%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM630+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:21:40 AM UTC 2025
% Result : Theorem 0.62s 0.78s
% Output : Proof 0.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 25
% Syntax : Number of formulae : 73 ( 26 unt; 0 typ; 0 def)
% Number of atoms : 481 ( 171 equ)
% Maximal formula atoms : 24 ( 6 avg)
% Number of connectives : 716 ( 327 ~; 254 |; 79 &)
% ( 40 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 19 ( 19 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 20 ( 20 usr; 12 con; 0-2 aty)
% Number of variables : 101 ( 96 !; 0 ?; 101 :)
% Comments :
%------------------------------------------------------------------------------
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(slbdtsldtrb0_type,type,
slbdtsldtrb0: ( $i * $i ) > $i ).
tff(xk_type,type,
xk: $i ).
tff(sdtmndt0_type,type,
sdtmndt0: ( $i * $i ) > $i ).
tff(szmzizndt0_type,type,
szmzizndt0: $i > $i ).
tff(sdtlpdtrp0_type,type,
sdtlpdtrp0: ( $i * $i ) > $i ).
tff(xn_type,type,
xn: $i ).
tff(xN_type,type,
xN: $i ).
tff(xQ_type,type,
xQ: $i ).
tff(xD_type,type,
xD: $i ).
tff(xP_type,type,
xP: $i ).
tff(aSet0_type,type,
aSet0: $i > $o ).
tff(sdtpldt0_type,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(xc_type,type,
xc: $i ).
tff(xC_type,type,
xC: $i ).
tff(szDzozmdt0_type,type,
szDzozmdt0: $i > $i ).
tff(aFunction0_type,type,
aFunction0: $i > $o ).
tff(szNzAzT0_type,type,
szNzAzT0: $i ).
tff(sdtlbdtrb0_type,type,
sdtlbdtrb0: ( $i * $i ) > $i ).
tff(szDzizrdt0_type,type,
szDzizrdt0: $i > $i ).
tff(xd_type,type,
xd: $i ).
tff(xp_type,type,
xp: $i ).
tff(xe_type,type,
xe: $i ).
tff(1,plain,
( ( xD = sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))) )
<=> ( xD = sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
xD = sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5585) ).
tff(3,plain,
xD = sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
slbdtsldtrb0(xD,xk) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk),
inference(monotonicity,[status(thm)],[3]) ).
tff(5,plain,
slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk) = slbdtsldtrb0(xD,xk),
inference(symmetry,[status(thm)],[4]) ).
tff(6,plain,
( ( xP = sdtmndt0(xQ,szmzizndt0(xQ)) )
<=> ( xP = sdtmndt0(xQ,szmzizndt0(xQ)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
( aSet0(xP)
& ( xP = sdtmndt0(xQ,szmzizndt0(xQ)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5164) ).
tff(8,plain,
xP = sdtmndt0(xQ,szmzizndt0(xQ)),
inference(and_elim,[status(thm)],[7]) ).
tff(9,plain,
xP = sdtmndt0(xQ,szmzizndt0(xQ)),
inference(modus_ponens,[status(thm)],[8,6]) ).
tff(10,plain,
sdtmndt0(xQ,szmzizndt0(xQ)) = xP,
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
( aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
<=> aElementOf0(xP,slbdtsldtrb0(xD,xk)) ),
inference(monotonicity,[status(thm)],[10,5]) ).
tff(12,plain,
( aElementOf0(xP,slbdtsldtrb0(xD,xk))
<=> aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk)) ),
inference(symmetry,[status(thm)],[11]) ).
tff(13,plain,
( aElementOf0(xP,slbdtsldtrb0(xD,xk))
<=> aElementOf0(xP,slbdtsldtrb0(xD,xk)) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,axiom,
aElementOf0(xP,slbdtsldtrb0(xD,xk)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5599) ).
tff(15,plain,
aElementOf0(xP,slbdtsldtrb0(xD,xk)),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk)),
inference(modus_ponens,[status(thm)],[15,12]) ).
