TSTP Solution File: NUM551+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM551+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n016.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 13:10:27 EDT 2022
% Result : Theorem 0.13s 0.36s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 43
% Syntax : Number of formulae : 93 ( 20 unt; 11 typ; 0 def)
% Number of atoms : 503 ( 94 equ)
% Maximal formula atoms : 12 ( 6 avg)
% Number of connectives : 812 ( 426 ~; 271 |; 51 &)
% ( 52 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 35 ( 35 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 7 >; 1 *; 0 +; 0 <<)
% Number of predicates : 13 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-1 aty)
% Number of variables : 165 ( 132 !; 20 ?; 165 :)
% Comments :
%------------------------------------------------------------------------------
tff(aElement0_type,type,
aElement0: $i > $o ).
tff(tptp_fun_W1_0_type,type,
tptp_fun_W1_0: $i > $i ).
tff(xQ_type,type,
xQ: $i ).
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(slbdtrb0_type,type,
slbdtrb0: $i > $i ).
tff(sz00_type,type,
sz00: $i ).
tff(aSet0_type,type,
aSet0: $i > $o ).
tff(slcrc0_type,type,
slcrc0: $i ).
tff(isFinite0_type,type,
isFinite0: $i > $o ).
tff(xk_type,type,
xk: $i ).
tff(sbrdtbr0_type,type,
sbrdtbr0: $i > $i ).
tff(1,plain,
^ [W0: $i] :
rewrite(
( ~ ( ~ ( ( W0 != slbdtrb0(sz00) )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ~ aSet0(W0)
| ( W0 = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ~ ( ~ ( ~ aSet0(W0)
| ( W0 = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(W0),W0) )
| ~ ( ( W0 != slbdtrb0(sz00) )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [W0: $i] :
~ ( ~ ( ( W0 != slbdtrb0(sz00) )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ~ aSet0(W0)
| ( W0 = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ! [W0: $i] :
~ ( ~ ( ~ aSet0(W0)
| ( W0 = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(W0),W0) )
| ~ ( ( W0 != slbdtrb0(sz00) )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [W0: $i] :
refl(
( ~ ( ~ ( ( W0 != slbdtrb0(sz00) )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ~ aSet0(W0)
| ( W0 = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ~ ( ~ ( ( W0 != slbdtrb0(sz00) )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ~ aSet0(W0)
| ( W0 = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) )),
inference(bind,[status(th)],]) ).
tff(4,plain,
( ! [W0: $i] :
~ ( ~ ( ( W0 != slbdtrb0(sz00) )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ~ aSet0(W0)
| ( W0 = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ! [W0: $i] :
~ ( ~ ( ( W0 != slbdtrb0(sz00) )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ~ aSet0(W0)
| ( W0 = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
^ [W0: $i] :
rewrite(
( ~ ( ~ ( ( W0 != slbdtrb0(sz00) )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ~ aSet0(W0)
| ( W0 = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ~ ( ~ ( ( W0 != slbdtrb0(sz00) )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ~ aSet0(W0)
| ( W0 = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) )),
inference(bind,[status(th)],]) ).
tff(6,plain,
( ! [W0: $i] :
~ ( ~ ( ( W0 != slbdtrb0(sz00) )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ~ aSet0(W0)
| ( W0 = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ! [W0: $i] :
~ ( ~ ( ( W0 != slbdtrb0(sz00) )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ~ aSet0(W0)
| ( W0 = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) ),
inference(quant_intro,[status(thm)],[5]) ).
tff(7,plain,
( ! [W0: $i] :
~ ( ~ ( ( W0 != slbdtrb0(sz00) )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ~ aSet0(W0)
| ( W0 = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ! [W0: $i] :
~ ( ~ ( ( W0 != slbdtrb0(sz00) )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ~ aSet0(W0)
| ( W0 = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) ),
inference(transitivity,[status(thm)],[6,4]) ).
tff(8,plain,
^ [W0: $i] :
trans(
monotonicity(
rewrite(
( ( ( W0 != slbdtrb0(sz00) )
| ( aSet0(W0)
& ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
<=> ( ( W0 != slbdtrb0(sz00) )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) ) )),
( ( ( ( W0 != slbdtrb0(sz00) )
| ( aSet0(W0)
& ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ~ aSet0(W0)
| ( W0 = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ( ( ( W0 != slbdtrb0(sz00) )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ~ aSet0(W0)
| ( W0 = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) )),
rewrite(
( ( ( ( W0 != slbdtrb0(sz00) )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ~ aSet0(W0)
| ( W0 = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ~ ( ~ ( ( W0 != slbdtrb0(sz00) )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ~ aSet0(W0)
| ( W0 = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) )),
( ( ( ( W0 != slbdtrb0(sz00) )
| ( aSet0(W0)
& ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ~ aSet0(W0)
| ( W0 = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ~ ( ~ ( ( W0 != slbdtrb0(sz00) )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ~ aSet0(W0)
| ( W0 = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) )),
inference(bind,[status(th)],]) ).
