TSTP Solution File: NUM611+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM611+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 18 13:10:53 EDT 2022
% Result : Theorem 3.56s 2.55s
% Output : Proof 3.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 103
% Syntax : Number of formulae : 226 ( 62 unt; 22 typ; 0 def)
% Number of atoms : 1350 ( 366 equ)
% Maximal formula atoms : 16 ( 6 avg)
% Number of connectives : 1789 ( 739 ~; 700 |; 129 &)
% ( 167 <=>; 54 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 96 ( 96 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 13 >; 5 *; 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 : 344 ( 292 !; 26 ?; 344 :)
% Comments :
%------------------------------------------------------------------------------
tff(xk_type,type,
xk: $i ).
tff(sbrdtbr0_type,type,
sbrdtbr0: $i > $i ).
tff(sdtmndt0_type,type,
sdtmndt0: ( $i * $i ) > $i ).
tff(szmzizndt0_type,type,
szmzizndt0: $i > $i ).
tff(xQ_type,type,
xQ: $i ).
tff(tptp_fun_W1_4_type,type,
tptp_fun_W1_4: $i > $i ).
tff(szszuzczcdt0_type,type,
szszuzczcdt0: $i > $i ).
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(szDzozmdt0_type,type,
szDzozmdt0: $i > $i ).
tff(xN_type,type,
xN: $i ).
tff(sz00_type,type,
sz00: $i ).
tff(xK_type,type,
xK: $i ).
tff(szNzAzT0_type,type,
szNzAzT0: $i ).
tff(isFinite0_type,type,
isFinite0: $i > $o ).
tff(aSet0_type,type,
aSet0: $i > $o ).
tff(xP_type,type,
xP: $i ).
tff(sdtlseqdt0_type,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(aElement0_type,type,
aElement0: $i > $o ).
tff(aSubsetOf0_type,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff(xO_type,type,
xO: $i ).
tff(slbdtsldtrb0_type,type,
slbdtsldtrb0: ( $i * $i ) > $i ).
tff(xp_type,type,
xp: $i ).
tff(1,plain,
( ( xK != sz00 )
<=> ( szszuzczcdt0(xk) != sz00 ) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ( xK != sz00 )
<=> ( xK != sz00 ) ),
inference(rewrite,[status(thm)],]) ).
tff(3,axiom,
xK != sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3462) ).
tff(4,plain,
xK != sz00,
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
szszuzczcdt0(xk) != sz00,
inference(modus_ponens,[status(thm)],[4,1]) ).
tff(6,plain,
( aElementOf0(xK,szNzAzT0)
<=> aElementOf0(szszuzczcdt0(xk),szDzozmdt0(xN)) ),
inference(rewrite,[status(thm)],]) ).
tff(7,plain,
( aElementOf0(xK,szNzAzT0)
<=> aElementOf0(xK,szNzAzT0) ),
inference(rewrite,[status(thm)],]) ).
tff(8,axiom,
aElementOf0(xK,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3418) ).
tff(9,plain,
aElementOf0(xK,szNzAzT0),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
aElementOf0(szszuzczcdt0(xk),szDzozmdt0(xN)),
inference(modus_ponens,[status(thm)],[9,6]) ).
tff(11,plain,
^ [W0: $i] :
refl(
( ( ( W0 = sz00 )
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(tptp_fun_W1_4(W0),szDzozmdt0(xN))
| ( W0 != szszuzczcdt0(tptp_fun_W1_4(W0)) ) ) )
<=> ( ( W0 = sz00 )
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(tptp_fun_W1_4(W0),szDzozmdt0(xN))
| ( W0 != szszuzczcdt0(tptp_fun_W1_4(W0)) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(12,plain,
( ! [W0: $i] :
( ( W0 = sz00 )
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(tptp_fun_W1_4(W0),szDzozmdt0(xN))
| ( W0 != szszuzczcdt0(tptp_fun_W1_4(W0)) ) ) )
<=> ! [W0: $i] :
( ( W0 = sz00 )
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(tptp_fun_W1_4(W0),szDzozmdt0(xN))
| ( W0 != szszuzczcdt0(tptp_fun_W1_4(W0)) ) ) ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
^ [W0: $i] :
trans(
monotonicity(
rewrite(
( ( aElementOf0(tptp_fun_W1_4(W0),szDzozmdt0(xN))
& ( W0 = szszuzczcdt0(tptp_fun_W1_4(W0)) ) )
<=> ~ ( ~ aElementOf0(tptp_fun_W1_4(W0),szDzozmdt0(xN))
| ( W0 != szszuzczcdt0(tptp_fun_W1_4(W0)) ) ) )),
( ( ( W0 = sz00 )
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ( aElementOf0(tptp_fun_W1_4(W0),szDzozmdt0(xN))
