%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN031-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 09:36:17 AM UTC 2026
% Result : Unsatisfiable 0.15s 10.40s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 14 ( 4 unt; 0 def)
% Number of atoms : 24 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 19 ( 9 ~; 10 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 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; 0-1 aty)
% Number of variables : 15 ( 4 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clause1,axiom,
! [VAR_0] :
( g(f(VAR_0),VAR_0)
| g(VAR_0,a) ),
file('theBenchmark.p',clause1) ).
cnf(c_1,plain,
( g(f(A),A)
| g(A,a) ),
inference(clausify,[status(thm)],[clause1]) ).
fof(clause2,axiom,
! [VAR_0] :
( g(VAR_0,f(VAR_0))
| g(VAR_0,a) ),
file('theBenchmark.p',clause2) ).
cnf(c_2,plain,
( g(A,f(A))
| g(A,a) ),
inference(clausify,[status(thm)],[clause2]) ).
fof(clause3,axiom,
! [VAR_0,VAR_1] :
( g(f(VAR_1),VAR_1)
| ~ g(VAR_0,VAR_1) ),
file('theBenchmark.p',clause3) ).
cnf(c_3,plain,
( g(f(B),B)
| ~ g(A,B) ),
inference(clausify,[status(thm)],[clause3]) ).
fof(theorem,axiom,
! [VAR_0,VAR_1] :
( ~ g(VAR_1,a)
| ~ g(VAR_0,VAR_1) ),
file('theBenchmark.p',theorem) ).
cnf(c_5,plain,
( ~ g(B,a)
| ~ g(A,B) ),
inference(clausify,[status(thm)],[theorem]) ).
cnf(c_6,plain,
~ g(a,a),
inference(factor,[status(thm)],[c_5]) ).
cnf(c_7,plain,
( g(A,a)
| g(f(f(A)),f(A)) ),
inference(resolve,[status(thm)],[c_3,c_2]) ).
cnf(c_12,plain,
( g(a,a)
| ~ g(A,f(a)) ),
inference(resolve,[status(thm)],[c_5,c_1]) ).
cnf(c_10,plain,
~ g(A,f(a)),
inference(resolve,[status(thm)],[c_6,c_12]) ).
cnf(c_13,plain,
g(a,a),
inference(resolve,[status(thm)],[c_10,c_7]) ).
cnf(c_11,plain,
$false,
inference(resolve,[status(thm)],[c_6,c_13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN031-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/10.38 % Computer : n002.cluster.edu
% 0.10/10.38 % Model : x86_64 x86_64
% 0.10/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.38 % Memory : 8046.5625MB
% 0.10/10.38 % OS : Linux 6.8.0-71-generic
% 0.10/10.38 % CPULimit : 300
% 0.10/10.38 % WCLimit : 300
% 0.10/10.38 % DateTime : Sat Sep 26 17:07:17 UTC 2026
% 0.10/10.38 % CPUTime :
% 0.10/10.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/10.39 % Process 2266773 was started by sandbox2 on n002,
% 0.10/10.39 % Sat Sep 26 17:07:17 2026
% 0.10/10.39 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/10.39
% 0.10/10.39 % From the command line: assign(max_seconds, 300).
% 0.15/10.40
% 0.15/10.40 % SZS status Unsatisfiable for theBenchmark
% 0.15/10.40
% 0.15/10.40 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.15/10.40 % Length of proof is 8.
% 0.15/10.40 % Level of proof is 3.
% 0.15/10.40 % Maximum clause weight is 9.000.
% 0.15/10.40 % Given clauses 8.
% 0.15/10.40
% 0.15/10.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------