%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : CAT014-2 : 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 : n012.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 06:55:59 AM UTC 2026
% Result : Unsatisfiable 0.04s 20.35s
% Output : CNFRefutation 0.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 3
% Syntax : Number of formulae : 9 ( 9 unt; 0 def)
% Number of atoms : 9 ( 8 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 6 ( 0 sgn 2 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(codomain_of_domain_is_domain,axiom,
! [VAR_0] : codomain(domain(VAR_0)) = domain(VAR_0),
file('theBenchmark.p',codomain_of_domain_is_domain) ).
cnf(c_1,plain,
codomain(domain(A)) = domain(A),
inference(clausify,[status(thm)],[codomain_of_domain_is_domain]) ).
fof(domain_of_codomain_is_codomain,axiom,
! [VAR_0] : domain(codomain(VAR_0)) = codomain(VAR_0),
file('theBenchmark.p',domain_of_codomain_is_codomain) ).
cnf(c_2,plain,
domain(codomain(A)) = codomain(A),
inference(clausify,[status(thm)],[domain_of_codomain_is_codomain]) ).
fof(prove_codomain_is_idempotent,axiom,
codomain(codomain(a)) != codomain(a),
file('theBenchmark.p',prove_codomain_is_idempotent) ).
cnf(c_9,plain,
codomain(codomain(a)) != codomain(a),
inference(clausify,[status(thm)],[prove_codomain_is_idempotent]) ).
cnf(c_12,plain,
codomain(codomain(A)) = domain(codomain(A)),
inference(paramod,[status(thm)],[c_2,c_1]) ).
cnf(c_10,plain,
codomain(codomain(A)) = codomain(A),
inference(paramod,[status(thm)],[c_2,c_12]) ).
cnf(c_11,plain,
$false,
inference(resolve,[status(thm)],[c_10,c_9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : CAT014-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.04/20.34 % Computer : n012.cluster.edu
% 0.04/20.34 % Model : x86_64 x86_64
% 0.04/20.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/20.34 % Memory : 8046.5625MB
% 0.04/20.34 % OS : Linux 6.8.0-71-generic
% 0.04/20.34 % CPULimit : 300
% 0.04/20.34 % WCLimit : 300
% 0.04/20.34 % DateTime : Sat Sep 26 22:49:43 UTC 2026
% 0.04/20.34 % CPUTime :
% 0.04/20.34 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.04/20.34 % Process 1679513 was started by sandbox2 on n012,
% 0.04/20.34 % Sat Sep 26 22:49:43 2026
% 0.04/20.34 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.04/20.34
% 0.04/20.34 % From the command line: assign(max_seconds, 300).
% 0.04/20.35
% 0.04/20.35 % SZS status Unsatisfiable for theBenchmark
% 0.04/20.35
% 0.04/20.35 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.04/20.35 % Length of proof is 5.
% 0.04/20.35 % Level of proof is 2.
% 0.04/20.35 % Maximum clause weight is 6.000.
% 0.04/20.35 % Given clauses 2.
% 0.04/20.35
% 0.04/20.35 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------