& ( W0 = szszuzczcdt0(tptp_fun_W1_4(W0)) ) ) )
<=> ( ( W0 = sz00 )
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(tptp_fun_W1_4(W0),szDzozmdt0(xN))
| ( W0 != szszuzczcdt0(tptp_fun_W1_4(W0)) ) ) ) )),
rewrite(
( ( ( W0 = sz00 )
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(tptp_fun_W1_4(W0),szDzozmdt0(xN))
| ( W0 != szszuzczcdt0(tptp_fun_W1_4(W0)) ) ) )
<=> ( ( W0 = sz00 )
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(tptp_fun_W1_4(W0),szDzozmdt0(xN))
| ( W0 != szszuzczcdt0(tptp_fun_W1_4(W0)) ) ) ) )),
( ( ( W0 = sz00 )
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ( aElementOf0(tptp_fun_W1_4(W0),szDzozmdt0(xN))
& ( W0 = szszuzczcdt0(tptp_fun_W1_4(W0)) ) ) )
<=> ( ( W0 = sz00 )
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(tptp_fun_W1_4(W0),szDzozmdt0(xN))
| ( W0 != szszuzczcdt0(tptp_fun_W1_4(W0)) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(14,plain,
( ! [W0: $i] :
( ( W0 = sz00 )
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ( aElementOf0(tptp_fun_W1_4(W0),szDzozmdt0(xN))
& ( W0 = szszuzczcdt0(tptp_fun_W1_4(W0)) ) ) )
<=> ! [W0: $i] :
( ( W0 = sz00 )
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(tptp_fun_W1_4(W0),szDzozmdt0(xN))
| ( W0 != szszuzczcdt0(tptp_fun_W1_4(W0)) ) ) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,plain,
^ [W0: $i] :
trans(
monotonicity(
quant_intro(
proof_bind(
^ [W1: $i] :
rewrite(
( ( aElementOf0(W1,szNzAzT0)
& ( W0 = szszuzczcdt0(W1) ) )
<=> ( aElementOf0(W1,szDzozmdt0(xN))
& ( W0 = szszuzczcdt0(W1) ) ) ))),
( ? [W1: $i] :
( aElementOf0(W1,szNzAzT0)
& ( W0 = szszuzczcdt0(W1) ) )
<=> ? [W1: $i] :
( aElementOf0(W1,szDzozmdt0(xN))
& ( W0 = szszuzczcdt0(W1) ) ) )),
rewrite(
( ~ aElementOf0(W0,szNzAzT0)
<=> ~ aElementOf0(W0,szDzozmdt0(xN)) )),
( ( ? [W1: $i] :
( aElementOf0(W1,szNzAzT0)
& ( W0 = szszuzczcdt0(W1) ) )
| ( W0 = sz00 )
| ~ aElementOf0(W0,szNzAzT0) )
<=> ( ? [W1: $i] :
( aElementOf0(W1,szDzozmdt0(xN))
& ( W0 = szszuzczcdt0(W1) ) )
| ( W0 = sz00 )
| ~ aElementOf0(W0,szDzozmdt0(xN)) ) )),
rewrite(
( ( ? [W1: $i] :
( aElementOf0(W1,szDzozmdt0(xN))
& ( W0 = szszuzczcdt0(W1) ) )
| ( W0 = sz00 )
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
<=> ( ( W0 = sz00 )
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ? [W1: $i] :
( aElementOf0(W1,szDzozmdt0(xN))
& ( W0 = szszuzczcdt0(W1) ) ) ) )),
( ( ? [W1: $i] :
( aElementOf0(W1,szNzAzT0)
& ( W0 = szszuzczcdt0(W1) ) )
| ( W0 = sz00 )
| ~ aElementOf0(W0,szNzAzT0) )
<=> ( ( W0 = sz00 )
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ? [W1: $i] :
( aElementOf0(W1,szDzozmdt0(xN))
& ( W0 = szszuzczcdt0(W1) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(16,plain,
( ! [W0: $i] :
( ? [W1: $i] :
( aElementOf0(W1,szNzAzT0)
& ( W0 = szszuzczcdt0(W1) ) )
| ( W0 = sz00 )
| ~ aElementOf0(W0,szNzAzT0) )
<=> ! [W0: $i] :
( ( W0 = sz00 )
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ? [W1: $i] :
( aElementOf0(W1,szDzozmdt0(xN))
& ( W0 = szszuzczcdt0(W1) ) ) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,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(18,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(19,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)],[18]) ).
tff(20,axiom,
! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> ( ( W0 = sz00 )
| ? [W1: $i] :
( aElementOf0(W1,szNzAzT0)
& ( W0 = szszuzczcdt0(W1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNatExtra) ).
tff(21,plain,
! [W0: $i] :
( ? [W1: $i] :
( aElementOf0(W1,szNzAzT0)
& ( W0 = szszuzczcdt0(W1) ) )
| ( W0 = sz00 )
| ~ aElementOf0(W0,szNzAzT0) ),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
! [W0: $i] :
( ? [W1: $i] :
( aElementOf0(W1,szNzAzT0)
& ( W0 = szszuzczcdt0(W1) ) )
| ( W0 = sz00 )
| ~ aElementOf0(W0,szNzAzT0) ),
inference(modus_ponens,[status(thm)],[21,17]) ).
