%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM631+3 : 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 0.73s 0.91s
% Output : Proof 0.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 53
% Syntax : Number of formulae : 154 ( 55 unt; 0 typ; 0 def)
% Number of atoms : 1180 ( 308 equ)
% Maximal formula atoms : 32 ( 7 avg)
% Number of connectives : 1700 ( 722 ~; 685 |; 151 &)
% ( 78 <=>; 64 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 48 ( 48 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 14 ( 12 usr; 1 prp; 0-3 aty)
% Number of functors : 24 ( 24 usr; 13 con; 0-2 aty)
% Number of variables : 288 ( 274 !; 0 ?; 288 :)
% Comments :
%------------------------------------------------------------------------------
tff(sdtlpdtrp0_type,type,
sdtlpdtrp0: ( $i * $i ) > $i ).
tff(xn_type,type,
xn: $i ).
tff(xd_type,type,
xd: $i ).
tff(xQ_type,type,
xQ: $i ).
tff(xc_type,type,
xc: $i ).
tff(sdtmndt0_type,type,
sdtmndt0: ( $i * $i ) > $i ).
tff(szmzizndt0_type,type,
szmzizndt0: $i > $i ).
tff(xC_type,type,
xC: $i ).
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(szszuzczcdt0_type,type,
szszuzczcdt0: $i > $i ).
tff(xN_type,type,
xN: $i ).
tff(tptp_fun_W2_39_type,type,
tptp_fun_W2_39: ( $i * $i ) > $i ).
tff(aSubsetOf0_type,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff(xk_type,type,
xk: $i ).
tff(sbrdtbr0_type,type,
sbrdtbr0: $i > $i ).
tff(slbdtsldtrb0_type,type,
slbdtsldtrb0: ( $i * $i ) > $i ).
tff(xP_type,type,
xP: $i ).
tff(aElement0_type,type,
aElement0: $i > $o ).
tff(sdtlseqdt0_type,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(aSet0_type,type,
aSet0: $i > $o ).
tff(szNzAzT0_type,type,
szNzAzT0: $i ).
tff(sdtlbdtrb0_type,type,
sdtlbdtrb0: ( $i * $i ) > $i ).
tff(szDzizrdt0_type,type,
szDzizrdt0: $i > $i ).
tff(szDzozmdt0_type,type,
szDzozmdt0: $i > $i ).
tff(xp_type,type,
xp: $i ).
tff(xe_type,type,
xe: $i ).
tff(aFunction0_type,type,
aFunction0: $i > $o ).
tff(sdtpldt0_type,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(xO_type,type,
xO: $i ).
tff(xK_type,type,
xK: $i ).
tff(1,plain,
( ( xP = sdtmndt0(xQ,szmzizndt0(xQ)) )
<=> ( xP = sdtmndt0(xQ,szmzizndt0(xQ)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
( aSet0(xP)
& ! [W0: $i] :
( aElementOf0(W0,xQ)
=> sdtlseqdt0(szmzizndt0(xQ),W0) )
& ! [W0: $i] :
( aElementOf0(W0,xP)
<=> ( aElement0(W0)
& aElementOf0(W0,xQ)
& ( W0 != szmzizndt0(xQ) ) ) )
& ( xP = sdtmndt0(xQ,szmzizndt0(xQ)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5164) ).
tff(3,plain,
xP = sdtmndt0(xQ,szmzizndt0(xQ)),
inference(and_elim,[status(thm)],[2]) ).
tff(4,plain,
xP = sdtmndt0(xQ,szmzizndt0(xQ)),
inference(modus_ponens,[status(thm)],[3,1]) ).
tff(5,plain,
sdtmndt0(xQ,szmzizndt0(xQ)) = xP,
inference(symmetry,[status(thm)],[4]) ).
tff(6,plain,
( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
<=> aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
inference(monotonicity,[status(thm)],[5]) ).
tff(7,plain,
( aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
<=> aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
inference(symmetry,[status(thm)],[6]) ).
tff(8,plain,
( aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
<=> aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
inference(rewrite,[status(thm)],[]) ).
tff(9,axiom,
( ! [W0: $i] :
( aElementOf0(W0,xP)
=> aElementOf0(W0,sdtlpdtrp0(xN,szszuzczcdt0(xn))) )
& aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5334) ).
tff(10,plain,
aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn))),
inference(and_elim,[status(thm)],[9]) ).
tff(11,plain,
aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn))),
inference(modus_ponens,[status(thm)],[10,8]) ).
tff(12,plain,
aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),
inference(modus_ponens,[status(thm)],[11,7]) ).
tff(13,plain,
( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
inference(tautology,[status(thm)],[]) ).
tff(14,plain,
( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
inference(unit_resolution,[status(thm)],[13,12]) ).
tff(15,plain,
( ( sbrdtbr0(xP) = xk )
<=> ( sbrdtbr0(xP) = xk ) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,axiom,
sbrdtbr0(xP) = xk,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5217) ).
