%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : CAT007-1 : 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 : n020.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 0.18s 0.47s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 17 ( 13 unt; 0 def)
% Number of atoms : 26 ( 2 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 22 ( 13 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 17 ( 1 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(domain_is_an_identity_map,axiom,
! [VAR_0] : identity_map(domain(VAR_0)),
file('theBenchmark.p',domain_is_an_identity_map) ).
cnf(c_1,plain,
identity_map(domain(A)),
inference(clausify,[status(thm)],[domain_is_an_identity_map]) ).
fof(category_theory_axiom6,axiom,
! [VAR_0,VAR_1,VAR_2] :
( defined(VAR_0,VAR_2)
| ~ identity_map(VAR_1)
| ~ defined(VAR_1,VAR_2)
| ~ defined(VAR_0,VAR_1) ),
file('theBenchmark.p',category_theory_axiom6) ).
cnf(c_2,plain,
( defined(A,C)
| ~ identity_map(B)
| ~ defined(B,C)
| ~ defined(A,B) ),
inference(clausify,[status(thm)],[category_theory_axiom6]) ).
cnf(c_11,plain,
( defined(A,C)
| ~ defined(domain(B),C)
| ~ defined(A,domain(B)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
fof(prove_ab_is_defined,axiom,
~ defined(a,b),
file('theBenchmark.p',prove_ab_is_defined) ).
cnf(c_12,plain,
~ defined(a,b),
inference(clausify,[status(thm)],[prove_ab_is_defined]) ).
fof(domain_of_a_equals_codomain_of_b,axiom,
domain(a) = codomain(b),
file('theBenchmark.p',domain_of_a_equals_codomain_of_b) ).
cnf(c_13,plain,
domain(a) = codomain(b),
inference(clausify,[status(thm)],[domain_of_a_equals_codomain_of_b]) ).
fof(mapping_from_codomain_of_x_to_x,axiom,
! [VAR_0] : defined(codomain(VAR_0),VAR_0),
file('theBenchmark.p',mapping_from_codomain_of_x_to_x) ).
cnf(c_17,plain,
defined(codomain(A),A),
inference(clausify,[status(thm)],[mapping_from_codomain_of_x_to_x]) ).
fof(mapping_from_x_to_its_domain,axiom,
! [VAR_0] : defined(VAR_0,domain(VAR_0)),
file('theBenchmark.p',mapping_from_x_to_its_domain) ).
cnf(c_18,plain,
defined(A,domain(A)),
inference(clausify,[status(thm)],[mapping_from_x_to_its_domain]) ).
cnf(c_39,plain,
( defined(A,B)
| ~ defined(domain(A),B) ),
inference(resolve,[status(thm)],[c_11,c_18]) ).
cnf(c_40,plain,
~ defined(domain(a),b),
inference(resolve,[status(thm)],[c_39,c_12]) ).
cnf(c_37,plain,
~ defined(codomain(b),b),
inference(paramod,[status(thm)],[c_13,c_40]) ).
cnf(c_38,plain,
$false,
inference(resolve,[status(thm)],[c_37,c_17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : CAT007-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n020.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Sat Sep 26 22:49:33 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.45 % Process 2719808 was started by sandbox2 on n020,
% 0.18/0.45 % Sat Sep 26 22:49:33 2026
% 0.18/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.45
% 0.18/0.45 % From the command line: assign(max_seconds, 300).
% 0.18/0.47
% 0.18/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.18/0.47
% 0.18/0.47 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.18/0.47 % Length of proof is 9.
% 0.18/0.47 % Level of proof is 3.
% 0.18/0.47 % Maximum clause weight is 11.000.
% 0.18/0.47 % Given clauses 13.
% 0.18/0.47
% 0.18/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------