tff(23,plain,
! [W0: $i] :
( ( W0 = sz00 )
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ? [W1: $i] :
( aElementOf0(W1,szDzozmdt0(xN))
& ( W0 = szszuzczcdt0(W1) ) ) ),
inference(modus_ponens,[status(thm)],[22,16]) ).
tff(24,plain,
! [W0: $i] :
( ( W0 = sz00 )
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ( aElementOf0(tptp_fun_W1_4(W0),szDzozmdt0(xN))
& ( W0 = szszuzczcdt0(tptp_fun_W1_4(W0)) ) ) ),
inference(skolemize,[status(sab)],[23]) ).
tff(25,plain,
! [W0: $i] :
( ( W0 = sz00 )
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(tptp_fun_W1_4(W0),szDzozmdt0(xN))
| ( W0 != szszuzczcdt0(tptp_fun_W1_4(W0)) ) ) ),
inference(modus_ponens,[status(thm)],[24,14]) ).
tff(26,plain,
! [W0: $i] :
( ( W0 = sz00 )
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(tptp_fun_W1_4(W0),szDzozmdt0(xN))
| ( W0 != szszuzczcdt0(tptp_fun_W1_4(W0)) ) ) ),
inference(modus_ponens,[status(thm)],[25,12]) ).
tff(27,plain,
( ( ~ ! [W0: $i] :
( ( W0 = sz00 )
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(tptp_fun_W1_4(W0),szDzozmdt0(xN))
| ( W0 != szszuzczcdt0(tptp_fun_W1_4(W0)) ) ) )
| ( szszuzczcdt0(xk) = sz00 )
| ~ aElementOf0(szszuzczcdt0(xk),szDzozmdt0(xN))
| ~ ( ~ aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xk)),szDzozmdt0(xN))
| ( szszuzczcdt0(xk) != szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xk))) ) ) )
<=> ( ~ ! [W0: $i] :
( ( W0 = sz00 )
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(tptp_fun_W1_4(W0),szDzozmdt0(xN))
| ( W0 != szszuzczcdt0(tptp_fun_W1_4(W0)) ) ) )
| ( szszuzczcdt0(xk) = sz00 )
| ~ aElementOf0(szszuzczcdt0(xk),szDzozmdt0(xN))
| ~ ( ~ aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xk)),szDzozmdt0(xN))
| ( szszuzczcdt0(xk) != szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xk))) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(28,plain,
( ~ ! [W0: $i] :
( ( W0 = sz00 )
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(tptp_fun_W1_4(W0),szDzozmdt0(xN))
| ( W0 != szszuzczcdt0(tptp_fun_W1_4(W0)) ) ) )
| ( szszuzczcdt0(xk) = sz00 )
| ~ aElementOf0(szszuzczcdt0(xk),szDzozmdt0(xN))
| ~ ( ~ aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xk)),szDzozmdt0(xN))
| ( szszuzczcdt0(xk) != szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xk))) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(29,plain,
( ~ ! [W0: $i] :
( ( W0 = sz00 )
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(tptp_fun_W1_4(W0),szDzozmdt0(xN))
| ( W0 != szszuzczcdt0(tptp_fun_W1_4(W0)) ) ) )
| ( szszuzczcdt0(xk) = sz00 )
| ~ aElementOf0(szszuzczcdt0(xk),szDzozmdt0(xN))
| ~ ( ~ aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xk)),szDzozmdt0(xN))
| ( szszuzczcdt0(xk) != szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xk))) ) ) ),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
~ ( ~ aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xk)),szDzozmdt0(xN))
| ( szszuzczcdt0(xk) != szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xk))) ) ),
inference(unit_resolution,[status(thm)],[29,26,10,5]) ).
tff(31,plain,
( ~ aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xk)),szDzozmdt0(xN))
| ( szszuzczcdt0(xk) != szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xk))) )
| ( szszuzczcdt0(xk) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xk))) ) ),
inference(tautology,[status(thm)],]) ).
tff(32,plain,
szszuzczcdt0(xk) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xk))),
inference(unit_resolution,[status(thm)],[31,30]) ).
tff(33,plain,
( ~ aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xk)),szDzozmdt0(xN))
| ( szszuzczcdt0(xk) != szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xk))) )
| aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xk)),szDzozmdt0(xN)) ),
inference(tautology,[status(thm)],]) ).
tff(34,plain,
aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xk)),szDzozmdt0(xN)),
inference(unit_resolution,[status(thm)],[33,30]) ).
tff(35,plain,
( aElementOf0(xk,szNzAzT0)
<=> aElementOf0(xk,szDzozmdt0(xN)) ),
inference(rewrite,[status(thm)],]) ).
