrite(
( ( ( W0 != slbdtrb0(sz00) )
| ~ aSet0(W0)
| ~ isCountable0(W0) )
<=> ( ~ aSet0(W0)
| ( W0 != slbdtrb0(sz00) )
| ~ isCountable0(W0) ) )),
( ( ( W0 != slbdtrb0(sz00) )
| ~ ( aSet0(W0)
& isCountable0(W0) ) )
<=> ( ~ aSet0(W0)
| ( W0 != slbdtrb0(sz00) )
| ~ isCountable0(W0) ) )),
inference(bind,[status(th)],]) ).
tff(100,plain,
( ! [W0: $i] :
( ( W0 != slbdtrb0(sz00) )
| ~ ( aSet0(W0)
& isCountable0(W0) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ( W0 != slbdtrb0(sz00) )
| ~ isCountable0(W0) ) ),
inference(quant_intro,[status(thm)],[99]) ).
tff(101,plain,
^ [W0: $i] :
rewrite(
( ( ( W0 != slcrc0 )
| ~ ( aSet0(W0)
& isCountable0(W0) ) )
<=> ( ( W0 != slbdtrb0(sz00) )
| ~ ( aSet0(W0)
& isCountable0(W0) ) ) )),
inference(bind,[status(th)],]) ).
tff(102,plain,
( ! [W0: $i] :
( ( W0 != slcrc0 )
| ~ ( aSet0(W0)
& isCountable0(W0) ) )
<=> ! [W0: $i] :
( ( W0 != slbdtrb0(sz00) )
| ~ ( aSet0(W0)
& isCountable0(W0) ) ) ),
inference(quant_intro,[status(thm)],[101]) ).
tff(103,plain,
( ! [W0: $i] :
( ( W0 != slcrc0 )
| ~ ( aSet0(W0)
& isCountable0(W0) ) )
<=> ! [W0: $i] :
( ( W0 != slcrc0 )
| ~ ( aSet0(W0)
& isCountable0(W0) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(104,plain,
^ [W0: $i] :
rewrite(
( ( ( aSet0(W0)
& isCountable0(W0) )
=> ( W0 != slcrc0 ) )
<=> ( ( W0 != slcrc0 )
| ~ ( aSet0(W0)
& isCountable0(W0) ) ) )),
inference(bind,[status(th)],]) ).
tff(105,plain,
( ! [W0: $i] :
( ( aSet0(W0)
& isCountable0(W0) )
=> ( W0 != slcrc0 ) )
<=> ! [W0: $i] :
( ( W0 != slcrc0 )
| ~ ( aSet0(W0)
& isCountable0(W0) ) ) ),
inference(quant_intro,[status(thm)],[104]) ).
tff(106,axiom,
! [W0: $i] :
( ( aSet0(W0)
& isCountable0(W0) )
=> ( W0 != slcrc0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCountNFin_01) ).
tff(107,plain,
! [W0: $i] :
( ( W0 != slcrc0 )
| ~ ( aSet0(W0)
& isCountable0(W0) ) ),
inference(modus_ponens,[status(thm)],[106,105]) ).
tff(108,plain,
! [W0: $i] :
( ( W0 != slcrc0 )
| ~ ( aSet0(W0)
& isCountable0(W0) ) ),
inference(modus_ponens,[status(thm)],[107,103]) ).
tff(109,plain,
! [W0: $i] :
( ( W0 != slbdtrb0(sz00) )
| ~ ( aSet0(W0)
& isCountable0(W0) ) ),
inference(modus_ponens,[status(thm)],[108,102]) ).
tff(110,plain,
! [W0: $i] :
( ( W0 != slbdtrb0(sz00) )
| ~ ( aSet0(W0)
& isCountable0(W0) ) ),
inference(skolemize,[status(sab)],[109]) ).
tff(111,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ( W0 != slbdtrb0(sz00) )
| ~ isCountable0(W0) ),
inference(modus_ponens,[status(thm)],[110,100]) ).
tff(112,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ( W0 != slbdtrb0(sz00) )
| ~ isCountable0(W0) ),
inference(modus_ponens,[status(thm)],[111,98]) ).
