TSTP Solution File: NUM591+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM591+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n011.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 13:10:43 EDT 2022
% Result : Theorem 13.59s 8.65s
% Output : Proof 13.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 77
% Syntax : Number of formulae : 149 ( 36 unt; 25 typ; 0 def)
% Number of atoms : 1674 ( 302 equ)
% Maximal formula atoms : 48 ( 13 avg)
% Number of connectives : 2656 (1174 ~; 987 |; 369 &)
% ( 69 <=>; 57 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 8 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 68 ( 68 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 28 ( 16 >; 12 *; 0 +; 0 <<)
% Number of predicates : 18 ( 15 usr; 1 prp; 0-5 aty)
% Number of functors : 19 ( 19 usr; 9 con; 0-3 aty)
% Number of variables : 488 ( 353 !; 120 ?; 488 :)
% Comments :
%------------------------------------------------------------------------------
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(slbdtsldtrb0_type,type,
slbdtsldtrb0: ( $i * $i ) > $i ).
tff(xk_type,type,
xk: $i ).
tff(tptp_fun_W4_20_type,type,
tptp_fun_W4_20: ( $i * $i * $i ) > $i ).
tff(sdtmndt0_type,type,
sdtmndt0: ( $i * $i ) > $i ).
tff(szmzizndt0_type,type,
szmzizndt0: $i > $i ).
tff(sdtlpdtrp0_type,type,
sdtlpdtrp0: ( $i * $i ) > $i ).
tff(xi_type,type,
xi: $i ).
tff(xN_type,type,
xN: $i ).
tff(xC_type,type,
xC: $i ).
tff(tptp_fun_W2_21_type,type,
tptp_fun_W2_21: ( $i * $i ) > $i ).
tff(tptp_fun_W3_19_type,type,
tptp_fun_W3_19: ( $i * $i * $i ) > $i ).
tff(aSet0_type,type,
aSet0: $i > $o ).
tff(isCountable0_type,type,
isCountable0: $i > $o ).
tff(aSubsetOf0_type,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff(xT_type,type,
xT: $i ).
tff(szDzozmdt0_type,type,
szDzozmdt0: $i > $i ).
tff(iLess0_type,type,
iLess0: ( $i * $i ) > $o ).
tff(szszuzczcdt0_type,type,
szszuzczcdt0: $i > $i ).
tff(sdtlcdtrc0_type,type,
sdtlcdtrc0: ( $i * $i ) > $i ).
tff(aFunction0_type,type,
aFunction0: $i > $o ).
tff(szNzAzT0_type,type,
szNzAzT0: $i ).
tff(xK_type,type,
xK: $i ).
tff(xY_type,type,
xY: $i ).
tff(xd_type,type,
xd: $i ).
tff(1,plain,
( aElementOf0(xk,szNzAzT0)
<=> aElementOf0(xk,szDzozmdt0(xN)) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( aElementOf0(xk,szNzAzT0)
<=> aElementOf0(xk,szNzAzT0) ),
inference(rewrite,[status(thm)],]) ).
tff(3,axiom,
( aElementOf0(xk,szNzAzT0)
& ( szszuzczcdt0(xk) = xK ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3533) ).
tff(4,plain,
aElementOf0(xk,szNzAzT0),
inference(and_elim,[status(thm)],[3]) ).
tff(5,plain,
aElementOf0(xk,szNzAzT0),
inference(modus_ponens,[status(thm)],[4,2]) ).
tff(6,plain,
aElementOf0(xk,szDzozmdt0(xN)),
inference(modus_ponens,[status(thm)],[5,1]) ).
tff(7,plain,
^ [W0: $i] :
refl(
( ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ! [W2: $i] :
( ~ aFunction0(W2)
| ~ iLess0(W0,szszuzczcdt0(xk))
| ( szDzozmdt0(W2) != slbdtsldtrb0(W1,W0) )
| ~ aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT)
| ~ ( ~ aElementOf0(tptp_fun_W3_19(W2,W1,W0),xT)
| ~ aSubsetOf0(tptp_fun_W4_20(W2,W1,W0),W1)
| ~ isCountable0(tptp_fun_W4_20(W2,W1,W0))
| ~ ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(W2,W1,W0),W0))
| ( sdtlpdtrp0(W2,W5) = tptp_fun_W3_19(W2,W1,W0) ) ) ) ) ) )
<=> ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ! [W2: $i] :
( ~ aFunction0(W2)
| ~ iLess0(W0,szszuzczcdt0(xk))
| ( szDzozmdt0(W2) != slbdtsldtrb0(W1,W0) )
| ~ aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT)
| ~ ( ~ aElementOf0(tptp_fun_W3_19(W2,W1,W0),xT)
| ~ aSubsetOf0(tptp_fun_W4_20(W2,W1,W0),W1)
| ~ isCountable0(tptp_fun_W4_20(W2,W1,W0))
| ~ ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(W2,W1,W0),W0))
| ( sdtlpdtrp0(W2,W5) = tptp_fun_W3_19(W2,W1,W0) ) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(8,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ! [W2: $i] :
( ~ aFunction0(W2)
| ~ iLess0(W0,szszuzczcdt0(xk))
| ( szDzozmdt0(W2) != slbdtsldtrb0(W1,W0) )
| ~ aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT)
| ~ ( ~ aElementOf0(tptp_fun_W3_19(W2,W1,W0),xT)
| ~ aSubsetOf0(tptp_fun_W4_20(W2,W1,W0),W1)
| ~ isCountable0(tptp_fun_W4_20(W2,W1,W0))
| ~ ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(W2,W1,W0),W0))
| ( sdtlpdtrp0(W2,W5) = tptp_fun_W3_19(W2,W1,W0) ) ) ) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ! [W2: $i] :
( ~ aFunction0(W2)
| ~ iLess0(W0,szszuzczcdt0(xk))
| ( szDzozmdt0(W2) != slbdtsldtrb0(W1,W0) )
| ~ aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT)
| ~ ( ~ aElementOf0(tptp_fun_W3_19(W2,W1,W0),xT)
| ~ aSubsetOf0(tptp_fun_W4_20(W2,W1,W0),W1)
| ~ isCountable0(tptp_fun_W4_20(W2,W1,W0))
| ~ ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(W2,W1,W0),W0))
| ( sdtlpdtrp0(W2,W5) = tptp_fun_W3_19(W2,W1,W0) ) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
^ [W0: $i] :
rewrite(
( ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ! [W2: $i] :
( ~ aFunction0(W2)
| ~ iLess0(W0,szszuzczcdt0(xk))
| ( szDzozmdt0(W2) != slbdtsldtrb0(W1,W0) )
| ~ aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT)
| ~ ( ~ aElementOf0(tptp_fun_W3_19(W2,W1,W0),xT)
| ~ aSubsetOf0(tptp_fun_W4_20(W2,W1,W0),W1)
| ~ isCountable0(tptp_fun_W4_20(W2,W1,W0))
| ~ ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(W2,W1,W0),W0))
| ( sdtlpdtrp0(W2,W5) = tptp_fun_W3_19(W2,W1,W0) ) ) ) ) ) )
<=> ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ! [W2: $i] :
( ~ aFunction0(W2)
| ~ iLess0(W0,szszuzczcdt0(xk))
| ( szDzozmdt0(W2) != slbdtsldtrb0(W1,W0) )
| ~ aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT)
| ~ ( ~ aElementOf0(tptp_fun_W3_19(W2,W1,W0),xT)
| ~ aSubsetOf0(tptp_fun_W4_20(W2,W1,W0),W1)
| ~ isCountable0(tptp_fun_W4_20(W2,W1,W0))
| ~ ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(W2,W1,W0),W0))
| ( sdtlpdtrp0(W2,W5) = tptp_fun_W3_19(W2,W1,W0) ) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(10,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ! [W2: $i] :
( ~ aFunction0(W2)
| ~ iLess0(W0,szszuzczcdt0(xk))
| ( szDzozmdt0(W2) != slbdtsldtrb0(W1,W0) )
| ~ aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT)
| ~ ( ~ aElementOf0(tptp_fun_W3_19(W2,W1,W0),xT)
| ~ aSubsetOf0(tptp_fun_W4_20(W2,W1,W0),W1)
| ~ isCountable0(tptp_fun_W4_20(W2,W1,W0))
| ~ ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(W2,W1,W0),W0))
| ( sdtlpdtrp0(W2,W5) = tptp_fun_W3_19(W2,W1,W0) ) ) ) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ! [W2: $i] :
( ~ aFunction0(W2)
| ~ iLess0(W0,szszuzczcdt0(xk))
| ( szDzozmdt0(W2) != slbdtsldtrb0(W1,W0) )
| ~ aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT)
| ~ ( ~ aElementOf0(tptp_fun_W3_19(W2,W1,W0),xT)
| ~ aSubsetOf0(tptp_fun_W4_20(W2,W1,W0),W1)
| ~ isCountable0(tptp_fun_W4_20(W2,W1,W0))
| ~ ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(W2,W1,W0),W0))
| ( sdtlpdtrp0(W2,W5) = tptp_fun_W3_19(W2,W1,W0) ) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[9]) ).
tff(11,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ! [W2: $i] :
( ~ aFunction0(W2)
| ~ iLess0(W0,szszuzczcdt0(xk))
| ( szDzozmdt0(W2) != slbdtsldtrb0(W1,W0) )
| ~ aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT)
| ~ ( ~ aElementOf0(tptp_fun_W3_19(W2,W1,W0),xT)
| ~ aSubsetOf0(tptp_fun_W4_20(W2,W1,W0),W1)
| ~ isCountable0(tptp_fun_W4_20(W2,W1,W0))
| ~ ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(W2,W1,W0),W0))
| ( sdtlpdtrp0(W2,W5) = tptp_fun_W3_19(W2,W1,W0) ) ) ) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ! [W2: $i] :
( ~ aFunction0(W2)
| ~ iLess0(W0,szszuzczcdt0(xk))
| ( szDzozmdt0(W2) != slbdtsldtrb0(W1,W0) )
| ~ aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT)
| ~ ( ~ aElementOf0(tptp_fun_W3_19(W2,W1,W0),xT)
| ~ aSubsetOf0(tptp_fun_W4_20(W2,W1,W0),W1)
| ~ isCountable0(tptp_fun_W4_20(W2,W1,W0))
| ~ ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(W2,W1,W0),W0))
| ( sdtlpdtrp0(W2,W5) = tptp_fun_W3_19(W2,W1,W0) ) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[10,8]) ).
tff(12,plain,
^ [W0: $i] :
rewrite(
( ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ ( aSubsetOf0(W1,szDzozmdt0(xN))
& isCountable0(W1) )
| ! [W2: $i] :
( ~ ( aFunction0(W2)
& ( szDzozmdt0(W2) = slbdtsldtrb0(W1,W0) )
& aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT) )
| ~ iLess0(W0,szszuzczcdt0(xk))
| ( aElementOf0(tptp_fun_W3_19(W2,W1,W0),xT)
& aSubsetOf0(tptp_fun_W4_20(W2,W1,W0),W1)
& isCountable0(tptp_fun_W4_20(W2,W1,W0))
& ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(W2,W1,W0),W0))
| ( sdtlpdtrp0(W2,W5) = tptp_fun_W3_19(W2,W1,W0) ) ) ) ) ) )
<=> ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ! [W2: $i] :
( ~ aFunction0(W2)
| ~ iLess0(W0,szszuzczcdt0(xk))
| ( szDzozmdt0(W2) != slbdtsldtrb0(W1,W0) )
| ~ aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT)
| ~ ( ~ aElementOf0(tptp_fun_W3_19(W2,W1,W0),xT)
| ~ aSubsetOf0(tptp_fun_W4_20(W2,W1,W0),W1)
| ~ isCountable0(tptp_fun_W4_20(W2,W1,W0))
| ~ ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(W2,W1,W0),W0))
| ( sdtlpdtrp0(W2,W5) = tptp_fun_W3_19(W2,W1,W0) ) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(13,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ ( aSubsetOf0(W1,szDzozmdt0(xN))
& isCountable0(W1) )
| ! [W2: $i] :
( ~ ( aFunction0(W2)
& ( szDzozmdt0(W2) = slbdtsldtrb0(W1,W0) )
& aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT) )
| ~ iLess0(W0,szszuzczcdt0(xk))
| ( aElementOf0(tptp_fun_W3_19(W2,W1,W0),xT)
& aSubsetOf0(tptp_fun_W4_20(W2,W1,W0),W1)
& isCountable0(tptp_fun_W4_20(W2,W1,W0))
& ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(W2,W1,W0),W0))
| ( sdtlpdtrp0(W2,W5) = tptp_fun_W3_19(W2,W1,W0) ) ) ) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ! [W2: $i] :
( ~ aFunction0(W2)
| ~ iLess0(W0,szszuzczcdt0(xk))
| ( szDzozmdt0(W2) != slbdtsldtrb0(W1,W0) )
| ~ aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT)
| ~ ( ~ aElementOf0(tptp_fun_W3_19(W2,W1,W0),xT)
| ~ aSubsetOf0(tptp_fun_W4_20(W2,W1,W0),W1)
| ~ isCountable0(tptp_fun_W4_20(W2,W1,W0))
| ~ ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(W2,W1,W0),W0))
| ( sdtlpdtrp0(W2,W5) = tptp_fun_W3_19(W2,W1,W0) ) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[12]) ).
