%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM611+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:21:35 AM UTC 2025
% Result : Theorem 21.79s 21.96s
% Output : Proof 21.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 91
% Syntax : Number of formulae : 258 ( 77 unt; 0 typ; 0 def)
% Number of atoms : 1621 ( 473 equ)
% Maximal formula atoms : 16 ( 6 avg)
% Number of connectives : 2308 (1035 ~; 894 |; 136 &)
% ( 188 <=>; 55 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of FOOLs : 90 ( 90 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 9 con; 0-2 aty)
% Number of variables : 399 ( 351 !; 21 ?; 399 :)
% Comments :
%------------------------------------------------------------------------------
tff(szszuzczcdt0_type,type,
szszuzczcdt0: $i > $i ).
tff(sbrdtbr0_type,type,
sbrdtbr0: $i > $i ).
tff(xP_type,type,
xP: $i ).
tff(tptp_fun_W1_4_type,type,
tptp_fun_W1_4: $i > $i ).
tff(xK_type,type,
xK: $i ).
tff(sdtmndt0_type,type,
sdtmndt0: ( $i * $i ) > $i ).
tff(tptp_fun_W1_0_type,type,
tptp_fun_W1_0: $i > $i ).
tff(xQ_type,type,
xQ: $i ).
tff(isFinite0_type,type,
isFinite0: $i > $o ).
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(szNzAzT0_type,type,
szNzAzT0: $i ).
tff(aSet0_type,type,
aSet0: $i > $o ).
tff(xO_type,type,
xO: $i ).
tff(aSubsetOf0_type,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff(slbdtsldtrb0_type,type,
slbdtsldtrb0: ( $i * $i ) > $i ).
tff(slcrc0_type,type,
slcrc0: $i ).
tff(sz00_type,type,
sz00: $i ).
tff(szmzizndt0_type,type,
szmzizndt0: $i > $i ).
tff(xp_type,type,
xp: $i ).
tff(sdtlseqdt0_type,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(aElement0_type,type,
aElement0: $i > $o ).
tff(xk_type,type,
xk: $i ).
tff(1,plain,
( ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,tptp_fun_W1_0(xQ)))) = szszuzczcdt0(sbrdtbr0(xP)) )
<=> ( szszuzczcdt0(sbrdtbr0(xP)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,tptp_fun_W1_0(xQ)))) ) ),
inference(commutativity,[status(thm)],[]) ).
tff(2,plain,
( aSet0(xQ)
<=> aSet0(xQ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3,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/sandbox/benchmark/theBenchmark.p',m__5078) ).
tff(4,plain,
( aSet0(xQ)
& ! [W0: $i] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,xO) )
& aSubsetOf0(xQ,xO)
& ( sbrdtbr0(xQ) = xK ) ),
inference(and_elim,[status(thm)],[3]) ).
tff(5,plain,
( aSet0(xQ)
& ! [W0: $i] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,xO) )
& aSubsetOf0(xQ,xO) ),
inference(and_elim,[status(thm)],[4]) ).
tff(6,plain,
( aSet0(xQ)
& ! [W0: $i] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,xO) ) ),
inference(and_elim,[status(thm)],[5]) ).
tff(7,plain,
aSet0(xQ),
inference(and_elim,[status(thm)],[6]) ).
tff(8,plain,
aSet0(xQ),
inference(modus_ponens,[status(thm)],[7,2]) ).
tff(9,plain,
^ [W0: $i] :
refl(( ( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) )
<=> ( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(10,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) ) ),
inference(quant_intro,[status(thm)],[9]) ).
tff(11,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
^ [W0: $i] :
rewrite(( ( aSet0(W0)
=> ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) )
<=> ( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(13,plain,
( ! [W0: $i] :
( aSet0(W0)
=> ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) ) ),
inference(quant_intro,[status(thm)],[12]) ).
tff(14,axiom,
! [W0: $i] :
( aSet0(W0)
=> ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCardNum) ).
tff(15,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) ),
inference(skolemize,[status(sab)],[16]) ).
tff(18,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) ),
inference(modus_ponens,[status(thm)],[17,10]) ).
tff(19,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) )
| ~ aSet0(xQ)
| ( aElementOf0(sbrdtbr0(xQ),szNzAzT0)
<=> isFinite0(xQ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) )
| ~ aSet0(xQ)
| ( aElementOf0(sbrdtbr0(xQ),szNzAzT0)
<=> isFinite0(xQ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) )
| ~ aSet0(xQ)
| ( aElementOf0(sbrdtbr0(xQ),szNzAzT0)
<=> isFinite0(xQ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(21,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) )
| ~ aSet0(xQ)
| ( aElementOf0(sbrdtbr0(xQ),szNzAzT0)
<=> isFinite0(xQ) ) ),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
( aElementOf0(sbrdtbr0(xQ),szNzAzT0)
<=> isFinite0(xQ) ),
inference(unit_resolution,[status(thm)],[21,18,8]) ).
tff(23,plain,
( ( sbrdtbr0(xQ) = xK )
<=> ( sbrdtbr0(xQ) = xK ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,plain,
sbrdtbr0(xQ) = xK,
inference(and_elim,[status(thm)],[4]) ).
tff(25,plain,
sbrdtbr0(xQ) = xK,
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
( aElementOf0(sbrdtbr0(xQ),szNzAzT0)
<=> aElementOf0(xK,szNzAzT0) ),
inference(monotonicity,[status(thm)],[25]) ).
tff(27,plain,
( aElementOf0(xK,szNzAzT0)
<=> aElementOf0(sbrdtbr0(xQ),szNzAzT0) ),
inference(symmetry,[status(thm)],[26]) ).
tff(28,plain,
( aElementOf0(xK,szNzAzT0)
<=> aElementOf0(xK,szNzAzT0) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,axiom,
aElementOf0(xK,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3418) ).
tff(30,plain,
aElementOf0(xK,szNzAzT0),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
aElementOf0(sbrdtbr0(xQ),szNzAzT0),
inference(modus_ponens,[status(thm)],[30,27]) ).
tff(32,plain,
( ~ ( aElementOf0(sbrdtbr0(xQ),szNzAzT0)
<=> isFinite0(xQ) )
| ~ aElementOf0(sbrdtbr0(xQ),szNzAzT0)
| isFinite0(xQ) ),
inference(tautology,[status(thm)],[]) ).
tff(33,plain,
isFinite0(xQ),
inference(unit_resolution,[status(thm)],[32,31,22]) ).
tff(34,plain,
^ [W0: $i] :
rewrite(( ~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ~ ( ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) )
| ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(35,plain,
( ! [W0: $i] :
~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ! [W0: $i] :
~ ( ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) )
| ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[34]) ).
tff(36,plain,
^ [W0: $i] :
refl(( ~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(37,plain,
( ! [W0: $i] :
~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ! [W0: $i] :
~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,plain,
^ [W0: $i] :
rewrite(( ~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(39,plain,
( ! [W0: $i] :
~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ! [W0: $i] :
~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) ),
inference(quant_intro,[status(thm)],[38]) ).
tff(40,plain,
( ! [W0: $i] :
~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ! [W0: $i] :
~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) ),
inference(transitivity,[status(thm)],[39,37]) ).
tff(41,plain,
^ [W0: $i] :
trans(monotonicity(rewrite(( ( ( W0 != slcrc0 )
| ( aSet0(W0)
& ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
<=> ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) ) )),
rewrite(( ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) )
<=> ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )),
( ( ( ( W0 != slcrc0 )
| ( aSet0(W0)
& ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ( ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) )),
rewrite(( ( ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) )),
( ( ( ( W0 != slcrc0 )
| ( aSet0(W0)
& ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(42,plain,
( ! [W0: $i] :
( ( ( W0 != slcrc0 )
| ( aSet0(W0)
& ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ! [W0: $i] :
~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) ),
inference(quant_intro,[status(thm)],[41]) ).
tff(43,plain,
^ [W0: $i] :
rewrite(( ( ( ( W0 != slcrc0 )
| ( aSet0(W0)
& ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ( ( ( W0 != slcrc0 )
| ( aSet0(W0)
& ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(44,plain,
( ! [W0: $i] :
( ( ( W0 != slcrc0 )
| ( aSet0(W0)
& ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ! [W0: $i] :
( ( ( W0 != slcrc0 )
| ( aSet0(W0)
& ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) ),
inference(quant_intro,[status(thm)],[43]) ).
tff(45,plain,
( ! [W0: $i] :
( ( W0 = slcrc0 )
<=> ( aSet0(W0)
& ~ ? [W1: $i] : aElementOf0(W1,W0) ) )
<=> ! [W0: $i] :
( ( W0 = slcrc0 )
<=> ( aSet0(W0)
& ~ ? [W1: $i] : aElementOf0(W1,W0) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(46,axiom,
! [W0: $i] :
( ( W0 = slcrc0 )
<=> ( aSet0(W0)
& ~ ? [W1: $i] : aElementOf0(W1,W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefEmp) ).