tff(9,plain,
( ! [W0: $i] :
( ( ( W0 != slbdtrb0(sz00) )
| ( aSet0(W0)
& ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ~ aSet0(W0)
| ( W0 = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ! [W0: $i] :
~ ( ~ ( ( W0 != slbdtrb0(sz00) )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ~ aSet0(W0)
| ( W0 = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
^ [W0: $i] :
rewrite(
( ( ( ( W0 != slbdtrb0(sz00) )
| ( aSet0(W0)
& ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ( W0 = slbdtrb0(sz00) )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ( ( ( W0 != slbdtrb0(sz00) )
| ( aSet0(W0)
& ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ~ aSet0(W0)
| ( W0 = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [W0: $i] :
( ( ( W0 != slbdtrb0(sz00) )
| ( aSet0(W0)
& ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ( W0 = slbdtrb0(sz00) )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ! [W0: $i] :
( ( ( W0 != slbdtrb0(sz00) )
| ( aSet0(W0)
& ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ~ aSet0(W0)
| ( W0 = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
^ [W0: $i] :
rewrite(
( ( ( W0 = slcrc0 )
<=> ( aSet0(W0)
& ~ ? [W1: $i] : aElementOf0(W1,W0) ) )
<=> ( ( W0 = slbdtrb0(sz00) )
<=> ( aSet0(W0)
& ~ ? [W1: $i] : aElementOf0(W1,W0) ) ) )),
inference(bind,[status(th)],]) ).
tff(13,plain,
( ! [W0: $i] :
( ( W0 = slcrc0 )
<=> ( aSet0(W0)
& ~ ? [W1: $i] : aElementOf0(W1,W0) ) )
<=> ! [W0: $i] :
( ( W0 = slbdtrb0(sz00) )
<=> ( aSet0(W0)
& ~ ? [W1: $i] : aElementOf0(W1,W0) ) ) ),
inference(quant_intro,[status(thm)],[12]) ).
tff(14,plain,
( ! [W0: $i] :
( ( W0 = slcrc0 )
<=> ( aSet0(W0)
& ~ ? [W1: $i] : aElementOf0(W1,W0) ) )
<=> ! [W0: $i] :
( ( W0 = slcrc0 )
<=> ( aSet0(W0)
& ~ ? [W1: $i] : aElementOf0(W1,W0) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(15,axiom,
! [W0: $i] :
( ( W0 = slcrc0 )
<=> ( aSet0(W0)
& ~ ? [W1: $i] : aElementOf0(W1,W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefEmp) ).
tff(16,plain,
! [W0: $i] :
( ( W0 = slcrc0 )
<=> ( aSet0(W0)
& ~ ? [W1: $i] : aElementOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [W0: $i] :
( ( W0 = slbdtrb0(sz00) )
<=> ( aSet0(W0)
& ~ ? [W1: $i] : aElementOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[16,13]) ).
tff(18,plain,
! [W0: $i] :
( ( ( W0 != slbdtrb0(sz00) )
| ( aSet0(W0)
& ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ( W0 = slbdtrb0(sz00) )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [W0: $i] :
( ( ( W0 != slbdtrb0(sz00) )
| ( aSet0(W0)
& ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ~ aSet0(W0)
| ( W0 = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ),
inference(modus_ponens,[status(thm)],[18,11]) ).
tff(20,plain,
! [W0: $i] :
~ ( ~ ( ( W0 != slbdtrb0(sz00) )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ~ aSet0(W0)
| ( W0 = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ),
inference(modus_ponens,[status(thm)],[19,9]) ).
tff(21,plain,
! [W0: $i] :
~ ( ~ ( ( W0 != slbdtrb0(sz00) )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ~ aSet0(W0)
| ( W0 = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ),
inference(modus_ponens,[status(thm)],[20,7]) ).