tff(113,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( W0 != slbdtrb0(sz00) )
| ~ isCountable0(W0) )
| ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ isCountable0(sdtlpdtrp0(xN,xm))
| ( sdtlpdtrp0(xN,xm) != slbdtrb0(sz00) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( W0 != slbdtrb0(sz00) )
| ~ isCountable0(W0) )
| ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ isCountable0(sdtlpdtrp0(xN,xm))
| ( sdtlpdtrp0(xN,xm) != slbdtrb0(sz00) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(114,plain,
( ( ~ aSet0(sdtlpdtrp0(xN,xm))
| ( sdtlpdtrp0(xN,xm) != slbdtrb0(sz00) )
| ~ isCountable0(sdtlpdtrp0(xN,xm)) )
<=> ( ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ isCountable0(sdtlpdtrp0(xN,xm))
| ( sdtlpdtrp0(xN,xm) != slbdtrb0(sz00) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(115,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( W0 != slbdtrb0(sz00) )
| ~ isCountable0(W0) )
| ~ aSet0(sdtlpdtrp0(xN,xm))
| ( sdtlpdtrp0(xN,xm) != slbdtrb0(sz00) )
| ~ isCountable0(sdtlpdtrp0(xN,xm)) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( W0 != slbdtrb0(sz00) )
| ~ isCountable0(W0) )
| ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ isCountable0(sdtlpdtrp0(xN,xm))
| ( sdtlpdtrp0(xN,xm) != slbdtrb0(sz00) ) ) ),
inference(monotonicity,[status(thm)],[114]) ).
tff(116,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( W0 != slbdtrb0(sz00) )
| ~ isCountable0(W0) )
| ~ aSet0(sdtlpdtrp0(xN,xm))
| ( sdtlpdtrp0(xN,xm) != slbdtrb0(sz00) )
| ~ isCountable0(sdtlpdtrp0(xN,xm)) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( W0 != slbdtrb0(sz00) )
| ~ isCountable0(W0) )
| ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ isCountable0(sdtlpdtrp0(xN,xm))
| ( sdtlpdtrp0(xN,xm) != slbdtrb0(sz00) ) ) ),
inference(transitivity,[status(thm)],[115,113]) ).
tff(117,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( W0 != slbdtrb0(sz00) )
| ~ isCountable0(W0) )
| ~ aSet0(sdtlpdtrp0(xN,xm))
| ( sdtlpdtrp0(xN,xm) != slbdtrb0(sz00) )
| ~ isCountable0(sdtlpdtrp0(xN,xm)) ),
inference(quant_inst,[status(thm)],]) ).
tff(118,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( W0 != slbdtrb0(sz00) )
| ~ isCountable0(W0) )
| ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ isCountable0(sdtlpdtrp0(xN,xm))
| ( sdtlpdtrp0(xN,xm) != slbdtrb0(sz00) ) ),
inference(modus_ponens,[status(thm)],[117,116]) ).
tff(119,plain,
( ~ aSet0(sdtlpdtrp0(xN,xm))
| ( sdtlpdtrp0(xN,xm) != slbdtrb0(sz00) ) ),
inference(unit_resolution,[status(thm)],[118,112,96]) ).
tff(120,plain,
~ aSet0(sdtlpdtrp0(xN,xm)),
inference(unit_resolution,[status(thm)],[119,94]) ).
tff(121,plain,
( aSet0(szNzAzT0)
<=> aSet0(szDzozmdt0(xN)) ),
inference(rewrite,[status(thm)],]) ).
tff(122,plain,
( aSet0(szNzAzT0)
<=> aSet0(szNzAzT0) ),
inference(rewrite,[status(thm)],]) ).
tff(123,axiom,
( aSet0(szNzAzT0)
& isCountable0(szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNATSet) ).
tff(124,plain,
aSet0(szNzAzT0),
inference(and_elim,[status(thm)],[123]) ).
tff(125,plain,
aSet0(szNzAzT0),
inference(modus_ponens,[status(thm)],[124,122]) ).
tff(126,plain,
aSet0(szDzozmdt0(xN)),
inference(modus_ponens,[status(thm)],[125,121]) ).
tff(127,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(128,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)],[127]) ).
tff(129,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(130,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)],[129]) ).
tff(131,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(132,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)],[131]) ).
tff(133,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)],[132,130]) ).
tff(134,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(135,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)],[134]) ).
tff(136,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(137,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)],[136]) ).
tff(138,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(139,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(140,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)],[139]) ).
tff(141,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(142,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)],[141,140]) ).
tff(143,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)],[142,138]) ).
tff(144,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)],[143]) ).
tff(145,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)],[144,137]) ).
tff(146,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)],[145,135]) ).
tff(147,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)],[146,133]) ).
tff(148,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)],[147,128]) ).