tff(47,plain,
! [W0: $i] :
( ( W0 = slcrc0 )
<=> ( aSet0(W0)
& ~ ? [W1: $i] : aElementOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
! [W0: $i] :
( ( ( W0 != slcrc0 )
| ( aSet0(W0)
& ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ),
inference(skolemize,[status(sab)],[47]) ).
tff(49,plain,
! [W0: $i] :
( ( ( W0 != slcrc0 )
| ( aSet0(W0)
& ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ),
inference(modus_ponens,[status(thm)],[48,44]) ).
tff(50,plain,
! [W0: $i] :
~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ),
inference(modus_ponens,[status(thm)],[49,42]) ).
tff(51,plain,
! [W0: $i] :
~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ),
inference(modus_ponens,[status(thm)],[50,40]) ).
tff(52,plain,
! [W0: $i] :
~ ( ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) )
| ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) ) ),
inference(modus_ponens,[status(thm)],[51,35]) ).
tff(53,plain,
( ~ ! [W0: $i] :
~ ( ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) )
| ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) ) )
| ~ ( ~ ( ( xQ = slcrc0 )
| ~ aSet0(xQ)
| aElementOf0(tptp_fun_W1_0(xQ),xQ) )
| ~ ( ( xQ != slcrc0 )
| ~ ( ~ aSet0(xQ)
| ~ ! [W1: $i] : ~ aElementOf0(W1,xQ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(54,plain,
~ ( ~ ( ( xQ = slcrc0 )
| ~ aSet0(xQ)
| aElementOf0(tptp_fun_W1_0(xQ),xQ) )
| ~ ( ( xQ != slcrc0 )
| ~ ( ~ aSet0(xQ)
| ~ ! [W1: $i] : ~ aElementOf0(W1,xQ) ) ) ),
inference(unit_resolution,[status(thm)],[53,52]) ).
tff(55,plain,
( ~ ( ( xQ = slcrc0 )
| ~ aSet0(xQ)
| aElementOf0(tptp_fun_W1_0(xQ),xQ) )
| ~ ( ( xQ != slcrc0 )
| ~ ( ~ aSet0(xQ)
| ~ ! [W1: $i] : ~ aElementOf0(W1,xQ) ) )
| ( xQ = slcrc0 )
| ~ aSet0(xQ)
| aElementOf0(tptp_fun_W1_0(xQ),xQ) ),
inference(tautology,[status(thm)],[]) ).
tff(56,plain,
( ( xQ = slcrc0 )
| ~ aSet0(xQ)
| aElementOf0(tptp_fun_W1_0(xQ),xQ) ),
inference(unit_resolution,[status(thm)],[55,54]) ).
tff(57,plain,
( ( xQ != slcrc0 )
<=> ( xQ != slcrc0 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(58,axiom,
( ! [W0: $i] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,xO) )
& ~ ( ~ ? [W0: $i] : aElementOf0(W0,xQ)
| ( xQ = slcrc0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5093) ).
tff(59,plain,
~ ( ~ ? [W0: $i] : aElementOf0(W0,xQ)
| ( xQ = slcrc0 ) ),
inference(and_elim,[status(thm)],[58]) ).
tff(60,plain,
xQ != slcrc0,
inference(or_elim,[status(thm)],[59]) ).
tff(61,plain,
xQ != slcrc0,
inference(modus_ponens,[status(thm)],[60,57]) ).
tff(62,plain,
( ~ ( ( xQ = slcrc0 )
| ~ aSet0(xQ)
| aElementOf0(tptp_fun_W1_0(xQ),xQ) )
| ( xQ = slcrc0 )
| ~ aSet0(xQ)
| aElementOf0(tptp_fun_W1_0(xQ),xQ) ),
inference(tautology,[status(thm)],[]) ).
tff(63,plain,
( ~ ( ( xQ = slcrc0 )
| ~ aSet0(xQ)
| aElementOf0(tptp_fun_W1_0(xQ),xQ) )
| aElementOf0(tptp_fun_W1_0(xQ),xQ) ),
inference(unit_resolution,[status(thm)],[62,8,61]) ).
tff(64,plain,
aElementOf0(tptp_fun_W1_0(xQ),xQ),
inference(unit_resolution,[status(thm)],[63,56]) ).
tff(65,plain,
^ [W0: $i] :
refl(( ( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) )
| ~ isFinite0(W0) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) )
| ~ isFinite0(W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(66,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) )
| ~ isFinite0(W0) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) )
| ~ isFinite0(W0) ) ) ),
inference(quant_intro,[status(thm)],[65]) ).
tff(67,plain,
^ [W0: $i] :
rewrite(( ( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) )
| ~ isFinite0(W0) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) )
| ~ isFinite0(W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(68,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) )
| ~ isFinite0(W0) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) )
| ~ isFinite0(W0) ) ) ),
inference(quant_intro,[status(thm)],[67]) ).
tff(69,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) )
| ~ isFinite0(W0) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) )
| ~ isFinite0(W0) ) ) ),
inference(transitivity,[status(thm)],[68,66]) ).
tff(70,plain,
^ [W0: $i] :
rewrite(( ( ~ aSet0(W0)
| ! [W1: $i] :
( ~ ( isFinite0(W0)
& aElementOf0(W1,W0) )
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) )
| ~ isFinite0(W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(71,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ ( isFinite0(W0)
& aElementOf0(W1,W0) )
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) )
| ~ isFinite0(W0) ) ) ),
inference(quant_intro,[status(thm)],[70]) ).
tff(72,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ ( isFinite0(W0)
& aElementOf0(W1,W0) )
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ ( isFinite0(W0)
& aElementOf0(W1,W0) )
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(73,plain,
^ [W0: $i] :
trans(monotonicity(quant_intro(proof_bind(^ [W1: $i] :
rewrite(( ( ( isFinite0(W0)
& aElementOf0(W1,W0) )
=> ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) ) )
<=> ( ~ ( isFinite0(W0)
& aElementOf0(W1,W0) )
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) ) ) ))),
( ! [W1: $i] :
( ( isFinite0(W0)
& aElementOf0(W1,W0) )
=> ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) ) )
<=> ! [W1: $i] :
( ~ ( isFinite0(W0)
& aElementOf0(W1,W0) )
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) ) ) )),
( ( aSet0(W0)
=> ! [W1: $i] :
( ( isFinite0(W0)
& aElementOf0(W1,W0) )
=> ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) ) ) )
<=> ( aSet0(W0)
=> ! [W1: $i] :
( ~ ( isFinite0(W0)
& aElementOf0(W1,W0) )
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) ) ) ) )),
rewrite(( ( aSet0(W0)
=> ! [W1: $i] :
( ~ ( isFinite0(W0)
& aElementOf0(W1,W0) )
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( ~ ( isFinite0(W0)
& aElementOf0(W1,W0) )
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) ) ) ) )),
( ( aSet0(W0)
=> ! [W1: $i] :
( ( isFinite0(W0)
& aElementOf0(W1,W0) )
=> ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( ~ ( isFinite0(W0)
& aElementOf0(W1,W0) )
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(74,plain,
( ! [W0: $i] :
( aSet0(W0)
=> ! [W1: $i] :
( ( isFinite0(W0)
& aElementOf0(W1,W0) )
=> ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ ( isFinite0(W0)
& aElementOf0(W1,W0) )
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) ) ) ) ),
inference(quant_intro,[status(thm)],[73]) ).
tff(75,axiom,
! [W0: $i] :
( aSet0(W0)
=> ! [W1: $i] :
( ( isFinite0(W0)
& aElementOf0(W1,W0) )
=> ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCardDiff) ).
tff(76,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ ( isFinite0(W0)
& aElementOf0(W1,W0) )
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) ) ) ),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ ( isFinite0(W0)
& aElementOf0(W1,W0) )
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) ) ) ),
inference(modus_ponens,[status(thm)],[76,72]) ).
tff(78,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ ( isFinite0(W0)
& aElementOf0(W1,W0) )
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) ) ) ),
inference(skolemize,[status(sab)],[77]) ).
tff(79,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) )
| ~ isFinite0(W0) ) ),
inference(modus_ponens,[status(thm)],[78,71]) ).
tff(80,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) )
| ~ isFinite0(W0) ) ),
inference(modus_ponens,[status(thm)],[79,69]) ).
