TSTP Solution File: NUM594+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM594+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n010.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 13:10:45 EDT 2022
% Result : Theorem 50.62s 32.57s
% Output : Proof 50.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 66
% Syntax : Number of formulae : 135 ( 27 unt; 19 typ; 0 def)
% Number of atoms : 1614 ( 533 equ)
% Maximal formula atoms : 72 ( 13 avg)
% Number of connectives : 3491 (2021 ~;1241 |; 125 &)
% ( 87 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 8 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 : 24 ( 13 >; 11 *; 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 : 496 ( 452 !; 32 ?; 496 :)
% 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(szDzozmdt0_type,type,
szDzozmdt0: $i > $i ).
tff(xN_type,type,
xN: $i ).
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(sdtlcdtrc0_type,type,
sdtlcdtrc0: ( $i * $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(szNzAzT0_type,type,
szNzAzT0: $i ).
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(isCountable0_type,type,
isCountable0: $i > $o ).
tff(1,plain,
( ( szDzozmdt0(xd) = szNzAzT0 )
<=> ( szDzozmdt0(xd) = szDzozmdt0(xN) ) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ( szDzozmdt0(xd) = szNzAzT0 )
<=> ( szDzozmdt0(xd) = szNzAzT0 ) ),
inference(rewrite,[status(thm)],]) ).
tff(3,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(4,plain,
( aFunction0(xd)
& ( szDzozmdt0(xd) = szNzAzT0 ) ),
inference(and_elim,[status(thm)],[3]) ).
tff(5,plain,
szDzozmdt0(xd) = szNzAzT0,
inference(and_elim,[status(thm)],[4]) ).
tff(6,plain,
szDzozmdt0(xd) = szNzAzT0,
inference(modus_ponens,[status(thm)],[5,2]) ).
tff(7,plain,
szDzozmdt0(xd) = szDzozmdt0(xN),
inference(modus_ponens,[status(thm)],[6,1]) ).
tff(8,plain,
( aSubsetOf0(szDzozmdt0(xN),szDzozmdt0(xd))
<=> aSubsetOf0(szDzozmdt0(xN),szDzozmdt0(xN)) ),
inference(monotonicity,[status(thm)],[7]) ).
tff(9,plain,
( aSubsetOf0(szDzozmdt0(xN),szDzozmdt0(xN))
<=> aSubsetOf0(szDzozmdt0(xN),szDzozmdt0(xd)) ),
inference(symmetry,[status(thm)],[8]) ).
tff(10,plain,
( aSet0(szNzAzT0)
<=> aSet0(szDzozmdt0(xN)) ),
inference(rewrite,[status(thm)],]) ).
tff(11,plain,
( aSet0(szNzAzT0)
<=> aSet0(szNzAzT0) ),
inference(rewrite,[status(thm)],]) ).
tff(12,axiom,
( aSet0(szNzAzT0)
& isCountable0(szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNATSet) ).
tff(13,plain,
aSet0(szNzAzT0),
inference(and_elim,[status(thm)],[12]) ).
tff(14,plain,
aSet0(szNzAzT0),
inference(modus_ponens,[status(thm)],[13,11]) ).
tff(15,plain,
aSet0(szDzozmdt0(xN)),
inference(modus_ponens,[status(thm)],[14,10]) ).
tff(16,plain,
^ [W0: $i] :
refl(
( ( ~ aSet0(W0)
| aSubsetOf0(W0,W0) )
<=> ( ~ aSet0(W0)
| aSubsetOf0(W0,W0) ) )),
inference(bind,[status(th)],]) ).
tff(17,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) ) ),
inference(rewrite,[status(thm)],]) ).
tff(19,plain,
^ [W0: $i] :
rewrite(
( ( aSet0(W0)
=> aSubsetOf0(W0,W0) )
<=> ( ~ aSet0(W0)
| aSubsetOf0(W0,W0) ) )),
inference(bind,[status(th)],]) ).
tff(20,plain,
( ! [W0: $i] :
( aSet0(W0)
=> aSubsetOf0(W0,W0) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,axiom,
! [W0: $i] :
( aSet0(W0)
=> aSubsetOf0(W0,W0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubRefl) ).
tff(22,plain,
! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) ),
inference(modus_ponens,[status(thm)],[22,18]) ).
tff(24,plain,
! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) ),
inference(skolemize,[status(sab)],[23]) ).
tff(25,plain,
! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) ),
inference(modus_ponens,[status(thm)],[24,17]) ).
tff(26,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) )
| ~ aSet0(szDzozmdt0(xN))
| aSubsetOf0(szDzozmdt0(xN),szDzozmdt0(xN)) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) )
| ~ aSet0(szDzozmdt0(xN))
| aSubsetOf0(szDzozmdt0(xN),szDzozmdt0(xN)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(27,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) )
| ~ aSet0(szDzozmdt0(xN))
| aSubsetOf0(szDzozmdt0(xN),szDzozmdt0(xN)) ),
inference(quant_inst,[status(thm)],]) ).
tff(28,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) )
| ~ aSet0(szDzozmdt0(xN))
| aSubsetOf0(szDzozmdt0(xN),szDzozmdt0(xN)) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
aSubsetOf0(szDzozmdt0(xN),szDzozmdt0(xN)),
inference(unit_resolution,[status(thm)],[28,25,15]) ).
tff(30,plain,
aSubsetOf0(szDzozmdt0(xN),szDzozmdt0(xd)),
inference(modus_ponens,[status(thm)],[29,9]) ).
tff(31,plain,
( aFunction0(xd)
<=> aFunction0(xd) ),
inference(rewrite,[status(thm)],]) ).
tff(32,plain,
aFunction0(xd),
inference(and_elim,[status(thm)],[4]) ).
tff(33,plain,
aFunction0(xd),
inference(modus_ponens,[status(thm)],[32,31]) ).
