%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : CAT009-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 08:14:08 AM UTC 2026
% Result : Unsatisfiable 206.23s 206.52s
% Output : Proof 206.52s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
cnf(closure_of_composition,axiom,
( product(X,Y,compose(X,Y))
| ~ defined(X,Y) ),
file('CAT001-0.ax',closure_of_composition) ).
cnf(associative_property1,axiom,
( defined(X,Y)
| ~ product(X,Y,Z) ),
file('CAT001-0.ax',associative_property1) ).
cnf(associative_property2,axiom,
( defined(Y,Z)
| ~ defined(Xy,Z)
| ~ product(X,Y,Xy) ),
file('CAT001-0.ax',associative_property2) ).
cnf(category_theory_axiom1,axiom,
( defined(X,Yz)
| ~ defined(Xy,Z)
| ~ product(Y,Z,Yz)
| ~ product(X,Y,Xy) ),
file('CAT001-0.ax',category_theory_axiom1) ).
cnf(category_theory_axiom2,axiom,
( product(X,Yz,Xyz)
| ~ product(Y,Z,Yz)
| ~ product(Xy,Z,Xyz)
| ~ product(X,Y,Xy) ),
file('CAT001-0.ax',category_theory_axiom2) ).
cnf(category_theory_axiom3,axiom,
( defined(X,Y)
| ~ defined(X,Yz)
| ~ product(Y,Z,Yz) ),
file('CAT001-0.ax',category_theory_axiom3) ).
cnf(category_theory_axiom4,axiom,
( defined(Xy,Z)
| ~ defined(X,Yz)
| ~ product(X,Y,Xy)
| ~ product(Y,Z,Yz) ),
file('CAT001-0.ax',category_theory_axiom4) ).
cnf(category_theory_axiom5,axiom,
( product(Xy,Z,Xyz)
| ~ product(X,Y,Xy)
| ~ product(X,Yz,Xyz)
| ~ product(Y,Z,Yz) ),
file('CAT001-0.ax',category_theory_axiom5) ).
cnf(category_theory_axiom6,axiom,
( defined(X,Z)
| ~ identity_map(Y)
| ~ defined(Y,Z)
| ~ defined(X,Y) ),
file('CAT001-0.ax',category_theory_axiom6) ).
cnf(domain_is_an_identity_map,axiom,
identity_map(domain(X)),
file('CAT001-0.ax',domain_is_an_identity_map) ).
cnf(codomain_is_an_identity_map,axiom,
identity_map(codomain(X)),
file('CAT001-0.ax',codomain_is_an_identity_map) ).
cnf(mapping_from_x_to_its_domain,axiom,
defined(X,domain(X)),
file('CAT001-0.ax',mapping_from_x_to_its_domain) ).
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(product_on_domain,axiom,
product(X,domain(X),X),
file('CAT001-0.ax',product_on_domain) ).
cnf(product_on_codomain,axiom,
product(codomain(X),X,X),
file('CAT001-0.ax',product_on_codomain) ).
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(ba_defined,hypothesis,
defined(b,a),
file('theBenchmark.p',ba_defined) ).
cnf(prove_domain_of_ba_equals_domain_of_a,negated_conjecture,
domain(compose(b,a)) != domain(a),
file('theBenchmark.p',prove_domain_of_ba_equals_domain_of_a) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_4,axiom,
( compose(Eq_x_0,Eq_x_1) = compose(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( domain(Eq_x_0) = domain(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( codomain(Eq_x_0) = codomain(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( defined(Eq_y_0,Eq_y_1)
| ~ defined(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_8,axiom,
( product(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ product(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_9,axiom,
( identity_map(Eq_y_0)
| ~ identity_map(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT009-1 : 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/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n011.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 : Sun Sep 20 14:07:55 UTC 2026
% 0.10/0.38 % CPUTime :
% 206.23/206.52 % SZS status Unsatisfiable for theBenchmark
% 206.23/206.52 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------