tff(81,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) )
| ~ isFinite0(W0) ) )
| ~ aSet0(xQ)
| ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| ~ isFinite0(xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,W1))) = sbrdtbr0(xQ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) )
| ~ isFinite0(W0) ) )
| ~ aSet0(xQ)
| ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| ~ isFinite0(xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,W1))) = sbrdtbr0(xQ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(82,plain,
( ( ~ aSet0(xQ)
| ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,W1))) = sbrdtbr0(xQ) )
| ~ isFinite0(xQ) ) )
<=> ( ~ aSet0(xQ)
| ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| ~ isFinite0(xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,W1))) = sbrdtbr0(xQ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(83,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) )
| ~ isFinite0(W0) ) )
| ~ aSet0(xQ)
| ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,W1))) = sbrdtbr0(xQ) )
| ~ isFinite0(xQ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) )
| ~ isFinite0(W0) ) )
| ~ aSet0(xQ)
| ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| ~ isFinite0(xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,W1))) = sbrdtbr0(xQ) ) ) ) ),
inference(monotonicity,[status(thm)],[82]) ).
tff(84,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) )
| ~ isFinite0(W0) ) )
| ~ aSet0(xQ)
| ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,W1))) = sbrdtbr0(xQ) )
| ~ isFinite0(xQ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) )
| ~ isFinite0(W0) ) )
| ~ aSet0(xQ)
| ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| ~ isFinite0(xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,W1))) = sbrdtbr0(xQ) ) ) ) ),
inference(transitivity,[status(thm)],[83,81]) ).
tff(85,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) )
| ~ isFinite0(W0) ) )
| ~ aSet0(xQ)
| ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,W1))) = sbrdtbr0(xQ) )
| ~ isFinite0(xQ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(86,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) )
| ~ isFinite0(W0) ) )
| ~ aSet0(xQ)
| ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| ~ isFinite0(xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,W1))) = sbrdtbr0(xQ) ) ) ),
inference(modus_ponens,[status(thm)],[85,84]) ).
tff(87,plain,
! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| ~ isFinite0(xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,W1))) = sbrdtbr0(xQ) ) ),
inference(unit_resolution,[status(thm)],[86,80,8]) ).
tff(88,plain,
( ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| ~ isFinite0(xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,W1))) = sbrdtbr0(xQ) ) )
| ~ isFinite0(xQ)
| ~ aElementOf0(tptp_fun_W1_0(xQ),xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,tptp_fun_W1_0(xQ)))) = sbrdtbr0(xQ) ) )
<=> ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| ~ isFinite0(xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,W1))) = sbrdtbr0(xQ) ) )
| ~ isFinite0(xQ)
| ~ aElementOf0(tptp_fun_W1_0(xQ),xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,tptp_fun_W1_0(xQ)))) = sbrdtbr0(xQ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(89,plain,
( ( ~ aElementOf0(tptp_fun_W1_0(xQ),xQ)
| ~ isFinite0(xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,tptp_fun_W1_0(xQ)))) = sbrdtbr0(xQ) ) )
<=> ( ~ isFinite0(xQ)
| ~ aElementOf0(tptp_fun_W1_0(xQ),xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,tptp_fun_W1_0(xQ)))) = sbrdtbr0(xQ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(90,plain,
( ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| ~ isFinite0(xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,W1))) = sbrdtbr0(xQ) ) )
| ~ aElementOf0(tptp_fun_W1_0(xQ),xQ)
| ~ isFinite0(xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,tptp_fun_W1_0(xQ)))) = sbrdtbr0(xQ) ) )
<=> ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| ~ isFinite0(xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,W1))) = sbrdtbr0(xQ) ) )
| ~ isFinite0(xQ)
| ~ aElementOf0(tptp_fun_W1_0(xQ),xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,tptp_fun_W1_0(xQ)))) = sbrdtbr0(xQ) ) ) ),
inference(monotonicity,[status(thm)],[89]) ).
tff(91,plain,
( ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| ~ isFinite0(xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,W1))) = sbrdtbr0(xQ) ) )
| ~ aElementOf0(tptp_fun_W1_0(xQ),xQ)
| ~ isFinite0(xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,tptp_fun_W1_0(xQ)))) = sbrdtbr0(xQ) ) )
<=> ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| ~ isFinite0(xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,W1))) = sbrdtbr0(xQ) ) )
| ~ isFinite0(xQ)
| ~ aElementOf0(tptp_fun_W1_0(xQ),xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,tptp_fun_W1_0(xQ)))) = sbrdtbr0(xQ) ) ) ),
inference(transitivity,[status(thm)],[90,88]) ).
tff(92,plain,
( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| ~ isFinite0(xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,W1))) = sbrdtbr0(xQ) ) )
| ~ aElementOf0(tptp_fun_W1_0(xQ),xQ)
| ~ isFinite0(xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,tptp_fun_W1_0(xQ)))) = sbrdtbr0(xQ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(93,plain,
( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| ~ isFinite0(xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,W1))) = sbrdtbr0(xQ) ) )
| ~ isFinite0(xQ)
| ~ aElementOf0(tptp_fun_W1_0(xQ),xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,tptp_fun_W1_0(xQ)))) = sbrdtbr0(xQ) ) ),
inference(modus_ponens,[status(thm)],[92,91]) ).
tff(94,plain,
( ~ isFinite0(xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,tptp_fun_W1_0(xQ)))) = sbrdtbr0(xQ) ) ),
inference(unit_resolution,[status(thm)],[93,87,64]) ).
tff(95,plain,
szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,tptp_fun_W1_0(xQ)))) = sbrdtbr0(xQ),
inference(unit_resolution,[status(thm)],[94,33]) ).
tff(96,plain,
sbrdtbr0(xQ) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,tptp_fun_W1_0(xQ)))),
inference(symmetry,[status(thm)],[95]) ).
tff(97,plain,
xK = sbrdtbr0(xQ),
inference(symmetry,[status(thm)],[25]) ).
tff(98,plain,
( ( xK != sz00 )
<=> ( xK != sz00 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(99,axiom,
xK != sz00,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3462) ).
tff(100,plain,
xK != sz00,
inference(modus_ponens,[status(thm)],[99,98]) ).
tff(101,plain,
^ [W0: $i] :
refl(( ( ( W0 = sz00 )
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aElementOf0(tptp_fun_W1_4(W0),szNzAzT0)
| ( W0 != szszuzczcdt0(tptp_fun_W1_4(W0)) ) ) )
<=> ( ( W0 = sz00 )
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aElementOf0(tptp_fun_W1_4(W0),szNzAzT0)
| ( W0 != szszuzczcdt0(tptp_fun_W1_4(W0)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(102,plain,
( ! [W0: $i] :
( ( W0 = sz00 )
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aElementOf0(tptp_fun_W1_4(W0),szNzAzT0)
| ( W0 != szszuzczcdt0(tptp_fun_W1_4(W0)) ) ) )
<=> ! [W0: $i] :
( ( W0 = sz00 )
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aElementOf0(tptp_fun_W1_4(W0),szNzAzT0)
| ( W0 != szszuzczcdt0(tptp_fun_W1_4(W0)) ) ) ) ),
inference(quant_intro,[status(thm)],[101]) ).
tff(103,plain,
^ [W0: $i] :
trans(monotonicity(rewrite(( ( aElementOf0(tptp_fun_W1_4(W0),szNzAzT0)
& ( W0 = szszuzczcdt0(tptp_fun_W1_4(W0)) ) )
<=> ~ ( ~ aElementOf0(tptp_fun_W1_4(W0),szNzAzT0)
| ( W0 != szszuzczcdt0(tptp_fun_W1_4(W0)) ) ) )),
( ( ( W0 = sz00 )
| ~ aElementOf0(W0,szNzAzT0)
| ( aElementOf0(tptp_fun_W1_4(W0),szNzAzT0)
& ( W0 = szszuzczcdt0(tptp_fun_W1_4(W0)) ) ) )
<=> ( ( W0 = sz00 )
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aElementOf0(tptp_fun_W1_4(W0),szNzAzT0)
| ( W0 != szszuzczcdt0(tptp_fun_W1_4(W0)) ) ) ) )),
rewrite(( ( ( W0 = sz00 )
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aElementOf0(tptp_fun_W1_4(W0),szNzAzT0)
| ( W0 != szszuzczcdt0(tptp_fun_W1_4(W0)) ) ) )
<=> ( ( W0 = sz00 )
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aElementOf0(tptp_fun_W1_4(W0),szNzAzT0)
| ( W0 != szszuzczcdt0(tptp_fun_W1_4(W0)) ) ) ) )),
( ( ( W0 = sz00 )
| ~ aElementOf0(W0,szNzAzT0)
| ( aElementOf0(tptp_fun_W1_4(W0),szNzAzT0)
& ( W0 = szszuzczcdt0(tptp_fun_W1_4(W0)) ) ) )
<=> ( ( W0 = sz00 )
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aElementOf0(tptp_fun_W1_4(W0),szNzAzT0)
| ( W0 != szszuzczcdt0(tptp_fun_W1_4(W0)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(104,plain,
( ! [W0: $i] :
( ( W0 = sz00 )
| ~ aElementOf0(W0,szNzAzT0)
| ( aElementOf0(tptp_fun_W1_4(W0),szNzAzT0)
& ( W0 = szszuzczcdt0(tptp_fun_W1_4(W0)) ) ) )
<=> ! [W0: $i] :
( ( W0 = sz00 )
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aElementOf0(tptp_fun_W1_4(W0),szNzAzT0)
| ( W0 != szszuzczcdt0(tptp_fun_W1_4(W0)) ) ) ) ),
inference(quant_intro,[status(thm)],[103]) ).
