%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN350-1 : TPTP v9.3.1. Released v1.2.0.
% 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 09:37:40 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.39s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 20 ( 5 unt; 0 def)
% Number of atoms : 43 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 42 ( 19 ~; 23 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-2 aty)
% Number of variables : 26 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clause1,axiom,
! [VAR_0,VAR_1] :
( f(z(VAR_0,VAR_1),a)
| ~ f(a,z(VAR_0,VAR_1)) ),
file('theBenchmark.p',clause1) ).
cnf(c_1,plain,
( f(z(A,B),a)
| ~ f(a,z(A,B)) ),
inference(clausify,[status(thm)],[clause1]) ).
fof(clause3,axiom,
! [VAR_0,VAR_1] :
( f(VAR_0,z(VAR_0,VAR_1))
| f(VAR_1,z(VAR_0,VAR_1))
| f(a,z(VAR_0,VAR_1)) ),
file('theBenchmark.p',clause3) ).
cnf(c_3,plain,
( f(A,z(A,B))
| f(B,z(A,B))
| f(a,z(A,B)) ),
inference(clausify,[status(thm)],[clause3]) ).
fof(clause4,axiom,
! [VAR_0,VAR_1] :
( f(VAR_0,z(VAR_0,VAR_1))
| ~ f(VAR_1,z(VAR_0,VAR_1))
| ~ f(a,z(VAR_0,VAR_1)) ),
file('theBenchmark.p',clause4) ).
cnf(c_4,plain,
( f(A,z(A,B))
| ~ f(B,z(A,B))
| ~ f(a,z(A,B)) ),
inference(clausify,[status(thm)],[clause4]) ).
fof(clause5,axiom,
! [VAR_0,VAR_1] :
( ~ f(VAR_0,VAR_1)
| f(VAR_1,z(VAR_0,VAR_1))
| f(a,z(VAR_0,VAR_1)) ),
file('theBenchmark.p',clause5) ).
cnf(c_5,plain,
( ~ f(A,B)
| f(B,z(A,B))
| f(a,z(A,B)) ),
inference(clausify,[status(thm)],[clause5]) ).
fof(clause6,axiom,
! [VAR_0,VAR_1] :
( ~ f(VAR_0,VAR_1)
| ~ f(VAR_1,z(VAR_0,VAR_1))
| ~ f(a,z(VAR_0,VAR_1)) ),
file('theBenchmark.p',clause6) ).
cnf(c_6,plain,
( ~ f(A,B)
| ~ f(B,z(A,B))
| ~ f(a,z(A,B)) ),
inference(clausify,[status(thm)],[clause6]) ).
cnf(c_7,plain,
( f(A,z(A,a))
| f(a,z(A,a)) ),
inference(factor,[status(thm)],[c_3]) ).
cnf(c_10,plain,
( f(A,z(A,a))
| ~ f(a,z(A,a)) ),
inference(factor,[status(thm)],[c_4]) ).
cnf(c_11,plain,
( ~ f(A,a)
| f(a,z(A,a)) ),
inference(factor,[status(thm)],[c_5]) ).
cnf(c_12,plain,
( ~ f(A,a)
| ~ f(a,z(A,a)) ),
inference(factor,[status(thm)],[c_6]) ).
cnf(c_43,plain,
( f(A,z(A,a))
| f(A,z(A,a)) ),
inference(resolve,[status(thm)],[c_10,c_7]) ).
cnf(c_32,plain,
f(A,z(A,a)),
inference(copy,[status(thm)],[c_43]) ).
cnf(c_40,plain,
f(z(a,a),a),
inference(resolve,[status(thm)],[c_32,c_1]) ).
cnf(c_41,plain,
~ f(a,z(z(a,a),a)),
inference(resolve,[status(thm)],[c_40,c_12]) ).
cnf(c_44,plain,
f(a,z(z(a,a),a)),
inference(resolve,[status(thm)],[c_40,c_11]) ).
cnf(c_42,plain,
$false,
inference(resolve,[status(thm)],[c_41,c_44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN350-1 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n006.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 17:36:40 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 1785878 was started by sandbox2 on n006,
% 0.10/0.37 % Sat Sep 26 17:36:40 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 0.10/0.39
% 0.10/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.39
% 0.10/0.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.10/0.39 % Length of proof is 13.
% 0.10/0.39 % Level of proof is 5.
% 0.10/0.39 % Maximum clause weight is 15.000.
% 0.10/0.39 % Given clauses 15.
% 0.10/0.39
% 0.10/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------