tff(22,plain,
! [W0: $i] :
~ ( ~ ( ~ aSet0(W0)
| ( W0 = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(W0),W0) )
| ~ ( ( W0 != slbdtrb0(sz00) )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) ) ),
inference(modus_ponens,[status(thm)],[21,2]) ).
tff(23,plain,
( ~ ! [W0: $i] :
~ ( ~ ( ~ aSet0(W0)
| ( W0 = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(W0),W0) )
| ~ ( ( W0 != slbdtrb0(sz00) )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) ) )
| ~ ( ~ ( ~ aSet0(xQ)
| ( xQ = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(xQ),xQ) )
| ~ ( ( xQ != slbdtrb0(sz00) )
| ~ ( ~ aSet0(xQ)
| ~ ! [W1: $i] : ~ aElementOf0(W1,xQ) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(24,plain,
~ ( ~ ( ~ aSet0(xQ)
| ( xQ = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(xQ),xQ) )
| ~ ( ( xQ != slbdtrb0(sz00) )
| ~ ( ~ aSet0(xQ)
| ~ ! [W1: $i] : ~ aElementOf0(W1,xQ) ) ) ),
inference(unit_resolution,[status(thm)],[23,22]) ).
tff(25,plain,
( ~ ( ~ aSet0(xQ)
| ( xQ = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(xQ),xQ) )
| ~ ( ( xQ != slbdtrb0(sz00) )
| ~ ( ~ aSet0(xQ)
| ~ ! [W1: $i] : ~ aElementOf0(W1,xQ) ) )
| ~ aSet0(xQ)
| ( xQ = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(xQ),xQ) ),
inference(tautology,[status(thm)],]) ).
tff(26,plain,
( ~ aSet0(xQ)
| ( xQ = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(xQ),xQ) ),
inference(unit_resolution,[status(thm)],[25,24]) ).
tff(27,plain,
( ( xQ != slcrc0 )
<=> ( xQ != slbdtrb0(sz00) ) ),
inference(rewrite,[status(thm)],]) ).
tff(28,plain,
( ( xQ != slcrc0 )
<=> ( xQ != slcrc0 ) ),
inference(rewrite,[status(thm)],]) ).
tff(29,axiom,
xQ != slcrc0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2313) ).
tff(30,plain,
xQ != slcrc0,
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
xQ != slbdtrb0(sz00),
inference(modus_ponens,[status(thm)],[30,27]) ).
tff(32,plain,
( aSet0(xQ)
<=> aSet0(xQ) ),
inference(rewrite,[status(thm)],]) ).
tff(33,axiom,
( aSet0(xQ)
& isFinite0(xQ)
& ( sbrdtbr0(xQ) = xk ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2291) ).
tff(34,plain,
( aSet0(xQ)
& isFinite0(xQ) ),
inference(and_elim,[status(thm)],[33]) ).
tff(35,plain,
aSet0(xQ),
inference(and_elim,[status(thm)],[34]) ).
tff(36,plain,
aSet0(xQ),
inference(modus_ponens,[status(thm)],[35,32]) ).
tff(37,plain,
( ~ ( ~ aSet0(xQ)
| ( xQ = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(xQ),xQ) )
| ~ aSet0(xQ)
| ( xQ = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(xQ),xQ) ),
inference(tautology,[status(thm)],]) ).
tff(38,plain,
( ~ ( ~ aSet0(xQ)
| ( xQ = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(xQ),xQ) )
| aElementOf0(tptp_fun_W1_0(xQ),xQ) ),
inference(unit_resolution,[status(thm)],[37,36,31]) ).
tff(39,plain,
aElementOf0(tptp_fun_W1_0(xQ),xQ),
inference(unit_resolution,[status(thm)],[38,26]) ).
tff(40,plain,
^ [W0: $i] :
refl(
( ( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) )),
inference(bind,[status(th)],]) ).
tff(41,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) ),
inference(quant_intro,[status(thm)],[40]) ).
tff(42,plain,
^ [W0: $i] :
rewrite(
( ( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) )),
inference(bind,[status(th)],]) ).
tff(43,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) ),
inference(quant_intro,[status(thm)],[42]) ).
tff(44,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) ),
inference(transitivity,[status(thm)],[43,41]) ).
