%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : HEN009-2 : 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 : n017.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 204.06s 204.37s
% Output : Proof 204.06s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
cnf(quotient_less_equal,axiom,
( quotient(X,Y,zero)
| ~ less_equal(X,Y) ),
file('HEN001-0.ax',quotient_less_equal) ).
cnf(less_equal_quotient,axiom,
( less_equal(X,Y)
| ~ quotient(X,Y,zero) ),
file('HEN001-0.ax',less_equal_quotient) ).
cnf(divisor_existence,axiom,
( less_equal(Z,X)
| ~ quotient(X,Y,Z) ),
file('HEN001-0.ax',divisor_existence) ).
cnf(quotient_property,axiom,
( less_equal(V4,V5)
| ~ quotient(V1,Z,V5)
| ~ quotient(V3,V2,V4)
| ~ quotient(X,Z,V3)
| ~ quotient(Y,Z,V2)
| ~ quotient(X,Y,V1) ),
file('HEN001-0.ax',quotient_property) ).
cnf(zero_is_smallest,axiom,
less_equal(zero,X),
file('HEN001-0.ax',zero_is_smallest) ).
cnf(less_equal_and_equal,axiom,
( X = Y
| ~ less_equal(Y,X)
| ~ less_equal(X,Y) ),
file('HEN001-0.ax',less_equal_and_equal) ).
cnf(identity_is_largest,axiom,
less_equal(X,identity),
file('HEN001-0.ax',identity_is_largest) ).
cnf(closure,axiom,
quotient(X,Y,divide(X,Y)),
file('HEN001-0.ax',closure) ).
cnf(well_defined,axiom,
( Z = W
| ~ quotient(X,Y,W)
| ~ quotient(X,Y,Z) ),
file('HEN001-0.ax',well_defined) ).
cnf(everything_divide_identity_is_zero,axiom,
quotient(X,identity,zero),
file('theBenchmark.p',everything_divide_identity_is_zero) ).
cnf(zero_divide_anything_is_zero,axiom,
quotient(zero,X,zero),
file('theBenchmark.p',zero_divide_anything_is_zero) ).
cnf(x_divide_x_is_zero,axiom,
quotient(X,X,zero),
file('theBenchmark.p',x_divide_x_is_zero) ).
cnf(x_divde_zero_is_x,axiom,
quotient(X,zero,X),
file('theBenchmark.p',x_divde_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(xQyLEz_implies_xQzLEy,axiom,
( less_equal(W2,Y)
| ~ quotient(X,Z,W2)
| ~ less_equal(W1,Z)
| ~ quotient(X,Y,W1) ),
file('theBenchmark.p',xQyLEz_implies_xQzLEy) ).
cnf(xLEy_implies_zQyLEzQx,axiom,
( less_equal(W1,W2)
| ~ quotient(Z,X,W2)
| ~ quotient(Z,Y,W1)
| ~ less_equal(X,Y) ),
file('theBenchmark.p',xLEy_implies_zQyLEzQx) ).
cnf(xLEy_implies_xQzLEyQz,axiom,
( less_equal(W1,W2)
| ~ quotient(Y,Z,W2)
| ~ quotient(X,Z,W1)
| ~ less_equal(X,Y) ),
file('theBenchmark.p',xLEy_implies_xQzLEyQz) ).
cnf(identity_divide_a,hypothesis,
quotient(identity,a,idQa),
file('theBenchmark.p',identity_divide_a) ).
cnf(identity_divide_idQa,hypothesis,
quotient(identity,idQa,idQ_idQa),
file('theBenchmark.p',identity_divide_idQa) ).
cnf(identity_divide_idQ_idQa,hypothesis,
quotient(identity,idQ_idQa,idQ__idQ_idQa),
file('theBenchmark.p',identity_divide_idQ_idQa) ).
cnf(prove_one_inversion_equals_three,negated_conjecture,
idQa != idQ__idQ_idQa,
file('theBenchmark.p',prove_one_inversion_equals_three) ).
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(equality_6,axiom,
( quotient(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ quotient(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| 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 : HEN009-2 : 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
% 0.08/0.34 % Computer : n017.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sat Sep 19 10:36:56 UTC 2026
% 0.08/0.35 % CPUTime :
% 204.06/204.37 % SZS status Unsatisfiable for theBenchmark
% 204.06/204.37 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------