tff(14,plain,
^ [W0: $i] :
rewrite(
( ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ ( aSubsetOf0(W1,szDzozmdt0(xN))
& isCountable0(W1) )
| ! [W2: $i] :
( ( aElementOf0(tptp_fun_W3_19(W2,W1,W0),xT)
& aSubsetOf0(tptp_fun_W4_20(W2,W1,W0),W1)
& isCountable0(tptp_fun_W4_20(W2,W1,W0))
& ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(W2,W1,W0),W0))
| ( sdtlpdtrp0(W2,W5) = tptp_fun_W3_19(W2,W1,W0) ) ) )
| ~ ( aFunction0(W2)
& ( szDzozmdt0(W2) = slbdtsldtrb0(W1,W0) )
& aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT) )
| ~ iLess0(W0,szszuzczcdt0(xk)) ) ) )
<=> ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ ( aSubsetOf0(W1,szDzozmdt0(xN))
& isCountable0(W1) )
| ! [W2: $i] :
( ~ ( aFunction0(W2)
& ( szDzozmdt0(W2) = slbdtsldtrb0(W1,W0) )
& aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT) )
| ~ iLess0(W0,szszuzczcdt0(xk))
| ( aElementOf0(tptp_fun_W3_19(W2,W1,W0),xT)
& aSubsetOf0(tptp_fun_W4_20(W2,W1,W0),W1)
& isCountable0(tptp_fun_W4_20(W2,W1,W0))
& ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(W2,W1,W0),W0))
| ( sdtlpdtrp0(W2,W5) = tptp_fun_W3_19(W2,W1,W0) ) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(15,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ ( aSubsetOf0(W1,szDzozmdt0(xN))
& isCountable0(W1) )
| ! [W2: $i] :
( ( aElementOf0(tptp_fun_W3_19(W2,W1,W0),xT)
& aSubsetOf0(tptp_fun_W4_20(W2,W1,W0),W1)
& isCountable0(tptp_fun_W4_20(W2,W1,W0))
& ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(W2,W1,W0),W0))
| ( sdtlpdtrp0(W2,W5) = tptp_fun_W3_19(W2,W1,W0) ) ) )
| ~ ( aFunction0(W2)
& ( szDzozmdt0(W2) = slbdtsldtrb0(W1,W0) )
& aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT) )
| ~ iLess0(W0,szszuzczcdt0(xk)) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ ( aSubsetOf0(W1,szDzozmdt0(xN))
& isCountable0(W1) )
| ! [W2: $i] :
( ~ ( aFunction0(W2)
& ( szDzozmdt0(W2) = slbdtsldtrb0(W1,W0) )
& aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT) )
| ~ iLess0(W0,szszuzczcdt0(xk))
| ( aElementOf0(tptp_fun_W3_19(W2,W1,W0),xT)
& aSubsetOf0(tptp_fun_W4_20(W2,W1,W0),W1)
& isCountable0(tptp_fun_W4_20(W2,W1,W0))
& ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(W2,W1,W0),W0))
| ( sdtlpdtrp0(W2,W5) = tptp_fun_W3_19(W2,W1,W0) ) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[14]) ).
tff(16,plain,
^ [W0: $i] :
rewrite(
( ( ~ aElementOf0(W0,szNzAzT0)
| ! [W1: $i] :
( ~ ( aSubsetOf0(W1,szNzAzT0)
& isCountable0(W1) )
| ! [W2: $i] :
( ? [W3: $i] :
( aElementOf0(W3,xT)
& ? [W4: $i] :
( aSubsetOf0(W4,W1)
& isCountable0(W4)
& ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(W4,W0))
| ( sdtlpdtrp0(W2,W5) = W3 ) ) ) )
| ~ iLess0(W0,xK)
| ~ ( aFunction0(W2)
& ( szDzozmdt0(W2) = slbdtsldtrb0(W1,W0) )
& aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT) ) ) ) )
<=> ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ ( aSubsetOf0(W1,szDzozmdt0(xN))
& isCountable0(W1) )
| ! [W2: $i] :
( ? [W3: $i] :
( aElementOf0(W3,xT)
& ? [W4: $i] :
( aSubsetOf0(W4,W1)
& isCountable0(W4)
& ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(W4,W0))
| ( sdtlpdtrp0(W2,W5) = W3 ) ) ) )
| ~ ( aFunction0(W2)
& ( szDzozmdt0(W2) = slbdtsldtrb0(W1,W0) )
& aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT) )
| ~ iLess0(W0,szszuzczcdt0(xk)) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(17,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ! [W1: $i] :
( ~ ( aSubsetOf0(W1,szNzAzT0)
& isCountable0(W1) )
| ! [W2: $i] :
( ? [W3: $i] :
( aElementOf0(W3,xT)
& ? [W4: $i] :
( aSubsetOf0(W4,W1)
& isCountable0(W4)
& ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(W4,W0))
| ( sdtlpdtrp0(W2,W5) = W3 ) ) ) )
| ~ iLess0(W0,xK)
| ~ ( aFunction0(W2)
& ( szDzozmdt0(W2) = slbdtsldtrb0(W1,W0) )
& aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT) ) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ ( aSubsetOf0(W1,szDzozmdt0(xN))
& isCountable0(W1) )
| ! [W2: $i] :
( ? [W3: $i] :
( aElementOf0(W3,xT)
& ? [W4: $i] :
( aSubsetOf0(W4,W1)
& isCountable0(W4)
& ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(W4,W0))
| ( sdtlpdtrp0(W2,W5) = W3 ) ) ) )
| ~ ( aFunction0(W2)
& ( szDzozmdt0(W2) = slbdtsldtrb0(W1,W0) )
& aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT) )
| ~ iLess0(W0,szszuzczcdt0(xk)) ) ) ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ! [W1: $i] :
( ~ ( aSubsetOf0(W1,szNzAzT0)
& isCountable0(W1) )
| ! [W2: $i] :
( ? [W3: $i] :
( aElementOf0(W3,xT)
& ? [W4: $i] :
( aSubsetOf0(W4,W1)
& isCountable0(W4)
& ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(W4,W0))
| ( sdtlpdtrp0(W2,W5) = W3 ) ) ) )
| ~ iLess0(W0,xK)
| ~ ( aFunction0(W2)
& ( szDzozmdt0(W2) = slbdtsldtrb0(W1,W0) )
& aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT) ) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ! [W1: $i] :
( ~ ( aSubsetOf0(W1,szNzAzT0)
& isCountable0(W1) )
| ! [W2: $i] :
( ? [W3: $i] :
( aElementOf0(W3,xT)
& ? [W4: $i] :
( aSubsetOf0(W4,W1)
& isCountable0(W4)
& ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(W4,W0))
| ( sdtlpdtrp0(W2,W5) = W3 ) ) ) )
| ~ iLess0(W0,xK)
| ~ ( aFunction0(W2)
& ( szDzozmdt0(W2) = slbdtsldtrb0(W1,W0) )
& aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(19,plain,
^ [W0: $i] :
trans(
monotonicity(
quant_intro(
proof_bind(
^ [W1: $i] :
trans(
monotonicity(
quant_intro(
proof_bind(
^ [W2: $i] :
trans(
monotonicity(
rewrite(
( ( aFunction0(W2)
& ( szDzozmdt0(W2) = slbdtsldtrb0(W1,W0) )
& aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT) )
<=> ( aFunction0(W2)
& ( szDzozmdt0(W2) = slbdtsldtrb0(W1,W0) )
& aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT) ) )),
trans(
monotonicity(
quant_intro(
proof_bind(
^ [W3: $i] :
rewrite(
( ( aElementOf0(W3,xT)
& ? [W4: $i] :
( aSubsetOf0(W4,W1)
& isCountable0(W4)
& ! [W5: $i] :
( aElementOf0(W5,slbdtsldtrb0(W4,W0))
=> ( sdtlpdtrp0(W2,W5) = W3 ) ) ) )
<=> ( aElementOf0(W3,xT)
& ? [W4: $i] :
( aSubsetOf0(W4,W1)
& isCountable0(W4)
& ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(W4,W0))
| ( sdtlpdtrp0(W2,W5) = W3 ) ) ) ) ))),
( ? [W3: $i] :
( aElementOf0(W3,xT)
& ? [W4: $i] :
( aSubsetOf0(W4,W1)
& isCountable0(W4)
& ! [W5: $i] :
( aElementOf0(W5,slbdtsldtrb0(W4,W0))
=> ( sdtlpdtrp0(W2,W5) = W3 ) ) ) )
<=> ? [W3: $i] :
( aElementOf0(W3,xT)
& ? [W4: $i] :
( aSubsetOf0(W4,W1)
& isCountable0(W4)
& ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(W4,W0))
| ( sdtlpdtrp0(W2,W5) = W3 ) ) ) ) )),
( ( iLess0(W0,xK)
=> ? [W3: $i] :
( aElementOf0(W3,xT)
& ? [W4: $i] :
( aSubsetOf0(W4,W1)
& isCountable0(W4)
& ! [W5: $i] :
( aElementOf0(W5,slbdtsldtrb0(W4,W0))
=> ( sdtlpdtrp0(W2,W5) = W3 ) ) ) ) )
<=> ( iLess0(W0,xK)
=> ? [W3: $i] :
( aElementOf0(W3,xT)
& ? [W4: $i] :
( aSubsetOf0(W4,W1)
& isCountable0(W4)
& ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(W4,W0))
| ( sdtlpdtrp0(W2,W5) = W3 ) ) ) ) ) )),
rewrite(
( ( iLess0(W0,xK)
=> ? [W3: $i] :
( aElementOf0(W3,xT)
& ? [W4: $i] :
( aSubsetOf0(W4,W1)
& isCountable0(W4)
& ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(W4,W0))
| ( sdtlpdtrp0(W2,W5) = W3 ) ) ) ) )
<=> ( ~ iLess0(W0,xK)
| ? [W3: $i] :
( aElementOf0(W3,xT)
& ? [W4: $i] :
( aSubsetOf0(W4,W1)
& isCountable0(W4)
& ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(W4,W0))
| ( sdtlpdtrp0(W2,W5) = W3 ) ) ) ) ) )),
( ( iLess0(W0,xK)
=> ? [W3: $i] :
( aElementOf0(W3,xT)
& ? [W4: $i] :
( aSubsetOf0(W4,W1)
& isCountable0(W4)
& ! [W5: $i] :
( aElementOf0(W5,slbdtsldtrb0(W4,W0))
=> ( sdtlpdtrp0(W2,W5) = W3 ) ) ) ) )
<=> ( ~ iLess0(W0,xK)
| ? [W3: $i] :
( aElementOf0(W3,xT)
& ? [W4: $i] :
( aSubsetOf0(W4,W1)
& isCountable0(W4)
& ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(W4,W0))
| ( sdtlpdtrp0(W2,W5) = W3 ) ) ) ) ) )),
( ( ( aFunction0(W2)
& ( szDzozmdt0(W2) = slbdtsldtrb0(W1,W0) )
& aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT) )
=> ( iLess0(W0,xK)
=> ? [W3: $i] :
( aElementOf0(W3,xT)
& ? [W4: $i] :
( aSubsetOf0(W4,W1)
& isCountable0(W4)
& ! [W5: $i] :
( aElementOf0(W5,slbdtsldtrb0(W4,W0))
=> ( sdtlpdtrp0(W2,W5) = W3 ) ) ) ) ) )
<=> ( ( aFunction0(W2)
& ( szDzozmdt0(W2) = slbdtsldtrb0(W1,W0) )
& aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT) )
=> ( ~ iLess0(W0,xK)
| ? [W3: $i] :
( aElementOf0(W3,xT)
& ? [W4: $i] :
( aSubsetOf0(W4,W1)
& isCountable0(W4)
& ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(W4,W0))
| ( sdtlpdtrp0(W2,W5) = W3 ) ) ) ) ) ) )),
rewrite(
( ( ( aFunction0(W2)
& ( szDzozmdt0(W2) = slbdtsldtrb0(W1,W0) )
& aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT) )
=> ( ~ iLess0(W0,xK)
| ? [W3: $i] :
( aElementOf0(W3,xT)
& ? [W4: $i] :
( aSubsetOf0(W4,W1)
& isCountable0(W4)
& ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(W4,W0))
| ( sdtlpdtrp0(W2,W5) = W3 ) ) ) ) ) )
<=> ( ? [W3: $i] :
( aElementOf0(W3,xT)
& ? [W4: $i] :
( aSubsetOf0(W4,W1)
& isCountable0(W4)
& ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(W4,W0))
| ( sdtlpdtrp0(W2,W5) = W3 ) ) ) )
| ~ iLess0(W0,xK)
| ~ ( aFunction0(W2)
