%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : HEN007-4 : 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 : n003.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 08:42:30 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.41s
% Output : Proof 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 6
% Syntax : Number of clauses : 19 ( 12 unt; 0 nHn; 18 RR)
% Number of literals : 28 ( 4 equ; 11 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 9 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(quotient_less_equal2,axiom,
( less_equal(X,Y)
| divide(X,Y) != zero ),
file('HEN002-0.ax',quotient_less_equal2) ).
cnf(x_divide_x_is_zero,axiom,
divide(X,X) = zero,
file('theBenchmark.p',x_divide_x_is_zero) ).
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(a_LE_b,hypothesis,
less_equal(a,b),
file('theBenchmark.p',a_LE_b) ).
cnf(prove_c_divide_b_LE_c_divide_a,negated_conjecture,
~ less_equal(divide(c,b),divide(c,a)),
file('theBenchmark.p',prove_c_divide_b_LE_c_divide_a) ).
cnf(t1,plain,
~ less_equal(divide(c,b),divide(c,a)),
inference(start,[status(thm),parent(0:0)],[prove_c_divide_b_LE_c_divide_a]) ).
cnf(t2,plain,
( ~ less_equal(divide(c,divide(c,a)),b)
| less_equal(divide(c,b),divide(c,a)) ),
inference(extension,[status(thm),parent(t1:1)],[property_of_divide1]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ less_equal(a,b)
| ~ less_equal(divide(c,divide(c,a)),a)
| less_equal(divide(c,divide(c,a)),b) ),
inference(extension,[status(thm),parent(t2:2)],[transitivity_of_less_equal]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( ~ less_equal(divide(c,a),divide(c,a))
| less_equal(divide(c,divide(c,a)),a) ),
inference(extension,[status(thm),parent(t4:2)],[property_of_divide1]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( divide(divide(c,a),divide(c,a)) != zero
| less_equal(divide(c,a),divide(c,a)) ),
inference(extension,[status(thm),parent(t6:2)],[quotient_less_equal2]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
divide(divide(c,a),divide(c,a)) = zero,
inference(extension,[status(thm),parent(t8:2)],[x_divide_x_is_zero]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
less_equal(a,b),
inference(extension,[status(thm),parent(t4:3)],[a_LE_b]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t4:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : HEN007-4 : 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
% 0.10/0.36 % Computer : n003.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 19 10:41:12 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.41 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.41 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------