%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM514+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 05:21:14 AM UTC 2025
% Result : Theorem 0.23s 0.46s
% Output : Proof 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of formulae : 31 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 117 ( 53 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 142 ( 67 ~; 30 |; 31 &)
% ( 12 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 11 ( 11 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 24 ( 11 !; 10 ?; 24 :)
% Comments :
%------------------------------------------------------------------------------
tff(sdtasdt0_type,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(sdtsldt0_type,type,
sdtsldt0: ( $i * $i ) > $i ).
tff(xr_type,type,
xr: $i ).
tff(xk_type,type,
xk: $i ).
tff(xp_type,type,
xp: $i ).
tff(xm_type,type,
xm: $i ).
tff(xn_type,type,
xn: $i ).
tff(aNaturalNumber0_type,type,
aNaturalNumber0: $i > $o ).
tff(doDivides0_type,type,
doDivides0: ( $i * $i ) > $o ).
tff(1,plain,
( ( sdtasdt0(xp,sdtsldt0(xk,xr)) = sdtasdt0(sdtsldt0(xn,xr),xm) )
<=> ( sdtasdt0(xp,sdtsldt0(xk,xr)) = sdtasdt0(sdtsldt0(xn,xr),xm) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
( aNaturalNumber0(sdtsldt0(xk,xr))
& ( xk = sdtasdt0(xr,sdtsldt0(xk,xr)) )
& aNaturalNumber0(sdtsldt0(xn,xr))
& ( xn = sdtasdt0(xr,sdtsldt0(xn,xr)) )
& ( sdtasdt0(xp,sdtsldt0(xk,xr)) = sdtasdt0(sdtsldt0(xn,xr),xm) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2613) ).
tff(3,plain,
sdtasdt0(xp,sdtsldt0(xk,xr)) = sdtasdt0(sdtsldt0(xn,xr),xm),
inference(and_elim,[status(thm)],[2]) ).
tff(4,plain,
sdtasdt0(xp,sdtsldt0(xk,xr)) = sdtasdt0(sdtsldt0(xn,xr),xm),
inference(modus_ponens,[status(thm)],[3,1]) ).
tff(5,plain,
sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,sdtsldt0(xk,xr)),
inference(symmetry,[status(thm)],[4]) ).
tff(6,plain,
^ [W0: $i] :
refl(( ( ~ aNaturalNumber0(W0)
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,W0) ) )
<=> ( ~ aNaturalNumber0(W0)
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(7,plain,
( ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,W0) ) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,W0) ) ) ),
inference(quant_intro,[status(thm)],[6]) ).
tff(8,plain,
^ [W0: $i] :
trans(monotonicity(rewrite(( ( aNaturalNumber0(W0)
& ( sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,W0) ) )
<=> ~ ( ~ aNaturalNumber0(W0)
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,W0) ) ) )),
( ~ ( aNaturalNumber0(W0)
& ( sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,W0) ) )
<=> ~ ~ ( ~ aNaturalNumber0(W0)
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,W0) ) ) )),
rewrite(( ~ ~ ( ~ aNaturalNumber0(W0)
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,W0) ) )
<=> ( ~ aNaturalNumber0(W0)
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,W0) ) ) )),
( ~ ( aNaturalNumber0(W0)
& ( sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,W0) ) )
<=> ( ~ aNaturalNumber0(W0)
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(9,plain,
( ! [W0: $i] :
~ ( aNaturalNumber0(W0)
& ( sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,W0) ) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,W0) ) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
( ~ ? [W0: $i] :
( aNaturalNumber0(W0)
& ( sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,W0) ) )
<=> ~ ? [W0: $i] :
( aNaturalNumber0(W0)
& ( sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,W0) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,plain,
( ~ ( ( aNaturalNumber0(sdtsldt0(xn,xr))
& ( xn = sdtasdt0(xr,sdtsldt0(xn,xr)) ) )
=> ( ? [W0: $i] :
( aNaturalNumber0(W0)
& ( sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,W0) ) )
| doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm)) ) )
<=> ~ ( doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
| ? [W0: $i] :
( aNaturalNumber0(W0)
& ( sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,W0) ) )
| ~ ( aNaturalNumber0(sdtsldt0(xn,xr))
& ( xn = sdtasdt0(xr,sdtsldt0(xn,xr)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
~ ( ( aNaturalNumber0(sdtsldt0(xn,xr))
& ( xn = sdtasdt0(xr,sdtsldt0(xn,xr)) ) )
=> ( ? [W0: $i] :
( aNaturalNumber0(W0)
& ( sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,W0) ) )
| doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(13,plain,
~ ( doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
| ? [W0: $i] :
( aNaturalNumber0(W0)
& ( sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,W0) ) )
| ~ ( aNaturalNumber0(sdtsldt0(xn,xr))
& ( xn = sdtasdt0(xr,sdtsldt0(xn,xr)) ) ) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
~ ? [W0: $i] :
( aNaturalNumber0(W0)
& ( sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,W0) ) ),
inference(or_elim,[status(thm)],[13]) ).