tff(105,plain,
^ [W0: $i] :
rewrite(( ( ( aElementOf0(tptp_fun_W1_4(W0),szNzAzT0)
& ( W0 = szszuzczcdt0(tptp_fun_W1_4(W0)) ) )
| ( W0 = sz00 )
| ~ aElementOf0(W0,szNzAzT0) )
<=> ( ( W0 = sz00 )
| ~ aElementOf0(W0,szNzAzT0)
| ( aElementOf0(tptp_fun_W1_4(W0),szNzAzT0)
& ( W0 = szszuzczcdt0(tptp_fun_W1_4(W0)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(106,plain,
( ! [W0: $i] :
( ( aElementOf0(tptp_fun_W1_4(W0),szNzAzT0)
& ( W0 = szszuzczcdt0(tptp_fun_W1_4(W0)) ) )
| ( W0 = sz00 )
| ~ aElementOf0(W0,szNzAzT0) )
<=> ! [W0: $i] :
( ( W0 = sz00 )
| ~ aElementOf0(W0,szNzAzT0)
| ( aElementOf0(tptp_fun_W1_4(W0),szNzAzT0)
& ( W0 = szszuzczcdt0(tptp_fun_W1_4(W0)) ) ) ) ),
inference(quant_intro,[status(thm)],[105]) ).
tff(107,plain,
( ! [W0: $i] :
( ? [W1: $i] :
( aElementOf0(W1,szNzAzT0)
& ( W0 = szszuzczcdt0(W1) ) )
| ( W0 = sz00 )
| ~ aElementOf0(W0,szNzAzT0) )
<=> ! [W0: $i] :
( ? [W1: $i] :
( aElementOf0(W1,szNzAzT0)
& ( W0 = szszuzczcdt0(W1) ) )
| ( W0 = sz00 )
| ~ aElementOf0(W0,szNzAzT0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(108,plain,
^ [W0: $i] :
trans(monotonicity(rewrite(( ( ( W0 = sz00 )
| ? [W1: $i] :
( aElementOf0(W1,szNzAzT0)
& ( W0 = szszuzczcdt0(W1) ) ) )
<=> ( ( W0 = sz00 )
| ? [W1: $i] :
( aElementOf0(W1,szNzAzT0)
& ( W0 = szszuzczcdt0(W1) ) ) ) )),
( ( aElementOf0(W0,szNzAzT0)
=> ( ( W0 = sz00 )
| ? [W1: $i] :
( aElementOf0(W1,szNzAzT0)
& ( W0 = szszuzczcdt0(W1) ) ) ) )
<=> ( aElementOf0(W0,szNzAzT0)
=> ( ( W0 = sz00 )
| ? [W1: $i] :
( aElementOf0(W1,szNzAzT0)
& ( W0 = szszuzczcdt0(W1) ) ) ) ) )),
rewrite(( ( aElementOf0(W0,szNzAzT0)
=> ( ( W0 = sz00 )
| ? [W1: $i] :
( aElementOf0(W1,szNzAzT0)
& ( W0 = szszuzczcdt0(W1) ) ) ) )
<=> ( ? [W1: $i] :
( aElementOf0(W1,szNzAzT0)
& ( W0 = szszuzczcdt0(W1) ) )
| ( W0 = sz00 )
| ~ aElementOf0(W0,szNzAzT0) ) )),
( ( aElementOf0(W0,szNzAzT0)
=> ( ( W0 = sz00 )
| ? [W1: $i] :
( aElementOf0(W1,szNzAzT0)
& ( W0 = szszuzczcdt0(W1) ) ) ) )
<=> ( ? [W1: $i] :
( aElementOf0(W1,szNzAzT0)
& ( W0 = szszuzczcdt0(W1) ) )
| ( W0 = sz00 )
| ~ aElementOf0(W0,szNzAzT0) ) )),
inference(bind,[status(th)],[]) ).
tff(109,plain,
( ! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> ( ( W0 = sz00 )
| ? [W1: $i] :
( aElementOf0(W1,szNzAzT0)
& ( W0 = szszuzczcdt0(W1) ) ) ) )
<=> ! [W0: $i] :
( ? [W1: $i] :
( aElementOf0(W1,szNzAzT0)
& ( W0 = szszuzczcdt0(W1) ) )
| ( W0 = sz00 )
| ~ aElementOf0(W0,szNzAzT0) ) ),
inference(quant_intro,[status(thm)],[108]) ).
tff(110,axiom,
! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> ( ( W0 = sz00 )
| ? [W1: $i] :
( aElementOf0(W1,szNzAzT0)
& ( W0 = szszuzczcdt0(W1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNatExtra) ).
tff(111,plain,
! [W0: $i] :
( ? [W1: $i] :
( aElementOf0(W1,szNzAzT0)
& ( W0 = szszuzczcdt0(W1) ) )
| ( W0 = sz00 )
| ~ aElementOf0(W0,szNzAzT0) ),
inference(modus_ponens,[status(thm)],[110,109]) ).
tff(112,plain,
! [W0: $i] :
( ? [W1: $i] :
( aElementOf0(W1,szNzAzT0)
& ( W0 = szszuzczcdt0(W1) ) )
| ( W0 = sz00 )
| ~ aElementOf0(W0,szNzAzT0) ),
inference(modus_ponens,[status(thm)],[111,107]) ).
tff(113,plain,
! [W0: $i] :
( ( aElementOf0(tptp_fun_W1_4(W0),szNzAzT0)
& ( W0 = szszuzczcdt0(tptp_fun_W1_4(W0)) ) )
| ( W0 = sz00 )
| ~ aElementOf0(W0,szNzAzT0) ),
inference(skolemize,[status(sab)],[112]) ).
tff(114,plain,
! [W0: $i] :
( ( W0 = sz00 )
| ~ aElementOf0(W0,szNzAzT0)
| ( aElementOf0(tptp_fun_W1_4(W0),szNzAzT0)
& ( W0 = szszuzczcdt0(tptp_fun_W1_4(W0)) ) ) ),
inference(modus_ponens,[status(thm)],[113,106]) ).
tff(115,plain,
! [W0: $i] :
( ( W0 = sz00 )
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aElementOf0(tptp_fun_W1_4(W0),szNzAzT0)
| ( W0 != szszuzczcdt0(tptp_fun_W1_4(W0)) ) ) ),
inference(modus_ponens,[status(thm)],[114,104]) ).
tff(116,plain,
! [W0: $i] :
( ( W0 = sz00 )
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aElementOf0(tptp_fun_W1_4(W0),szNzAzT0)
| ( W0 != szszuzczcdt0(tptp_fun_W1_4(W0)) ) ) ),
inference(modus_ponens,[status(thm)],[115,102]) ).
tff(117,plain,
( ( ~ ! [W0: $i] :
( ( W0 = sz00 )
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aElementOf0(tptp_fun_W1_4(W0),szNzAzT0)
| ( W0 != szszuzczcdt0(tptp_fun_W1_4(W0)) ) ) )
| ( xK = sz00 )
| ~ aElementOf0(xK,szNzAzT0)
| ~ ( ~ aElementOf0(tptp_fun_W1_4(xK),szNzAzT0)
| ( xK != szszuzczcdt0(tptp_fun_W1_4(xK)) ) ) )
<=> ( ~ ! [W0: $i] :
( ( W0 = sz00 )
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aElementOf0(tptp_fun_W1_4(W0),szNzAzT0)
| ( W0 != szszuzczcdt0(tptp_fun_W1_4(W0)) ) ) )
| ( xK = sz00 )
| ~ aElementOf0(xK,szNzAzT0)
| ~ ( ~ aElementOf0(tptp_fun_W1_4(xK),szNzAzT0)
| ( xK != szszuzczcdt0(tptp_fun_W1_4(xK)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(118,plain,
( ~ ! [W0: $i] :
( ( W0 = sz00 )
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aElementOf0(tptp_fun_W1_4(W0),szNzAzT0)
| ( W0 != szszuzczcdt0(tptp_fun_W1_4(W0)) ) ) )
| ( xK = sz00 )
| ~ aElementOf0(xK,szNzAzT0)
| ~ ( ~ aElementOf0(tptp_fun_W1_4(xK),szNzAzT0)
| ( xK != szszuzczcdt0(tptp_fun_W1_4(xK)) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(119,plain,
( ~ ! [W0: $i] :
( ( W0 = sz00 )
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aElementOf0(tptp_fun_W1_4(W0),szNzAzT0)
| ( W0 != szszuzczcdt0(tptp_fun_W1_4(W0)) ) ) )
| ( xK = sz00 )
| ~ aElementOf0(xK,szNzAzT0)
| ~ ( ~ aElementOf0(tptp_fun_W1_4(xK),szNzAzT0)
| ( xK != szszuzczcdt0(tptp_fun_W1_4(xK)) ) ) ),
inference(modus_ponens,[status(thm)],[118,117]) ).