tff(17,plain,
sbrdtbr0(xP) = xk,
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) = sbrdtbr0(xP),
inference(monotonicity,[status(thm)],[5]) ).
tff(19,plain,
sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) = xk,
inference(transitivity,[status(thm)],[18,17]) ).
tff(20,plain,
( ~ ( ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != xk )
| ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) )
| ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != xk )
| ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ),
inference(tautology,[status(thm)],[]) ).
tff(21,plain,
~ ( ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != xk )
| ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ),
inference(unit_resolution,[status(thm)],[20,19,14]) ).
tff(22,plain,
( aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
| ~ ( ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != xk )
| ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) )
| ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != xk )
| ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ),
inference(tautology,[status(thm)],[]) ).
tff(23,plain,
( aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
| ~ ( ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != xk )
| ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ),
inference(unit_resolution,[status(thm)],[22,21]) ).
tff(24,plain,
( aElementOf0(xn,szNzAzT0)
<=> aElementOf0(xn,szNzAzT0) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,axiom,
( aElementOf0(xn,szDzozmdt0(xd))
& ( sdtlpdtrp0(xd,xn) = szDzizrdt0(xd) )
& aElementOf0(xn,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aElementOf0(xn,szNzAzT0)
& ( sdtlpdtrp0(xe,xn) = xp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5309) ).
tff(26,plain,
( aElementOf0(xn,szDzozmdt0(xd))
& ( sdtlpdtrp0(xd,xn) = szDzizrdt0(xd) )
& aElementOf0(xn,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aElementOf0(xn,szNzAzT0) ),
inference(and_elim,[status(thm)],[25]) ).
tff(27,plain,
aElementOf0(xn,szNzAzT0),
inference(and_elim,[status(thm)],[26]) ).
tff(28,plain,
aElementOf0(xn,szNzAzT0),
inference(modus_ponens,[status(thm)],[27,24]) ).
tff(29,plain,
^ [W0: $i] :
refl(( ( ~ aElementOf0(W0,szNzAzT0)
| ! [W1: $i] :
( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
| ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
| ~ ( ( sbrdtbr0(W1) != xk )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
| aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) )
<=> ( ~ aElementOf0(W0,szNzAzT0)
| ! [W1: $i] :
( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
| ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
| ~ ( ( sbrdtbr0(W1) != xk )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
| aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(30,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ! [W1: $i] :
( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
| ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
| ~ ( ( sbrdtbr0(W1) != xk )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
| aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ! [W1: $i] :
( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
| ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
| ~ ( ( sbrdtbr0(W1) != xk )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
| aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,plain,
^ [W0: $i] :
rewrite(( ( ~ aElementOf0(W0,szNzAzT0)
| ! [W1: $i] :
( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
| ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
| ~ ( ( sbrdtbr0(W1) != xk )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
| aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) )
<=> ( ~ aElementOf0(W0,szNzAzT0)
| ! [W1: $i] :
( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
| ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
| ~ ( ( sbrdtbr0(W1) != xk )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
| aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(32,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ! [W1: $i] :
( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
| ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
| ~ ( ( sbrdtbr0(W1) != xk )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
| aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ! [W1: $i] :
( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
| ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
| ~ ( ( sbrdtbr0(W1) != xk )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
| aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[31]) ).
tff(33,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ! [W1: $i] :
( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
| ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
| ~ ( ( sbrdtbr0(W1) != xk )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
| aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ! [W1: $i] :
( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
| ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
| ~ ( ( sbrdtbr0(W1) != xk )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
| aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[32,30]) ).
tff(34,plain,
^ [W0: $i] :
rewrite(( ( ~ aElementOf0(W0,szNzAzT0)
| ! [W1: $i] :
( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
| ~ aSet0(W1)
| ( ~ aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
& ( ( sbrdtbr0(W1) != xk )
| ( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ~ ( ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
| aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) ) )
<=> ( ~ aElementOf0(W0,szNzAzT0)
| ! [W1: $i] :
( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
| ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
| ~ ( ( sbrdtbr0(W1) != xk )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
| aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(35,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ! [W1: $i] :
( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
| ~ aSet0(W1)
| ( ~ aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
& ( ( sbrdtbr0(W1) != xk )
| ( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ~ ( ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
| aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ! [W1: $i] :
( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
| ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
| ~ ( ( sbrdtbr0(W1) != xk )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
| aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[34]) ).
