TSTP Solution File: NUM612+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM612+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n020.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 13:10:54 EDT 2022
% Result : Theorem 3.06s 2.31s
% Output : Proof 3.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 76
% Syntax : Number of formulae : 159 ( 35 unt; 20 typ; 0 def)
% Number of atoms : 797 ( 106 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 1040 ( 423 ~; 385 |; 77 &)
% ( 118 <=>; 37 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 41 ( 41 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 17 ( 12 >; 5 *; 0 +; 0 <<)
% Number of predicates : 14 ( 12 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 8 con; 0-2 aty)
% Number of variables : 218 ( 205 !; 0 ?; 218 :)
% Comments :
%------------------------------------------------------------------------------
tff(isFinite0_type,type,
isFinite0: $i > $o ).
tff(sdtmndt0_type,type,
sdtmndt0: ( $i * $i ) > $i ).
tff(szmzizndt0_type,type,
szmzizndt0: $i > $i ).
tff(xQ_type,type,
xQ: $i ).
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(szDzozmdt0_type,type,
szDzozmdt0: $i > $i ).
tff(xN_type,type,
xN: $i ).
tff(sbrdtbr0_type,type,
sbrdtbr0: $i > $i ).
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(szNzAzT0_type,type,
szNzAzT0: $i ).
tff(aSubsetOf0_type,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff(xO_type,type,
xO: $i ).
tff(xK_type,type,
xK: $i ).
tff(slbdtsldtrb0_type,type,
slbdtsldtrb0: ( $i * $i ) > $i ).
tff(szszuzczcdt0_type,type,
szszuzczcdt0: $i > $i ).
tff(xk_type,type,
xk: $i ).
tff(xp_type,type,
xp: $i ).
tff(1,plain,
( aSet0(xP)
<=> aSet0(sdtmndt0(xQ,szmzizndt0(xQ))) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( aSet0(xP)
<=> aSet0(xP) ),
inference(rewrite,[status(thm)],]) ).
tff(3,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(4,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)],[3]) ).
tff(5,plain,
( aSet0(xP)
& ! [W0: $i] :
( aElementOf0(W0,xQ)
=> sdtlseqdt0(szmzizndt0(xQ),W0) ) ),
inference(and_elim,[status(thm)],[4]) ).
tff(6,plain,
aSet0(xP),
inference(and_elim,[status(thm)],[5]) ).
tff(7,plain,
aSet0(xP),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
aSet0(sdtmndt0(xQ,szmzizndt0(xQ))),
inference(modus_ponens,[status(thm)],[7,1]) ).
tff(9,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(10,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)],[9]) ).
tff(11,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(12,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)],[11]) ).
tff(13,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(14,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(15,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)],[14]) ).
tff(16,axiom,
! [W0: $i] :
( aSet0(W0)
=> ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardNum) ).
tff(17,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) ),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) ),
inference(modus_ponens,[status(thm)],[17,13]) ).
tff(19,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szDzozmdt0(xN))
<=> isFinite0(W0) ) ),
inference(modus_ponens,[status(thm)],[18,12]) ).
tff(20,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szDzozmdt0(xN))
<=> isFinite0(W0) ) ),
inference(skolemize,[status(sab)],[19]) ).
tff(21,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szDzozmdt0(xN))
<=> isFinite0(W0) ) ),
inference(modus_ponens,[status(thm)],[20,10]) ).
tff(22,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(23,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(24,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)],[23,22]) ).
tff(25,plain,
( aElementOf0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))),szDzozmdt0(xN))
<=> isFinite0(sdtmndt0(xQ,szmzizndt0(xQ))) ),
inference(unit_resolution,[status(thm)],[24,21,8]) ).
tff(26,plain,
( aSet0(xQ)
<=> aSet0(xQ) ),
inference(rewrite,[status(thm)],]) ).
tff(27,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(28,plain,
( aSet0(xQ)
& ! [W0: $i] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,xO) )
& aSubsetOf0(xQ,xO)
& ( sbrdtbr0(xQ) = xK ) ),
inference(and_elim,[status(thm)],[27]) ).
tff(29,plain,
( aSet0(xQ)
& ! [W0: $i] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,xO) )
& aSubsetOf0(xQ,xO) ),
inference(and_elim,[status(thm)],[28]) ).
tff(30,plain,
( aSet0(xQ)
& ! [W0: $i] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,xO) ) ),
inference(and_elim,[status(thm)],[29]) ).
tff(31,plain,
aSet0(xQ),
inference(and_elim,[status(thm)],[30]) ).
tff(32,plain,
aSet0(xQ),
inference(modus_ponens,[status(thm)],[31,26]) ).
tff(33,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(34,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(35,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)],[34,33]) ).