tff(17,plain,
( ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP) = sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
<=> ( sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP) ) ),
inference(commutativity,[status(thm)],[]) ).
tff(18,plain,
sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn))) = sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))),
inference(monotonicity,[status(thm)],[10]) ).
tff(19,plain,
sdtlpdtrp0(xc,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) = sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP),
inference(monotonicity,[status(thm)],[10]) ).
tff(21,plain,
( ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) = sdtlpdtrp0(xc,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
<=> ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP) = sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ),
inference(monotonicity,[status(thm)],[20,19]) ).
tff(22,plain,
( ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) = sdtlpdtrp0(xc,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
<=> ( sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP) ) ),
inference(transitivity,[status(thm)],[21,17]) ).
tff(23,plain,
( ( sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP) )
<=> ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) = sdtlpdtrp0(xc,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ),
inference(symmetry,[status(thm)],[22]) ).
tff(24,plain,
( ( sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) != sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP) )
<=> ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) != sdtlpdtrp0(xc,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ),
inference(monotonicity,[status(thm)],[23]) ).
tff(25,plain,
( ( sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) != sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP) )
<=> ( sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) != sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,axiom,
sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) != sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(27,plain,
sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) != sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) != sdtlpdtrp0(xc,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))),
inference(modus_ponens,[status(thm)],[27,24]) ).
tff(29,plain,
( aElementOf0(xn,szNzAzT0)
<=> aElementOf0(xn,szNzAzT0) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,axiom,
( aElementOf0(xn,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aElementOf0(xn,szNzAzT0)
& ( sdtlpdtrp0(xe,xn) = xp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5309) ).
tff(31,plain,
( aElementOf0(xn,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aElementOf0(xn,szNzAzT0) ),
inference(and_elim,[status(thm)],[30]) ).
tff(32,plain,
aElementOf0(xn,szNzAzT0),
inference(and_elim,[status(thm)],[31]) ).
tff(33,plain,
aElementOf0(xn,szNzAzT0),
inference(modus_ponens,[status(thm)],[32,29]) ).
tff(34,plain,
^ [W0: $i] :
refl(( ( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aFunction0(sdtlpdtrp0(xC,W0))
| ( szDzozmdt0(sdtlpdtrp0(xC,W0)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
| ~ ! [W1: $i] :
( ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSet0(W1)
| ~ aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) )
<=> ( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aFunction0(sdtlpdtrp0(xC,W0))
| ( szDzozmdt0(sdtlpdtrp0(xC,W0)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
| ~ ! [W1: $i] :
( ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSet0(W1)
| ~ aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(35,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aFunction0(sdtlpdtrp0(xC,W0))
| ( szDzozmdt0(sdtlpdtrp0(xC,W0)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
| ~ ! [W1: $i] :
( ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSet0(W1)
| ~ aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aFunction0(sdtlpdtrp0(xC,W0))
| ( szDzozmdt0(sdtlpdtrp0(xC,W0)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
| ~ ! [W1: $i] :
( ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSet0(W1)
| ~ aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) ) ),
inference(quant_intro,[status(thm)],[34]) ).
tff(36,plain,
^ [W0: $i] :
rewrite(( ( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aFunction0(sdtlpdtrp0(xC,W0))
| ( szDzozmdt0(sdtlpdtrp0(xC,W0)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
| ~ ! [W1: $i] :
( ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSet0(W1)
| ~ aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) )
<=> ( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aFunction0(sdtlpdtrp0(xC,W0))
| ( szDzozmdt0(sdtlpdtrp0(xC,W0)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
| ~ ! [W1: $i] :
( ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSet0(W1)
| ~ aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(37,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aFunction0(sdtlpdtrp0(xC,W0))
| ( szDzozmdt0(sdtlpdtrp0(xC,W0)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
| ~ ! [W1: $i] :
( ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSet0(W1)
| ~ aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aFunction0(sdtlpdtrp0(xC,W0))
| ( szDzozmdt0(sdtlpdtrp0(xC,W0)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
| ~ ! [W1: $i] :
( ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSet0(W1)
| ~ aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) ) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aFunction0(sdtlpdtrp0(xC,W0))
| ( szDzozmdt0(sdtlpdtrp0(xC,W0)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
| ~ ! [W1: $i] :
( ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSet0(W1)
| ~ aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aFunction0(sdtlpdtrp0(xC,W0))
| ( szDzozmdt0(sdtlpdtrp0(xC,W0)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
| ~ ! [W1: $i] :
( ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSet0(W1)
| ~ aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) ) ),
inference(transitivity,[status(thm)],[37,35]) ).
