%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM594+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 : Sat Jun 21 05:21:31 AM UTC 2025
% Result : Theorem 24.58s 24.76s
% Output : Proof 24.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 43
% Syntax : Number of formulae : 110 ( 27 unt; 0 typ; 0 def)
% Number of atoms : 1639 ( 542 equ)
% Maximal formula atoms : 72 ( 14 avg)
% Number of connectives : 3579 (2078 ~;1286 |; 117 &)
% ( 81 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 9 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of FOOLs : 28 ( 28 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 14 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-3 aty)
% Number of variables : 501 ( 465 !; 24 ?; 501 :)
% Comments :
%------------------------------------------------------------------------------
tff(xx_type,type,
xx: $i ).
tff(sdtlpdtrp0_type,type,
sdtlpdtrp0: ( $i * $i ) > $i ).
tff(tptp_fun_W4_13_type,type,
tptp_fun_W4_13: ( $i * $i * $i ) > $i ).
tff(xd_type,type,
xd: $i ).
tff(szNzAzT0_type,type,
szNzAzT0: $i ).
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(sdtlcdtrc0_type,type,
sdtlcdtrc0: ( $i * $i ) > $i ).
tff(szDzozmdt0_type,type,
szDzozmdt0: $i > $i ).
tff(aSet0_type,type,
aSet0: $i > $o ).
tff(tptp_fun_W3_14_type,type,
tptp_fun_W3_14: ( $i * $i * $i ) > $i ).
tff(tptp_fun_W4_15_type,type,
tptp_fun_W4_15: ( $i * $i * $i ) > $i ).
tff(aSubsetOf0_type,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff(aFunction0_type,type,
aFunction0: $i > $o ).
tff(xC_type,type,
xC: $i ).
tff(slbdtsldtrb0_type,type,
slbdtsldtrb0: ( $i * $i ) > $i ).
tff(xk_type,type,
xk: $i ).
tff(szszuzczcdt0_type,type,
szszuzczcdt0: $i > $i ).
tff(xN_type,type,
xN: $i ).
tff(isCountable0_type,type,
isCountable0: $i > $o ).
tff(1,plain,
( ( szDzozmdt0(xd) = szNzAzT0 )
<=> ( szDzozmdt0(xd) = szNzAzT0 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
( aFunction0(xd)
& ( szDzozmdt0(xd) = szNzAzT0 )
& ! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> ! [W1: $i] :
( ( aSet0(W1)
& aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk)) )
=> ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4730) ).
tff(3,plain,
( aFunction0(xd)
& ( szDzozmdt0(xd) = szNzAzT0 ) ),
inference(and_elim,[status(thm)],[2]) ).
tff(4,plain,
szDzozmdt0(xd) = szNzAzT0,
inference(and_elim,[status(thm)],[3]) ).
tff(5,plain,
szDzozmdt0(xd) = szNzAzT0,
inference(modus_ponens,[status(thm)],[4,1]) ).
tff(6,plain,
( aSubsetOf0(szNzAzT0,szDzozmdt0(xd))
<=> aSubsetOf0(szNzAzT0,szNzAzT0) ),
inference(monotonicity,[status(thm)],[5]) ).
tff(7,plain,
( aSubsetOf0(szNzAzT0,szNzAzT0)
<=> aSubsetOf0(szNzAzT0,szDzozmdt0(xd)) ),
inference(symmetry,[status(thm)],[6]) ).
tff(8,plain,
( aSet0(szNzAzT0)
<=> aSet0(szNzAzT0) ),
inference(rewrite,[status(thm)],[]) ).
tff(9,axiom,
( aSet0(szNzAzT0)
& isCountable0(szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNATSet) ).
tff(10,plain,
aSet0(szNzAzT0),
inference(and_elim,[status(thm)],[9]) ).
tff(11,plain,
aSet0(szNzAzT0),
inference(modus_ponens,[status(thm)],[10,8]) ).
tff(12,plain,
^ [W0: $i] :
refl(( ( ~ aSet0(W0)
| aSubsetOf0(W0,W0) )
<=> ( ~ aSet0(W0)
| aSubsetOf0(W0,W0) ) )),
inference(bind,[status(th)],[]) ).
tff(13,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) ) ),
inference(quant_intro,[status(thm)],[12]) ).
tff(14,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,plain,
^ [W0: $i] :
rewrite(( ( aSet0(W0)
=> aSubsetOf0(W0,W0) )
<=> ( ~ aSet0(W0)
| aSubsetOf0(W0,W0) ) )),
inference(bind,[status(th)],[]) ).
tff(16,plain,
( ! [W0: $i] :
( aSet0(W0)
=> aSubsetOf0(W0,W0) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,axiom,
! [W0: $i] :
( aSet0(W0)
=> aSubsetOf0(W0,W0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubRefl) ).
tff(18,plain,
! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) ),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) ),
inference(modus_ponens,[status(thm)],[18,14]) ).
tff(20,plain,
! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) ),
inference(skolemize,[status(sab)],[19]) ).
tff(21,plain,
! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) ),
inference(modus_ponens,[status(thm)],[20,13]) ).
tff(22,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) )
| ~ aSet0(szNzAzT0)
| aSubsetOf0(szNzAzT0,szNzAzT0) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) )
| ~ aSet0(szNzAzT0)
| aSubsetOf0(szNzAzT0,szNzAzT0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) )
| ~ aSet0(szNzAzT0)
| aSubsetOf0(szNzAzT0,szNzAzT0) ),
inference(quant_inst,[status(thm)],[]) ).
tff(24,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) )
| ~ aSet0(szNzAzT0)
| aSubsetOf0(szNzAzT0,szNzAzT0) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
aSubsetOf0(szNzAzT0,szNzAzT0),
inference(unit_resolution,[status(thm)],[24,21,11]) ).
tff(26,plain,
aSubsetOf0(szNzAzT0,szDzozmdt0(xd)),
inference(modus_ponens,[status(thm)],[25,7]) ).
tff(27,plain,
( aFunction0(xd)
<=> aFunction0(xd) ),
inference(rewrite,[status(thm)],[]) ).
tff(28,plain,
aFunction0(xd),
inference(and_elim,[status(thm)],[3]) ).
