%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : CAT006-1 : 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 08:14:07 AM UTC 2026
% Result : Unsatisfiable 13.08s 13.42s
% Output : Proof 13.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 9
% Syntax : Number of clauses : 32 ( 23 unt; 0 nHn; 30 RR)
% Number of literals : 50 ( 4 equ; 20 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 14 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(category_theory_axiom3,axiom,
( defined(X,Y)
| ~ defined(X,Yz)
| ~ product(Y,Z,Yz) ),
file('CAT001-0.ax',category_theory_axiom3) ).
cnf(codomain_is_an_identity_map,axiom,
identity_map(codomain(X)),
file('CAT001-0.ax',codomain_is_an_identity_map) ).
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(ha_defined,hypothesis,
defined(h,a),
file('theBenchmark.p',ha_defined) ).
cnf(h_is_the_identity_map,hypothesis,
identity_map(h),
file('theBenchmark.p',h_is_the_identity_map) ).
cnf(prove_codomain_of_a_is_h,negated_conjecture,
codomain(a) != h,
file('theBenchmark.p',prove_codomain_of_a_is_h) ).
cnf(t1,plain,
codomain(a) != h,
inference(start,[status(thm),parent(0:0)],[prove_codomain_of_a_is_h]) ).
cnf(t2,plain,
( ~ product(h,codomain(a),h)
| ~ product(h,codomain(a),codomain(a))
| codomain(a) = h ),
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(h)
| ~ defined(h,codomain(a))
| product(h,codomain(a),codomain(a)) ),
inference(extension,[status(thm),parent(t2:2)],[identity1]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( ~ defined(h,a)
| ~ product(codomain(a),a,a)
| defined(h,codomain(a)) ),
inference(extension,[status(thm),parent(t4:2)],[category_theory_axiom3]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
product(codomain(a),a,a),
inference(extension,[status(thm),parent(t6:2)],[product_on_codomain]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
defined(h,a),
inference(extension,[status(thm),parent(t6:3)],[ha_defined]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t6:3]) ).
cnf(t12,plain,
identity_map(h),
inference(extension,[status(thm),parent(t4:3)],[h_is_the_identity_map]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t4:3]) ).
cnf(t14,plain,
( ~ identity_map(codomain(a))
| ~ defined(h,codomain(a))
| product(h,codomain(a),h) ),
inference(extension,[status(thm),parent(t2:3)],[identity2]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t2:3]) ).
cnf(t16,plain,
( ~ defined(h,a)
| ~ product(codomain(a),a,a)
| defined(h,codomain(a)) ),
inference(extension,[status(thm),parent(t14:2)],[category_theory_axiom3]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
product(codomain(a),a,a),
inference(extension,[status(thm),parent(t16:2)],[product_on_codomain]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(t20,plain,
defined(h,a),
inference(extension,[status(thm),parent(t16:3)],[ha_defined]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t16:3]) ).
cnf(t22,plain,
identity_map(codomain(a)),
inference(extension,[status(thm),parent(t14:3)],[codomain_is_an_identity_map]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t14:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : CAT006-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 This is a CNF_UNS_RFO_SEQ_HRN problem
% 0.00/0.07 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.49 % Computer : n005.cluster.edu
% 0.19/0.49 % Model : x86_64 x86_64
% 0.19/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.49 % Memory : 8046.5625MB
% 0.19/0.49 % OS : Linux 6.8.0-71-generic
% 0.19/0.49 % CPULimit : 300
% 0.19/0.49 % WCLimit : 300
% 0.19/0.49 % DateTime : Sun Sep 20 14:02:03 UTC 2026
% 0.19/0.49 % CPUTime :
% 13.08/13.42 % SZS status Unsatisfiable for theBenchmark
% 13.08/13.42 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------