& ( szDzozmdt0(W2) = slbdtsldtrb0(W1,W0) )
& aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT) ) ) )),
( ( ( aFunction0(W2)
& ( szDzozmdt0(W2) = slbdtsldtrb0(W1,W0) )
& aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT) )
=> ( iLess0(W0,xK)
=> ? [W3: $i] :
( aElementOf0(W3,xT)
& ? [W4: $i] :
( aSubsetOf0(W4,W1)
& isCountable0(W4)
& ! [W5: $i] :
( aElementOf0(W5,slbdtsldtrb0(W4,W0))
=> ( sdtlpdtrp0(W2,W5) = W3 ) ) ) ) ) )
<=> ( ? [W3: $i] :
( aElementOf0(W3,xT)
& ? [W4: $i] :
( aSubsetOf0(W4,W1)
& isCountable0(W4)
& ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(W4,W0))
| ( sdtlpdtrp0(W2,W5) = W3 ) ) ) )
| ~ iLess0(W0,xK)
| ~ ( aFunction0(W2)
& ( szDzozmdt0(W2) = slbdtsldtrb0(W1,W0) )
& aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT) ) ) ))),
( ! [W2: $i] :
( ( aFunction0(W2)
& ( szDzozmdt0(W2) = slbdtsldtrb0(W1,W0) )
& aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT) )
=> ( iLess0(W0,xK)
=> ? [W3: $i] :
( aElementOf0(W3,xT)
& ? [W4: $i] :
( aSubsetOf0(W4,W1)
& isCountable0(W4)
& ! [W5: $i] :
( aElementOf0(W5,slbdtsldtrb0(W4,W0))
=> ( sdtlpdtrp0(W2,W5) = W3 ) ) ) ) ) )
<=> ! [W2: $i] :
( ? [W3: $i] :
( aElementOf0(W3,xT)
& ? [W4: $i] :
( aSubsetOf0(W4,W1)
& isCountable0(W4)
& ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(W4,W0))
| ( sdtlpdtrp0(W2,W5) = W3 ) ) ) )
| ~ iLess0(W0,xK)
| ~ ( aFunction0(W2)
& ( szDzozmdt0(W2) = slbdtsldtrb0(W1,W0) )
& aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT) ) ) )),
( ( ( aSubsetOf0(W1,szNzAzT0)
& isCountable0(W1) )
=> ! [W2: $i] :
( ( aFunction0(W2)
& ( szDzozmdt0(W2) = slbdtsldtrb0(W1,W0) )
& aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT) )
=> ( iLess0(W0,xK)
=> ? [W3: $i] :
( aElementOf0(W3,xT)
& ? [W4: $i] :
( aSubsetOf0(W4,W1)
& isCountable0(W4)
& ! [W5: $i] :
( aElementOf0(W5,slbdtsldtrb0(W4,W0))
=> ( sdtlpdtrp0(W2,W5) = W3 ) ) ) ) ) ) )
<=> ( ( aSubsetOf0(W1,szNzAzT0)
& isCountable0(W1) )
=> ! [W2: $i] :
( ? [W3: $i] :
( aElementOf0(W3,xT)
& ? [W4: $i] :
( aSubsetOf0(W4,W1)
& isCountable0(W4)
& ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(W4,W0))
| ( sdtlpdtrp0(W2,W5) = W3 ) ) ) )
| ~ iLess0(W0,xK)
| ~ ( aFunction0(W2)
& ( szDzozmdt0(W2) = slbdtsldtrb0(W1,W0) )
& aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT) ) ) ) )),
rewrite(
( ( ( aSubsetOf0(W1,szNzAzT0)
& isCountable0(W1) )
=> ! [W2: $i] :
( ? [W3: $i] :
( aElementOf0(W3,xT)
& ? [W4: $i] :
( aSubsetOf0(W4,W1)
& isCountable0(W4)
& ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(W4,W0))
| ( sdtlpdtrp0(W2,W5) = W3 ) ) ) )
| ~ iLess0(W0,xK)
| ~ ( aFunction0(W2)
& ( szDzozmdt0(W2) = slbdtsldtrb0(W1,W0) )
& aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT) ) ) )
<=> ( ~ ( aSubsetOf0(W1,szNzAzT0)
& isCountable0(W1) )
| ! [W2: $i] :
( ? [W3: $i] :
( aElementOf0(W3,xT)
& ? [W4: $i] :
( aSubsetOf0(W4,W1)
& isCountable0(W4)
& ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(W4,W0))
| ( sdtlpdtrp0(W2,W5) = W3 ) ) ) )
| ~ iLess0(W0,xK)
| ~ ( aFunction0(W2)
& ( szDzozmdt0(W2) = slbdtsldtrb0(W1,W0) )
& aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT) ) ) ) )),
( ( ( aSubsetOf0(W1,szNzAzT0)
& isCountable0(W1) )
=> ! [W2: $i] :
( ( aFunction0(W2)
& ( szDzozmdt0(W2) = slbdtsldtrb0(W1,W0) )
& aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT) )
=> ( iLess0(W0,xK)
=> ? [W3: $i] :
( aElementOf0(W3,xT)
& ? [W4: $i] :
( aSubsetOf0(W4,W1)
& isCountable0(W4)
& ! [W5: $i] :
( aElementOf0(W5,slbdtsldtrb0(W4,W0))
=> ( sdtlpdtrp0(W2,W5) = W3 ) ) ) ) ) ) )
<=> ( ~ ( aSubsetOf0(W1,szNzAzT0)
& isCountable0(W1) )
| ! [W2: $i] :
( ? [W3: $i] :
( aElementOf0(W3,xT)
& ? [W4: $i] :
( aSubsetOf0(W4,W1)
& isCountable0(W4)
& ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(W4,W0))
| ( sdtlpdtrp0(W2,W5) = W3 ) ) ) )
| ~ iLess0(W0,xK)
| ~ ( aFunction0(W2)
& ( szDzozmdt0(W2) = slbdtsldtrb0(W1,W0) )
& aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT) ) ) ) ))),
( ! [W1: $i] :
( ( aSubsetOf0(W1,szNzAzT0)
& isCountable0(W1) )
=> ! [W2: $i] :
( ( aFunction0(W2)
& ( szDzozmdt0(W2) = slbdtsldtrb0(W1,W0) )
& aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT) )
=> ( iLess0(W0,xK)
=> ? [W3: $i] :
( aElementOf0(W3,xT)
& ? [W4: $i] :
( aSubsetOf0(W4,W1)
& isCountable0(W4)
& ! [W5: $i] :
( aElementOf0(W5,slbdtsldtrb0(W4,W0))
=> ( sdtlpdtrp0(W2,W5) = W3 ) ) ) ) ) ) )
<=> ! [W1: $i] :
( ~ ( aSubsetOf0(W1,szNzAzT0)
& isCountable0(W1) )
| ! [W2: $i] :
( ? [W3: $i] :
( aElementOf0(W3,xT)
& ? [W4: $i] :
( aSubsetOf0(W4,W1)
& isCountable0(W4)
& ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(W4,W0))
| ( sdtlpdtrp0(W2,W5) = W3 ) ) ) )
| ~ iLess0(W0,xK)
| ~ ( aFunction0(W2)
& ( szDzozmdt0(W2) = slbdtsldtrb0(W1,W0) )
& aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT) ) ) ) )),
( ( aElementOf0(W0,szNzAzT0)
=> ! [W1: $i] :
( ( aSubsetOf0(W1,szNzAzT0)
& isCountable0(W1) )
=> ! [W2: $i] :
( ( aFunction0(W2)
& ( szDzozmdt0(W2) = slbdtsldtrb0(W1,W0) )
& aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT) )
=> ( iLess0(W0,xK)
=> ? [W3: $i] :
( aElementOf0(W3,xT)
& ? [W4: $i] :
( aSubsetOf0(W4,W1)
& isCountable0(W4)
& ! [W5: $i] :
( aElementOf0(W5,slbdtsldtrb0(W4,W0))
=> ( sdtlpdtrp0(W2,W5) = W3 ) ) ) ) ) ) ) )
<=> ( aElementOf0(W0,szNzAzT0)
=> ! [W1: $i] :
( ~ ( aSubsetOf0(W1,szNzAzT0)
& isCountable0(W1) )
| ! [W2: $i] :
( ? [W3: $i] :
( aElementOf0(W3,xT)
& ? [W4: $i] :
( aSubsetOf0(W4,W1)
& isCountable0(W4)
& ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(W4,W0))
| ( sdtlpdtrp0(W2,W5) = W3 ) ) ) )
| ~ iLess0(W0,xK)
| ~ ( aFunction0(W2)
& ( szDzozmdt0(W2) = slbdtsldtrb0(W1,W0) )
& aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT) ) ) ) ) )),
rewrite(
( ( aElementOf0(W0,szNzAzT0)
=> ! [W1: $i] :
( ~ ( aSubsetOf0(W1,szNzAzT0)
& isCountable0(W1) )
| ! [W2: $i] :
( ? [W3: $i] :
( aElementOf0(W3,xT)
& ? [W4: $i] :
( aSubsetOf0(W4,W1)
& isCountable0(W4)
& ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(W4,W0))
| ( sdtlpdtrp0(W2,W5) = W3 ) ) ) )
| ~ iLess0(W0,xK)
| ~ ( aFunction0(W2)
& ( szDzozmdt0(W2) = slbdtsldtrb0(W1,W0) )
& aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT) ) ) ) )
<=> ( ~ aElementOf0(W0,szNzAzT0)
| ! [W1: $i] :
( ~ ( aSubsetOf0(W1,szNzAzT0)
& isCountable0(W1) )
| ! [W2: $i] :
( ? [W3: $i] :
( aElementOf0(W3,xT)
& ? [W4: $i] :
( aSubsetOf0(W4,W1)
& isCountable0(W4)
& ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(W4,W0))
| ( sdtlpdtrp0(W2,W5) = W3 ) ) ) )
| ~ iLess0(W0,xK)
| ~ ( aFunction0(W2)
& ( szDzozmdt0(W2) = slbdtsldtrb0(W1,W0) )
& aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT) ) ) ) ) )),
( ( aElementOf0(W0,szNzAzT0)
=> ! [W1: $i] :
( ( aSubsetOf0(W1,szNzAzT0)
& isCountable0(W1) )
=> ! [W2: $i] :
( ( aFunction0(W2)
& ( szDzozmdt0(W2) = slbdtsldtrb0(W1,W0) )
& aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT) )
=> ( iLess0(W0,xK)
=> ? [W3: $i] :
( aElementOf0(W3,xT)
& ? [W4: $i] :
( aSubsetOf0(W4,W1)
& isCountable0(W4)
& ! [W5: $i] :
( aElementOf0(W5,slbdtsldtrb0(W4,W0))
=> ( sdtlpdtrp0(W2,W5) = W3 ) ) ) ) ) ) ) )
<=> ( ~ aElementOf0(W0,szNzAzT0)
| ! [W1: $i] :
( ~ ( aSubsetOf0(W1,szNzAzT0)
& isCountable0(W1) )
| ! [W2: $i] :
( ? [W3: $i] :
( aElementOf0(W3,xT)
& ? [W4: $i] :
( aSubsetOf0(W4,W1)
& isCountable0(W4)
& ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(W4,W0))
| ( sdtlpdtrp0(W2,W5) = W3 ) ) ) )
| ~ iLess0(W0,xK)
| ~ ( aFunction0(W2)
& ( szDzozmdt0(W2) = slbdtsldtrb0(W1,W0) )
& aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(20,plain,
( ! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> ! [W1: $i] :
( ( aSubsetOf0(W1,szNzAzT0)
& isCountable0(W1) )
=> ! [W2: $i] :
( ( aFunction0(W2)
& ( szDzozmdt0(W2) = slbdtsldtrb0(W1,W0) )
& aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT) )
=> ( iLess0(W0,xK)
=> ? [W3: $i] :
( aElementOf0(W3,xT)
& ? [W4: $i] :
( aSubsetOf0(W4,W1)
& isCountable0(W4)
& ! [W5: $i] :
( aElementOf0(W5,slbdtsldtrb0(W4,W0))
=> ( sdtlpdtrp0(W2,W5) = W3 ) ) ) ) ) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ! [W1: $i] :
( ~ ( aSubsetOf0(W1,szNzAzT0)
& isCountable0(W1) )
| ! [W2: $i] :
( ? [W3: $i] :
( aElementOf0(W3,xT)
& ? [W4: $i] :
( aSubsetOf0(W4,W1)
& isCountable0(W4)
& ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(W4,W0))
| ( sdtlpdtrp0(W2,W5) = W3 ) ) ) )
| ~ iLess0(W0,xK)
| ~ ( aFunction0(W2)
& ( szDzozmdt0(W2) = slbdtsldtrb0(W1,W0) )
& aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT) ) ) ) ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,axiom,
! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> ! [W1: $i] :
( ( aSubsetOf0(W1,szNzAzT0)
& isCountable0(W1) )
=> ! [W2: $i] :
( ( aFunction0(W2)
& ( szDzozmdt0(W2) = slbdtsldtrb0(W1,W0) )
& aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT) )
=> ( iLess0(W0,xK)
=> ? [W3: $i] :
( aElementOf0(W3,xT)
& ? [W4: $i] :
( aSubsetOf0(W4,W1)
& isCountable0(W4)
& ! [W5: $i] :
( aElementOf0(W5,slbdtsldtrb0(W4,W0))
=> ( sdtlpdtrp0(W2,W5) = W3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3398) ).