tff(29,plain,
aFunction0(xd),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
^ [W0: $i] :
rewrite(( ( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtlcdtrc0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_13(W3,W1,W0)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != W3 ) ) ) ) ) )
| ~ ( ( W2 = sdtlcdtrc0(W0,W1) )
| ~ aSet0(W2)
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_15(W2,W1,W0)) != tptp_fun_W3_14(W2,W1,W0) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != tptp_fun_W3_14(W2,W1,W0) ) ) ) ) ) ) ) )
<=> ( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtlcdtrc0(W0,W1) )
| ~ aSet0(W2)
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_15(W2,W1,W0)) != tptp_fun_W3_14(W2,W1,W0) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != tptp_fun_W3_14(W2,W1,W0) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_13(W3,W1,W0)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != W3 ) ) ) ) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(31,plain,
( ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtlcdtrc0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_13(W3,W1,W0)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != W3 ) ) ) ) ) )
| ~ ( ( W2 = sdtlcdtrc0(W0,W1) )
| ~ aSet0(W2)
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_15(W2,W1,W0)) != tptp_fun_W3_14(W2,W1,W0) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != tptp_fun_W3_14(W2,W1,W0) ) ) ) ) ) ) ) )
<=> ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtlcdtrc0(W0,W1) )
| ~ aSet0(W2)
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_15(W2,W1,W0)) != tptp_fun_W3_14(W2,W1,W0) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != tptp_fun_W3_14(W2,W1,W0) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_13(W3,W1,W0)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != W3 ) ) ) ) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,plain,
^ [W0: $i] :
refl(( ( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtlcdtrc0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_13(W3,W1,W0)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != W3 ) ) ) ) ) )
| ~ ( ( W2 = sdtlcdtrc0(W0,W1) )
| ~ aSet0(W2)
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_15(W2,W1,W0)) != tptp_fun_W3_14(W2,W1,W0) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != tptp_fun_W3_14(W2,W1,W0) ) ) ) ) ) ) ) )
<=> ( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtlcdtrc0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_13(W3,W1,W0)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != W3 ) ) ) ) ) )
| ~ ( ( W2 = sdtlcdtrc0(W0,W1) )
| ~ aSet0(W2)
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_15(W2,W1,W0)) != tptp_fun_W3_14(W2,W1,W0) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != tptp_fun_W3_14(W2,W1,W0) ) ) ) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(33,plain,
( ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtlcdtrc0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_13(W3,W1,W0)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != W3 ) ) ) ) ) )
| ~ ( ( W2 = sdtlcdtrc0(W0,W1) )
| ~ aSet0(W2)
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_15(W2,W1,W0)) != tptp_fun_W3_14(W2,W1,W0) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != tptp_fun_W3_14(W2,W1,W0) ) ) ) ) ) ) ) )
<=> ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtlcdtrc0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_13(W3,W1,W0)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != W3 ) ) ) ) ) )
| ~ ( ( W2 = sdtlcdtrc0(W0,W1) )
| ~ aSet0(W2)
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_15(W2,W1,W0)) != tptp_fun_W3_14(W2,W1,W0) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != tptp_fun_W3_14(W2,W1,W0) ) ) ) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
^ [W0: $i] :
rewrite(( ( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtlcdtrc0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_13(W3,W1,W0)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != W3 ) ) ) ) ) )
| ~ ( ( W2 = sdtlcdtrc0(W0,W1) )
| ~ aSet0(W2)
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_15(W2,W1,W0)) != tptp_fun_W3_14(W2,W1,W0) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != tptp_fun_W3_14(W2,W1,W0) ) ) ) ) ) ) ) )
<=> ( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtlcdtrc0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_13(W3,W1,W0)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != W3 ) ) ) ) ) )
| ~ ( ( W2 = sdtlcdtrc0(W0,W1) )
| ~ aSet0(W2)
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_15(W2,W1,W0)) != tptp_fun_W3_14(W2,W1,W0) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != tptp_fun_W3_14(W2,W1,W0) ) ) ) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(35,plain,
( ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtlcdtrc0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_13(W3,W1,W0)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != W3 ) ) ) ) ) )
| ~ ( ( W2 = sdtlcdtrc0(W0,W1) )
| ~ aSet0(W2)
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_15(W2,W1,W0)) != tptp_fun_W3_14(W2,W1,W0) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != tptp_fun_W3_14(W2,W1,W0) ) ) ) ) ) ) ) )
<=> ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtlcdtrc0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_13(W3,W1,W0)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != W3 ) ) ) ) ) )
| ~ ( ( W2 = sdtlcdtrc0(W0,W1) )
| ~ aSet0(W2)
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_15(W2,W1,W0)) != tptp_fun_W3_14(W2,W1,W0) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != tptp_fun_W3_14(W2,W1,W0) ) ) ) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[34]) ).
tff(36,plain,
( ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtlcdtrc0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_13(W3,W1,W0)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != W3 ) ) ) ) ) )
| ~ ( ( W2 = sdtlcdtrc0(W0,W1) )
| ~ aSet0(W2)
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_15(W2,W1,W0)) != tptp_fun_W3_14(W2,W1,W0) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != tptp_fun_W3_14(W2,W1,W0) ) ) ) ) ) ) ) )
<=> ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtlcdtrc0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_13(W3,W1,W0)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != W3 ) ) ) ) ) )
| ~ ( ( W2 = sdtlcdtrc0(W0,W1) )
| ~ aSet0(W2)
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_15(W2,W1,W0)) != tptp_fun_W3_14(W2,W1,W0) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != tptp_fun_W3_14(W2,W1,W0) ) ) ) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[35,33]) ).
tff(37,plain,
^ [W0: $i] :
rewrite(( ( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
( ( ( W2 != sdtlcdtrc0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( ( ~ aElementOf0(W3,W2)
| ( aElementOf0(tptp_fun_W4_13(W3,W1,W0),W1)
& ( sdtlpdtrp0(W0,tptp_fun_W4_13(W3,W1,W0)) = W3 ) ) )
& ( aElementOf0(W3,W2)
| ! [W4: $i] :
~ ( aElementOf0(W4,W1)
& ( sdtlpdtrp0(W0,W4) = W3 ) ) ) ) ) )
& ( ( W2 = sdtlcdtrc0(W0,W1) )
| ~ aSet0(W2)
| ( ( aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ( aElementOf0(tptp_fun_W4_15(W2,W1,W0),W1)
& ( sdtlpdtrp0(W0,tptp_fun_W4_15(W2,W1,W0)) = tptp_fun_W3_14(W2,W1,W0) ) ) )
& ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ! [W4: $i] :
~ ( aElementOf0(W4,W1)
& ( sdtlpdtrp0(W0,W4) = tptp_fun_W3_14(W2,W1,W0) ) ) ) ) ) ) ) )
<=> ( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtlcdtrc0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_13(W3,W1,W0)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != W3 ) ) ) ) ) )
| ~ ( ( W2 = sdtlcdtrc0(W0,W1) )
| ~ aSet0(W2)
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_15(W2,W1,W0)) != tptp_fun_W3_14(W2,W1,W0) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != tptp_fun_W3_14(W2,W1,W0) ) ) ) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(38,plain,
( ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
( ( ( W2 != sdtlcdtrc0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( ( ~ aElementOf0(W3,W2)
| ( aElementOf0(tptp_fun_W4_13(W3,W1,W0),W1)
& ( sdtlpdtrp0(W0,tptp_fun_W4_13(W3,W1,W0)) = W3 ) ) )
& ( aElementOf0(W3,W2)
| ! [W4: $i] :
~ ( aElementOf0(W4,W1)
& ( sdtlpdtrp0(W0,W4) = W3 ) ) ) ) ) )
& ( ( W2 = sdtlcdtrc0(W0,W1) )
| ~ aSet0(W2)
| ( ( aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ( aElementOf0(tptp_fun_W4_15(W2,W1,W0),W1)
& ( sdtlpdtrp0(W0,tptp_fun_W4_15(W2,W1,W0)) = tptp_fun_W3_14(W2,W1,W0) ) ) )
& ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ! [W4: $i] :
~ ( aElementOf0(W4,W1)
& ( sdtlpdtrp0(W0,W4) = tptp_fun_W3_14(W2,W1,W0) ) ) ) ) ) ) ) )
<=> ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtlcdtrc0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_13(W3,W1,W0)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != W3 ) ) ) ) ) )
| ~ ( ( W2 = sdtlcdtrc0(W0,W1) )
| ~ aSet0(W2)
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_15(W2,W1,W0)) != tptp_fun_W3_14(W2,W1,W0) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != tptp_fun_W3_14(W2,W1,W0) ) ) ) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[37]) ).