tff(45,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(46,plain,
^ [W0: $i] :
trans(
monotonicity(
quant_intro(
proof_bind(
^ [W1: $i] :
rewrite(
( ( aElementOf0(W1,W0)
=> aElement0(W1) )
<=> ( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ))),
( ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElement0(W1) )
<=> ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )),
( ( aSet0(W0)
=> ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) )
<=> ( aSet0(W0)
=> ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) )),
rewrite(
( ( aSet0(W0)
=> ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) )),
( ( aSet0(W0)
=> ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) )),
inference(bind,[status(th)],]) ).
tff(47,plain,
( ! [W0: $i] :
( aSet0(W0)
=> ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) ),
inference(quant_intro,[status(thm)],[46]) ).
tff(48,axiom,
! [W0: $i] :
( aSet0(W0)
=> ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
tff(49,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[49,45]) ).
tff(51,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ),
inference(skolemize,[status(sab)],[50]) ).
tff(52,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[51,44]) ).
tff(53,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(xQ)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xQ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(xQ)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xQ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(54,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(xQ)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xQ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(55,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(xQ)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xQ) ) ),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xQ) ),
inference(unit_resolution,[status(thm)],[55,52,36]) ).
tff(57,plain,
( ( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xQ) )
| aElement0(tptp_fun_W1_0(xQ))
| ~ aElementOf0(tptp_fun_W1_0(xQ),xQ) )
<=> ( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xQ) )
| aElement0(tptp_fun_W1_0(xQ))
| ~ aElementOf0(tptp_fun_W1_0(xQ),xQ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(58,plain,
( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xQ) )
| aElement0(tptp_fun_W1_0(xQ))
| ~ aElementOf0(tptp_fun_W1_0(xQ),xQ) ),
inference(quant_inst,[status(thm)],]) ).
tff(59,plain,
( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xQ) )
| aElement0(tptp_fun_W1_0(xQ))
| ~ aElementOf0(tptp_fun_W1_0(xQ),xQ) ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
aElement0(tptp_fun_W1_0(xQ)),
inference(unit_resolution,[status(thm)],[59,56,39]) ).
tff(61,plain,
^ [W0: $i] :
refl(
( ( ~ aElement0(W0)
| ~ aElementOf0(W0,xQ) )
<=> ( ~ aElement0(W0)
| ~ aElementOf0(W0,xQ) ) )),
inference(bind,[status(th)],]) ).
tff(62,plain,
( ! [W0: $i] :
( ~ aElement0(W0)
| ~ aElementOf0(W0,xQ) )
<=> ! [W0: $i] :
( ~ aElement0(W0)
| ~ aElementOf0(W0,xQ) ) ),
inference(quant_intro,[status(thm)],[61]) ).
tff(63,plain,
^ [W0: $i] :
trans(
monotonicity(
rewrite(
( ( aElement0(W0)
& aElementOf0(W0,xQ) )
<=> ~ ( ~ aElement0(W0)
| ~ aElementOf0(W0,xQ) ) )),
( ~ ( aElement0(W0)
& aElementOf0(W0,xQ) )
<=> ~ ~ ( ~ aElement0(W0)
| ~ aElementOf0(W0,xQ) ) )),
rewrite(
( ~ ~ ( ~ aElement0(W0)
| ~ aElementOf0(W0,xQ) )
<=> ( ~ aElement0(W0)
| ~ aElementOf0(W0,xQ) ) )),
( ~ ( aElement0(W0)
& aElementOf0(W0,xQ) )
<=> ( ~ aElement0(W0)
| ~ aElementOf0(W0,xQ) ) )),
inference(bind,[status(th)],]) ).
tff(64,plain,
( ! [W0: $i] :
~ ( aElement0(W0)
& aElementOf0(W0,xQ) )
<=> ! [W0: $i] :
( ~ aElement0(W0)
| ~ aElementOf0(W0,xQ) ) ),
inference(quant_intro,[status(thm)],[63]) ).
tff(65,plain,
( ~ ? [W0: $i] :
( aElement0(W0)
& aElementOf0(W0,xQ) )
<=> ~ ? [W0: $i] :
( aElement0(W0)
& aElementOf0(W0,xQ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(66,axiom,
~ ? [W0: $i] :
( aElement0(W0)
& aElementOf0(W0,xQ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(67,plain,
~ ? [W0: $i] :
( aElement0(W0)
& aElementOf0(W0,xQ) ),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
~ ? [W0: $i] :
( aElement0(W0)
& aElementOf0(W0,xQ) ),
inference(modus_ponens,[status(thm)],[67,65]) ).
