%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN345-1 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 09:37:38 AM UTC 2026
% Result : Unsatisfiable 0.20s 0.47s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 29 ( 5 unt; 0 def)
% Number of atoms : 70 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 67 ( 26 ~; 41 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 32 ( 9 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clause1,axiom,
! [VAR_0] :
( f(a,b,b)
| ~ f(a,a,b)
| f(a,b,VAR_0) ),
file('theBenchmark.p',clause1) ).
cnf(c_1,plain,
( f(a,b,b)
| ~ f(a,a,b)
| f(a,b,A) ),
inference(clausify,[status(thm)],[clause1]) ).
fof(clause3,axiom,
! [VAR_0,VAR_1] :
( ~ f(a,b,b)
| f(a,a,b)
| f(b,VAR_0,VAR_1) ),
file('theBenchmark.p',clause3) ).
cnf(c_3,plain,
( ~ f(a,b,b)
| f(a,a,b)
| f(b,A,B) ),
inference(clausify,[status(thm)],[clause3]) ).
fof(clause4,axiom,
! [VAR_0,VAR_1] :
( ~ f(a,b,b)
| f(a,a,b)
| ~ f(VAR_0,z(VAR_0,VAR_1),z(VAR_0,VAR_1)) ),
file('theBenchmark.p',clause4) ).
cnf(c_4,plain,
( ~ f(a,b,b)
| f(a,a,b)
| ~ f(A,z(A,B),z(A,B)) ),
inference(clausify,[status(thm)],[clause4]) ).
fof(clause5,axiom,
! [VAR_0,VAR_1] :
( f(a,b,b)
| f(a,a,b)
| f(VAR_0,VAR_1,z(VAR_0,VAR_1)) ),
file('theBenchmark.p',clause5) ).
cnf(c_5,plain,
( f(a,b,b)
| f(a,a,b)
| f(A,B,z(A,B)) ),
inference(clausify,[status(thm)],[clause5]) ).
fof(clause6,axiom,
! [VAR_0,VAR_1] :
( ~ f(a,b,b)
| ~ f(a,a,b)
| f(VAR_0,VAR_1,z(VAR_0,VAR_1)) ),
file('theBenchmark.p',clause6) ).
cnf(c_6,plain,
( ~ f(a,b,b)
| ~ f(a,a,b)
| f(A,B,z(A,B)) ),
inference(clausify,[status(thm)],[clause6]) ).
fof(clause7,axiom,
! [VAR_0] :
( f(a,b,b)
| f(a,a,b)
| ~ f(b,b,VAR_0) ),
file('theBenchmark.p',clause7) ).
cnf(c_7,plain,
( f(a,b,b)
| f(a,a,b)
| ~ f(b,b,A) ),
inference(clausify,[status(thm)],[clause7]) ).
fof(clause8,axiom,
! [VAR_0] :
( ~ f(a,b,b)
| ~ f(a,a,b)
| ~ f(b,b,VAR_0) ),
file('theBenchmark.p',clause8) ).
cnf(c_8,plain,
( ~ f(a,b,b)
| ~ f(a,a,b)
| ~ f(b,b,A) ),
inference(clausify,[status(thm)],[clause8]) ).
cnf(c_9,plain,
( ~ f(a,a,b)
| f(a,b,b) ),
inference(factor,[status(thm)],[c_1]) ).
cnf(c_23,plain,
( f(a,b,b)
| f(a,a,b)
| f(a,b,b)
| f(a,a,b) ),
inference(resolve,[status(thm)],[c_7,c_5]) ).
cnf(c_24,plain,
( f(a,b,b)
| f(a,b,b)
| f(a,a,b) ),
inference(copy,[status(thm)],[c_23]) ).
cnf(c_10,plain,
( f(a,b,b)
| f(a,a,b) ),
inference(copy,[status(thm)],[c_24]) ).
cnf(c_25,plain,
( f(a,b,b)
| f(a,b,b) ),
inference(resolve,[status(thm)],[c_10,c_9]) ).
cnf(c_11,plain,
f(a,b,b),
inference(copy,[status(thm)],[c_25]) ).
cnf(c_12,plain,
( ~ f(a,a,b)
| ~ f(b,b,A) ),
inference(resolve,[status(thm)],[c_11,c_8]) ).
cnf(c_13,plain,
( ~ f(a,a,b)
| f(A,B,z(A,B)) ),
inference(resolve,[status(thm)],[c_11,c_6]) ).
cnf(c_14,plain,
( f(a,a,b)
| ~ f(A,z(A,B),z(A,B)) ),
inference(resolve,[status(thm)],[c_11,c_4]) ).
cnf(c_15,plain,
( f(a,a,b)
| f(b,A,B) ),
inference(resolve,[status(thm)],[c_11,c_3]) ).
cnf(c_26,plain,
( f(a,a,b)
| f(a,a,b) ),
inference(resolve,[status(thm)],[c_14,c_15]) ).
cnf(c_19,plain,
f(a,a,b),
inference(copy,[status(thm)],[c_26]) ).
cnf(c_20,plain,
f(A,B,z(A,B)),
inference(resolve,[status(thm)],[c_19,c_13]) ).
cnf(c_21,plain,
~ f(b,b,A),
inference(resolve,[status(thm)],[c_19,c_12]) ).
cnf(c_22,plain,
$false,
inference(resolve,[status(thm)],[c_21,c_20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SYN345-1 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.45 % Computer : n009.cluster.edu
% 0.20/0.45 % Model : x86_64 x86_64
% 0.20/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.45 % Memory : 8046.5625MB
% 0.20/0.45 % OS : Linux 6.8.0-71-generic
% 0.20/0.45 % CPULimit : 300
% 0.20/0.45 % WCLimit : 300
% 0.20/0.45 % DateTime : Sat Sep 26 17:36:29 UTC 2026
% 0.20/0.45 % CPUTime :
% 0.20/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.20/0.45 % Process 731434 was started by sandbox on n009,
% 0.20/0.45 % Sat Sep 26 17:36:29 2026
% 0.20/0.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.20/0.46
% 0.20/0.46 % From the command line: assign(max_seconds, 300).
% 0.20/0.47
% 0.20/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.20/0.47
% 0.20/0.47 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.20/0.47 % Length of proof is 18.
% 0.20/0.47 % Level of proof is 6.
% 0.20/0.47 % Maximum clause weight is 16.000.
% 0.20/0.47 % Given clauses 14.
% 0.20/0.47
% 0.20/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------