tff(36,plain,
( aElementOf0(sbrdtbr0(xQ),szDzozmdt0(xN))
<=> isFinite0(xQ) ),
inference(unit_resolution,[status(thm)],[35,21,32]) ).
tff(37,plain,
( ( sbrdtbr0(xQ) = xK )
<=> ( sbrdtbr0(xQ) = szszuzczcdt0(xk) ) ),
inference(rewrite,[status(thm)],]) ).
tff(38,plain,
( ( sbrdtbr0(xQ) = xK )
<=> ( sbrdtbr0(xQ) = xK ) ),
inference(rewrite,[status(thm)],]) ).
tff(39,plain,
sbrdtbr0(xQ) = xK,
inference(and_elim,[status(thm)],[28]) ).
tff(40,plain,
sbrdtbr0(xQ) = xK,
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
sbrdtbr0(xQ) = szszuzczcdt0(xk),
inference(modus_ponens,[status(thm)],[40,37]) ).
tff(42,plain,
( aElementOf0(sbrdtbr0(xQ),szDzozmdt0(xN))
<=> aElementOf0(szszuzczcdt0(xk),szDzozmdt0(xN)) ),
inference(monotonicity,[status(thm)],[41]) ).
tff(43,plain,
( aElementOf0(szszuzczcdt0(xk),szDzozmdt0(xN))
<=> aElementOf0(sbrdtbr0(xQ),szDzozmdt0(xN)) ),
inference(symmetry,[status(thm)],[42]) ).
tff(44,plain,
( aElementOf0(xK,szNzAzT0)
<=> aElementOf0(szszuzczcdt0(xk),szDzozmdt0(xN)) ),
inference(rewrite,[status(thm)],]) ).
tff(45,plain,
( aElementOf0(xK,szNzAzT0)
<=> aElementOf0(xK,szNzAzT0) ),
inference(rewrite,[status(thm)],]) ).
tff(46,axiom,
aElementOf0(xK,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3418) ).
tff(47,plain,
aElementOf0(xK,szNzAzT0),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
aElementOf0(szszuzczcdt0(xk),szDzozmdt0(xN)),
inference(modus_ponens,[status(thm)],[47,44]) ).
tff(49,plain,
aElementOf0(sbrdtbr0(xQ),szDzozmdt0(xN)),
inference(modus_ponens,[status(thm)],[48,43]) ).
tff(50,plain,
( ~ ( aElementOf0(sbrdtbr0(xQ),szDzozmdt0(xN))
<=> isFinite0(xQ) )
| ~ aElementOf0(sbrdtbr0(xQ),szDzozmdt0(xN))
| isFinite0(xQ) ),
inference(tautology,[status(thm)],]) ).
tff(51,plain,
isFinite0(xQ),
inference(unit_resolution,[status(thm)],[50,49,36]) ).
tff(52,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(53,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)],[52]) ).
tff(54,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(55,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)],[54]) ).
tff(56,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)],[55,53]) ).
tff(57,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(58,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)],[57]) ).
tff(59,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(60,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(61,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)],[60]) ).
tff(62,axiom,
! [W0: $i] :
( ( aSet0(W0)
& isFinite0(W0) )
=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
=> isFinite0(W1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubFSet) ).
tff(63,plain,
! [W0: $i] :
( ~ ( aSet0(W0)
& isFinite0(W0) )
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
! [W0: $i] :
( ~ ( aSet0(W0)
& isFinite0(W0) )
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[63,59]) ).
tff(65,plain,
! [W0: $i] :
( ~ ( aSet0(W0)
& isFinite0(W0) )
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) ),
inference(skolemize,[status(sab)],[64]) ).
tff(66,plain,
! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[65,58]) ).
tff(67,plain,
! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[66,56]) ).
tff(68,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(69,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(70,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)],[69]) ).
tff(71,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)],[70,68]) ).
tff(72,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(73,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)],[72,71]) ).
tff(74,plain,
( ~ isFinite0(xQ)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,xQ) ) ),
inference(unit_resolution,[status(thm)],[73,67,32]) ).
tff(75,plain,
! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,xQ) ),
inference(unit_resolution,[status(thm)],[74,51]) ).
tff(76,plain,
( aSubsetOf0(xP,xQ)
<=> aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ) ),
inference(rewrite,[status(thm)],]) ).
tff(77,plain,
( aSubsetOf0(xP,xQ)
<=> aSubsetOf0(xP,xQ) ),
inference(rewrite,[status(thm)],]) ).
tff(78,axiom,
( ! [W0: $i] :
( aElementOf0(W0,xP)
=> aElementOf0(W0,xQ) )
& aSubsetOf0(xP,xQ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5195) ).
tff(79,plain,
aSubsetOf0(xP,xQ),
inference(and_elim,[status(thm)],[78]) ).