tff(120,plain,
~ ( ~ aElementOf0(tptp_fun_W1_4(xK),szNzAzT0)
| ( xK != szszuzczcdt0(tptp_fun_W1_4(xK)) ) ),
inference(unit_resolution,[status(thm)],[119,116,30,100]) ).
tff(121,plain,
( ~ aElementOf0(tptp_fun_W1_4(xK),szNzAzT0)
| ( xK != szszuzczcdt0(tptp_fun_W1_4(xK)) )
| ( xK = szszuzczcdt0(tptp_fun_W1_4(xK)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(122,plain,
xK = szszuzczcdt0(tptp_fun_W1_4(xK)),
inference(unit_resolution,[status(thm)],[121,120]) ).
tff(123,plain,
szszuzczcdt0(tptp_fun_W1_4(xK)) = xK,
inference(symmetry,[status(thm)],[122]) ).
tff(124,plain,
szszuzczcdt0(tptp_fun_W1_4(xK)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,tptp_fun_W1_0(xQ)))),
inference(transitivity,[status(thm)],[123,97,96]) ).
tff(125,plain,
( ( szszuzczcdt0(tptp_fun_W1_4(xK)) = szszuzczcdt0(sbrdtbr0(xP)) )
<=> ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,tptp_fun_W1_0(xQ)))) = szszuzczcdt0(sbrdtbr0(xP)) ) ),
inference(monotonicity,[status(thm)],[124]) ).
tff(126,plain,
( ( szszuzczcdt0(tptp_fun_W1_4(xK)) = szszuzczcdt0(sbrdtbr0(xP)) )
<=> ( szszuzczcdt0(sbrdtbr0(xP)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,tptp_fun_W1_0(xQ)))) ) ),
inference(transitivity,[status(thm)],[125,1]) ).
tff(127,plain,
( ( szszuzczcdt0(sbrdtbr0(xP)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,tptp_fun_W1_0(xQ)))) )
<=> ( szszuzczcdt0(tptp_fun_W1_4(xK)) = szszuzczcdt0(sbrdtbr0(xP)) ) ),
inference(symmetry,[status(thm)],[126]) ).
tff(128,plain,
( ( xp = szmzizndt0(xQ) )
<=> ( xp = szmzizndt0(xQ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(129,axiom,
( aElementOf0(xp,xQ)
& ! [W0: $i] :
( aElementOf0(W0,xQ)
=> sdtlseqdt0(xp,W0) )
& ( xp = szmzizndt0(xQ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5147) ).
tff(130,plain,
xp = szmzizndt0(xQ),
inference(and_elim,[status(thm)],[129]) ).
tff(131,plain,
xp = szmzizndt0(xQ),
inference(modus_ponens,[status(thm)],[130,128]) ).
tff(132,plain,
szmzizndt0(xQ) = xp,
inference(symmetry,[status(thm)],[131]) ).
tff(133,plain,
( aElementOf0(szmzizndt0(xQ),xQ)
<=> aElementOf0(xp,xQ) ),
inference(monotonicity,[status(thm)],[132]) ).
tff(134,plain,
( aElementOf0(xp,xQ)
<=> aElementOf0(szmzizndt0(xQ),xQ) ),
inference(symmetry,[status(thm)],[133]) ).
tff(135,plain,
( aElementOf0(xp,xQ)
<=> aElementOf0(xp,xQ) ),
inference(rewrite,[status(thm)],[]) ).
tff(136,plain,
( aElementOf0(xp,xQ)
& ! [W0: $i] :
( aElementOf0(W0,xQ)
=> sdtlseqdt0(xp,W0) ) ),
inference(and_elim,[status(thm)],[129]) ).
tff(137,plain,
aElementOf0(xp,xQ),
inference(and_elim,[status(thm)],[136]) ).
tff(138,plain,
aElementOf0(xp,xQ),
inference(modus_ponens,[status(thm)],[137,135]) ).
tff(139,plain,
aElementOf0(szmzizndt0(xQ),xQ),
inference(modus_ponens,[status(thm)],[138,134]) ).
tff(140,plain,
( ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| ~ isFinite0(xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,W1))) = sbrdtbr0(xQ) ) )
| ~ isFinite0(xQ)
| ~ aElementOf0(szmzizndt0(xQ),xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) = sbrdtbr0(xQ) ) )
<=> ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| ~ isFinite0(xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,W1))) = sbrdtbr0(xQ) ) )
| ~ isFinite0(xQ)
| ~ aElementOf0(szmzizndt0(xQ),xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) = sbrdtbr0(xQ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(141,plain,
( ( ~ aElementOf0(szmzizndt0(xQ),xQ)
| ~ isFinite0(xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) = sbrdtbr0(xQ) ) )
<=> ( ~ isFinite0(xQ)
| ~ aElementOf0(szmzizndt0(xQ),xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) = sbrdtbr0(xQ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(142,plain,
( ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| ~ isFinite0(xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,W1))) = sbrdtbr0(xQ) ) )
| ~ aElementOf0(szmzizndt0(xQ),xQ)
| ~ isFinite0(xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) = sbrdtbr0(xQ) ) )
<=> ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| ~ isFinite0(xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,W1))) = sbrdtbr0(xQ) ) )
| ~ isFinite0(xQ)
| ~ aElementOf0(szmzizndt0(xQ),xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) = sbrdtbr0(xQ) ) ) ),
inference(monotonicity,[status(thm)],[141]) ).
tff(143,plain,
( ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| ~ isFinite0(xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,W1))) = sbrdtbr0(xQ) ) )
| ~ aElementOf0(szmzizndt0(xQ),xQ)
| ~ isFinite0(xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) = sbrdtbr0(xQ) ) )
<=> ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| ~ isFinite0(xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,W1))) = sbrdtbr0(xQ) ) )
| ~ isFinite0(xQ)
| ~ aElementOf0(szmzizndt0(xQ),xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) = sbrdtbr0(xQ) ) ) ),
inference(transitivity,[status(thm)],[142,140]) ).
tff(144,plain,
( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| ~ isFinite0(xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,W1))) = sbrdtbr0(xQ) ) )
| ~ aElementOf0(szmzizndt0(xQ),xQ)
| ~ isFinite0(xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) = sbrdtbr0(xQ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(145,plain,
( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| ~ isFinite0(xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,W1))) = sbrdtbr0(xQ) ) )
| ~ isFinite0(xQ)
| ~ aElementOf0(szmzizndt0(xQ),xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) = sbrdtbr0(xQ) ) ),
inference(modus_ponens,[status(thm)],[144,143]) ).
tff(146,plain,
( ~ isFinite0(xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) = sbrdtbr0(xQ) ) ),
inference(unit_resolution,[status(thm)],[145,87,139]) ).
tff(147,plain,
szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) = sbrdtbr0(xQ),
inference(unit_resolution,[status(thm)],[146,33]) ).
tff(148,plain,
( ( xP = sdtmndt0(xQ,szmzizndt0(xQ)) )
<=> ( xP = sdtmndt0(xQ,szmzizndt0(xQ)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(149,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/sandbox/benchmark/theBenchmark.p',m__5164) ).
tff(150,plain,
xP = sdtmndt0(xQ,szmzizndt0(xQ)),
inference(and_elim,[status(thm)],[149]) ).
tff(151,plain,
xP = sdtmndt0(xQ,szmzizndt0(xQ)),
inference(modus_ponens,[status(thm)],[150,148]) ).
tff(152,plain,
sdtmndt0(xQ,szmzizndt0(xQ)) = xP,
inference(symmetry,[status(thm)],[151]) ).
tff(153,plain,
sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) = sbrdtbr0(xP),
inference(monotonicity,[status(thm)],[152]) ).
tff(154,plain,
sbrdtbr0(xP) = sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))),
inference(symmetry,[status(thm)],[153]) ).
tff(155,plain,
szszuzczcdt0(sbrdtbr0(xP)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))),
inference(monotonicity,[status(thm)],[154]) ).
tff(156,plain,
szszuzczcdt0(sbrdtbr0(xP)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,tptp_fun_W1_0(xQ)))),
inference(transitivity,[status(thm)],[155,147,96]) ).
