%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : CAT014-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 : Thu Sep 24 08:14:09 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.40s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 6
% Syntax : Number of clauses : 21 ( 15 unt; 0 nHn; 19 RR)
% Number of literals : 33 ( 4 equ; 14 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 10 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(codomain_is_an_identity_map,axiom,
identity_map(codomain(X)),
file('CAT001-0.ax',codomain_is_an_identity_map) ).
cnf(mapping_from_codomain_of_x_to_x,axiom,
defined(codomain(X),X),
file('CAT001-0.ax',mapping_from_codomain_of_x_to_x) ).
cnf(identity1,axiom,
( product(X,Y,Y)
| ~ identity_map(X)
| ~ defined(X,Y) ),
file('CAT001-0.ax',identity1) ).
cnf(identity2,axiom,
( product(X,Y,X)
| ~ identity_map(Y)
| ~ defined(X,Y) ),
file('CAT001-0.ax',identity2) ).
cnf(composition_is_well_defined,axiom,
( Z = W
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ),
file('CAT001-0.ax',composition_is_well_defined) ).
cnf(prove_codomain_is_idempotent,negated_conjecture,
codomain(codomain(a)) != codomain(a),
file('theBenchmark.p',prove_codomain_is_idempotent) ).
cnf(t1,plain,
codomain(codomain(a)) != codomain(a),
inference(start,[status(thm),parent(0:0)],[prove_codomain_is_idempotent]) ).
cnf(t2,plain,
( ~ product(codomain(codomain(a)),codomain(a),codomain(a))
| ~ product(codomain(codomain(a)),codomain(a),codomain(codomain(a)))
| codomain(codomain(a)) = codomain(a) ),
inference(extension,[status(thm),parent(t1:1)],[composition_is_well_defined]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ identity_map(codomain(a))
| ~ defined(codomain(codomain(a)),codomain(a))
| product(codomain(codomain(a)),codomain(a),codomain(codomain(a))) ),
inference(extension,[status(thm),parent(t2:2)],[identity2]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
defined(codomain(codomain(a)),codomain(a)),
inference(extension,[status(thm),parent(t4:2)],[mapping_from_codomain_of_x_to_x]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
identity_map(codomain(a)),
inference(extension,[status(thm),parent(t4:3)],[codomain_is_an_identity_map]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t4:3]) ).
cnf(t10,plain,
( ~ identity_map(codomain(codomain(a)))
| ~ defined(codomain(codomain(a)),codomain(a))
| product(codomain(codomain(a)),codomain(a),codomain(a)) ),
inference(extension,[status(thm),parent(t2:3)],[identity1]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t2:3]) ).
cnf(t12,plain,
defined(codomain(codomain(a)),codomain(a)),
inference(extension,[status(thm),parent(t10:2)],[mapping_from_codomain_of_x_to_x]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
identity_map(codomain(codomain(a))),
inference(extension,[status(thm),parent(t10:3)],[codomain_is_an_identity_map]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t10:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT014-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 This is a CNF_UNS_RFO_SEQ_HRN problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n005.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 20 14:08:04 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.13/0.40 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.40 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------