tff(80,plain,
aSubsetOf0(xP,xQ),
inference(modus_ponens,[status(thm)],[79,77]) ).
tff(81,plain,
aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ),
inference(modus_ponens,[status(thm)],[80,76]) ).
tff(82,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(83,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(84,plain,
( ~ ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,xQ) )
| isFinite0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ) ),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
isFinite0(sdtmndt0(xQ,szmzizndt0(xQ))),
inference(unit_resolution,[status(thm)],[84,81,75]) ).
tff(86,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(87,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)],[86]) ).
tff(88,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(89,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)],[88]) ).
tff(90,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)],[89,87]) ).
tff(91,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(92,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)],[91]) ).
tff(93,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(94,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(95,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)],[94]) ).
tff(96,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(97,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ ( isFinite0(W0)
& aElementOf0(W1,W0) )
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) ) ) ),
inference(modus_ponens,[status(thm)],[96,95]) ).
tff(98,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ ( isFinite0(W0)
& aElementOf0(W1,W0) )
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) ) ) ),
inference(modus_ponens,[status(thm)],[97,93]) ).
tff(99,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ ( isFinite0(W0)
& aElementOf0(W1,W0) )
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) ) ) ),
inference(skolemize,[status(sab)],[98]) ).
tff(100,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) )
| ~ isFinite0(W0) ) ),
inference(modus_ponens,[status(thm)],[99,92]) ).
tff(101,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) )
| ~ isFinite0(W0) ) ),
inference(modus_ponens,[status(thm)],[100,90]) ).
tff(102,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(103,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(104,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)],[103]) ).
tff(105,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)],[104,102]) ).
tff(106,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(107,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)],[106,105]) ).
tff(108,plain,
! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| ~ isFinite0(xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,W1))) = sbrdtbr0(xQ) ) ),
inference(unit_resolution,[status(thm)],[107,101,32]) ).
tff(109,plain,
( aElementOf0(xp,xQ)
<=> aElementOf0(szmzizndt0(xQ),xQ) ),
inference(rewrite,[status(thm)],]) ).
tff(110,plain,
( aElementOf0(xp,xQ)
<=> aElementOf0(xp,xQ) ),
inference(rewrite,[status(thm)],]) ).
tff(111,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(112,plain,
( aElementOf0(xp,xQ)
& ! [W0: $i] :
( aElementOf0(W0,xQ)
=> sdtlseqdt0(xp,W0) ) ),
inference(and_elim,[status(thm)],[111]) ).
tff(113,plain,
aElementOf0(xp,xQ),
inference(and_elim,[status(thm)],[112]) ).
tff(114,plain,
aElementOf0(xp,xQ),
inference(modus_ponens,[status(thm)],[113,110]) ).
tff(115,plain,
aElementOf0(szmzizndt0(xQ),xQ),
inference(modus_ponens,[status(thm)],[114,109]) ).
tff(116,plain,
( ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| ~ isFinite0(xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,W1))) = sbrdtbr0(xQ) ) )
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) = sbrdtbr0(xQ) )
| ~ isFinite0(xQ)
| ~ aElementOf0(szmzizndt0(xQ),xQ) )
<=> ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| ~ isFinite0(xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,W1))) = sbrdtbr0(xQ) ) )
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) = sbrdtbr0(xQ) )
| ~ isFinite0(xQ)
| ~ aElementOf0(szmzizndt0(xQ),xQ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(117,plain,
( ( ~ aElementOf0(szmzizndt0(xQ),xQ)
| ~ isFinite0(xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) = sbrdtbr0(xQ) ) )
<=> ( ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) = sbrdtbr0(xQ) )
| ~ isFinite0(xQ)
| ~ aElementOf0(szmzizndt0(xQ),xQ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(118,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) ) )
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) = sbrdtbr0(xQ) )
| ~ isFinite0(xQ)
| ~ aElementOf0(szmzizndt0(xQ),xQ) ) ),
inference(monotonicity,[status(thm)],[117]) ).
tff(119,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) ) )
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) = sbrdtbr0(xQ) )
| ~ isFinite0(xQ)
| ~ aElementOf0(szmzizndt0(xQ),xQ) ) ),
inference(transitivity,[status(thm)],[118,116]) ).
tff(120,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(121,plain,
( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| ~ isFinite0(xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,W1))) = sbrdtbr0(xQ) ) )
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) = sbrdtbr0(xQ) )
| ~ isFinite0(xQ)
| ~ aElementOf0(szmzizndt0(xQ),xQ) ),
inference(modus_ponens,[status(thm)],[120,119]) ).
tff(122,plain,
( ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) = sbrdtbr0(xQ) )
| ~ isFinite0(xQ) ),
inference(unit_resolution,[status(thm)],[121,115,108]) ).
