%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN986+1.000 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 05:41:07 AM UTC 2025
% Result : Theorem 0.12s 0.36s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of formulae : 22 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 35 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 27 ( 19 ~; 2 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 5 ( 5 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 24 ( 14 !; 7 ?; 24 :)
% Comments :
%------------------------------------------------------------------------------
tff(r_type,type,
r: ( $i * $i * $i ) > $o ).
tff(succ_type,type,
succ: $i > $i ).
tff(zero_type,type,
zero: $i ).
tff(1,plain,
^ [Y: $i] :
refl(( r(Y,zero,succ(Y))
<=> r(Y,zero,succ(Y)) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [Y: $i] : r(Y,zero,succ(Y))
<=> ! [Y: $i] : r(Y,zero,succ(Y)) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Y: $i] : r(Y,zero,succ(Y))
<=> ! [Y: $i] : r(Y,zero,succ(Y)) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [Y: $i] : r(Y,zero,succ(Y)),
file('/export/starexec/sandbox/benchmark/Axioms/SYN002+0.ax',hyp1) ).
tff(5,plain,
! [Y: $i] : r(Y,zero,succ(Y)),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Y: $i] : r(Y,zero,succ(Y)),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Y: $i] : r(Y,zero,succ(Y)),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Y: $i] : r(Y,zero,succ(Y))
| r(zero,zero,succ(zero)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
r(zero,zero,succ(zero)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [Z0: $i] :
refl(( ~ r(zero,zero,Z0)
<=> ~ r(zero,zero,Z0) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [Z0: $i] : ~ r(zero,zero,Z0)
<=> ! [Z0: $i] : ~ r(zero,zero,Z0) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ~ ? [Z0: $i] : r(zero,zero,Z0)
<=> ~ ? [Z0: $i] : r(zero,zero,Z0) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
~ ? [Z0: $i] : r(zero,zero,Z0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ck) ).
tff(14,plain,
~ ? [Z0: $i] : r(zero,zero,Z0),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
~ ? [Z0: $i] : r(zero,zero,Z0),
inference(modus_ponens,[status(thm)],[14,12]) ).
tff(16,plain,
~ ? [Z0: $i] : r(zero,zero,Z0),
inference(modus_ponens,[status(thm)],[15,12]) ).
tff(17,plain,
~ ? [Z0: $i] : r(zero,zero,Z0),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
^ [Z0: $i] : refl($oeq(~ r(zero,zero,Z0),~ r(zero,zero,Z0))),
inference(bind,[status(th)],[]) ).
tff(19,plain,
! [Z0: $i] : ~ r(zero,zero,Z0),
inference(nnf-neg,[status(sab)],[17,18]) ).
tff(20,plain,
! [Z0: $i] : ~ r(zero,zero,Z0),
inference(modus_ponens,[status(thm)],[19,11]) ).
tff(21,plain,
( ~ ! [Z0: $i] : ~ r(zero,zero,Z0)
| ~ r(zero,zero,succ(zero)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(22,plain,
$false,
inference(unit_resolution,[status(thm)],[21,20,9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYN986+1.000 : TPTP v9.0.0. Released v4.0.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n009.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 13:02:18 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.36 % SZS status Theorem
% 0.12/0.36 % SZS output start Proof
% See solution above
% 0.12/0.37 % E exiting
%------------------------------------------------------------------------------