tff(39,plain,
^ [W0: $i] :
rewrite(( ( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
( ( ( W2 != sdtlcdtrc0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( ( ~ aElementOf0(W3,W2)
| ( aElementOf0(tptp_fun_W4_13(W3,W1,W0),W1)
& ( sdtlpdtrp0(W0,tptp_fun_W4_13(W3,W1,W0)) = W3 ) ) )
& ( aElementOf0(W3,W2)
| ! [W4: $i] :
~ ( aElementOf0(W4,W1)
& ( sdtlpdtrp0(W0,W4) = W3 ) ) ) ) ) )
& ( ( W2 = sdtlcdtrc0(W0,W1) )
| ~ aSet0(W2)
| ( ( aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ( aElementOf0(tptp_fun_W4_15(W2,W1,W0),W1)
& ( sdtlpdtrp0(W0,tptp_fun_W4_15(W2,W1,W0)) = tptp_fun_W3_14(W2,W1,W0) ) ) )
& ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ! [W4: $i] :
~ ( aElementOf0(W4,W1)
& ( sdtlpdtrp0(W0,W4) = tptp_fun_W3_14(W2,W1,W0) ) ) ) ) ) ) ) )
<=> ( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
( ( ( W2 != sdtlcdtrc0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( ( ~ aElementOf0(W3,W2)
| ( aElementOf0(tptp_fun_W4_13(W3,W1,W0),W1)
& ( sdtlpdtrp0(W0,tptp_fun_W4_13(W3,W1,W0)) = W3 ) ) )
& ( aElementOf0(W3,W2)
| ! [W4: $i] :
~ ( aElementOf0(W4,W1)
& ( sdtlpdtrp0(W0,W4) = W3 ) ) ) ) ) )
& ( ( W2 = sdtlcdtrc0(W0,W1) )
| ~ aSet0(W2)
| ( ( aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ( aElementOf0(tptp_fun_W4_15(W2,W1,W0),W1)
& ( sdtlpdtrp0(W0,tptp_fun_W4_15(W2,W1,W0)) = tptp_fun_W3_14(W2,W1,W0) ) ) )
& ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ! [W4: $i] :
~ ( aElementOf0(W4,W1)
& ( sdtlpdtrp0(W0,W4) = tptp_fun_W3_14(W2,W1,W0) ) ) ) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(40,plain,
( ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
( ( ( W2 != sdtlcdtrc0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( ( ~ aElementOf0(W3,W2)
| ( aElementOf0(tptp_fun_W4_13(W3,W1,W0),W1)
& ( sdtlpdtrp0(W0,tptp_fun_W4_13(W3,W1,W0)) = W3 ) ) )
& ( aElementOf0(W3,W2)
| ! [W4: $i] :
~ ( aElementOf0(W4,W1)
& ( sdtlpdtrp0(W0,W4) = W3 ) ) ) ) ) )
& ( ( W2 = sdtlcdtrc0(W0,W1) )
| ~ aSet0(W2)
| ( ( aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ( aElementOf0(tptp_fun_W4_15(W2,W1,W0),W1)
& ( sdtlpdtrp0(W0,tptp_fun_W4_15(W2,W1,W0)) = tptp_fun_W3_14(W2,W1,W0) ) ) )
& ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ! [W4: $i] :
~ ( aElementOf0(W4,W1)
& ( sdtlpdtrp0(W0,W4) = tptp_fun_W3_14(W2,W1,W0) ) ) ) ) ) ) ) )
<=> ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
( ( ( W2 != sdtlcdtrc0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( ( ~ aElementOf0(W3,W2)
| ( aElementOf0(tptp_fun_W4_13(W3,W1,W0),W1)
& ( sdtlpdtrp0(W0,tptp_fun_W4_13(W3,W1,W0)) = W3 ) ) )
& ( aElementOf0(W3,W2)
| ! [W4: $i] :
~ ( aElementOf0(W4,W1)
& ( sdtlpdtrp0(W0,W4) = W3 ) ) ) ) ) )
& ( ( W2 = sdtlcdtrc0(W0,W1) )
| ~ aSet0(W2)
| ( ( aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ( aElementOf0(tptp_fun_W4_15(W2,W1,W0),W1)
& ( sdtlpdtrp0(W0,tptp_fun_W4_15(W2,W1,W0)) = tptp_fun_W3_14(W2,W1,W0) ) ) )
& ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ! [W4: $i] :
~ ( aElementOf0(W4,W1)
& ( sdtlpdtrp0(W0,W4) = tptp_fun_W3_14(W2,W1,W0) ) ) ) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,plain,
( ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
( ( W2 = sdtlcdtrc0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ? [W4: $i] :
( aElementOf0(W4,W1)
& ( sdtlpdtrp0(W0,W4) = W3 ) ) ) ) ) ) )
<=> ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
( ( W2 = sdtlcdtrc0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ? [W4: $i] :
( aElementOf0(W4,W1)
& ( sdtlpdtrp0(W0,W4) = W3 ) ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,plain,
^ [W0: $i] :
trans(monotonicity(quant_intro(proof_bind(^ [W1: $i] :
rewrite(( ( aSubsetOf0(W1,szDzozmdt0(W0))
=> ! [W2: $i] :
( ( W2 = sdtlcdtrc0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ? [W4: $i] :
( aElementOf0(W4,W1)
& ( sdtlpdtrp0(W0,W4) = W3 ) ) ) ) ) )
<=> ( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
( ( W2 = sdtlcdtrc0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ? [W4: $i] :
( aElementOf0(W4,W1)
& ( sdtlpdtrp0(W0,W4) = W3 ) ) ) ) ) ) ))),
( ! [W1: $i] :
( aSubsetOf0(W1,szDzozmdt0(W0))
=> ! [W2: $i] :
( ( W2 = sdtlcdtrc0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ? [W4: $i] :
( aElementOf0(W4,W1)
& ( sdtlpdtrp0(W0,W4) = W3 ) ) ) ) ) )
<=> ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
( ( W2 = sdtlcdtrc0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ? [W4: $i] :
( aElementOf0(W4,W1)
& ( sdtlpdtrp0(W0,W4) = W3 ) ) ) ) ) ) )),
( ( aFunction0(W0)
=> ! [W1: $i] :
( aSubsetOf0(W1,szDzozmdt0(W0))
=> ! [W2: $i] :
( ( W2 = sdtlcdtrc0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ? [W4: $i] :
( aElementOf0(W4,W1)
& ( sdtlpdtrp0(W0,W4) = W3 ) ) ) ) ) ) )
<=> ( aFunction0(W0)
=> ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
( ( W2 = sdtlcdtrc0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ? [W4: $i] :
( aElementOf0(W4,W1)
& ( sdtlpdtrp0(W0,W4) = W3 ) ) ) ) ) ) ) )),
rewrite(( ( aFunction0(W0)
=> ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
( ( W2 = sdtlcdtrc0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ? [W4: $i] :
( aElementOf0(W4,W1)
& ( sdtlpdtrp0(W0,W4) = W3 ) ) ) ) ) ) )
<=> ( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
( ( W2 = sdtlcdtrc0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ? [W4: $i] :
( aElementOf0(W4,W1)
& ( sdtlpdtrp0(W0,W4) = W3 ) ) ) ) ) ) ) )),
( ( aFunction0(W0)
=> ! [W1: $i] :
( aSubsetOf0(W1,szDzozmdt0(W0))
=> ! [W2: $i] :
( ( W2 = sdtlcdtrc0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ? [W4: $i] :
( aElementOf0(W4,W1)
& ( sdtlpdtrp0(W0,W4) = W3 ) ) ) ) ) ) )
<=> ( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
( ( W2 = sdtlcdtrc0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ? [W4: $i] :
( aElementOf0(W4,W1)
& ( sdtlpdtrp0(W0,W4) = W3 ) ) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(43,plain,
( ! [W0: $i] :
( aFunction0(W0)
=> ! [W1: $i] :
( aSubsetOf0(W1,szDzozmdt0(W0))
=> ! [W2: $i] :
( ( W2 = sdtlcdtrc0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ? [W4: $i] :
( aElementOf0(W4,W1)
& ( sdtlpdtrp0(W0,W4) = W3 ) ) ) ) ) ) )
<=> ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
( ( W2 = sdtlcdtrc0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ? [W4: $i] :
( aElementOf0(W4,W1)
& ( sdtlpdtrp0(W0,W4) = W3 ) ) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[42]) ).