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)
| ~ ( ~ ( 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(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)
| ~ ( ~ ( 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)],[34]) ).
tff(36,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(37,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)],[36]) ).
tff(38,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(39,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)],[38]) ).
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(transitivity,[status(thm)],[39,37]) ).
tff(41,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(42,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)],[41]) ).
tff(43,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(44,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)],[43]) ).
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 ) ) ) ) ) ) )
<=> ! [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(46,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(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)
<=> ? [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)],[46]) ).
tff(48,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(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)
<=> ? [W4: $i] :
( aElementOf0(W4,W1)
& ( sdtlpdtrp0(W0,W4) = W3 ) ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[48,47]) ).
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)
<=> ? [W4: $i] :
( aElementOf0(W4,W1)
& ( sdtlpdtrp0(W0,W4) = W3 ) ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[49,45]) ).
tff(51,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)],[50]) ).
tff(52,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)],[51,44]) ).
tff(53,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)],[52,42]) ).
tff(54,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)],[53,40]) ).
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 ) ) ) ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[54,35]) ).
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] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlcdtrc0(xd,W1) )
| ~ ( ~ ( 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)
| ~ ( ~ 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(rewrite,[status(thm)],]) ).
tff(57,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)
| ~ ( ~ 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(rewrite,[status(thm)],]) ).
tff(58,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)
| ~ ( ~ 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(monotonicity,[status(thm)],[57]) ).
tff(59,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)
| ~ ( ~ 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(transitivity,[status(thm)],[58,56]) ).
tff(60,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(61,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)
| ~ ( ~ 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(modus_ponens,[status(thm)],[60,59]) ).
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)
| ~ ( ~ 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(unit_resolution,[status(thm)],[61,55,33]) ).
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)
| ~ ( ~ 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 ) ) ) ) ) ) ) )
| ~ aSubsetOf0(szDzozmdt0(xN),szDzozmdt0(xd))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlcdtrc0(xd,szDzozmdt0(xN)) )
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,szDzozmdt0(xN),xd),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,szDzozmdt0(xN),xd),szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,szDzozmdt0(xN),xd)) != tptp_fun_W3_14(W2,szDzozmdt0(xN),xd) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,szDzozmdt0(xN),xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,szDzozmdt0(xN),xd) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,szDzozmdt0(xN)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szDzozmdt0(xN),xd),szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szDzozmdt0(xN),xd)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,W4) != W3 ) ) ) ) ) ) ) )
<=> ( ~ ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(xd))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlcdtrc0(xd,W1) )
| ~ ( ~ ( 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 ) ) ) ) ) ) ) )
| ~ aSubsetOf0(szDzozmdt0(xN),szDzozmdt0(xd))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlcdtrc0(xd,szDzozmdt0(xN)) )
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,szDzozmdt0(xN),xd),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,szDzozmdt0(xN),xd),szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,szDzozmdt0(xN),xd)) != tptp_fun_W3_14(W2,szDzozmdt0(xN),xd) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,szDzozmdt0(xN),xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,szDzozmdt0(xN),xd) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,szDzozmdt0(xN)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szDzozmdt0(xN),xd),szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szDzozmdt0(xN),xd)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,W4) != W3 ) ) ) ) ) ) ) ) ),
inference(rewrite,[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)
| ~ ( ~ 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 ) ) ) ) ) ) ) )
| ~ aSubsetOf0(szDzozmdt0(xN),szDzozmdt0(xd))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlcdtrc0(xd,szDzozmdt0(xN)) )
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,szDzozmdt0(xN),xd),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,szDzozmdt0(xN),xd),szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,szDzozmdt0(xN),xd)) != tptp_fun_W3_14(W2,szDzozmdt0(xN),xd) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,szDzozmdt0(xN),xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,szDzozmdt0(xN),xd) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,szDzozmdt0(xN)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szDzozmdt0(xN),xd),szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szDzozmdt0(xN),xd)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,W4) != W3 ) ) ) ) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(65,plain,
( ~ ! [W1: $i] :
( ~ aSubsetOf0(W1,szDzozmdt0(xd))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlcdtrc0(xd,W1) )
| ~ ( ~ ( 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 ) ) ) ) ) ) ) )
| ~ aSubsetOf0(szDzozmdt0(xN),szDzozmdt0(xd))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlcdtrc0(xd,szDzozmdt0(xN)) )
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,szDzozmdt0(xN),xd),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,szDzozmdt0(xN),xd),szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,szDzozmdt0(xN),xd)) != tptp_fun_W3_14(W2,szDzozmdt0(xN),xd) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,szDzozmdt0(xN),xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,szDzozmdt0(xN),xd) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,szDzozmdt0(xN)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szDzozmdt0(xN),xd),szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szDzozmdt0(xN),xd)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,W4) != W3 ) ) ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[64,63]) ).
