%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM617+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:21:36 AM UTC 2025
% Result : Theorem 0.19s 0.48s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% Syntax : Number of formulae : 24 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 69 ( 2 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 73 ( 30 ~; 24 |; 7 &)
% ( 8 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 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 : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 18 ( 16 !; 0 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(szNzAzT0_type,type,
szNzAzT0: $i ).
tff(xx_type,type,
xx: $i ).
tff(xQ_type,type,
xQ: $i ).
tff(aElement0_type,type,
aElement0: $i > $o ).
tff(szmzizndt0_type,type,
szmzizndt0: $i > $i ).
tff(xP_type,type,
xP: $i ).
tff(aSubsetOf0_type,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff(1,plain,
( ~ aElementOf0(xx,szNzAzT0)
<=> ~ aElementOf0(xx,szNzAzT0) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ aElementOf0(xx,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(3,plain,
~ aElementOf0(xx,szNzAzT0),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( aElementOf0(xx,xQ)
<=> aElementOf0(xx,xQ) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
( aElement0(xx)
& aElementOf0(xx,xQ)
& ( xx != szmzizndt0(xQ) )
& aElementOf0(xx,xP) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5348) ).
tff(6,plain,
( aElement0(xx)
& aElementOf0(xx,xQ)
& ( xx != szmzizndt0(xQ) ) ),
inference(and_elim,[status(thm)],[5]) ).
tff(7,plain,
( aElement0(xx)
& aElementOf0(xx,xQ) ),
inference(and_elim,[status(thm)],[6]) ).
tff(8,plain,
aElementOf0(xx,xQ),
inference(and_elim,[status(thm)],[7]) ).
tff(9,plain,
aElementOf0(xx,xQ),
inference(modus_ponens,[status(thm)],[8,4]) ).
tff(10,plain,
^ [W0: $i] :
refl(( ( ~ aElementOf0(W0,xQ)
| aElementOf0(W0,szNzAzT0) )
<=> ( ~ aElementOf0(W0,xQ)
| aElementOf0(W0,szNzAzT0) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xQ)
| aElementOf0(W0,szNzAzT0) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xQ)
| aElementOf0(W0,szNzAzT0) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xQ)
| aElementOf0(W0,szNzAzT0) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xQ)
| aElementOf0(W0,szNzAzT0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,plain,
^ [W0: $i] :
rewrite(( ( aElementOf0(W0,xQ)
=> aElementOf0(W0,szNzAzT0) )
<=> ( ~ aElementOf0(W0,xQ)
| aElementOf0(W0,szNzAzT0) ) )),
inference(bind,[status(th)],[]) ).
tff(14,plain,
( ! [W0: $i] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,szNzAzT0) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xQ)
| aElementOf0(W0,szNzAzT0) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,axiom,
( ! [W0: $i] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,szNzAzT0) )
& aSubsetOf0(xQ,szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5106) ).
tff(16,plain,
! [W0: $i] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,szNzAzT0) ),
inference(and_elim,[status(thm)],[15]) ).
tff(17,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xQ)
| aElementOf0(W0,szNzAzT0) ),
inference(modus_ponens,[status(thm)],[16,14]) ).
tff(18,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xQ)
| aElementOf0(W0,szNzAzT0) ),
inference(modus_ponens,[status(thm)],[17,12]) ).
tff(19,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xQ)
| aElementOf0(W0,szNzAzT0) ),
inference(skolemize,[status(sab)],[18]) ).
tff(20,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xQ)
| aElementOf0(W0,szNzAzT0) ),
inference(modus_ponens,[status(thm)],[19,11]) ).
tff(21,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xQ)
| aElementOf0(W0,szNzAzT0) )
| ~ aElementOf0(xx,xQ)
| aElementOf0(xx,szNzAzT0) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xQ)
| aElementOf0(W0,szNzAzT0) )
| ~ aElementOf0(xx,xQ)
| aElementOf0(xx,szNzAzT0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xQ)
| aElementOf0(W0,szNzAzT0) )
| ~ aElementOf0(xx,xQ)
| aElementOf0(xx,szNzAzT0) ),
inference(quant_inst,[status(thm)],[]) ).
tff(23,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xQ)
| aElementOf0(W0,szNzAzT0) )
| ~ aElementOf0(xx,xQ)
| aElementOf0(xx,szNzAzT0) ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
$false,
inference(unit_resolution,[status(thm)],[23,20,9,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM617+3 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n010.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 01:37:41 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.48 % SZS status Theorem
% 0.19/0.48 % SZS output start Proof
% See solution above
% 0.19/0.49 % E exiting
%------------------------------------------------------------------------------