tff(123,plain,
szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) = sbrdtbr0(xQ),
inference(unit_resolution,[status(thm)],[122,51]) ).
tff(124,plain,
szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) = szszuzczcdt0(xk),
inference(transitivity,[status(thm)],[123,41]) ).
tff(125,plain,
( ~ ~ ( ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) != szszuzczcdt0(xk) )
| ~ aElementOf0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))),szDzozmdt0(xN)) )
<=> ( ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) != szszuzczcdt0(xk) )
| ~ aElementOf0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))),szDzozmdt0(xN)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(126,plain,
( ( ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) = szszuzczcdt0(xk) )
& aElementOf0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))),szDzozmdt0(xN)) )
<=> ~ ( ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) != szszuzczcdt0(xk) )
| ~ aElementOf0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))),szDzozmdt0(xN)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(127,plain,
( ~ ( ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) = szszuzczcdt0(xk) )
& aElementOf0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))),szDzozmdt0(xN)) )
<=> ~ ~ ( ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) != szszuzczcdt0(xk) )
| ~ aElementOf0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))),szDzozmdt0(xN)) ) ),
inference(monotonicity,[status(thm)],[126]) ).
tff(128,plain,
( ~ ( ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) = szszuzczcdt0(xk) )
& aElementOf0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))),szDzozmdt0(xN)) )
<=> ( ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) != szszuzczcdt0(xk) )
| ~ aElementOf0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))),szDzozmdt0(xN)) ) ),
inference(transitivity,[status(thm)],[127,125]) ).
tff(129,plain,
( ~ ( ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) = sbrdtbr0(xQ) )
& aElementOf0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))),szDzozmdt0(xN)) )
<=> ~ ( ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) = szszuzczcdt0(xk) )
& aElementOf0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))),szDzozmdt0(xN)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(130,plain,
( ~ ( ( szszuzczcdt0(sbrdtbr0(xP)) = sbrdtbr0(xQ) )
& aElementOf0(sbrdtbr0(xP),szNzAzT0) )
<=> ~ ( ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) = sbrdtbr0(xQ) )
& aElementOf0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))),szDzozmdt0(xN)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(131,plain,
( ~ ( ( szszuzczcdt0(sbrdtbr0(xP)) = sbrdtbr0(xQ) )
& aElementOf0(sbrdtbr0(xP),szNzAzT0) )
<=> ~ ( ( szszuzczcdt0(sbrdtbr0(xP)) = sbrdtbr0(xQ) )
& aElementOf0(sbrdtbr0(xP),szNzAzT0) ) ),
inference(rewrite,[status(thm)],]) ).
tff(132,axiom,
~ ( ( szszuzczcdt0(sbrdtbr0(xP)) = sbrdtbr0(xQ) )
& aElementOf0(sbrdtbr0(xP),szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(133,plain,
~ ( ( szszuzczcdt0(sbrdtbr0(xP)) = sbrdtbr0(xQ) )
& aElementOf0(sbrdtbr0(xP),szNzAzT0) ),
inference(modus_ponens,[status(thm)],[132,131]) ).
tff(134,plain,
~ ( ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) = sbrdtbr0(xQ) )
& aElementOf0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))),szDzozmdt0(xN)) ),
inference(modus_ponens,[status(thm)],[133,130]) ).
tff(135,plain,
~ ( ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) = szszuzczcdt0(xk) )
& aElementOf0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))),szDzozmdt0(xN)) ),
inference(modus_ponens,[status(thm)],[134,129]) ).
tff(136,plain,
( ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) != szszuzczcdt0(xk) )
| ~ aElementOf0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))),szDzozmdt0(xN)) ),
inference(modus_ponens,[status(thm)],[135,128]) ).
tff(137,plain,
~ aElementOf0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))),szDzozmdt0(xN)),
inference(unit_resolution,[status(thm)],[136,124]) ).
tff(138,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(139,plain,
$false,
inference(unit_resolution,[status(thm)],[138,137,85,25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM612+3 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n020.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Sep 2 12:23:44 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.20/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.20/0.35 Usage: tptp [options] [-file:]file
% 0.20/0.35 -h, -? prints this message.
% 0.20/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.20/0.35 -m, -model generate model.
% 0.20/0.35 -p, -proof generate proof.
% 0.20/0.35 -c, -core generate unsat core of named formulas.
% 0.20/0.35 -st, -statistics display statistics.
% 0.20/0.35 -t:timeout set timeout (in second).
% 0.20/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.20/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.20/0.35 -<param>:<value> configuration parameter and value.
% 0.20/0.35 -o:<output-file> file to place output in.
% 3.06/2.31 % SZS status Theorem
% 3.06/2.31 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------