tff(36,plain,
^ [W0: $i] :
rewrite(( ( ~ aElementOf0(W0,szNzAzT0)
| ! [W1: $i] :
( ~ aSet0(W1)
| ( ~ aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
& ( ( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ~ ( ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
| aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )
| ( sbrdtbr0(W1) != xk ) ) )
| ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) )
<=> ( ~ aElementOf0(W0,szNzAzT0)
| ! [W1: $i] :
( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
| ~ aSet0(W1)
| ( ~ aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
& ( ( sbrdtbr0(W1) != xk )
| ( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ~ ( ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
| aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(37,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ! [W1: $i] :
( ~ aSet0(W1)
| ( ~ aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
& ( ( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ~ ( ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
| aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )
| ( sbrdtbr0(W1) != xk ) ) )
| ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ! [W1: $i] :
( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
| ~ aSet0(W1)
| ( ~ aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
& ( ( sbrdtbr0(W1) != xk )
| ( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ~ ( ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
| aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ! [W1: $i] :
( ~ ( aSet0(W1)
& ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
| ( ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )
& ( sbrdtbr0(W1) = xk ) ) ) )
| ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ! [W1: $i] :
( ~ ( aSet0(W1)
& ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
| ( ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )
& ( sbrdtbr0(W1) = xk ) ) ) )
| ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,plain,
^ [W0: $i] :
trans(monotonicity(quant_intro(proof_bind(^ [W1: $i] :
trans(monotonicity(rewrite(( ( aSet0(W1)
& ( ( ( ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
| aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
& ( sbrdtbr0(W1) = xk ) )
| aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk)) ) )
<=> ( aSet0(W1)
& ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
| ( ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )
& ( sbrdtbr0(W1) = xk ) ) ) ) )),
( ( ( aSet0(W1)
& ( ( ( ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
| aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
& ( sbrdtbr0(W1) = xk ) )
| aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk)) ) )
=> ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) )
<=> ( ( aSet0(W1)
& ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
| ( ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )
& ( sbrdtbr0(W1) = xk ) ) ) )
=> ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) )),
rewrite(( ( ( aSet0(W1)
& ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
| ( ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )
& ( sbrdtbr0(W1) = xk ) ) ) )
=> ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) )
<=> ( ~ ( aSet0(W1)
& ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
| ( ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )
& ( sbrdtbr0(W1) = xk ) ) ) )
| ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) )),
( ( ( aSet0(W1)
& ( ( ( ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
| aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
& ( sbrdtbr0(W1) = xk ) )
| aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk)) ) )
=> ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) )
<=> ( ~ ( aSet0(W1)
& ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
| ( ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )
& ( sbrdtbr0(W1) = xk ) ) ) )
| ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) ))),
( ! [W1: $i] :
( ( aSet0(W1)
& ( ( ( ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
| aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
& ( sbrdtbr0(W1) = xk ) )
| aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk)) ) )
=> ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) )
<=> ! [W1: $i] :
( ~ ( aSet0(W1)
& ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
| ( ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )
& ( sbrdtbr0(W1) = xk ) ) ) )
| ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) )),
( ( aElementOf0(W0,szNzAzT0)
=> ! [W1: $i] :
( ( aSet0(W1)
& ( ( ( ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
| aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
& ( sbrdtbr0(W1) = xk ) )
| aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk)) ) )
=> ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) )
<=> ( aElementOf0(W0,szNzAzT0)
=> ! [W1: $i] :
( ~ ( aSet0(W1)
& ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
| ( ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )
& ( sbrdtbr0(W1) = xk ) ) ) )
| ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) ) )),
rewrite(( ( aElementOf0(W0,szNzAzT0)
=> ! [W1: $i] :
( ~ ( aSet0(W1)
& ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
| ( ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )
& ( sbrdtbr0(W1) = xk ) ) ) )
| ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) )
<=> ( ~ aElementOf0(W0,szNzAzT0)
| ! [W1: $i] :
( ~ ( aSet0(W1)
& ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
| ( ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )
& ( sbrdtbr0(W1) = xk ) ) ) )
| ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) ) )),
( ( aElementOf0(W0,szNzAzT0)
=> ! [W1: $i] :
( ( aSet0(W1)
& ( ( ( ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
| aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
& ( sbrdtbr0(W1) = xk ) )
| aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk)) ) )
=> ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) )
<=> ( ~ aElementOf0(W0,szNzAzT0)
| ! [W1: $i] :
( ~ ( aSet0(W1)
& ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
| ( ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )
& ( sbrdtbr0(W1) = xk ) ) ) )
| ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(40,plain,
( ! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> ! [W1: $i] :
( ( aSet0(W1)
& ( ( ( ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
| aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
& ( sbrdtbr0(W1) = xk ) )
| aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk)) ) )
=> ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ! [W1: $i] :
( ~ ( aSet0(W1)
& ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
| ( ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )
& ( sbrdtbr0(W1) = xk ) ) ) )
| ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,axiom,
( aFunction0(xd)
& ( szDzozmdt0(xd) = szNzAzT0 )
& ! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> ! [W1: $i] :
( ( aSet0(W1)
& ( ( ( ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
| aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
& ( sbrdtbr0(W1) = xk ) )
| 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(42,plain,
! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> ! [W1: $i] :
( ( aSet0(W1)
& ( ( ( ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
| aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
& ( sbrdtbr0(W1) = xk ) )
| aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk)) ) )
=> ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) ),
inference(and_elim,[status(thm)],[41]) ).
tff(43,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ! [W1: $i] :
( ~ ( aSet0(W1)
& ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
| ( ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )
& ( sbrdtbr0(W1) = xk ) ) ) )
| ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) ),
inference(modus_ponens,[status(thm)],[42,40]) ).