tff(39,plain,
^ [W0: $i] :
rewrite(( ( ~ aElementOf0(W0,szNzAzT0)
| ( aFunction0(sdtlpdtrp0(xC,W0))
& ( szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
& ! [W1: $i] :
( ~ ( aSet0(W1)
& aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) )
| ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) )
<=> ( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aFunction0(sdtlpdtrp0(xC,W0))
| ( szDzozmdt0(sdtlpdtrp0(xC,W0)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
| ~ ! [W1: $i] :
( ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSet0(W1)
| ~ aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(40,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aFunction0(sdtlpdtrp0(xC,W0))
& ( szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
& ! [W1: $i] :
( ~ ( aSet0(W1)
& aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) )
| ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aFunction0(sdtlpdtrp0(xC,W0))
| ( szDzozmdt0(sdtlpdtrp0(xC,W0)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
| ~ ! [W1: $i] :
( ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSet0(W1)
| ~ aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aFunction0(sdtlpdtrp0(xC,W0))
& ( szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
& ! [W1: $i] :
( ~ ( aSet0(W1)
& aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) )
| ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aFunction0(sdtlpdtrp0(xC,W0))
& ( szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
& ! [W1: $i] :
( ~ ( aSet0(W1)
& aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) )
| ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,plain,
^ [W0: $i] :
trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^ [W1: $i] :
rewrite(( ( ( aSet0(W1)
& aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) )
=> ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
<=> ( ~ ( aSet0(W1)
& aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) )
| ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ))),
( ! [W1: $i] :
( ( aSet0(W1)
& aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) )
=> ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
<=> ! [W1: $i] :
( ~ ( aSet0(W1)
& aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) )
| ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )),
( ( aFunction0(sdtlpdtrp0(xC,W0))
& ( szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
& ! [W1: $i] :
( ( aSet0(W1)
& aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) )
=> ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
<=> ( aFunction0(sdtlpdtrp0(xC,W0))
& ( szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
& ! [W1: $i] :
( ~ ( aSet0(W1)
& aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) )
| ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) )),
rewrite(( ( aFunction0(sdtlpdtrp0(xC,W0))
& ( szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
& ! [W1: $i] :
( ~ ( aSet0(W1)
& aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) )
| ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
<=> ( aFunction0(sdtlpdtrp0(xC,W0))
& ( szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
& ! [W1: $i] :
( ~ ( aSet0(W1)
& aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) )
| ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) )),
( ( aFunction0(sdtlpdtrp0(xC,W0))
& ( szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
& ! [W1: $i] :
( ( aSet0(W1)
& aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) )
=> ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
<=> ( aFunction0(sdtlpdtrp0(xC,W0))
& ( szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
& ! [W1: $i] :
( ~ ( aSet0(W1)
& aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) )
| ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) )),
( ( aElementOf0(W0,szNzAzT0)
=> ( aFunction0(sdtlpdtrp0(xC,W0))
& ( szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
& ! [W1: $i] :
( ( aSet0(W1)
& aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) )
=> ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) )
<=> ( aElementOf0(W0,szNzAzT0)
=> ( aFunction0(sdtlpdtrp0(xC,W0))
& ( szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
& ! [W1: $i] :
( ~ ( aSet0(W1)
& aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) )
| ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )),
rewrite(( ( aElementOf0(W0,szNzAzT0)
=> ( aFunction0(sdtlpdtrp0(xC,W0))
& ( szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
& ! [W1: $i] :
( ~ ( aSet0(W1)
& aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) )
| ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) )
<=> ( ~ aElementOf0(W0,szNzAzT0)
| ( aFunction0(sdtlpdtrp0(xC,W0))
& ( szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
& ! [W1: $i] :
( ~ ( aSet0(W1)
& aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) )
| ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )),
( ( aElementOf0(W0,szNzAzT0)
=> ( aFunction0(sdtlpdtrp0(xC,W0))
& ( szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
& ! [W1: $i] :
( ( aSet0(W1)
& aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) )
=> ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) )
<=> ( ~ aElementOf0(W0,szNzAzT0)
| ( aFunction0(sdtlpdtrp0(xC,W0))
& ( szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
& ! [W1: $i] :
( ~ ( aSet0(W1)
& aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) )
| ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(43,plain,
( ! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> ( aFunction0(sdtlpdtrp0(xC,W0))
& ( szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
& ! [W1: $i] :
( ( aSet0(W1)
& aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) )
=> ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aFunction0(sdtlpdtrp0(xC,W0))
& ( szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
& ! [W1: $i] :
( ~ ( aSet0(W1)
& aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) )
| ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) ),
inference(quant_intro,[status(thm)],[42]) ).
tff(44,axiom,
( aFunction0(xC)
& ( szDzozmdt0(xC) = szNzAzT0 )
& ! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> ( aFunction0(sdtlpdtrp0(xC,W0))
& ( szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
& ! [W1: $i] :
( ( aSet0(W1)
& aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) )
=> ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4151) ).
tff(45,plain,
! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> ( aFunction0(sdtlpdtrp0(xC,W0))
& ( szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
& ! [W1: $i] :
( ( aSet0(W1)
& aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) )
=> ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ),
inference(and_elim,[status(thm)],[44]) ).
tff(46,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aFunction0(sdtlpdtrp0(xC,W0))
& ( szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
& ! [W1: $i] :
( ~ ( aSet0(W1)
& aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) )
| ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ),
inference(modus_ponens,[status(thm)],[45,43]) ).
tff(47,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aFunction0(sdtlpdtrp0(xC,W0))
& ( szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
& ! [W1: $i] :
( ~ ( aSet0(W1)
& aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) )
| ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ),
inference(modus_ponens,[status(thm)],[46,41]) ).
tff(48,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aFunction0(sdtlpdtrp0(xC,W0))
& ( szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
& ! [W1: $i] :
( ~ ( aSet0(W1)
& aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) )
| ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ),
inference(skolemize,[status(sab)],[47]) ).
tff(49,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aFunction0(sdtlpdtrp0(xC,W0))
| ( szDzozmdt0(sdtlpdtrp0(xC,W0)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
| ~ ! [W1: $i] :
( ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSet0(W1)
| ~ aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) ),
inference(modus_ponens,[status(thm)],[48,40]) ).
tff(50,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aFunction0(sdtlpdtrp0(xC,W0))
| ( szDzozmdt0(sdtlpdtrp0(xC,W0)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
| ~ ! [W1: $i] :
( ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSet0(W1)
| ~ aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) ),
inference(modus_ponens,[status(thm)],[49,38]) ).
