%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : CAT013-1 : 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 : n007.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 06:55:58 AM UTC 2026
% Result : Unsatisfiable 0.15s 0.39s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of formulae : 17 ( 11 unt; 0 def)
% Number of atoms : 27 ( 5 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 23 ( 13 ~; 10 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 23 ( 1 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(codomain_is_an_identity_map,axiom,
! [VAR_0] : identity_map(codomain(VAR_0)),
file('theBenchmark.p',codomain_is_an_identity_map) ).
cnf(c_3,plain,
identity_map(codomain(A)),
inference(clausify,[status(thm)],[codomain_is_an_identity_map]) ).
fof(identity1,axiom,
! [VAR_0,VAR_1] :
( product(VAR_0,VAR_1,VAR_1)
| ~ identity_map(VAR_0)
| ~ defined(VAR_0,VAR_1) ),
file('theBenchmark.p',identity1) ).
cnf(c_4,plain,
( product(A,B,B)
| ~ identity_map(A)
| ~ defined(A,B) ),
inference(clausify,[status(thm)],[identity1]) ).
cnf(c_9,plain,
( product(codomain(A),B,B)
| ~ defined(codomain(A),B) ),
inference(resolve,[status(thm)],[c_4,c_3]) ).
fof(prove_domain_of_codomain_is_codomain,axiom,
domain(codomain(a)) != codomain(a),
file('theBenchmark.p',prove_domain_of_codomain_is_codomain) ).
cnf(c_12,plain,
domain(codomain(a)) != codomain(a),
inference(clausify,[status(thm)],[prove_domain_of_codomain_is_codomain]) ).
fof(composition_is_well_defined,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_2 = VAR_3
| ~ product(VAR_0,VAR_1,VAR_3)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',composition_is_well_defined) ).
cnf(c_13,plain,
( C = D
| ~ product(A,B,D)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[composition_is_well_defined]) ).
fof(product_on_domain,axiom,
! [VAR_0] : product(VAR_0,domain(VAR_0),VAR_0),
file('theBenchmark.p',product_on_domain) ).
cnf(c_15,plain,
product(A,domain(A),A),
inference(clausify,[status(thm)],[product_on_domain]) ).
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_17,plain,
defined(A,domain(A)),
inference(clausify,[status(thm)],[mapping_from_x_to_its_domain]) ).
cnf(c_38,plain,
( B = A
| ~ product(A,domain(A),B) ),
inference(resolve,[status(thm)],[c_13,c_15]) ).
cnf(c_28,plain,
~ product(codomain(a),domain(codomain(a)),domain(codomain(a))),
inference(resolve,[status(thm)],[c_38,c_12]) ).
cnf(c_36,plain,
product(codomain(A),domain(codomain(A)),domain(codomain(A))),
inference(resolve,[status(thm)],[c_9,c_17]) ).
cnf(c_37,plain,
$false,
inference(resolve,[status(thm)],[c_36,c_28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT013-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n007.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 22:47:24 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 677889 was started by sandbox on n007,
% 0.10/0.37 % Sat Sep 26 22:47:24 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 0.15/0.39
% 0.15/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.39
% 0.15/0.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.15/0.39 % Length of proof is 10.
% 0.15/0.39 % Level of proof is 3.
% 0.15/0.39 % Maximum clause weight is 11.000.
% 0.15/0.39 % Given clauses 12.
% 0.15/0.39
% 0.15/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------