tff(36,plain,
( aElementOf0(xk,szNzAzT0)
<=> aElementOf0(xk,szNzAzT0) ),
inference(rewrite,[status(thm)],]) ).
tff(37,axiom,
( aElementOf0(xk,szNzAzT0)
& ( szszuzczcdt0(xk) = xK ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3533) ).
tff(38,plain,
aElementOf0(xk,szNzAzT0),
inference(and_elim,[status(thm)],[37]) ).
tff(39,plain,
aElementOf0(xk,szNzAzT0),
inference(modus_ponens,[status(thm)],[38,36]) ).
tff(40,plain,
aElementOf0(xk,szDzozmdt0(xN)),
inference(modus_ponens,[status(thm)],[39,35]) ).
tff(41,plain,
^ [W0: $i,W1: $i] :
refl(
( ( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
<=> ( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ) )),
inference(bind,[status(th)],]) ).
tff(42,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ) ),
inference(quant_intro,[status(thm)],[41]) ).
tff(43,plain,
^ [W0: $i,W1: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) )
<=> ~ ( ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ) )),
( ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) )
<=> ~ ~ ( ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ) )),
rewrite(
( ~ ~ ( ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
<=> ( ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ) )),
( ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) )
<=> ( ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ) )),
( ( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) )
<=> ( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ) )),
rewrite(
( ( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
<=> ( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ) )),
( ( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) )
<=> ( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ) )),
inference(bind,[status(th)],]) ).
tff(44,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ) ),
inference(quant_intro,[status(thm)],[43]) ).
tff(45,plain,
^ [W0: $i,W1: $i] :
trans(
monotonicity(
rewrite(
( ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
<=> ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) )),
( ( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) ) )
<=> ( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) ) )),
rewrite(
( ( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) )
<=> ( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) ) )),
( ( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) ) )
<=> ( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) ) )),
inference(bind,[status(th)],]) ).
tff(46,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,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) ) ),
inference(quant_intro,[status(thm)],[45]) ).
tff(47,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(48,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(49,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)],[48]) ).
tff(50,axiom,
! [W0: $i,W1: $i] :
( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( ( szszuzczcdt0(W0) = szszuzczcdt0(W1) )
=> ( W0 = W1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSuccEquSucc) ).
tff(51,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) ) ),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) ) ),
inference(modus_ponens,[status(thm)],[51,47]) ).
tff(53,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) ),
inference(modus_ponens,[status(thm)],[52,46]) ).
tff(54,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) ),
inference(skolemize,[status(sab)],[53]) ).
tff(55,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ),
inference(modus_ponens,[status(thm)],[54,44]) ).
tff(56,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ),
inference(modus_ponens,[status(thm)],[55,42]) ).
tff(57,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| ~ aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xk)),szDzozmdt0(xN))
| ( szszuzczcdt0(xk) != szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xk))) )
| ~ aElementOf0(xk,szDzozmdt0(xN))
| ( xk = tptp_fun_W1_4(szszuzczcdt0(xk)) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| ~ aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xk)),szDzozmdt0(xN))
| ( szszuzczcdt0(xk) != szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xk))) )
| ~ aElementOf0(xk,szDzozmdt0(xN))
| ( xk = tptp_fun_W1_4(szszuzczcdt0(xk)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(58,plain,
( ( ( xk = tptp_fun_W1_4(szszuzczcdt0(xk)) )
| ( szszuzczcdt0(xk) != szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xk))) )
| ~ aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xk)),szDzozmdt0(xN))
| ~ aElementOf0(xk,szDzozmdt0(xN)) )
<=> ( ~ aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xk)),szDzozmdt0(xN))
| ( szszuzczcdt0(xk) != szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xk))) )
| ~ aElementOf0(xk,szDzozmdt0(xN))
| ( xk = tptp_fun_W1_4(szszuzczcdt0(xk)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(59,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| ( xk = tptp_fun_W1_4(szszuzczcdt0(xk)) )
| ( szszuzczcdt0(xk) != szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xk))) )
| ~ aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xk)),szDzozmdt0(xN))
| ~ aElementOf0(xk,szDzozmdt0(xN)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| ~ aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xk)),szDzozmdt0(xN))
| ( szszuzczcdt0(xk) != szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xk))) )
| ~ aElementOf0(xk,szDzozmdt0(xN))
| ( xk = tptp_fun_W1_4(szszuzczcdt0(xk)) ) ) ),
inference(monotonicity,[status(thm)],[58]) ).
tff(60,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| ( xk = tptp_fun_W1_4(szszuzczcdt0(xk)) )
| ( szszuzczcdt0(xk) != szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xk))) )
| ~ aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xk)),szDzozmdt0(xN))
| ~ aElementOf0(xk,szDzozmdt0(xN)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| ~ aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xk)),szDzozmdt0(xN))
| ( szszuzczcdt0(xk) != szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xk))) )
| ~ aElementOf0(xk,szDzozmdt0(xN))
| ( xk = tptp_fun_W1_4(szszuzczcdt0(xk)) ) ) ),
inference(transitivity,[status(thm)],[59,57]) ).