tff(66,plain,
( ~ aSubsetOf0(szDzozmdt0(xN),szDzozmdt0(xd))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlcdtrc0(xd,szDzozmdt0(xN)) )
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,szDzozmdt0(xN),xd),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,szDzozmdt0(xN),xd),szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,szDzozmdt0(xN),xd)) != tptp_fun_W3_14(W2,szDzozmdt0(xN),xd) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,szDzozmdt0(xN),xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,szDzozmdt0(xN),xd) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,szDzozmdt0(xN)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szDzozmdt0(xN),xd),szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szDzozmdt0(xN),xd)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,W4) != W3 ) ) ) ) ) ) ) ),
inference(unit_resolution,[status(thm)],[65,62]) ).
tff(67,plain,
! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlcdtrc0(xd,szDzozmdt0(xN)) )
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,szDzozmdt0(xN),xd),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,szDzozmdt0(xN),xd),szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,szDzozmdt0(xN),xd)) != tptp_fun_W3_14(W2,szDzozmdt0(xN),xd) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,szDzozmdt0(xN),xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,szDzozmdt0(xN),xd) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,szDzozmdt0(xN)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szDzozmdt0(xN),xd),szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szDzozmdt0(xN),xd)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,W4) != W3 ) ) ) ) ) ) ),
inference(unit_resolution,[status(thm)],[66,30]) ).
tff(68,plain,
( ( ~ ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlcdtrc0(xd,szDzozmdt0(xN)) )
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,szDzozmdt0(xN),xd),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,szDzozmdt0(xN),xd),szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,szDzozmdt0(xN),xd)) != tptp_fun_W3_14(W2,szDzozmdt0(xN),xd) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,szDzozmdt0(xN),xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,szDzozmdt0(xN),xd) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,szDzozmdt0(xN)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szDzozmdt0(xN),xd),szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szDzozmdt0(xN),xd)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,W4) != W3 ) ) ) ) ) ) )
| ~ ( ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xN)))
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xN)))
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szDzozmdt0(xN),xd),szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szDzozmdt0(xN),xd)) != W3 ) ) )
| ~ ( aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xN)))
| ! [W4: $i] :
( ~ aElementOf0(W4,szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,W4) != W3 ) ) ) ) ) )
<=> ( ~ ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlcdtrc0(xd,szDzozmdt0(xN)) )
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,szDzozmdt0(xN),xd),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,szDzozmdt0(xN),xd),szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,szDzozmdt0(xN),xd)) != tptp_fun_W3_14(W2,szDzozmdt0(xN),xd) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,szDzozmdt0(xN),xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,szDzozmdt0(xN),xd) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,szDzozmdt0(xN)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szDzozmdt0(xN),xd),szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szDzozmdt0(xN),xd)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,W4) != W3 ) ) ) ) ) ) )
| ~ ( ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xN)))
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xN)))
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szDzozmdt0(xN),xd),szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szDzozmdt0(xN),xd)) != W3 ) ) )
| ~ ( aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xN)))
| ! [W4: $i] :
( ~ aElementOf0(W4,szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,W4) != W3 ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(69,plain,
( ~ ( ~ ( ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xN)))
| ( sdtlcdtrc0(xd,szDzozmdt0(xN)) = sdtlcdtrc0(xd,szDzozmdt0(xN)) )
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(sdtlcdtrc0(xd,szDzozmdt0(xN)),szDzozmdt0(xN),xd),sdtlcdtrc0(xd,szDzozmdt0(xN)))
| ~ ( ~ aElementOf0(tptp_fun_W4_15(sdtlcdtrc0(xd,szDzozmdt0(xN)),szDzozmdt0(xN),xd),szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(sdtlcdtrc0(xd,szDzozmdt0(xN)),szDzozmdt0(xN),xd)) != tptp_fun_W3_14(sdtlcdtrc0(xd,szDzozmdt0(xN)),szDzozmdt0(xN),xd) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(sdtlcdtrc0(xd,szDzozmdt0(xN)),szDzozmdt0(xN),xd),sdtlcdtrc0(xd,szDzozmdt0(xN)))
| ! [W4: $i] :
( ~ aElementOf0(W4,szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(sdtlcdtrc0(xd,szDzozmdt0(xN)),szDzozmdt0(xN),xd) ) ) ) ) )
| ~ ( ( sdtlcdtrc0(xd,szDzozmdt0(xN)) != sdtlcdtrc0(xd,szDzozmdt0(xN)) )
| ~ ( ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xN)))
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xN)))
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szDzozmdt0(xN),xd),szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szDzozmdt0(xN),xd)) != W3 ) ) )
| ~ ( aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xN)))
| ! [W4: $i] :
( ~ aElementOf0(W4,szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,W4) != W3 ) ) ) ) ) ) )
<=> ~ ( ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xN)))
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xN)))
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szDzozmdt0(xN),xd),szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szDzozmdt0(xN),xd)) != W3 ) ) )
| ~ ( aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xN)))
| ! [W4: $i] :
( ~ aElementOf0(W4,szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,W4) != W3 ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(70,plain,
( ( ~ ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlcdtrc0(xd,szDzozmdt0(xN)) )
