%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM548+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:21:21 AM UTC 2025
% Result : Theorem 0.23s 0.45s
% Output : Proof 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 14
% Syntax : Number of formulae : 37 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 121 ( 6 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 115 ( 33 ~; 27 |; 10 &)
% ( 38 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 2 ( 2 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 21 ( 19 !; 0 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(szNzAzT0_type,type,
szNzAzT0: $i ).
tff(sbrdtbr0_type,type,
sbrdtbr0: $i > $i ).
tff(xQ_type,type,
xQ: $i ).
tff(xk_type,type,
xk: $i ).
tff(aSubsetOf0_type,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff(xS_type,type,
xS: $i ).
tff(aSet0_type,type,
aSet0: $i > $o ).
tff(slbdtsldtrb0_type,type,
slbdtsldtrb0: ( $i * $i ) > $i ).
tff(isFinite0_type,type,
isFinite0: $i > $o ).
tff(1,plain,
( ( sbrdtbr0(xQ) = xk )
<=> ( sbrdtbr0(xQ) = xk ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
( aSet0(xQ)
& ! [W0: $i] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,xS) )
& aSubsetOf0(xQ,xS)
& ( sbrdtbr0(xQ) = xk )
& aElementOf0(xQ,slbdtsldtrb0(xS,xk)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2270) ).
tff(3,plain,
( aSet0(xQ)
& ! [W0: $i] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,xS) )
& aSubsetOf0(xQ,xS)
& ( sbrdtbr0(xQ) = xk ) ),
inference(and_elim,[status(thm)],[2]) ).
tff(4,plain,
sbrdtbr0(xQ) = xk,
inference(and_elim,[status(thm)],[3]) ).
tff(5,plain,
sbrdtbr0(xQ) = xk,
inference(modus_ponens,[status(thm)],[4,1]) ).
tff(6,plain,
( aElementOf0(sbrdtbr0(xQ),szNzAzT0)
<=> aElementOf0(xk,szNzAzT0) ),
inference(monotonicity,[status(thm)],[5]) ).
tff(7,plain,
( aElementOf0(xk,szNzAzT0)
<=> aElementOf0(sbrdtbr0(xQ),szNzAzT0) ),
inference(symmetry,[status(thm)],[6]) ).
tff(8,plain,
( aElementOf0(xk,szNzAzT0)
<=> aElementOf0(xk,szNzAzT0) ),
inference(rewrite,[status(thm)],[]) ).
tff(9,axiom,
aElementOf0(xk,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2202) ).
tff(10,plain,
aElementOf0(xk,szNzAzT0),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
aElementOf0(sbrdtbr0(xQ),szNzAzT0),
inference(modus_ponens,[status(thm)],[10,7]) ).
tff(12,plain,
( aSet0(xQ)
<=> aSet0(xQ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,plain,
( aSet0(xQ)
& ! [W0: $i] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,xS) )
& aSubsetOf0(xQ,xS) ),
inference(and_elim,[status(thm)],[3]) ).
tff(14,plain,
( aSet0(xQ)
& ! [W0: $i] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,xS) ) ),
inference(and_elim,[status(thm)],[13]) ).
tff(15,plain,
aSet0(xQ),
inference(and_elim,[status(thm)],[14]) ).
tff(16,plain,
aSet0(xQ),
inference(modus_ponens,[status(thm)],[15,12]) ).
tff(17,plain,
^ [W0: $i] :
refl(( ( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) )
<=> ( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(18,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)],[17]) ).
tff(19,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(20,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(21,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)],[20]) ).
tff(22,axiom,
! [W0: $i] :
( aSet0(W0)
=> ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCardNum) ).
tff(23,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) ),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) ),
inference(skolemize,[status(sab)],[24]) ).
tff(26,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) ),
inference(modus_ponens,[status(thm)],[25,18]) ).
tff(27,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) )
| ~ aSet0(xQ)
| ( aElementOf0(sbrdtbr0(xQ),szNzAzT0)
<=> isFinite0(xQ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) )
| ~ aSet0(xQ)
| ( aElementOf0(sbrdtbr0(xQ),szNzAzT0)
<=> isFinite0(xQ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(28,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) )
| ~ aSet0(xQ)
| ( aElementOf0(sbrdtbr0(xQ),szNzAzT0)
<=> isFinite0(xQ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(29,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) )
| ~ aSet0(xQ)
| ( aElementOf0(sbrdtbr0(xQ),szNzAzT0)
<=> isFinite0(xQ) ) ),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
( aElementOf0(sbrdtbr0(xQ),szNzAzT0)
<=> isFinite0(xQ) ),
inference(unit_resolution,[status(thm)],[29,26,16]) ).
tff(31,plain,
( ~ isFinite0(xQ)
<=> ~ isFinite0(xQ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,axiom,
~ isFinite0(xQ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(33,plain,
~ isFinite0(xQ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
( ~ ( aElementOf0(sbrdtbr0(xQ),szNzAzT0)
<=> isFinite0(xQ) )
| ~ aElementOf0(sbrdtbr0(xQ),szNzAzT0)
| isFinite0(xQ) ),
inference(tautology,[status(thm)],[]) ).
tff(35,plain,
( ~ ( aElementOf0(sbrdtbr0(xQ),szNzAzT0)
<=> isFinite0(xQ) )
| ~ aElementOf0(sbrdtbr0(xQ),szNzAzT0) ),
inference(unit_resolution,[status(thm)],[34,33]) ).
tff(36,plain,
~ aElementOf0(sbrdtbr0(xQ),szNzAzT0),
inference(unit_resolution,[status(thm)],[35,30]) ).
tff(37,plain,
$false,
inference(unit_resolution,[status(thm)],[36,11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : NUM548+3 : TPTP v9.0.0. Released v4.0.0.
% 0.04/0.14 % Command : run_E %s %d THM
% 0.15/0.36 % Computer : n015.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri Jun 20 01:24:41 EDT 2025
% 0.22/0.37 % CPUTime :
% 0.23/0.45 % SZS status Theorem
% 0.23/0.45 % SZS output start Proof
% See solution above
% 0.23/0.45 % E exiting
%------------------------------------------------------------------------------