tff(22,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ! [W1: $i] :
( ~ ( aSubsetOf0(W1,szNzAzT0)
& isCountable0(W1) )
| ! [W2: $i] :
( ? [W3: $i] :
( aElementOf0(W3,xT)
& ? [W4: $i] :
( aSubsetOf0(W4,W1)
& isCountable0(W4)
& ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(W4,W0))
| ( sdtlpdtrp0(W2,W5) = W3 ) ) ) )
| ~ iLess0(W0,xK)
| ~ ( aFunction0(W2)
& ( szDzozmdt0(W2) = slbdtsldtrb0(W1,W0) )
& aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT) ) ) ) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ! [W1: $i] :
( ~ ( aSubsetOf0(W1,szNzAzT0)
& isCountable0(W1) )
| ! [W2: $i] :
( ? [W3: $i] :
( aElementOf0(W3,xT)
& ? [W4: $i] :
( aSubsetOf0(W4,W1)
& isCountable0(W4)
& ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(W4,W0))
| ( sdtlpdtrp0(W2,W5) = W3 ) ) ) )
| ~ iLess0(W0,xK)
| ~ ( aFunction0(W2)
& ( szDzozmdt0(W2) = slbdtsldtrb0(W1,W0) )
& aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT) ) ) ) ),
inference(modus_ponens,[status(thm)],[22,18]) ).
tff(24,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ ( aSubsetOf0(W1,szDzozmdt0(xN))
& isCountable0(W1) )
| ! [W2: $i] :
( ? [W3: $i] :
( aElementOf0(W3,xT)
& ? [W4: $i] :
( aSubsetOf0(W4,W1)
& isCountable0(W4)
& ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(W4,W0))
| ( sdtlpdtrp0(W2,W5) = W3 ) ) ) )
| ~ ( aFunction0(W2)
& ( szDzozmdt0(W2) = slbdtsldtrb0(W1,W0) )
& aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT) )
| ~ iLess0(W0,szszuzczcdt0(xk)) ) ) ),
inference(modus_ponens,[status(thm)],[23,17]) ).
tff(25,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ ( aSubsetOf0(W1,szDzozmdt0(xN))
& isCountable0(W1) )
| ! [W2: $i] :
( ( aElementOf0(tptp_fun_W3_19(W2,W1,W0),xT)
& aSubsetOf0(tptp_fun_W4_20(W2,W1,W0),W1)
& isCountable0(tptp_fun_W4_20(W2,W1,W0))
& ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(W2,W1,W0),W0))
| ( sdtlpdtrp0(W2,W5) = tptp_fun_W3_19(W2,W1,W0) ) ) )
| ~ ( aFunction0(W2)
& ( szDzozmdt0(W2) = slbdtsldtrb0(W1,W0) )
& aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT) )
| ~ iLess0(W0,szszuzczcdt0(xk)) ) ) ),
inference(skolemize,[status(sab)],[24]) ).
tff(26,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ ( aSubsetOf0(W1,szDzozmdt0(xN))
& isCountable0(W1) )
| ! [W2: $i] :
( ~ ( aFunction0(W2)
& ( szDzozmdt0(W2) = slbdtsldtrb0(W1,W0) )
& aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT) )
| ~ iLess0(W0,szszuzczcdt0(xk))
| ( aElementOf0(tptp_fun_W3_19(W2,W1,W0),xT)
& aSubsetOf0(tptp_fun_W4_20(W2,W1,W0),W1)
& isCountable0(tptp_fun_W4_20(W2,W1,W0))
& ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(W2,W1,W0),W0))
| ( sdtlpdtrp0(W2,W5) = tptp_fun_W3_19(W2,W1,W0) ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[25,15]) ).
tff(27,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ! [W2: $i] :
( ~ aFunction0(W2)
| ~ iLess0(W0,szszuzczcdt0(xk))
| ( szDzozmdt0(W2) != slbdtsldtrb0(W1,W0) )
| ~ aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT)
| ~ ( ~ aElementOf0(tptp_fun_W3_19(W2,W1,W0),xT)
| ~ aSubsetOf0(tptp_fun_W4_20(W2,W1,W0),W1)
| ~ isCountable0(tptp_fun_W4_20(W2,W1,W0))
| ~ ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(W2,W1,W0),W0))
| ( sdtlpdtrp0(W2,W5) = tptp_fun_W3_19(W2,W1,W0) ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[26,13]) ).
tff(28,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ! [W2: $i] :
( ~ aFunction0(W2)
| ~ iLess0(W0,szszuzczcdt0(xk))
| ( szDzozmdt0(W2) != slbdtsldtrb0(W1,W0) )
| ~ aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT)
| ~ ( ~ aElementOf0(tptp_fun_W3_19(W2,W1,W0),xT)
| ~ aSubsetOf0(tptp_fun_W4_20(W2,W1,W0),W1)
| ~ isCountable0(tptp_fun_W4_20(W2,W1,W0))
| ~ ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(W2,W1,W0),W0))
| ( sdtlpdtrp0(W2,W5) = tptp_fun_W3_19(W2,W1,W0) ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[27,11]) ).
tff(29,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ! [W2: $i] :
( ~ aFunction0(W2)
| ~ iLess0(W0,szszuzczcdt0(xk))
| ( szDzozmdt0(W2) != slbdtsldtrb0(W1,W0) )
| ~ aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT)
| ~ ( ~ aElementOf0(tptp_fun_W3_19(W2,W1,W0),xT)
| ~ aSubsetOf0(tptp_fun_W4_20(W2,W1,W0),W1)
| ~ isCountable0(tptp_fun_W4_20(W2,W1,W0))
| ~ ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(W2,W1,W0),W0))
| ( sdtlpdtrp0(W2,W5) = tptp_fun_W3_19(W2,W1,W0) ) ) ) ) ) )
| ~ aElementOf0(xk,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ! [W2: $i] :
( ~ aFunction0(W2)
| ~ aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT)
| ~ iLess0(xk,szszuzczcdt0(xk))
| ( szDzozmdt0(W2) != slbdtsldtrb0(W1,xk) )
| ~ ( ~ aElementOf0(tptp_fun_W3_19(W2,W1,xk),xT)
| ~ aSubsetOf0(tptp_fun_W4_20(W2,W1,xk),W1)
| ~ isCountable0(tptp_fun_W4_20(W2,W1,xk))
| ~ ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(W2,W1,xk),xk))
| ( sdtlpdtrp0(W2,W5) = tptp_fun_W3_19(W2,W1,xk) ) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ! [W2: $i] :
( ~ aFunction0(W2)
| ~ iLess0(W0,szszuzczcdt0(xk))
| ( szDzozmdt0(W2) != slbdtsldtrb0(W1,W0) )
| ~ aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT)
| ~ ( ~ aElementOf0(tptp_fun_W3_19(W2,W1,W0),xT)
| ~ aSubsetOf0(tptp_fun_W4_20(W2,W1,W0),W1)
| ~ isCountable0(tptp_fun_W4_20(W2,W1,W0))
| ~ ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(W2,W1,W0),W0))
| ( sdtlpdtrp0(W2,W5) = tptp_fun_W3_19(W2,W1,W0) ) ) ) ) ) )
| ~ aElementOf0(xk,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ! [W2: $i] :
( ~ aFunction0(W2)
| ~ aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT)
| ~ iLess0(xk,szszuzczcdt0(xk))
| ( szDzozmdt0(W2) != slbdtsldtrb0(W1,xk) )
| ~ ( ~ aElementOf0(tptp_fun_W3_19(W2,W1,xk),xT)
| ~ aSubsetOf0(tptp_fun_W4_20(W2,W1,xk),W1)
| ~ isCountable0(tptp_fun_W4_20(W2,W1,xk))
| ~ ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(W2,W1,xk),xk))
| ( sdtlpdtrp0(W2,W5) = tptp_fun_W3_19(W2,W1,xk) ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,plain,
( ( ~ aElementOf0(xk,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ! [W2: $i] :
( ~ aFunction0(W2)
| ~ iLess0(xk,szszuzczcdt0(xk))
| ( szDzozmdt0(W2) != slbdtsldtrb0(W1,xk) )
| ~ aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT)
| ~ ( ~ aElementOf0(tptp_fun_W3_19(W2,W1,xk),xT)
| ~ aSubsetOf0(tptp_fun_W4_20(W2,W1,xk),W1)
| ~ isCountable0(tptp_fun_W4_20(W2,W1,xk))
| ~ ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(W2,W1,xk),xk))
| ( sdtlpdtrp0(W2,W5) = tptp_fun_W3_19(W2,W1,xk) ) ) ) ) ) )
<=> ( ~ aElementOf0(xk,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ! [W2: $i] :
( ~ aFunction0(W2)
| ~ aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT)
| ~ iLess0(xk,szszuzczcdt0(xk))
| ( szDzozmdt0(W2) != slbdtsldtrb0(W1,xk) )
| ~ ( ~ aElementOf0(tptp_fun_W3_19(W2,W1,xk),xT)
| ~ aSubsetOf0(tptp_fun_W4_20(W2,W1,xk),W1)
| ~ isCountable0(tptp_fun_W4_20(W2,W1,xk))
| ~ ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(W2,W1,xk),xk))
| ( sdtlpdtrp0(W2,W5) = tptp_fun_W3_19(W2,W1,xk) ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(31,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ! [W2: $i] :
( ~ aFunction0(W2)
| ~ iLess0(W0,szszuzczcdt0(xk))
| ( szDzozmdt0(W2) != slbdtsldtrb0(W1,W0) )
| ~ aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT)
| ~ ( ~ aElementOf0(tptp_fun_W3_19(W2,W1,W0),xT)
| ~ aSubsetOf0(tptp_fun_W4_20(W2,W1,W0),W1)
| ~ isCountable0(tptp_fun_W4_20(W2,W1,W0))
| ~ ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(W2,W1,W0),W0))
| ( sdtlpdtrp0(W2,W5) = tptp_fun_W3_19(W2,W1,W0) ) ) ) ) ) )
| ~ aElementOf0(xk,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ! [W2: $i] :
( ~ aFunction0(W2)
| ~ iLess0(xk,szszuzczcdt0(xk))
| ( szDzozmdt0(W2) != slbdtsldtrb0(W1,xk) )
| ~ aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT)
| ~ ( ~ aElementOf0(tptp_fun_W3_19(W2,W1,xk),xT)
| ~ aSubsetOf0(tptp_fun_W4_20(W2,W1,xk),W1)
| ~ isCountable0(tptp_fun_W4_20(W2,W1,xk))
| ~ ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(W2,W1,xk),xk))
| ( sdtlpdtrp0(W2,W5) = tptp_fun_W3_19(W2,W1,xk) ) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ! [W2: $i] :
( ~ aFunction0(W2)
| ~ iLess0(W0,szszuzczcdt0(xk))
| ( szDzozmdt0(W2) != slbdtsldtrb0(W1,W0) )
| ~ aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT)
| ~ ( ~ aElementOf0(tptp_fun_W3_19(W2,W1,W0),xT)
| ~ aSubsetOf0(tptp_fun_W4_20(W2,W1,W0),W1)
| ~ isCountable0(tptp_fun_W4_20(W2,W1,W0))
| ~ ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(W2,W1,W0),W0))
| ( sdtlpdtrp0(W2,W5) = tptp_fun_W3_19(W2,W1,W0) ) ) ) ) ) )
| ~ aElementOf0(xk,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ! [W2: $i] :
( ~ aFunction0(W2)
| ~ aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT)
| ~ iLess0(xk,szszuzczcdt0(xk))
| ( szDzozmdt0(W2) != slbdtsldtrb0(W1,xk) )
| ~ ( ~ aElementOf0(tptp_fun_W3_19(W2,W1,xk),xT)
| ~ aSubsetOf0(tptp_fun_W4_20(W2,W1,xk),W1)
| ~ isCountable0(tptp_fun_W4_20(W2,W1,xk))
| ~ ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(W2,W1,xk),xk))
| ( sdtlpdtrp0(W2,W5) = tptp_fun_W3_19(W2,W1,xk) ) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[30]) ).