tff(61,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| ( xk = tptp_fun_W1_4(szszuzczcdt0(xk)) )
| ( szszuzczcdt0(xk) != szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xk))) )
| ~ aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xk)),szDzozmdt0(xN))
| ~ aElementOf0(xk,szDzozmdt0(xN)) ),
inference(quant_inst,[status(thm)],]) ).
tff(62,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| ~ aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xk)),szDzozmdt0(xN))
| ( szszuzczcdt0(xk) != szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xk))) )
| ~ aElementOf0(xk,szDzozmdt0(xN))
| ( xk = tptp_fun_W1_4(szszuzczcdt0(xk)) ) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
xk = tptp_fun_W1_4(szszuzczcdt0(xk)),
inference(unit_resolution,[status(thm)],[62,56,40,34,32]) ).
tff(64,plain,
tptp_fun_W1_4(szszuzczcdt0(xk)) = xk,
inference(symmetry,[status(thm)],[63]) ).
tff(65,plain,
( aSet0(xP)
<=> aSet0(sdtmndt0(xQ,szmzizndt0(xQ))) ),
inference(rewrite,[status(thm)],]) ).
tff(66,plain,
( aSet0(xP)
<=> aSet0(xP) ),
inference(rewrite,[status(thm)],]) ).
tff(67,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(68,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)],[67]) ).
tff(69,plain,
( aSet0(xP)
& ! [W0: $i] :
( aElementOf0(W0,xQ)
=> sdtlseqdt0(szmzizndt0(xQ),W0) ) ),
inference(and_elim,[status(thm)],[68]) ).
tff(70,plain,
aSet0(xP),
inference(and_elim,[status(thm)],[69]) ).
tff(71,plain,
aSet0(xP),
inference(modus_ponens,[status(thm)],[70,66]) ).
tff(72,plain,
aSet0(sdtmndt0(xQ,szmzizndt0(xQ))),
inference(modus_ponens,[status(thm)],[71,65]) ).
tff(73,plain,
^ [W0: $i] :
refl(
( ( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szDzozmdt0(xN))
<=> isFinite0(W0) ) )
<=> ( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szDzozmdt0(xN))
<=> isFinite0(W0) ) ) )),
inference(bind,[status(th)],]) ).
tff(74,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szDzozmdt0(xN))
<=> isFinite0(W0) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szDzozmdt0(xN))
<=> isFinite0(W0) ) ) ),
inference(quant_intro,[status(thm)],[73]) ).
tff(75,plain,
^ [W0: $i] :
rewrite(
( ( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) )
<=> ( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szDzozmdt0(xN))
<=> isFinite0(W0) ) ) )),
inference(bind,[status(th)],]) ).
tff(76,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szDzozmdt0(xN))
<=> isFinite0(W0) ) ) ),
inference(quant_intro,[status(thm)],[75]) ).
tff(77,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(78,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(79,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)],[78]) ).
tff(80,axiom,
! [W0: $i] :
( aSet0(W0)
=> ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardNum) ).
tff(81,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) ),
inference(modus_ponens,[status(thm)],[80,79]) ).
tff(82,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) ),
inference(modus_ponens,[status(thm)],[81,77]) ).
tff(83,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szDzozmdt0(xN))
<=> isFinite0(W0) ) ),
inference(modus_ponens,[status(thm)],[82,76]) ).
tff(84,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szDzozmdt0(xN))
<=> isFinite0(W0) ) ),
inference(skolemize,[status(sab)],[83]) ).
tff(85,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szDzozmdt0(xN))
<=> isFinite0(W0) ) ),
inference(modus_ponens,[status(thm)],[84,74]) ).
tff(86,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szDzozmdt0(xN))
<=> isFinite0(W0) ) )
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ( aElementOf0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))),szDzozmdt0(xN))
<=> isFinite0(sdtmndt0(xQ,szmzizndt0(xQ))) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szDzozmdt0(xN))
<=> isFinite0(W0) ) )
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ( aElementOf0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))),szDzozmdt0(xN))
<=> isFinite0(sdtmndt0(xQ,szmzizndt0(xQ))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(87,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szDzozmdt0(xN))
<=> isFinite0(W0) ) )
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ( aElementOf0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))),szDzozmdt0(xN))
<=> isFinite0(sdtmndt0(xQ,szmzizndt0(xQ))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(88,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szDzozmdt0(xN))
<=> isFinite0(W0) ) )
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ( aElementOf0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))),szDzozmdt0(xN))
<=> isFinite0(sdtmndt0(xQ,szmzizndt0(xQ))) ) ),
inference(modus_ponens,[status(thm)],[87,86]) ).
tff(89,plain,
( aElementOf0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))),szDzozmdt0(xN))
<=> isFinite0(sdtmndt0(xQ,szmzizndt0(xQ))) ),
inference(unit_resolution,[status(thm)],[88,85,72]) ).
