%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM550+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 05:21:22 AM UTC 2025
% Result : Theorem 0.19s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 16
% Syntax : Number of formulae : 50 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 168 ( 93 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 185 ( 69 ~; 38 |; 24 &)
% ( 47 <=>; 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 : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 39 ( 23 !; 14 ?; 39 :)
% Comments :
%------------------------------------------------------------------------------
tff(sz00_type,type,
sz00: $i ).
tff(xk_type,type,
xk: $i ).
tff(sbrdtbr0_type,type,
sbrdtbr0: $i > $i ).
tff(slcrc0_type,type,
slcrc0: $i ).
tff(aSet0_type,type,
aSet0: $i > $o ).
tff(xQ_type,type,
xQ: $i ).
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(xS_type,type,
xS: $i ).
tff(aSubsetOf0_type,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff(slbdtsldtrb0_type,type,
slbdtsldtrb0: ( $i * $i ) > $i ).
tff(xT_type,type,
xT: $i ).
tff(1,plain,
^ [W0: $i] :
refl(( ( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) )
<=> ( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,plain,
^ [W0: $i] :
rewrite(( ( aSet0(W0)
=> ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) )
<=> ( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [W0: $i] :
( aSet0(W0)
=> ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,axiom,
! [W0: $i] :
( aSet0(W0)
=> ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardEmpty) ).
tff(7,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) ),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( ( xQ = slcrc0 )
<=> ( xQ = slcrc0 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ~ ~ ( ~ ? [W0: $i] : aElementOf0(W0,xQ)
& ( xQ = slcrc0 ) )
<=> ( ~ ? [W0: $i] : aElementOf0(W0,xQ)
& ( xQ = slcrc0 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,plain,
( ~ ? [W0: $i] : aElementOf0(W0,xQ)
<=> ~ ? [W0: $i] : aElementOf0(W0,xQ) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,plain,
( ( ~ ? [W0: $i] : aElementOf0(W0,xQ)
& ( xQ = slcrc0 ) )
<=> ( ~ ? [W0: $i] : aElementOf0(W0,xQ)
& ( xQ = slcrc0 ) ) ),
inference(monotonicity,[status(thm)],[13]) ).
tff(15,plain,
( ~ ( ~ ? [W0: $i] : aElementOf0(W0,xQ)
& ( xQ = slcrc0 ) )
<=> ~ ( ~ ? [W0: $i] : aElementOf0(W0,xQ)
& ( xQ = slcrc0 ) ) ),
inference(monotonicity,[status(thm)],[14]) ).
tff(16,plain,
( ~ ~ ( ~ ? [W0: $i] : aElementOf0(W0,xQ)
& ( xQ = slcrc0 ) )
<=> ~ ~ ( ~ ? [W0: $i] : aElementOf0(W0,xQ)
& ( xQ = slcrc0 ) ) ),
inference(monotonicity,[status(thm)],[15]) ).
tff(17,plain,
( ~ ~ ( ~ ? [W0: $i] : aElementOf0(W0,xQ)
& ( xQ = slcrc0 ) )
<=> ( ~ ? [W0: $i] : aElementOf0(W0,xQ)
& ( xQ = slcrc0 ) ) ),
inference(transitivity,[status(thm)],[16,12]) ).
tff(18,axiom,
~ ~ ( ~ ? [W0: $i] : aElementOf0(W0,xQ)
& ( xQ = slcrc0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(19,plain,
( ~ ? [W0: $i] : aElementOf0(W0,xQ)
& ( xQ = slcrc0 ) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
xQ = slcrc0,
inference(and_elim,[status(thm)],[19]) ).
tff(21,plain,
xQ = slcrc0,
inference(modus_ponens,[status(thm)],[20,11]) ).
tff(22,plain,
( aSet0(xQ)
<=> aSet0(slcrc0) ),
inference(monotonicity,[status(thm)],[21]) ).
tff(23,plain,
( aSet0(xQ)
<=> aSet0(xQ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,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/sandbox2/benchmark/theBenchmark.p',m__2270) ).
tff(25,plain,
( aSet0(xQ)
& ! [W0: $i] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,xS) )
& aSubsetOf0(xQ,xS)
& ( sbrdtbr0(xQ) = xk ) ),
inference(and_elim,[status(thm)],[24]) ).