tff(157,plain,
szszuzczcdt0(tptp_fun_W1_4(xK)) = szszuzczcdt0(sbrdtbr0(xP)),
inference(modus_ponens,[status(thm)],[156,127]) ).
tff(158,plain,
( aElementOf0(sbrdtbr0(xP),szNzAzT0)
<=> aElementOf0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))),szNzAzT0) ),
inference(monotonicity,[status(thm)],[154]) ).
tff(159,plain,
( aElementOf0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))),szNzAzT0)
<=> aElementOf0(sbrdtbr0(xP),szNzAzT0) ),
inference(symmetry,[status(thm)],[158]) ).
tff(160,plain,
( aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
<=> aSet0(xP) ),
inference(monotonicity,[status(thm)],[152]) ).
tff(161,plain,
( aSet0(xP)
<=> aSet0(sdtmndt0(xQ,szmzizndt0(xQ))) ),
inference(symmetry,[status(thm)],[160]) ).
tff(162,plain,
( aSet0(xP)
<=> aSet0(xP) ),
inference(rewrite,[status(thm)],[]) ).
tff(163,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)],[149]) ).
tff(164,plain,
( aSet0(xP)
& ! [W0: $i] :
( aElementOf0(W0,xQ)
=> sdtlseqdt0(szmzizndt0(xQ),W0) ) ),
inference(and_elim,[status(thm)],[163]) ).
tff(165,plain,
aSet0(xP),
inference(and_elim,[status(thm)],[164]) ).
tff(166,plain,
aSet0(xP),
inference(modus_ponens,[status(thm)],[165,162]) ).
tff(167,plain,
aSet0(sdtmndt0(xQ,szmzizndt0(xQ))),
inference(modus_ponens,[status(thm)],[166,161]) ).
tff(168,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) )
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ( aElementOf0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))),szNzAzT0)
<=> isFinite0(sdtmndt0(xQ,szmzizndt0(xQ))) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) )
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ( aElementOf0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))),szNzAzT0)
<=> isFinite0(sdtmndt0(xQ,szmzizndt0(xQ))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(169,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) )
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ( aElementOf0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))),szNzAzT0)
<=> isFinite0(sdtmndt0(xQ,szmzizndt0(xQ))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(170,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) )
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ( aElementOf0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))),szNzAzT0)
<=> isFinite0(sdtmndt0(xQ,szmzizndt0(xQ))) ) ),
inference(modus_ponens,[status(thm)],[169,168]) ).
tff(171,plain,
( ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ( aElementOf0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))),szNzAzT0)
<=> isFinite0(sdtmndt0(xQ,szmzizndt0(xQ))) ) ),
inference(unit_resolution,[status(thm)],[170,18]) ).
tff(172,plain,
( aElementOf0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))),szNzAzT0)
<=> isFinite0(sdtmndt0(xQ,szmzizndt0(xQ))) ),
inference(unit_resolution,[status(thm)],[171,167]) ).
tff(173,plain,
( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ)
<=> aSubsetOf0(xP,xQ) ),
inference(monotonicity,[status(thm)],[152]) ).
tff(174,plain,
( aSubsetOf0(xP,xQ)
<=> aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ) ),
inference(symmetry,[status(thm)],[173]) ).
tff(175,plain,
( aSubsetOf0(xP,xQ)
<=> aSubsetOf0(xP,xQ) ),
inference(rewrite,[status(thm)],[]) ).
tff(176,axiom,
( ! [W0: $i] :
( aElementOf0(W0,xP)
=> aElementOf0(W0,xQ) )
& aSubsetOf0(xP,xQ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5195) ).
tff(177,plain,
aSubsetOf0(xP,xQ),
inference(and_elim,[status(thm)],[176]) ).
tff(178,plain,
aSubsetOf0(xP,xQ),
inference(modus_ponens,[status(thm)],[177,175]) ).
tff(179,plain,
aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ),
inference(modus_ponens,[status(thm)],[178,174]) ).
tff(180,plain,
^ [W0: $i] :
refl(( ( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) )
<=> ( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(181,plain,
( ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) )
<=> ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) ) ),
inference(quant_intro,[status(thm)],[180]) ).
tff(182,plain,
^ [W0: $i] :
rewrite(( ( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) )
<=> ( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(183,plain,
( ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) )
<=> ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) ) ),
inference(quant_intro,[status(thm)],[182]) ).
tff(184,plain,
( ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) )
<=> ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) ) ),
inference(transitivity,[status(thm)],[183,181]) ).
tff(185,plain,
^ [W0: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aSet0(W0)
& isFinite0(W0) )
<=> ~ ( ~ aSet0(W0)
| ~ isFinite0(W0) ) )),
( ~ ( aSet0(W0)
& isFinite0(W0) )
<=> ~ ~ ( ~ aSet0(W0)
| ~ isFinite0(W0) ) )),
rewrite(( ~ ~ ( ~ aSet0(W0)
| ~ isFinite0(W0) )
<=> ( ~ aSet0(W0)
| ~ isFinite0(W0) ) )),
( ~ ( aSet0(W0)
& isFinite0(W0) )
<=> ( ~ aSet0(W0)
| ~ isFinite0(W0) ) )),
( ( ~ ( aSet0(W0)
& isFinite0(W0) )
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) )
<=> ( ~ aSet0(W0)
| ~ isFinite0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) ) )),
rewrite(( ( ~ aSet0(W0)
| ~ isFinite0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) )
<=> ( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) ) )),
( ( ~ ( aSet0(W0)
& isFinite0(W0) )
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) )
<=> ( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(186,plain,
( ! [W0: $i] :
( ~ ( aSet0(W0)
& isFinite0(W0) )
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) )
<=> ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) ) ),
inference(quant_intro,[status(thm)],[185]) ).
tff(187,plain,
( ! [W0: $i] :
( ~ ( aSet0(W0)
& isFinite0(W0) )
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) )
<=> ! [W0: $i] :
( ~ ( aSet0(W0)
& isFinite0(W0) )
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(188,plain,
^ [W0: $i] :
trans(monotonicity(quant_intro(proof_bind(^ [W1: $i] :
rewrite(( ( aSubsetOf0(W1,W0)
=> isFinite0(W1) )
<=> ( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) ))),
( ! [W1: $i] :
( aSubsetOf0(W1,W0)
=> isFinite0(W1) )
<=> ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) )),
( ( ( aSet0(W0)
& isFinite0(W0) )
=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
=> isFinite0(W1) ) )
<=> ( ( aSet0(W0)
& isFinite0(W0) )
=> ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) ) )),
rewrite(( ( ( aSet0(W0)
& isFinite0(W0) )
=> ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) )
<=> ( ~ ( aSet0(W0)
& isFinite0(W0) )
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) ) )),
( ( ( aSet0(W0)
& isFinite0(W0) )
=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
=> isFinite0(W1) ) )
<=> ( ~ ( aSet0(W0)
& isFinite0(W0) )
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(189,plain,
( ! [W0: $i] :
( ( aSet0(W0)
& isFinite0(W0) )
=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
=> isFinite0(W1) ) )
<=> ! [W0: $i] :
( ~ ( aSet0(W0)
& isFinite0(W0) )
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) ) ),
inference(quant_intro,[status(thm)],[188]) ).
tff(190,axiom,
! [W0: $i] :
( ( aSet0(W0)
& isFinite0(W0) )
=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
=> isFinite0(W1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSubFSet) ).
tff(191,plain,
! [W0: $i] :
( ~ ( aSet0(W0)
& isFinite0(W0) )
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[190,189]) ).
tff(192,plain,
! [W0: $i] :
( ~ ( aSet0(W0)
& isFinite0(W0) )
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[191,187]) ).
tff(193,plain,
! [W0: $i] :
( ~ ( aSet0(W0)
& isFinite0(W0) )
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) ),
inference(skolemize,[status(sab)],[192]) ).
tff(194,plain,
! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[193,186]) ).
tff(195,plain,
! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[194,184]) ).
tff(196,plain,
( ( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) )
| ~ aSet0(xQ)
| ~ isFinite0(xQ)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,xQ) ) )
<=> ( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) )
| ~ aSet0(xQ)
| ~ isFinite0(xQ)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,xQ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(197,plain,
( ( ~ isFinite0(xQ)
| ~ aSet0(xQ)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,xQ) ) )
<=> ( ~ aSet0(xQ)
| ~ isFinite0(xQ)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,xQ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(198,plain,
( ( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) )
| ~ isFinite0(xQ)
| ~ aSet0(xQ)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,xQ) ) )
<=> ( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) )
| ~ aSet0(xQ)
| ~ isFinite0(xQ)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,xQ) ) ) ),
inference(monotonicity,[status(thm)],[197]) ).