tff(69,plain,
~ ? [W0: $i] :
( aElement0(W0)
& aElementOf0(W0,xQ) ),
inference(modus_ponens,[status(thm)],[68,65]) ).
tff(70,plain,
~ ? [W0: $i] :
( aElement0(W0)
& aElementOf0(W0,xQ) ),
inference(modus_ponens,[status(thm)],[69,65]) ).
tff(71,plain,
~ ? [W0: $i] :
( aElement0(W0)
& aElementOf0(W0,xQ) ),
inference(modus_ponens,[status(thm)],[70,65]) ).
tff(72,plain,
~ ? [W0: $i] :
( aElement0(W0)
& aElementOf0(W0,xQ) ),
inference(modus_ponens,[status(thm)],[71,65]) ).
tff(73,plain,
~ ? [W0: $i] :
( aElement0(W0)
& aElementOf0(W0,xQ) ),
inference(modus_ponens,[status(thm)],[72,65]) ).
tff(74,plain,
~ ? [W0: $i] :
( aElement0(W0)
& aElementOf0(W0,xQ) ),
inference(modus_ponens,[status(thm)],[73,65]) ).
tff(75,plain,
^ [W0: $i] :
refl(
$oeq(
~ ( aElement0(W0)
& aElementOf0(W0,xQ) ),
~ ( aElement0(W0)
& aElementOf0(W0,xQ) ))),
inference(bind,[status(th)],]) ).
tff(76,plain,
! [W0: $i] :
~ ( aElement0(W0)
& aElementOf0(W0,xQ) ),
inference(nnf-neg,[status(sab)],[74,75]) ).
tff(77,plain,
! [W0: $i] :
( ~ aElement0(W0)
| ~ aElementOf0(W0,xQ) ),
inference(modus_ponens,[status(thm)],[76,64]) ).
tff(78,plain,
! [W0: $i] :
( ~ aElement0(W0)
| ~ aElementOf0(W0,xQ) ),
inference(modus_ponens,[status(thm)],[77,62]) ).
tff(79,plain,
( ( ~ ! [W0: $i] :
( ~ aElement0(W0)
| ~ aElementOf0(W0,xQ) )
| ~ aElement0(tptp_fun_W1_0(xQ))
| ~ aElementOf0(tptp_fun_W1_0(xQ),xQ) )
<=> ( ~ ! [W0: $i] :
( ~ aElement0(W0)
| ~ aElementOf0(W0,xQ) )
| ~ aElement0(tptp_fun_W1_0(xQ))
| ~ aElementOf0(tptp_fun_W1_0(xQ),xQ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(80,plain,
( ~ ! [W0: $i] :
( ~ aElement0(W0)
| ~ aElementOf0(W0,xQ) )
| ~ aElement0(tptp_fun_W1_0(xQ))
| ~ aElementOf0(tptp_fun_W1_0(xQ),xQ) ),
inference(quant_inst,[status(thm)],]) ).
tff(81,plain,
( ~ ! [W0: $i] :
( ~ aElement0(W0)
| ~ aElementOf0(W0,xQ) )
| ~ aElement0(tptp_fun_W1_0(xQ))
| ~ aElementOf0(tptp_fun_W1_0(xQ),xQ) ),
inference(modus_ponens,[status(thm)],[80,79]) ).
tff(82,plain,
$false,
inference(unit_resolution,[status(thm)],[81,78,39,60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.08 % Problem : NUM551+1 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.09 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.09/0.28 % Computer : n016.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 300
% 0.09/0.28 % DateTime : Fri Sep 2 12:03:35 EDT 2022
% 0.09/0.28 % CPUTime :
% 0.09/0.29 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.09/0.29 Usage: tptp [options] [-file:]file
% 0.09/0.29 -h, -? prints this message.
% 0.09/0.29 -smt2 print SMT-LIB2 benchmark.
% 0.09/0.29 -m, -model generate model.
% 0.09/0.29 -p, -proof generate proof.
% 0.09/0.29 -c, -core generate unsat core of named formulas.
% 0.09/0.29 -st, -statistics display statistics.
% 0.09/0.29 -t:timeout set timeout (in second).
% 0.09/0.29 -smt2status display status in smt2 format instead of SZS.
% 0.09/0.29 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.09/0.29 -<param>:<value> configuration parameter and value.
% 0.09/0.29 -o:<output-file> file to place output in.
% 0.13/0.36 % SZS status Theorem
% 0.13/0.36 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------