tff(26,plain,
( aSet0(xQ)
& ! [W0: $i] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,xS) )
& aSubsetOf0(xQ,xS) ),
inference(and_elim,[status(thm)],[25]) ).
tff(27,plain,
( aSet0(xQ)
& ! [W0: $i] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,xS) ) ),
inference(and_elim,[status(thm)],[26]) ).
tff(28,plain,
aSet0(xQ),
inference(and_elim,[status(thm)],[27]) ).
tff(29,plain,
aSet0(xQ),
inference(modus_ponens,[status(thm)],[28,23]) ).
tff(30,plain,
aSet0(slcrc0),
inference(modus_ponens,[status(thm)],[29,22]) ).
tff(31,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) )
| ~ aSet0(slcrc0)
| ( sbrdtbr0(slcrc0) = sz00 ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) )
| ~ aSet0(slcrc0)
| ( sbrdtbr0(slcrc0) = sz00 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,plain,
( ( ~ aSet0(slcrc0)
| ( ( sbrdtbr0(slcrc0) = sz00 )
<=> ( slcrc0 = slcrc0 ) ) )
<=> ( ~ aSet0(slcrc0)
| ( sbrdtbr0(slcrc0) = sz00 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) )
| ~ aSet0(slcrc0)
| ( ( sbrdtbr0(slcrc0) = sz00 )
<=> ( slcrc0 = slcrc0 ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) )
| ~ aSet0(slcrc0)
| ( sbrdtbr0(slcrc0) = sz00 ) ) ),
inference(monotonicity,[status(thm)],[32]) ).
tff(34,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) )
| ~ aSet0(slcrc0)
| ( ( sbrdtbr0(slcrc0) = sz00 )
<=> ( slcrc0 = slcrc0 ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) )
| ~ aSet0(slcrc0)
| ( sbrdtbr0(slcrc0) = sz00 ) ) ),
inference(transitivity,[status(thm)],[33,31]) ).
tff(35,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) )
| ~ aSet0(slcrc0)
| ( ( sbrdtbr0(slcrc0) = sz00 )
<=> ( slcrc0 = slcrc0 ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(36,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) )
| ~ aSet0(slcrc0)
| ( sbrdtbr0(slcrc0) = sz00 ) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
sbrdtbr0(slcrc0) = sz00,
inference(unit_resolution,[status(thm)],[36,30,10]) ).
tff(38,plain,
slcrc0 = xQ,
inference(symmetry,[status(thm)],[21]) ).
tff(39,plain,
sbrdtbr0(slcrc0) = sbrdtbr0(xQ),
inference(monotonicity,[status(thm)],[38]) ).
tff(40,plain,
sbrdtbr0(xQ) = sbrdtbr0(slcrc0),
inference(symmetry,[status(thm)],[39]) ).
tff(41,plain,
( ( sbrdtbr0(xQ) = xk )
<=> ( sbrdtbr0(xQ) = xk ) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,plain,
sbrdtbr0(xQ) = xk,
inference(and_elim,[status(thm)],[25]) ).
tff(43,plain,
sbrdtbr0(xQ) = xk,
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
xk = sbrdtbr0(xQ),
inference(symmetry,[status(thm)],[43]) ).
tff(45,plain,
xk = sz00,
inference(transitivity,[status(thm)],[44,40,37]) ).
tff(46,plain,
( ( xk != sz00 )
<=> ( xk != sz00 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,axiom,
( aSet0(xS)
& aSet0(xT)
& ( xk != sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2202_02) ).
tff(48,plain,
xk != sz00,
inference(and_elim,[status(thm)],[47]) ).
tff(49,plain,
xk != sz00,
inference(modus_ponens,[status(thm)],[48,46]) ).
tff(50,plain,
$false,
inference(unit_resolution,[status(thm)],[49,45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : NUM550+3 : TPTP v9.0.0. Released v4.0.0.
% 0.08/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 01:26:05 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.40 % SZS status Theorem
% 0.19/0.40 % SZS output start Proof
% See solution above
% 0.19/0.41 % E exiting
%------------------------------------------------------------------------------