tff(44,axiom,
! [W0: $i] :
( aFunction0(W0)
=> ! [W1: $i] :
( aSubsetOf0(W1,szDzozmdt0(W0))
=> ! [W2: $i] :
( ( W2 = sdtlcdtrc0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ? [W4: $i] :
( aElementOf0(W4,W1)
& ( sdtlpdtrp0(W0,W4) = W3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSImg) ).
tff(45,plain,
! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
( ( W2 = sdtlcdtrc0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ? [W4: $i] :
( aElementOf0(W4,W1)
& ( sdtlpdtrp0(W0,W4) = W3 ) ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
( ( W2 = sdtlcdtrc0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ? [W4: $i] :
( aElementOf0(W4,W1)
& ( sdtlpdtrp0(W0,W4) = W3 ) ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[45,41]) ).
tff(47,plain,
! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
( ( ( W2 != sdtlcdtrc0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( ( ~ aElementOf0(W3,W2)
| ( aElementOf0(tptp_fun_W4_13(W3,W1,W0),W1)
& ( sdtlpdtrp0(W0,tptp_fun_W4_13(W3,W1,W0)) = W3 ) ) )
& ( aElementOf0(W3,W2)
| ! [W4: $i] :
~ ( aElementOf0(W4,W1)
& ( sdtlpdtrp0(W0,W4) = W3 ) ) ) ) ) )
& ( ( W2 = sdtlcdtrc0(W0,W1) )
| ~ aSet0(W2)
| ( ( aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ( aElementOf0(tptp_fun_W4_15(W2,W1,W0),W1)
& ( sdtlpdtrp0(W0,tptp_fun_W4_15(W2,W1,W0)) = tptp_fun_W3_14(W2,W1,W0) ) ) )
& ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ! [W4: $i] :
~ ( aElementOf0(W4,W1)
& ( sdtlpdtrp0(W0,W4) = tptp_fun_W3_14(W2,W1,W0) ) ) ) ) ) ) ) ),
inference(skolemize,[status(sab)],[46]) ).
tff(48,plain,
! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
( ( ( W2 != sdtlcdtrc0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( ( ~ aElementOf0(W3,W2)
| ( aElementOf0(tptp_fun_W4_13(W3,W1,W0),W1)
& ( sdtlpdtrp0(W0,tptp_fun_W4_13(W3,W1,W0)) = W3 ) ) )
& ( aElementOf0(W3,W2)
| ! [W4: $i] :
~ ( aElementOf0(W4,W1)
& ( sdtlpdtrp0(W0,W4) = W3 ) ) ) ) ) )
& ( ( W2 = sdtlcdtrc0(W0,W1) )
| ~ aSet0(W2)
| ( ( aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ( aElementOf0(tptp_fun_W4_15(W2,W1,W0),W1)
& ( sdtlpdtrp0(W0,tptp_fun_W4_15(W2,W1,W0)) = tptp_fun_W3_14(W2,W1,W0) ) ) )
& ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ! [W4: $i] :
~ ( aElementOf0(W4,W1)
& ( sdtlpdtrp0(W0,W4) = tptp_fun_W3_14(W2,W1,W0) ) ) ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[47,40]) ).
tff(49,plain,
! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtlcdtrc0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_13(W3,W1,W0)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != W3 ) ) ) ) ) )
| ~ ( ( W2 = sdtlcdtrc0(W0,W1) )
| ~ aSet0(W2)
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_15(W2,W1,W0)) != tptp_fun_W3_14(W2,W1,W0) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != tptp_fun_W3_14(W2,W1,W0) ) ) ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[48,38]) ).
tff(50,plain,
! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtlcdtrc0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_13(W3,W1,W0)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != W3 ) ) ) ) ) )
| ~ ( ( W2 = sdtlcdtrc0(W0,W1) )
| ~ aSet0(W2)
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_15(W2,W1,W0)) != tptp_fun_W3_14(W2,W1,W0) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != tptp_fun_W3_14(W2,W1,W0) ) ) ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[49,36]) ).
tff(51,plain,
! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtlcdtrc0(W0,W1) )
| ~ aSet0(W2)
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_15(W2,W1,W0)) != tptp_fun_W3_14(W2,W1,W0) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != tptp_fun_W3_14(W2,W1,W0) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_13(W3,W1,W0)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != W3 ) ) ) ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[50,31]) ).
tff(52,plain,
( ( ~ ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtlcdtrc0(W0,W1) )
| ~ aSet0(W2)
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_15(W2,W1,W0)) != tptp_fun_W3_14(W2,W1,W0) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != tptp_fun_W3_14(W2,W1,W0) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_13(W3,W1,W0)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != W3 ) ) ) ) ) ) ) ) )
| ~ aFunction0(xd)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(xd))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlcdtrc0(xd,W1) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,W1,xd) ) ) )
| ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,W1,xd)) != tptp_fun_W3_14(W2,W1,xd) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,W1,xd)) != W3 ) ) ) ) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtlcdtrc0(W0,W1) )
| ~ aSet0(W2)
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_15(W2,W1,W0)) != tptp_fun_W3_14(W2,W1,W0) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != tptp_fun_W3_14(W2,W1,W0) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_13(W3,W1,W0)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != W3 ) ) ) ) ) ) ) ) )
| ~ aFunction0(xd)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(xd))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlcdtrc0(xd,W1) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,W1,xd) ) ) )
| ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,W1,xd)) != tptp_fun_W3_14(W2,W1,xd) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,W1,xd)) != W3 ) ) ) ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,plain,
( ( ~ aFunction0(xd)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(xd))
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtlcdtrc0(xd,W1) )
| ~ aSet0(W2)
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,W1,xd)) != tptp_fun_W3_14(W2,W1,xd) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,W1,xd) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,W1,xd)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) ) ) ) ) ) ) )
<=> ( ~ aFunction0(xd)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(xd))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlcdtrc0(xd,W1) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,W1,xd) ) ) )
| ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,W1,xd)) != tptp_fun_W3_14(W2,W1,xd) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,W1,xd)) != W3 ) ) ) ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(54,plain,
( ( ~ ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtlcdtrc0(W0,W1) )
| ~ aSet0(W2)
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_15(W2,W1,W0)) != tptp_fun_W3_14(W2,W1,W0) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != tptp_fun_W3_14(W2,W1,W0) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_13(W3,W1,W0)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != W3 ) ) ) ) ) ) ) ) )
| ~ aFunction0(xd)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(xd))
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtlcdtrc0(xd,W1) )
| ~ aSet0(W2)
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,W1,xd)) != tptp_fun_W3_14(W2,W1,xd) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,W1,xd) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,W1,xd)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) ) ) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtlcdtrc0(W0,W1) )
| ~ aSet0(W2)
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_15(W2,W1,W0)) != tptp_fun_W3_14(W2,W1,W0) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != tptp_fun_W3_14(W2,W1,W0) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_13(W3,W1,W0)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != W3 ) ) ) ) ) ) ) ) )
| ~ aFunction0(xd)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(xd))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlcdtrc0(xd,W1) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,W1,xd) ) ) )
| ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,W1,xd)) != tptp_fun_W3_14(W2,W1,xd) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,W1,xd)) != W3 ) ) ) ) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[53]) ).
