%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : CAT007-3 : 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 : n014.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 06:55:56 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.37s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 11 ( 8 unt; 0 def)
% Number of atoms : 16 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 12 ( 7 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 4 ( 0 sgn 2 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(domain_codomain_composition2,axiom,
! [VAR_0,VAR_1] :
( there_exists(compose(VAR_0,VAR_1))
| ~ equalish(domain(VAR_0),codomain(VAR_1))
| ~ there_exists(domain(VAR_0)) ),
file('theBenchmark.p',domain_codomain_composition2) ).
cnf(c_5,plain,
( there_exists(compose(A,B))
| ~ equalish(domain(A),codomain(B))
| ~ there_exists(domain(A)) ),
inference(clausify,[status(thm)],[domain_codomain_composition2]) ).
fof(domain_of_c2_exists,axiom,
there_exists(domain(c2)),
file('theBenchmark.p',domain_of_c2_exists) ).
cnf(c_9,plain,
there_exists(domain(c2)),
inference(clausify,[status(thm)],[domain_of_c2_exists]) ).
fof(domain_of_c2_equals_codomain_of_c1,axiom,
equalish(domain(c2),codomain(c1)),
file('theBenchmark.p',domain_of_c2_equals_codomain_of_c1) ).
cnf(c_11,plain,
equalish(domain(c2),codomain(c1)),
inference(clausify,[status(thm)],[domain_of_c2_equals_codomain_of_c1]) ).
fof(prove_c1_c2_is_defined,axiom,
~ there_exists(compose(c2,c1)),
file('theBenchmark.p',prove_c1_c2_is_defined) ).
cnf(c_12,plain,
~ there_exists(compose(c2,c1)),
inference(clausify,[status(thm)],[prove_c1_c2_is_defined]) ).
cnf(c_28,plain,
( there_exists(compose(c2,c1))
| ~ there_exists(domain(c2)) ),
inference(resolve,[status(thm)],[c_11,c_5]) ).
cnf(c_29,plain,
there_exists(compose(c2,c1)),
inference(resolve,[status(thm)],[c_9,c_28]) ).
cnf(c_27,plain,
$false,
inference(resolve,[status(thm)],[c_12,c_29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT007-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n014.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 22:48:46 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 101251 was started by sandbox2 on n014,
% 0.10/0.36 % Sat Sep 26 22:48:46 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.36
% 0.10/0.36 % From the command line: assign(max_seconds, 300).
% 0.10/0.37
% 0.10/0.37 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.37
% 0.10/0.37 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.10/0.37 % Length of proof is 5.
% 0.10/0.37 % Level of proof is 1.
% 0.10/0.37 % Maximum clause weight is 12.000.
% 0.10/0.37 % Given clauses 11.
% 0.10/0.37
% 0.10/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------