tff(32,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ! [W2: $i] :
( ~ aFunction0(W2)
| ~ iLess0(W0,szszuzczcdt0(xk))
| ( szDzozmdt0(W2) != slbdtsldtrb0(W1,W0) )
| ~ aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT)
| ~ ( ~ aElementOf0(tptp_fun_W3_19(W2,W1,W0),xT)
| ~ aSubsetOf0(tptp_fun_W4_20(W2,W1,W0),W1)
| ~ isCountable0(tptp_fun_W4_20(W2,W1,W0))
| ~ ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(W2,W1,W0),W0))
| ( sdtlpdtrp0(W2,W5) = tptp_fun_W3_19(W2,W1,W0) ) ) ) ) ) )
| ~ aElementOf0(xk,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ! [W2: $i] :
( ~ aFunction0(W2)
| ~ iLess0(xk,szszuzczcdt0(xk))
| ( szDzozmdt0(W2) != slbdtsldtrb0(W1,xk) )
| ~ aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT)
| ~ ( ~ aElementOf0(tptp_fun_W3_19(W2,W1,xk),xT)
| ~ aSubsetOf0(tptp_fun_W4_20(W2,W1,xk),W1)
| ~ isCountable0(tptp_fun_W4_20(W2,W1,xk))
| ~ ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(W2,W1,xk),xk))
| ( sdtlpdtrp0(W2,W5) = tptp_fun_W3_19(W2,W1,xk) ) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ! [W2: $i] :
( ~ aFunction0(W2)
| ~ iLess0(W0,szszuzczcdt0(xk))
| ( szDzozmdt0(W2) != slbdtsldtrb0(W1,W0) )
| ~ aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT)
| ~ ( ~ aElementOf0(tptp_fun_W3_19(W2,W1,W0),xT)
| ~ aSubsetOf0(tptp_fun_W4_20(W2,W1,W0),W1)
| ~ isCountable0(tptp_fun_W4_20(W2,W1,W0))
| ~ ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(W2,W1,W0),W0))
| ( sdtlpdtrp0(W2,W5) = tptp_fun_W3_19(W2,W1,W0) ) ) ) ) ) )
| ~ aElementOf0(xk,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ! [W2: $i] :
( ~ aFunction0(W2)
| ~ aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT)
| ~ iLess0(xk,szszuzczcdt0(xk))
| ( szDzozmdt0(W2) != slbdtsldtrb0(W1,xk) )
| ~ ( ~ aElementOf0(tptp_fun_W3_19(W2,W1,xk),xT)
| ~ aSubsetOf0(tptp_fun_W4_20(W2,W1,xk),W1)
| ~ isCountable0(tptp_fun_W4_20(W2,W1,xk))
| ~ ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(W2,W1,xk),xk))
| ( sdtlpdtrp0(W2,W5) = tptp_fun_W3_19(W2,W1,xk) ) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[31,29]) ).
tff(33,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ! [W2: $i] :
( ~ aFunction0(W2)
| ~ iLess0(W0,szszuzczcdt0(xk))
| ( szDzozmdt0(W2) != slbdtsldtrb0(W1,W0) )
| ~ aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT)
| ~ ( ~ aElementOf0(tptp_fun_W3_19(W2,W1,W0),xT)
| ~ aSubsetOf0(tptp_fun_W4_20(W2,W1,W0),W1)
| ~ isCountable0(tptp_fun_W4_20(W2,W1,W0))
| ~ ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(W2,W1,W0),W0))
| ( sdtlpdtrp0(W2,W5) = tptp_fun_W3_19(W2,W1,W0) ) ) ) ) ) )
| ~ aElementOf0(xk,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ! [W2: $i] :
( ~ aFunction0(W2)
| ~ iLess0(xk,szszuzczcdt0(xk))
| ( szDzozmdt0(W2) != slbdtsldtrb0(W1,xk) )
| ~ aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT)
| ~ ( ~ aElementOf0(tptp_fun_W3_19(W2,W1,xk),xT)
| ~ aSubsetOf0(tptp_fun_W4_20(W2,W1,xk),W1)
| ~ isCountable0(tptp_fun_W4_20(W2,W1,xk))
| ~ ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(W2,W1,xk),xk))
| ( sdtlpdtrp0(W2,W5) = tptp_fun_W3_19(W2,W1,xk) ) ) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(34,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ! [W2: $i] :
( ~ aFunction0(W2)
| ~ iLess0(W0,szszuzczcdt0(xk))
| ( szDzozmdt0(W2) != slbdtsldtrb0(W1,W0) )
| ~ aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT)
| ~ ( ~ aElementOf0(tptp_fun_W3_19(W2,W1,W0),xT)
| ~ aSubsetOf0(tptp_fun_W4_20(W2,W1,W0),W1)
| ~ isCountable0(tptp_fun_W4_20(W2,W1,W0))
| ~ ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(W2,W1,W0),W0))
| ( sdtlpdtrp0(W2,W5) = tptp_fun_W3_19(W2,W1,W0) ) ) ) ) ) )
| ~ aElementOf0(xk,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ! [W2: $i] :
( ~ aFunction0(W2)
| ~ aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT)
| ~ iLess0(xk,szszuzczcdt0(xk))
| ( szDzozmdt0(W2) != slbdtsldtrb0(W1,xk) )
| ~ ( ~ aElementOf0(tptp_fun_W3_19(W2,W1,xk),xT)
| ~ aSubsetOf0(tptp_fun_W4_20(W2,W1,xk),W1)
| ~ isCountable0(tptp_fun_W4_20(W2,W1,xk))
| ~ ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(W2,W1,xk),xk))
| ( sdtlpdtrp0(W2,W5) = tptp_fun_W3_19(W2,W1,xk) ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ! [W2: $i] :
( ~ aFunction0(W2)
| ~ aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT)
| ~ iLess0(xk,szszuzczcdt0(xk))
| ( szDzozmdt0(W2) != slbdtsldtrb0(W1,xk) )
| ~ ( ~ aElementOf0(tptp_fun_W3_19(W2,W1,xk),xT)
| ~ aSubsetOf0(tptp_fun_W4_20(W2,W1,xk),W1)
| ~ isCountable0(tptp_fun_W4_20(W2,W1,xk))
| ~ ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(W2,W1,xk),xk))
| ( sdtlpdtrp0(W2,W5) = tptp_fun_W3_19(W2,W1,xk) ) ) ) ) ),
inference(unit_resolution,[status(thm)],[34,28,6]) ).
tff(36,plain,
( isCountable0(xY)
<=> isCountable0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ),
inference(rewrite,[status(thm)],]) ).
tff(37,plain,
( isCountable0(xY)
<=> isCountable0(xY) ),
inference(rewrite,[status(thm)],]) ).
tff(38,axiom,
( aSubsetOf0(xY,szNzAzT0)
& isCountable0(xY)
& aFunction0(xd)
& ( szDzozmdt0(xd) = slbdtsldtrb0(xY,xk) )
& aSubsetOf0(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4482) ).
tff(39,plain,
( aSubsetOf0(xY,szNzAzT0)
& isCountable0(xY)
& aFunction0(xd)
& ( szDzozmdt0(xd) = slbdtsldtrb0(xY,xk) ) ),
inference(and_elim,[status(thm)],[38]) ).
tff(40,plain,
( aSubsetOf0(xY,szNzAzT0)
& isCountable0(xY)
& aFunction0(xd) ),
inference(and_elim,[status(thm)],[39]) ).
tff(41,plain,
( aSubsetOf0(xY,szNzAzT0)
& isCountable0(xY) ),
inference(and_elim,[status(thm)],[40]) ).
tff(42,plain,
isCountable0(xY),
inference(and_elim,[status(thm)],[41]) ).
tff(43,plain,
isCountable0(xY),
inference(modus_ponens,[status(thm)],[42,37]) ).
tff(44,plain,
isCountable0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))),
inference(modus_ponens,[status(thm)],[43,36]) ).
tff(45,plain,
( aSubsetOf0(xY,szNzAzT0)
<=> aSubsetOf0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),szDzozmdt0(xN)) ),
inference(rewrite,[status(thm)],]) ).
tff(46,plain,
( aSubsetOf0(xY,szNzAzT0)
<=> aSubsetOf0(xY,szNzAzT0) ),
inference(rewrite,[status(thm)],]) ).
tff(47,plain,
aSubsetOf0(xY,szNzAzT0),
inference(and_elim,[status(thm)],[41]) ).
tff(48,plain,
aSubsetOf0(xY,szNzAzT0),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
aSubsetOf0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),szDzozmdt0(xN)),
inference(modus_ponens,[status(thm)],[48,45]) ).