tff(55,plain,
( ( ~ ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtlcdtrc0(W0,W1) )
| ~ aSet0(W2)
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_15(W2,W1,W0)) != tptp_fun_W3_14(W2,W1,W0) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != tptp_fun_W3_14(W2,W1,W0) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_13(W3,W1,W0)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != W3 ) ) ) ) ) ) ) ) )
| ~ aFunction0(xd)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(xd))
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtlcdtrc0(xd,W1) )
| ~ aSet0(W2)
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,W1,xd)) != tptp_fun_W3_14(W2,W1,xd) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,W1,xd) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,W1,xd)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) ) ) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtlcdtrc0(W0,W1) )
| ~ aSet0(W2)
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_15(W2,W1,W0)) != tptp_fun_W3_14(W2,W1,W0) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != tptp_fun_W3_14(W2,W1,W0) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_13(W3,W1,W0)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != W3 ) ) ) ) ) ) ) ) )
| ~ aFunction0(xd)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(xd))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlcdtrc0(xd,W1) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,W1,xd) ) ) )
| ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,W1,xd)) != tptp_fun_W3_14(W2,W1,xd) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,W1,xd)) != W3 ) ) ) ) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[54,52]) ).
tff(56,plain,
( ~ ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtlcdtrc0(W0,W1) )
| ~ aSet0(W2)
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_15(W2,W1,W0)) != tptp_fun_W3_14(W2,W1,W0) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != tptp_fun_W3_14(W2,W1,W0) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_13(W3,W1,W0)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != W3 ) ) ) ) ) ) ) ) )
| ~ aFunction0(xd)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(xd))
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtlcdtrc0(xd,W1) )
| ~ aSet0(W2)
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,W1,xd)) != tptp_fun_W3_14(W2,W1,xd) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,W1,xd) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,W1,xd)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) ) ) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(57,plain,
( ~ ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtlcdtrc0(W0,W1) )
| ~ aSet0(W2)
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_15(W2,W1,W0)) != tptp_fun_W3_14(W2,W1,W0) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,W0),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != tptp_fun_W3_14(W2,W1,W0) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,W0),W1)
| ( sdtlpdtrp0(W0,tptp_fun_W4_13(W3,W1,W0)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(W0,W4) != W3 ) ) ) ) ) ) ) ) )
| ~ aFunction0(xd)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(xd))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlcdtrc0(xd,W1) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,W1,xd) ) ) )
| ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,W1,xd)) != tptp_fun_W3_14(W2,W1,xd) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,W1,xd)) != W3 ) ) ) ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(xd))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlcdtrc0(xd,W1) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,W1,xd) ) ) )
| ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,W1,xd)) != tptp_fun_W3_14(W2,W1,xd) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,W1,xd)) != W3 ) ) ) ) ) ) ) ),
inference(unit_resolution,[status(thm)],[57,51,29]) ).
tff(59,plain,
( ( ~ ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(xd))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlcdtrc0(xd,W1) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,W1,xd) ) ) )
| ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,W1,xd)) != tptp_fun_W3_14(W2,W1,xd) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,W1,xd)) != W3 ) ) ) ) ) ) ) )
| ~ aSubsetOf0(szNzAzT0,szDzozmdt0(xd))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlcdtrc0(xd,szNzAzT0) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,szNzAzT0,xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,szNzAzT0,xd) ) ) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,szNzAzT0,xd)) != tptp_fun_W3_14(W2,szNzAzT0,xd) ) )
| aElementOf0(tptp_fun_W3_14(W2,szNzAzT0,xd),W2) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,szNzAzT0) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szNzAzT0,xd)) != W3 ) ) ) ) ) ) ) )
<=> ( ~ ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(xd))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlcdtrc0(xd,W1) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,W1,xd) ) ) )
| ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,W1,xd)) != tptp_fun_W3_14(W2,W1,xd) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,W1,xd)) != W3 ) ) ) ) ) ) ) )
| ~ aSubsetOf0(szNzAzT0,szDzozmdt0(xd))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlcdtrc0(xd,szNzAzT0) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,szNzAzT0,xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,szNzAzT0,xd) ) ) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,szNzAzT0,xd)) != tptp_fun_W3_14(W2,szNzAzT0,xd) ) )
| aElementOf0(tptp_fun_W3_14(W2,szNzAzT0,xd),W2) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,szNzAzT0) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szNzAzT0,xd)) != W3 ) ) ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(60,plain,
( ( ~ aSubsetOf0(szNzAzT0,szDzozmdt0(xd))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlcdtrc0(xd,szNzAzT0) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,szNzAzT0,xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,szNzAzT0,xd) ) ) )
| ~ ( aElementOf0(tptp_fun_W3_14(W2,szNzAzT0,xd),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,szNzAzT0,xd)) != tptp_fun_W3_14(W2,szNzAzT0,xd) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,szNzAzT0) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szNzAzT0,xd)) != W3 ) ) ) ) ) ) ) )
<=> ( ~ aSubsetOf0(szNzAzT0,szDzozmdt0(xd))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlcdtrc0(xd,szNzAzT0) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,szNzAzT0,xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,szNzAzT0,xd) ) ) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,szNzAzT0,xd)) != tptp_fun_W3_14(W2,szNzAzT0,xd) ) )
| aElementOf0(tptp_fun_W3_14(W2,szNzAzT0,xd),W2) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,szNzAzT0) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szNzAzT0,xd)) != W3 ) ) ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(61,plain,
( ( ~ ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(xd))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlcdtrc0(xd,W1) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,W1,xd) ) ) )
| ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,W1,xd)) != tptp_fun_W3_14(W2,W1,xd) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,W1,xd)) != W3 ) ) ) ) ) ) ) )
| ~ aSubsetOf0(szNzAzT0,szDzozmdt0(xd))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlcdtrc0(xd,szNzAzT0) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,szNzAzT0,xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,szNzAzT0,xd) ) ) )
| ~ ( aElementOf0(tptp_fun_W3_14(W2,szNzAzT0,xd),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,szNzAzT0,xd)) != tptp_fun_W3_14(W2,szNzAzT0,xd) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,szNzAzT0) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szNzAzT0,xd)) != W3 ) ) ) ) ) ) ) )
<=> ( ~ ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(xd))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlcdtrc0(xd,W1) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,W1,xd) ) ) )
| ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,W1,xd)) != tptp_fun_W3_14(W2,W1,xd) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,W1,xd)) != W3 ) ) ) ) ) ) ) )
| ~ aSubsetOf0(szNzAzT0,szDzozmdt0(xd))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlcdtrc0(xd,szNzAzT0) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,szNzAzT0,xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,szNzAzT0,xd) ) ) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,szNzAzT0,xd)) != tptp_fun_W3_14(W2,szNzAzT0,xd) ) )
| aElementOf0(tptp_fun_W3_14(W2,szNzAzT0,xd),W2) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,szNzAzT0) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szNzAzT0,xd)) != W3 ) ) ) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[60]) ).