tff(90,plain,
( aSet0(xQ)
<=> aSet0(xQ) ),
inference(rewrite,[status(thm)],]) ).
tff(91,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(92,plain,
( aSet0(xQ)
& ! [W0: $i] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,xO) )
& aSubsetOf0(xQ,xO)
& ( sbrdtbr0(xQ) = xK ) ),
inference(and_elim,[status(thm)],[91]) ).
tff(93,plain,
( aSet0(xQ)
& ! [W0: $i] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,xO) )
& aSubsetOf0(xQ,xO) ),
inference(and_elim,[status(thm)],[92]) ).
tff(94,plain,
( aSet0(xQ)
& ! [W0: $i] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,xO) ) ),
inference(and_elim,[status(thm)],[93]) ).
tff(95,plain,
aSet0(xQ),
inference(and_elim,[status(thm)],[94]) ).
tff(96,plain,
aSet0(xQ),
inference(modus_ponens,[status(thm)],[95,90]) ).
tff(97,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szDzozmdt0(xN))
<=> isFinite0(W0) ) )
| ~ aSet0(xQ)
| ( aElementOf0(sbrdtbr0(xQ),szDzozmdt0(xN))
<=> isFinite0(xQ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szDzozmdt0(xN))
<=> isFinite0(W0) ) )
| ~ aSet0(xQ)
| ( aElementOf0(sbrdtbr0(xQ),szDzozmdt0(xN))
<=> isFinite0(xQ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(98,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szDzozmdt0(xN))
<=> isFinite0(W0) ) )
| ~ aSet0(xQ)
| ( aElementOf0(sbrdtbr0(xQ),szDzozmdt0(xN))
<=> isFinite0(xQ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(99,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szDzozmdt0(xN))
<=> isFinite0(W0) ) )
| ~ aSet0(xQ)
| ( aElementOf0(sbrdtbr0(xQ),szDzozmdt0(xN))
<=> isFinite0(xQ) ) ),
inference(modus_ponens,[status(thm)],[98,97]) ).
tff(100,plain,
( aElementOf0(sbrdtbr0(xQ),szDzozmdt0(xN))
<=> isFinite0(xQ) ),
inference(unit_resolution,[status(thm)],[99,85,96]) ).
tff(101,plain,
( ( sbrdtbr0(xQ) = xK )
<=> ( sbrdtbr0(xQ) = szszuzczcdt0(xk) ) ),
inference(rewrite,[status(thm)],]) ).
tff(102,plain,
( ( sbrdtbr0(xQ) = xK )
<=> ( sbrdtbr0(xQ) = xK ) ),
inference(rewrite,[status(thm)],]) ).
tff(103,plain,
sbrdtbr0(xQ) = xK,
inference(and_elim,[status(thm)],[92]) ).
tff(104,plain,
sbrdtbr0(xQ) = xK,
inference(modus_ponens,[status(thm)],[103,102]) ).
tff(105,plain,
sbrdtbr0(xQ) = szszuzczcdt0(xk),
inference(modus_ponens,[status(thm)],[104,101]) ).
tff(106,plain,
( aElementOf0(sbrdtbr0(xQ),szDzozmdt0(xN))
<=> aElementOf0(szszuzczcdt0(xk),szDzozmdt0(xN)) ),
inference(monotonicity,[status(thm)],[105]) ).
tff(107,plain,
( aElementOf0(szszuzczcdt0(xk),szDzozmdt0(xN))
<=> aElementOf0(sbrdtbr0(xQ),szDzozmdt0(xN)) ),
inference(symmetry,[status(thm)],[106]) ).
tff(108,plain,
aElementOf0(sbrdtbr0(xQ),szDzozmdt0(xN)),
inference(modus_ponens,[status(thm)],[10,107]) ).
tff(109,plain,
( ~ ( aElementOf0(sbrdtbr0(xQ),szDzozmdt0(xN))
<=> isFinite0(xQ) )
| ~ aElementOf0(sbrdtbr0(xQ),szDzozmdt0(xN))
| isFinite0(xQ) ),
inference(tautology,[status(thm)],]) ).
tff(110,plain,
isFinite0(xQ),
inference(unit_resolution,[status(thm)],[109,108,100]) ).
tff(111,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(112,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)],[111]) ).
tff(113,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(114,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)],[113]) ).
tff(115,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)],[114,112]) ).
tff(116,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(117,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)],[116]) ).
tff(118,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(119,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(120,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)],[119]) ).
tff(121,axiom,
! [W0: $i] :
( ( aSet0(W0)
& isFinite0(W0) )
=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
=> isFinite0(W1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubFSet) ).
tff(122,plain,
! [W0: $i] :
( ~ ( aSet0(W0)
& isFinite0(W0) )
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[121,120]) ).
tff(123,plain,
! [W0: $i] :
( ~ ( aSet0(W0)
& isFinite0(W0) )
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[122,118]) ).