tff(44,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ! [W1: $i] :
( ~ ( aSet0(W1)
& ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
| ( ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )
& ( sbrdtbr0(W1) = xk ) ) ) )
| ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) ),
inference(modus_ponens,[status(thm)],[43,38]) ).
tff(45,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ! [W1: $i] :
( ~ aSet0(W1)
| ( ~ aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
& ( ( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ~ ( ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
| aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )
| ( sbrdtbr0(W1) != xk ) ) )
| ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) ),
inference(skolemize,[status(sab)],[44]) ).
tff(46,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ! [W1: $i] :
( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
| ~ aSet0(W1)
| ( ~ aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
& ( ( sbrdtbr0(W1) != xk )
| ( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ~ ( ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
| aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[45,37]) ).
tff(47,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ! [W1: $i] :
( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
| ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
| ~ ( ( sbrdtbr0(W1) != xk )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
| aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[46,35]) ).
tff(48,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ! [W1: $i] :
( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
| ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
| ~ ( ( sbrdtbr0(W1) != xk )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
| aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[47,33]) ).
tff(49,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ! [W1: $i] :
( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
| ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
| ~ ( ( sbrdtbr0(W1) != xk )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
| aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) )
| ~ aElementOf0(xn,szNzAzT0)
| ! [W1: $i] :
( ~ aSet0(W1)
| ( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) )
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
| ~ ( ( sbrdtbr0(W1) != xk )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W2_39(W1,xn),W1)
| aElementOf0(tptp_fun_W2_39(W1,xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ! [W1: $i] :
( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
| ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
| ~ ( ( sbrdtbr0(W1) != xk )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
| aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) )
| ~ aElementOf0(xn,szNzAzT0)
| ! [W1: $i] :
( ~ aSet0(W1)
| ( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) )
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
| ~ ( ( sbrdtbr0(W1) != xk )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W2_39(W1,xn),W1)
| aElementOf0(tptp_fun_W2_39(W1,xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(50,plain,
( ( ~ aElementOf0(xn,szNzAzT0)
| ! [W1: $i] :
( ( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) )
| ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
| ~ ( ( sbrdtbr0(W1) != xk )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W2_39(W1,xn),W1)
| aElementOf0(tptp_fun_W2_39(W1,xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) ) )
<=> ( ~ aElementOf0(xn,szNzAzT0)
| ! [W1: $i] :
( ~ aSet0(W1)
| ( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) )
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
| ~ ( ( sbrdtbr0(W1) != xk )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W2_39(W1,xn),W1)
| aElementOf0(tptp_fun_W2_39(W1,xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(51,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ! [W1: $i] :
( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
| ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
| ~ ( ( sbrdtbr0(W1) != xk )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
| aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) )
| ~ aElementOf0(xn,szNzAzT0)
| ! [W1: $i] :
( ( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) )
| ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
| ~ ( ( sbrdtbr0(W1) != xk )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W2_39(W1,xn),W1)
| aElementOf0(tptp_fun_W2_39(W1,xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ! [W1: $i] :
( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
| ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
| ~ ( ( sbrdtbr0(W1) != xk )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
| aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) )
| ~ aElementOf0(xn,szNzAzT0)
| ! [W1: $i] :
( ~ aSet0(W1)
| ( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) )
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
| ~ ( ( sbrdtbr0(W1) != xk )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W2_39(W1,xn),W1)
| aElementOf0(tptp_fun_W2_39(W1,xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[50]) ).
tff(52,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ! [W1: $i] :
( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
| ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
| ~ ( ( sbrdtbr0(W1) != xk )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
| aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) )
| ~ aElementOf0(xn,szNzAzT0)
| ! [W1: $i] :
( ( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) )
| ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
| ~ ( ( sbrdtbr0(W1) != xk )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W2_39(W1,xn),W1)
| aElementOf0(tptp_fun_W2_39(W1,xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ! [W1: $i] :
( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
| ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
| ~ ( ( sbrdtbr0(W1) != xk )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
| aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) )
| ~ aElementOf0(xn,szNzAzT0)
| ! [W1: $i] :
( ~ aSet0(W1)
| ( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) )
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
| ~ ( ( sbrdtbr0(W1) != xk )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W2_39(W1,xn),W1)
| aElementOf0(tptp_fun_W2_39(W1,xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[51,49]) ).
tff(53,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ! [W1: $i] :
( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
| ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
| ~ ( ( sbrdtbr0(W1) != xk )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
| aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) )
| ~ aElementOf0(xn,szNzAzT0)
| ! [W1: $i] :
( ( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) )
| ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
| ~ ( ( sbrdtbr0(W1) != xk )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W2_39(W1,xn),W1)
| aElementOf0(tptp_fun_W2_39(W1,xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(54,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ! [W1: $i] :
( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
| ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
| ~ ( ( sbrdtbr0(W1) != xk )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
| aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) )
| ~ aElementOf0(xn,szNzAzT0)
| ! [W1: $i] :
( ~ aSet0(W1)
| ( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) )
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
| ~ ( ( sbrdtbr0(W1) != xk )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W2_39(W1,xn),W1)
| aElementOf0(tptp_fun_W2_39(W1,xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
! [W1: $i] :
( ~ aSet0(W1)
| ( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) )
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
| ~ ( ( sbrdtbr0(W1) != xk )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W2_39(W1,xn),W1)
| aElementOf0(tptp_fun_W2_39(W1,xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) ),
inference(unit_resolution,[status(thm)],[54,48,28]) ).