tff(50,plain,
( ( ~ ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ! [W2: $i] :
( ~ aFunction0(W2)
| ~ aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT)
| ~ iLess0(xk,szszuzczcdt0(xk))
| ( szDzozmdt0(W2) != slbdtsldtrb0(W1,xk) )
| ~ ( ~ aElementOf0(tptp_fun_W3_19(W2,W1,xk),xT)
| ~ aSubsetOf0(tptp_fun_W4_20(W2,W1,xk),W1)
| ~ isCountable0(tptp_fun_W4_20(W2,W1,xk))
| ~ ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(W2,W1,xk),xk))
| ( sdtlpdtrp0(W2,W5) = tptp_fun_W3_19(W2,W1,xk) ) ) ) ) )
| ~ isCountable0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aSubsetOf0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),szDzozmdt0(xN))
| ! [W2: $i] :
( ~ aFunction0(W2)
| ~ aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT)
| ~ iLess0(xk,szszuzczcdt0(xk))
| ( szDzozmdt0(W2) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) )
| ~ ( ~ aElementOf0(tptp_fun_W3_19(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xT)
| ~ aSubsetOf0(tptp_fun_W4_20(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(tptp_fun_W4_20(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))
| ~ ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xk))
| ( sdtlpdtrp0(W2,W5) = tptp_fun_W3_19(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) ) ) ) ) )
<=> ( ~ ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ! [W2: $i] :
( ~ aFunction0(W2)
| ~ aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT)
| ~ iLess0(xk,szszuzczcdt0(xk))
| ( szDzozmdt0(W2) != slbdtsldtrb0(W1,xk) )
| ~ ( ~ aElementOf0(tptp_fun_W3_19(W2,W1,xk),xT)
| ~ aSubsetOf0(tptp_fun_W4_20(W2,W1,xk),W1)
| ~ isCountable0(tptp_fun_W4_20(W2,W1,xk))
| ~ ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(W2,W1,xk),xk))
| ( sdtlpdtrp0(W2,W5) = tptp_fun_W3_19(W2,W1,xk) ) ) ) ) )
| ~ isCountable0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aSubsetOf0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),szDzozmdt0(xN))
| ! [W2: $i] :
( ~ aFunction0(W2)
| ~ aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT)
| ~ iLess0(xk,szszuzczcdt0(xk))
| ( szDzozmdt0(W2) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) )
| ~ ( ~ aElementOf0(tptp_fun_W3_19(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xT)
| ~ aSubsetOf0(tptp_fun_W4_20(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(tptp_fun_W4_20(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))
| ~ ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xk))
| ( sdtlpdtrp0(W2,W5) = tptp_fun_W3_19(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(51,plain,
( ~ ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ! [W2: $i] :
( ~ aFunction0(W2)
| ~ aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT)
| ~ iLess0(xk,szszuzczcdt0(xk))
| ( szDzozmdt0(W2) != slbdtsldtrb0(W1,xk) )
| ~ ( ~ aElementOf0(tptp_fun_W3_19(W2,W1,xk),xT)
| ~ aSubsetOf0(tptp_fun_W4_20(W2,W1,xk),W1)
| ~ isCountable0(tptp_fun_W4_20(W2,W1,xk))
| ~ ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(W2,W1,xk),xk))
| ( sdtlpdtrp0(W2,W5) = tptp_fun_W3_19(W2,W1,xk) ) ) ) ) )
| ~ isCountable0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aSubsetOf0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),szDzozmdt0(xN))
| ! [W2: $i] :
( ~ aFunction0(W2)
| ~ aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT)
| ~ iLess0(xk,szszuzczcdt0(xk))
| ( szDzozmdt0(W2) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) )
| ~ ( ~ aElementOf0(tptp_fun_W3_19(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xT)
| ~ aSubsetOf0(tptp_fun_W4_20(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(tptp_fun_W4_20(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))
| ~ ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xk))
| ( sdtlpdtrp0(W2,W5) = tptp_fun_W3_19(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) ) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(52,plain,
( ~ ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,szDzozmdt0(xN))
| ! [W2: $i] :
( ~ aFunction0(W2)
| ~ aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT)
| ~ iLess0(xk,szszuzczcdt0(xk))
| ( szDzozmdt0(W2) != slbdtsldtrb0(W1,xk) )
| ~ ( ~ aElementOf0(tptp_fun_W3_19(W2,W1,xk),xT)
| ~ aSubsetOf0(tptp_fun_W4_20(W2,W1,xk),W1)
| ~ isCountable0(tptp_fun_W4_20(W2,W1,xk))
| ~ ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(W2,W1,xk),xk))
| ( sdtlpdtrp0(W2,W5) = tptp_fun_W3_19(W2,W1,xk) ) ) ) ) )
| ~ isCountable0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aSubsetOf0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),szDzozmdt0(xN))
| ! [W2: $i] :
( ~ aFunction0(W2)
| ~ aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT)
| ~ iLess0(xk,szszuzczcdt0(xk))
| ( szDzozmdt0(W2) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) )
| ~ ( ~ aElementOf0(tptp_fun_W3_19(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xT)
| ~ aSubsetOf0(tptp_fun_W4_20(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(tptp_fun_W4_20(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))
| ~ ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xk))
| ( sdtlpdtrp0(W2,W5) = tptp_fun_W3_19(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
! [W2: $i] :
( ~ aFunction0(W2)
| ~ aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT)
| ~ iLess0(xk,szszuzczcdt0(xk))
| ( szDzozmdt0(W2) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) )
| ~ ( ~ aElementOf0(tptp_fun_W3_19(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xT)
| ~ aSubsetOf0(tptp_fun_W4_20(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(tptp_fun_W4_20(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))
| ~ ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xk))
| ( sdtlpdtrp0(W2,W5) = tptp_fun_W3_19(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) ) ) ) ),
inference(unit_resolution,[status(thm)],[52,49,44,35]) ).
tff(54,plain,
( aSubsetOf0(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT)
<=> aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,xi),szDzozmdt0(sdtlpdtrp0(xC,xi))),xT) ),
inference(rewrite,[status(thm)],]) ).
tff(55,plain,
( aSubsetOf0(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT)
<=> aSubsetOf0(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT) ),
inference(rewrite,[status(thm)],]) ).
tff(56,plain,
aSubsetOf0(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT),
inference(and_elim,[status(thm)],[38]) ).
tff(57,plain,
aSubsetOf0(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,xi),szDzozmdt0(sdtlpdtrp0(xC,xi))),xT),
inference(modus_ponens,[status(thm)],[57,54]) ).
tff(59,plain,
( ( szDzozmdt0(xd) = slbdtsldtrb0(xY,xk) )
<=> ( szDzozmdt0(sdtlpdtrp0(xC,xi)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) ) ),
inference(rewrite,[status(thm)],]) ).
tff(60,plain,
( ( szDzozmdt0(xd) = slbdtsldtrb0(xY,xk) )
<=> ( szDzozmdt0(xd) = slbdtsldtrb0(xY,xk) ) ),
inference(rewrite,[status(thm)],]) ).
tff(61,plain,
szDzozmdt0(xd) = slbdtsldtrb0(xY,xk),
inference(and_elim,[status(thm)],[39]) ).
tff(62,plain,
szDzozmdt0(xd) = slbdtsldtrb0(xY,xk),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
szDzozmdt0(sdtlpdtrp0(xC,xi)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),
inference(modus_ponens,[status(thm)],[62,59]) ).
tff(64,plain,
( aFunction0(xd)
<=> aFunction0(sdtlpdtrp0(xC,xi)) ),
inference(rewrite,[status(thm)],]) ).
tff(65,plain,
( aFunction0(xd)
<=> aFunction0(xd) ),
inference(rewrite,[status(thm)],]) ).
tff(66,plain,
aFunction0(xd),
inference(and_elim,[status(thm)],[40]) ).
tff(67,plain,
aFunction0(xd),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
aFunction0(sdtlpdtrp0(xC,xi)),
inference(modus_ponens,[status(thm)],[67,64]) ).
tff(69,plain,
( iLess0(xk,xK)
<=> iLess0(xk,szszuzczcdt0(xk)) ),
inference(rewrite,[status(thm)],]) ).
tff(70,plain,
( iLess0(xk,xK)
<=> iLess0(xk,xK) ),
inference(rewrite,[status(thm)],]) ).
tff(71,axiom,
iLess0(xk,xK),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4423) ).
tff(72,plain,
iLess0(xk,xK),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
iLess0(xk,szszuzczcdt0(xk)),
inference(modus_ponens,[status(thm)],[72,69]) ).
tff(74,plain,
( ( ~ ! [W2: $i] :
( ~ aFunction0(W2)
| ~ aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT)
| ~ iLess0(xk,szszuzczcdt0(xk))
| ( szDzozmdt0(W2) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) )
| ~ ( ~ aElementOf0(tptp_fun_W3_19(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xT)
| ~ aSubsetOf0(tptp_fun_W4_20(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(tptp_fun_W4_20(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))
| ~ ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xk))
| ( sdtlpdtrp0(W2,W5) = tptp_fun_W3_19(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) ) ) ) )
| ~ aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,xi),szDzozmdt0(sdtlpdtrp0(xC,xi))),xT)
| ~ iLess0(xk,szszuzczcdt0(xk))
| ~ aFunction0(sdtlpdtrp0(xC,xi))
| ( szDzozmdt0(sdtlpdtrp0(xC,xi)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) )
| ~ ( ~ aElementOf0(tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xT)
| ~ aSubsetOf0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))
| ~ ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xk))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W5) = tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) ) ) ) )
<=> ( ~ ! [W2: $i] :
( ~ aFunction0(W2)
| ~ aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT)
| ~ iLess0(xk,szszuzczcdt0(xk))
| ( szDzozmdt0(W2) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) )
| ~ ( ~ aElementOf0(tptp_fun_W3_19(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xT)
| ~ aSubsetOf0(tptp_fun_W4_20(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(tptp_fun_W4_20(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))
| ~ ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xk))
| ( sdtlpdtrp0(W2,W5) = tptp_fun_W3_19(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) ) ) ) )
| ~ aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,xi),szDzozmdt0(sdtlpdtrp0(xC,xi))),xT)
| ~ iLess0(xk,szszuzczcdt0(xk))
| ~ aFunction0(sdtlpdtrp0(xC,xi))
| ( szDzozmdt0(sdtlpdtrp0(xC,xi)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) )
| ~ ( ~ aElementOf0(tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xT)
| ~ aSubsetOf0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))
| ~ ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xk))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W5) = tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(75,plain,
( ( ~ aFunction0(sdtlpdtrp0(xC,xi))
| ~ aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,xi),szDzozmdt0(sdtlpdtrp0(xC,xi))),xT)
| ~ iLess0(xk,szszuzczcdt0(xk))
| ( szDzozmdt0(sdtlpdtrp0(xC,xi)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) )
| ~ ( ~ aElementOf0(tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xT)
| ~ aSubsetOf0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))
| ~ ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xk))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W5) = tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) ) ) ) )
<=> ( ~ aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,xi),szDzozmdt0(sdtlpdtrp0(xC,xi))),xT)
| ~ iLess0(xk,szszuzczcdt0(xk))
| ~ aFunction0(sdtlpdtrp0(xC,xi))
| ( szDzozmdt0(sdtlpdtrp0(xC,xi)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) )
| ~ ( ~ aElementOf0(tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xT)
| ~ aSubsetOf0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))
| ~ ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xk))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W5) = tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(76,plain,
( ~ ( ~ aElementOf0(tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xT)
| ~ aSubsetOf0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))
| ~ ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xk))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W5) = tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) ) ) )
<=> ~ ( ~ aElementOf0(tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xT)
| ~ aSubsetOf0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))
| ~ ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xk))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W5) = tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(77,plain,
( ( ~ aFunction0(sdtlpdtrp0(xC,xi))
| ~ aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,xi),szDzozmdt0(sdtlpdtrp0(xC,xi))),xT)
| ~ iLess0(xk,szszuzczcdt0(xk))
| ( szDzozmdt0(sdtlpdtrp0(xC,xi)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) )
| ~ ( ~ aElementOf0(tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xT)
| ~ aSubsetOf0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))
| ~ ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xk))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W5) = tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) ) ) ) )
<=> ( ~ aFunction0(sdtlpdtrp0(xC,xi))
| ~ aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,xi),szDzozmdt0(sdtlpdtrp0(xC,xi))),xT)
| ~ iLess0(xk,szszuzczcdt0(xk))
| ( szDzozmdt0(sdtlpdtrp0(xC,xi)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) )
| ~ ( ~ aElementOf0(tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xT)
| ~ aSubsetOf0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))
| ~ ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xk))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W5) = tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) ) ) ) ) ),
inference(monotonicity,[status(thm)],[76]) ).