tff(51,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aFunction0(sdtlpdtrp0(xC,W0))
| ( szDzozmdt0(sdtlpdtrp0(xC,W0)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
| ~ ! [W1: $i] :
( ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSet0(W1)
| ~ aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) )
| ~ aElementOf0(xn,szNzAzT0)
| ~ ( ~ aFunction0(sdtlpdtrp0(xC,xn))
| ( szDzozmdt0(sdtlpdtrp0(xC,xn)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk) )
| ~ ! [W1: $i] :
( ~ aSet0(W1)
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk)) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aFunction0(sdtlpdtrp0(xC,W0))
| ( szDzozmdt0(sdtlpdtrp0(xC,W0)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
| ~ ! [W1: $i] :
( ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSet0(W1)
| ~ aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) )
| ~ aElementOf0(xn,szNzAzT0)
| ~ ( ~ aFunction0(sdtlpdtrp0(xC,xn))
| ( szDzozmdt0(sdtlpdtrp0(xC,xn)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk) )
| ~ ! [W1: $i] :
( ~ aSet0(W1)
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(52,plain,
( ( ~ aElementOf0(xn,szNzAzT0)
| ~ ( ~ aFunction0(sdtlpdtrp0(xC,xn))
| ( szDzozmdt0(sdtlpdtrp0(xC,xn)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk) )
| ~ ! [W1: $i] :
( ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ aSet0(W1)
| ~ aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk)) ) ) )
<=> ( ~ aElementOf0(xn,szNzAzT0)
| ~ ( ~ aFunction0(sdtlpdtrp0(xC,xn))
| ( szDzozmdt0(sdtlpdtrp0(xC,xn)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk) )
| ~ ! [W1: $i] :
( ~ aSet0(W1)
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aFunction0(sdtlpdtrp0(xC,W0))
| ( szDzozmdt0(sdtlpdtrp0(xC,W0)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
| ~ ! [W1: $i] :
( ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSet0(W1)
| ~ aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) )
| ~ aElementOf0(xn,szNzAzT0)
| ~ ( ~ aFunction0(sdtlpdtrp0(xC,xn))
| ( szDzozmdt0(sdtlpdtrp0(xC,xn)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk) )
| ~ ! [W1: $i] :
( ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ aSet0(W1)
| ~ aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk)) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aFunction0(sdtlpdtrp0(xC,W0))
| ( szDzozmdt0(sdtlpdtrp0(xC,W0)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
| ~ ! [W1: $i] :
( ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSet0(W1)
| ~ aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) )
| ~ aElementOf0(xn,szNzAzT0)
| ~ ( ~ aFunction0(sdtlpdtrp0(xC,xn))
| ( szDzozmdt0(sdtlpdtrp0(xC,xn)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk) )
| ~ ! [W1: $i] :
( ~ aSet0(W1)
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk)) ) ) ) ),
inference(monotonicity,[status(thm)],[52]) ).
tff(54,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aFunction0(sdtlpdtrp0(xC,W0))
| ( szDzozmdt0(sdtlpdtrp0(xC,W0)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
| ~ ! [W1: $i] :
( ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSet0(W1)
| ~ aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) )
| ~ aElementOf0(xn,szNzAzT0)
| ~ ( ~ aFunction0(sdtlpdtrp0(xC,xn))
| ( szDzozmdt0(sdtlpdtrp0(xC,xn)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk) )
| ~ ! [W1: $i] :
( ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ aSet0(W1)
| ~ aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk)) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aFunction0(sdtlpdtrp0(xC,W0))
| ( szDzozmdt0(sdtlpdtrp0(xC,W0)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
| ~ ! [W1: $i] :
( ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSet0(W1)
| ~ aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) )
| ~ aElementOf0(xn,szNzAzT0)
| ~ ( ~ aFunction0(sdtlpdtrp0(xC,xn))
| ( szDzozmdt0(sdtlpdtrp0(xC,xn)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk) )
| ~ ! [W1: $i] :
( ~ aSet0(W1)
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk)) ) ) ) ),
inference(transitivity,[status(thm)],[53,51]) ).
