%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : CAT005-3 : 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 : n004.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 2.23s 2.57s
% Output : Proof 2.40s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
cnf(equivalence_implies_existence1,axiom,
( there_exists(X)
| ~ equivalent(X,Y) ),
file('CAT003-0.ax',equivalence_implies_existence1) ).
cnf(equivalence_implies_existence2,axiom,
( X = Y
| ~ equivalent(X,Y) ),
file('CAT003-0.ax',equivalence_implies_existence2) ).
cnf(existence_and_equality_implies_equivalence1,axiom,
( equivalent(X,Y)
| X != Y
| ~ there_exists(X) ),
file('CAT003-0.ax',existence_and_equality_implies_equivalence1) ).
cnf(domain_has_elements,axiom,
( there_exists(X)
| ~ there_exists(domain(X)) ),
file('CAT003-0.ax',domain_has_elements) ).
cnf(codomain_has_elements,axiom,
( there_exists(X)
| ~ there_exists(codomain(X)) ),
file('CAT003-0.ax',codomain_has_elements) ).
cnf(composition_implies_domain,axiom,
( there_exists(domain(X))
| ~ there_exists(compose(X,Y)) ),
file('CAT003-0.ax',composition_implies_domain) ).
cnf(domain_codomain_composition1,axiom,
( domain(X) = codomain(Y)
| ~ there_exists(compose(X,Y)) ),
file('CAT003-0.ax',domain_codomain_composition1) ).
cnf(domain_codomain_composition2,axiom,
( there_exists(compose(X,Y))
| domain(X) != codomain(Y)
| ~ there_exists(domain(X)) ),
file('CAT003-0.ax',domain_codomain_composition2) ).
cnf(associativity_of_compose,axiom,
compose(X,compose(Y,Z)) = compose(compose(X,Y),Z),
file('CAT003-0.ax',associativity_of_compose) ).
cnf(compose_domain,axiom,
compose(X,domain(X)) = X,
file('CAT003-0.ax',compose_domain) ).
cnf(compose_codomain,axiom,
compose(codomain(X),X) = X,
file('CAT003-0.ax',compose_codomain) ).
cnf(equivalence_implies_existence3,axiom,
( there_exists(Y)
| ~ equivalent(X,Y) ),
file('CAT003-0.ax',equivalence_implies_existence3) ).
cnf(existence_and_equality_implies_equivalence2,axiom,
( equivalent(X,Y)
| X != Y
| ~ there_exists(Y)
| ~ there_exists(X) ),
file('CAT003-0.ax',existence_and_equality_implies_equivalence2) ).
cnf(composition_implies_codomain,axiom,
( there_exists(codomain(X))
| ~ there_exists(compose(X,Y)) ),
file('CAT003-0.ax',composition_implies_codomain) ).
cnf(indiscernibles1,axiom,
( X = Y
| there_exists(f1(X,Y)) ),
file('CAT003-0.ax',indiscernibles1) ).
cnf(indiscernibles2,axiom,
( X = Y
| Y = f1(X,Y)
| X = f1(X,Y) ),
file('CAT003-0.ax',indiscernibles2) ).
cnf(indiscernibles3,axiom,
( X = Y
| Y != f1(X,Y)
| X != f1(X,Y) ),
file('CAT003-0.ax',indiscernibles3) ).
cnf(ad_exists,hypothesis,
there_exists(compose(a,d)),
file('theBenchmark.p',ad_exists) ).
cnf(xd_equals_x,hypothesis,
( compose(X,d) = X
| ~ there_exists(compose(X,d)) ),
file('theBenchmark.p',xd_equals_x) ).
cnf(dy_equals_y,hypothesis,
( compose(d,Y) = Y
| ~ there_exists(compose(d,Y)) ),
file('theBenchmark.p',dy_equals_y) ).
cnf(prove_domain_of_a_is_d,negated_conjecture,
domain(a) != d,
file('theBenchmark.p',prove_domain_of_a_is_d) ).
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,
( domain(Eq_x_0) = domain(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( codomain(Eq_x_0) = codomain(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,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_7,axiom,
( f1(Eq_x_0,Eq_x_1) = f1(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( equivalent(Eq_y_0,Eq_y_1)
| ~ equivalent(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_9,axiom,
( there_exists(Eq_y_0)
| ~ there_exists(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 : CAT005-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 This is a CNF_UNS_RFO_SEQ_NHN 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
% 0.09/0.39 % Computer : n004.cluster.edu
% 0.09/0.39 % Model : x86_64 x86_64
% 0.09/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.39 % Memory : 8046.5625MB
% 0.09/0.39 % OS : Linux 6.8.0-71-generic
% 0.09/0.39 % CPULimit : 300
% 0.09/0.39 % WCLimit : 300
% 0.09/0.39 % DateTime : Sun Sep 20 14:00:50 UTC 2026
% 0.09/0.39 % CPUTime :
% 2.23/2.57 % SZS status Unsatisfiable for theBenchmark
% 2.23/2.57 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------