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,szDzozmdt0(xN),xd),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,szDzozmdt0(xN),xd),szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,szDzozmdt0(xN),xd)) != tptp_fun_W3_14(W2,szDzozmdt0(xN),xd) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,szDzozmdt0(xN),xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,szDzozmdt0(xN),xd) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,szDzozmdt0(xN)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szDzozmdt0(xN),xd),szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szDzozmdt0(xN),xd)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,W4) != W3 ) ) ) ) ) ) )
| ~ ( ~ ( ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xN)))
| ( sdtlcdtrc0(xd,szDzozmdt0(xN)) = sdtlcdtrc0(xd,szDzozmdt0(xN)) )
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(sdtlcdtrc0(xd,szDzozmdt0(xN)),szDzozmdt0(xN),xd),sdtlcdtrc0(xd,szDzozmdt0(xN)))
| ~ ( ~ aElementOf0(tptp_fun_W4_15(sdtlcdtrc0(xd,szDzozmdt0(xN)),szDzozmdt0(xN),xd),szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(sdtlcdtrc0(xd,szDzozmdt0(xN)),szDzozmdt0(xN),xd)) != tptp_fun_W3_14(sdtlcdtrc0(xd,szDzozmdt0(xN)),szDzozmdt0(xN),xd) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(sdtlcdtrc0(xd,szDzozmdt0(xN)),szDzozmdt0(xN),xd),sdtlcdtrc0(xd,szDzozmdt0(xN)))
| ! [W4: $i] :
( ~ aElementOf0(W4,szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(sdtlcdtrc0(xd,szDzozmdt0(xN)),szDzozmdt0(xN),xd) ) ) ) ) )
| ~ ( ( sdtlcdtrc0(xd,szDzozmdt0(xN)) != sdtlcdtrc0(xd,szDzozmdt0(xN)) )
| ~ ( ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xN)))
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xN)))
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szDzozmdt0(xN),xd),szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szDzozmdt0(xN),xd)) != W3 ) ) )
| ~ ( aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xN)))
| ! [W4: $i] :
( ~ aElementOf0(W4,szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,W4) != W3 ) ) ) ) ) ) ) )
<=> ( ~ ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlcdtrc0(xd,szDzozmdt0(xN)) )
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,szDzozmdt0(xN),xd),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,szDzozmdt0(xN),xd),szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,szDzozmdt0(xN),xd)) != tptp_fun_W3_14(W2,szDzozmdt0(xN),xd) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,szDzozmdt0(xN),xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,szDzozmdt0(xN),xd) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,szDzozmdt0(xN)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szDzozmdt0(xN),xd),szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szDzozmdt0(xN),xd)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,W4) != W3 ) ) ) ) ) ) )
| ~ ( ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xN)))
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xN)))
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szDzozmdt0(xN),xd),szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szDzozmdt0(xN),xd)) != W3 ) ) )
| ~ ( aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xN)))
| ! [W4: $i] :
( ~ aElementOf0(W4,szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,W4) != W3 ) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[69]) ).
tff(71,plain,
( ( ~ ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlcdtrc0(xd,szDzozmdt0(xN)) )
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,szDzozmdt0(xN),xd),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,szDzozmdt0(xN),xd),szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,szDzozmdt0(xN),xd)) != tptp_fun_W3_14(W2,szDzozmdt0(xN),xd) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,szDzozmdt0(xN),xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,szDzozmdt0(xN),xd) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,szDzozmdt0(xN)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szDzozmdt0(xN),xd),szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szDzozmdt0(xN),xd)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,W4) != W3 ) ) ) ) ) ) )
| ~ ( ~ ( ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xN)))
| ( sdtlcdtrc0(xd,szDzozmdt0(xN)) = sdtlcdtrc0(xd,szDzozmdt0(xN)) )
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(sdtlcdtrc0(xd,szDzozmdt0(xN)),szDzozmdt0(xN),xd),sdtlcdtrc0(xd,szDzozmdt0(xN)))
| ~ ( ~ aElementOf0(tptp_fun_W4_15(sdtlcdtrc0(xd,szDzozmdt0(xN)),szDzozmdt0(xN),xd),szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(sdtlcdtrc0(xd,szDzozmdt0(xN)),szDzozmdt0(xN),xd)) != tptp_fun_W3_14(sdtlcdtrc0(xd,szDzozmdt0(xN)),szDzozmdt0(xN),xd) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(sdtlcdtrc0(xd,szDzozmdt0(xN)),szDzozmdt0(xN),xd),sdtlcdtrc0(xd,szDzozmdt0(xN)))
| ! [W4: $i] :
( ~ aElementOf0(W4,szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(sdtlcdtrc0(xd,szDzozmdt0(xN)),szDzozmdt0(xN),xd) ) ) ) ) )
| ~ ( ( sdtlcdtrc0(xd,szDzozmdt0(xN)) != sdtlcdtrc0(xd,szDzozmdt0(xN)) )
| ~ ( ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xN)))
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xN)))
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szDzozmdt0(xN),xd),szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szDzozmdt0(xN),xd)) != W3 ) ) )
| ~ ( aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xN)))
| ! [W4: $i] :
( ~ aElementOf0(W4,szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,W4) != W3 ) ) ) ) ) ) ) )
<=> ( ~ ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlcdtrc0(xd,szDzozmdt0(xN)) )
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,szDzozmdt0(xN),xd),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,szDzozmdt0(xN),xd),szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,szDzozmdt0(xN),xd)) != tptp_fun_W3_14(W2,szDzozmdt0(xN),xd) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,szDzozmdt0(xN),xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,szDzozmdt0(xN),xd) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,szDzozmdt0(xN)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szDzozmdt0(xN),xd),szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szDzozmdt0(xN),xd)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,W4) != W3 ) ) ) ) ) ) )
| ~ ( ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xN)))
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xN)))
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szDzozmdt0(xN),xd),szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szDzozmdt0(xN),xd)) != W3 ) ) )
| ~ ( aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xN)))
| ! [W4: $i] :
( ~ aElementOf0(W4,szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,W4) != W3 ) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[70,68]) ).