tff(55,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aFunction0(sdtlpdtrp0(xC,W0))
| ( szDzozmdt0(sdtlpdtrp0(xC,W0)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
| ~ ! [W1: $i] :
( ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSet0(W1)
| ~ aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) )
| ~ aElementOf0(xn,szNzAzT0)
| ~ ( ~ aFunction0(sdtlpdtrp0(xC,xn))
| ( szDzozmdt0(sdtlpdtrp0(xC,xn)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk) )
| ~ ! [W1: $i] :
( ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ aSet0(W1)
| ~ aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk)) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(56,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aFunction0(sdtlpdtrp0(xC,W0))
| ( szDzozmdt0(sdtlpdtrp0(xC,W0)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
| ~ ! [W1: $i] :
( ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSet0(W1)
| ~ aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) )
| ~ aElementOf0(xn,szNzAzT0)
| ~ ( ~ aFunction0(sdtlpdtrp0(xC,xn))
| ( szDzozmdt0(sdtlpdtrp0(xC,xn)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk) )
| ~ ! [W1: $i] :
( ~ aSet0(W1)
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk)) ) ) ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
~ ( ~ aFunction0(sdtlpdtrp0(xC,xn))
| ( szDzozmdt0(sdtlpdtrp0(xC,xn)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk) )
| ~ ! [W1: $i] :
( ~ aSet0(W1)
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk)) ) ),
inference(unit_resolution,[status(thm)],[56,50,33]) ).
tff(58,plain,
( ~ aFunction0(sdtlpdtrp0(xC,xn))
| ( szDzozmdt0(sdtlpdtrp0(xC,xn)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk) )
| ~ ! [W1: $i] :
( ~ aSet0(W1)
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk)) )
| ! [W1: $i] :
( ~ aSet0(W1)
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(59,plain,
! [W1: $i] :
( ~ aSet0(W1)
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk)) ),
inference(unit_resolution,[status(thm)],[58,57]) ).
tff(60,plain,
( aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
<=> aSet0(xP) ),
inference(monotonicity,[status(thm)],[10]) ).
tff(61,plain,
( aSet0(xP)
<=> aSet0(sdtmndt0(xQ,szmzizndt0(xQ))) ),
inference(symmetry,[status(thm)],[60]) ).
tff(62,plain,
( aSet0(xP)
<=> aSet0(xP) ),
inference(rewrite,[status(thm)],[]) ).
tff(63,plain,
aSet0(xP),
inference(and_elim,[status(thm)],[7]) ).
tff(64,plain,
aSet0(xP),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
aSet0(sdtmndt0(xQ,szmzizndt0(xQ))),
inference(modus_ponens,[status(thm)],[64,61]) ).
tff(66,plain,
( ( ~ ! [W1: $i] :
( ~ aSet0(W1)
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk)) )
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) = sdtlpdtrp0(xc,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
<=> ( ~ ! [W1: $i] :
( ~ aSet0(W1)
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk)) )
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) = sdtlpdtrp0(xc,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(67,plain,
( ( ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) = sdtlpdtrp0(xc,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk)) )
<=> ( ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) = sdtlpdtrp0(xc,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(68,plain,
( ( ~ ! [W1: $i] :
( ~ aSet0(W1)
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk)) )
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) = sdtlpdtrp0(xc,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk)) )
<=> ( ~ ! [W1: $i] :
( ~ aSet0(W1)
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk)) )
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) = sdtlpdtrp0(xc,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ),
inference(monotonicity,[status(thm)],[67]) ).
tff(69,plain,
( ( ~ ! [W1: $i] :
( ~ aSet0(W1)
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk)) )
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) = sdtlpdtrp0(xc,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk)) )
<=> ( ~ ! [W1: $i] :
( ~ aSet0(W1)
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk)) )
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) = sdtlpdtrp0(xc,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ),
inference(transitivity,[status(thm)],[68,66]) ).
tff(70,plain,
( ~ ! [W1: $i] :
( ~ aSet0(W1)
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk)) )
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) = sdtlpdtrp0(xc,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(71,plain,
( ~ ! [W1: $i] :
( ~ aSet0(W1)
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk)) )
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) = sdtlpdtrp0(xc,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ),
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,plain,
( ~ aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) = sdtlpdtrp0(xc,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ),
inference(unit_resolution,[status(thm)],[71,65,59]) ).
tff(73,plain,
$false,
inference(unit_resolution,[status(thm)],[72,28,16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : NUM630+1 : TPTP v9.0.0. Released v4.0.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n011.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Jun 20 01:37:26 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.62/0.78 % SZS status Theorem
% 0.62/0.78 % SZS output start Proof
% See solution above
% 0.62/0.81 % E exiting
%------------------------------------------------------------------------------