%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : HEN002-4 : 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 : n018.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 08:42:27 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.38s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 4
% Syntax : Number of clauses : 11 ( 9 unt; 0 nHn; 9 RR)
% Number of literals : 15 ( 4 equ; 6 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 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 : 5 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(quotient_smaller_than_numerator,axiom,
less_equal(divide(X,Y),X),
file('HEN002-0.ax',quotient_smaller_than_numerator) ).
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(prove_zero_over_a_is_zero,negated_conjecture,
divide(zero,a) != zero,
file('theBenchmark.p',prove_zero_over_a_is_zero) ).
cnf(t1,plain,
divide(zero,a) != zero,
inference(start,[status(thm),parent(0:0)],[prove_zero_over_a_is_zero]) ).
cnf(t2,plain,
( ~ less_equal(zero,divide(zero,a))
| ~ less_equal(divide(zero,a),zero)
| divide(zero,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,
less_equal(divide(zero,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,
less_equal(zero,divide(zero,a)),
inference(extension,[status(thm),parent(t2:3)],[zero_is_smallest]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : HEN002-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 This is a CNF_UNS_RFO_SEQ_HRN problem
% 0.00/0.03 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n018.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sat Sep 19 10:39:10 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.13/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.38 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------