tff(72,plain,
( ~ ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlcdtrc0(xd,szDzozmdt0(xN)) )
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,szDzozmdt0(xN),xd),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,szDzozmdt0(xN),xd),szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,szDzozmdt0(xN),xd)) != tptp_fun_W3_14(W2,szDzozmdt0(xN),xd) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,szDzozmdt0(xN),xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,szDzozmdt0(xN),xd) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,szDzozmdt0(xN)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szDzozmdt0(xN),xd),szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szDzozmdt0(xN),xd)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,W4) != W3 ) ) ) ) ) ) )
| ~ ( ~ ( ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xN)))
| ( sdtlcdtrc0(xd,szDzozmdt0(xN)) = sdtlcdtrc0(xd,szDzozmdt0(xN)) )
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(sdtlcdtrc0(xd,szDzozmdt0(xN)),szDzozmdt0(xN),xd),sdtlcdtrc0(xd,szDzozmdt0(xN)))
| ~ ( ~ aElementOf0(tptp_fun_W4_15(sdtlcdtrc0(xd,szDzozmdt0(xN)),szDzozmdt0(xN),xd),szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(sdtlcdtrc0(xd,szDzozmdt0(xN)),szDzozmdt0(xN),xd)) != tptp_fun_W3_14(sdtlcdtrc0(xd,szDzozmdt0(xN)),szDzozmdt0(xN),xd) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(sdtlcdtrc0(xd,szDzozmdt0(xN)),szDzozmdt0(xN),xd),sdtlcdtrc0(xd,szDzozmdt0(xN)))
| ! [W4: $i] :
( ~ aElementOf0(W4,szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(sdtlcdtrc0(xd,szDzozmdt0(xN)),szDzozmdt0(xN),xd) ) ) ) ) )
| ~ ( ( sdtlcdtrc0(xd,szDzozmdt0(xN)) != sdtlcdtrc0(xd,szDzozmdt0(xN)) )
| ~ ( ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xN)))
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xN)))
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szDzozmdt0(xN),xd),szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szDzozmdt0(xN),xd)) != W3 ) ) )
| ~ ( aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xN)))
| ! [W4: $i] :
( ~ aElementOf0(W4,szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,W4) != W3 ) ) ) ) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(73,plain,
( ~ ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtlcdtrc0(xd,szDzozmdt0(xN)) )
| ~ ( ~ ( aElementOf0(tptp_fun_W3_14(W2,szDzozmdt0(xN),xd),W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_15(W2,szDzozmdt0(xN),xd),szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,tptp_fun_W4_15(W2,szDzozmdt0(xN),xd)) != tptp_fun_W3_14(W2,szDzozmdt0(xN),xd) ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W3_14(W2,szDzozmdt0(xN),xd),W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,W4) != tptp_fun_W3_14(W2,szDzozmdt0(xN),xd) ) ) ) ) )
| ~ ( ( W2 != sdtlcdtrc0(xd,szDzozmdt0(xN)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,W2)
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szDzozmdt0(xN),xd),szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szDzozmdt0(xN),xd)) != W3 ) ) )
| ~ ( aElementOf0(W3,W2)
| ! [W4: $i] :
( ~ aElementOf0(W4,szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,W4) != W3 ) ) ) ) ) ) )
| ~ ( ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xN)))
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xN)))
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szDzozmdt0(xN),xd),szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szDzozmdt0(xN),xd)) != W3 ) ) )
| ~ ( aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xN)))
| ! [W4: $i] :
( ~ aElementOf0(W4,szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,W4) != W3 ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,plain,
~ ( ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xN)))
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xN)))
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szDzozmdt0(xN),xd),szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szDzozmdt0(xN),xd)) != W3 ) ) )
| ~ ( aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xN)))
| ! [W4: $i] :
( ~ aElementOf0(W4,szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,W4) != W3 ) ) ) ) ),
inference(unit_resolution,[status(thm)],[73,67]) ).
