%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : HEN009-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 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 : n014.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 08:42:31 AM UTC 2026
% Result : Unsatisfiable 0.11s 0.42s
% Output : Proof 0.11s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
cnf(quotient_less_equal1,axiom,
( divide(X,Y) = zero
| ~ less_equal(X,Y) ),
file('HEN002-0.ax',quotient_less_equal1) ).
cnf(quotient_less_equal2,axiom,
( less_equal(X,Y)
| divide(X,Y) != zero ),
file('HEN002-0.ax',quotient_less_equal2) ).
cnf(quotient_smaller_than_numerator,axiom,
less_equal(divide(X,Y),X),
file('HEN002-0.ax',quotient_smaller_than_numerator) ).
cnf(quotient_property,axiom,
less_equal(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)),
file('HEN002-0.ax',quotient_property) ).
cnf(zero_is_smallest,axiom,
less_equal(zero,X),
file('HEN002-0.ax',zero_is_smallest) ).
cnf(less_equal_and_equal,axiom,
( X = Y
| ~ less_equal(Y,X)
| ~ less_equal(X,Y) ),
file('HEN002-0.ax',less_equal_and_equal) ).
cnf(identity_is_largest,axiom,
less_equal(X,identity),
file('HEN002-0.ax',identity_is_largest) ).
cnf(everything_divide_id_is_zero,axiom,
divide(X,identity) = zero,
file('theBenchmark.p',everything_divide_id_is_zero) ).
cnf(zero_divide_anything_is_zero,axiom,
divide(zero,X) = zero,
file('theBenchmark.p',zero_divide_anything_is_zero) ).
cnf(x_divide_x_is_zero,axiom,
divide(X,X) = zero,
file('theBenchmark.p',x_divide_x_is_zero) ).
cnf(x_divide_zero_is_x,axiom,
divide(a,zero) = a,
file('theBenchmark.p',x_divide_zero_is_x) ).
cnf(transitivity_of_less_equal,axiom,
( less_equal(X,Z)
| ~ less_equal(Y,Z)
| ~ less_equal(X,Y) ),
file('theBenchmark.p',transitivity_of_less_equal) ).
cnf(property_of_divide1,axiom,
( less_equal(divide(X,Z),Y)
| ~ less_equal(divide(X,Y),Z) ),
file('theBenchmark.p',property_of_divide1) ).
cnf(property_of_divide2,axiom,
( less_equal(divide(Z,Y),divide(Z,X))
| ~ less_equal(X,Y) ),
file('theBenchmark.p',property_of_divide2) ).
cnf(property_of_divide3,axiom,
( less_equal(divide(X,Z),divide(Y,Z))
| ~ less_equal(X,Y) ),
file('theBenchmark.p',property_of_divide3) ).
cnf(prove_this,negated_conjecture,
divide(identity,a) != divide(identity,divide(identity,divide(identity,a))),
file('theBenchmark.p',prove_this) ).
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,
( divide(Eq_x_0,Eq_x_1) = divide(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,
( less_equal(Eq_y_0,Eq_y_1)
| ~ less_equal(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| 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 : HEN009-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 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
% 0.11/0.37 % Computer : n014.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 19 10:41:21 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.42 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.42 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------