tff(78,plain,
( ( ~ aFunction0(sdtlpdtrp0(xC,xi))
| ~ aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,xi),szDzozmdt0(sdtlpdtrp0(xC,xi))),xT)
| ~ iLess0(xk,szszuzczcdt0(xk))
| ( szDzozmdt0(sdtlpdtrp0(xC,xi)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) )
| ~ ( ~ aElementOf0(tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xT)
| ~ aSubsetOf0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))
| ~ ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xk))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W5) = tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) ) ) ) )
<=> ( ~ aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,xi),szDzozmdt0(sdtlpdtrp0(xC,xi))),xT)
| ~ iLess0(xk,szszuzczcdt0(xk))
| ~ aFunction0(sdtlpdtrp0(xC,xi))
| ( szDzozmdt0(sdtlpdtrp0(xC,xi)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) )
| ~ ( ~ aElementOf0(tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xT)
| ~ aSubsetOf0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))
| ~ ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xk))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W5) = tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) ) ) ) ) ),
inference(transitivity,[status(thm)],[77,75]) ).
tff(79,plain,
( ( ~ ! [W2: $i] :
( ~ aFunction0(W2)
| ~ aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT)
| ~ iLess0(xk,szszuzczcdt0(xk))
| ( szDzozmdt0(W2) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) )
| ~ ( ~ aElementOf0(tptp_fun_W3_19(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xT)
| ~ aSubsetOf0(tptp_fun_W4_20(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(tptp_fun_W4_20(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))
| ~ ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xk))
| ( sdtlpdtrp0(W2,W5) = tptp_fun_W3_19(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) ) ) ) )
| ~ aFunction0(sdtlpdtrp0(xC,xi))
| ~ aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,xi),szDzozmdt0(sdtlpdtrp0(xC,xi))),xT)
| ~ iLess0(xk,szszuzczcdt0(xk))
| ( szDzozmdt0(sdtlpdtrp0(xC,xi)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) )
| ~ ( ~ aElementOf0(tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xT)
| ~ aSubsetOf0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))
| ~ ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xk))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W5) = tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) ) ) ) )
<=> ( ~ ! [W2: $i] :
( ~ aFunction0(W2)
| ~ aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT)
| ~ iLess0(xk,szszuzczcdt0(xk))
| ( szDzozmdt0(W2) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) )
| ~ ( ~ aElementOf0(tptp_fun_W3_19(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xT)
| ~ aSubsetOf0(tptp_fun_W4_20(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(tptp_fun_W4_20(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))
| ~ ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xk))
| ( sdtlpdtrp0(W2,W5) = tptp_fun_W3_19(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) ) ) ) )
| ~ aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,xi),szDzozmdt0(sdtlpdtrp0(xC,xi))),xT)
| ~ iLess0(xk,szszuzczcdt0(xk))
| ~ aFunction0(sdtlpdtrp0(xC,xi))
| ( szDzozmdt0(sdtlpdtrp0(xC,xi)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) )
| ~ ( ~ aElementOf0(tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xT)
| ~ aSubsetOf0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))
| ~ ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xk))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W5) = tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) ) ) ) ) ),
inference(monotonicity,[status(thm)],[78]) ).
tff(80,plain,
( ( ~ ! [W2: $i] :
( ~ aFunction0(W2)
| ~ aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT)
| ~ iLess0(xk,szszuzczcdt0(xk))
| ( szDzozmdt0(W2) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) )
| ~ ( ~ aElementOf0(tptp_fun_W3_19(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xT)
| ~ aSubsetOf0(tptp_fun_W4_20(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(tptp_fun_W4_20(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))
| ~ ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xk))
| ( sdtlpdtrp0(W2,W5) = tptp_fun_W3_19(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) ) ) ) )
| ~ aFunction0(sdtlpdtrp0(xC,xi))
| ~ aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,xi),szDzozmdt0(sdtlpdtrp0(xC,xi))),xT)
| ~ iLess0(xk,szszuzczcdt0(xk))
| ( szDzozmdt0(sdtlpdtrp0(xC,xi)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) )
| ~ ( ~ aElementOf0(tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xT)
| ~ aSubsetOf0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))
| ~ ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xk))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W5) = tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) ) ) ) )
<=> ( ~ ! [W2: $i] :
( ~ aFunction0(W2)
| ~ aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT)
| ~ iLess0(xk,szszuzczcdt0(xk))
| ( szDzozmdt0(W2) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) )
| ~ ( ~ aElementOf0(tptp_fun_W3_19(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xT)
| ~ aSubsetOf0(tptp_fun_W4_20(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(tptp_fun_W4_20(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))
| ~ ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xk))
| ( sdtlpdtrp0(W2,W5) = tptp_fun_W3_19(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) ) ) ) )
| ~ aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,xi),szDzozmdt0(sdtlpdtrp0(xC,xi))),xT)
| ~ iLess0(xk,szszuzczcdt0(xk))
| ~ aFunction0(sdtlpdtrp0(xC,xi))
| ( szDzozmdt0(sdtlpdtrp0(xC,xi)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) )
| ~ ( ~ aElementOf0(tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xT)
| ~ aSubsetOf0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))
| ~ ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xk))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W5) = tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) ) ) ) ) ),
inference(transitivity,[status(thm)],[79,74]) ).
tff(81,plain,
( ~ ! [W2: $i] :
( ~ aFunction0(W2)
| ~ aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT)
| ~ iLess0(xk,szszuzczcdt0(xk))
| ( szDzozmdt0(W2) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) )
| ~ ( ~ aElementOf0(tptp_fun_W3_19(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xT)
| ~ aSubsetOf0(tptp_fun_W4_20(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(tptp_fun_W4_20(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))
| ~ ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xk))
| ( sdtlpdtrp0(W2,W5) = tptp_fun_W3_19(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) ) ) ) )
| ~ aFunction0(sdtlpdtrp0(xC,xi))
| ~ aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,xi),szDzozmdt0(sdtlpdtrp0(xC,xi))),xT)
| ~ iLess0(xk,szszuzczcdt0(xk))
| ( szDzozmdt0(sdtlpdtrp0(xC,xi)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) )
| ~ ( ~ aElementOf0(tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xT)
| ~ aSubsetOf0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))
| ~ ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xk))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W5) = tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(82,plain,
( ~ ! [W2: $i] :
( ~ aFunction0(W2)
| ~ aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT)
| ~ iLess0(xk,szszuzczcdt0(xk))
| ( szDzozmdt0(W2) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) )
| ~ ( ~ aElementOf0(tptp_fun_W3_19(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xT)
| ~ aSubsetOf0(tptp_fun_W4_20(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(tptp_fun_W4_20(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))
| ~ ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xk))
| ( sdtlpdtrp0(W2,W5) = tptp_fun_W3_19(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) ) ) ) )
| ~ aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,xi),szDzozmdt0(sdtlpdtrp0(xC,xi))),xT)
| ~ iLess0(xk,szszuzczcdt0(xk))
| ~ aFunction0(sdtlpdtrp0(xC,xi))
| ( szDzozmdt0(sdtlpdtrp0(xC,xi)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) )
| ~ ( ~ aElementOf0(tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xT)
| ~ aSubsetOf0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))
| ~ ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xk))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W5) = tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) ) ) ) ),
inference(modus_ponens,[status(thm)],[81,80]) ).
tff(83,plain,
~ ( ~ aElementOf0(tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xT)
| ~ aSubsetOf0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))
| ~ ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xk))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W5) = tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) ) ) ),
inference(unit_resolution,[status(thm)],[82,73,68,63,58,53]) ).
tff(84,plain,
( ~ aElementOf0(tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xT)
| ~ aSubsetOf0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))
| ~ ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xk))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W5) = tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) ) )
| isCountable0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk)) ),
inference(tautology,[status(thm)],]) ).
tff(85,plain,
isCountable0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk)),
inference(unit_resolution,[status(thm)],[84,83]) ).
tff(86,plain,
( ~ aElementOf0(tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xT)
| ~ aSubsetOf0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))
| ~ ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xk))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W5) = tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) ) )
| aSubsetOf0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ),
inference(tautology,[status(thm)],]) ).
tff(87,plain,
aSubsetOf0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))),
inference(unit_resolution,[status(thm)],[86,83]) ).
tff(88,plain,
( ~ aElementOf0(tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xT)
| ~ aSubsetOf0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))
| ~ ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xk))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W5) = tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) ) )
| aElementOf0(tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xT) ),
inference(tautology,[status(thm)],]) ).
tff(89,plain,
aElementOf0(tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xT),
inference(unit_resolution,[status(thm)],[88,83]) ).
tff(90,plain,
^ [W0: $i,W1: $i] :
refl(
( ( ~ aElementOf0(W0,xT)
| ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(W1)
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_21(W1,W0))
| ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xk)) ) )
<=> ( ~ aElementOf0(W0,xT)
| ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(W1)
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_21(W1,W0))
| ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xk)) ) ) )),
inference(bind,[status(th)],]) ).
tff(91,plain,
( ! [W0: $i,W1: $i] :
( ~ aElementOf0(W0,xT)
| ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(W1)
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_21(W1,W0))
| ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xk)) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aElementOf0(W0,xT)
| ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(W1)
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_21(W1,W0))
| ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xk)) ) ) ),
inference(quant_intro,[status(thm)],[90]) ).
tff(92,plain,
^ [W0: $i,W1: $i] :
trans(
monotonicity(
rewrite(
( ~ ( ~ ( aSet0(tptp_fun_W2_21(W1,W0))
& aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xk)) )
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(W1,W0)) = W0 ) )
<=> ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_21(W1,W0))
| ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xk)) ) )),
( ( ~ aElementOf0(W0,xT)
| ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(W1)
| ~ ( ~ ( aSet0(tptp_fun_W2_21(W1,W0))
& aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xk)) )
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(W1,W0)) = W0 ) ) )
<=> ( ~ aElementOf0(W0,xT)
| ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(W1)
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_21(W1,W0))
| ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xk)) ) ) )),
rewrite(
( ( ~ aElementOf0(W0,xT)
| ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(W1)
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_21(W1,W0))
| ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xk)) ) )
<=> ( ~ aElementOf0(W0,xT)
| ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(W1)
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_21(W1,W0))
| ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xk)) ) ) )),
( ( ~ aElementOf0(W0,xT)
| ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(W1)
| ~ ( ~ ( aSet0(tptp_fun_W2_21(W1,W0))
& aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xk)) )
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(W1,W0)) = W0 ) ) )
<=> ( ~ aElementOf0(W0,xT)
| ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(W1)
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_21(W1,W0))
| ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xk)) ) ) )),
inference(bind,[status(th)],]) ).
tff(93,plain,
( ! [W0: $i,W1: $i] :
( ~ aElementOf0(W0,xT)
| ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(W1)
| ~ ( ~ ( aSet0(tptp_fun_W2_21(W1,W0))
& aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xk)) )
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(W1,W0)) = W0 ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aElementOf0(W0,xT)
| ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(W1)
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_21(W1,W0))
| ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xk)) ) ) ),
inference(quant_intro,[status(thm)],[92]) ).