tff(62,plain,
( ( ~ ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(xd))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlcdtrc0(xd,W1) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,W1,xd) ) ) )
| ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,W1,xd)) != tptp_fun_W3_14(W2,W1,xd) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,W1,xd)) != W3 ) ) ) ) ) ) ) )
| ~ aSubsetOf0(szNzAzT0,szDzozmdt0(xd))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlcdtrc0(xd,szNzAzT0) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,szNzAzT0,xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,szNzAzT0,xd) ) ) )
| ~ ( aElementOf0(tptp_fun_W3_14(W2,szNzAzT0,xd),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,szNzAzT0,xd)) != tptp_fun_W3_14(W2,szNzAzT0,xd) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,szNzAzT0) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szNzAzT0,xd)) != W3 ) ) ) ) ) ) ) )
<=> ( ~ ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(xd))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlcdtrc0(xd,W1) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,W1,xd) ) ) )
| ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,W1,xd)) != tptp_fun_W3_14(W2,W1,xd) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,W1,xd)) != W3 ) ) ) ) ) ) ) )
| ~ aSubsetOf0(szNzAzT0,szDzozmdt0(xd))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlcdtrc0(xd,szNzAzT0) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,szNzAzT0,xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,szNzAzT0,xd) ) ) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,szNzAzT0,xd)) != tptp_fun_W3_14(W2,szNzAzT0,xd) ) )
| aElementOf0(tptp_fun_W3_14(W2,szNzAzT0,xd),W2) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,szNzAzT0) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szNzAzT0,xd)) != W3 ) ) ) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[61,59]) ).
tff(63,plain,
( ~ ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(xd))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlcdtrc0(xd,W1) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,W1,xd) ) ) )
| ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,W1,xd)) != tptp_fun_W3_14(W2,W1,xd) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,W1,xd)) != W3 ) ) ) ) ) ) ) )
| ~ aSubsetOf0(szNzAzT0,szDzozmdt0(xd))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlcdtrc0(xd,szNzAzT0) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,szNzAzT0,xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,szNzAzT0,xd) ) ) )
| ~ ( aElementOf0(tptp_fun_W3_14(W2,szNzAzT0,xd),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,szNzAzT0,xd)) != tptp_fun_W3_14(W2,szNzAzT0,xd) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,szNzAzT0) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szNzAzT0,xd)) != W3 ) ) ) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(64,plain,
( ~ ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(xd))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlcdtrc0(xd,W1) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,W1,xd) ) ) )
| ~ ( aElementOf0(tptp_fun_W3_14(W2,W1,xd),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,W1,xd)) != tptp_fun_W3_14(W2,W1,xd) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,W1)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,W1,xd),W1)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,W1,xd)) != W3 ) ) ) ) ) ) ) )
| ~ aSubsetOf0(szNzAzT0,szDzozmdt0(xd))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlcdtrc0(xd,szNzAzT0) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,szNzAzT0,xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,szNzAzT0,xd) ) ) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,szNzAzT0,xd)) != tptp_fun_W3_14(W2,szNzAzT0,xd) ) )
| aElementOf0(tptp_fun_W3_14(W2,szNzAzT0,xd),W2) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,szNzAzT0) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szNzAzT0,xd)) != W3 ) ) ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
( ~ aSubsetOf0(szNzAzT0,szDzozmdt0(xd))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlcdtrc0(xd,szNzAzT0) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,szNzAzT0,xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,szNzAzT0,xd) ) ) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,szNzAzT0,xd)) != tptp_fun_W3_14(W2,szNzAzT0,xd) ) )
| aElementOf0(tptp_fun_W3_14(W2,szNzAzT0,xd),W2) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,szNzAzT0) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szNzAzT0,xd)) != W3 ) ) ) ) ) ) ) ),
inference(unit_resolution,[status(thm)],[64,58]) ).
tff(66,plain,
! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlcdtrc0(xd,szNzAzT0) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,szNzAzT0,xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,szNzAzT0,xd) ) ) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,szNzAzT0,xd)) != tptp_fun_W3_14(W2,szNzAzT0,xd) ) )
| aElementOf0(tptp_fun_W3_14(W2,szNzAzT0,xd),W2) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,szNzAzT0) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szNzAzT0,xd)) != W3 ) ) ) ) ) ) ),
inference(unit_resolution,[status(thm)],[65,26]) ).
tff(67,plain,
( ~ ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlcdtrc0(xd,szNzAzT0) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,szNzAzT0,xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,szNzAzT0,xd) ) ) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,szNzAzT0,xd)) != tptp_fun_W3_14(W2,szNzAzT0,xd) ) )
| aElementOf0(tptp_fun_W3_14(W2,szNzAzT0,xd),W2) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,szNzAzT0) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szNzAzT0,xd)) != W3 ) ) ) ) ) ) )
| ~ ( ~ ( ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ( sdtlcdtrc0(xd,szDzozmdt0(xd)) = sdtlcdtrc0(xd,szNzAzT0) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W3_14(sdtlcdtrc0(xd,szDzozmdt0(xd)),szNzAzT0,xd),sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(sdtlcdtrc0(xd,szDzozmdt0(xd)),szNzAzT0,xd) ) ) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W4_15(sdtlcdtrc0(xd,szDzozmdt0(xd)),szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(sdtlcdtrc0(xd,szDzozmdt0(xd)),szNzAzT0,xd)) != tptp_fun_W3_14(sdtlcdtrc0(xd,szDzozmdt0(xd)),szNzAzT0,xd) ) )
| aElementOf0(tptp_fun_W3_14(sdtlcdtrc0(xd,szDzozmdt0(xd)),szNzAzT0,xd),sdtlcdtrc0(xd,szDzozmdt0(xd))) ) ) )
| ~ ( ( sdtlcdtrc0(xd,szDzozmdt0(xd)) != sdtlcdtrc0(xd,szNzAzT0) )
| ~ ( ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szNzAzT0,xd)) != W3 ) ) ) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(68,plain,
~ ( ~ ( ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ( sdtlcdtrc0(xd,szDzozmdt0(xd)) = sdtlcdtrc0(xd,szNzAzT0) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W3_14(sdtlcdtrc0(xd,szDzozmdt0(xd)),szNzAzT0,xd),sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(sdtlcdtrc0(xd,szDzozmdt0(xd)),szNzAzT0,xd) ) ) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W4_15(sdtlcdtrc0(xd,szDzozmdt0(xd)),szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(sdtlcdtrc0(xd,szDzozmdt0(xd)),szNzAzT0,xd)) != tptp_fun_W3_14(sdtlcdtrc0(xd,szDzozmdt0(xd)),szNzAzT0,xd) ) )
| aElementOf0(tptp_fun_W3_14(sdtlcdtrc0(xd,szDzozmdt0(xd)),szNzAzT0,xd),sdtlcdtrc0(xd,szDzozmdt0(xd))) ) ) )
| ~ ( ( sdtlcdtrc0(xd,szDzozmdt0(xd)) != sdtlcdtrc0(xd,szNzAzT0) )
| ~ ( ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szNzAzT0,xd)) != W3 ) ) ) ) ) ) ),
inference(unit_resolution,[status(thm)],[67,66]) ).
