%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : HEN003-4 : 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 : n005.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 3.45s 3.72s
% Output : Proof 3.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 11
% Syntax : Number of clauses : 36 ( 25 unt; 0 nHn; 31 RR)
% Number of literals : 56 ( 23 equ; 22 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 22 ( 3 sgn)
% 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(zero_divide_anything_is_zero,axiom,
divide(zero,X) = zero,
file('theBenchmark.p',zero_divide_anything_is_zero) ).
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_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(t1,plain,
divide(a,a) != zero,
inference(start,[status(thm),parent(0:0)],[prove_x_divide_x_is_zero]) ).
cnf(t2,plain,
( ~ less_equal(zero,divide(a,a))
| ~ less_equal(divide(a,a),zero)
| divide(a,a) = zero ),
inference(extension,[status(thm),parent(t1:1)],[less_equal_and_equal]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( divide(divide(a,a),zero) != zero
| less_equal(divide(a,a),zero) ),
inference(extension,[status(thm),parent(t2:2)],[quotient_less_equal2]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( ~ less_equal(zero,divide(divide(a,a),zero))
| ~ less_equal(divide(divide(a,a),zero),zero)
| divide(divide(a,a),zero) = zero ),
inference(extension,[status(thm),parent(t4:2)],[less_equal_and_equal]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( divide(divide(a,zero),a) != zero
| ~ less_equal(divide(divide(a,a),divide(zero,a)),divide(divide(a,zero),a))
| divide(divide(a,a),divide(zero,a)) != divide(divide(a,a),zero)
| less_equal(divide(divide(a,a),zero),zero) ),
inference(extension,[status(thm),parent(t6:2)],[equality_5]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
( divide(zero,a) != zero
| divide(a,a) != divide(a,a)
| divide(divide(a,a),divide(zero,a)) = divide(divide(a,a),zero) ),
inference(extension,[status(thm),parent(t8:2)],[equality_4]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
divide(a,a) = divide(a,a),
inference(extension,[status(thm),parent(t10:2)],[equality_1]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
divide(zero,a) = zero,
inference(extension,[status(thm),parent(t10:3)],[zero_divide_anything_is_zero]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t10:3]) ).
cnf(t16,plain,
less_equal(divide(divide(a,a),divide(zero,a)),divide(divide(a,zero),a)),
inference(extension,[status(thm),parent(t8:3)],[quotient_property]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t8:3]) ).
cnf(t18,plain,
( ~ less_equal(divide(a,zero),a)
| divide(divide(a,zero),a) = zero ),
inference(extension,[status(thm),parent(t8:4)],[quotient_less_equal1]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t8:4]) ).
cnf(t20,plain,
less_equal(divide(a,zero),a),
inference(extension,[status(thm),parent(t18:2)],[quotient_smaller_than_numerator]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t18:2]) ).
cnf(t22,plain,
less_equal(zero,divide(divide(a,a),zero)),
inference(extension,[status(thm),parent(t6:3)],[zero_is_smallest]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t6:3]) ).
cnf(t24,plain,
less_equal(zero,divide(a,a)),
inference(extension,[status(thm),parent(t2:3)],[zero_is_smallest]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t2:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN003-4 : 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/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.37 % Computer : n005.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Sat Sep 19 10:37:18 UTC 2026
% 0.08/0.37 % CPUTime :
% 3.45/3.72 % SZS status Unsatisfiable for theBenchmark
% 3.45/3.72 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------