%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN006-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/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 09:36:14 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.55s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 20 ( 11 unt; 0 def)
% Number of atoms : 33 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 25 ( 12 ~; 13 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 31 ( 9 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clause_2,axiom,
! [VAR_0] : p1(a,VAR_0),
file('theBenchmark.p',clause_2) ).
cnf(c_1,plain,
p1(a,A),
inference(clausify,[status(thm)],[clause_2]) ).
fof(clause_1,axiom,
! [VAR_0,VAR_1] :
( q2(VAR_0,f(VAR_1))
| q1(f(VAR_0),VAR_1)
| ~ p1(VAR_0,f(VAR_1)) ),
file('theBenchmark.p',clause_1) ).
cnf(c_2,plain,
( q2(A,f(B))
| q1(f(A),B)
| ~ p1(A,f(B)) ),
inference(clausify,[status(thm)],[clause_1]) ).
fof(clause_7,axiom,
! [VAR_0,VAR_1] :
( p2(f(VAR_0),VAR_1)
| ~ q1(VAR_0,f(VAR_1)) ),
file('theBenchmark.p',clause_7) ).
cnf(c_3,plain,
( p2(f(A),B)
| ~ q1(A,f(B)) ),
inference(clausify,[status(thm)],[clause_7]) ).
cnf(c_4,plain,
( q2(a,f(A))
| q1(f(a),A) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
fof(clause_3,axiom,
! [VAR_0,VAR_1] : ~ q2(VAR_0,f(VAR_1)),
file('theBenchmark.p',clause_3) ).
cnf(c_5,plain,
~ q2(A,f(B)),
inference(clausify,[status(thm)],[clause_3]) ).
cnf(c_6,plain,
( q2(a,f(f(A)))
| p2(f(f(a)),A) ),
inference(resolve,[status(thm)],[c_3,c_4]) ).
fof(clause_4,axiom,
! [VAR_0,VAR_1] :
( q4(VAR_0,f(VAR_1))
| q3(f(VAR_0),VAR_1)
| ~ p2(VAR_0,f(VAR_1)) ),
file('theBenchmark.p',clause_4) ).
cnf(c_7,plain,
( q4(A,f(B))
| q3(f(A),B)
| ~ p2(A,f(B)) ),
inference(clausify,[status(thm)],[clause_4]) ).
cnf(c_8,plain,
p2(f(f(a)),A),
inference(resolve,[status(thm)],[c_5,c_6]) ).
fof(clause_5,axiom,
! [VAR_0,VAR_1] : ~ q3(VAR_0,g(VAR_1)),
file('theBenchmark.p',clause_5) ).
cnf(c_9,plain,
~ q3(A,g(B)),
inference(clausify,[status(thm)],[clause_5]) ).
cnf(c_10,plain,
( q4(f(f(a)),f(A))
| q3(f(f(f(a))),A) ),
inference(resolve,[status(thm)],[c_7,c_8]) ).
fof(clause_6,axiom,
! [VAR_0,VAR_1] : ~ q4(f(f(VAR_0)),f(g(f(VAR_1)))),
file('theBenchmark.p',clause_6) ).
cnf(c_11,plain,
~ q4(f(f(A)),f(g(f(B)))),
inference(clausify,[status(thm)],[clause_6]) ).
cnf(c_12,plain,
q4(f(f(a)),f(g(A))),
inference(resolve,[status(thm)],[c_9,c_10]) ).
cnf(c_13,plain,
$false,
inference(resolve,[status(thm)],[c_11,c_12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN006-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.53 % Computer : n006.cluster.edu
% 0.10/0.53 % Model : x86_64 x86_64
% 0.10/0.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.53 % Memory : 8046.5625MB
% 0.10/0.53 % OS : Linux 6.8.0-71-generic
% 0.10/0.53 % CPULimit : 300
% 0.10/0.53 % WCLimit : 300
% 0.10/0.53 % DateTime : Sat Sep 26 17:03:28 UTC 2026
% 0.10/0.53 % CPUTime :
% 0.10/0.53 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.53 % Process 1736412 was started by sandbox on n006,
% 0.10/0.53 % Sat Sep 26 17:03:28 2026
% 0.10/0.53 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.53
% 0.10/0.53 % From the command line: assign(max_seconds, 300).
% 0.10/0.55
% 0.10/0.55 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.55
% 0.10/0.55 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.10/0.55 % Length of proof is 13.
% 0.10/0.55 % Level of proof is 6.
% 0.10/0.55 % Maximum clause weight is 0.000.
% 0.10/0.55 % Given clauses 0.
% 0.10/0.55
% 0.10/0.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------