tff(56,plain,
( aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
<=> aSet0(xP) ),
inference(monotonicity,[status(thm)],[5]) ).
tff(57,plain,
( aSet0(xP)
<=> aSet0(sdtmndt0(xQ,szmzizndt0(xQ))) ),
inference(symmetry,[status(thm)],[56]) ).
tff(58,plain,
( aSet0(xP)
<=> aSet0(xP) ),
inference(rewrite,[status(thm)],[]) ).
tff(59,plain,
( aSet0(xP)
& ! [W0: $i] :
( aElementOf0(W0,xQ)
=> sdtlseqdt0(szmzizndt0(xQ),W0) )
& ! [W0: $i] :
( aElementOf0(W0,xP)
<=> ( aElement0(W0)
& aElementOf0(W0,xQ)
& ( W0 != szmzizndt0(xQ) ) ) ) ),
inference(and_elim,[status(thm)],[2]) ).
tff(60,plain,
( aSet0(xP)
& ! [W0: $i] :
( aElementOf0(W0,xQ)
=> sdtlseqdt0(szmzizndt0(xQ),W0) ) ),
inference(and_elim,[status(thm)],[59]) ).
tff(61,plain,
aSet0(xP),
inference(and_elim,[status(thm)],[60]) ).
tff(62,plain,
aSet0(xP),
inference(modus_ponens,[status(thm)],[61,58]) ).
tff(63,plain,
aSet0(sdtmndt0(xQ,szmzizndt0(xQ))),
inference(modus_ponens,[status(thm)],[62,57]) ).
tff(64,plain,
( ( ~ ! [W1: $i] :
( ~ aSet0(W1)
| ( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) )
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
| ~ ( ( sbrdtbr0(W1) != xk )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W2_39(W1,xn),W1)
| aElementOf0(tptp_fun_W2_39(W1,xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) )
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
| ~ ( ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != xk )
| ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) )
<=> ( ~ ! [W1: $i] :
( ~ aSet0(W1)
| ( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) )
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
| ~ ( ( sbrdtbr0(W1) != xk )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W2_39(W1,xn),W1)
| aElementOf0(tptp_fun_W2_39(W1,xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) )
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
| ~ ( ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != xk )
| ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(65,plain,
( ~ ! [W1: $i] :
( ~ aSet0(W1)
| ( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) )
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
| ~ ( ( sbrdtbr0(W1) != xk )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W2_39(W1,xn),W1)
| aElementOf0(tptp_fun_W2_39(W1,xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) )
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
| ~ ( ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != xk )
| ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(66,plain,
( ~ ! [W1: $i] :
( ~ aSet0(W1)
| ( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) )
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
| ~ ( ( sbrdtbr0(W1) != xk )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W2_39(W1,xn),W1)
| aElementOf0(tptp_fun_W2_39(W1,xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) )
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
| ~ ( ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != xk )
| ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) ),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))),
inference(unit_resolution,[status(thm)],[66,63,55,23]) ).
tff(68,plain,
sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) = sdtlpdtrp0(xd,xn),
inference(symmetry,[status(thm)],[67]) ).
tff(69,plain,
sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))),
inference(monotonicity,[status(thm)],[4]) ).
tff(70,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(71,axiom,
( ! [W0: $i] :
( aElementOf0(W0,sdtlpdtrp0(xN,xn))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W0) )
& aSet0(sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
& ! [W0: $i] :
( aElementOf0(W0,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ( aElement0(W0)
& ( aElementOf0(W0,xP)
| ( W0 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) ) )
& ( sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5632) ).
tff(72,plain,
sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP),
inference(and_elim,[status(thm)],[71]) ).
tff(73,plain,
sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP),
inference(modus_ponens,[status(thm)],[72,70]) ).
tff(74,plain,
( ( xp = szmzizndt0(xQ) )
<=> ( xp = szmzizndt0(xQ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(75,axiom,
( aElementOf0(xp,xQ)
& ! [W0: $i] :
( aElementOf0(W0,xQ)
=> sdtlseqdt0(xp,W0) )
& ( xp = szmzizndt0(xQ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5147) ).
tff(76,plain,
xp = szmzizndt0(xQ),
inference(and_elim,[status(thm)],[75]) ).
tff(77,plain,
xp = szmzizndt0(xQ),
inference(modus_ponens,[status(thm)],[76,74]) ).
tff(78,plain,
( ( sdtlpdtrp0(xe,xn) = xp )
<=> ( sdtlpdtrp0(xe,xn) = xp ) ),
inference(rewrite,[status(thm)],[]) ).
tff(79,plain,
sdtlpdtrp0(xe,xn) = xp,
inference(and_elim,[status(thm)],[25]) ).