tff(69,plain,
( ~ ( ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ( sdtlcdtrc0(xd,szDzozmdt0(xd)) = sdtlcdtrc0(xd,szNzAzT0) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W3_14(sdtlcdtrc0(xd,szDzozmdt0(xd)),szNzAzT0,xd),sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(sdtlcdtrc0(xd,szDzozmdt0(xd)),szNzAzT0,xd) ) ) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W4_15(sdtlcdtrc0(xd,szDzozmdt0(xd)),szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(sdtlcdtrc0(xd,szDzozmdt0(xd)),szNzAzT0,xd)) != tptp_fun_W3_14(sdtlcdtrc0(xd,szDzozmdt0(xd)),szNzAzT0,xd) ) )
| aElementOf0(tptp_fun_W3_14(sdtlcdtrc0(xd,szDzozmdt0(xd)),szNzAzT0,xd),sdtlcdtrc0(xd,szDzozmdt0(xd))) ) ) )
| ~ ( ( sdtlcdtrc0(xd,szDzozmdt0(xd)) != sdtlcdtrc0(xd,szNzAzT0) )
| ~ ( ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szNzAzT0,xd)) != W3 ) ) ) ) ) )
| ( sdtlcdtrc0(xd,szDzozmdt0(xd)) != sdtlcdtrc0(xd,szNzAzT0) )
| ~ ( ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szNzAzT0,xd)) != W3 ) ) ) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(70,plain,
( ( sdtlcdtrc0(xd,szDzozmdt0(xd)) != sdtlcdtrc0(xd,szNzAzT0) )
| ~ ( ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szNzAzT0,xd)) != W3 ) ) ) ) ) ),
inference(unit_resolution,[status(thm)],[69,68]) ).
tff(71,plain,
szNzAzT0 = szDzozmdt0(xd),
inference(symmetry,[status(thm)],[5]) ).
tff(72,plain,
sdtlcdtrc0(xd,szNzAzT0) = sdtlcdtrc0(xd,szDzozmdt0(xd)),
inference(monotonicity,[status(thm)],[71]) ).
tff(73,plain,
sdtlcdtrc0(xd,szDzozmdt0(xd)) = sdtlcdtrc0(xd,szNzAzT0),
inference(symmetry,[status(thm)],[72]) ).
tff(74,plain,
( ~ ( ( sdtlcdtrc0(xd,szDzozmdt0(xd)) != sdtlcdtrc0(xd,szNzAzT0) )
| ~ ( ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szNzAzT0,xd)) != W3 ) ) ) ) ) )
| ( sdtlcdtrc0(xd,szDzozmdt0(xd)) != sdtlcdtrc0(xd,szNzAzT0) )
| ~ ( ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szNzAzT0,xd)) != W3 ) ) ) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(75,plain,
( ~ ( ( sdtlcdtrc0(xd,szDzozmdt0(xd)) != sdtlcdtrc0(xd,szNzAzT0) )
| ~ ( ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szNzAzT0,xd)) != W3 ) ) ) ) ) )
| ~ ( ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szNzAzT0,xd)) != W3 ) ) ) ) ) ),
inference(unit_resolution,[status(thm)],[74,73]) ).
tff(76,plain,
~ ( ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szNzAzT0,xd)) != W3 ) ) ) ) ),
inference(unit_resolution,[status(thm)],[75,70]) ).
tff(77,plain,
( ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szNzAzT0,xd)) != W3 ) ) ) )
| ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szNzAzT0,xd)) != W3 ) ) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(78,plain,
! [W3: $i] :
~ ( ~ ( aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szNzAzT0,xd)) != W3 ) ) ) ),
inference(unit_resolution,[status(thm)],[77,76]) ).
tff(79,plain,
( ~ ! [W3: $i] :
~ ( ~ ( aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != W3 ) ) )
| ~ ( ~ aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szNzAzT0,xd)) != W3 ) ) ) )
| ~ ( ~ ( aElementOf0(xx,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != xx ) ) )
| ~ ( ~ aElementOf0(xx,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ( ~ aElementOf0(tptp_fun_W4_13(xx,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(xx,szNzAzT0,xd)) != xx ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(80,plain,
~ ( ~ ( aElementOf0(xx,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != xx ) ) )
| ~ ( ~ aElementOf0(xx,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ( ~ aElementOf0(tptp_fun_W4_13(xx,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(xx,szNzAzT0,xd)) != xx ) ) ) ),
inference(unit_resolution,[status(thm)],[79,78]) ).
tff(81,plain,
( ~ ( aElementOf0(xx,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ! [W4: $i] :
( ~ aElementOf0(W4,szNzAzT0)
| ( sdtlpdtrp0(xd,W4) != xx ) ) )
| ~ ( ~ aElementOf0(xx,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ( ~ aElementOf0(tptp_fun_W4_13(xx,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(xx,szNzAzT0,xd)) != xx ) ) )
| ~ aElementOf0(xx,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ( ~ aElementOf0(tptp_fun_W4_13(xx,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(xx,szNzAzT0,xd)) != xx ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(82,plain,
( ~ aElementOf0(xx,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ( ~ aElementOf0(tptp_fun_W4_13(xx,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(xx,szNzAzT0,xd)) != xx ) ) ),
inference(unit_resolution,[status(thm)],[81,80]) ).
tff(83,plain,
( aElementOf0(xx,sdtlcdtrc0(xd,szDzozmdt0(xd)))
<=> aElementOf0(xx,sdtlcdtrc0(xd,szDzozmdt0(xd))) ),
inference(rewrite,[status(thm)],[]) ).
tff(84,axiom,
aElementOf0(xx,sdtlcdtrc0(xd,szDzozmdt0(xd))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4781) ).
tff(85,plain,
aElementOf0(xx,sdtlcdtrc0(xd,szDzozmdt0(xd))),
inference(modus_ponens,[status(thm)],[84,83]) ).
tff(86,plain,
( ~ ( ~ aElementOf0(xx,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ( ~ aElementOf0(tptp_fun_W4_13(xx,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(xx,szNzAzT0,xd)) != xx ) ) )
| ~ aElementOf0(xx,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ( ~ aElementOf0(tptp_fun_W4_13(xx,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(xx,szNzAzT0,xd)) != xx ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(87,plain,
( ~ ( ~ aElementOf0(xx,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ ( ~ aElementOf0(tptp_fun_W4_13(xx,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(xx,szNzAzT0,xd)) != xx ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W4_13(xx,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(xx,szNzAzT0,xd)) != xx ) ) ),
inference(unit_resolution,[status(thm)],[86,85]) ).
