%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN986+1.003 : 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 : n006.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 0.17s 0.46s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 8 unt; 0 def)
% Number of atoms : 39 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 37 ( 17 ~; 12 |; 6 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 17 ( 3 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 : 40 ( 4 sgn 5 !; 8 ?)
% 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,
? [Z3,Z2,Z1,Z0] :
( r(zero,Z1,Z0)
& r(zero,Z2,Z1)
& r(zero,Z3,Z2)
& r(zero,zero,Z3) ),
file('theBenchmark.p',ck) ).
fof(ck_neg,negated_conjecture,
~ ? [Z3,Z2,Z1,Z0] :
( r(zero,Z1,Z0)
& r(zero,Z2,Z1)
& r(zero,Z3,Z2)
& r(zero,zero,Z3) ),
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,C,D)
| ~ r(zero,B,C)
| ~ r(zero,A,B)
| ~ r(zero,zero,A) ),
inference(clausify,[status(thm)],[ck_neg]) ).
cnf(c_41,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_41,c_4]) ).
cnf(c_42,plain,
( r(A,succ(succ(zero)),B)
| ~ r(succ(succ(A)),succ(zero),B) ),
inference(resolve,[status(thm)],[c_5,c_7]) ).
cnf(c_18,plain,
r(A,succ(succ(zero)),succ(succ(succ(succ(A))))),
inference(resolve,[status(thm)],[c_42,c_7]) ).
cnf(c_43,plain,
( r(A,succ(succ(succ(zero))),B)
| ~ r(succ(succ(succ(succ(A)))),succ(succ(zero)),B) ),
inference(resolve,[status(thm)],[c_5,c_18]) ).
cnf(c_31,plain,
r(A,succ(succ(succ(zero))),succ(succ(succ(succ(succ(succ(succ(succ(A))))))))),
inference(resolve,[status(thm)],[c_43,c_18]) ).
cnf(c_44,negated_conjecture,
( ~ r(zero,B,C)
| ~ r(zero,A,B)
| ~ r(zero,succ(zero),A) ),
inference(resolve,[status(thm)],[c_6,c_4]) ).
cnf(c_45,negated_conjecture,
( ~ r(zero,A,B)
| ~ r(zero,succ(succ(zero)),A) ),
inference(resolve,[status(thm)],[c_44,c_7]) ).
cnf(c_35,negated_conjecture,
~ r(zero,succ(succ(succ(succ(zero)))),A),
inference(resolve,[status(thm)],[c_45,c_18]) ).
cnf(c_46,plain,
( r(A,succ(succ(succ(succ(zero)))),B)
| ~ r(succ(succ(succ(succ(succ(succ(succ(succ(A)))))))),succ(succ(succ(zero))),B) ),
inference(resolve,[status(thm)],[c_5,c_31]) ).
cnf(c_39,plain,
r(A,succ(succ(succ(succ(zero)))),succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(A))))))))))))))))),
inference(resolve,[status(thm)],[c_46,c_31]) ).
cnf(c_40,plain,
$false,
inference(resolve,[status(thm)],[c_39,c_35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SYN986+1.003 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n006.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Sat Sep 26 18:53:25 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.44 % Process 1900580 was started by sandbox2 on n006,
% 0.17/0.44 % Sat Sep 26 18:53:25 2026
% 0.17/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.45
% 0.17/0.45 % From the command line: assign(max_seconds, 300).
% 0.17/0.46
% 0.17/0.46 % SZS status Theorem for theBenchmark
% 0.17/0.46
% 0.17/0.46 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.17/0.46 % Length of proof is 12.
% 0.17/0.46 % Level of proof is 6.
% 0.17/0.46 % Maximum clause weight is 24.000.
% 0.17/0.46 % Given clauses 10.
% 0.17/0.46
% 0.17/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------