tff(199,plain,
( ( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) )
| ~ isFinite0(xQ)
| ~ aSet0(xQ)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,xQ) ) )
<=> ( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) )
| ~ aSet0(xQ)
| ~ isFinite0(xQ)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,xQ) ) ) ),
inference(transitivity,[status(thm)],[198,196]) ).
tff(200,plain,
( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) )
| ~ isFinite0(xQ)
| ~ aSet0(xQ)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,xQ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(201,plain,
( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) )
| ~ aSet0(xQ)
| ~ isFinite0(xQ)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,xQ) ) ),
inference(modus_ponens,[status(thm)],[200,199]) ).
tff(202,plain,
( ~ isFinite0(xQ)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,xQ) ) ),
inference(unit_resolution,[status(thm)],[201,195,8]) ).
tff(203,plain,
! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,xQ) ),
inference(unit_resolution,[status(thm)],[202,33]) ).
tff(204,plain,
( ( ~ ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,xQ) )
| isFinite0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ) )
<=> ( ~ ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,xQ) )
| isFinite0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(205,plain,
( ~ ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,xQ) )
| isFinite0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(206,plain,
( ~ ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,xQ) )
| isFinite0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ) ),
inference(modus_ponens,[status(thm)],[205,204]) ).
tff(207,plain,
isFinite0(sdtmndt0(xQ,szmzizndt0(xQ))),
inference(unit_resolution,[status(thm)],[206,203,179]) ).
tff(208,plain,
( ~ ( aElementOf0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))),szNzAzT0)
<=> isFinite0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| aElementOf0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))),szNzAzT0)
| ~ isFinite0(sdtmndt0(xQ,szmzizndt0(xQ))) ),
inference(tautology,[status(thm)],[]) ).
tff(209,plain,
aElementOf0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))),szNzAzT0),
inference(unit_resolution,[status(thm)],[208,207,172]) ).
tff(210,plain,
aElementOf0(sbrdtbr0(xP),szNzAzT0),
inference(modus_ponens,[status(thm)],[209,159]) ).
tff(211,plain,
( ( xk = sbrdtbr0(xP) )
<=> ( sbrdtbr0(xP) = xk ) ),
inference(commutativity,[status(thm)],[]) ).
tff(212,plain,
( ( szszuzczcdt0(xk) = xK )
<=> ( szszuzczcdt0(xk) = xK ) ),
inference(rewrite,[status(thm)],[]) ).
tff(213,axiom,
( aElementOf0(xk,szNzAzT0)
& ( szszuzczcdt0(xk) = xK ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3533) ).
tff(214,plain,
szszuzczcdt0(xk) = xK,
inference(and_elim,[status(thm)],[213]) ).
tff(215,plain,
szszuzczcdt0(xk) = xK,
inference(modus_ponens,[status(thm)],[214,212]) ).
tff(216,plain,
szszuzczcdt0(xk) = szszuzczcdt0(tptp_fun_W1_4(xK)),
inference(transitivity,[status(thm)],[215,122]) ).
tff(217,plain,
( ~ aElementOf0(tptp_fun_W1_4(xK),szNzAzT0)
| ( xK != szszuzczcdt0(tptp_fun_W1_4(xK)) )
| aElementOf0(tptp_fun_W1_4(xK),szNzAzT0) ),
inference(tautology,[status(thm)],[]) ).
tff(218,plain,
aElementOf0(tptp_fun_W1_4(xK),szNzAzT0),
inference(unit_resolution,[status(thm)],[217,120]) ).
tff(219,plain,
( aElementOf0(xk,szNzAzT0)
<=> aElementOf0(xk,szNzAzT0) ),
inference(rewrite,[status(thm)],[]) ).
tff(220,plain,
aElementOf0(xk,szNzAzT0),
inference(and_elim,[status(thm)],[213]) ).
tff(221,plain,
aElementOf0(xk,szNzAzT0),
inference(modus_ponens,[status(thm)],[220,219]) ).
tff(222,plain,
^ [W0: $i,W1: $i] :
refl(( ( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aElementOf0(W0,szNzAzT0) )
<=> ( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aElementOf0(W0,szNzAzT0) ) )),
inference(bind,[status(th)],[]) ).
tff(223,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aElementOf0(W0,szNzAzT0) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aElementOf0(W0,szNzAzT0) ) ),
inference(quant_intro,[status(thm)],[222]) ).
tff(224,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
<=> ~ ( ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) ) )),
( ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
<=> ~ ~ ( ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) ) )),
rewrite(( ~ ~ ( ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) )
<=> ( ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) ) )),
( ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
<=> ( ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) ) )),
( ( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) ) )
<=> ( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) ) )),
rewrite(( ( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) )
<=> ( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aElementOf0(W0,szNzAzT0) ) )),
( ( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) ) )
<=> ( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aElementOf0(W0,szNzAzT0) ) )),
inference(bind,[status(th)],[]) ).
tff(225,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) ) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aElementOf0(W0,szNzAzT0) ) ),
inference(quant_intro,[status(thm)],[224]) ).
tff(226,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) ) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(227,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(rewrite(( ( ( szszuzczcdt0(W0) = szszuzczcdt0(W1) )
=> ( W0 = W1 ) )
<=> ( ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ( W0 = W1 ) ) )),
( ( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( ( szszuzczcdt0(W0) = szszuzczcdt0(W1) )
=> ( W0 = W1 ) ) )
<=> ( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ( W0 = W1 ) ) ) )),
rewrite(( ( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ( W0 = W1 ) ) )
<=> ( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) ) ) )),
( ( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( ( szszuzczcdt0(W0) = szszuzczcdt0(W1) )
=> ( W0 = W1 ) ) )
<=> ( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(228,plain,
( ! [W0: $i,W1: $i] :
( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( ( szszuzczcdt0(W0) = szszuzczcdt0(W1) )
=> ( W0 = W1 ) ) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) ) ) ),
inference(quant_intro,[status(thm)],[227]) ).
tff(229,axiom,
! [W0: $i,W1: $i] :
( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( ( szszuzczcdt0(W0) = szszuzczcdt0(W1) )
=> ( W0 = W1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSuccEquSucc) ).
tff(230,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) ) ),
inference(modus_ponens,[status(thm)],[229,228]) ).
tff(231,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) ) ),
inference(modus_ponens,[status(thm)],[230,226]) ).
tff(232,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) ) ),
inference(skolemize,[status(sab)],[231]) ).
tff(233,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aElementOf0(W0,szNzAzT0) ),
inference(modus_ponens,[status(thm)],[232,225]) ).
tff(234,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aElementOf0(W0,szNzAzT0) ),
inference(modus_ponens,[status(thm)],[233,223]) ).
tff(235,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aElementOf0(W0,szNzAzT0) )
| ~ aElementOf0(tptp_fun_W1_4(xK),szNzAzT0)
| ~ aElementOf0(xk,szNzAzT0)
| ( xk = tptp_fun_W1_4(xK) )
| ( szszuzczcdt0(xk) != szszuzczcdt0(tptp_fun_W1_4(xK)) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aElementOf0(W0,szNzAzT0) )
| ~ aElementOf0(tptp_fun_W1_4(xK),szNzAzT0)
| ~ aElementOf0(xk,szNzAzT0)
| ( xk = tptp_fun_W1_4(xK) )
| ( szszuzczcdt0(xk) != szszuzczcdt0(tptp_fun_W1_4(xK)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(236,plain,
( ( ( xk = tptp_fun_W1_4(xK) )
| ~ aElementOf0(tptp_fun_W1_4(xK),szNzAzT0)
| ( szszuzczcdt0(xk) != szszuzczcdt0(tptp_fun_W1_4(xK)) )
| ~ aElementOf0(xk,szNzAzT0) )
<=> ( ~ aElementOf0(tptp_fun_W1_4(xK),szNzAzT0)
| ~ aElementOf0(xk,szNzAzT0)
| ( xk = tptp_fun_W1_4(xK) )
| ( szszuzczcdt0(xk) != szszuzczcdt0(tptp_fun_W1_4(xK)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(237,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aElementOf0(W0,szNzAzT0) )
| ( xk = tptp_fun_W1_4(xK) )
| ~ aElementOf0(tptp_fun_W1_4(xK),szNzAzT0)
| ( szszuzczcdt0(xk) != szszuzczcdt0(tptp_fun_W1_4(xK)) )
| ~ aElementOf0(xk,szNzAzT0) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aElementOf0(W0,szNzAzT0) )
| ~ aElementOf0(tptp_fun_W1_4(xK),szNzAzT0)
| ~ aElementOf0(xk,szNzAzT0)
| ( xk = tptp_fun_W1_4(xK) )
| ( szszuzczcdt0(xk) != szszuzczcdt0(tptp_fun_W1_4(xK)) ) ) ),
inference(monotonicity,[status(thm)],[236]) ).