tff(149,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(szDzozmdt0(xN))
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),W1)
| aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),szDzozmdt0(xN)) ) )
| ~ ( ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(szDzozmdt0(xN))
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),W1)
| aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),szDzozmdt0(xN)) ) )
| ~ ( ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(150,plain,
( ( ~ aSet0(szDzozmdt0(xN))
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,szDzozmdt0(xN))
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),W1)
| aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),szDzozmdt0(xN)) ) )
| ~ ( ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ) ) )
<=> ( ~ aSet0(szDzozmdt0(xN))
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),W1)
| aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),szDzozmdt0(xN)) ) )
| ~ ( ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(151,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(szDzozmdt0(xN))
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,szDzozmdt0(xN))
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),W1)
| aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),szDzozmdt0(xN)) ) )
| ~ ( ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(szDzozmdt0(xN))
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),W1)
| aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),szDzozmdt0(xN)) ) )
| ~ ( ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[150]) ).
tff(152,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(szDzozmdt0(xN))
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,szDzozmdt0(xN))
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),W1)
| aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),szDzozmdt0(xN)) ) )
| ~ ( ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(szDzozmdt0(xN))
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),W1)
| aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),szDzozmdt0(xN)) ) )
| ~ ( ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[151,149]) ).
tff(153,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(szDzozmdt0(xN))
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,szDzozmdt0(xN))
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),W1)
| aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),szDzozmdt0(xN)) ) )
| ~ ( ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(154,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(szDzozmdt0(xN))
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),W1)
| aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),szDzozmdt0(xN)) ) )
| ~ ( ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[153,152]) ).
tff(155,plain,
! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),W1)
| aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),szDzozmdt0(xN)) ) )
| ~ ( ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ) ),
inference(unit_resolution,[status(thm)],[154,148,126]) ).
tff(156,plain,
( ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),W1)
| aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),szDzozmdt0(xN)) ) )
| ~ ( ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ) )
| ~ ( ~ ( aSubsetOf0(sdtlpdtrp0(xN,xm),szDzozmdt0(xN))
| ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,xm),szDzozmdt0(xN)),sdtlpdtrp0(xN,xm))
| aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,xm),szDzozmdt0(xN)),szDzozmdt0(xN)) ) )
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xm))
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ) ) )
<=> ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),W1)
| aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),szDzozmdt0(xN)) ) )
| ~ ( ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ) )
| ~ ( ~ ( aSubsetOf0(sdtlpdtrp0(xN,xm),szDzozmdt0(xN))
| ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,xm),szDzozmdt0(xN)),sdtlpdtrp0(xN,xm))
| aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,xm),szDzozmdt0(xN)),szDzozmdt0(xN)) ) )
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xm))
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(157,plain,
( ~ ( ~ ( ~ aSet0(sdtlpdtrp0(xN,xm))
| aSubsetOf0(sdtlpdtrp0(xN,xm),szDzozmdt0(xN))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,xm),szDzozmdt0(xN)),sdtlpdtrp0(xN,xm))
| aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,xm),szDzozmdt0(xN)),szDzozmdt0(xN)) ) )
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xm))
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ) )
<=> ~ ( ~ ( aSubsetOf0(sdtlpdtrp0(xN,xm),szDzozmdt0(xN))
| ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,xm),szDzozmdt0(xN)),sdtlpdtrp0(xN,xm))
| aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,xm),szDzozmdt0(xN)),szDzozmdt0(xN)) ) )
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xm))
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(158,plain,
( ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),W1)
| aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),szDzozmdt0(xN)) ) )
| ~ ( ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ) )
| ~ ( ~ ( ~ aSet0(sdtlpdtrp0(xN,xm))
| aSubsetOf0(sdtlpdtrp0(xN,xm),szDzozmdt0(xN))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,xm),szDzozmdt0(xN)),sdtlpdtrp0(xN,xm))
| aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,xm),szDzozmdt0(xN)),szDzozmdt0(xN)) ) )
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xm))
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ) ) )
<=> ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),W1)
| aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),szDzozmdt0(xN)) ) )
| ~ ( ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ) )
| ~ ( ~ ( aSubsetOf0(sdtlpdtrp0(xN,xm),szDzozmdt0(xN))
| ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,xm),szDzozmdt0(xN)),sdtlpdtrp0(xN,xm))
| aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,xm),szDzozmdt0(xN)),szDzozmdt0(xN)) ) )
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xm))
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[157]) ).
