%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM531+2 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 05:21:18 AM UTC 2025
% Result : Theorem 0.12s 0.38s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 14
% Syntax : Number of formulae : 32 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 178 ( 2 equ)
% Maximal formula atoms : 12 ( 5 avg)
% Number of connectives : 278 ( 147 ~; 85 |; 20 &)
% ( 21 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 15 ( 15 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 1 ( 1 usr; 1 con; 0-0 aty)
% Number of variables : 31 ( 24 !; 4 ?; 31 :)
% Comments :
%------------------------------------------------------------------------------
tff(isCountable0_type,type,
isCountable0: $i > $o ).
tff(slcrc0_type,type,
slcrc0: $i ).
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(aSet0_type,type,
aSet0: $i > $o ).
tff(isFinite0_type,type,
isFinite0: $i > $o ).
tff(1,plain,
( isCountable0(slcrc0)
<=> isCountable0(slcrc0) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,plain,
( ~ ! [W0: $i] :
( ( aSet0(W0)
& isCountable0(W0) )
=> ~ ( ~ ? [W1: $i] : aElementOf0(W1,W0)
& ( W0 = slcrc0 ) ) )
<=> ~ ( ~ aSet0(slcrc0)
| ? [W1: $i] : aElementOf0(W1,slcrc0)
| ~ isCountable0(slcrc0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3,axiom,
~ ! [W0: $i] :
( ( aSet0(W0)
& isCountable0(W0) )
=> ~ ( ~ ? [W1: $i] : aElementOf0(W1,W0)
& ( W0 = slcrc0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(4,plain,
~ ( ~ aSet0(slcrc0)
| ? [W1: $i] : aElementOf0(W1,slcrc0)
| ~ isCountable0(slcrc0) ),
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
isCountable0(slcrc0),
inference(or_elim,[status(thm)],[4]) ).
tff(6,plain,
isCountable0(slcrc0),
inference(modus_ponens,[status(thm)],[5,1]) ).
tff(7,plain,
( aSet0(slcrc0)
<=> aSet0(slcrc0) ),
inference(rewrite,[status(thm)],[]) ).
tff(8,plain,
aSet0(slcrc0),
inference(or_elim,[status(thm)],[4]) ).
tff(9,plain,
aSet0(slcrc0),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
^ [W0: $i] :
refl(( ( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) )
<=> ( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) )
<=> ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
^ [W0: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aSet0(W0)
& isCountable0(W0) )
<=> ~ ( ~ aSet0(W0)
| ~ isCountable0(W0) ) )),
( ~ ( aSet0(W0)
& isCountable0(W0) )
<=> ~ ~ ( ~ aSet0(W0)
| ~ isCountable0(W0) ) )),
rewrite(( ~ ~ ( ~ aSet0(W0)
| ~ isCountable0(W0) )
<=> ( ~ aSet0(W0)
| ~ isCountable0(W0) ) )),
( ~ ( aSet0(W0)
& isCountable0(W0) )
<=> ( ~ aSet0(W0)
| ~ isCountable0(W0) ) )),
( ( ~ isFinite0(W0)
| ~ ( aSet0(W0)
& isCountable0(W0) ) )
<=> ( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) ) )),
rewrite(( ( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) )
<=> ( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) ) )),
( ( ~ isFinite0(W0)
| ~ ( aSet0(W0)
& isCountable0(W0) ) )
<=> ( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(13,plain,
( ! [W0: $i] :
( ~ isFinite0(W0)
| ~ ( aSet0(W0)
& isCountable0(W0) ) )
<=> ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) ) ),
inference(quant_intro,[status(thm)],[12]) ).