tff(238,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aElementOf0(W0,szNzAzT0) )
| ( xk = tptp_fun_W1_4(xK) )
| ~ aElementOf0(tptp_fun_W1_4(xK),szNzAzT0)
| ( szszuzczcdt0(xk) != szszuzczcdt0(tptp_fun_W1_4(xK)) )
| ~ aElementOf0(xk,szNzAzT0) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aElementOf0(W0,szNzAzT0) )
| ~ aElementOf0(tptp_fun_W1_4(xK),szNzAzT0)
| ~ aElementOf0(xk,szNzAzT0)
| ( xk = tptp_fun_W1_4(xK) )
| ( szszuzczcdt0(xk) != szszuzczcdt0(tptp_fun_W1_4(xK)) ) ) ),
inference(transitivity,[status(thm)],[237,235]) ).
tff(239,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aElementOf0(W0,szNzAzT0) )
| ( xk = tptp_fun_W1_4(xK) )
| ~ aElementOf0(tptp_fun_W1_4(xK),szNzAzT0)
| ( szszuzczcdt0(xk) != szszuzczcdt0(tptp_fun_W1_4(xK)) )
| ~ aElementOf0(xk,szNzAzT0) ),
inference(quant_inst,[status(thm)],[]) ).
tff(240,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aElementOf0(W0,szNzAzT0) )
| ~ aElementOf0(tptp_fun_W1_4(xK),szNzAzT0)
| ~ aElementOf0(xk,szNzAzT0)
| ( xk = tptp_fun_W1_4(xK) )
| ( szszuzczcdt0(xk) != szszuzczcdt0(tptp_fun_W1_4(xK)) ) ),
inference(modus_ponens,[status(thm)],[239,238]) ).
tff(241,plain,
xk = tptp_fun_W1_4(xK),
inference(unit_resolution,[status(thm)],[240,234,221,218,216]) ).
tff(242,plain,
tptp_fun_W1_4(xK) = xk,
inference(symmetry,[status(thm)],[241]) ).
tff(243,plain,
( ( tptp_fun_W1_4(xK) = sbrdtbr0(xP) )
<=> ( xk = sbrdtbr0(xP) ) ),
inference(monotonicity,[status(thm)],[242]) ).
tff(244,plain,
( ( tptp_fun_W1_4(xK) = sbrdtbr0(xP) )
<=> ( sbrdtbr0(xP) = xk ) ),
inference(transitivity,[status(thm)],[243,211]) ).
tff(245,plain,
( ( sbrdtbr0(xP) = xk )
<=> ( tptp_fun_W1_4(xK) = sbrdtbr0(xP) ) ),
inference(symmetry,[status(thm)],[244]) ).
tff(246,plain,
( ( sbrdtbr0(xP) != xk )
<=> ( tptp_fun_W1_4(xK) != sbrdtbr0(xP) ) ),
inference(monotonicity,[status(thm)],[245]) ).
tff(247,plain,
( ( sbrdtbr0(xP) != xk )
<=> ( sbrdtbr0(xP) != xk ) ),
inference(rewrite,[status(thm)],[]) ).
tff(248,axiom,
sbrdtbr0(xP) != xk,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(249,plain,
sbrdtbr0(xP) != xk,
inference(modus_ponens,[status(thm)],[248,247]) ).
tff(250,plain,
tptp_fun_W1_4(xK) != sbrdtbr0(xP),
inference(modus_ponens,[status(thm)],[249,246]) ).
tff(251,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aElementOf0(W0,szNzAzT0) )
| ~ aElementOf0(tptp_fun_W1_4(xK),szNzAzT0)
| ~ aElementOf0(sbrdtbr0(xP),szNzAzT0)
| ( tptp_fun_W1_4(xK) = sbrdtbr0(xP) )
| ( szszuzczcdt0(tptp_fun_W1_4(xK)) != szszuzczcdt0(sbrdtbr0(xP)) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aElementOf0(W0,szNzAzT0) )
| ~ aElementOf0(tptp_fun_W1_4(xK),szNzAzT0)
| ~ aElementOf0(sbrdtbr0(xP),szNzAzT0)
| ( tptp_fun_W1_4(xK) = sbrdtbr0(xP) )
| ( szszuzczcdt0(tptp_fun_W1_4(xK)) != szszuzczcdt0(sbrdtbr0(xP)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(252,plain,
( ( ( tptp_fun_W1_4(xK) = sbrdtbr0(xP) )
| ~ aElementOf0(sbrdtbr0(xP),szNzAzT0)
| ( szszuzczcdt0(tptp_fun_W1_4(xK)) != szszuzczcdt0(sbrdtbr0(xP)) )
| ~ aElementOf0(tptp_fun_W1_4(xK),szNzAzT0) )
<=> ( ~ aElementOf0(tptp_fun_W1_4(xK),szNzAzT0)
| ~ aElementOf0(sbrdtbr0(xP),szNzAzT0)
| ( tptp_fun_W1_4(xK) = sbrdtbr0(xP) )
| ( szszuzczcdt0(tptp_fun_W1_4(xK)) != szszuzczcdt0(sbrdtbr0(xP)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(253,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aElementOf0(W0,szNzAzT0) )
| ( tptp_fun_W1_4(xK) = sbrdtbr0(xP) )
| ~ aElementOf0(sbrdtbr0(xP),szNzAzT0)
| ( szszuzczcdt0(tptp_fun_W1_4(xK)) != szszuzczcdt0(sbrdtbr0(xP)) )
| ~ aElementOf0(tptp_fun_W1_4(xK),szNzAzT0) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aElementOf0(W0,szNzAzT0) )
| ~ aElementOf0(tptp_fun_W1_4(xK),szNzAzT0)
| ~ aElementOf0(sbrdtbr0(xP),szNzAzT0)
| ( tptp_fun_W1_4(xK) = sbrdtbr0(xP) )
| ( szszuzczcdt0(tptp_fun_W1_4(xK)) != szszuzczcdt0(sbrdtbr0(xP)) ) ) ),
inference(monotonicity,[status(thm)],[252]) ).
tff(254,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aElementOf0(W0,szNzAzT0) )
| ( tptp_fun_W1_4(xK) = sbrdtbr0(xP) )
| ~ aElementOf0(sbrdtbr0(xP),szNzAzT0)
| ( szszuzczcdt0(tptp_fun_W1_4(xK)) != szszuzczcdt0(sbrdtbr0(xP)) )
| ~ aElementOf0(tptp_fun_W1_4(xK),szNzAzT0) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aElementOf0(W0,szNzAzT0) )
| ~ aElementOf0(tptp_fun_W1_4(xK),szNzAzT0)
| ~ aElementOf0(sbrdtbr0(xP),szNzAzT0)
| ( tptp_fun_W1_4(xK) = sbrdtbr0(xP) )
| ( szszuzczcdt0(tptp_fun_W1_4(xK)) != szszuzczcdt0(sbrdtbr0(xP)) ) ) ),
inference(transitivity,[status(thm)],[253,251]) ).
tff(255,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aElementOf0(W0,szNzAzT0) )
| ( tptp_fun_W1_4(xK) = sbrdtbr0(xP) )
| ~ aElementOf0(sbrdtbr0(xP),szNzAzT0)
| ( szszuzczcdt0(tptp_fun_W1_4(xK)) != szszuzczcdt0(sbrdtbr0(xP)) )
| ~ aElementOf0(tptp_fun_W1_4(xK),szNzAzT0) ),
inference(quant_inst,[status(thm)],[]) ).
tff(256,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aElementOf0(W0,szNzAzT0) )
| ~ aElementOf0(tptp_fun_W1_4(xK),szNzAzT0)
| ~ aElementOf0(sbrdtbr0(xP),szNzAzT0)
| ( tptp_fun_W1_4(xK) = sbrdtbr0(xP) )
| ( szszuzczcdt0(tptp_fun_W1_4(xK)) != szszuzczcdt0(sbrdtbr0(xP)) ) ),
inference(modus_ponens,[status(thm)],[255,254]) ).
tff(257,plain,
( ~ aElementOf0(sbrdtbr0(xP),szNzAzT0)
| ( tptp_fun_W1_4(xK) = sbrdtbr0(xP) )
| ( szszuzczcdt0(tptp_fun_W1_4(xK)) != szszuzczcdt0(sbrdtbr0(xP)) ) ),
inference(unit_resolution,[status(thm)],[256,234,218]) ).
tff(258,plain,
$false,
inference(unit_resolution,[status(thm)],[257,250,210,157]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM611+3 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n010.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 01:36:41 EDT 2025
% 0.12/0.33 % CPUTime :
% 21.79/21.96 % SZS status Theorem
% 21.79/21.96 % SZS output start Proof
% See solution above
% 21.84/22.05 % E exiting
%------------------------------------------------------------------------------