tff(88,plain,
~ ( ~ aElementOf0(tptp_fun_W4_13(xx,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(xx,szNzAzT0,xd)) != xx ) ),
inference(unit_resolution,[status(thm)],[87,82]) ).
tff(89,plain,
( ~ aElementOf0(tptp_fun_W4_13(xx,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(xx,szNzAzT0,xd)) != xx )
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(xx,szNzAzT0,xd)) = xx ) ),
inference(tautology,[status(thm)],[]) ).
tff(90,plain,
sdtlpdtrp0(xd,tptp_fun_W4_13(xx,szNzAzT0,xd)) = xx,
inference(unit_resolution,[status(thm)],[89,88]) ).
tff(91,plain,
( ~ aElementOf0(tptp_fun_W4_13(xx,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(xx,szNzAzT0,xd)) != xx )
| aElementOf0(tptp_fun_W4_13(xx,szNzAzT0,xd),szNzAzT0) ),
inference(tautology,[status(thm)],[]) ).
tff(92,plain,
aElementOf0(tptp_fun_W4_13(xx,szNzAzT0,xd),szNzAzT0),
inference(unit_resolution,[status(thm)],[91,88]) ).
tff(93,plain,
^ [W0: $i] :
refl(( ( ~ aElementOf0(W0,szNzAzT0)
| ( sdtlpdtrp0(xd,W0) != xx ) )
<=> ( ~ aElementOf0(W0,szNzAzT0)
| ( sdtlpdtrp0(xd,W0) != xx ) ) )),
inference(bind,[status(th)],[]) ).
tff(94,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( sdtlpdtrp0(xd,W0) != xx ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( sdtlpdtrp0(xd,W0) != xx ) ) ),
inference(quant_intro,[status(thm)],[93]) ).
tff(95,plain,
^ [W0: $i] :
trans(monotonicity(rewrite(( ( aElementOf0(W0,szNzAzT0)
& ( sdtlpdtrp0(xd,W0) = xx ) )
<=> ~ ( ~ aElementOf0(W0,szNzAzT0)
| ( sdtlpdtrp0(xd,W0) != xx ) ) )),
( ~ ( aElementOf0(W0,szNzAzT0)
& ( sdtlpdtrp0(xd,W0) = xx ) )
<=> ~ ~ ( ~ aElementOf0(W0,szNzAzT0)
| ( sdtlpdtrp0(xd,W0) != xx ) ) )),
rewrite(( ~ ~ ( ~ aElementOf0(W0,szNzAzT0)
| ( sdtlpdtrp0(xd,W0) != xx ) )
<=> ( ~ aElementOf0(W0,szNzAzT0)
| ( sdtlpdtrp0(xd,W0) != xx ) ) )),
( ~ ( aElementOf0(W0,szNzAzT0)
& ( sdtlpdtrp0(xd,W0) = xx ) )
<=> ( ~ aElementOf0(W0,szNzAzT0)
| ( sdtlpdtrp0(xd,W0) != xx ) ) )),
inference(bind,[status(th)],[]) ).
tff(96,plain,
( ! [W0: $i] :
~ ( aElementOf0(W0,szNzAzT0)
& ( sdtlpdtrp0(xd,W0) = xx ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( sdtlpdtrp0(xd,W0) != xx ) ) ),
inference(quant_intro,[status(thm)],[95]) ).
tff(97,plain,
( ~ ? [W0: $i] :
( aElementOf0(W0,szNzAzT0)
& ( sdtlpdtrp0(xd,W0) = xx ) )
<=> ~ ? [W0: $i] :
( aElementOf0(W0,szNzAzT0)
& ( sdtlpdtrp0(xd,W0) = xx ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(98,axiom,
~ ? [W0: $i] :
( aElementOf0(W0,szNzAzT0)
& ( sdtlpdtrp0(xd,W0) = xx ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(99,plain,
~ ? [W0: $i] :
( aElementOf0(W0,szNzAzT0)
& ( sdtlpdtrp0(xd,W0) = xx ) ),
inference(modus_ponens,[status(thm)],[98,97]) ).
tff(100,plain,
~ ? [W0: $i] :
( aElementOf0(W0,szNzAzT0)
& ( sdtlpdtrp0(xd,W0) = xx ) ),
inference(modus_ponens,[status(thm)],[99,97]) ).
tff(101,plain,
~ ? [W0: $i] :
( aElementOf0(W0,szNzAzT0)
& ( sdtlpdtrp0(xd,W0) = xx ) ),
inference(modus_ponens,[status(thm)],[100,97]) ).
tff(102,plain,
~ ? [W0: $i] :
( aElementOf0(W0,szNzAzT0)
& ( sdtlpdtrp0(xd,W0) = xx ) ),
inference(modus_ponens,[status(thm)],[101,97]) ).
tff(103,plain,
^ [W0: $i] :
refl($oeq(~ ( aElementOf0(W0,szNzAzT0)
& ( sdtlpdtrp0(xd,W0) = xx ) ),
~ ( aElementOf0(W0,szNzAzT0)
& ( sdtlpdtrp0(xd,W0) = xx ) ))),
inference(bind,[status(th)],[]) ).
tff(104,plain,
! [W0: $i] :
~ ( aElementOf0(W0,szNzAzT0)
& ( sdtlpdtrp0(xd,W0) = xx ) ),
inference(nnf-neg,[status(sab)],[102,103]) ).
tff(105,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( sdtlpdtrp0(xd,W0) != xx ) ),
inference(modus_ponens,[status(thm)],[104,96]) ).
tff(106,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( sdtlpdtrp0(xd,W0) != xx ) ),
inference(modus_ponens,[status(thm)],[105,94]) ).
tff(107,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( sdtlpdtrp0(xd,W0) != xx ) )
| ~ aElementOf0(tptp_fun_W4_13(xx,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(xx,szNzAzT0,xd)) != xx ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( sdtlpdtrp0(xd,W0) != xx ) )
| ~ aElementOf0(tptp_fun_W4_13(xx,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(xx,szNzAzT0,xd)) != xx ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(108,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( sdtlpdtrp0(xd,W0) != xx ) )
| ~ aElementOf0(tptp_fun_W4_13(xx,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(xx,szNzAzT0,xd)) != xx ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(109,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( sdtlpdtrp0(xd,W0) != xx ) )
| ~ aElementOf0(tptp_fun_W4_13(xx,szNzAzT0,xd),szNzAzT0)
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(xx,szNzAzT0,xd)) != xx ) ),
inference(modus_ponens,[status(thm)],[108,107]) ).
tff(110,plain,
$false,
inference(unit_resolution,[status(thm)],[109,106,92,90]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : NUM594+1 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.12/0.35 % Computer : n001.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Fri Jun 20 01:36:34 EDT 2025
% 0.12/0.35 % CPUTime :
% 24.58/24.76 % SZS status Theorem
% 24.58/24.76 % SZS output start Proof
% See solution above
% 24.66/24.87 % E exiting
%------------------------------------------------------------------------------