tff(94,plain,
( ~ ? [W0: $i,W1: $i] :
( aElementOf0(W0,xT)
& aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& isCountable0(W1)
& ! [W2: $i] :
( ~ ( aSet0(W2)
& aElementOf0(W2,slbdtsldtrb0(W1,xk)) )
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W2) = W0 ) ) )
<=> ~ ? [W0: $i,W1: $i] :
( aElementOf0(W0,xT)
& aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& isCountable0(W1)
& ! [W2: $i] :
( ~ ( aSet0(W2)
& aElementOf0(W2,slbdtsldtrb0(W1,xk)) )
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W2) = W0 ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(95,plain,
( ~ ? [W0: $i,W1: $i] :
( aElementOf0(W0,xT)
& aSubsetOf0(W1,xY)
& isCountable0(W1)
& ! [W2: $i] :
( ~ ( aSet0(W2)
& aElementOf0(W2,slbdtsldtrb0(W1,xk)) )
| ( sdtlpdtrp0(xd,W2) = W0 ) ) )
<=> ~ ? [W0: $i,W1: $i] :
( aElementOf0(W0,xT)
& aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& isCountable0(W1)
& ! [W2: $i] :
( ~ ( aSet0(W2)
& aElementOf0(W2,slbdtsldtrb0(W1,xk)) )
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W2) = W0 ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(96,plain,
( ~ ? [W0: $i,W1: $i] :
( aElementOf0(W0,xT)
& aSubsetOf0(W1,xY)
& isCountable0(W1)
& ! [W2: $i] :
( ~ ( aSet0(W2)
& aElementOf0(W2,slbdtsldtrb0(W1,xk)) )
| ( sdtlpdtrp0(xd,W2) = W0 ) ) )
<=> ~ ? [W0: $i,W1: $i] :
( aElementOf0(W0,xT)
& aSubsetOf0(W1,xY)
& isCountable0(W1)
& ! [W2: $i] :
( ~ ( aSet0(W2)
& aElementOf0(W2,slbdtsldtrb0(W1,xk)) )
| ( sdtlpdtrp0(xd,W2) = W0 ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(97,plain,
( ~ ? [W0: $i,W1: $i] :
( aElementOf0(W0,xT)
& aSubsetOf0(W1,xY)
& isCountable0(W1)
& ! [W2: $i] :
( ( aSet0(W2)
& aElementOf0(W2,slbdtsldtrb0(W1,xk)) )
=> ( sdtlpdtrp0(xd,W2) = W0 ) ) )
<=> ~ ? [W0: $i,W1: $i] :
( aElementOf0(W0,xT)
& aSubsetOf0(W1,xY)
& isCountable0(W1)
& ! [W2: $i] :
( ~ ( aSet0(W2)
& aElementOf0(W2,slbdtsldtrb0(W1,xk)) )
| ( sdtlpdtrp0(xd,W2) = W0 ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(98,axiom,
~ ? [W0: $i,W1: $i] :
( aElementOf0(W0,xT)
& aSubsetOf0(W1,xY)
& isCountable0(W1)
& ! [W2: $i] :
( ( aSet0(W2)
& aElementOf0(W2,slbdtsldtrb0(W1,xk)) )
=> ( sdtlpdtrp0(xd,W2) = W0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(99,plain,
~ ? [W0: $i,W1: $i] :
( aElementOf0(W0,xT)
& aSubsetOf0(W1,xY)
& isCountable0(W1)
& ! [W2: $i] :
( ~ ( aSet0(W2)
& aElementOf0(W2,slbdtsldtrb0(W1,xk)) )
| ( sdtlpdtrp0(xd,W2) = W0 ) ) ),
inference(modus_ponens,[status(thm)],[98,97]) ).
tff(100,plain,
~ ? [W0: $i,W1: $i] :
( aElementOf0(W0,xT)
& aSubsetOf0(W1,xY)
& isCountable0(W1)
& ! [W2: $i] :
( ~ ( aSet0(W2)
& aElementOf0(W2,slbdtsldtrb0(W1,xk)) )
| ( sdtlpdtrp0(xd,W2) = W0 ) ) ),
inference(modus_ponens,[status(thm)],[99,96]) ).
tff(101,plain,
~ ? [W0: $i,W1: $i] :
( aElementOf0(W0,xT)
& aSubsetOf0(W1,xY)
& isCountable0(W1)
& ! [W2: $i] :
( ~ ( aSet0(W2)
& aElementOf0(W2,slbdtsldtrb0(W1,xk)) )
| ( sdtlpdtrp0(xd,W2) = W0 ) ) ),
inference(modus_ponens,[status(thm)],[100,96]) ).
tff(102,plain,
~ ? [W0: $i,W1: $i] :
( aElementOf0(W0,xT)
& aSubsetOf0(W1,xY)
& isCountable0(W1)
& ! [W2: $i] :
( ~ ( aSet0(W2)
& aElementOf0(W2,slbdtsldtrb0(W1,xk)) )
| ( sdtlpdtrp0(xd,W2) = W0 ) ) ),
inference(modus_ponens,[status(thm)],[101,96]) ).
tff(103,plain,
~ ? [W0: $i,W1: $i] :
( aElementOf0(W0,xT)
& aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& isCountable0(W1)
& ! [W2: $i] :
( ~ ( aSet0(W2)
& aElementOf0(W2,slbdtsldtrb0(W1,xk)) )
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W2) = W0 ) ) ),
inference(modus_ponens,[status(thm)],[102,95]) ).
tff(104,plain,
~ ? [W0: $i,W1: $i] :
( aElementOf0(W0,xT)
& aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& isCountable0(W1)
& ! [W2: $i] :
( ~ ( aSet0(W2)
& aElementOf0(W2,slbdtsldtrb0(W1,xk)) )
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W2) = W0 ) ) ),
inference(modus_ponens,[status(thm)],[103,94]) ).
tff(105,plain,
~ ? [W0: $i,W1: $i] :
( aElementOf0(W0,xT)
& aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& isCountable0(W1)
& ! [W2: $i] :
( ~ ( aSet0(W2)
& aElementOf0(W2,slbdtsldtrb0(W1,xk)) )
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W2) = W0 ) ) ),
inference(modus_ponens,[status(thm)],[104,94]) ).
tff(106,plain,
~ ? [W0: $i,W1: $i] :
( aElementOf0(W0,xT)
& aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& isCountable0(W1)
& ! [W2: $i] :
( ~ ( aSet0(W2)
& aElementOf0(W2,slbdtsldtrb0(W1,xk)) )
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W2) = W0 ) ) ),
inference(modus_ponens,[status(thm)],[105,94]) ).
tff(107,plain,
^ [W0: $i,W1: $i] :
nnf_neg(refl($oeq(~ aElementOf0(W0,xT),~ aElementOf0(W0,xT))),refl($oeq(~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))),~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))))),refl($oeq(~ isCountable0(W1),~ isCountable0(W1))),
sk(
$oeq(
~ ! [W2: $i] :
( ~ ( aSet0(W2)
& aElementOf0(W2,slbdtsldtrb0(W1,xk)) )
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W2) = W0 ) ),
~ ( ~ ( aSet0(tptp_fun_W2_21(W1,W0))
& aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xk)) )
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(W1,W0)) = W0 ) ))),
$oeq(
~ ( aElementOf0(W0,xT)
& aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& isCountable0(W1)
& ! [W2: $i] :
( ~ ( aSet0(W2)
& aElementOf0(W2,slbdtsldtrb0(W1,xk)) )
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W2) = W0 ) ) ),
( ~ aElementOf0(W0,xT)
| ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(W1)
| ~ ( ~ ( aSet0(tptp_fun_W2_21(W1,W0))
& aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xk)) )
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(W1,W0)) = W0 ) ) ))),
inference(bind,[status(th)],]) ).
tff(108,plain,
! [W0: $i,W1: $i] :
( ~ aElementOf0(W0,xT)
| ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(W1)
| ~ ( ~ ( aSet0(tptp_fun_W2_21(W1,W0))
& aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xk)) )
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(W1,W0)) = W0 ) ) ),
inference(nnf-neg,[status(sab)],[106,107]) ).
tff(109,plain,
! [W0: $i,W1: $i] :
( ~ aElementOf0(W0,xT)
| ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(W1)
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_21(W1,W0))
| ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xk)) ) ),
inference(modus_ponens,[status(thm)],[108,93]) ).
tff(110,plain,
! [W0: $i,W1: $i] :
( ~ aElementOf0(W0,xT)
| ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(W1)
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_21(W1,W0))
| ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xk)) ) ),
inference(modus_ponens,[status(thm)],[109,91]) ).
tff(111,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W0,xT)
| ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(W1)
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_21(W1,W0))
| ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xk)) ) )
| ~ aElementOf0(tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xT)
| ~ aSubsetOf0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))) = tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) )
| ~ aSet0(tptp_fun_W2_21(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk)))
| ~ aElementOf0(tptp_fun_W2_21(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk)),slbdtsldtrb0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xk)) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W0,xT)
| ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(W1)
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_21(W1,W0))
| ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xk)) ) )
| ~ aElementOf0(tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xT)
| ~ aSubsetOf0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))) = tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) )
| ~ aSet0(tptp_fun_W2_21(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk)))
| ~ aElementOf0(tptp_fun_W2_21(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk)),slbdtsldtrb0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xk)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(112,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W0,xT)
| ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(W1)
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_21(W1,W0))
| ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xk)) ) )
| ~ aElementOf0(tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xT)
| ~ aSubsetOf0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))) = tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) )
| ~ aSet0(tptp_fun_W2_21(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk)))
| ~ aElementOf0(tptp_fun_W2_21(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk)),slbdtsldtrb0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xk)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(113,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W0,xT)
| ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(W1)
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_21(W1,W0))
| ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xk)) ) )
| ~ aElementOf0(tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xT)
| ~ aSubsetOf0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))) = tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) )
| ~ aSet0(tptp_fun_W2_21(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk)))
| ~ aElementOf0(tptp_fun_W2_21(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk)),slbdtsldtrb0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xk)) ) ),
inference(modus_ponens,[status(thm)],[112,111]) ).
tff(114,plain,
~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))) = tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) )
| ~ aSet0(tptp_fun_W2_21(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk)))
| ~ aElementOf0(tptp_fun_W2_21(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk)),slbdtsldtrb0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xk)) ),
inference(unit_resolution,[status(thm)],[113,110,89,87,85]) ).
tff(115,plain,
( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))) = tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) )
| ~ aSet0(tptp_fun_W2_21(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk)))
| ~ aElementOf0(tptp_fun_W2_21(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk)),slbdtsldtrb0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xk))
| aElementOf0(tptp_fun_W2_21(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk)),slbdtsldtrb0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xk)) ),
inference(tautology,[status(thm)],]) ).
tff(116,plain,
aElementOf0(tptp_fun_W2_21(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk)),slbdtsldtrb0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xk)),
inference(unit_resolution,[status(thm)],[115,114]) ).
tff(117,plain,
( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))) = tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) )
| ~ aSet0(tptp_fun_W2_21(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk)))
| ~ aElementOf0(tptp_fun_W2_21(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk)),slbdtsldtrb0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xk))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))) != tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) ) ),
inference(tautology,[status(thm)],]) ).
tff(118,plain,
sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))) != tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),
inference(unit_resolution,[status(thm)],[117,114]) ).
tff(119,plain,
( ~ aElementOf0(tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xT)
| ~ aSubsetOf0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))
| ~ ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xk))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W5) = tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) ) )
| ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xk))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W5) = tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(120,plain,
! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xk))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W5) = tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) ) ),
inference(unit_resolution,[status(thm)],[119,83]) ).
tff(121,plain,
( ( ~ ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xk))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W5) = tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) ) )
| ~ aElementOf0(tptp_fun_W2_21(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk)),slbdtsldtrb0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xk))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))) = tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) ) )
<=> ( ~ ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xk))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W5) = tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) ) )
| ~ aElementOf0(tptp_fun_W2_21(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk)),slbdtsldtrb0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xk))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))) = tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(122,plain,
( ~ ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xk))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W5) = tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) ) )
| ~ aElementOf0(tptp_fun_W2_21(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk)),slbdtsldtrb0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xk))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))) = tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(123,plain,
( ~ ! [W5: $i] :
( ~ aElementOf0(W5,slbdtsldtrb0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xk))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W5) = tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) ) )
| ~ aElementOf0(tptp_fun_W2_21(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk)),slbdtsldtrb0(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),xk))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(tptp_fun_W4_20(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk),tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))) = tptp_fun_W3_19(sdtlpdtrp0(xC,xi),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) ) ),
inference(modus_ponens,[status(thm)],[122,121]) ).
tff(124,plain,
$false,
inference(unit_resolution,[status(thm)],[123,120,118,116]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : NUM591+1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.10/0.32 % Computer : n011.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Fri Sep 2 12:03:57 EDT 2022
% 0.10/0.32 % CPUTime :
% 0.10/0.32 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.10/0.32 Usage: tptp [options] [-file:]file
% 0.10/0.32 -h, -? prints this message.
% 0.10/0.32 -smt2 print SMT-LIB2 benchmark.
% 0.10/0.32 -m, -model generate model.
% 0.10/0.32 -p, -proof generate proof.
% 0.10/0.32 -c, -core generate unsat core of named formulas.
% 0.10/0.32 -st, -statistics display statistics.
% 0.10/0.32 -t:timeout set timeout (in second).
% 0.10/0.32 -smt2status display status in smt2 format instead of SZS.
% 0.10/0.32 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.10/0.32 -<param>:<value> configuration parameter and value.
% 0.10/0.32 -o:<output-file> file to place output in.
% 13.59/8.65 % SZS status Theorem
% 13.59/8.65 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------