tff(80,plain,
sdtlpdtrp0(xe,xn) = xp,
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
^ [W0: $i] :
refl(( ( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) )
<=> ( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(82,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) ) ),
inference(quant_intro,[status(thm)],[81]) ).
tff(83,plain,
^ [W0: $i] :
rewrite(( ( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) )
<=> ( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(84,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) ) ),
inference(quant_intro,[status(thm)],[83]) ).
tff(85,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) ) ),
inference(transitivity,[status(thm)],[84,82]) ).
tff(86,plain,
^ [W0: $i] :
rewrite(( ( ~ aElementOf0(W0,szNzAzT0)
| ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
<=> ( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(87,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) ) ),
inference(quant_intro,[status(thm)],[86]) ).
tff(88,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(89,plain,
^ [W0: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) )
<=> ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) )),
( ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )),
rewrite(( ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )),
( ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )),
( ( aElementOf0(W0,szNzAzT0)
=> ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
<=> ( aElementOf0(W0,szNzAzT0)
=> ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )),
rewrite(( ( aElementOf0(W0,szNzAzT0)
=> ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
<=> ( ~ aElementOf0(W0,szNzAzT0)
| ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )),
( ( aElementOf0(W0,szNzAzT0)
=> ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
<=> ( ~ aElementOf0(W0,szNzAzT0)
| ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(90,plain,
( ! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ),
inference(quant_intro,[status(thm)],[89]) ).
tff(91,axiom,
( aFunction0(xe)
& ( szDzozmdt0(xe) = szNzAzT0 )
& ! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4660) ).
tff(92,plain,
! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ),
inference(and_elim,[status(thm)],[91]) ).
tff(93,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ),
inference(modus_ponens,[status(thm)],[92,90]) ).
tff(94,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ),
inference(modus_ponens,[status(thm)],[93,88]) ).
tff(95,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ),
inference(skolemize,[status(sab)],[94]) ).
tff(96,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) ),
inference(modus_ponens,[status(thm)],[95,87]) ).
tff(97,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) ),
inference(modus_ponens,[status(thm)],[96,85]) ).
tff(98,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) )
| ~ aElementOf0(xn,szNzAzT0)
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(sdtlpdtrp0(xe,xn),W1) )
| ~ aElementOf0(sdtlpdtrp0(xe,xn),sdtlpdtrp0(xN,xn))
| ( sdtlpdtrp0(xe,xn) != szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) )
| ~ aElementOf0(xn,szNzAzT0)
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(sdtlpdtrp0(xe,xn),W1) )
| ~ aElementOf0(sdtlpdtrp0(xe,xn),sdtlpdtrp0(xN,xn))
| ( sdtlpdtrp0(xe,xn) != szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(99,plain,
( ( ~ aElementOf0(xn,szNzAzT0)
| ~ ( ( sdtlpdtrp0(xe,xn) != szmzizndt0(sdtlpdtrp0(xN,xn)) )
| ~ aElementOf0(sdtlpdtrp0(xe,xn),sdtlpdtrp0(xN,xn))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(sdtlpdtrp0(xe,xn),W1) ) ) )
<=> ( ~ aElementOf0(xn,szNzAzT0)
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(sdtlpdtrp0(xe,xn),W1) )
| ~ aElementOf0(sdtlpdtrp0(xe,xn),sdtlpdtrp0(xN,xn))
| ( sdtlpdtrp0(xe,xn) != szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(100,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) )
| ~ aElementOf0(xn,szNzAzT0)
| ~ ( ( sdtlpdtrp0(xe,xn) != szmzizndt0(sdtlpdtrp0(xN,xn)) )
| ~ aElementOf0(sdtlpdtrp0(xe,xn),sdtlpdtrp0(xN,xn))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(sdtlpdtrp0(xe,xn),W1) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) )
| ~ aElementOf0(xn,szNzAzT0)
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(sdtlpdtrp0(xe,xn),W1) )
| ~ aElementOf0(sdtlpdtrp0(xe,xn),sdtlpdtrp0(xN,xn))
| ( sdtlpdtrp0(xe,xn) != szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) ) ),
inference(monotonicity,[status(thm)],[99]) ).
tff(101,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) )
| ~ aElementOf0(xn,szNzAzT0)
| ~ ( ( sdtlpdtrp0(xe,xn) != szmzizndt0(sdtlpdtrp0(xN,xn)) )
| ~ aElementOf0(sdtlpdtrp0(xe,xn),sdtlpdtrp0(xN,xn))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(sdtlpdtrp0(xe,xn),W1) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) )
| ~ aElementOf0(xn,szNzAzT0)
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(sdtlpdtrp0(xe,xn),W1) )
| ~ aElementOf0(sdtlpdtrp0(xe,xn),sdtlpdtrp0(xN,xn))
| ( sdtlpdtrp0(xe,xn) != szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) ) ),
inference(transitivity,[status(thm)],[100,98]) ).
