%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : HEN003-5 : 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 : n019.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 08:42:28 AM UTC 2026
% Result : Unsatisfiable 222.43s 222.72s
% Output : Proof 222.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 9
% Syntax : Number of clauses : 36 ( 25 unt; 0 nHn; 32 RR)
% Number of literals : 55 ( 42 equ; 21 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 18 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(quotient_smaller_than_numerator,axiom,
divide(divide(X,Y),X) = zero,
file('HEN003-0.ax',quotient_smaller_than_numerator) ).
cnf(quotient_property,axiom,
divide(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)) = zero,
file('HEN003-0.ax',quotient_property) ).
cnf(zero_is_smallest,axiom,
divide(zero,X) = zero,
file('HEN003-0.ax',zero_is_smallest) ).
cnf(divide_and_equal,axiom,
( X = Y
| divide(Y,X) != zero
| divide(X,Y) != zero ),
file('HEN003-0.ax',divide_and_equal) ).
cnf(prove_x_divide_x_is_zero,negated_conjecture,
divide(a,a) != zero,
file('theBenchmark.p',prove_x_divide_x_is_zero) ).
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(t1,plain,
divide(a,a) != zero,
inference(start,[status(thm),parent(0:0)],[prove_x_divide_x_is_zero]) ).
cnf(t2,plain,
( divide(a,a) != divide(divide(a,a),a)
| divide(divide(a,a),a) != zero
| divide(a,a) = zero ),
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,
divide(divide(a,a),a) = zero,
inference(extension,[status(thm),parent(t2:2)],[quotient_smaller_than_numerator]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( divide(divide(divide(a,a),a),divide(a,a)) != zero
| divide(divide(a,a),divide(divide(a,a),a)) != zero
| divide(a,a) = divide(divide(a,a),a) ),
inference(extension,[status(thm),parent(t2:3)],[divide_and_equal]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
cnf(t8,plain,
( divide(zero,divide(divide(a,a),divide(divide(a,a),a))) != zero
| divide(divide(divide(a,a),divide(divide(a,a),a)),zero) != zero
| divide(divide(a,a),divide(divide(a,a),a)) = zero ),
inference(extension,[status(thm),parent(t6:2)],[divide_and_equal]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
( zero != divide(divide(divide(a,a),divide(divide(a,a),a)),zero)
| divide(divide(divide(a,a),divide(divide(a,a),a)),zero) = zero ),
inference(extension,[status(thm),parent(t8:2)],[equality_2]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
( zero != divide(divide(divide(a,a),divide(divide(a,a),a)),divide(divide(a,divide(a,a)),a))
| divide(divide(divide(a,a),divide(divide(a,a),a)),divide(divide(a,divide(a,a)),a)) != divide(divide(divide(a,a),divide(divide(a,a),a)),zero)
| zero = divide(divide(divide(a,a),divide(divide(a,a),a)),zero) ),
inference(extension,[status(thm),parent(t10:2)],[equality_3]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
( divide(divide(a,divide(a,a)),a) != zero
| divide(divide(a,a),divide(divide(a,a),a)) != divide(divide(a,a),divide(divide(a,a),a))
| divide(divide(divide(a,a),divide(divide(a,a),a)),divide(divide(a,divide(a,a)),a)) = divide(divide(divide(a,a),divide(divide(a,a),a)),zero) ),
inference(extension,[status(thm),parent(t12:2)],[equality_4]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
divide(divide(a,a),divide(divide(a,a),a)) = divide(divide(a,a),divide(divide(a,a),a)),
inference(extension,[status(thm),parent(t14:2)],[equality_1]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
divide(divide(a,divide(a,a)),a) = zero,
inference(extension,[status(thm),parent(t14:3)],[quotient_smaller_than_numerator]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t14:3]) ).
cnf(t20,plain,
( divide(divide(divide(a,a),divide(divide(a,a),a)),divide(divide(a,divide(a,a)),a)) != zero
| zero = divide(divide(divide(a,a),divide(divide(a,a),a)),divide(divide(a,divide(a,a)),a)) ),
inference(extension,[status(thm),parent(t12:3)],[equality_2]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t12:3]) ).
cnf(t22,plain,
divide(divide(divide(a,a),divide(divide(a,a),a)),divide(divide(a,divide(a,a)),a)) = zero,
inference(extension,[status(thm),parent(t20:2)],[quotient_property]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t20:2]) ).
cnf(t24,plain,
divide(zero,divide(divide(a,a),divide(divide(a,a),a))) = zero,
inference(extension,[status(thm),parent(t8:3)],[zero_is_smallest]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t8:3]) ).
cnf(t26,plain,
divide(divide(divide(a,a),a),divide(a,a)) = zero,
inference(extension,[status(thm),parent(t6:3)],[quotient_smaller_than_numerator]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t6:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : HEN003-5 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 This is a CNF_UNS_RFO_PEQ_NUE problem
% 0.00/0.03 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n019.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 10:37:35 UTC 2026
% 0.08/0.34 % CPUTime :
% 222.43/222.72 % SZS status Unsatisfiable for theBenchmark
% 222.43/222.72 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------