tff(124,plain,
! [W0: $i] :
( ~ ( aSet0(W0)
& isFinite0(W0) )
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) ),
inference(skolemize,[status(sab)],[123]) ).
tff(125,plain,
! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[124,117]) ).
tff(126,plain,
! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[125,115]) ).
tff(127,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(128,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(129,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)],[128]) ).
tff(130,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)],[129,127]) ).
tff(131,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(132,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)],[131,130]) ).
tff(133,plain,
( ~ isFinite0(xQ)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,xQ) ) ),
inference(unit_resolution,[status(thm)],[132,126,96]) ).
tff(134,plain,
! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,xQ) ),
inference(unit_resolution,[status(thm)],[133,110]) ).
tff(135,plain,
( aSubsetOf0(xP,xQ)
<=> aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ) ),
inference(rewrite,[status(thm)],]) ).
tff(136,plain,
( aSubsetOf0(xP,xQ)
<=> aSubsetOf0(xP,xQ) ),
inference(rewrite,[status(thm)],]) ).
tff(137,axiom,
( ! [W0: $i] :
( aElementOf0(W0,xP)
=> aElementOf0(W0,xQ) )
& aSubsetOf0(xP,xQ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5195) ).
tff(138,plain,
aSubsetOf0(xP,xQ),
inference(and_elim,[status(thm)],[137]) ).
tff(139,plain,
aSubsetOf0(xP,xQ),
inference(modus_ponens,[status(thm)],[138,136]) ).
tff(140,plain,
aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ),
inference(modus_ponens,[status(thm)],[139,135]) ).
tff(141,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(142,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(143,plain,
( ~ ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,xQ) )
| isFinite0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ) ),
inference(modus_ponens,[status(thm)],[142,141]) ).
tff(144,plain,
isFinite0(sdtmndt0(xQ,szmzizndt0(xQ))),
inference(unit_resolution,[status(thm)],[143,140,134]) ).
tff(145,plain,
( ~ ( aElementOf0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))),szDzozmdt0(xN))
<=> isFinite0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| aElementOf0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))),szDzozmdt0(xN))
| ~ isFinite0(sdtmndt0(xQ,szmzizndt0(xQ))) ),
inference(tautology,[status(thm)],]) ).
tff(146,plain,
aElementOf0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))),szDzozmdt0(xN)),
inference(unit_resolution,[status(thm)],[145,144,89]) ).
tff(147,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(148,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)],[147]) ).
tff(149,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(150,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)],[149]) ).
tff(151,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)],[150,148]) ).
tff(152,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(153,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)],[152]) ).
tff(154,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(155,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(156,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)],[155]) ).
tff(157,axiom,
! [W0: $i] :
( aSet0(W0)
=> ! [W1: $i] :
( ( isFinite0(W0)
& aElementOf0(W1,W0) )
=> ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardDiff) ).
tff(158,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ ( isFinite0(W0)
& aElementOf0(W1,W0) )
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) ) ) ),
inference(modus_ponens,[status(thm)],[157,156]) ).
tff(159,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ ( isFinite0(W0)
& aElementOf0(W1,W0) )
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) ) ) ),
inference(modus_ponens,[status(thm)],[158,154]) ).
tff(160,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ ( isFinite0(W0)
& aElementOf0(W1,W0) )
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) ) ) ),
inference(skolemize,[status(sab)],[159]) ).
tff(161,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) )
| ~ isFinite0(W0) ) ),
inference(modus_ponens,[status(thm)],[160,153]) ).
tff(162,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) )
| ~ isFinite0(W0) ) ),
inference(modus_ponens,[status(thm)],[161,151]) ).
tff(163,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(164,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(165,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)],[164]) ).
tff(166,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)],[165,163]) ).
tff(167,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(168,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)],[167,166]) ).
tff(169,plain,
! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| ~ isFinite0(xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,W1))) = sbrdtbr0(xQ) ) ),
inference(unit_resolution,[status(thm)],[168,162,96]) ).
tff(170,plain,
( aElementOf0(xp,xQ)
<=> aElementOf0(szmzizndt0(xQ),xQ) ),
inference(rewrite,[status(thm)],]) ).
tff(171,plain,
( aElementOf0(xp,xQ)
<=> aElementOf0(xp,xQ) ),
inference(rewrite,[status(thm)],]) ).
tff(172,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(173,plain,
( aElementOf0(xp,xQ)
& ! [W0: $i] :
( aElementOf0(W0,xQ)
=> sdtlseqdt0(xp,W0) ) ),
inference(and_elim,[status(thm)],[172]) ).
tff(174,plain,
aElementOf0(xp,xQ),
inference(and_elim,[status(thm)],[173]) ).
tff(175,plain,
aElementOf0(xp,xQ),
inference(modus_ponens,[status(thm)],[174,171]) ).
tff(176,plain,
aElementOf0(szmzizndt0(xQ),xQ),
inference(modus_ponens,[status(thm)],[175,170]) ).