tff(102,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) )
| ~ aElementOf0(xn,szNzAzT0)
| ~ ( ( sdtlpdtrp0(xe,xn) != szmzizndt0(sdtlpdtrp0(xN,xn)) )
| ~ aElementOf0(sdtlpdtrp0(xe,xn),sdtlpdtrp0(xN,xn))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(sdtlpdtrp0(xe,xn),W1) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(103,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) )
| ~ aElementOf0(xn,szNzAzT0)
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(sdtlpdtrp0(xe,xn),W1) )
| ~ aElementOf0(sdtlpdtrp0(xe,xn),sdtlpdtrp0(xN,xn))
| ( sdtlpdtrp0(xe,xn) != szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) ),
inference(modus_ponens,[status(thm)],[102,101]) ).
tff(104,plain,
~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(sdtlpdtrp0(xe,xn),W1) )
| ~ aElementOf0(sdtlpdtrp0(xe,xn),sdtlpdtrp0(xN,xn))
| ( sdtlpdtrp0(xe,xn) != szmzizndt0(sdtlpdtrp0(xN,xn)) ) ),
inference(unit_resolution,[status(thm)],[103,97,28]) ).
tff(105,plain,
( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(sdtlpdtrp0(xe,xn),W1) )
| ~ aElementOf0(sdtlpdtrp0(xe,xn),sdtlpdtrp0(xN,xn))
| ( sdtlpdtrp0(xe,xn) != szmzizndt0(sdtlpdtrp0(xN,xn)) )
| ( sdtlpdtrp0(xe,xn) = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(106,plain,
sdtlpdtrp0(xe,xn) = szmzizndt0(sdtlpdtrp0(xN,xn)),
inference(unit_resolution,[status(thm)],[105,104]) ).
tff(107,plain,
szmzizndt0(sdtlpdtrp0(xN,xn)) = sdtlpdtrp0(xe,xn),
inference(symmetry,[status(thm)],[106]) ).
tff(108,plain,
szmzizndt0(sdtlpdtrp0(xN,xn)) = szmzizndt0(xQ),
inference(transitivity,[status(thm)],[107,80,77]) ).
tff(109,plain,
sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))) = sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(xQ)),
inference(monotonicity,[status(thm)],[4,108]) ).
tff(110,plain,
sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(xQ)) = sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))),
inference(symmetry,[status(thm)],[109]) ).
tff(111,plain,
szmzizndt0(xQ) = xp,
inference(symmetry,[status(thm)],[77]) ).
tff(112,plain,
( aElementOf0(szmzizndt0(xQ),xQ)
<=> aElementOf0(xp,xQ) ),
inference(monotonicity,[status(thm)],[111]) ).
tff(113,plain,
( aElementOf0(xp,xQ)
<=> aElementOf0(szmzizndt0(xQ),xQ) ),
inference(symmetry,[status(thm)],[112]) ).
tff(114,plain,
( aElementOf0(xp,xQ)
<=> aElementOf0(xp,xQ) ),
inference(rewrite,[status(thm)],[]) ).
tff(115,plain,
( aElementOf0(xp,xQ)
& ! [W0: $i] :
( aElementOf0(W0,xQ)
=> sdtlseqdt0(xp,W0) ) ),
inference(and_elim,[status(thm)],[75]) ).
tff(116,plain,
aElementOf0(xp,xQ),
inference(and_elim,[status(thm)],[115]) ).
tff(117,plain,
aElementOf0(xp,xQ),
inference(modus_ponens,[status(thm)],[116,114]) ).
tff(118,plain,
aElementOf0(szmzizndt0(xQ),xQ),
inference(modus_ponens,[status(thm)],[117,113]) ).
tff(119,plain,
( aSet0(xQ)
<=> aSet0(xQ) ),
inference(rewrite,[status(thm)],[]) ).
tff(120,axiom,
( aSet0(xQ)
& ! [W0: $i] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,xO) )
& aSubsetOf0(xQ,xO)
& ( sbrdtbr0(xQ) = xK )
& aElementOf0(xQ,slbdtsldtrb0(xO,xK)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5078) ).
tff(121,plain,
( aSet0(xQ)
& ! [W0: $i] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,xO) )
& aSubsetOf0(xQ,xO)
& ( sbrdtbr0(xQ) = xK ) ),
inference(and_elim,[status(thm)],[120]) ).
tff(122,plain,
( aSet0(xQ)
& ! [W0: $i] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,xO) )
& aSubsetOf0(xQ,xO) ),
inference(and_elim,[status(thm)],[121]) ).
tff(123,plain,
( aSet0(xQ)
& ! [W0: $i] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,xO) ) ),
inference(and_elim,[status(thm)],[122]) ).
tff(124,plain,
aSet0(xQ),
inference(and_elim,[status(thm)],[123]) ).
tff(125,plain,
aSet0(xQ),
inference(modus_ponens,[status(thm)],[124,119]) ).
tff(126,plain,
^ [W0: $i] :
refl(( ( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(127,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ) ),
inference(quant_intro,[status(thm)],[126]) ).