tff(159,plain,
( ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),W1)
| aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),szDzozmdt0(xN)) ) )
| ~ ( ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ) )
| ~ ( ~ ( ~ aSet0(sdtlpdtrp0(xN,xm))
| aSubsetOf0(sdtlpdtrp0(xN,xm),szDzozmdt0(xN))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,xm),szDzozmdt0(xN)),sdtlpdtrp0(xN,xm))
| aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,xm),szDzozmdt0(xN)),szDzozmdt0(xN)) ) )
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xm))
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ) ) )
<=> ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),W1)
| aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),szDzozmdt0(xN)) ) )
| ~ ( ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ) )
| ~ ( ~ ( aSubsetOf0(sdtlpdtrp0(xN,xm),szDzozmdt0(xN))
| ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,xm),szDzozmdt0(xN)),sdtlpdtrp0(xN,xm))
| aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,xm),szDzozmdt0(xN)),szDzozmdt0(xN)) ) )
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xm))
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[158,156]) ).
tff(160,plain,
( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),W1)
| aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),szDzozmdt0(xN)) ) )
| ~ ( ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ) )
| ~ ( ~ ( ~ aSet0(sdtlpdtrp0(xN,xm))
| aSubsetOf0(sdtlpdtrp0(xN,xm),szDzozmdt0(xN))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,xm),szDzozmdt0(xN)),sdtlpdtrp0(xN,xm))
| aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,xm),szDzozmdt0(xN)),szDzozmdt0(xN)) ) )
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xm))
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(161,plain,
( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),W1)
| aElementOf0(tptp_fun_W2_1(W1,szDzozmdt0(xN)),szDzozmdt0(xN)) ) )
| ~ ( ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ) )
| ~ ( ~ ( aSubsetOf0(sdtlpdtrp0(xN,xm),szDzozmdt0(xN))
| ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,xm),szDzozmdt0(xN)),sdtlpdtrp0(xN,xm))
| aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,xm),szDzozmdt0(xN)),szDzozmdt0(xN)) ) )
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xm))
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[160,159]) ).
tff(162,plain,
~ ( ~ ( aSubsetOf0(sdtlpdtrp0(xN,xm),szDzozmdt0(xN))
| ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,xm),szDzozmdt0(xN)),sdtlpdtrp0(xN,xm))
| aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,xm),szDzozmdt0(xN)),szDzozmdt0(xN)) ) )
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xm))
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ) ),
inference(unit_resolution,[status(thm)],[161,155]) ).
tff(163,plain,
( ~ ( aSubsetOf0(sdtlpdtrp0(xN,xm),szDzozmdt0(xN))
| ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,xm),szDzozmdt0(xN)),sdtlpdtrp0(xN,xm))
| aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,xm),szDzozmdt0(xN)),szDzozmdt0(xN)) ) )
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xm))
| aElementOf0(W2,szDzozmdt0(xN)) ) ) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xm))
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(164,plain,
( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xm))
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ),
inference(unit_resolution,[status(thm)],[163,162]) ).
tff(165,plain,
( ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xm))
| aElementOf0(W2,szDzozmdt0(xN)) ) ) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xm))
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(166,plain,
( ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xm))
| aElementOf0(W2,szDzozmdt0(xN)) ) ) )
| ~ ( ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xm))
| aElementOf0(W2,szDzozmdt0(xN)) ) ) ),
inference(unit_resolution,[status(thm)],[165,43]) ).
tff(167,plain,
~ ( ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xm))
| aElementOf0(W2,szDzozmdt0(xN)) ) ),
inference(unit_resolution,[status(thm)],[166,164]) ).
tff(168,plain,
( ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xm))
| aElementOf0(W2,szDzozmdt0(xN)) )
| aSet0(sdtlpdtrp0(xN,xm)) ),
inference(tautology,[status(thm)],]) ).
tff(169,plain,
$false,
inference(unit_resolution,[status(thm)],[168,167,120]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM623+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.33 % Computer : n018.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Fri Sep 2 12:31:13 EDT 2022
% 0.14/0.33 % CPUTime :
% 0.14/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.34 Usage: tptp [options] [-file:]file
% 0.14/0.34 -h, -? prints this message.
% 0.14/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.34 -m, -model generate model.
% 0.14/0.34 -p, -proof generate proof.
% 0.14/0.34 -c, -core generate unsat core of named formulas.
% 0.14/0.34 -st, -statistics display statistics.
% 0.14/0.34 -t:timeout set timeout (in second).
% 0.14/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.34 -<param>:<value> configuration parameter and value.
% 0.14/0.34 -o:<output-file> file to place output in.
% 0.48/0.54 % SZS status Theorem
% 0.48/0.54 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------