%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN986+1.001 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:43:31 AM UTC 2026
% Result : Theorem 0.15s 0.38s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 3
% Syntax : Number of formulae : 11 ( 5 unt; 0 def)
% Number of atoms : 19 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 15 ( 7 ~; 4 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 20 ( 2 sgn 5 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(hyp1,axiom,
! [Y] : r(Y,zero,succ(Y)),
file('theBenchmark.p',hyp1) ).
fof(hyp2,axiom,
! [Y,X,Z,Z1] :
( r(Y,X,Z)
=> ( r(Z,X,Z1)
=> r(Y,succ(X),Z1) ) ),
file('theBenchmark.p',hyp2) ).
fof(ck,conjecture,
? [Z1,Z0] :
( r(zero,Z1,Z0)
& r(zero,zero,Z1) ),
file('theBenchmark.p',ck) ).
fof(ck_neg,negated_conjecture,
~ ? [Z1,Z0] :
( r(zero,Z1,Z0)
& r(zero,zero,Z1) ),
inference(assume_negation,[status(cth)],[ck]) ).
cnf(c_4,plain,
r(A,zero,succ(A)),
inference(clausify,[status(thm)],[hyp1]) ).
cnf(c_5,plain,
( r(A,succ(B),D)
| ~ r(C,B,D)
| ~ r(A,B,C) ),
inference(clausify,[status(thm)],[hyp2]) ).
cnf(c_6,negated_conjecture,
( ~ r(zero,A,B)
| ~ r(zero,zero,A) ),
inference(clausify,[status(thm)],[ck_neg]) ).
cnf(c_10,plain,
( r(A,succ(zero),B)
| ~ r(succ(A),zero,B) ),
inference(resolve,[status(thm)],[c_5,c_4]) ).
cnf(c_7,plain,
r(A,succ(zero),succ(succ(A))),
inference(resolve,[status(thm)],[c_10,c_4]) ).
cnf(c_8,plain,
~ r(zero,succ(zero),A),
inference(resolve,[status(thm)],[c_6,c_4]) ).
cnf(c_9,plain,
$false,
inference(resolve,[status(thm)],[c_8,c_7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN986+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n001.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 18:59:13 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 2463719 was started by sandbox2 on n001,
% 0.10/0.37 % Sat Sep 26 18:59:13 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 0.15/0.38
% 0.15/0.38 % SZS status Theorem for theBenchmark
% 0.15/0.38
% 0.15/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.15/0.38 % Length of proof is 9.
% 0.15/0.38 % Level of proof is 3.
% 0.15/0.38 % Maximum clause weight is 13.000.
% 0.15/0.38 % Given clauses 3.
% 0.15/0.38
% 0.15/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------