%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : CAT011-2 : 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 : 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 08:14:08 AM UTC 2026
% Result : Unsatisfiable 0.17s 0.55s
% Output : Proof 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 6
% Syntax : Number of clauses : 21 ( 14 unt; 0 nHn; 19 RR)
% Number of literals : 31 ( 24 equ; 12 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 9 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(codomain_of_domain_is_domain,axiom,
codomain(domain(X)) = domain(X),
file('CAT002-0.ax',codomain_of_domain_is_domain) ).
cnf(domain_of_codomain_is_codomain,axiom,
domain(codomain(X)) = codomain(X),
file('CAT002-0.ax',domain_of_codomain_is_codomain) ).
cnf(prove_domain_is_idempotent,negated_conjecture,
domain(domain(a)) != domain(a),
file('theBenchmark.p',prove_domain_is_idempotent) ).
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,
( domain(Eq_x_0) = domain(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(t1,plain,
domain(domain(a)) != domain(a),
inference(start,[status(thm),parent(0:0)],[prove_domain_is_idempotent]) ).
cnf(t2,plain,
( domain(codomain(domain(a))) != domain(a)
| domain(domain(a)) != domain(codomain(domain(a)))
| domain(domain(a)) = domain(a) ),
inference(extension,[status(thm),parent(t1:1)],[equality_3]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( domain(a) != codomain(domain(a))
| domain(domain(a)) = domain(codomain(domain(a))) ),
inference(extension,[status(thm),parent(t2:2)],[equality_4]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( codomain(domain(a)) != domain(a)
| domain(a) = codomain(domain(a)) ),
inference(extension,[status(thm),parent(t4:2)],[equality_2]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
codomain(domain(a)) = domain(a),
inference(extension,[status(thm),parent(t6:2)],[codomain_of_domain_is_domain]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
( codomain(domain(a)) != domain(a)
| domain(codomain(domain(a))) != codomain(domain(a))
| domain(codomain(domain(a))) = domain(a) ),
inference(extension,[status(thm),parent(t2:3)],[equality_3]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t2:3]) ).
cnf(t12,plain,
domain(codomain(domain(a))) = codomain(domain(a)),
inference(extension,[status(thm),parent(t10:2)],[domain_of_codomain_is_codomain]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
codomain(domain(a)) = domain(a),
inference(extension,[status(thm),parent(t10:3)],[codomain_of_domain_is_domain]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t10:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : CAT011-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 This is a CNF_UNS_RFO_PEQ_NUE problem
% 0.00/0.05 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n005.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Sun Sep 20 14:06:03 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.55 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.55 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------