%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM434+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:20:58 AM UTC 2025
% Result : Theorem 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 3
% Syntax : Number of formulae : 8 ( 1 unt; 0 typ; 0 def)
% Number of atoms : 23 ( 11 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 22 ( 7 ~; 0 |; 14 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 4 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 8 ( 0 !; 8 ?; 8 :)
% Comments :
%------------------------------------------------------------------------------
tff(sdtpldt0_type,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(smndt0_type,type,
smndt0: $i > $i ).
tff(xb_type,type,
xb: $i ).
tff(xa_type,type,
xa: $i ).
tff(sdtasdt0_type,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(xq_type,type,
xq: $i ).
tff(xp_type,type,
xp: $i ).
tff(aInteger0_type,type,
aInteger0: $i > $o ).
tff(sz00_type,type,
sz00: $i ).
tff(aDivisorOf0_type,type,
aDivisorOf0: ( $i * $i ) > $o ).
tff(sdteqdtlpzmzozddtrp0_type,type,
sdteqdtlpzmzozddtrp0: ( $i * $i * $i ) > $o ).
tff(1,plain,
( ~ ? [W0: $i] :
( aInteger0(W0)
& ( sdtasdt0(sdtasdt0(xp,xq),W0) = sdtpldt0(xa,smndt0(xb)) ) )
<=> ~ ? [W0: $i] :
( aInteger0(W0)
& ( sdtasdt0(sdtasdt0(xp,xq),W0) = sdtpldt0(xa,smndt0(xb)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ ? [W0: $i] :
( aInteger0(W0)
& ( sdtasdt0(sdtasdt0(xp,xq),W0) = sdtpldt0(xa,smndt0(xb)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(3,plain,
~ ? [W0: $i] :
( aInteger0(W0)
& ( sdtasdt0(sdtasdt0(xp,xq),W0) = sdtpldt0(xa,smndt0(xb)) ) ),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,axiom,
( ( sdtasdt0(xp,xq) != sz00 )
& ? [W0: $i] :
( aInteger0(W0)
& ( sdtasdt0(sdtasdt0(xp,xq),W0) = sdtpldt0(xa,smndt0(xb)) ) )
& aDivisorOf0(sdtasdt0(xp,xq),sdtpldt0(xa,smndt0(xb)))
& sdteqdtlpzmzozddtrp0(xa,xb,sdtasdt0(xp,xq)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1003) ).
tff(5,plain,
( ( sdtasdt0(xp,xq) != sz00 )
& ? [W0: $i] :
( aInteger0(W0)
& ( sdtasdt0(sdtasdt0(xp,xq),W0) = sdtpldt0(xa,smndt0(xb)) ) )
& aDivisorOf0(sdtasdt0(xp,xq),sdtpldt0(xa,smndt0(xb))) ),
inference(and_elim,[status(thm)],[4]) ).
tff(6,plain,
( ( sdtasdt0(xp,xq) != sz00 )
& ? [W0: $i] :
( aInteger0(W0)
& ( sdtasdt0(sdtasdt0(xp,xq),W0) = sdtpldt0(xa,smndt0(xb)) ) ) ),
inference(and_elim,[status(thm)],[5]) ).
tff(7,plain,
? [W0: $i] :
( aInteger0(W0)
& ( sdtasdt0(sdtasdt0(xp,xq),W0) = sdtpldt0(xa,smndt0(xb)) ) ),
inference(and_elim,[status(thm)],[6]) ).
tff(8,plain,
$false,
inference(unit_resolution,[status(thm)],[7,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM434+3 : TPTP v9.0.0. Released v4.0.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n008.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 01:06:34 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.37 % SZS status Theorem
% 0.12/0.37 % SZS output start Proof
% See solution above
% 0.12/0.37 % E exiting
%------------------------------------------------------------------------------