%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : CAT004-4 : 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 : n002.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 08:14:06 AM UTC 2026
% Result : Unsatisfiable 228.54s 228.84s
% Output : Proof 228.71s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
cnf(equivalence_implies_existence1,axiom,
( there_exists(X)
| ~ equivalent(X,Y) ),
file('CAT004-0.ax',equivalence_implies_existence1) ).
cnf(equivalence_implies_existence2,axiom,
( X = Y
| ~ equivalent(X,Y) ),
file('CAT004-0.ax',equivalence_implies_existence2) ).
cnf(existence_and_equality_implies_equivalence1,axiom,
( equivalent(X,Y)
| X != Y
| ~ there_exists(X) ),
file('CAT004-0.ax',existence_and_equality_implies_equivalence1) ).
cnf(domain_has_elements,axiom,
( there_exists(X)
| ~ there_exists(domain(X)) ),
file('CAT004-0.ax',domain_has_elements) ).
cnf(codomain_has_elements,axiom,
( there_exists(X)
| ~ there_exists(codomain(X)) ),
file('CAT004-0.ax',codomain_has_elements) ).
cnf(composition_implies_domain,axiom,
( there_exists(domain(X))
| ~ there_exists(compose(X,Y)) ),
file('CAT004-0.ax',composition_implies_domain) ).
cnf(domain_codomain_composition1,axiom,
( domain(X) = codomain(Y)
| ~ there_exists(compose(X,Y)) ),
file('CAT004-0.ax',domain_codomain_composition1) ).
cnf(domain_codomain_composition2,axiom,
( there_exists(compose(X,Y))
| domain(X) != codomain(Y)
| ~ there_exists(domain(X)) ),
file('CAT004-0.ax',domain_codomain_composition2) ).
cnf(associativity_of_compose,axiom,
compose(X,compose(Y,Z)) = compose(compose(X,Y),Z),
file('CAT004-0.ax',associativity_of_compose) ).
cnf(compose_domain,axiom,
compose(X,domain(X)) = X,
file('CAT004-0.ax',compose_domain) ).
cnf(compose_codomain,axiom,
compose(codomain(X),X) = X,
file('CAT004-0.ax',compose_codomain) ).
cnf(assume_ab_exists,hypothesis,
there_exists(compose(a,b)),
file('theBenchmark.p',assume_ab_exists) ).
cnf(cancellation_for_product1,hypothesis,
( X = Z
| compose(Z,a) != Y
| compose(X,a) != Y ),
file('theBenchmark.p',cancellation_for_product1) ).
cnf(cancellation_for_product2,hypothesis,
( X = Z
| compose(Z,b) != Y
| compose(X,b) != Y ),
file('theBenchmark.p',cancellation_for_product2) ).
cnf(assume_h_exists,hypothesis,
there_exists(h),
file('theBenchmark.p',assume_h_exists) ).
cnf(h_ab_equals_g_ab,hypothesis,
compose(h,compose(a,b)) = compose(g,compose(a,b)),
file('theBenchmark.p',h_ab_equals_g_ab) ).
cnf(prove_h_equals_g,negated_conjecture,
h != g,
file('theBenchmark.p',prove_h_equals_g) ).
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,
( 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_8,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 : CAT004-4 : 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
% 0.09/0.37 % Computer : n002.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 20 14:02:32 UTC 2026
% 0.09/0.37 % CPUTime :
% 228.54/228.84 % SZS status Unsatisfiable for theBenchmark
% 228.54/228.84 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------