tff(177,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(178,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(179,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)],[178]) ).
tff(180,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)],[179,177]) ).
tff(181,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(182,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)],[181,180]) ).
tff(183,plain,
( ~ isFinite0(xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) = sbrdtbr0(xQ) ) ),
inference(unit_resolution,[status(thm)],[182,176,169]) ).
tff(184,plain,
szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) = sbrdtbr0(xQ),
inference(unit_resolution,[status(thm)],[183,110]) ).
tff(185,plain,
sbrdtbr0(xQ) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))),
inference(symmetry,[status(thm)],[184]) ).
tff(186,plain,
szszuzczcdt0(xk) = sbrdtbr0(xQ),
inference(symmetry,[status(thm)],[105]) ).
tff(187,plain,
szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xk))) = szszuzczcdt0(xk),
inference(symmetry,[status(thm)],[32]) ).
tff(188,plain,
szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xk))) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))),
inference(transitivity,[status(thm)],[187,186,185]) ).
tff(189,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| ~ aElementOf0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))),szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xk)),szDzozmdt0(xN))
| ( tptp_fun_W1_4(szszuzczcdt0(xk)) = sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ( szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xk))) != szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| ~ aElementOf0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))),szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xk)),szDzozmdt0(xN))
| ( tptp_fun_W1_4(szszuzczcdt0(xk)) = sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ( szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xk))) != szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(190,plain,
( ( ( tptp_fun_W1_4(szszuzczcdt0(xk)) = sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ( szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xk))) != szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) )
| ~ aElementOf0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))),szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xk)),szDzozmdt0(xN)) )
<=> ( ~ aElementOf0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))),szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xk)),szDzozmdt0(xN))
| ( tptp_fun_W1_4(szszuzczcdt0(xk)) = sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ( szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xk))) != szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(191,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| ( tptp_fun_W1_4(szszuzczcdt0(xk)) = sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ( szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xk))) != szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) )
| ~ aElementOf0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))),szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xk)),szDzozmdt0(xN)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| ~ aElementOf0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))),szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xk)),szDzozmdt0(xN))
| ( tptp_fun_W1_4(szszuzczcdt0(xk)) = sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ( szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xk))) != szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) ) ) ),
inference(monotonicity,[status(thm)],[190]) ).
tff(192,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| ( tptp_fun_W1_4(szszuzczcdt0(xk)) = sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ( szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xk))) != szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) )
| ~ aElementOf0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))),szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xk)),szDzozmdt0(xN)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| ~ aElementOf0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))),szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xk)),szDzozmdt0(xN))
| ( tptp_fun_W1_4(szszuzczcdt0(xk)) = sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ( szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xk))) != szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) ) ) ),
inference(transitivity,[status(thm)],[191,189]) ).
tff(193,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| ( tptp_fun_W1_4(szszuzczcdt0(xk)) = sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ( szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xk))) != szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) )
| ~ aElementOf0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))),szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xk)),szDzozmdt0(xN)) ),
inference(quant_inst,[status(thm)],]) ).
tff(194,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| ~ aElementOf0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))),szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xk)),szDzozmdt0(xN))
| ( tptp_fun_W1_4(szszuzczcdt0(xk)) = sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ( szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xk))) != szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) ) ),
inference(modus_ponens,[status(thm)],[193,192]) ).
tff(195,plain,
( ~ aElementOf0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))),szDzozmdt0(xN))
| ( tptp_fun_W1_4(szszuzczcdt0(xk)) = sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) ) ),
inference(unit_resolution,[status(thm)],[194,56,34,188]) ).
tff(196,plain,
tptp_fun_W1_4(szszuzczcdt0(xk)) = sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))),
inference(unit_resolution,[status(thm)],[195,146]) ).
tff(197,plain,
sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) = tptp_fun_W1_4(szszuzczcdt0(xk)),
inference(symmetry,[status(thm)],[196]) ).
tff(198,plain,
sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) = xk,
inference(transitivity,[status(thm)],[197,64]) ).
tff(199,plain,
( ( sbrdtbr0(xP) != xk )
<=> ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != xk ) ),
inference(rewrite,[status(thm)],]) ).
tff(200,plain,
( ( sbrdtbr0(xP) != xk )
<=> ( sbrdtbr0(xP) != xk ) ),
inference(rewrite,[status(thm)],]) ).
tff(201,axiom,
sbrdtbr0(xP) != xk,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(202,plain,
sbrdtbr0(xP) != xk,
inference(modus_ponens,[status(thm)],[201,200]) ).
tff(203,plain,
sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != xk,
inference(modus_ponens,[status(thm)],[202,199]) ).
tff(204,plain,
$false,
inference(unit_resolution,[status(thm)],[203,198]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM611+3 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n005.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 Sep 2 12:21:18 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 3.56/2.55 % SZS status Theorem
% 3.56/2.55 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------