tff(14,plain,
( ! [W0: $i] :
( ~ isFinite0(W0)
| ~ ( aSet0(W0)
& isCountable0(W0) ) )
<=> ! [W0: $i] :
( ~ isFinite0(W0)
| ~ ( aSet0(W0)
& isCountable0(W0) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,plain,
^ [W0: $i] :
rewrite(( ( ( aSet0(W0)
& isCountable0(W0) )
=> ~ isFinite0(W0) )
<=> ( ~ isFinite0(W0)
| ~ ( aSet0(W0)
& isCountable0(W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(16,plain,
( ! [W0: $i] :
( ( aSet0(W0)
& isCountable0(W0) )
=> ~ isFinite0(W0) )
<=> ! [W0: $i] :
( ~ isFinite0(W0)
| ~ ( aSet0(W0)
& isCountable0(W0) ) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,axiom,
! [W0: $i] :
( ( aSet0(W0)
& isCountable0(W0) )
=> ~ isFinite0(W0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCountNFin) ).
tff(18,plain,
! [W0: $i] :
( ~ isFinite0(W0)
| ~ ( aSet0(W0)
& isCountable0(W0) ) ),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
! [W0: $i] :
( ~ isFinite0(W0)
| ~ ( aSet0(W0)
& isCountable0(W0) ) ),
inference(modus_ponens,[status(thm)],[18,14]) ).
tff(20,plain,
! [W0: $i] :
( ~ isFinite0(W0)
| ~ ( aSet0(W0)
& isCountable0(W0) ) ),
inference(skolemize,[status(sab)],[19]) ).
tff(21,plain,
! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) ),
inference(modus_ponens,[status(thm)],[20,13]) ).
tff(22,plain,
! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) ),
inference(modus_ponens,[status(thm)],[21,11]) ).
tff(23,plain,
( isFinite0(slcrc0)
<=> isFinite0(slcrc0) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,axiom,
isFinite0(slcrc0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEmpFin) ).
tff(25,plain,
isFinite0(slcrc0),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
( ( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) )
| ~ aSet0(slcrc0)
| ~ isCountable0(slcrc0)
| ~ isFinite0(slcrc0) )
<=> ( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) )
| ~ aSet0(slcrc0)
| ~ isCountable0(slcrc0)
| ~ isFinite0(slcrc0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,plain,
( ( ~ isFinite0(slcrc0)
| ~ aSet0(slcrc0)
| ~ isCountable0(slcrc0) )
<=> ( ~ aSet0(slcrc0)
| ~ isCountable0(slcrc0)
| ~ isFinite0(slcrc0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(28,plain,
( ( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) )
| ~ isFinite0(slcrc0)
| ~ aSet0(slcrc0)
| ~ isCountable0(slcrc0) )
<=> ( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) )
| ~ aSet0(slcrc0)
| ~ isCountable0(slcrc0)
| ~ isFinite0(slcrc0) ) ),
inference(monotonicity,[status(thm)],[27]) ).
tff(29,plain,
( ( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) )
| ~ isFinite0(slcrc0)
| ~ aSet0(slcrc0)
| ~ isCountable0(slcrc0) )
<=> ( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) )
| ~ aSet0(slcrc0)
| ~ isCountable0(slcrc0)
| ~ isFinite0(slcrc0) ) ),
inference(transitivity,[status(thm)],[28,26]) ).
tff(30,plain,
( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) )
| ~ isFinite0(slcrc0)
| ~ aSet0(slcrc0)
| ~ isCountable0(slcrc0) ),
inference(quant_inst,[status(thm)],[]) ).
tff(31,plain,
( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) )
| ~ aSet0(slcrc0)
| ~ isCountable0(slcrc0)
| ~ isFinite0(slcrc0) ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
$false,
inference(unit_resolution,[status(thm)],[31,25,22,9,6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : NUM531+2 : TPTP v9.0.0. Released v4.0.0.
% 0.08/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n013.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 Jun 20 01:23:53 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.38 % SZS status Theorem
% 0.12/0.38 % SZS output start Proof
% See solution above
% 0.12/0.38 % E exiting
%------------------------------------------------------------------------------