tff(75,plain,
( ~ aSet0(sdtlcdtrc0(xd,szDzozmdt0(xN)))
| ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xN)))
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szDzozmdt0(xN),xd),szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szDzozmdt0(xN),xd)) != W3 ) ) )
| ~ ( aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xN)))
| ! [W4: $i] :
( ~ aElementOf0(W4,szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,W4) != W3 ) ) ) )
| ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xN)))
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szDzozmdt0(xN),xd),szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szDzozmdt0(xN),xd)) != W3 ) ) )
| ~ ( aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xN)))
| ! [W4: $i] :
( ~ aElementOf0(W4,szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,W4) != W3 ) ) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(76,plain,
! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xN)))
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szDzozmdt0(xN),xd),szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szDzozmdt0(xN),xd)) != W3 ) ) )
| ~ ( aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xN)))
| ! [W4: $i] :
( ~ aElementOf0(W4,szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,W4) != W3 ) ) ) ),
inference(unit_resolution,[status(thm)],[75,74]) ).
tff(77,plain,
( ~ ! [W3: $i] :
~ ( ~ ( ~ aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xN)))
| ~ ( ~ aElementOf0(tptp_fun_W4_13(W3,szDzozmdt0(xN),xd),szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(W3,szDzozmdt0(xN),xd)) != W3 ) ) )
| ~ ( aElementOf0(W3,sdtlcdtrc0(xd,szDzozmdt0(xN)))
| ! [W4: $i] :
( ~ aElementOf0(W4,szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,W4) != W3 ) ) ) )
| ~ ( ~ ( ~ aElementOf0(xx,sdtlcdtrc0(xd,szDzozmdt0(xN)))
| ~ ( ~ aElementOf0(tptp_fun_W4_13(xx,szDzozmdt0(xN),xd),szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(xx,szDzozmdt0(xN),xd)) != xx ) ) )
| ~ ( aElementOf0(xx,sdtlcdtrc0(xd,szDzozmdt0(xN)))
| ! [W4: $i] :
( ~ aElementOf0(W4,szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,W4) != xx ) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(78,plain,
~ ( ~ ( ~ aElementOf0(xx,sdtlcdtrc0(xd,szDzozmdt0(xN)))
| ~ ( ~ aElementOf0(tptp_fun_W4_13(xx,szDzozmdt0(xN),xd),szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(xx,szDzozmdt0(xN),xd)) != xx ) ) )
| ~ ( aElementOf0(xx,sdtlcdtrc0(xd,szDzozmdt0(xN)))
| ! [W4: $i] :
( ~ aElementOf0(W4,szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,W4) != xx ) ) ) ),
inference(unit_resolution,[status(thm)],[77,76]) ).
tff(79,plain,
( ~ ( ~ aElementOf0(xx,sdtlcdtrc0(xd,szDzozmdt0(xN)))
| ~ ( ~ aElementOf0(tptp_fun_W4_13(xx,szDzozmdt0(xN),xd),szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(xx,szDzozmdt0(xN),xd)) != xx ) ) )
| ~ ( aElementOf0(xx,sdtlcdtrc0(xd,szDzozmdt0(xN)))
| ! [W4: $i] :
( ~ aElementOf0(W4,szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,W4) != xx ) ) )
| ~ aElementOf0(xx,sdtlcdtrc0(xd,szDzozmdt0(xN)))
| ~ ( ~ aElementOf0(tptp_fun_W4_13(xx,szDzozmdt0(xN),xd),szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(xx,szDzozmdt0(xN),xd)) != xx ) ) ),
inference(tautology,[status(thm)],]) ).
tff(80,plain,
( ~ aElementOf0(xx,sdtlcdtrc0(xd,szDzozmdt0(xN)))
| ~ ( ~ aElementOf0(tptp_fun_W4_13(xx,szDzozmdt0(xN),xd),szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(xx,szDzozmdt0(xN),xd)) != xx ) ) ),
inference(unit_resolution,[status(thm)],[79,78]) ).
tff(81,plain,
( aElementOf0(xx,sdtlcdtrc0(xd,szDzozmdt0(xd)))
<=> aElementOf0(xx,sdtlcdtrc0(xd,szDzozmdt0(xN))) ),
inference(rewrite,[status(thm)],]) ).
tff(82,plain,
( aElementOf0(xx,sdtlcdtrc0(xd,szDzozmdt0(xd)))
<=> aElementOf0(xx,sdtlcdtrc0(xd,szDzozmdt0(xd))) ),
inference(rewrite,[status(thm)],]) ).
tff(83,axiom,
aElementOf0(xx,sdtlcdtrc0(xd,szDzozmdt0(xd))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4781) ).
tff(84,plain,
aElementOf0(xx,sdtlcdtrc0(xd,szDzozmdt0(xd))),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
aElementOf0(xx,sdtlcdtrc0(xd,szDzozmdt0(xN))),
inference(modus_ponens,[status(thm)],[84,81]) ).