tff(15,plain,
~ ? [W0: $i] :
( aNaturalNumber0(W0)
& ( sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,W0) ) ),
inference(modus_ponens,[status(thm)],[14,10]) ).
tff(16,plain,
~ ? [W0: $i] :
( aNaturalNumber0(W0)
& ( sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,W0) ) ),
inference(modus_ponens,[status(thm)],[15,10]) ).
tff(17,plain,
~ ? [W0: $i] :
( aNaturalNumber0(W0)
& ( sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,W0) ) ),
inference(modus_ponens,[status(thm)],[16,10]) ).
tff(18,plain,
^ [W0: $i] :
refl($oeq(~ ( aNaturalNumber0(W0)
& ( sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,W0) ) ),
~ ( aNaturalNumber0(W0)
& ( sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,W0) ) ))),
inference(bind,[status(th)],[]) ).
tff(19,plain,
! [W0: $i] :
~ ( aNaturalNumber0(W0)
& ( sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,W0) ) ),
inference(nnf-neg,[status(sab)],[17,18]) ).
tff(20,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,W0) ) ),
inference(modus_ponens,[status(thm)],[19,9]) ).
tff(21,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,W0) ) ),
inference(modus_ponens,[status(thm)],[20,7]) ).
tff(22,plain,
( aNaturalNumber0(sdtsldt0(xk,xr))
<=> aNaturalNumber0(sdtsldt0(xk,xr)) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,plain,
( aNaturalNumber0(sdtsldt0(xk,xr))
& ( xk = sdtasdt0(xr,sdtsldt0(xk,xr)) )
& aNaturalNumber0(sdtsldt0(xn,xr))
& ( xn = sdtasdt0(xr,sdtsldt0(xn,xr)) ) ),
inference(and_elim,[status(thm)],[2]) ).
tff(24,plain,
( aNaturalNumber0(sdtsldt0(xk,xr))
& ( xk = sdtasdt0(xr,sdtsldt0(xk,xr)) )
& aNaturalNumber0(sdtsldt0(xn,xr)) ),
inference(and_elim,[status(thm)],[23]) ).
tff(25,plain,
( aNaturalNumber0(sdtsldt0(xk,xr))
& ( xk = sdtasdt0(xr,sdtsldt0(xk,xr)) ) ),
inference(and_elim,[status(thm)],[24]) ).
tff(26,plain,
aNaturalNumber0(sdtsldt0(xk,xr)),
inference(and_elim,[status(thm)],[25]) ).
tff(27,plain,
aNaturalNumber0(sdtsldt0(xk,xr)),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
( ( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,W0) ) )
| ~ aNaturalNumber0(sdtsldt0(xk,xr))
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,sdtsldt0(xk,xr)) ) )
<=> ( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,W0) ) )
| ~ aNaturalNumber0(sdtsldt0(xk,xr))
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,sdtsldt0(xk,xr)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,plain,
( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,W0) ) )
| ~ aNaturalNumber0(sdtsldt0(xk,xr))
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,sdtsldt0(xk,xr)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(30,plain,
( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,W0) ) )
| ~ aNaturalNumber0(sdtsldt0(xk,xr))
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,sdtsldt0(xk,xr)) ) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
$false,
inference(unit_resolution,[status(thm)],[30,27,21,5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14 % Problem : NUM514+3 : TPTP v9.0.0. Released v4.0.0.
% 0.09/0.14 % Command : run_E %s %d THM
% 0.15/0.36 % Computer : n002.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 01:22:46 EDT 2025
% 0.15/0.37 % CPUTime :
% 0.23/0.46 % SZS status Theorem
% 0.23/0.46 % SZS output start Proof
% See solution above
% 0.23/0.47 % E exiting
%------------------------------------------------------------------------------