tff(128,plain,
^ [W0: $i] :
rewrite(( ( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(129,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ) ),
inference(quant_intro,[status(thm)],[128]) ).
tff(130,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ) ),
inference(transitivity,[status(thm)],[129,127]) ).
tff(131,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(132,plain,
^ [W0: $i] :
trans(monotonicity(quant_intro(proof_bind(^ [W1: $i] :
rewrite(( ( aElementOf0(W1,W0)
=> ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) )
<=> ( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ))),
( ! [W1: $i] :
( aElementOf0(W1,W0)
=> ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) )
<=> ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) )),
( ( aSet0(W0)
=> ! [W1: $i] :
( aElementOf0(W1,W0)
=> ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) )
<=> ( aSet0(W0)
=> ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ) )),
rewrite(( ( aSet0(W0)
=> ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ) )),
( ( aSet0(W0)
=> ! [W1: $i] :
( aElementOf0(W1,W0)
=> ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(133,plain,
( ! [W0: $i] :
( aSet0(W0)
=> ! [W1: $i] :
( aElementOf0(W1,W0)
=> ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ) ),
inference(quant_intro,[status(thm)],[132]) ).
tff(134,axiom,
! [W0: $i] :
( aSet0(W0)
=> ! [W1: $i] :
( aElementOf0(W1,W0)
=> ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mConsDiff) ).
tff(135,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ),
inference(modus_ponens,[status(thm)],[134,133]) ).
tff(136,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ),
inference(modus_ponens,[status(thm)],[135,131]) ).
tff(137,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ),
inference(skolemize,[status(sab)],[136]) ).
tff(138,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ),
inference(modus_ponens,[status(thm)],[137,130]) ).
tff(139,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) )
| ~ aSet0(xQ)
| ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| ( sdtpldt0(sdtmndt0(xQ,W1),W1) = xQ ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) )
| ~ aSet0(xQ)
| ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| ( sdtpldt0(sdtmndt0(xQ,W1),W1) = xQ ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(140,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) )
| ~ aSet0(xQ)
| ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| ( sdtpldt0(sdtmndt0(xQ,W1),W1) = xQ ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(141,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) )
| ~ aSet0(xQ)
| ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| ( sdtpldt0(sdtmndt0(xQ,W1),W1) = xQ ) ) ),
inference(modus_ponens,[status(thm)],[140,139]) ).
tff(142,plain,
! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| ( sdtpldt0(sdtmndt0(xQ,W1),W1) = xQ ) ),
inference(unit_resolution,[status(thm)],[141,138,125]) ).
tff(143,plain,
( ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| ( sdtpldt0(sdtmndt0(xQ,W1),W1) = xQ ) )
| ~ aElementOf0(szmzizndt0(xQ),xQ)
| ( sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(xQ)) = xQ ) )
<=> ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| ( sdtpldt0(sdtmndt0(xQ,W1),W1) = xQ ) )
| ~ aElementOf0(szmzizndt0(xQ),xQ)
| ( sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(xQ)) = xQ ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(144,plain,
( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| ( sdtpldt0(sdtmndt0(xQ,W1),W1) = xQ ) )
| ~ aElementOf0(szmzizndt0(xQ),xQ)
| ( sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(xQ)) = xQ ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(145,plain,
( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| ( sdtpldt0(sdtmndt0(xQ,W1),W1) = xQ ) )
| ~ aElementOf0(szmzizndt0(xQ),xQ)
| ( sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(xQ)) = xQ ) ),
inference(modus_ponens,[status(thm)],[144,143]) ).
tff(146,plain,
sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(xQ)) = xQ,
inference(unit_resolution,[status(thm)],[145,142,118]) ).
tff(147,plain,
xQ = sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(xQ)),
inference(symmetry,[status(thm)],[146]) ).
tff(148,plain,
xQ = sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))),
inference(transitivity,[status(thm)],[147,110]) ).
tff(149,plain,
sdtlpdtrp0(xc,xQ) = sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))),
inference(monotonicity,[status(thm)],[148]) ).
tff(150,plain,
sdtlpdtrp0(xc,xQ) = sdtlpdtrp0(xd,xn),
inference(transitivity,[status(thm)],[149,73,69,68]) ).
tff(151,plain,
( ( sdtlpdtrp0(xc,xQ) != sdtlpdtrp0(xd,xn) )
<=> ( sdtlpdtrp0(xc,xQ) != sdtlpdtrp0(xd,xn) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(152,axiom,
sdtlpdtrp0(xc,xQ) != sdtlpdtrp0(xd,xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(153,plain,
sdtlpdtrp0(xc,xQ) != sdtlpdtrp0(xd,xn),
inference(modus_ponens,[status(thm)],[152,151]) ).
tff(154,plain,
$false,
inference(unit_resolution,[status(thm)],[153,150]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : NUM631+3 : TPTP v9.0.0. Released v4.0.0.
% 0.08/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 01:37:11 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.73/0.91 % SZS status Theorem
% 0.73/0.91 % SZS output start Proof
% See solution above
% 0.78/0.94 % E exiting
%------------------------------------------------------------------------------