tff(86,plain,
( ~ ( ~ aElementOf0(xx,sdtlcdtrc0(xd,szDzozmdt0(xN)))
| ~ ( ~ aElementOf0(tptp_fun_W4_13(xx,szDzozmdt0(xN),xd),szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(xx,szDzozmdt0(xN),xd)) != xx ) ) )
| ~ aElementOf0(xx,sdtlcdtrc0(xd,szDzozmdt0(xN)))
| ~ ( ~ aElementOf0(tptp_fun_W4_13(xx,szDzozmdt0(xN),xd),szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(xx,szDzozmdt0(xN),xd)) != xx ) ) ),
inference(tautology,[status(thm)],]) ).
tff(87,plain,
( ~ ( ~ aElementOf0(xx,sdtlcdtrc0(xd,szDzozmdt0(xN)))
| ~ ( ~ aElementOf0(tptp_fun_W4_13(xx,szDzozmdt0(xN),xd),szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(xx,szDzozmdt0(xN),xd)) != xx ) ) )
| ~ ( ~ aElementOf0(tptp_fun_W4_13(xx,szDzozmdt0(xN),xd),szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(xx,szDzozmdt0(xN),xd)) != xx ) ) ),
inference(unit_resolution,[status(thm)],[86,85]) ).
tff(88,plain,
~ ( ~ aElementOf0(tptp_fun_W4_13(xx,szDzozmdt0(xN),xd),szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(xx,szDzozmdt0(xN),xd)) != xx ) ),
inference(unit_resolution,[status(thm)],[87,80]) ).
tff(89,plain,
( ~ aElementOf0(tptp_fun_W4_13(xx,szDzozmdt0(xN),xd),szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(xx,szDzozmdt0(xN),xd)) != xx )
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(xx,szDzozmdt0(xN),xd)) = xx ) ),
inference(tautology,[status(thm)],]) ).
tff(90,plain,
sdtlpdtrp0(xd,tptp_fun_W4_13(xx,szDzozmdt0(xN),xd)) = xx,
inference(unit_resolution,[status(thm)],[89,88]) ).
tff(91,plain,
( ~ aElementOf0(tptp_fun_W4_13(xx,szDzozmdt0(xN),xd),szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(xx,szDzozmdt0(xN),xd)) != xx )
| aElementOf0(tptp_fun_W4_13(xx,szDzozmdt0(xN),xd),szDzozmdt0(xN)) ),
inference(tautology,[status(thm)],]) ).
tff(92,plain,
aElementOf0(tptp_fun_W4_13(xx,szDzozmdt0(xN),xd),szDzozmdt0(xN)),
inference(unit_resolution,[status(thm)],[91,88]) ).
tff(93,plain,
^ [W0: $i] :
refl(
( ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,W0) != xx ) )
<=> ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,W0) != xx ) ) )),
inference(bind,[status(th)],]) ).
tff(94,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,W0) != xx ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,W0) != xx ) ) ),
inference(quant_intro,[status(thm)],[93]) ).
tff(95,plain,
^ [W0: $i] :
trans(
monotonicity(
rewrite(
( ( aElementOf0(W0,szDzozmdt0(xN))
& ( sdtlpdtrp0(xd,W0) = xx ) )
<=> ~ ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,W0) != xx ) ) )),
( ~ ( aElementOf0(W0,szDzozmdt0(xN))
& ( sdtlpdtrp0(xd,W0) = xx ) )
<=> ~ ~ ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,W0) != xx ) ) )),
rewrite(
( ~ ~ ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,W0) != xx ) )
<=> ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,W0) != xx ) ) )),
( ~ ( aElementOf0(W0,szDzozmdt0(xN))
& ( sdtlpdtrp0(xd,W0) = xx ) )
<=> ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,W0) != xx ) ) )),
inference(bind,[status(th)],]) ).
tff(96,plain,
( ! [W0: $i] :
~ ( aElementOf0(W0,szDzozmdt0(xN))
& ( sdtlpdtrp0(xd,W0) = xx ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,W0) != xx ) ) ),
inference(quant_intro,[status(thm)],[95]) ).
tff(97,plain,
( ~ ? [W0: $i] :
( aElementOf0(W0,szDzozmdt0(xN))
& ( sdtlpdtrp0(xd,W0) = xx ) )
<=> ~ ? [W0: $i] :
( aElementOf0(W0,szDzozmdt0(xN))
& ( sdtlpdtrp0(xd,W0) = xx ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(98,plain,
( ~ ? [W0: $i] :
( aElementOf0(W0,szNzAzT0)
& ( sdtlpdtrp0(xd,W0) = xx ) )
<=> ~ ? [W0: $i] :
( aElementOf0(W0,szDzozmdt0(xN))
& ( sdtlpdtrp0(xd,W0) = xx ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(99,plain,
( ~ ? [W0: $i] :
( aElementOf0(W0,szNzAzT0)
& ( sdtlpdtrp0(xd,W0) = xx ) )
<=> ~ ? [W0: $i] :
( aElementOf0(W0,szNzAzT0)
& ( sdtlpdtrp0(xd,W0) = xx ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(100,axiom,
~ ? [W0: $i] :
( aElementOf0(W0,szNzAzT0)
& ( sdtlpdtrp0(xd,W0) = xx ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(101,plain,
~ ? [W0: $i] :
( aElementOf0(W0,szNzAzT0)
& ( sdtlpdtrp0(xd,W0) = xx ) ),
inference(modus_ponens,[status(thm)],[100,99]) ).
tff(102,plain,
~ ? [W0: $i] :
( aElementOf0(W0,szNzAzT0)
& ( sdtlpdtrp0(xd,W0) = xx ) ),
inference(modus_ponens,[status(thm)],[101,99]) ).
tff(103,plain,
~ ? [W0: $i] :
( aElementOf0(W0,szNzAzT0)
& ( sdtlpdtrp0(xd,W0) = xx ) ),
inference(modus_ponens,[status(thm)],[102,99]) ).
tff(104,plain,
~ ? [W0: $i] :
( aElementOf0(W0,szNzAzT0)
& ( sdtlpdtrp0(xd,W0) = xx ) ),
inference(modus_ponens,[status(thm)],[103,99]) ).
tff(105,plain,
~ ? [W0: $i] :
( aElementOf0(W0,szDzozmdt0(xN))
& ( sdtlpdtrp0(xd,W0) = xx ) ),
inference(modus_ponens,[status(thm)],[104,98]) ).
tff(106,plain,
~ ? [W0: $i] :
( aElementOf0(W0,szDzozmdt0(xN))
& ( sdtlpdtrp0(xd,W0) = xx ) ),
inference(modus_ponens,[status(thm)],[105,97]) ).
tff(107,plain,
~ ? [W0: $i] :
( aElementOf0(W0,szDzozmdt0(xN))
& ( sdtlpdtrp0(xd,W0) = xx ) ),
inference(modus_ponens,[status(thm)],[106,97]) ).
tff(108,plain,
~ ? [W0: $i] :
( aElementOf0(W0,szDzozmdt0(xN))
& ( sdtlpdtrp0(xd,W0) = xx ) ),
inference(modus_ponens,[status(thm)],[107,97]) ).
tff(109,plain,
^ [W0: $i] :
refl(
$oeq(
~ ( aElementOf0(W0,szDzozmdt0(xN))
& ( sdtlpdtrp0(xd,W0) = xx ) ),
~ ( aElementOf0(W0,szDzozmdt0(xN))
& ( sdtlpdtrp0(xd,W0) = xx ) ))),
inference(bind,[status(th)],]) ).
tff(110,plain,
! [W0: $i] :
~ ( aElementOf0(W0,szDzozmdt0(xN))
& ( sdtlpdtrp0(xd,W0) = xx ) ),
inference(nnf-neg,[status(sab)],[108,109]) ).
tff(111,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,W0) != xx ) ),
inference(modus_ponens,[status(thm)],[110,96]) ).
tff(112,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,W0) != xx ) ),
inference(modus_ponens,[status(thm)],[111,94]) ).
tff(113,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,W0) != xx ) )
| ~ aElementOf0(tptp_fun_W4_13(xx,szDzozmdt0(xN),xd),szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(xx,szDzozmdt0(xN),xd)) != xx ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,W0) != xx ) )
| ~ aElementOf0(tptp_fun_W4_13(xx,szDzozmdt0(xN),xd),szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(xx,szDzozmdt0(xN),xd)) != xx ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(114,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,W0) != xx ) )
| ~ aElementOf0(tptp_fun_W4_13(xx,szDzozmdt0(xN),xd),szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(xx,szDzozmdt0(xN),xd)) != xx ) ),
inference(quant_inst,[status(thm)],]) ).
tff(115,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,W0) != xx ) )
| ~ aElementOf0(tptp_fun_W4_13(xx,szDzozmdt0(xN),xd),szDzozmdt0(xN))
| ( sdtlpdtrp0(xd,tptp_fun_W4_13(xx,szDzozmdt0(xN),xd)) != xx ) ),
inference(modus_ponens,[status(thm)],[114,113]) ).
tff(116,plain,
$false,
inference(unit_resolution,[status(thm)],[115,112,92,90]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09 % Problem : NUM594+1 : TPTP v8.1.0. Released v4.0.0.
% 0.05/0.10 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.09/0.30 % Computer : n010.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Fri Sep 2 12:01:58 EDT 2022
% 0.09/0.30 % CPUTime :
% 0.09/0.30 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.09/0.30 Usage: tptp [options] [-file:]file
% 0.09/0.30 -h, -? prints this message.
% 0.09/0.30 -smt2 print SMT-LIB2 benchmark.
% 0.09/0.30 -m, -model generate model.
% 0.09/0.30 -p, -proof generate proof.
% 0.09/0.30 -c, -core generate unsat core of named formulas.
% 0.09/0.30 -st, -statistics display statistics.
% 0.09/0.30 -t:timeout set timeout (in second).
% 0.09/0.30 -smt2status display status in smt2 format instead of SZS.
% 0.09/0.30 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.09/0.30 -<param>:<value> configuration parameter and value.
% 0.09/0.30 -o:<output-file> file to place output in.
% 50.62/32.57 % SZS status Theorem
% 50.62/32.57 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------